Noise and Vibration Mitigation for Rail Transportation Systems: Proceedings of the 14th International Workshop on Railway Noise, 07–09 December 2022, ... (Lecture Notes in Mechanical Engineering) 9819978513, 9789819978519

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Lecture Notes in Mechanical Engineering

Xiaozhen Sheng · David Thompson · Geert Degrande · Jens C. O. Nielsen · Pierre-Etienne Gautier · Kiyoshi Nagakura · Ard Kuijpers · James Tuman Nelson · David A. Towers · David Anderson · Thorsten Tielkes   Editors

Noise and Vibration Mitigation for Rail Transportation Systems Proceedings of the 14th International Workshop on Railway Noise, 07–09 December 2022, Shanghai, China

Lecture Notes in Mechanical Engineering Series Editors Fakher Chaari, National School of Engineers, University of Sfax, Sfax, Tunisia Francesco Gherardini , Dipartimento di Ingegneria “Enzo Ferrari”, Università di Modena e Reggio Emilia, Modena, Italy Vitalii Ivanov, Department of Manufacturing Engineering, Machines and Tools, Sumy State University, Sumy, Ukraine Mohamed Haddar, National School of Engineers of Sfax (ENIS), Sfax, Tunisia Editorial Board Francisco Cavas-Martínez , Departamento de Estructuras, Construcción y Expresión Gráfica Universidad Politécnica de Cartagena, Cartagena, Murcia, Spain Francesca di Mare, Institute of Energy Technology, Ruhr-Universität Bochum, Bochum, Nordrhein-Westfalen, Germany Young W. Kwon, Department of Manufacturing Engineering and Aerospace Engineering, Graduate School of Engineering and Applied Science, Monterey, CA, USA Justyna Trojanowska, Poznan University of Technology, Poznan, Poland Jinyang Xu, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China

Lecture Notes in Mechanical Engineering (LNME) publishes the latest developments in Mechanical Engineering—quickly, informally and with high quality. Original research reported in proceedings and post-proceedings represents the core of LNME. Volumes published in LNME embrace all aspects, subfields and new challenges of mechanical engineering. To submit a proposal or request further information, please contact the Springer Editor of your location: Europe, USA, Africa: Leontina Di Cecco at [email protected] China: Ella Zhang at [email protected] India: Priya Vyas at [email protected] Rest of Asia, Australia, New Zealand: Swati Meherishi at [email protected] Topics in the series include: • • • • • • • • • • • • • • • • •

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Xiaozhen Sheng · David Thompson · Geert Degrande · Jens C. O. Nielsen · Pierre-Etienne Gautier · Kiyoshi Nagakura · Ard Kuijpers · James Tuman Nelson · David A. Towers · David Anderson · Thorsten Tielkes Editors

Noise and Vibration Mitigation for Rail Transportation Systems Proceedings of the 14th International Workshop on Railway Noise, 07–09 December 2022, Shanghai, China

Editors See next page

ISSN 2195-4356 ISSN 2195-4364 (electronic) Lecture Notes in Mechanical Engineering ISBN 978-981-99-7851-9 ISBN 978-981-99-7852-6 (eBook) https://doi.org/10.1007/978-981-99-7852-6 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Paper in this product is recyclable.

Editors Xiaozhen Sheng School of Urban Railway Transportation Shanghai University of Engineering Science Shanghai, China

David Thompson Institute of Sound and Vibration Research University of Southampton Southampton, UK

Geert Degrande Department of Civil Engineering KU Leuven Leuven, Belgium

Jens C. O. Nielsen Department of Mechanics and Maritime Sciences Chalmers University of Technology Gothenburg, Sweden

Pierre-Etienne Gautier SNCF Réseau La Plaine Saint Denis, France

Kiyoshi Nagakura Railway Technical Research Institute Kokubunji, Tokyo, Japan

Ard Kuijpers M+P Raadgevende Ingenieurs BV Aalsmeer, Noord-Holland, The Netherlands

James Tuman Nelson Wilson, Ihrig and Associates Emeryville, CA, USA

David A. Towers Cross-Spectrum Acoustics Inc. Burlington, MA, USA Thorsten Tielkes DB Systemtechnik GmbH Center of Competence Center Aerodynamics and HVAC Munich, Germany

David Anderson Acoustic Studio Stanmore, NSW, Australia

Preface

This volume contains peer-reviewed contributions to the 14th International Workshop on Railway Noise (IWRN14), which took place in Shanghai, China, from 7 to 9 December 2022. The workshop was hosted by the School of Urban Railway Transportation at Shanghai University of Engineering Science in collaboration with Shanghai Intex Exhibition Co. Ltd. The COVID-19 pandemic brought great difficulty and uncertainty to the preparation of IWRN14. However, IWRN14 still attracted 124 abstracts covering the various aspects of railway noise and vibration. A number of 175 delegates from 17 countries and regions on 4 continents registered for the workshop. Although the workshop had to be shortened from the originally planned 5 days to 3 days (7–9 December 2022) and held only with delegates from Shanghai being allowed to sit in the physical conference room, it went quite smoothly in a single session, with 1 keynote lecture, 54 oral presentations and 34 poster presentations. After the workshop, authors of 78 papers opted to submit full papers for peer review. These papers were rigorously peer-reviewed and carefully revised by the authors and are all published in this book. The following themes are covered: Predictions, Measurements, Monitoring and Modelling (12 papers); High-Speed Rail and Aerodynamic Noise (9 papers); Wheel Out-of-Round and Polygonalisation (1 paper); Rail Roughness, Corrugation and Grinding (3 papers); Wheel and Rail Noise (15 papers); Squeal Noise (8 papers); Interior Noise (7 papers); Structure-Borne Noise and Ground-Borne Vibration (15 papers); Resilient Track Forms (2 papers); Bridge Noise and Vibration (4 papers); and finally, Pantograph-Catenary System Vibration (2 papers). Since the first IWRN workshop held in Derby in 1976, it has been established as a regular event (held every three years) that brings together the leading researchers and engineers in all fields related to railway noise and vibration. The IWRN workshops have contributed significantly to the understanding and solution of many problems in railway noise and vibration, building a scientific foundation for reducing environmental impact by airborne, ground-borne and structure-borne noise and vibration. There is no formal organisation behind IWRN but rather an informal, committed international committee. It supports the chairman during the preparation process with the experience and expertise of its members. vii

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The international committee is grateful to the local organising committee of IWRN14, the School of Urban Railway Transportation at Shanghai University of Engineering Science, and Shanghai Intex Exhibition Co. Ltd. for their hard work which made IWRN14 a great success in the wake of the COVID-19 pandemic. The editors of this volume are grateful to Nan Zhang from Springer for their hard work in the publication of this book. We hope that this volume will be used as a “state-of-the-art” reference by scientists and engineers in solving railway noise and vibration problems. Shanghai, China Southampton, UK Leuven, Belgium Gothenburg, Sweden La Plaine Saint Denis, France Tokyo, Japan Aalsmeer, The Netherlands Emeryville, USA Burlington, USA Stanmore, Australia Munich, Germany

Xiaozhen Sheng David Thompson Geert Degrande Jens C. O. Nielsen Pierre-Etienne Gautier Kiyoshi Nagakura Ard Kuijpers James Tuman Nelson David A. Towers David Anderson Thorsten Tielkes

About This book

This book reports on the 14th International Workshop on Railway Noise (IWRN14), held on 7–9 December 2022 in Shanghai, China. It gathers original peer-reviewed papers covering a broad range of railway noise and vibration topics, such as Predictions, Measurements, Monitoring and Modelling; High-Speed Rail and Aerodynamic Noise; Wheel Out-of-Round and Polygonalisation; Rail Roughness, Corrugation and Grinding; Wheel and Rail Noise; Squeal Noise; Interior Noise; Structure-Borne Noise and Ground-Borne Vibration; Resilient Track Forms; Bridge Noise and Vibration; and Pantograph-Catenary System Vibration. Offering extensive and timely information to both scientists and engineers, this book can help them in their daily efforts to identify, understand and solve problems related to railway noise and vibration and to achieve the ultimate goal of controlling the environmental impact of railway systems.

Highlights • Gathers peer-reviewed papers from the 14th International Workshop on Railway Noise. • Presents the latest research findings by leading scholars and experienced engineers. • Describes noise and vibration issues and solutions of railway systems in 19 countries/regions.

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Keynote Lectures Research Advances on Aerodynamic Noise of High-Speed Trains . . . . . . Li Zhuoming, Li Qiliang, Lu Ruisi, and Yang Zhigang

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Predictions, Measurements, Monitoring and Modelling Prediction Model for Railway Noise Emission in Curves . . . . . . . . . . . . . . . Michael Ostermann Multiple Sensors and Partial Calibration for On-Board Measurement of Rail Acoustic Roughness: Results of Rolling Tests . . . . . Olivier Chiello, Marie-Agnès Pallas, Adrien Le Bellec, Rita Tufano, Romain Augez, Benjamin Malardier, Emanuel Reynaud, Nicolas Vincent, and Baldrik Faure Development of Methods for Virtual Exterior Noise Validation . . . . . . . . Rita Caminal Barderi, Romain Rumpler, Antoine Curien, Aurélien Cloix, Martin Rissmann, Ainara Guiral Garcia, Iñigo Eugui Larrea, and Joan Sapena Use of Heterogeneous Microphone Triplets for Simplified Noise Apportionment in Pass-By Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . Jaume Solé, Pierre Huguenet, and Mercedes Gutierrez Ferrandiz Fast and Reliable Noise Predictions for Rolling Stock by Means of Pre-calculated Reference Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Andrea Bistagnino, Maxime Ripert, Clement Dalmagne, and Joan Sapena Requirements and Challenges for Vibration Prediction Tools and the Associated Validation Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sascha Hermann, Dorothée Stiebel, Nils Mahlert, and Rüdiger Garburg

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Framework for Optimization of Multi-source Railway High Speed Noise Models Through Hybrid Methods Combining Acoustic Simulations and Close Perimetric Noise Measurements . . . . . . . . . . . . . . . 103 Gennaro Sica, Jaume Solé, Pierre Huguenet, and Oliver Bewes Noise Incentivisation for UK High Speed Train Procurement . . . . . . . . . . 113 Gennaro Sica, Tom Marshall, Jon Sims, David Owen, and Oliver Bewes Analysis of the Uncertainty of High-Speed Rail Noise Predictions . . . . . . 121 James Woodcock, Tom Marshall, Jon Sims, David Owen, Oliver Bewes, and Gennaro Sica Towards Rail Noise Identification and Localization Based on Deep Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Rui Xue, Guohua Li, and Xiaoning Ma Relationship Between Train Horn Sound Levels Tested at 25 m and Sound Levels Experienced at Distance by Track Workers . . . . . . . . . 141 Martin Toward, Marcus Wiseman, Michael Lower, and David Thompson Considerations for the Implementation of a Train Vibration Monitoring System in Subway Tunnels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Shannon McKenna, Shankar Rajaram, James Tuman Nelson, and Hugh J. Saurenman Design and Performance of a Comprehensive Vibration Monitoring System for Trains Under University of Washington Campus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Shankar Rajaram, James Tuman Nelson, and Marc Pearlman High-Speed Rail and Aerodynamic Noise Numerical Simulation of the Aerodynamic Noise of the Leading Bogie of a High-Speed Train . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 Yuan He, David Thompson, and Zhiwei Hu Prediction of the Aerodynamic Sound Power Level of a High Speed Train Bogie Based on Unsteady FW-H Simulation . . . . . . . . . . . . . . . . . . . . 181 Martin Rissmann, Romain Leneveu, Claire Chaufour, Alexandre Clauzet, and Fabrice Aubin Optimization of Window Pattern of Tunnel Hood Installed at Long Slab Track Tunnel for Reducing Micro-Pressure Waves . . . . . . . . . . . . . . . 191 Shinya Nakamura, Tokuzo Miyachi, Takashi Fukuda, and Masanobu Iida Component-Based Model to Predict Aerodynamic Noise from High-Speed Train Bogies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 Tatsuya Tonai, Eduardo Latorre Iglesias, Toki Uda, Toshiki Kitagawa, Jorge Muñoz Paniagua, and Javier García García

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Reduction of Aerodynamic Noise Emitted from Pantograph by Applying Multi-Segmented Smooth Profile Pantograph Head and Low Noise Pantograph Head Support . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 Takeshi Mitsumoji, Takayuki Usuda, Shigeyuki Kobayashi, Kyohei Nagao, Yuki Amano, and Yusuke Wakabayashi Influence of Flow Disturbing Grooves Underneath the Cowcatcher on Aerodynamic Noise Generated Around a High-Speed Train Bogie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 J. Y. Zhu, Y. Z. Wang, G. D. Cheng, Y. Y. Yuan, and Y. H. Lu Boundary Condition and Equivalent Mass-Spring-Damper System for a Truncated Railway Track . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 X. Sheng and Y. Peng A Method for Predicting the Aerodynamic Pass-By Noise Based on FW-H Equation Without Using Sliding Mesh or Overset Mesh . . . . . . 243 Shumin Zhang, Jiawei Shi, and Xiaozhen Sheng Wheel Out-of-Round and Polygonalisation Influence of Running Speed on the Development of Metro Wheel Polygon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Rang Zhang, Weiming Wang, Gang Shen, and Jiangyu Xiao Rail Roughness, Corrugation and Grinding Cause Analysis of Metro Rail Corrugation Based on Mode Coupling Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 Zhiqiang Wang and Zhenyu Lei Use of Flexible Wheelset Model, Comb Filter and Track Identification to Derive Rail Roughness from Axle-Box Acceleration in the Presence of Wheel Roughness . . . . . . . . . . . . . . . . . . . . . 275 Tobias D. Carrigan and James P. Talbot Analysis of the Mechanism of Rail Corrugation by Using Temperature Dependent Friction Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . 285 Kuikui Ma and Xinwen Yang Wheel and Rail Noise Determination of Acoustic Properties of Railway Ballast . . . . . . . . . . . . . . 297 Xianying Zhang, Giacomo Squicciarini, Hongseok Jeong, and David Thompson Rolling Noise on Curved Track: An Efficient Time Domain Model Including Coupling Between the Two Wheels and Rails . . . . . . . . . . . . . . . 307 Jiawei Wang, David Thompson, and Giacomo Squicciarini

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P2 Resonance Analysis of Multiple Wheels Interacting with a Railway Track . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 Qinghua Guan, Changlong Li, Zefeng Wen, and Xuesong Jin Quantifying Rolling Noise Reduction by Improvements to Wheel-Rail Interface Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 Peeter Vesik, Briony Croft, Mark Reimer, and Donald Eadie Research and Analysis on Disc Brake Noise of High Speed Trains . . . . . . 337 Wensheng Xue, Chaogang Yu, Wenliang Zhu, and Peiwen Chen The Effect of Wheel Rotation on the Rolling Noise Predictions . . . . . . . . . 347 Christopher Knuth, Giacomo Squicciarini, and David Thompson Improved Methods for the Separation of Track and Wheel Noise Components During a Train Pass-By . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 David Thompson, Dong Zhao, Ester Cierco, Erwin Jansen, and Michael Dittrich Experimental Study on Modal Damping Ratios of a Ring Damped Wheel Mounted with Different Damper Types and Preloads . . . . . . . . . . . 367 Shuoqiao Zhong, Xin Zhou, Kun Wu, and Xiaozhen Sheng The Influence of the Vehicle Body on the Sound Radiation from the Rail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 Dong Zhao, David Thompson, Evangelos Ntotsios, Ester Cierco, and Erwin Jansen Noise Sensitivity Analysis of a Two-Stage Baseplate Fastening System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 Evangelos Ntotsios, Boniface Hima, David Thompson, Giacomo Squicciarini, and David Herron Study on the Wide-Frequency Tuned Mass Damper Inhibiting Rail Corrugation and Noise in Floating Slab Track . . . . . . . . . . . . . . . . . . . 397 Xuejun Yin, Xiaotang Xu, Huichao Li, Qian’an Wang, and Yunfeng Gao A Program for Predicting Wheel/Rail Rolling Noise from High-Speed Slab Railway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 Cheng Gong, Sheng Xiaozhen, Zhang Shuming, and Feng Qingsong Strong Rail Damper Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417 Wilson Ho, Ron Wong, Max Yiu, Ghazaleh Soltanieh, Marco Ip, and Yi-Qing Ni Inclined Plane TMD with Independent Vertical and Lateral Frequency Vibration Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 Marco Ip, Yi-Qing Ni, Ghazaleh Soltanieh, Wilson Ho, and Max Yiu

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An Investigation into the Effect of the Number of the Rubber Blocks of a Resilient Wheel on Wheel-Rail Noise . . . . . . . . . . . . . . . . . . . . . 439 Q. Zhou, Y. He, F. Xu, X. Sheng, Y. He, and Z. Liu Squeal Noise A High Frequency Wheel/Rail Contact Model for Curve Squeal in Time Domain Using Impulse Response Function Method . . . . . . . . . . . 451 Xinwen Yang, Shutong Liu, and Jin Wang No Dependence on Speed? Investigation of High Noise Events at a Tight Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461 P. Pandey, J. Howes, R. Kochanowski, and E. Milton Estimation of Vibration Limit Cycles from Wheel/Rail Mobilities for the Prediction of Curve Squeal Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 Olivier Chiello, Rita Tufano, and Martin Rissmann Survey of Curve Squeal Occurrence for an Entire Metro System . . . . . . . 483 Olle Eriksson, Peter T. Torstensson, Astrid Pieringer, Rickard Nilsson, ´ Martin Höjer, Matthias Asplund, and Anna Swierkoska Transient Modelling of Curve Squeal Considering Varying Contact Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491 Astrid Pieringer, Peter Torstensson, Jannik Theyssen, and Wolfgang Kropp Predictive Modelling of Curve Squeal Occurrence in Tramways: Influence of Wheel/Rail Double Contact Points . . . . . . . . . . . . . . . . . . . . . . . 501 Federico Castellini, Leonardo Faccini, Egidio Di Gialleonardo, Stefano Alfi, Roberto Corradi, and Giacomo Squicciarini Experimental Study on Curve Squeal Noise with a Running Train . . . . . 511 Yasuhiro Shimizu, Takeshi Sueki, Tsugutoshi Kawaguchi, Toshiki Kitagawa, Hiroyuki Kanemoto, and Masahito Kuzuta Interior Noise A Study on Vibration Transmission in the Suspension/bogie System of a High-Speed Train . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523 Mingyue Wang and Xiaozhen Sheng Bi-objective Sound Transmission Loss Optimal Design of Double Panels Using a Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533 Y. M. Zhang, Y. Zhao, D. Yao, Y. Li, X. B. Xiao, K. C. Zuo, and W. J. Pan

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SEA Modelling Approach of Rail Vehicle Interior Noise Considering Complete Carbody Composite Structures . . . . . . . . . . . . . . . . 543 Dan Yao, Jie Zhang, Ruiqian Wang, Jie Pang, Yue Zhao, Yumei Zhang, and Xinbiao Xiao A Statistical Energy Analysis Model of a Metro Train Running in a Tunnel for Prediction of the Internal Noise . . . . . . . . . . . . . . . . . . . . . . . 553 Yunfei Zhang, Li Li, and Hongxiao Li Numerical Investigation on the Low-Frequency Vibroacoustic Response of an Aluminium Extrusion Compounded with Acoustic Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563 Jie Zhang, Junlin Chen, Dan Yao, Jiang Li, and Shaoyun Guo Sound-Insulation Prediction for High-Speed Train Walls Based on Neural Network Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573 Ruiqian Wang, Dan Yao, Jie Zhang, Xinbiao Xiao, and Ye Li Vibroacoustic of Extruded Panels Excited by a Turbulent Boundary Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583 Y. Li, X. B. Xiao, Y. Yang, Y. M. Zhang, and R. Q. Wang Structure-Borne Noise and Ground-Borne Vibration The Influence of a Building on the Ground-Borne Vibration from Railways in Its Vicinity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595 Xiangyu Qu, David Thompson, Evangelos Ntotsios, and Giacomo Squicciarini Prediction of Ground Vibration Induced by a High-Speed Train Moving Along a Track Supported by a Pile-Plank Structure . . . . . . . . . . . 605 Yuhao Peng, Jianfei Lu, and Xiaozhen Sheng Train Ground-Borne Vibration Control Measures and Validation Tests to Meet Stringent Vibration Thresholds for University of Washington Research Labs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615 Shankar Rajaram, James Tuman Nelson, and Thomas Bergen Design and Implementation of Measures to Reduce the Vibration Levels of Metro Trains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625 Wout Schwanen and Jacco de Regt Simulation and Analysis on Ground Vibrations of Pile-Net Composite Subgrade Under High-Speed Train Loadings . . . . . . . . . . . . . . 633 Guangyun Gao, Jianlong Geng, Junwei Bi, and Yuanyang You Transferability of Railway Vibration Emission from One Site to Another . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643 M. Villot, C. Guigou-Carter, and P. Jean

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Ground Vibration Reduction Analysis of Pile-Supported Subgrade for High-Speed Railway Using 2.5D FEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653 Guang-yun Gao, Ji-yan Zhang, and Bi Jun-wei Noise and Vibration Measurement and Analysis at a Metro Depot and Above Transit-Oriented-Development . . . . . . . . . . . . . . . . . . . . . . . . . . . 663 Hongdong Huang, Jian Wang, Xiaohan Phrain Gu, Anbin Wang, Longhua Ju, Xinwei Luo, and Qingming Tu Optimizing Components in the Rail Support System for Dynamic Vibration Absorption and Pass-By Noise Reduction . . . . . . . . . . . . . . . . . . . 673 Jannik Theyssen, Astrid Pieringer, and Wolfgang Kropp A Hybrid Prediction Tool for Railway Induced Vibration . . . . . . . . . . . . . . 683 Pascal Bouvet, Brice Nélain, David Thompson, Evangelos Ntotsios, Andreas Nuber, Bernd Fröhling, Pieter Reumers, Fakhraddin Seyfaddini, Geertrui Herremans, Geert Lombaert, and Geert Degrande Response of Periodic Railway Bridges Under Moving Loads Accounting for Dynamic Soil-Structure Interaction . . . . . . . . . . . . . . . . . . . 693 Pieter Reumers, Geert Lombaert, and Geert Degrande Investigation of Differences in Wayside Ground Vibration Associated with Train Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703 Briony Croft, Radoslaw Kochanowski, David Hanson, and David Anderson Theoretical and Numerical Study on the Effect of TMD in Ground Borne Noise Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713 Ghazaleh Soltanieh, Yi-Qing Ni, Marco Ip, and Wilson Ho Finite Element Modelling of Tunnel Shielding in Vibration Measurements of Ground-Borne Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723 Fatemeh Dashti, Patrik Höstmad, and Jens Forssén Assessment of Building Performance Against Train Induced Vibrations by a Hybrid Experimental-Numerical Methodology . . . . . . . . 731 Hamid Masoumi, Behshad Noori, Joan Cardona, and Patrick Carels Resilient Track Forms Resilient Track Components Modelling Options for Time Domain Train-Track Interaction Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743 Qianqian Li, Egidio Di Gialleonardo, Roberto Corradi, and Andrea Collina

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An Analytical Model in Frequency Domain for Embedded Rail Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753 Leonardo Faccini, Federico Castellini, Stefano Alfi, Egidio Di Gialleonardo, Andrea Collina, and Roberto Corradi Bridge Noise and Vibration A Rapid Calculation of the Vibration of the Bridge with Constrained Layer Damping Based on the Wave and Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765 Quanmin Liu, Yifei Sun, Peipei Xu, and Lizhong Song Study on Devices to Reduce Pass-by Noise Along Viaducts with Snow-Removing Openings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775 Toshiki Kitagawa, Toki Uda, Kiyoshi Nagakura, Kaoru Murata, and Hiroki Aoyagi Bridge Noise Reduction by Acoustic Short Circuit . . . . . . . . . . . . . . . . . . . . 785 Yuanpeng He, Xinghuan Wang, Qing Zhou, Xiaozhen Sheng, and Yulong He Comparison of Vibration Characteristics of Floating Slab Track in Rail Transit Viaduct with Time-Domain and Frequency-Domain Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 793 Qingyuan Song and Qi Li Pantograph-Catenary System Vibration A Preliminary Study Towards the Understanding of the Pantograph-Catenary Irregular Wear Problem in the Rigid Overhead Catenary System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805 Xiaohan Phrain Gu, Anbin Wang, Qirui Wu, and Ziyan Ma Research of Influence of Pantograph-Catenary System Vibration on Irregular Wear of Carbon Contact Strip . . . . . . . . . . . . . . . . . . . . . . . . . . 815 Qirui Wu, Xiaohan Phrain Gu, and Anbin Wang

Keynote Lectures

Research Advances on Aerodynamic Noise of High-Speed Trains Li Zhuoming, Li Qiliang, Lu Ruisi, and Yang Zhigang

Abstract With the increase in operating speed, aerodynamic noise become the technical bottleneck restricting the development of the high-speed railway. This paper reviews the research on the aerodynamic noise of high-speed trains from the perspectives of prediction, mechanism analysis and noise control methods. In terms of prediction methods, the research on the aerodynamic noise of high-speed trains is mainly based on static and dynamic trains, and the wind tunnel test and the field tests are the typical corresponding experimental methods, respectively. Based on the flow-filed simulation, the FW-H equation, the APE equation, and other calculation methods are mainly applied to predict the far and near field noise accurately in simulation. The regions with severe flow separation, such as bogies and pantographs, etc., are identified as the primary noise sources. In terms of mechanism analysis, unsteady flow statistics are helpful in identifying sound sources empirically. Furthermore, the sound source term based on the aerodynamic noise calculation methods can theoretically characterize the sound source characteristics. The reduced-order method, coherence analysis and other statistical analysis methods are applied to clarify the relationship between the flow field. The aerodynamic noise can be optimized by passive control methods, such as the bogie cavity fairing, and active control methods, such as the airflow jet. The noise control methods can be further optimized combined with parametric modeling, genetic algorithm and other methods, which deserve more attention.

L. Zhuoming · L. Qiliang · L. Ruisi · Y. Zhigang (B) School of Automotive Studies, Tongji University, Shanghai 201804, China e-mail: [email protected] L. Zhuoming · L. Qiliang · Y. Zhigang Shanghai Automotive Wind Tunnel Center, Tongji University, Shanghai 201804, China Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Shanghai 201804, China Y. Zhigang Beijing Aeronautical Science and Technology Research Institute, Beijing 102211, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_1

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Keywords Aerodynamic noise · High-speed trains · Wind tunnel test · Numerical simulation

1 Introduction High-speed trains are an important part of the national transportation system. As a popular means of transportation, high-speed railway has the characteristics of speed, reliability, comfort and economy. The rapid development of high-speed railway is of great significance to the economic development of cities along the line, reducing the energy consumption of transportation and the advancement of railway technology. In China, high-speed trains cover 95% of cities with a population of 1 million and above, and undertake more than 60% of the national railway passenger volume. It is the main artery of the national economy. By the end of 2030, the operating mileage of China’s high-speed railways is expected to reach 45,000 km, and more than 7000 high-speed trains will operate online [1]. There are systematic technologies of highspeed trains in Japan, France, Germany, and there are also some high-speed rail technical reserves in South Korea and Spain and other countries. In the development of high-speed trains at various stages, speed is the main concern. At present, Chinese high speed trains run up to 360 km/h, and the operating speed of high-speed railways has generally increased to more than 300 km/h [2], while aerodynamics and noise problems are the main factors restricting the further increase of speed if not properly addressed and controlled. During operation, the noise generated by high-speed trains is mainly composed of traction noise, wheel-rail noise, and aerodynamic noise. The traction noise and wheel-rail noise are proportional to the first power and the third power of the speed, respectively, while the aerodynamic noise is proportional to the sixth power of the operating speed, as shown in Fig. 1. As the train running speed increases, the contribution of aerodynamic noise to the total noise also increases gradually. It is generally believed that when the train speed exceeds 300–350 km/h, the aerodynamic noise will exceed the rolling noise and become the main noise source [3–5]. Considering that high-speed trains are mostly passenger trains and often pass through densely populated areas, the noise generated by the trains has a serious impact on the comfort of residents and passengers along the line. According to surveys [6–8], when the continuous equivalent sound pressure level of railway noise is greater than 60 dB(A), 30% of the population will feel annoyed, and the noise generated by high-speed trains currently operating on the line can be greater than this. This also puts forward higher requirements for the aerodynamic noise standards of 350 km/h high-speed trains currently operating on the line, as well as 400 km/h and above high-speed trains under development, especially on the line where the population density is high and the traffic volume is large.

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Fig. 1 The relationship between noise and speed of high speed train [9]

In order to explore the characteristics of aerodynamic noise sources of high-speed trains, a large number of scholars have carried out relevant research on the characteristics of the aerodynamic noise of the train through experimental tests and simulation methods. With the development of data processing method and the continuous improvement of computing ability, more prediction and analysis methods have been introduced into the research of aerodynamic performance and aerodynamic noise of high-speed trains, which is expected to further improve people’s understanding of the relationship between aerodynamic noise and flow, so as to achieve trains’ low-noise design. This paper summarized the development of research on aerodynamic noise of high-speed trains in the past ten years, and organizes relevant research results of experiments and numerical simulations from the perspectives of prediction, analysis and control. This paper also shows the research progress on aerodynamic noise of high-speed trains running on real road conditions, such as slab and ballast tracks. In the field of flow and acoustics, some promising approaches for train aerodynamic noise control have also been mentioned. This paper will introduce the relevant research contents from the following aspects: (1) Prediction methods of aerodynamic noise of high-speed trains are introduced, including the commonly used wind tunnel, field test and simulation methods from the perspective of dynamic and static models. (2) Flow and noise analysis methods are expected to be applied to high-speed trains, containing the sound source term analysis and the statistical analysis methods. (3) The aerodynamic noise control methods are discussed, combing the common noise reduction measures for the main

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noise sources of the train, and focusing on the active and passive control of noise reduction methods involving multi-parameter optimization.

2 Aerodynamic Noise Prediction The aerodynamic noise of the train is mainly generated from the interaction between the train and the high-speed airflow. In order to reproduce the interaction between the train and the flow, there are usually two research methods. One is to study the flow characteristics of high-speed airflow when it flows through a stationary highspeed train model, and the other is to study the flow characteristics of the airflow driven by a dynamic high-speed train. In view of the aerodynamic noise of highspeed trains, many scholars at home and abroad have carried out relevant research through experiments and simulation methods. Through wind tunnel tests, field tests, and numerical simulations, the flow and aerodynamic noise characteristics of static and dynamic high-speed trains are predicted.

2.1 Static High-Speed Trains Test Acoustic wind tunnel test is a typical research method of aerodynamic noise of the static high-speed train. In addition, researchers also use the wind tunnel test as a benchmark to simulate static train aerodynamic noise characteristics under different working conditions. Acoustic wind tunnels are mostly open-jet wind tunnels, and noise reduction design is required in the whole wind tunnel, so as to minimize the background noise in the test section. Limited by the size of the wind tunnel nozzle, the wind tunnel test of the aerodynamic noise of high-speed trains is often carried out based on the scale model of the train. During experiments, it is difficult to flow all the similarity laws, and usually the most important dimensionless numbers are the Reynolds number (Re), the Mach number (Ma), and the Strouhal number (St). It is often difficult to satisfy the similarity laws of Re and Ma simultaneously. Fortunately, when the Re used in the test is larger than the critical value, the characteristics of the aerodynamic and aerodynamic noise of the train model are basically independent of the Reynolds number [10]. However, due to the complexity of local flow field, the similarity laws cannot fully represent the conversion relationship between scale model and full-scale model. The scale method of flow and noise near the complex components such as bogies remains to be further investigated. The test is usually carried out in a semianechoic chamber, and the far-field aerodynamic noise characteristics of the train can be obtained through a free-field microphone. Through the surface microphone, the unsteady pressure characteristics on the body surface can be obtained and when the turbulence filter is applied, the near-field sound characteristics can be further obtained. In order to identify the main noise source of the test model, the microphone

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array is the main measurement facility. Based on the beamforming algorithm of delay summation, the main noise source of the train can be approximately determined by processing the acoustic signals of each position of the microphone array. During the process, it is necessary to consider the sound source drift caused by the wind tunnel flow field and the sound propagation refraction correction of the jet shear layer noise in the open-jet wind tunnel [11]. In China, the aerodynamic and aero-acoustic wind tunnels at the Wind Tunnel Center of Tongji University in Shanghai, and the aero-acoustics wind tunnels at the China Aerodynamics Research and Development Center in Mianyang are mainly used to carry out high-speed train aerodynamic noise tests. As shown in Fig. 2, Gao et al. [12, 13] conducted an acoustic test on a high-speed train model in the acoustic wind tunnel of Tongji University. Using far-field microphones and microphone arrays, through comparing the test results of different models, they analyzed the main noise source characteristics and their contributions to the far-field noise. The test results show that when the high-speed train model is completely smooth and there is no ground clearance, it basically does not generate additional noise. For the 1:8 scaled three carriage train model with more details, the bogie and pantograph are the main noise sources, followed by the connection of the carriages, the cowcatcher, the head and the tail of the train. Furthermore, the main frequency characteristics of the sources are analyzed. Hao et al. [14] conducted aerodynamic noise tests on 1:8 scaled three carriage trains in Mianyang, and also found that bogies and pantographs contributed greatly to far-field aerodynamic noise. In addition, the noise caused by bogies is mainly distributed in the middle- and low-frequency bands, with no obvious peak. However, as shown in Fig. 3, the noise generated by the pantograph is mainly medium- and high-frequency noise, and there is peak noise. Internationally, high-speed train aerodynamic noise tests are often carried out in German-Dutch wind tunnels (DNW), German Aerospace Center (DLR) and Japan

Fig. 2 High speed train model and microphone array in the aero-acoustic wind tunnel of Tongji University

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Fig. 3 Aerodynamic noise spectrum of high-speed train with pantograph at 250 km/h [14]

Railway Technical Research Institute (RTRI). Taking RTRI as an example, Yamazaki et al. [15, 16] measured the aerodynamic noise of a 1:7 scaled high-speed train model, and used the TWINS model to predict the wheel-rail noise. It can be found that the results of the wind tunnel test are in good agreement with the results of the field test, and the bogie noise is the main source of the train bottom noise. Below 500 Hz, the contribution of bogie aerodynamic noise to far-field noise is greater than that of wheel-rail and traction noise. And they used the impulse response method to study the transmission path from the noise source to the measuring point. The results show that the noise received by the measuring point is mainly the sound wave reflected from the ground, while the direct sound wave will be covered and weaken by the bogie fairings. Except for the wheel and the cavity structure making loud noise under the influence of incoming flow, the motor and brake also have a great influence on the aerodynamic noise of the bogie. Iglesias et al. [17] tested a 1:7 scaled train model in the same wind tunnel, studied the aerodynamic noise of different bogie structures and inlet conditions, and analyzed the relationship between the speed and directionality of the noise. The results show that the overall sound pressure level varies with the 6.4–6.7th power of velocity, and the components exposed to the free flow are very important to the overall noise, while the bogie components in the bogie cavity radiate much less noise. It is challenging to realize the relative movement between the train and the ground, and it’s always a key problem to reproduce the near-ground flow under the train. Some scholars have tried to simulate the ground effect through moving belt and tangential airflow jet [18–20], and found that ground conditions have a significant impact on aerodynamic force measurement. Even for stationary ground, the ground structure significantly affects the near-ground flow. Bell et al. [21] carried out the wind tunnel

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tests of the high-speed train model under the flat ground and the ground with track. Compared with the ground condition of the embankment and track, the tail vortex movement speed and intensity are greater under flat ground. There are significant differences in the lower flow field of the train. Schober et al. [22] carried out wind tunnel tests to investigate the aerodynamic performance of trains under different ground conditions. It is found that vortex structures that did not exist in the field test would be generated when trains were tested under the ground condition of embankments, which significantly affected aerodynamic measurement. In wind tunnels, simulating ground effects often introduces additional mechanical noise sources, and complex ground structures may also lead to incorrect flow fields. In general, it is difficult to reproduce the aerodynamic noise under real ground conditions in static wind tunnel tests. The test cost of the high-speed train wind tunnel test is lower than that of field test. A well-designed wind tunnel can reproduce the actual flow field of the high-speed train, realize aerodynamic noise tests under different working conditions, and have a good repeatability. In addition, since the train is fixed in the test section of the wind tunnel, the aerodynamic noise is about to be the only noise source, which helps to accurately study the characteristics of each aerodynamic noise source and control it. However, most of the high-speed train acoustic wind tunnel test platforms are modified from automotive or aviation acoustic wind tunnels, which are limited in size and original functions, especially it is difficult to fully reproduce the near-ground flow of the real environment. For the general wind tunnel test platform, the length of the test section is limited, so it is often only possible to study the scaled model and the short train.

2.2 Static High-Speed Trains Simulation A well-corrected wind tunnel test can better obtain the aerodynamic noise characteristics of high-speed trains. With the development of computer software and hardware, computational fluid dynamics, computational acoustics and other methods have been gradually applied in the study of aerodynamic noise of high-speed trains. In engineering, the averaged aerodynamic characteristics of the research object over a period of time are often concerned. The Reynolds Averaged Navier–stokes (RANS) is proposed in this case. However, the generation of aerodynamic noise mainly comes from unsteady phenomena such as vortex shedding and pressure fluctuation, and the RANS method based on the flow statistics theory is difficult to apply in the calculation of aerodynamic noise. For unsteady flow phenomena, it is mainly implemented by the Large Eddy Simulation (LES) [23–25] method and the Detached Eddy Simulation (DES) [26, 27] method. Turbulence is composed of eddies with different scales. Large-scale eddies have a significant impact on the flow, while small-scale eddies tend to be directly dissipated and have the characteristics of isotropic, which are easy to simulate by mathematical models. The main idea of LES is to solve the larger-scale vortices by calculation, and the influence of the small-scale

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vortices is simulated through the model. Due to the simplified calculation of smallscale vortices, the computational complexity of LES is much smaller than that of direct numerical simulations, but it still requires large computational resources [28]. For this reason, the flow near the wall is considered nearly stable, and it is simplified by the RANS method. The rest of the flow field tends to be calculated by the LES method. As an alternative to the traditional N-S equation-based CFD method, the lattice Boltzmann method has also been applied to the simulation of high-speed train aerodynamic noise [29]. For the numerical calculation of aerodynamic noise, the acoustic analogy method was first proposed by Lighthill [30, 31]. By arranging the N-S equation and moving the wave equation to the left side of the equation, the relationship between the wave equation and the sound source term can be clarified. The equation considers the effects of convection and refraction in the acoustic calculation. However, when calculating and solving the quadrupole sound source term of the Lighthill equation, it is necessary to solve the partial derivative of the pressure at each spatial point in the entire computational domain, which requires a lot of computing resources and is difficult to achieve. Since then, in order to find a reasonable engineering calculation method for aerodynamic noise, Ffowcs Williams and Hawkings et al. [32–34] improved and further extended the work of Lighthill and Curle [35]. Applying the method of Green’s function, it is only needed to calculate the pressure integral of the control surface and extrapolate the resulting far-field aerodynamic noise. The aerodynamic noise calculation method is summarized into the FW-H equation, which makes the acoustic analogy method proposed by Lighthill widely used in engineering calculations. After assumptions and simplifications, the FW-H equation only calculates the sound field based on the flow field on the surface, and does not consider the mutual influence of sound waves during the propagation process. Strict preconditions are required in the use process. For example, the distance between the far-field noise measurement points and the sound source is far enough to avoid errors caused by the propagation of the sound source. In 2003, Ewert et al. [36] proposed a set of Acoustic Perturbation Equations (APE) that can be used to simulate and calculate the flowinduced sound field in time and space. By the source term filtering method, the flow field information is filtered to obtain the acoustic information, and the feasibility of its calculation is verified. In addition, the calculation theory of aerodynamic noise also includes the equations of Philips [37] and Lilley [38], the vortex sound equations proposed by Powell [39] and Howe [40], etc. For high-speed train aerodynamic noise simulation, the FW-H equation and the APE equation are widely used. Many scholars have applied numerical simulation to the analysis of aerodynamic noise. Generally speaking, the solution of aeroacoustics often starts with the simulation of the flow field, and the flow field of the high-speed train is solved by RANS, LES or DES method. As shown in Fig. 4, it is the instantaneous vortex structures near the pantograph simulated through LES. Furthermore, combined with aerodynamic noise methods such as FW-H equation, APE equation, etc., the aerodynamic noise of the train can be solved. Sun et al. [42] used RANS to calculate the external flow field of the high-speed train, combined the nonlinear acoustic solution method and the FW-H equation, calculated the aerodynamic noise in the near and far fields, and

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discussed the acoustic contributions of different parts and the characteristics of the far-field noise. Studies have shown that the grooves and nose cones at the connection of the carriages will aggravate the changes in the boundary layer, resulting in greater aerodynamic noise. However, a lot of simplifications were made on high-speed trains in this study, and important noise sources such as bogies and pantographs were not considered. Gao et al. [43] combined the wind tunnel test and aerodynamic noise simulation to solve the far-field and near-field noise through the FW-H equation and the APE equation on the basis of solving the train flow field by the LES equation. The total sound pressure level of the far-field noise obtained from the simulation is only 2 dB different from the wind tunnel test results, and the noise spectrum is basically the same. Further, based on the APE method, the near-field sound distribution of each component of head vehicle can be solved, and it can be found that the sound pressure level of the bogie is more prominent, much larger than that of the windows, nose and other components. Whether it is the far-field sound spectrum or the near-field sound source distribution, the simulation and test results are in good agreement, which proves the feasibility and accuracy of the simulation calculation method. Zhang et al. [44] and Zhu et al. [45] also used an approximate method to calculate the far-field noise, which also verified the effectiveness of the far-field noise simulation method, and clarified the large contribution of the lead car bogie to the far-field noise. However, the above research simplifies the pantograph, which is a critical source of aerodynamic noise. Zhang et al.[46] analyzed the main aerodynamic noise sources and far-field characteristics of the three-carriage train through the broadband noise model, LES and FW-H equations. The results showed that the pantograph, bogie, inter-coach and other locations where the flow separation is intense produce significant aerodynamic noise. Pantograph generates larger noise in the open mode, and the deflector can realize a noise reduction effect. Liu et al.[47] used a similar simulation method to compare the far-field noise characteristics of the pantograph under different train speeds and measuring points. The aerodynamic noise band of the pantograph was narrow and gradually moved to high frequency with the increase of train speed. It can be found that the simulation has sufficient accuracy, the comparisons of simulation results and experimental results at different receive points are shown in Fig. 5. For the characteristics of the train aerodynamic noise source, similar conclusions can be obtained with the wind tunnel test. Compared with the noise characteristics of the whole train, which are often studied by through wind tunnel tests, it is easier to analyze the aerodynamic noise contribution of each component in simulation. Zhang et al. [48] analyzed the aerodynamic noise contribution of each component of the trailer bogie based on the broadband noise model, LES and FW-H equations. Among the various components of the bogie, the bogie frame contributes more to the far-field noise, followed by the wheelset and then the other components. At the same time, by setting up multiple measuring points and sound source planes, each component’s acoustic directivity and spectral characteristics are discussed. Zhu et al. [49, 50] studied the aerodynamic noise characteristics of the simplified bogie model using the DDES method and the FW-H equation, carried out a detailed discussion on the aerodynamic noise in the wheelset area, and found that the flow separation

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Fig. 4 Instantaneous vortex structures near the pantograph [41]

generated by the leading edge of the bogie interacts with the wheelset. Meanwhile, the trailing edge of the bogie is also impacted by the flow, resulting in a strong source of aerodynamic noise. Tan et al. [51] discussed the acoustic characteristics and vortex structure of each part of the pantograph according to the FW-H equation. It can be found that the sound source intensity of each part of the pantograph is closely related to the vortex structure nearby. The vortex structure and aero-acoustic characteristics at the pantograph head are quite different, and the control of the vortex structure can realize noise reduction of the pantograph region. For the simulation of aerodynamic noise of high-speed trains, the simulation can better achieve the statistical characteristics of flow field, so as to carry out the detailed analysis of the aerodynamic noise characteristics, and establish the relationship between the flow and acoustic characteristics. The method of aerodynamic noise analysis will be further sorted out in the Sect. 3. The combination of the acoustic analogy method and the LES or DES equation is a common mean of aerodynamic noise simulation. In addition, other flow or acoustic simulation methods also have their advantages and are applied to the aerodynamic noise simulation of high-speed trains. The boundary element method first obtains the turbulent pressure fluctuation on the train surface through unsteady calculation, and then uses the boundary element method to calculate the aero-acoustic characteristics. Compared with the traditional combination of unsteady calculations and FW-H equations, the boundary element method can obtain sound source characteristics faster under limited computing resources. Zheng et al. [52] discussed the distribution of aerodynamic noise sources on the train surface through the boundary element method, and compared it with the traditional FW-H method to verify the accuracy of the surface sound source calculated by the boundary element method. The sound source distribution shows that the noise in the bogie area is stronger. Luo et al.[53]

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Fig. 5 Spectral comparison of the simulation results and experimental results [45]

combined LES and boundary element methods to study the aerodynamic noise in the pantograph area. In addition, the boundary element method is also often used in the fields of wheel-rail noise and vibration noise of high-speed trains, which is not described here. The lattice Boltzmann method (LBM) has significant advantages in dealing with the external flow field of complex high-speed trains, and often does not require model simplification or reduction. Meskine et al.[54] verified the accuracy of the LBM method in numerical simulation of aerodynamic noise. Compared with other aero-acoustics prediction methods, the component-based method is a semiempirical prediction model, and the model coefficients of each component of the research object can be obtained through the database, which can realize the rapid prediction of aerodynamic noise. Based on the empirical database of different rods, Iglesias et al.[55] realized the overall aerodynamic noise prediction of the pantograph, and verified the accuracy of the empirical model according to the wind tunnel test results. In addition, the vortex sound equation is also a choice to replace the FW-H equation for aerodynamic noise prediction. Zhang et al.[56] used the vortex sound theory to calculate the cavity noise and carried out experimental verification. Zhu et al.[50] also used the source term of the vortex acoustic equation to analyze the relationship between the flow and acoustic characteristics of the wheelset. It is worth noting that, similar to the static wind tunnel test, there are some differences in the simulation results under different ground conditions, especially for nearground flows. Xia et al. [58] used the DES method to study the influence of ground

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Fig. 6 Average velocity distributions under different ground conditions [57]

conditions on the flow field. Under the condition of the static ground, the lateral and lift force of the train fluctuate greatly, the diffusion rate of vorticity is accelerated, and the oscillation of the longitudinal vortex pair is more intense. Wang et al. [59] also derived similar conclusions. Ground conditions and the surrounding environment also influence aerodynamic noise. For static high-speed train simulation, Su et al. [60] simulated the far-field noise of static high-speed trains under different environments and found that aerodynamic noise under the bridge was significantly greater than that under the flat ground. Combined with simulation and experiment, Yang et al. [61] discussed the influence of support floor on aerodynamic noise measurement results in the wind tunnel, and found that the support floor had a significant effect on the flow field near the head and tail vehicle, especially the bogie, as well as on aerodynamic noise. Li et al. [57] studied the aerodynamic noise on the ground of flat and ballast track through simulation. It is found that there are obvious differences in bottom flow under different ground conditions. Figure 6 shows the distribution of average streamwise velocity under different ground conditions. The aerodynamic noise of ballast track is smaller than that of flat track. The sound absorption effect and rough surface of ballast track both affect the far-field aerodynamic noise, and the sound absorption effect is significant. Minelli et al. [62] also simulated the influence of sound barriers on the aerodynamic noise in the far field of the train. A well-designed sound barrier has a good noise reduction effect and affects the flow structure of the train’s wake flow.

2.3 Research on Dynamic High-Speed Trains In the static high-speed train research method, the high-speed airflow flows through the static high-speed train model and produces typical flow phenomena such as vortex shedding, which is also the main cause of aerodynamic noise. However, it is often difficult to reproduce the interaction of trains in a real environment through static

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train studies, whether in wind tunnel tests or simulations. This is mainly due to the fact that in the natural environment, the train interacts not only with the airflow, but also with the surrounding environment, such as the ground, track, sound barriers, etc. In the dynamic high-speed train research, the moving train drives the airflow around it to generate flow and acoustic phenomena worthy of attention, which can reproduce the external flow field and aerodynamic noise of the high-speed train in the real environment. The field test is a typical research method of dynamic high-speed train aerodynamic noise. Zhang et al. [63] studied the influence of sound sources on the external noise of high-speed trains from the aspects of experiments and simulations. As shown in Fig. 7, the microphone array measurement of the real high-speed train running on the viaduct was carried out, and they found that the noise mainly came from the bogie, the lower area and the pantograph, and the contribution of the head car was greater than that of the tail car. The noise contribution of different sound source regions at different speeds and test distances was explored. Based on linear acoustics, a numerical model that is consistent with the experiment is established. The study found that the noise of the bogie, pantograph, lower area and inter-coach of the train contributed significantly to the pass-by noise, but the contributions to the far-field measuring points at different positions are different. Wang et al. [64] also conducted similar research. Wang et al. [65] also carried out sound source identification measurements on high-speed trains running on the line. The results showed that the distribution of noise sources at different speeds was basically similar, and the bogie noise contributed more. By comparing the noise of bogies at different positions, it is found that the proportion of aerodynamic noise gradually increases with the increase of speed. For high-speed trains running on the line, there are multiple complex sound sources, in addition to aerodynamic noise, wheel-rail noise and traction noise are mixed in the measurement results. Fortunately, the field test is often carried out based on real trains running on the line. Compared to the huge size of the real train, tiny sensors often do not affect the noise characteristics of the train itself, which provides greater convenience for the study of specific components. Frémion et al. [66] placed sensors near the individual components of the bogie and the inter-coach,

Fig. 7 Filed test and microphone array [63]

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and introduced a coherent analysis method to clarify the contribution of each part to the far-field noise. The analysis shows that the bogie cannot be regarded as a whole sound source, the acoustic characteristics of the external radiation in different positions are different, and the noise near the front and rear wheel pairs cannot be ignored. Song et al. [67] use a similar approach, combined with the transfer path analysis method to separate the aerodynamic noise from the total noise. The results show that the structural radiated noise of the bogie is primarily concentrated in the low frequency, while the aerodynamic noise is mainly concentrated in the medium and high frequencies. It is clear that when the operating speed is greater than 250 km/ h, the bogie noise is mainly derived from the aerodynamic noise, and its proportion increases with the increase of speed. Zhu et al. [5] used the transmission path analysis method for noise separation, and also found that the contribution of aerodynamic noise increased with the increase of speed. When the speed was greater than 200 km/ h, the contribution of aerodynamic noise dominated. The characteristics of aerodynamic noise are also different under different ground and line conditions. Yang et al. [68] studied the far-field noise of high-speed trains running on bridges and embankments. The test results of the microphone array showed that the passing noise under the embankment condition was higher than that under the bridge condition, and the noise of the bogie region under the embankment was slightly lower than that under the bridge, while the noise of the train surface was slightly higher, which was presumably due to the noise reflection of the ground. Zhang et al. [69] studied the noise inside the vehicle at different speeds and environments through the field test. Under slab track at the speed of 250 km/h, the noise inside the vehicle at the high-frequency band above 500 Hz was significantly smaller than that of slab track. At 350 km/h, the noise inside the train running in the tunnel is more significant than that under open line condition. This also confirms indirectly that under different ground conditions and line environments, the characteristics and intensity of the aerodynamic noise generated by the train are different. In addition to field tests, the dynamic model bench test is also an important method to achieve dynamic train model research. The moving model of the train is driven by energy storage or transmission, and the dynamic model test bench is often used to reproduce the running state of the train moving in and out of the tunnel, train passing, etc. Central South University, the University of Southampton in the United Kingdom and the Institute of Mechanics of the Chinese Academy of Sciences have all carried out relevant studies. Figure 8 shows the TRAIN rig facility in the University of Southampton. However, due to the huge noise generated by the transmission during operation, it was difficult to carry out aerodynamic noise-related studies in the test of the dynamic model bench, and the researchers mainly focused on the aerodynamic performance of the train in a complex environment. From the perspective of aerodynamics, Dorigatti et al. [70] conducted dynamic and static studies under crosswind conditions on the wind tunnel test bench and the dynamic model test bench, respectively. The results show that there is no significant difference in the constant force coefficient of the static and dynamic train, and the flow of the upper part of the train is basically similar. However, there is a big difference in the bottom flow under the two research methods. Although there is no further discussion of aerodynamic noise,

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Fig. 8 the simplified ICE2 model on the TRAIN rig [71]

this will undoubtedly have a greater impact on the aerodynamic noise generated from the bottom of the train, especially the bogie part. Dynamic model simulation is also an important method of dynamic high-speed train research. In the simulation process, by giving the train model speed, it can realize the interaction between the train and the complex environment, and reproduce the characteristics of the train outflow field in the real environment. For simple flatground conditions, the flow characteristics of the dynamic model can be reproduced through data processing based on the outflow field simulation of the static model. For example, Hemida et al. [72] simulated the static train outflow field through LES, observed the flow characteristics near the train through a row of measurement points arranged along the flow direction, and converted them into the flow characteristics obtained by the dynamic train passing by a fixed measurement point. The results show that the static model simulation under the simplified ground condition of free space can be converted to the dynamic model test results. However, for the slightly more complex actual environment, Soper et al. [73] found that static train simulation is difficult to achieve accurate simulation of bottom flow near the rough ground, and the correspondence with the test results is poor. For complex ground conditions, it is often achieved by the method of sliding mesh or moving reference frame in simulation. Paz et al. [74, 75] realize the simulation of the outflow field of high-speed trains under ballasted track conditions with the help of the sliding mesh method. As shown in Fig. 9, the computing domain is decomposed into dynamic and static regions, and the dynamic region moves relatively to the stationary area through the sliding mesh method. Ground structures such as sleepers and ballasts are established in the static region. The flow simulation calculation is realized by the LES method and is basically consistent with the test data. The results show that the presence of ballast track makes the turbulence structures near the ground more intense and smaller than under the flat-ground conditions. Compared with the current simplified flat conditions, the complex, realistic ground conditions will significantly affect the bottom flow of the train. In general, aerodynamic noise prediction methods are divided into static and dynamic methods, and commonly used research methods include wind tunnel tests, field tests and numerical simulation. Among them, field test and dynamic model test can undoubtedly fully reproduce the flow and acoustic characteristics of high-speed

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Fig. 9 The dynamic model simulation method proposed by Paz et al. [74]

trains under natural ground conditions, but their test cost is high, the repeatability is poor, and the sound source characteristics are more complex, which makes it difficult to separate aerodynamic noise. Wind tunnel test has played an essential role in studying the aerodynamic noise of high-speed trains, it has good repeatability and its cost is relatively moderate, but it is difficult to carry out aerodynamic noise research in complex environments. Compared to experiments, simulations are within acceptable accuracy, and flow and acoustic details are easier to obtain at a lower cost. Similar to the experiment, dynamic train simulation is more likely to reproduce the outflow field of high-speed trains in real-world environments, but the computational cost is higher than that of static simulation.

3 Aerodynamic Noise Analysis Methods For both static and dynamic trains, aerodynamic noise is generated mainly from the intense airflow interaction with the train. As often mentioned in aerodynamic noise prediction, bogies, pantographs, inter-coach, etc. are the main sources of aerodynamic noise, and these positions are also locations where the flow separation is more intense and the pressure fluctuation is stronger. With the development of measurement and simulation methods, a large number of flow and acoustic data are acquired. Different researchers conduct investigations based on the data, trying to explore the inherent laws of flow and noise, as well as the relationship between flow and acoustics.

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3.1 Sound Source Term Analysis For flow-induced noise, complex unsteady flow phenomena often produce significant flow noise, and the flow separation of the bogies, pantographs, etc. is violent. The location where the noticeable unsteady fluctuation is often identified as the primary noise source. Therefore, many researchers often analyze the turbulent near-field characteristics through flow analysis to determine the source of aerodynamic noise. In order to pay attention to the distribution and intensity of aerodynamic noise, we often pay attention to the statistics related to unsteady flow, such as turbulent kinetic energy, vorticity, pressure fluctuation, etc., and the vortex structure identified by the vortex identification method such as the Q criterion is also a flow characteristic of common concern. Kim et al. [76, 77] studied the flow and aerodynamic noise characteristics of different pantograph cabin structures through simulation. The turbulence kinetic energy, surface fluctuation pressure and the distribution of Q-criterion isosurfaces under different geometries are compared, and found that the unsteady flow at the edge of the pantograph cabin had a significant impact on the far-field sound. Weakening the unsteady flow energy could help to control the aerodynamic noise. Zhang et al. [78] investigated the aerodynamic noise of the pantograph under crosswind conditions through the simulations. The asymmetric eddy structure under crosswind conditions is the main source of aerodynamic noise difference by comparing the distribution of vortex structure. It is also clarified that the change of unsteady vortex structure and the change of aerodynamic noise have a certain relationship. Wang et al. [79] also used a similar method to compare the aerodynamic noise characteristics of different bogie cavity structures. As shown in Fig. 10, they found that achieving far-field noise reduction often corresponds to reducing the turbulent fluctuation pressure of the roof plate of the bogie cabin at the same time, which also indicates the general relationship between the two. When Li et al. [80] optimized the design of the pantograph components, they also found that compared with the circular cylinder, the far-field aerodynamic noise of the twisted cylinder is 1.5 dB smaller with less aerodynamic pulsation and smaller wake unsteady pressure energy. In the studies of high-speed trains, the generation of aerodynamic noise is often accompanied by strong pulsations brought by unsteady flow, which is often characterized by turbulent pressure, aerodynamic force, turbulent kinetic energy vorticity, etc. In addition, in engineering applications, when the train interacts with the airflow, it often produces both aerodynamic noise and vibration noise, which are affected by the unsteady flow. Especially, vibration noise usually occurs in locations with significant pressure fluctuation. Therefore, flow statistics receive widespread attention in the engineering analysis of aerodynamic noise. Unsteady flow statistics often do not directly represent the intensity of aerodynamic noise sources, although their application is common. The relationship between the two is mainly based on experience and comparative analysis. In order to establish the connection between acoustic properties and flow, some scholars try to analyze the characteristics of aerodynamic sound sources through flow characteristics from the perspective of sound source analysis. Such studies are often based on the theory

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Fig. 10 The distributions of turbulent pressure level and acoustic pressure level of the bogie regions [43]

of acoustic analogy calculation methods such as the Lighthill equation and the FWH equation. As described in Sect. 2, the acoustic analogy calculation methods often organize the N-S equation into a combination of propagation terms and sound source terms, where the sound source term is directly related to the flow. Cabana et al. [81] decomposed the original Lighthill formula into multiple sub-terms and carried out the direct numerical simulation of the two-dimensional compressible mixed layer flow. It is found that there is an asymmetric relationship between multiple sub-terms in the Lighthill source term. The analysis believes that the slight asymmetry between the individual sub-terms is the main cause of noise generation. The main sub-terms which generate noise are compressible equivalents of the Lamb vector divergence and TKE Laplacian terms. It was also found that small changes in flow can have a significant effect on noise. Tan et al. [51] analyzed the sound source distribution on the surface of the pantograph of the high-speed train based on the Curle acoustics integral formula [35], it can be found that the acoustic power intensity of the sound source is proportional to the square of the pressure fluctuation on the model surface, and the sound source intensity distribution can be characterized by the fluctuation pressure change rate and its root mean square value, and the sound source distribution is visualized. The correlation between flow and aerodynamic noise was discussed by combining flow analysis and sound source intensity distribution. Further, the nearfield noise distribution and far-field noise contribution of different components at different frequencies and speeds were analyzed through Fourier transform. Zhu et al.

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Fig. 11 Spatial dipole source and quadrupole source distributions near the bogie wheel-set [50]

[50] introduced the sound source terms in the vortex sound theory when analyzing the aerodynamic noise of high-speed train wheels. Taking the divergence of the Lamb vector and the uneven distribution of turbulent kinetic energy as the source terms, the distribution of spatial dipole and quadrupole sound sources are visualized, as shown in Fig. 11. It is found that the locations where the vortex separation and vortex shedding occur were the main noise source, and the intensity of the dipole sound source was greater than that of the quadrupole sound source. Yang et al. [82, 83] also used the divergence of the Lamb vector as a reference value for aerodynamic noise in the analysis of cylinder and airfoil. The relationship between flow and aerodynamic noise sources was analyzed through the value. The FW-H equation is the main calculation method of aerodynamic noise, and the sound source term analysis based on the FW-H equation is also one of the discussed contents. According to the FW-H equation, the main sound source of aerodynamic noise consists of three parts, namely monopole sound source produced by the change in the mass or volume of the fluid itself, dipole sound source produced by the interaction of flow with the surface of the object, and quadrupole sound source dominated by the shear deformation of the fluid. For the aerodynamic noise of high-speed trains, the test found that the change law of aerodynamic noise with speed is approximately in line with the change law of dipole noise, and it is generally believed that dipole noise is the main source of aerodynamic noise [9]. In view of this conclusion, the research of Wang [84], Zhao [41], Li [57] and others also verified from the perspective of numerical simulation that the intensity of dipole sound sources is significantly greater than that of quadrupole sound sources, which is the main source of far-field noise. From the perspective of sound source identification, Wang et al. [84] analyzed the flow components that have the main impact on sound pressure based on the numerical solution of the sound pressure propagation formulas of dipole and quadrupole sound sources. The radiation ability of dipole sound sources is mainly related to the change rate of pressure gradient with time, while the quadrupole sound source is mainly related to the temporal second derivative of vortex velocity. Through the visualization of aerodynamic sound sources, it can be found that dipole sound

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Fig. 12 The distributions of dipole source term based on FW-H equation under different ground conditions [57]

sources mainly appear near structures where airflow directly impacts and separation occurs, while quadrupole sound sources mainly appear near shear flow and shedding vortex near the body. At the same time, combined with the vortex sound equation, the relationship between the spatial flow field and the aerodynamic sound source was analyzed, and it was found that the dipole sound source is mainly concentrated near the train surface, and the quadrupole sound source is mainly distributed in the spatial turbulence, and the violent vorticity change often produces a strong sound source. Based on the numerical solution of the FW-H equation proposed by Brentner et al. [33], Li et al. [57] presented the distribution of the RMS value of dipole sound source intensity, as shown in Fig. 12. It is found that the dipole sound source mainly appears in the bogie and other positions where the flow impaction and the vortex shedding occur. It is worth pointing out that although the relationship between the sound source term and the noise source is in line with intuitive experience and theoretical derivation, it is still difficult to achieve direct verification in the complex aerodynamic noise analysis of high-speed trains. However, in engineering applications, unsteady flow analysis and sound source term analysis based on aero-acoustic calculation methods are often used for aerodynamic noise source distribution and intensity analysis of high-speed trains, which helps to clarify the relationship between flow and acoustics.

3.2 Statistical Analysis Method Different typical vortex structures are generated when the airflow interacts with the train, such as side edge vortex, wake vortex, shear layer flow, and shedding vortex. These flow phenomena interact with each other, creating multiple sources of aerodynamic noise near the complex geometry of the train. Further, each aerodynamic noise source interacts with each other to generate sound pressure and propagate to the far-field. With the development of simulation methods and the improvement of computing capability, a large amount of data is generated, accompanied by the calculation of complex flow structure evolution and acoustic propagation phenomena.

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Statistical analysis methods have played an important role in processing these data, and have played an important role in helping researchers obtain the inherent laws of flow and acoustic phenomena. In the positions where the flow separation is more intense, there are various scales of vortex structure, which also generate the flow of different frequency characteristics mixed. It is often necessary to use time–frequency analysis methods such as Fourier transform to distinguish the distribution and propagation of different flow and acoustic phenomena. Zhong et al. [85] combined the DES method and the APE equation to calculate the near-field noise and flow. Through the Fourier transform and its inverse transform, they found that the turbulent pressure and sound pressure at 1000 Hz showed different propagation modes. The turbulent pressure propagated downstream with the flow, while the sound pressure spread around with the sound source as the center of the sphere. On the basis of time–frequency transformation, signal analysis methods such as power spectral density and coherence analysis are also often used to analyze the relationship between noise and flow. Li et al. [86] carried out experiments and simulation analysis on the pantograph. It is found that there are mainly two peaks in the far-field noise of the pantograph, which occur at 252 and 353 Hz. Based on the coherent analysis method, the correlation between the near-field pressure and the far-field noise is analyzed. As shown in Fig. 13, for the 252 Hz far-field noise, it has a strong correlation with the pressure fluctuation at both ends of the three rods of the pantograph head, and the pressure fluctuation energy of the corresponding position is also high, while the 353 Hz far-field noise mainly corresponds to the middle part of the three bars of the pantograph head. Furthermore, through the phase analysis based on Fourier transformation of the cross-section flow, it is found that the flow of different frequencies is affected by the rod differently. Fan et al. [87] measured the interior noise of high-speed trains and analyzed the main noise sources using the coherent analysis method. The results show that the noise near the windows and the floor has a strong corresponding relationship with its vibration, and the main source of the interior noise is the body floor. Some reduced-order analysis methods are used to analyze the flow and aerodynamic noise to capture typical aerodynamic and acoustic structures of high-speed trains and clarify the evolution mechanism between different flow and acoustic phenomena. Among the reduced-order analysis methods, proper orthogonal decomposition (POD) is often used to obtain the main structure. The POD method was first introduced into flow analysis by Lumley et al. [88] and has been widely used to find relevant structures within the flow since the snapshot POD method [89] was proposed. Based on the principle of singular value decomposition, the POD method provides an algorithm to decompose the flow motion data into a set of orthonormal basis functions, and make it capture as much flow energy as possible. Li et al. [90] decomposed the wake of a high-speed train by the POD method, analyzed the four main modes of the wake of a single-unit and double-unit high-speed train, and found that the flow structure under the two working conditions was similar, but the characteristic frequency was slightly different. Through reconstruction, the main flow structures of the wake flow under the two conditions are obtained, and the turbulent flow with less energy is ignored. On the basis of wind tunnel test, Bell et al. [91, 92]

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Fig. 13 The coherence coefficient and its auto-power spectral density distributions on the pantograph head [86]

conducted a reduced-order analysis of the pressure pulsation on the train surface and the tail flow by the POD method. Figure 14 shows the main pressure fluctuation structure on the train surface. The results show that the train wake is mainly composed of a pair of spanwise shedding vortexes with opposite phases and an arch vortex close to the ground. The reduced-order analysis found that there were different main flow structures in different flow directions of the wake, and the evolution relationship between the main flows was clarified. The main characteristic frequency of the wake flow has a strong correlation with the pressure fluctuation frequency on the surface of the tail vehicle. In addition to the POD method, there are many other modal analysis methods, such as the dynamic mode decomposition (DMD) method, etc. [93], which can also be used in the reduced-order analysis of flow. During the evolution of flow and noise, flow and acoustic phenomena of different scales are generated. To further observe phenomena at specific characteristic frequencies, the spectral proper orthogonal decomposition (SPOD) method was proposed by Towne et al. [94] and used to analyze the main components at different frequencies. The SPOD method combines the Fourier transform with the POD method. Compared with the traditional POD method, the SPOD method decouples the instantaneous

Fig. 14 The first three-order POD modes of pressure on the tail vehicle [91]

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data at different time scales, which is helpful for the understanding of unsteady phenomena. Li et al. [86] analyzed the unsteady velocity of the flow near the pantograph, and performed SPOD decomposition for the wake flow field of the pantograph head, and the results showed that the first-order mode was embodied as an alternating vortex structure flowing through the three bars of the pantograph head, and its main energy appeared at about 353 Hz, accounting for 78% of the total energy. This is also consistent with the main peak frequency of the far-field noise. Combined with the coherent analysis, it can be seen that the flow distribution represented by the firstorder mode obtained by the SPOD method has a strong contribution to the far-field noise at the corresponding frequency. Li et al. [57] decomposed the bottom flow under different ground conditions by POD and SPOD methods. Compared with the POD method, the SPOD method captures more energy in the first-order mode, and obtains the proportion of modal energy at different frequencies. For the first-order mode at the frequency with the most energy, the side vortex is the main flow structure. In addition to the acquisition of the main flow structure, the mutual transformation relationship of the flow field or acoustic field is also often concerned. Kaiser et al. [95] propose the Cluster-based Reduced-Order Model (CROM) method. It is also a reduced-order analysis method, a potential alternative to the POD method, and can be used to further analyze the mutual transformation relationship between typical unsteady phenomena. Wei et al. [96] used the CROM method to analyze the flow structures of the cylindric cylinder and the twisted cylinder. Compared with the POD analysis method, the CROM method is more identifiable in the modal distribution of different sections of the twisted cylinder, and it can be found that the wake vortex mainly sheds behind the cylinder in two flow states. Li et al. also used the CROM method in the analysis of pantograph wakes to identify three flow state transition paths of the wake flow. Östh et al. [97] conducted a simulation analysis on the wake of a high-speed train, and decomposed the unsteady wake flow into two typical periodic flow structures by the CROM method, which corresponded to the overall vortex shedding and the longitudinal vortex fluctuation of the wake, respectively. The drag force of the train was smaller under the flow state of the longitudinal vortex fluctuation, which proved the effectiveness of the CROM method in the analysis of complex flow structures. The reduced-order analysis method can better identify the main flow structure and help to analyze the typical characteristics of aerodynamic noise through the flow characteristics. However, reduced-order analysis methods are rarely used directly in the analysis of aerodynamic noise. Zhao et al. [41] combined the LES, FW-H and APE equations to calculate the flow and acoustic pressure distribution near the pantograph, and analyzed the acoustic pressure propagation law near the pantograph wake by the POD method, and found that the pantograph head was the main sound source, and the sound wave mainly propagated in the height direction and the span direction. The sound propagation characteristics are further analyzed based on the CROM method. As shown in Fig. 15, it can be found that the sound propagation process can be mainly divided into three typical models, and the direction of acoustic propagation is not the same, but it is approximately consistent with the directivity results of far-field

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Fig. 15 The cluster centroids of the sound pressure behind the pantograph acquired by CROM [41]

noise. This also provides a good start for the application of reduced-order analysis in acoustic analysis. Among the statistical analysis methods, the previously mentioned reduced-order analysis methods such as POD, DMD, and CROM can be easily applied to the analysis of other unsteady data to obtain the main evolution forms and relationships. In addition, the applicability of many machine learning methods to flow analysis is being extensively discussed [98]. For the generation and evolution of unsteady flow and aerodynamic noise, the unsteady data is easy to be presented in the form of images, so image recognition and analysis algorithms are also easy to be applied for flow and aerodynamic noise analysis. Research in this area deserves more attention.

4 Aerodynamic Noise Control With the development of aerodynamic noise prediction and analysis methods for high-speed trains, the generation mechanism of aerodynamic noise has been gradually clarified, which also laid a good foundation for aerodynamic noise control methods. There are mainly active control and passive control methods based on different control mechanisms. In addition to high-speed trains, aerodynamic noise control has also received extensive attention in other fields, and some control methods have good reference significance.

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4.1 Passive Control The passive control method mainly changes the flow structure, sound pressure propagation path, surface pressure distribution and so on by changing the installation method, geometry, installing sound-absorbing materials, installing guide fairing etc. Based on the understanding of train aerodynamic noise sources, passive control methods are often arranged near main noise sources such as bogies, pantographs, and inter-coach to suppress the generation of aerodynamic noise. For the passive control method near the bogie, Yang et al. [99] found that the bogie fairings can significantly optimize the aerodynamic performance of the train, resulting in a 12.7% reduction in total resistance. Especially, the leading and trailing bogies play a major role. Huang et al. [100] investigated the aerodynamic noise of the bogie using simulation and pointed out that the aerodynamic noise of the bogie was broadband noise, which mainly concentrated in the frequency bands of 3151250 Hz. Compared with the original bogie aerodynamic noise, the far-field noise of each measurement points after the installation of the bogie fairings decreased significantly. The sound pressure level has finally reduced by 2 dB, and the proportion of the decline is about 12%, after increasing the coverage area of the fairing. Zhu et al. [101] also studied the influence of bogie cabin on the aerodynamic noise of bogie. Compared with the independent bogie, when the bogie cabin is installed, the trailing edge of the bogie cabin is impacted by the airflow, which becomes a new noise source. However, the bogie cabin weakens the aerodynamic peak noise generated by the bogie, changes the directionality of noise propagation, and reduces the far-field noise. Yamazaki et al. [15] also measured the aerodynamic noise near the bogie in the wind tunnel test and found that the larger the shielding area of the bogie fairings, the smaller the far-field aerodynamic noise. The aerodynamic bogie noise reduces approximately 3–5 dB due to the full side covers. Wang et al. [79] changed the flow into the bogie cavity by adding grooves, sawtooth plates at the cowcatcher, and thickening the cowcatcher. The study found that thickening the cowcatcher or installing the airflow baffle could effectively reduce the far-field aerodynamic noise of the bogie. The far-field noise of the optimal case is reduced by 1.4 dB. In the process of generating the aerodynamic noise of the bogie, the bogie fairing mainly protects the bogie from the impact of the side vortex, and at the same time, it also blocks the propagation of the aerodynamic noise. In addition to the impact of the side vortex, for the bogie of the head vehicle with obvious aerodynamic noise, the impact of the flow below the cowcatcher on the bogie is also one of the causes of the aerodynamic noise, and the optimization of the aerodynamic noise of the bogie is also considered from these two aspects. Besides bogies, many aerodynamic noise control methods have also been proposed for other primary sound sources. Yao et al. [102] discussed the installation methods of different pantographs, and found that the far-field noise generated by the pantograph with sunken base had a lower impact on the line than that with flush base, and the difference in sound pressure level between the two was about 4–5 dB. Kim et al. [76] also calculated the far-field noise of different pantograph

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mounting grooves based on passive control methods, compared the flow and farfield noise changes caused by different groove edge treatment methods, and optimized the shape of the pantograph groove’s edge to significantly reduce the noise generated. The optimal cavity configuration gives a 15.2 dB reduction in noise at the side receiver position. Changing the geometry of the pantograph bars can also have a noise control effect [83, 96]. Li et al. [103] applied the grooved bionic surface to the surface of the train body. Through simulation, it was found that the bionic groove structure could change the thickness and separation of the boundary layer, so as to control the aerodynamic noise of the train body surface. For the inter-coach, Huang et al. [104] s simulate the aerodynamic noise of the inter-coach with different size parameters. The far-field sound pressure level generated at the inter-coach increases with its depth and length, and the installation of the windshield can achieve a noise reduction effect. When the full windshield is adopted, the total sound pressure level drops by about 4.3 dB (A). Kurita et al. [105] introduced the application of low-noise pantograph design, pantograph baffles, bogie fairings, sound-absorbing panels, etc. in low-noise design based on the Shinkansen trains running on the line. Figure 16 shows the noise control method applied in the Shinkansen. In addition to the air deflector structure, directly optimizing the modeling, and surface microstructures such as porous materials have also been proved to have the effect of controlling aerodynamic noise. Li et al. [106] carried out a multi-objective optimization design for the geometric shape of the head train. Through parametric modeling and genetic algorithm, as shown in Fig. 17, the key geometric parameters were iteratively optimized. Through the change of geometric parameters, the 5.9% reduction of aerodynamic noise and 7.6% reduction of aerodynamic resistance can

Fig. 16 Noise control methods applied in Shinkansen trains [105]

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Fig. 17 Original parametric model and optimized head shape [106]

Fig. 18 Far-field noise and directivity of cylinders when applying different porous materials [108]

be achieved. Yu et al. [107] also adopted an approximate method and carried out a multi-objective optimization design based on the head train structure to achieve aerodynamic optimization. Zhang et al. [108] studied the flow and noise characteristics of cylinders coated with non-uniform porous coatings through experiments and simulation methods, and clarified that porous material coatings in the separation zone could delay vortex shedding, reducing cylinder resistance and far-field noise. Figure 18 shows the far-field noise and directivity when different porous materials are applied. The porous material on the cylindrical surface has a significant effect on reducing of aerodynamic noise.

4.2 Active Control Active control methods mainly use airflow jets, plasma jets, etc., by absorbing or injecting different forms of energy to achieve active intervention in the flow, thereby affecting aerodynamic noise. Compared with passive control, the active control method was developed later. However, more attention was paid to the control of aerodynamic characteristics, and less work on aerodynamic noise control was carried out. However, the existing work shows that active control has played a very good role in optimizing aerodynamic noise. Mitsumoji et al. [109] installed the plasma actuator

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Fig. 19 Effect of plasma jet on instantaneous spanwise vorticity at the tail of the rod [109]

near the flow separation point of the pantograph head and studied its effect on flow and aerodynamic noise. The study found that the plasma actuator could control the flow field more effectively when installed downstream of the separation point. As shown in Fig. 19, it can weaken the separation of the flow near the pantograph head, reduce the speed pulsation, and still play a good noise reduction effect even at a high incoming flow speed. Huang et al. [110] used the method of active jet to control the aerodynamic noise of the pantograph cavity, and found that at the speed of 350 km/ h, the use of the forward jet can reduce the far-field noise by about 6 dB, and the noise reduction effect is obvious. For the inter-coach of CRH train, the arrangement of an active jet at the front of the outer windshield gap is proposed and evaluated, and when the jet speed is 0.3 times the speed, the average vortex of the gap area and the total fluctuation pressure energy of the measured point at 40 Hz can be significantly reduced, which can effectively reduce the noise in the train [111]. In some studies of the classical flow, active control also shows a good aerodynamic noise control effect. Abbasi et al. [112] studied the aerodynamic and noise impacts of active blowing and suction airflow on the airfoil with rods. It is found that when the blowing and suction flow velocity is half of the incoming flow, the generation of vortexes can be alleviated and suppressed, the far-field noise can be reduced by 70%, and the lift and drag coefficients are optimized. Szoke et al. [113] studied the effect of active airflow jet on the noise in the wind tunnel test, and found that different jet angles and speeds had a significant impact on the downstream noise, and the noise reduction in the middle- and high-frequency bands could reach 15 dB. It is also found that the jet can cause changes in the flow phenomenon, affecting the aerodynamic performance. Since the active control method involves absorbing or injecting different forms of energy into the flow field, it often means that additional energy and noise sources need to be introduced, and the cost of active control of aerodynamic noise is relatively high, so there are not many applications in engineering practice. However, it shows a significant noise reduction ability. Based on the understanding of the flow structure, it is easy to achieve the noise reduction effect that is difficult to achieve by passive control. Further, with the development of analysis and control methods, real-time closed-loop control and multi-parameter optimization are the potential development directions of active control. These methods help achieve aerodynamic noise reduction

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under different working conditions, which is also difficult to achieve with passive control.

5 Conclusion and Outlook The research on the aerodynamic noise of high-speed trains is mainly based on static and dynamic trains. The train is fixed relative to the environment for the static research method, and the airflow passes by the high-speed train. The wind tunnel test is a typical static research method with moderate cost and good repeatability, and aerodynamic noise is the main noise source during the test. However, due to the difficulty in simulating the relative motion between the environment and the train, it is often difficult to reproduce the aerodynamic noise in a complex line environment in a wind tunnel. For the dynamic high-speed train aerodynamic noise research method, the moving train drives the surrounding airflow. Dynamic model tests and field tests are typical dynamic research methods, which can fully reproduce the flow and acoustic properties under the natural railway environment. However, during the dynamic train test, the total noise components are complex, so it is difficult to separate the aerodynamic noise, and the cost is high. Through measurement methods such as microphone arrays, free-field microphones, and pressure sensors, the aerodynamic noise characteristics of the train can be obtained in the test, and the acoustic characteristics of different noise sources can be clarified. The bogies, pantograph, inter-coach, etc. are identified as the main noise sources. The aerodynamic noise simulation has also been widely used to study the aerodynamic noise characteristics of different components of the train. After experimental verification, the accuracy of the simulation calculation method has been well validated. The simulation of aerodynamic noise is generally divided into two parts: flow and acoustics. The far-field and near-field acoustic characteristics of the train can be solved by combining the FW-H equation and the APE equation with the turbulence model. In addition, boundary element method, LBM method, component-based method and vortex sound theory are all applied in the simulation of train aerodynamic noise. The simulation methods based on static models are mostly carried out in a simplified environment based on free space, and the related research is sufficient, and the cost is low. The simulation methods based on dynamic models can often realize the relative motion between the environment and the train through sliding mesh or reference frame. It can realize the simulation of the train in a complex environment, but its application is rarely carried out and the cost is higher. Compared with experiments, it is easier to obtain the details of flow and acoustics characteristics through simulation. From the results of the simulation and test, the regions with severe flow separation, such as bogies and pantographs, etc. are identified as the main noise sources. In the real environment, complex ground conditions affect the near-ground flow and acoustic characteristics. Aerodynamic noise generation is often accompanied by complex unsteady flow phenomena, such as vortex shedding and flow impaction. By observing the relevant

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statistics of unsteady flow, the intensity of unsteady flow can be quantified, and the distribution of aerodynamic noise sources can be further identified. From the perspective of aerodynamic noise calculation method, the sound source term in the aerodynamic noise calculation methods such as the vortex sound equation and the FW-H equation can theoretically characterize the sound source characteristics. The far-field noise of high-speed trains is mainly generated by dipole and quadrupole sound sources, and the intensity of dipole sound sources is much larger than that of quadrupoles. By observing the distribution of noise-related statistics such as the divergence of the lamb vector and the change rate of the pressure gradient with time, the distribution and intensity of the aerodynamic noise sources of high-speed trains can be characterized, which has a good reference significance for the research on the generation of aerodynamic noise. Statistical analysis methods are widely used to analyze unsteady flows and acoustic phenomena, which can effectively capture the main flow structures and sound propagation patterns, and analyze the correlation between flow and noise. Based on the generation and evolution law of flow structure and its influence on aerodynamic noise, it can provide a reference for aerodynamic noise control. In addition to this, the application of machine learning in flow and acoustic analysis is also an area of interest. Aerodynamic noise control mainly includes passive control and active control. By changing the geometric structure, installing an airflow deflector, etc., the flow can be passively changed, and the intensity and propagation characteristics of the aerodynamic noise source can be changed. Adding fairings to the bogie, changing the structure of the cowcatcher, and installing airflow deflectors can reduce the impact of the flow on the bogie and reduce the aerodynamic noise. For other primary sources of aerodynamic noise, such as pantographs, inter-coach, etc., aerodynamic noise control can also be achieved by adding deflectors, changing the installation form and optimizing the geometry of components. Surface microstructures and deflectors based on bionic principles are also potential approaches for aerodynamic noise control of high-speed trains. Compared with passive control, the active control method actively intervenes the energy in the flow, optimizes the aerodynamic noise through energy jets, and plays a significant role in controlling the aerodynamic noise of the pantograph. For passive and active control, aerodynamic noise control is mainly achieved by weakening or destroying the unsteady flow structures that generate noise. Iterative optimization combined with the multi-objective algorithm and closed-loop active control has the potential to improve the effect of aerodynamic noise optimization further. Funding This work was supported by the National Natural Science Foundation of China (No. U1834201). All authors thanks to Wang Yigang, Chen Yu, Zhu Jianyue, for participating in manuscript discussion.

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Predictions, Measurements, Monitoring and Modelling

Prediction Model for Railway Noise Emission in Curves Michael Ostermann

Abstract Based on five measurement campaigns in different sections of the Austrian heavy rail network (radii between 226 and 440 m), a prediction model to estimate railway noise emission in curves is developed. Scopes in model building are practical usefulness and general applicability. After data filtering a total of 29,097 train pass bys are available for further evaluation. To consider different boundary conditions in each section, 190 directly measured or calculated predictors are defined. A feature selection process reduces the predictor quantity to 17. The final model is built with the random forest algorithm and is trained on two long-term measurement campaigns. To estimate general applicability, validation is done on data points of three short-term campaigns with completely different curve radii, climatic conditions and train type distributions. Considering benchmarks on the latter, predictive performance is 4 dB RMSE and 0.57 R2 . Predictions averaged among a longer time span deviate by − 0.5 dB to −1.1 dB in energetic mean and −0.2 dB to 1.4 dB in median from the original values. Keywords Railway noise emission · Curve squeal · Predictive modelling

1 Introduction In the field of tension between track capacity increase and decreasing noise regulation thresholds, huge investments in noise mitigation measures are required to prevent that noise becomes a limiting factor in railway operation. Thus, standardized, accurate and practical models to dimension noise mitigation measures adequately are needed. Despite partly rather detailed standardized calculation models in certain countries, they generally lack to consider railway noise emission in curves sufficiently [1]. This paper deals with an approach of a practice-oriented noise emission model for curved sections. M. Ostermann (B) Department of Permanent Way, Wiener Linien, 1030 Vienna, Austria e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_2

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1.1 Noise Emission in Curves Rolling noise dominates the emission in the range of the most common velocities in railway operation between roughly 30 and 200 kmh−1 [2]. Elevated emissions in curves compared with tangent track have three root causes [3]: (i) multiple contact points between rail and wheel; (ii) increased rail corrugation; (iii) occurrence of curve squeal. While (i) and (ii) lead to increased rolling noise, (iii) states a phenomenon of high frequency noise emission, which is amongst the severest and most annoying noise sources in the whole railway system. The term “curve squeal” is not consistently defined throughout the literature. In the present paper, it is distinguished between “squeal noise”, “flanging noise” and “high frequency (HF) squeal noise”. The first means strongly tonal noise caused by lateral stick–slip oscillations of the wheel on the rail tread [4]. The second describes a shear noise with a more broad-band characteristic and associated with contact between wheel flange and rail gauge face [4]. The third involves a tonal noise with much higher fundamental frequencies and slower behavior in the time domain compared to squeal noise. The excitation mechanism is not entirely clear [5]. The phrase “curve squeal” is used as an umbrella term for all three distinguished types.

2 Measurement Data Measurement data are collected at five different curves in the Austrian heavy rail network between 2013 and 2017. The following subsections provide an overview of the dataset.

2.1 General Setup and Section Overview Measurements are carried out with a mobile acoustic railway monitoring system (called acramos®), which allows automatically triggered pass by measurements. The configuration contains at least one microphone—located in the standardized position according to ISO 3095 [6]—7.5 m from the track axis and 1.2 m above rail level –, three axle counter sensors, a mobile weather station beside the track and a rail temperature sensor. Two axle counter sensors are used to measure axle speeds as well as to identify the train type by axle pattern evaluation. A third one is located on the other track (always two-track lines) to detect parallel train pass bys. Moreover, vertical and lateral track decay rate and rail roughness are monitored at least once during the whole measurement campaign in each section. Table 1 gives an overview of track parameters, traffic share and quantity of data points. All sections have ballast superstructure. While pass bys in C1, C4 and C5 are dominated by commuter traffic,

Prediction Model for Railway Noise Emission in Curves

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C2 and C3 involve 40% (C2) and 55% (C3) freight traffic as well as long-distance passenger trains. Seven common train types are distinguished. Other monitored trains are summarized in one heterogenous category. Further details are provided in [1].

2.2 Building Datasets To reach comparability among data points, pass bys with acceleration or deceleration (> 0.2 ms−2 or > 10 kmh−1 ), with wind speeds over 5 ms−1 , with parallel train passes on the other track and with operation against the standard driving direction are excluded. After data filtering, 29,097 train passes are left for further evaluation. For the distribution among sections refer to Table 1. To take different boundary conditions into account, a set of 190 directly measured or calculated variables (i.e. predictors) are included. A detailed overview of them and their derivation can be found in [1]. The dependent variable is equivalent continuous noise level of a train pass by (i.e. covering the whole pass by noise emission). It is derived from the energetic sum of third-octave band levels between 50 Hz and 10,000 Hz in each time increment (64 ms short-time averaged) and afterwards energetically averaged among the pass by time—cut between buffer and buffer.

3 Predictive Modelling The general scope of the modelling task is to train predictive algorithms using realworld data to estimate equivalent continuous noise level of trains in curves. The whole purpose for the future is to apply the model on sections, where no measurements are available. The behavior of coping with different boundary conditions and complex underlying correlations cannot be accurately achieved by a simple statistical calculation. Thus, predictive algorithms are applied. Categorical predictors are integrated using dummy variables (values 0 and 1) in the quantity of the number of categories minus one. Necessary pre-processing steps depending on the applied algorithm are taken in that order: Filter near-zero variance, filter between predictor correlations, adjust skewness (Yeo-Johnson transformation) and standardization [8]. Since no literature is present for a similar modelling task, the scope of algorithm selection is to cover a wide variety of approaches—linear, non-linear and tree/rulebased ones. In total, twelve regression algorithms are applied.1 1

Applied algorithms were linear regression, partial least squares, elastic net, neural networks, multivariate adaptive regression splines, k-nearest neighbor, basic tree, conditional inference tree, bagged tree, boosted tree, random forest, cubist. For further details refer to [1].

440

310

226

230

C2

C3

C4

C5

49E1

49E1

60E1

54E2

60E1

Rail

90–95

90

150

131

70

Cant/mm

Wood

Wood

Concrete

Concrete

Concrete

Sleeper

60

60

80

90

60

Speed limit/ kmh−1

The altitude is stated as meters above mean sea level (m a. MSL) [7]

256

C1

a

Radius/m

Short name

Table 1 Overview of measurement sections

42.5

41.5

62.8

69.9

39.0

Balanced speed/ kmh−1

173

217

748

376

165

Altitudea /ma. MSL

1

4

55

40

4

Freight/%

99

94

37

59

95

Passenger/%

17,194

1,246

479

864

9,314

Total data points

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For all statistical calculations R version 3.6.3 is used mainly in combination with the caret package (version 6.0–86) [9].

3.1 Feature Selection After the previously mentioned steps of data cleaning and dataset building, the final step before developing predictive models is feature selection. On the one hand, each predictor is plotted against the dependent variable to empirically investigate twodimensional correlations as well as artificial anomalies—e.g. certain track features, which may be misinterpreted by a statistical algorithm. On the other hand, considered regression algorithms, which have embedded feature selection or at least allow to evaluate a predictor importance score, are applied to the datasets. The combined outcome of both examinations leads to the formulation of the final predictor set, which is used for predictive modelling. The scope is to stay practicable with regards to total predictor quantity as well as possibility for derivation. Beside already well-known influences on equivalent continuous noise level—rail roughness, track decay rate, sleeper type, train type and speed –, lateral acceleration (derived by speed, radius and cant) as well as environmental conditions show a distinct impact. The latter is included with predictors for rail temperature, specific humidity, relative rail humidity [10], wet conditions (categorical—wet rail surface likely due to rainfall or dew presence [1]) and icing conditions (categorical—frozen water or hoarfrost on the rail surface likely). To reduce the number of predictors, rail roughness and track decay rates in both directions are included by the first four principal components,2 which catch 95% of variance across all data points. Sleeper type is considered as categorical predictor (wood and concrete). Train type is distinguished in three categories with similar rolling noise level—high, medium and low. Further analyses show that it is beneficial to include the occurrence of each distinguished curve squeal type into the prediction model. They are predicted by three classification models, which are developed in the same way as the stated regression model. For all three models, 8 predictors were used: train type, double unit operation, radial steering index [11], lateral acceleration, relative humidity, rain occurrence, dew presence and frost conditions. For the derivation of the classification models and their predictors be referred to [1].

2

A principal component analysis creates linear combinations of predictors to build an uncorrelated predictor set. For further information be referred to [8].

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Fig. 1 Data splitting approach for model training and validation [1]

3.2 Developing the Prediction Model Beside practical usefulness to estimate railway noise emission in curves more accurate and hence design mitigation measures adequately, the scope is to achieve general applicability. In the first step, models are trained and tested on data points of the two long-term measurement campaigns C1 and C5. Data points are split into trainings set (75%) and test set (25%). The remaining data points from sections C2, C3 and C4 are referred as validation set. The data splitting approach is illustrated in Fig. 1. To improve predictive ability of the model and evaluate the best performing tuning parameters, a resampling technique—five times repeated tenfold cross validation [8]—is also applied. The validation set contains data points with completely different curve radii, climatic conditions and train type distributions. Hence, the achieved predictive performance depicts a value for general applicability on other sections and datasets. The final model is chosen on behalf of the benchmark root mean squared error (RMSE). It is also used in model training to evaluate the best performing tuning parameters for the models.

3.3 Final Model Considering the prediction accuracy of all twelve applied regression algorithms on the validation set, the random forest approach outperforms the other ones significantly. The final model consists of 500 regression trees, which states a compromise between calculation effort and predictive ability in the present task, and each of them contains over 10,000 nodes. The resampling process evaluates a random predictor sample of 5 for each split decision as best performing. Algorithmic details are provided in [12].

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4 Results 4.1 Predictor Importance Despite the black-box behavior of the model, predictor importance can be evaluated by their minimal depth3 in each tree. Figure 2 depicts the minimal depth of each predictor among all 500 trees. In addition, the average value is illustrated as well as dictates the order of the predictors regarding importance. A train type dummy variable (distinguishing between low noise levels and the rest) as well as the first principal component of rail roughness and track decay rates are most important. Curve squeal predictors (Broad, TonalLow and TonalHigh) achieve high ranks, which justifies their inclusion. Environmental predictors achieve the last places, which indicates a low importance compared to the other predictors. Influence of sleeper type shows an interesting behavior. On the one hand, it has the second most inclusion in the terminal node. On the other hand, it is the only parameter, which is not included in over 100 trees at all. Since sleeper type is not thought to be as important as other predictors and hence should not have too much decisive impact, it seems well represented in the model. Altogether, predictor representation in the model complies with correlations identified in the feature selection process (described in Chap. 3.1).

4.2 Achieved Benchmarks and Discussion The final model achieves a performance of 2.5 dB RMSE on the test set and 4.0 dB RMSE on the validation set. R2 -values are 0.85 (test) and 0.57 (validation). While RMSE values are rather high indicating a distinct uncertainty for the prediction of single train pass bys, the R2 -values indicate a good overall correlation between predictions and measurements. Further stated benchmark values are always related to the validation set. A prediction model without environmental predictors worsens the performance minorly (≤ 0.1 dB RMSE). Application of ISO 3095 [6] threshold spectra for rail roughness and track decay rates instead of measuring in the field results in a minor performance loss (≤ 0.2 dB RMSE). However, it has to be pointed out that significant excesses of the threshold spectra in the real track conditions could worsen the accuracy majorly. Exclusion of all 3 curve squeal predictors (refer to Chap. 3.1) has a mediocre impact on prediction accuracy (worsening of > 0.5 dB RMSE). To conclude, skipping inclusion of environmental predictors as well as field measurements for rail roughness and track decay rates—depending on track condition—results in minor performance losses, while inclusion of curve squeal occurrence is recommended. Thus, it’s generally recommended to implement curve squeal occurrence in standardized calculation models for railway noise emission. 3

Minimal depth means the depth of the first appearance of a predictor in a splitting criterion in a tree model. Generally, a low minimal depth indicates a higher importance. [8]

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Fig. 2 Plot of all considered predictors with their minimal depth among all 500 trees in the model and their mean value of minimal depth [1]

Beside statistical benchmarks, deviations in median and energetic mean among the whole measurement period in each section of the validation set is investigated. The following combinations are evaluated and depicted in Table 2: 1. Originally measured equivalent continuous noise level 2. Predicted levels with no curve squeal occurrence (i.e. all three curve squeal predictors are set to zero) 3. Predicted levels using predicted curve squeal 4. Predicted levels using ISO 3095 spectra and predicted curve squeal.

Table 2 Originally measured level in dB and deviations in median and energetic mean among all three sections of the validation set in dB with varying predictor sets Median

Energetic mean

Dataset

1

2

3

4

C2

87.6

C3

88.9

+0.5

+1.2

−1.5

−1.5

−0.2

C4

−2.1

78.4

+0.9

+1.4

0.0

C2

89.4

−1.4

−0.8

−3.1

C3

90.0

−2.1

−1.1

−2.7

C4

83.3

−2.2

−0.5

−1.3

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The discussion of the results is focused on energetic mean, since it is commonly applied in noise calculation models. Among combination approaches, it can be concluded that consideration of no curve squeal occurrence as well as using ISO 3095 spectra lead to underestimations in averaged values in a range of −1.3 and −3.1 dB. The latter is caused by common exceedances of the ISO 3095 spectra regarding mostly rail roughness as well as partly track decay rates in all sections. Consideration of curve squeal occurrence loses importance in C2 and C3—decrease magnitudes between approach 2 and 3 are up to 0.5 dB, while in C4 it is 1.6 dB. Due to higher radii as well as higher freight traffic share, that tendency is reasonable and well covered by the model. Detailed evaluations with time line plots and train type specific predictions show that especially in C2 and C3, very high and very low occurring levels cannot predicted accurately. In C2 and C3, approach 3 leads to underestimations in energetic mean of freight train levels by 3.5 dB (C2) and 3.2 dB (C3), while the most frequent passenger train type is overestimated by 2 dB (C2) and 5.4 dB (C3). Thus, the high overall accuracy of the predictions in C2 and C3 regarding averaged values among the whole measurement period (refer to Table 2) is reached by a balanced underestimation of freight traffic and overestimation of passenger traffic. Moreover, in terms of energetic mean, the underestimation of freight trains leads to generally lower prediction values among the whole measurement period compared to the monitored ones. Predicted levels in C4 show good accordance to the originally measured ones. The reason behind is the similarity of train types and radius to C5, since the section is located on the same line and thus the model is trained with similar data points. Altogether, it has to be pointed out that train type distribution—especially ratio between freight and passenger trains—seems to have a distinct impact on predictive accuracy of averaged values. Assuming the same boundary conditions as in C2 and C3, the model would significantly underestimate the actual levels in case of 100% freight train operation and otherwise, in case of 100% passenger traffic, overestimations would result. Since the bulk of monitored freight coaches are operated with cast-iron block brakes, which is going to be forbidden at least on certain routes in the EU, the underestimation of those may cause more accurate predictions for freight trains consisting only of coaches with disc brakes or composite brake pads. A discussion about general limitations of the model is provided in [1]. All finally applied model objects in R are available online.4 They can be taken and applied to new sections as well as extended by application to new data points with deep learning algorithms to improve their accuracy and general applicability.

4

https://github.com/M-Ostermann/curve-noise-prediction, last accessed 2022/05/16.

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5 Conclusion The innovative approach of investigating and predicting railway noise emission in curves by machine learning methods results in a practical and accurate model for prediction of equivalent continuous noise level of single train pass bys in curves in the standardized measurement point according to ISO 3095 [6]—7.5 m distance from track axis and 1.2 m above rail level. It is based on sound measurements collected at five different curves (radii between 226 and 440 m) between 2013 and 2017 in the Austrian heavy rail network. After data filtering, 29,097 train passes were left for further evaluation. Two long-term measurement campaigns are chosen for model training. The data of the remaining three sections (validation set) are used to test the model performance in completely different boundary conditions (deviating radii, train mix, speeds and environmental conditions). The best predictive performance on the validation set (benchmark RMSE) is achieved by the random forest algorithm. The model reaches benchmarks of 4.0 dB RMSE and 0.57 R2 with inclusion of previously predicted curve squeal occurrence. Averaged values among the whole measurement period of each section of the validation set achieve median deviations in a range from −0.2 dB to 1.4 dB and energetic mean differences in a range from − 0.5 dB to −1.1 dB between predictions and original measurements. Building on the promising results, further validation and improvement of the model on other datasets is recommended. Acknowledgements The measurement data were collected in two research projects (final reports in German C1—C3 [5] and C4/C5 [13])—funded by the Federal Ministry of Climate Action, Environment, Energy, Mobility, Innovation and Technology, by the Austrian Research Promotion Agency and by the Austrian Federal Railways.

References 1. Ostermann M (2021) Noise prediction of trains in curves. Doctoral thesis. TU Wien, Vienna 2. Ostermann N (ed) (2013) Anwenderhandbuch—Systematische Bahnlärmbekämpfung. Eurailpress, Hamburg 3. Stallaert B, Vanhonacker P (2016) Rolling noise and corrugation in curves: modelling and solutions. In: 12th international workshop on railway noise. Terrigal (12–16 Sept 2016) 4. Thompson D (2009) Railway noise and vibration: Mechanisms, modelling and means of control, 1st edn. Elsevier, Oxford 5. BEGEL (2022) https://www2.ffg.at/verkehr/studien.php?%20id=1101&lang=de&browse= programm. Last Accessed 16 May 2022 6. International Organization for Standardization: ISO 3095:2013 (2013) Acoustics—Railway applications—Measurement of noise emitted by Railbound vehicles 7. World Meteorological Organization (1992) International meteorological vocabulary, 2nd edn. WMO, Geneva 8. Kuhn M, Johnson K (2013) Applied predictive modeling, 1st edn. Springer, New York 9. Kuhn M (2008) Building predictive models in R using the caret package. J Stat Softw 28(5):1–26 10. Lujnov JM, Kossikov SI (1963) Paper 3: friction on railway rails. Proc Inst Mech Eng Conf Proc 178(5):16–23

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11. DIN Deutsches Institut für Normung e. V. DIN EN 14363:2019 (2019) Railway applications— Testing and simulation for the acceptance of running characteristics of railway vehicles— Running behaviour and stationary tests 12. Breiman L (2001) Random forests. Mach Learn 45:5–32 13. ESB (2022) https://projekte.ffg.at/projekt/1413863. Last accessed 16 May 2022

Multiple Sensors and Partial Calibration for On-Board Measurement of Rail Acoustic Roughness: Results of Rolling Tests Olivier Chiello, Marie-Agnès Pallas, Adrien Le Bellec, Rita Tufano, Romain Augez, Benjamin Malardier, Emanuel Reynaud, Nicolas Vincent, and Baldrik Faure

Abstract The indirect measurement of roughness using vibro-acoustic sensors on board rolling stock is promising, as shown by recent research on this topic. However, a number of improvements can be made to the existing methods to extend their range of validity. In this paper, the performance of the multi-sensor method developed in the framework of the French research project MEEQUAI is presented. The estimation of the effective roughness is performed for different sensor families using a least squares method in the frequency domain, from the signal spectra in third octave and modelled transfer functions corresponding to the detected track layout. A partial calibration method is also proposed. The calibration gain is relative and allows the variability of the transfers with the track support to be retained, thanks to the models. The method was tested in France with sensors installed on a test train running at several speeds on a track section of a railway test center as well as on two track sections of the national railway network with different supports. Keywords Rolling noise · Rail roughness · On-board measurement · Calibration

O. Chiello (B) · M.-A. Pallas · A. Le Bellec Univ Gustave Eiffel, CEREMA, Univ Lyon, UMRAE, F-69675 Lyon, France e-mail: [email protected] R. Tufano · R. Augez · B. Malardier · E. Reynaud · N. Vincent Vibratec, Railway Business Unit, 28 Chemin du Petit Bois, 69131 Ecully Cedex, France B. Faure SNCF, Innovation and Research, 1/3 Avenue François Mitterrand, 93212 La Plaine St Denis Cedex, France © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_3

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1 Introduction The evolution of models for the prediction of railway noise emitted in the environment implies an increasingly detailed knowledge of the characteristics of the vehicles and the tracks at the origin of the noise. The knowledge of the rail acoustic roughness and its evolution in time on a whole railway network becomes useful nowadays. The indirect measurement of roughness using vibro-acoustic sensors on board rolling stock is promising, as shown by recent research on this topic [1–8]. However, a number of improvements can be made to the existing methods to extend their range of validity. In particular, it is necessary to guarantee a correct accuracy over a wide range of wavelengths, independently of the measurement conditions such as the vehicle speed or the track support. To achieve these objectives, research has been carried out within the framework of the French research project MEEQUAI [5, 7]. Several advances are proposed. On the one hand, the combination of several families of sensors for indirect measurement allows a wider wavelength band to be covered. On the other hand, the use of models for estimating the transfer functions between sensors and roughness allows some parametrisation of the transfer functions, particularly with regard to speed and track support. Finally, a partial calibration principle improves the accuracy of the method while keeping the interest of the modelling. In this paper, the results obtained during rolling on different types of tracks and at several speeds are presented. Prior to this, the characteristics of the proposed method are reviewed. The paper aims to assess the performance of the indirect measurement method, independently of a roughness separation stage. Conclusions are therefore drawn on the basis of comparisons between direct and indirect measurements of wheel/rail combined roughness and not rail roughness.

2 Proposed Approach 2.1 Selected Sensors Based on the models developed in the first phase of the project, three families of vibroacoustic sensors have been selected according to the frequency ranges as described in Table 1. Methods using other type of sensors like non-contact displacement sensors have not been investigated. This selection includes sensors that have already been tested in several studies, such as axle-box accelerometers [2] and under-bogie microphones [1], but also sensors that were considered in other works but not tested during rolling, such as microphones close to the rails [4]. The results of the models and various tests carried out prior to this final validation led to the exclusion of microphones close to the wheels (see for instance refs. [3, 4]). Indeed, a lack of robustness was observed, related to the fact that the wheel-on-rail resonances are very pronounced and that

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Table 1 Description of sensors selected for the indirect measurement Sensors

Axle-box accelerometers

Under-bogie microphones

Microphones close to the rail

Number

2

4

2

Location

On each axle side, close Carefully distributed in On each axle side, above to the wheel the cavity the rail

Frequency range 125 − 1600 Hz

250 − 5000 Hz

400 − 2000 Hz

their frequency and damping are very sensitive to parameters that are not easy to estimate or even variable during the measurement, such as the lateral position of the wheel/rail contact point. The frequency ranges selected for each family of sensors also come from preliminary studies showing high risks of uncertainty outside these ranges. For example, above 1600 Hz, the transfer functions corresponding to axlebox accelerometers fall sharply, while below 400 Hz the sound pressure close to the rails is strongly disturbed by aerodynamic noise.

2.2 Estimation of Transfer Functions Models have been developed to determine, for a representative selection of tracks, the transfer functions between the effective combined wheel/rail roughness in the frequency domain and the on-board sensors selected for indirect measurement. The selected tracks include various types of support characterized by rail-pad dynamic properties (soft, medium or stiff) and sleeper type (concrete monobloc, concrete bibloc, wooden). A single vehicle type is considered corresponding to the “Corail” vehicle of SNCF-AEF (Railway Test Agency) used for the rolling tests. A detailed description of the models used is not intended here, but the following points should be noted: • For axle-box and track vibrations below 2000 Hz, a receptance coupling method is used, based on “rolling noise” contact models [10] and results provided by finite element models of tracks and wheelset. The wheel/rail contacts on both sides of the wheelset are considered via two degrees of freedom (vertical and lateral). • For sound pressure close to the rails below 2000 Hz, an exterior sound radiation model is used, based on acoustic finite elements for the free-field combined with perfectly matched layers for the far-field. It includes reflections on the platform through impedance boundary conditions. • For sound pressure radiated under the bogie up to 5000 Hz, the proposed method combines the TWINS software [10] for the calculation of sound radiated powers, with a semi-analytical propagation model based on elementary sources (monopoles, dipoles) taking into account the extended character of the track radiation.

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Fig. 1 Transfer functions used for axle-box accelerometers (same side, third-octave bands)

Finally, a database of transfer functions has been built from the models and initial calibration on a standstill vehicle [7]. Figure 1 shows the results obtained in the case of axle-box accelerometers. It highlights the influence of the track support.

2.3 Inversion Method The indirect measurement method is based on a pre-processing of the signals coming from the different sensors on a given length of track, including the detection of possible short defects, the spectral analysis, the suppression of the contribution of the wheel roughness (see refs. [6, 9]), as well as the identification of the track support. These steps are not detailed in this paper although they are important from a practical point of view. For this paper, the contribution of the wheel roughness is kept in the signals since the validation is performed in terms of combined roughness. The inversion method itself assumes linearity between the combined effective roughness of the two rails and the signals from the sensors. For a set of N sensors, the linear relationship between the signals z i from the sensors grouped in a vector {z} and the combined effective roughness of right and left rails r R and r L , can be written as: {z} = {C R }r R + {C L }r L

(1)

where vectors {C R } and {C L } contain the track-specific transfer functions between the sensors and the combined effective roughness of left and right rails. The spectral

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analysis   of the signals from the sensors leads to the estimation of a spectral matrix Szz of dimension N × N . Considering a probabilistic context and assuming a decorrelation between the combined effective roughness of both rails, Eq. (1) leads to: 

     Szz = C R C R∗ Sr R r R + C L C L∗ Sr L r L

(2)

where Sr R r R and Sr L r L stand respectively for the roughness spectra of the right and left rails. In terms of auto-spectra, Eq. (2) may be written as: ◦

◦

{diag(Szz )} = |{C R }| 2 Sr R r R + |{C L }| 2 Sr L r L

(3)

where the components of vector {diag(Szz )} are the measured auto-spectra whereas ◦ ◦ the vectors |{C R }| 2 and |{C R }| 2 contain the moduli of the squared transfer functions between the sensors and the combined effective roughness of both rails. Assuming the same roughness on both rails, the estimation of the combined effective roughness is thus performed for each sensor family using a least squares method in the frequency domain, from the measured signal spectra in third octave bands and transfer functions:      ◦ ◦  Sˆrr = argmin Srr diag Szz,mes − |{C R }| 2 + |{C L }| 2 Srr 

(4)

Using transfer functions in third octave bands and estimating only an average roughness for both rails increases the robustness of the method. The post-processing of the effective roughness includes the conversion of the spectra into the wavelength domain using the rolling speed V and the correction by the DPRS contact filter H (λ) [10]: V S˜rr (λ) = H −1 (λ) Sˆrr ( f ) with λ = f

(5)

2.4 Calibration Method An additional partial calibration method is also proposed. It consists in adjusting the transfer functions using calibration gains αi2 defined for each sensor by rolling on a reference track with known roughness spectra: αi2 =

Szi zi ,mes |C Ri | Sr R r R ,mes + |C Li |2 Sr L r L ,mes 2

(6)

In this equation, roughness spectra Sr R r R ,mes and Sr L r L ,mes must be obtained by using a direct measurement method whereas the transfer functions C Ri and C Li

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correspond to the reference track. The calibration should preferably be performed using the spectra obtained after removing the contribution of wheel roughness. In case this pre-processing is not possible, calibration would have to be carried out using the combined wheel/rail roughness spectra which also implies a prior measurement of the wheel roughness spectra. Whatever the track, the relation between uncalibrated and calibrated transfer functions is then given by: |C Ri |2cal = αi2 |C Ri |2 and |C Li |2cal = αi2 |C Li |2

(7)

It is important to note that the gain is relative and track-independent which allows the variability of the transfers with the track support to be retained for later measurements, thanks to the models. The calibration factors are also independent on speed. The speed effect is only taken into account in the post-processing step (see Eq. 5).

3 Results 3.1 Rolling Tests at Railway Test Centre (CEF2) The method was first tested in France with sensors installed on one wheelset of the “Corail” test vehicle running at several speeds on a 400 m track section of the Tronville-en-Barrois railway test center (CEF2). A trainset consisting of five wagons was used for rolling tests. Prior to the rolling indirect measurement, direct measurements of the wheel roughness (for the instrumented axle) and the rail roughness were carried out. On the track section, no significant short defects were identified, which was a necessary condition for the validation of the method. The track support consists of bi-bloc concrete sleepers. Measurements of the receptance and the track decay rate (with hammer and during pass-by) were used to identify the average stiffness of the rail-pads. The stiffness obtained is between the medium and stiff values used in the track selection. A first test of the indirect method was carried out at 80 km/h using the initial transfer functions determined for a medium bi-bloc track for the three families of sensors. The results are compared with the direct measurements in terms of wheel/ rail combined roughness (i.e., without suppression of the wheel contribution) in Fig. 2. The maximum deviations obtained are close to 5 dB per third of an octave, with the exception of those corresponding to the under-coach microphones at large wavelengths which are more pronounced. The partial calibration at speed 80 km/ h at CEF2 was then tested, considering that the rail-pad stiffness was between soft and medium. With this calibration, the maximum differences between the direct and indirect measurements obtained at other speeds on the same section are around 3 dB per third of an octave, as shown in Fig. 3, whereas the roughness estimation obviously becomes perfect at 80 km/h.

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Fig. 2 Comparison of direct and indirect measurements without partial calibration (CEF2)

Fig. 3 Comparison of direct and indirect measurements with partial calibration (CEF2)

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Fig. 4 Comparison of direct and indirect measurements with partial calibration (RFN)

3.2 Rolling Tests on French Railway Network (RFN) The method was then tested on the French national network (RFN). Indirect and direct roughness measurements were compared on several track sections of the network. The results are given in Fig. 4 for two particular sections, travelled at 80 km/h: • Pierrelatte: the track support is made of bibloc concrete sleepers with rail-pads of medium stiffness (softer than those identified at CEF2). • Mâlain: the track support is made of wooden sleepers. It must also be emphasized that the roughness measured on these sections are much lower than those measured at CEF2. The results given in Fig. 4 are obtained with the partial calibration performed at CEF2 for a speed of 80 km/h. Compared with the perfect estimation with calibration at 80 km/h on CEF2 (calibration speed and track), they are impacted by the variation of the actual track support. However, the proposed hybrid method (a relative calibration gain allowing the variability of the transfers with the track support) induces a contained degradation of the results except for those obtained from the microphones close to the rail during the passage on the section characterized by wooden sleepers.

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4 Conclusion In this paper, a multi-sensor method is proposed for the indirect on-board estimation of the rail acoustic roughness. The combination of several families of sensors allows a wider wavelength band to be covered, whereas the use of models for estimating the transfer functions between sensors and roughness allows some parametrisation of the transfer functions, particularly with regard to speed and track support. The principle of partial calibration finally combines the accuracy of the experimental calibration and the parameterization allowed by the models. The performance of the method is tested through measurements while driving on different track sections, at several speeds, showing encouraging results with maximum errors mostly around +/− 3 dB per octave. Although still higher than the uncertainties of direct measurements, the errors become acceptable considering the global rolling noise levels calculated from the estimated roughness. It remains to work mainly on the realism of the vibroacoustic track models to further improve the accuracy. A prototype of an industrial system using the method developed in the MEEQUAI project is currently being tested on an SNCF vehicle travelling on some parts of the French railway network and recording data along the way. For the moment, it is planned that the system will be linked to an operator’s database allowing the identification of the track type from the GPS location. However, a method aiming at identifying the track type using the sensors is currently under study, which would make it possible to dispense with the link to the database.

References 1. Asmussen B, Onnich H, Strube R, Greven LM, Schröder S, Jäger K, Degen KG (2006) Status and perspectives of the “specially monitored track.” J Sound Vib 293:1070–1077 2. Bongini E, Grassie SL, Saxon MJ (2012) Noise mapping’ of a railway network: validation and use of a system based on measurement of Axlebox vibration. In: Maeda T et al (eds) Noise and vibration mitigation for rail transportation systems. Notes on numerical fluid mechanics and multidisciplinary design, vol 118 Springer, Tokyo, pp 505–513 3. Kuijpers AHWM, Schwanen W, Bongini E (2012) Indirect rail roughness measurement: the ARRoW system within the LECAV project. In: Maeda T et al (eds) Noise and vibration mitigation for rail transportation systems. Notes on numerical fluid mechanics and multidisciplinary design, vol 118. Springer, Tokyo, pp 563–570 4. Chartrain PE (2013) Lecture acoustique de la voie ferre´e, Ph.D. thesis, Aix-Marseille, France 5. Tufano AR et al (2021) Numerical and experimental analysis of transfer functions for onboard indirect measurements of rail acoustic roughness. In: Degrande G et al (eds) Noise and vibration mitigation for rail transportation systems. Notes On Numerical Fluid Mechanics And Multidisciplinary Design, vol 150. Springer, Cham, pp 295–302 6. Carrigan TD, Talbot JP (2021) Extracting information from axle-box acceleration: on the derivation of rail roughness spectra in the presence of wheel roughness. In: Degrande G et al (eds) Noise and vibration mitigation for rail transportation systems. Notes on numerical fluid mechanics and multidisciplinary design, vol 150. Springer, Cham, pp 286–294 7. Tufano AR et al (2020) Calibration of transfer functions on a standstill vehicle for on-board indirect measurements of rail acoustic roughness. Proc. 9th Forum Acusticum, Lyon, France

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8. Pieringer A, Kropp W (2022) Model-based estimation of rail roughness from axle box acceleration. Appl Acoust 193:108760 9. Pallas M-A, Tufano AR, Chiello O (2020) Separation of rail and wheel roughness from on-board vibroacoustic measurements. Proc. 9th Forum Acusticum, Lyon, France 10. Thompson DJ (2009) Railway Noise and vibration: mechanisms, modelling and means of control. Elsevier

Development of Methods for Virtual Exterior Noise Validation Rita Caminal Barderi, Romain Rumpler, Antoine Curien, Aurélien Cloix, Martin Rissmann, Ainara Guiral Garcia, Iñigo Eugui Larrea, and Joan Sapena

Abstract Simulating the exterior noise levels created by the train equipment requires a good representation of the equipment integration, the noise propagation, the ground reflection and, for some cases, the diffraction in the different train surfaces. In the framework of the European project Shift2Rail program S2R-CFM-CCA-01-2019 Energy and Noise and Vibration, the state-of-the-art of the exterior noise of rolling stock vehicle simulation is being compared between railway manufacturers and operators and the advanced techniques proposed by the consortium Open Call project

R. C. Barderi (B) · J. Sapena ALSTOM, 48 Rue Albert Dhalenne, 93400 Saint-Ouen, France e-mail: [email protected] J. Sapena e-mail: [email protected] R. Rumpler · A. Curien KTH Royal Institute of Technology, Engineering Mechanics, The Marcus Wallenberg Laboratory for Sound and Vibration Research, Teknikringen 8, SE-100 44 Stockholm, Sweden e-mail: [email protected] A. Curien e-mail: [email protected] A. Cloix · M. Rissmann Vibratec, 28 Chemin du Petit Bois, CS 80210, 69130 Ecully Cedex, France e-mail: [email protected] M. Rissmann e-mail: [email protected] A. G. Garcia · I. E. Larrea CAF, J.M. Iturrioz, 26, 20200 Beasain, Spain e-mail: [email protected] I. E. Larrea e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_4

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S2R-OC-CCA-01-2019 (TRANSIT https://transit-prj.eu). With respect to previous work done in the same direction (ACOUTRAIN https://cordis.europa.eu/project/id/ 284877/reporting/es, SILENCE http://www.silence-ip.org, FINE-1 https://projects. shift2rail.org/s2r_ipcc_n.aspx?p=FINE%201), the focus of the work is on the train integration effects of equipment in a rolling stock. Keywords Virtual certification · Exterior noise simulation · Acceptance criterion

1 Introduction The work presented in this paper is done in the context of the virtual validation for certain railway noise performances that are good enough reproduced by simulation. The simulation validation is done following these steps: 1. Measurement of train equipment stand alone in test bench in terms of sound power level (SWL) and directivity 2. Measurement of the train equipment installed on the train and isolated from the other noise sources in terms of sound pressure level (SPL) around the train 3. Simulation of the equipment installed on the train using the measured SWL and directivity of first step in terms of sound pressure level (SPL) around the train 4. Comparison between the simulated and measured SPL around the train and assessment of the difference according to an objective criterion. The comparison allows the determination of the accuracy of these simulations in view of their use for virtual validation and certification of rolling-stock products. The methodologies implemented are evaluated by comparing the results against measurements; and by defining an objective criterion of acceptance. The main difficulty is to compare situations where all the noise contributors are known and “controlled”. For this reason, both simulations and measurements are done isolating one single train equipment from the rest of the sources. The additional added value with respect to previous work is: • Big effort was done to measure the source stand alone in the same conditions than installed on the train • Different techniques other than classical analytical source models are proposed by VIBRATEC and KTH, and compared with the measurements. The focus of this paper is on one of the sources measured and simulated during the work of FINE-2 WP6 [5]: one auxiliary converter1 mounted on the train underframe. This equipment was chosen since it emits both electrical and cooling noise, which makes it an interesting and challenging case to reproduce by simulation, particularly from the perspective of the frequency components to be properly captured. 1

Equipment used in rolling-stock products to prepare the electrical signal in terms of voltage (V), current (A) and phase to the train auxiliary equipment working at medium voltage (i.e. Heating, Ventilation and Air Conditioning Unit) and low voltage (i.e. batteries).

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Fig. 1 Auxiliary converter located on the train underframe

Table 1 Auxiliary converter operating conditions during the two measurement campaigns in terms of load and switching frequencies Measurement campaign

Medium Low voltage Frequency Frequency Frequency voltage power (kW) buck three-phase transformer (Hz) power (kW) converter (Hz) inductor (Hz)

Measurements 45.5 stand alone

14.6

900

2550

3750

Measurements 2.0 on the train

15.0

900

2250

3750

2 Measurement Methodology The auxiliary converter was measured stand-alone between 50 and 10 kHz and installed on the train. The equipment installation on the train underframe can be seen in Fig. 1. One key point, to compare the equipment radiation stand alone and installed on the train, is to control and measure the electrical power and switching frequency of each electrical component, which modify the acoustical emission of the transformer and inductors inside a cubicle of an auxiliary converter, see Table 1. These parameters were chosen to be as close as possible in both measurements campaigns—stand alone and with the equipment integrated on the train. However, the three-phase inductor switching frequency, slightly higher in the measurement stand-alone, and the medium voltage power2 were not exactly the same.3

2.1 SWL Measurement The SWL measurement of the equipment was done in terms of sound intensity according to ISO 9614-2 [6]. The scanning was done in two configurations: reflecting

2

Power here is defined as the product of the voltage (V) by the current (I). It was not possible to increase the load more than 2 kW on the train without switching on the HVAC and with only two vehicles presents from the whole train.

3

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P6 L

P5 L

P4 L

P3 L

P2 L

P1 L

3.0 m

7.5 m Auxiliary converter

P6 R

P5 R

P4 R

P3 R

Fig. 2 Measured positions with the equipment installed on the train. The position in front of the equipment is P3. Each position is measured at 1.2 m and 3.5 m from the top of the rail

floor and considering the radiation of the four lateral surfaces; and absorbing floor and considering also the bottom surface.

2.2 Measurements Installed on the Train The measurement of the equipment installed on the train was done in terms of sound pressure level at twenty different positions (see Fig. 2): ten positions at 7.5 m from the track center and at a height of 1.2 m (indicated with label “a”); and ten at height of 3.5 m (indicated with label “b”). Six positions were measured on the left of the train (indicated with the letter “L”); and four positions on the right (indicated with “R”). The narrow band content was compared between the measurements stand alone and with the equipment installed on the train (see Fig. 3). The conclusions of this comparison are: • Fan frequency corresponds to a single peak which can be clearly seen at 425 Hz, in both measurement campaigns • Buck switching frequency corresponds to a single peak at 1800 Hz (2f) in both measurement campaigns • Three-phase inductor switching frequency was slightly different in both measurement campaigns by approximately 300 Hz, see Table 1. Therefore, the energy is divided between the third octave of 2000 and 2500 Hz for the measurements at train level; and concentrated at 2500 Hz in the measurements stand alone. • Transformer frequency at 3750 and 7500 Hz are visible at component level. At train level, only the 2f at 7500 Hz is visible. The reason remains unknown at the moment of writing this article.

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Fig. 3 Comparison in narrow band between the measurements stand-alone (red line) and installed on the train (blue line)

3 Simulation Methodology The measured values are subsequently compared with the simulation results obtained with a range of difference approaches: • SITARE: analytical tool from ALSTOM. It uses analytical equations in third octave bands for standstill, acceleration and pass-by, and ray tracing for cavity bogie calculation [7–10]. The input sound power level is distributed in the different equipment surfaces and the different ground absorptions (ballast and grass) are also considered. Train geometry, including underframe, is considered in the calculation for the noise diffraction. • Finite element modelling (FEM): COMSOL FE model together with a KTH inhouse implementation, including perfectly-matched layers for the non-reflecting boundaries, allowing for fast frequency sweep techniques in narrow bands [11]. The input sound power level is represented by a monopole for each face; and the opposite monopole is deactivated to reproduce the sound pressure level.4 • TraiNoiS: in-house tool for exterior noise, part of the CAF Virtual Noise Suite. Analytical predictions for exterior noise at standstill and pass-by in third octave bands or narrow band. Noise sources are defined by the sound power level as point sources or box sources, where each face is an individual source. Ground reflections are considered. Train geometry, including underframe, is considered in the calculation for the noise diffraction. • SONOR: commercially available software from VIBRATEC based on a lightsound analogy and the Boundary Energy Element Method (BEEM). It is particularly adapted for medium to high frequencies and complex geometries [12, 13]. The input sound power is distributed on the elements at pro-rata of their surface and radiates diffusely in all directions, according to their view factors to the other 4

For example, when simulating the left side of the train, the monopole on the right is deactivated.

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Fig. 4 Delta global comparison is shown at 1.2 m on the left; and 3.5 m on the right. The figure represents the delta using SITARE (red line), TraiNoiS (green line), SONOR (pink line) and FEM (blue line) for the points at 7.5 m from the track center and 1.2 m from the rail head. The acceptance criterion is plotted in red at + 2 dB and −2 dB with respect the measured values

faces (solid angle between boundary element faces in the model). The model uses frequency dependent absorption for the ballast, the solid faces of the rolling stock and the grass. The equipment SWL measured in four surfaces according to ISO 9614-2 [6] was used for all the simulations excepting for SONOR, where the SWL was defined including the bottom surface -see Sect. 2.1 for more details.

4 Assessment of the Results The defined acceptance criterion used to compare the measurements and the simulation in microphone positions at 7.5 m from the track center is: • The overall difference shall be lower than 2 dB (see Fig. 4). The value of 2 dB is chosen because is the order of magnitude of the exterior noise measurement uncertainty according to ISO 3095 [14] • For the main contributing frequencies,5 magnitude of differences shall be equal or lower than 4 dB, see Fig. 5 Simulated levels within these ranges are considered to be acceptable. The global noise value between the simulated and measured value was calculated for all the positions in terms of delta, defined per point i:

5

Delta globali = LpAeq,T[simulated],i − LpAeq,T[measured],i

(1)

Delta f r equencyi = LpAeq,T,freq[simulated],i − LpAeq,T,freq[measured],i

(2)

Main contributing frequencies are defined as the third octave bands with sound pressure level that lies between the overall global noise measured and 6 dB below.

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Fig. 5 Delta frequency comparison using SITARE (green line), TraiNoiS (red line), SONOR (pink line) and FEM (blue line) for the third octave bands contributing to the global noise in the different positions. The acceptance criterion is plotted in red at + 4 dB and −4 dB with respect the measured values. The positions indicated with “a” are at 1.2 m from the top of the rail and “b” indicates at 3.5 m

The assessment of the results is synthetized in Tables 2 and 3; and Figs. 4 and 5. The main relevant conclusions are: • Results obtained with SITARE and FEM tools reproduce with enough accuracy the global noise level along the different positions at 7.5 m from the track center and at 1.2 and 3.5 m with respect to the top of the rail Table 2 Delta global, see Eq. (1), results for each simulation tool at 7.5 m from the track center and heights of 1.2 m and 3.5 m Delta ≤ 2 dB criterion

SITARE

TraiNoiS

SONOR

FEM

Height of 1.2 m

OK

NOK in P2 L and P6 R

NOK in P6 L

OK

Height of 3.5 m

OK

OK

NOK in P2 L and P6 L

OK

Table 3 Delta frequency, see Eq. (2), results for each simulation tool for the different positions Delta ≤ 4 dB SITARE criterion Points at contributing frequency

TraiNoiS

SONOR

FEM

NOK at 2500 Hz NOK at 2500 Hz NOK at 2500 Hz in NOK at in P2 L a, P4 L b in P2 L a, P6 L a/ P2 L a, P4 L b, P6 L 2500 Hz in P6 and P6 L a/b b and P5 R a a/b and P5 R a L a/b and P5 R a

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• Results obtained with TraiNoiS and SONOR tools reproduce with enough accuracy all the positions in terms of global noise except from positions P2 and P6 -where the noise is underestimated slightly with regard to the acceptance criteria. • The frequency content criterion was fulfilled at 400 Hz (frequency related to the auxiliary converter fan), but not at 2500 Hz (frequency related to the three-phase inductor). The third octave band of 2500 Hz is generally underestimated by all the tools. The reason for this difference is attributed to the shifted frequency during the stand alone measurement campaign which concentrates all the energy in the same third octave band.

5 Conclusions The conclusions of the simulation assessment are: • The current classical models used by manufacturers which consider the equipment directivity (more complex than a monopole directivity) are good enough to reproduce the global noise level around the train as requested by the ISO 3095 [14] and TSI Noise [15]. For the given example of the auxiliary converter, the more advanced models (FEM or SONOR) are at similar level as the classical models. • Further improvement shall be done to improve the accuracy of the frequency content emitted by the electrical components of the train equipment in terms of representability on the test bench. This point is essential for the virtual validation since the measured laboratory sound power is used as input for the models. • As a follow-up, the comparisons between the different tools and approaches should be extended to other noise sources and other locations, e.g. roof-mounted. Acknowledgements The FINE-2 project, with this paper and the described work, is linked, has received funding from the Shift2Rail Joint Undertaking under the European Union’s Horizon 2020 research and innovation program under Grant Agreement No 881791, there we authors are grateful.

References 1. 2. 3. 4. 5. 6.

TRANSIT Homepage. https://transit-prj.eu ACOUTRAIN. https://cordis.europa.eu/project/id/284877/reporting/es SILENCE Homepage. http://www.silence-ip.org FINE-1. https://projects.shift2rail.org/s2r_ipcc_n.aspx?p=FINE%201 FINE-2. https://projects.shift2rail.org/s2r_ipcc_n.aspx?p=fine-2 ISO 9614-2:1996 Acoustics -Determination of sound power levels of noise sources using sound intensity, Part 2: Meausrement by scanning 7. Bistagnino A., Squicciarini G, Orrenius U, Bongini E, Sapena J, Thompson D (2015) Acoustical source modelling for rolling stock vehicles: the Modeller’s point of view. EURONOISE 2015 8. Gambard N, Sapena J, Planeau V (2009) A methodology for exterior noise prediction of railways rolling stock. Proc Euronoise 740–746

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9. Castellana A, Caminal Barderi R, Sapena J (2022) Validation of interior and exterior noise predictions for a regional train. 16eme Congres Français d’Acoustique 10. FINE-1 Virtual certification of acoustic performance for freight and passenger trains, Deliverable D4.5 Report with correlation/validation of the results with reference data including future improvements 11. Vermeil de Conchard A, Mao H, Rumpler R (2019) A perfectly matched layer formulation adapted for fast frequency sweeps of exterior acoustics finite element models. J Comput Phys 398:108878. https://doi.org/10.1016/j.jcp.2019.108878 12. Thivant M et al (2018) Pass-by noise simulation and optimization of powertrain acoustic shielding package. SIA Le Mans 17–18 Oct 2018 13. Betgen B et al (2011) Boundary element energy method for the acoustic prediction of vehicle external and interior noise—Validation on a mockup and industrial application. DAGA, Düsseldorf, Allemagne, Mar 2011 14. ISO 3095:2013 Acoustics—Railway applications—Measurement of noise emitted by railbound vehicles 15. Technical specification for interoperability (TSI) relating to the subsystem ‘rolling stock noise 2014

Use of Heterogeneous Microphone Triplets for Simplified Noise Apportionment in Pass-By Measurements Jaume Solé, Pierre Huguenet, and Mercedes Gutierrez Ferrandiz

Abstract Localization of different noise sources in a high-speed train has been endeavored in the past with reasonable success. In most cases, this localization has been achieved by means of microphone arrays and also with the help of fixed or removable barriers. However, these techniques had the drawback of needing complex post-processing and frequently have complicated set-ups. Also, very often the assessment obtained with these methods has been predominantly qualitative, and not quantitative. High speed railways have the distinctive feature (with respect to conventional railways) of emitting significant amounts of aerodynamic noise. Aerodynamical noise levels emitted by different high-speed units depend on a number of design details which can significantly change emission values. High speed railway lines are increasingly spreading in modern countries where, simultaneously, environmental concerns about noise levels are also on the rise. Therefore, a practical methodology for assessing and comparing aerodynamic noise levels coming from high speed units has been declared as desirable both by international railway organizations such as UIC and national railway network managers. This article presents a quite simplified methodology capable of achieving a quantitative apportionment of noise coming from different directions in a high-speed railway pass-by. Keywords Railway noise prediction · Pantograph · Rolling noise

J. Solé (B) · P. Huguenet Noise and Vibration Technical Office, SENER Ingeniería y Sistemas, C/. Creu Casas I Sicart 86-88, Cerdanyola del Valles, 08290 Barcelona, Spain e-mail: [email protected] M. G. Ferrandiz UIC International Union of Railways, Head of Asset Management, Infrastructure and Interfaces with Rolling Stock, 16 rue Jean Rey, 75015 Paris, France © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_5

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1 Introduction Acoustic diagnostic of rolling stock, with approximate localization of the different noise sources, has been attempted in the past with reasonable success [1–3]. Unfortunately, this has been so far achieved by using complex setups (e.g. microphone arrays) needing elaborate post-processing methods such as beamforming algorithms. Due to their complexity and related resources (hardware and cost), it is unrealistic to incorporate such techniques in any pass-by measurement methodology intended for widespread use. This work suggests a possible simplified setup with three sensors and a quite simple post process, which despite its simplicity is able to assess quantitatively noise coming from different train parts, in a reasonably approximate way. In particular, the suggested methodology is based on the use of supercardioid shotgun microphones, which are not commonly used in acoustic measurements for railways but have been successfully used in other acoustic disciplines such as broadcasting, fauna noise recording, etc.

2 Methodology The methodology used is based on the following steps: • Use of two identical supercardioid shotgun microphones pointing to different reference directions, established according to directions where significant sources are expected. • A bisector plane B dividing the space in two halves is defined by two vectors: one  going from the observation point where horizontal and another transversal BC, the triplet is installed to a point in the train body where no dominant sources are expected, as shown in Fig. 1.  crosses a point in the • Orientation of shotguns must be also adjusted so that BC supercardioid directivity pattern where attenuation is higher than 6 dB. • Both supercardioid microphones are complemented with a calibrated omnidirectional microphone (M omn ) providing absolute global values of acoustic pressure. • Approximate apportionment of noise energy captured by M omn is done according to Eqs. (1) and (2) below (or their derivates (3) and (4)). These equations apply an energetical proportionality to the absolute global values reported by the omnidirectional calibrated microphone M omn . • Small differences between both theoretically identical supercardioid shotgun microphones are accounted in a previous spectral calibration process. These concepts can be mathematically formulated as follows: 2 2 2 L p,high y L p,omnid + 10 · log(S Hhigh /(S Hhigh + k · S Hlow ))

(1)

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Fig. 1 Left, superposition of polar cardioid diagrams for a given band in the triplet setup, with  Right, preliminary spectral calibration of the shotgun microphones against the bisector vector BC previously calibrated omnidirectional microphone placed in the center of the setup

2 2 2 L p,low y L p,omnid + 10 · log(k · S Hlow /(S Hhigh + k · S Hlow ))

(2)

where Lp,omnid is the logarithmic pressure level measured by the omnidirectional (class-A) calibrated microphone in the triplet, SH high and SH low are respectively the voltages coming from the identical shotgun microphones pointing high and low. Parameter k is a correction factor to be applied to lower shotgun square voltage output, and is obtained during a preliminary calibration process of the shotguns involved in the setup. This calibration factor accounts for small differences between these shotguns. It can be easily obtained by placing horizontally the three microphones in the triplet, with both shotgun microphones aligned in parallel and pointing to a reference noise source, as shown in Fig. 1, right. Horizontal placement of the triplet during calibration in semi-anechoic (open field) conditions is necessary in order to account for ground reflections, which would otherwise introduce a difference of lectures in both shotguns. Open field (almost semi-anechoic) conditions during this calibration are assumed. Reference source is an omnidirectional loudspeaker emitting pink noise, placed in the same horizontal plane of the triplet and at a sufficient distance to assume acoustic waves are already planar when reaching the triplet. In the above described conditions, two perfectly identical shotgun microphones should theoretically deliver exactly the same RMS voltage. In practice, some minor output voltage differences will appear between both shotguns. Correction factor k is thus the ratio between both square voltage outputs (ideally, for 2 perfectly identical shotguns, factor k should be equal to 1). Calibration factor k is frequency dependent and shall be obtained for each band, and similarly Eqs. (1) and (2) shall be applied spectrally for each band of interest. Equations (1) and (2) can be reformulated to be expressed as a factor of the signal power ratio R of both microphones: 2 2 R = (S Hhigh / S Hlow )

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Thus, obtaining the following expressions: L p,high y L p,omnid + 10 · log(R/(R + k))

(3)

L p,low y L p,omnid + 10 · log(k/(R + k))

(4)

Since the directivity pattern of shotgun microphones changes with frequency, angle between them should be adjusted for each octave band under analysis. Therefore, a complete frequential apportionment of pass-by noise can be obtained either by pass-by repetition with the triplet successively adjusted in angle, or alternatively by installing several triplets with different angles, previously adjusted.

3 Results Performance of triplets has been tested experimentally in a section of the MadridBarcelona high speed line where units typically circulate at 300 km/h (see Fig. 2). Both shotgun microphones responded well during the test and were not saturated by wind blows induced at pass by. Low frequency transient wind blows were sensed by the three micros in the triplet, but were comparatively more evident in the shotguns than in the omnidirectional microphone. However, a high pass filter with cutoff frequency at 200 Hz managed to clean the signal in the shotguns, while still keeping most part of the relevant audible bandwidth (200–20,000 Hz). Reference position (center) for the triplet was placed at a distance of 6 m from the track axis and at a height of 4 m above rail head. In that position, different angles between the shotguns and the horizonal plane were tested. Shotgun microphone pointing high at 20º–30º from the horizontal nicely reproduced what was observed

Fig. 2 Left, close view of a heterogeneous microphone triplet (2 supercardioids + 1 omnidirectional). Right, test of the setup in the Madrid-Barcelona high speed line with Siemens Velaro units running at 300 km/h

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Fig. 3 Scheme of the BOYA BY-PVM3000M directional shotgun microphone used in the highspeed pass-by tests (from the shotgun microphone manual, BOYA Shenzhen Jiayz Photo Industrial, Ltd.)

in the microphone placed above pantograph in las Inviernas test setup (see reference [4]). Figure 7 shows a graphical comparison between the results of high-level aerodynamic noise achieved with triplets and results of the same concept obtained with the catenary portal setup described in [4]. In both cases, the typical peaks associated to inter-coach gaps and the differentiated peaks with the extended and folded pantographs can be clearly observed, but with a much lower logistical complexity in the test based on triplets. Directional shotgun microphones used in the triplet test are of the model BOYA BY-PVM3000M (Fig. 3). This microphone has a supercardioid directional pattern, with a typical pick-up angle about 40–50° (see Fig. 4) in the most relevant bands. As can be observed in Fig. 5, frequency response of model BY-PVM3000M is not flat; but being both shotguns identical, signal ratio R among them is still valid if carried out band by band. Results obtained have shown a good discrimination among directions, allowing for a quantitative apportionment of noise coming from different directions in a railway pass-by. This quantitative apportionment has been obtained in a quite simplified way, which is considered as potentially acceptable in the future for generalized use during noise assessment of rolling stock units. Future more elaborated setups based on the use of several microphone triplets installed at different heights can be envisaged, allowing for more detailed quantitative diagnostics of noise emissions coming from different parts of the train.

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Fig. 4 Polar directivity diagrams of the used shotgun microphones for different frequency bands (from the shotgun microphone manual, BOYA Shenzhen Jiayz Photo Industrial, Ltd.)

Fig. 5 Spectral frequency response of directional shotgun model BY-PVM3000M used in the tests (from the shotgun microphone manual, BOYA Shenzhen Jiayz Photo Industrial, Ltd.)

4 Conclusions and Further Work A simple methodology for quantitative railway noise apportionment has been proposed and tested, with positive results. Apportionment obtained is reasonably approximated, but it is considered that more advanced setups based on triplet combinations can be envisaged in order to enhance accuracy. As previously explained, each triplet allows to approximately split noise in two halves according to incidence directions, but some contamination between these two halves happen, particularly if noise comes from the direction splitting these two halves. It is for this reason that triplets should point to a train area in which no dominant noise sources are expected. As an example, Fig. 8 shows two setup variants in which three different triplets are oriented to a middle height in the train, where no dominant noise emissions are

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MIC_1

Fig. 6 Scheme and view of the setup for comparison, based on near microphones installed in a catenary portal (ADIF high speed network, Las Inviernas, Spain), as described in reference [4]

Pantograph recess Pantograph (raised)

Fig. 7 Qualitative comparison of the signature obtained from the triplet shotgun pointing to higher parts in the train (left) and (right) the signature observed in the upper left microphone (above pantograph, MIC_1) in the reference setup using a catenary portal, as described in reference [4] and shown in Fig. 6. Values in the left figure are direct voltages coming from the shotgun, not acoustic pressure values as shown in the image at the right

expected. Each of the three triplets allow to split levels between high-level noise and low-level noise, but results come reported in three points placed at a different height in the catenary. A geometric correction can be used to derive source power from source pressure in these three positions. This can be repeated for each triplet, which would yield three different source power estimates that can be averaged in order to lower uncertainty. The need for some orientation readjustments and pass-by repetitions is a comparative drawback in this method. But it must be noted that a repetition needs not strictly to

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Fig. 8 Two possible setup variants based on several triplets, allowing to lower uncertainty in the apportionment

be carried out for each frequency band; just for band groups for which shotgun directivity changes very significantly. (many close bands have similar directivity patterns). Investigation on that will be added to further work. It is considered that despite repetitions, savings are important in instrumentation, setup and post processing costs, compared to typical microphone arrays implementing beamforming algorithms. It must also be noted that manual adjustment of shotgun orientations can be time consuming, or even not be allowed during commercial operation of the infrastructure, for safety reasons. Improvements based on installation of microphones on servo motors are envisaged as future work in order to overcome this problem. These setups are neither difficult not particularly expensive (servos for that purpose do not need high torque neither fast operation speed) and offer an easy and accurate remote re-orientation of shotguns in the triplet. Acknowledgements We acknowledge the Spanish railway network administrator ADIF and the international railways association UIC (particularly, the workgroup composing the Aeronoise research project) for their active support and collaboration.

References 1. Noh H, Choi S, Hong S, Kim S (2014) Investigation of noise sources in high-speed trains. J Rail Rapid Transit 228(3):307–322 2. Gautier P, Poisson F, Letourneaux F (2008) High speed trains external noise: a review of measurements and source models for the TGV case up to 360km/h. In: 8th world congress on railway research, Seoul

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3. He B, Xiao X, Zhou Q, Li Z, Jin X (2014) Investigation into external noise of a high-speed train at different speeds. J Zhejiang Univ (Appl Phys Eng) 15(12):1019–1033 4. Sica G, Solé J, Huguenet P (2019) Pass-by noise assessment of high-speed units by means of acoustic measurements in a perimeter close to the train. IWRN13

Fast and Reliable Noise Predictions for Rolling Stock by Means of Pre-calculated Reference Models Andrea Bistagnino, Maxime Ripert, Clement Dalmagne, and Joan Sapena

Abstract The prediction of the passby noise of trains, in the definition of ISO 3095, can be simplified by looking at how each source contributes to the global level. With some hypotheses, it is possible to write in a very simple way how the passby level of any train configuration depends on the passby level of each source type. This article describes an analytical method to extend known passby noise levels to any train configuration. Its application to numerical simulations is described in depth and compared to existing simulation and experimental results; application to specific measurement setups is only described. Even assuming the access to high computational resources, when using advanced, complex modelling and tools for noise predictions the bottleneck is often the availability of the user/acoustician. This paper presents a framework to pre-calculate passby noise levels with advanced modelling for specific trains, to later extrapolate them exactly to any other configuration of vehicles and sources. Keywords Passby noise · Noise prediction · Numerical methods

1 Introduction One of the typical dilemmas of engineering, recurrently appearing in all Rolling Stock design, is: should I use a simplified model (with higher uncertainties but faster to set up) or a complex model (slower but more precise)? It holds true for most acoustic studies. One way to obtain quickly results with few compromises is to use pre-calculated results. Advanced modelling based on correlations of existing trains can be used to pre-calculate a set of reference cases that can then be expanded by means of A. Bistagnino (B) · M. Ripert Alstom France, 48 Rue Albert Dhalenne, 93482 Saint-Ouen, France e-mail: [email protected] C. Dalmagne · J. Sapena Alstom Spain, Ctra. B-140 Santa Perpetua a Mollet, 08130 Santa Perpetua de Mogodà, Spain © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_6

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theoretical analyses. This approach is presented in this paper. Considerations on the definition of passby noise allows us to show how it is possible to extrapolate correctly levels to trains that have a different architecture. Also, the role of sources placed on the extremities of vehicles is calculated and taken into account for in this modelling. Thanks to this, we can use any method to construct a complex model for passby noise prediction and extrapolate to any train configuration exactly. This paper shows how this was achieved and implemented for exterior passby noise at constant speed, in the interpretation of ISO 3095 [1].

2 Methodology When predicting passby noise of vehicles, it is very common to model the vehicle as a collection of elementary sources with given power and directivity. Sources are typically considered uncorrelated and their contribution to the passby level can be simulated independently. For a train, we can consider separately all wheel/rail contacts, the traction drives, aerodynamic sources and other equipment that may be functioning. The pressure level in a given position during the train passby will be the sum of the pressure level contributions from each source. When following ISO 3095, passby noise is evaluated as the equivalent level over the passby time, measured at 7.5 m from the track centerline. We can write the equation for the passby level, taking into account source decomposition, as:

L p,eq,T p

1 = 10 log Tp

{Tp 0

p(t)2 1 dt = 10 log Tp p02

{Tp ∑ 0

i

pi (t)2 dt p02

(1)

It derives from Eq. (1) that we can write the passby level of a train as the sum of the passbys of the single sources. One of the advantages of decomposing the train into single sources is that now sources are small with respect to the train. For specific cases, we can even write analytically the solution. The case of the monopole is treated in Sect. 2.1. Anyway, in all practical cases, the directivity of the sources and their relative size versus the train is such that the passby of the full train and that of two point-like sources is roughly depicted in Fig. 1. Whenever we consider sources away from the extremities, the contribution of the tails of the time signature will be very low and we can say that the integral of the source contribution between 0 and Tp can be replaced by its integral between − ∞ and + ∞. This is generally not true for sources at the train’s extremities—this case is treated in Sect. 2.1. Now we can replace this in Eq. (1) and do the integral over space instead of time (replacing passby time Tp with L/V, where L is the train’s length and V its speed). We obtain that (still neglecting sources close to the train’s ends):

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Fig. 1 Hypothetical passby of a train and of two compact sources within it. Dotted lines show the beginning and the end of the train. The filled area is the passby level of a single source; when one is close to the train’s end, its contribution is truncated at the train’s extremity

L p Aeq,T p

{∞ {∞ pi (t)2 pi (x)2 V ∑ 1∑ = 10 log dt = 10 log dx 2 L i L i p0 p02 −∞

(2)

−∞

Having replaced the limits of the integral, now its value for all sources having the same directivity and strength is strictly identical. It means that, as long as we know the value of the equivalent passby level of a source, we can straightforwardly calculate its contribution to a train passby of whatever speed and length, and containing an arbitrary number of such sources. Notice that LpAeq,Tp does not explicitly depend on the train’s speed, except for the level of its sources; the relationship between sound power level and train speed is usually known. Notice also that reflections do not appear explicitly in this equation but are implicitly considered as we are looking at the pressure contribution at the reception point, after taking into account all effects like ground reflections. The last step consists in writing the average pressure contribution pi (t)2 as the sum of the sound power level of the source i plus a transfer function that takes into account for all other effects: ground reflection, screening of the train’s sides, {∞ 2 distance, height, etc. We may thus write 10 log −∞ pip(t)2 d x = Wi + T Fi where Wi 0 is the sound power level of source i and TFi is the transfer function that converts the sound power level to the pressure contribution. It is worth noticing that the transfer functions TFi can be calculated for any microphone position and environment; they could for example be calculated at a given distance, not necessarily 7.5 m as in ISO3095, and in presence of a noise barrier. Whatever tool is used to evaluate TFi , the methodology presented in this paper will let the acoustician extrapolate easily to a different train configuration. The discussion of the application of this result to practical cases will be done in Sect. 4.

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2.1 Sources at the Train’s Extremities As observed, for sources close to the train’s end, Eq. (2) does not hold. For a source placed exactly on the train’s nose, for example, the integral would have to be evaluated between T0 and + ∞, thus half its contribution for sources axed perpendicularly to the tracks and symmetrical. The correction to be applied for such sources in general depends on their directivity; it is interesting to look at the specific case of the monopole. Consider a monopole of constant power W and disregard reflections on the ground; sound pressure in the reception point at a distance d is: p(t) =

W 4π d 2 (t)

(3)

Passing from time coordinates to spatial coordinates by means of the train’s speed, we can easily solve the integral for the passby contribution of a single source at the position x0 within a train of length L:

L p,eq,T p

1 W2 = 10 log T p 4π p02

L−x { 0

−x0

1 dx x2 + y 2 + z 2

[ ( )] L−x0 1 W2 1 x √ = 10 log atan √ T p 4π p02 y 2 + z 2 y2 + z2

(4)

−x0

Here x, y and z are the coordinates of the source in the reference system of the reception point, x0 is the position of the source in the reference system of the train and L is the train’s length. As customary, square brackets are used to mean the evaluation of the definite integral between the two values specified next to right one. With Eq. (4) we can easily compute the difference between the equivalent passby contribution of sources far away from the extremities and sources near the extremities; this can be interpreted as the correction factor Cext that we have to apply to extremity sources if we want to use the passby contribution of “regular” sources say in the √ middle of the train. Denoting with D = y 2 + z 2 the distance from the source and the microphone:

Cext = L peq − L peq,ext

[ ( )] L atan Dx −2 L 2 = 10 log [ ( x )] L−x0 atan D −x0

(5)

For L = 200 m, y = 7.5 m and z = 1.2 m the correction factor for monopolar sources is shown in Fig. 2. It goes to zero rather quickly when moving away from the train’s nose; also consider that sources with stronger directivity in y (as dipoles aligned transversally to the track) will have correction factors that decrease even more quickly.

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Fig. 2 Correction factor for monopolar sources at the train’s extremities, as per Eq. (5)

Globally, we are now able to reconstruct analytically passby levels of any train configuration based on the knowledge of the passby levels of each source type present on the train and their position, by writing: L p Aeq,T p = −10 log L + 10 log

∑

10

Wi +T Fi −Cext,i 10

(6)

i

In Eq. (6) we use the correction factor of monopole sources, which should be sufficiently correct (given typical measurement uncertainties) when sources on the train’s extremities do not possess very strong directivity.

3 Validation The methodology presented in Sect. 2 is based on the knowledge of the pressure contributions pi (t)2 ; the easiest way to obtain them is by calculation. In this study we used SITARE, Alstom’s internal tool for the prediction of exterior noise [2], but any other tool could be used in a very similar way; see for example [3] for existing alternatives. In Fig. 3 we compare results of this methodology with results of SITARE and direct passby measurements obtained during the validation of a 5-car rolling stock compound; we observe a very good agreement of both approaches to measured data. On the global level, SITARE is only 0.5 dB away from the measured overall LpAeqTp level; the new approach here presented is 0.12 dB different from what was obtained with SITARE. The new approach is based on the calculation of

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Fig. 3 Passby spectrum LpAeqTp in 1/3 octave bands for a train: comparison of measurements, a full calculation and an application of the methodology presented in this paper

the passby levels of a single bogie, including traction equipment, extrapolated to the real 5-car configuration. We can push the validation a bit further by comparing results obtained with a full-fledged prediction tool (SITARE in this case) in several different architectures to results obtained with the methodology presented in this paper, solely based on the results obtained with SITARE for single sources. This has been done for 18 fictitious trainsets constituted by a mix of motorized and trailers cars, dubbed respectively “M” and “T”. For all 18 configurations, a full calculation with SITARE has been done. The same passby level was calculated with the methodology presented in this paper. The result is shown in Fig. 4. The gap between the two approaches is on average 0.1 dB. A single case shows a gap of 0.3 dB, in one of the smallest configuration (MM). This small error may be due to the time discretization error that occurs when calculating very short trains. Globally, the approach is shown to compare extremely well to full-fledged simulations. The use of source types described in this paper may seem akin to other approaches used in the context of environmental noise studies, such as CNOSSOS-EU [4], but the approach and application are different. CNOSSOS-EU aims at reducing noise sources to their sound power level, to create fictitious line sources that replicate the total average noise emissions on a specific rail line. The method proposed in this paper concentrates on the ability to predict a single passby event and model it in a way that makes analytical extrapolations due to the number of sources and train length easier.

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Fig. 4 Difference in dB between the passby level calculated with SITARE and with the methodology proposed in this paper, for 18 different train configurations. The gap is rounded to the nearest decimal

4 Application The methodology presented in Sect. 2 can be used in different ways. It is not interesting to use it to develop a prediction tool for train passby noise: several pieces are missing (ground effects, directivity of sources, etc.). It is much more useful to think of it as a simple way to extrapolate correctly results obtained with very advanced and complex models. Imagine an acoustician has a powerful yet complicated tool to predict noise emissions of a train. Especially in the preliminary phases of a project, it is very common to evaluate the performances of several different train architectures. In this context the acoustician may not have the time to evaluate all configurations in the greatest detail and may be forced to use simplified models to be able to complete the study in time. Using the approach described here, we can see that it is enough to characterize once the main sources to be able to evaluate analytically the impact of a large number of parameters. Once this is done, it is even possible to build a library of sources to treat any train configuration, while retaining the precision of the advanced calculations done to characterize the sources. This possibility is based on the access to advanced and precise tools for the prediction of passby noise; state-of-the-art of such calculations are shown for example in [5]. This can be useful in several ways: • To streamline the calculation of train architectures, minimizing the risk of user mistakes while retaining the accuracy of the baseline model, possibly correlated to a measurement. • To extend the applicability of the “simplified evaluation” discussed in the Guide for the application of the NOI TSI [6].

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• To greatly simplify the introduction of passby noise parameters in machine learning, optimization algorithms or similar methods that may have a hard time with complex software but can easily manage spreadsheet calculations. A special application could be the use of measured contributions, for example for coaches (they have the advantage of having a single source to be considered, rolling noise). This approach has not been tested and is for the moment only a proposal. Let us imagine the case of the validation of the passby noise of a wagon type. Today ISO 3095 proposes an approach that has the advantage of being measurable, but that doesn’t take into account some effects, like for example the influence of nearby coaches to the LpAeq,Tp value measured. The standard itself requires vehicles adjacent to the one under test to be “acoustically neutral”, but acoustically neutral is defined as vehicles increasing LpAeq,Tp by not more than 2 dB when considered in the passby time, which can hardly be defined as neutral. ISO 3095 has the merit to provide a clear and measurable way of assessing passby noise, but the drawback of assessing a quantity that is not well defined: the measured level is not in fact the level of a single coach nor of that particular consist. The methodology described in this paper could be applied in this case to deduce from the measured equivalent passby level what is the correct passby level of a single wagon (carefully including the contribution of the hauling locomotive). Then, it could again be used to extrapolate to any combination of such wagons. Even better, different wagon types could be tested and the methodology here presented could calculate the passby level of any combination of wagons.

5 Conclusions The methodology presented in this work is based on the purely analytical rework of the equations defining passby noise as per ISO 3095. Coupled with the possibilities offered by numerical simulations, it offers a scheme to extend analytically the result of arbitrarily complicated passby noise calculations to any train configuration. Its use based only on measurements has been proposed but not tested on the field. This work offers a rational and simple view of the contribution to passby noise levels not of single sources, but of source types. As trains are usually the sum of few different source types, it allows a very clear understanding on how the placement of sources on a train will influence its passby noise. It also offers an exact calculation of the correction factor to be applied for sources close to the train’s extremities, at least for monopolar ones. By clarifying the simple part of the equivalent passby noise level calculation, railway acoustician will have more time to dedicate to the more complicated evaluation of the generation and propagation of single source types.

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References 1. International Organization for Standardization (2013) ISO 3095:2013 acoustics—railway applications—measurement of noise emitted by railbound vehicles 2. Gambard N, Sapena J, Planeau V (2009) A methodology for exterior noise prediction of railways rolling stock. Proc Euronoise: 740–746 3. Furio N, Starnberg M, Bongini E, Thompson D, Orrenius U, Cuny N (2016) ACOUTRAIN: virtual certification of acoustic performance for freight and passenger trains. Energy Environ 1:491–500 4. Joint Research Centre, Institute for Health and Consumer Protection, Anfosso-Lédée F, Paviotti M, Kephalopoulos S (2012) Common noise assessment methods in Europe (CNOSSOS-EU): to be used by the EU member states for strategic noise mapping following adoption as specified in the Environmental Noise Directive 2002/49/EC, Publications Office, 2012. https://data.europa. eu/doi/10.2788/32029 5. Castellana A, Caminal Barderi R, Sapena J (2022) Validation of interior and exterior noise predictions for a regional train. Presented in “16ème Congrès Français d’Acoustique”, 11–15 Apr 2022, under publication 6. European Union Agency for Railways (2019) Guide for the application of the NOI TSI GUI/ NOI TSI/2019. www.era.europe.eu

Requirements and Challenges for Vibration Prediction Tools and the Associated Validation Processes Sascha Hermann, Dorothée Stiebel, Nils Mahlert, and Rüdiger Garburg

Abstract One of the aims of the European research project FINE-2 is to contribute to reducing noise and vibrations caused by railway traffic. In this context, FINE-2 supports the development of a prediction tool for vibration caused by rail traffic. The tool is developed by the partner project SILVARSTAR. For this purpose, in the “Ground Vibration” work package (WP 8) of FINE-2, which is led by DB Systemtechnik GmbH, requirements and descriptors for a European vibration tool were specified. The general approach for a prediction tool is based on a decoupled modular calculation model which could be useable for both rough estimations and detailed analysis of train-induced vibrations next to the track and inside buildings. Moreover, a validation concept developed by FINE-2 for evaluation of the prediction tool has been developed. The paper shows a two-step procedure to validate the computational core and the final prediction tool. The validation of the computational core will be mainly based on measured data. Here, a comparison between measured results and the computed data of the prediction tool will be performed. The tool itself is evaluated against the specified requirements and the computation of the descriptors is checked according to the standards. Keywords Prediction of vibration · Validation concept · Requirements for prediction tool

1 Introduction Traffic-induced annoyance of inhabitants is not only caused by acoustics but also by vibration. In Germany, problems mainly arise when train traffic increases, or railway lines are newly built or upgraded. As people’s awareness of vibrations is growing, S. Hermann (B) · D. Stiebel · N. Mahlert DB Systemtechnik GmbH, Völckerstraße 5, 80939 Munich, Germany e-mail: [email protected] R. Garburg Deutsche Bahn AG, Europaplatz 1, 10557 Berlin, Germany © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_7

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there is a need to investigate the effects of vibrations in early planning phases of projects. In contrast to noise assessment, there are no regulations for the estimation of traininduced vibrations which are European-wide accepted by all national government authorities. Today, only few prediction tools exist and none of them are widespread accepted for the simulation of train-induced vibrations in Europe. Because only few requirements for the implementation of a vibration prediction do exist, measurement regulations such as DIN 4150 [1] or VDI 3837 [2] are frequently used for vibration predictions. To establish a European-wide accepted prediction tool for train-induced vibrations, uniform and generally applicable requirements were defined in the first stage of the Shift2Rail project FINE-2 (work package 8). Moreover, proposals for the input data as well as for models which can be used were given. Based on these requirements, a vibration tool is being developed by the partner project SILVARSTAR [3]. The developed tool will then be validated by the FINE-2 partners based on existing measurements and measurements performed during the projects.

2 Requirements and Descriptors for a Prediction Tool In the FINE-2 project, one of the main tasks was to define the descriptors used for the vibration evaluation and the requirements for the prediction tool developed within the SILVARSTAR project. The requirements were defined in cooperation with participants from European infrastructure operators and vehicle manufacturers. The proposed requirements for a prediction tool and provided models could give tool developers an orientation for the design of the prediction models. This helps to promote innovations while keeping the quality of the tools. The elaborations in Deliverable 8.1 of FINE-2 [4] are therefore also to be understood as a guideline for the design of vibration tools. In general, the prediction tool should be useable for both rough estimations and detailed analysis of train-induced vibrations next to the track and inside buildings. Rough estimates are used to estimate whether critical vibration impacts may exist in an area and to what extent they may occur. Then, these critical areas can be investigated in detail. The frequency-based prediction tool should be based on measurements as well as empirical and hybrid models.

2.1 Descriptors Used for the Assessment of Annoyance Up to now, no European-wide legal consensus on which descriptors or criteria are used to describe the effects of vibrations on humans in buildings do exist. For example, the EU project RIVAS [5] provides an overview of 11 standards or national regulations for the evaluation of ground vibrations. Because it is not feasible to

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compute such descriptors on basis of so many different standards or national regulations, a reduction was needed. Therefore, the partners of the FINE-2 project agreed on the following three descriptors which will be used in the final prediction tool for the evaluation of vibration at the receiver position. • MTVV (maximum transient vibration value)/VDV (forth power vibration dose value) according to ISO 2631-1:1997/ISO 2631-2:2003 [6, 7] • KBFmax /KBFTr according to DIN 4150-2:1999 [1] • LvSmax according to ISO/TS 14837-31:2017 [8].

2.2 General Approach The general approach for a prediction tool will be based on a decoupled modular computation model as described e.g. in VDI 3837 [2]: L v ( f ) = L S ( f ) + L P ( f ) + L R ( f )

(1)

where L v ( f ) is the vibration spectra at the receiver position, L S ( f ) are the sourcerelated vibration emissions, ΔL P ( f ) is the transfer function through the ground and ΔL R ( f ) describes the transfer from the ground at a receiver in front of the building to the receiver inside a building, i.e., it comprises ground and building characteristics. For the input spectra, measured data or input data from numerical calculations should be used. Calculations of the prediction tool shall be made in the frequency range between 1 Hz ≤ f ≤ 315 Hz in one-third octave bands.

2.3 Function of the Tool Based on the requirements from the FINE-2 project, the prediction is divided into different phases with increasing accuracy of the prediction. It starts with a basic evaluation in which the planned construction and operational plans or changes are compiled. In the next step, the so-called impact corridor (area next to the track where an annoyance of inhabitants due to train-induced vibrations cannot be excluded) is estimated. Here, a classification of the buildings according to the use is carried out. Furthermore, the operational data (for each train category, the type, the numbers per day and night period and the speed) are compiled. Therefore, an important requirement for the prediction tool is that there is a database of relevant input parameters. For example, general ground and building transfer functions, emission spectra of trains and reference track parameters should be available in the tool. The database should be able to be updated by the user. The prediction tool should offer the possibility of a rough estimation for the calculation of an impact corridor where an annoyance of the inhabitants cannot be excluded and where the corresponding limit or reference values will be probably

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exceeded. In the next step, a detailed investigation is required for the buildings inside the impact corridor. Therefore, an interface to import geographical information system (GIS-based data) such as house coordinates and an altitude model is needed. In this phase of the investigation, existing measurement data and the prediction parameters from the data base of the tool are used as an input of the transfer functions. In many cases, the exact prediction based on measurements cannot be made for all buildings possibly affected. In this case, measurements and predictions are performed only in representative buildings, from which an overall statement on the required examination area can be derived. Once the critical buildings have been identified, it may be necessary to consider possible vibration mitigation measures and recommend a preferred option. It could also be decisive that the vibrations may only increase by a certain factor compared to the initial state. Especially in Germany, it is often necessary to compare two different situations (e.g. situation with and without changes planned in the infrastructure or the train operation forecast). An illustration how the calculation results for a specific configuration could be realized is shown in Fig. 1. Here, the blue rectangular elements represent buildings, the blue lines are tracks, red lines describe the impact corridor and the green and red dots inside the elements in the impact corridor correspond to noncritical and critical changes of vibration levels inside specific buildings. An ordered list of the calculated vibration values at the receiver positions shall be exported to a separate file together with the limit values for the configuration to be evaluated.

Fig. 1 Illustration of the two-phase evaluation process. First, an impact corridor will be determined. Then the exact vibrations in the buildings are predicted

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3 Validation Concept The validation of models is becoming increasingly important. In the literature, there are numerous different approaches for performing validations with different focuses. To date, however, there is no generally applicable objective validation method. Often, compromises have to be made with respect to requirements, traceability, practicability and objectivity. The validation methods described and performed in the literature allow for subjective decisions in the validation process, e.g., the definition of requirements, test selection, the validation technique itself and the evaluation of the validation results. Therefore, the authors of this paper are aware that the following validation concept is also influenced by subjective decisions. Here, the developed validation concept is designed to provide specifications for the validation of every vibration prediction tool. In general, the methodological approaches and internal structure of any conceivable tool specified by the developers will be unknown and the source code will not be available for the user. The methodological approaches as well as the numerical models, as they are developed by the SILVARSTAR project in their Deliverable 1.1 [3], and the embedding in the structure of the vibration tool by the SILVERSTAR developers, are therefore no subject of investigation. The validation of the final prediction tool has to consider two additional aspects. On the one hand, the final tool includes a graphical user interface which will be used to upload spatial objects into the tool (e.g. buildings, railroads, altitude model) and to carry out a prediction. The calculated vibrations will be evaluated by using the descriptors mentioned above. On the other hand, there is the so-called computational core in the prediction tool including the mathematical models to perform the vibration prediction. From our point of view, the validation of the computational core is needed first. Subsequently, the final tool including the graphical interface will be used for the evaluation whether the requirements set up by the FINE-2 project are fulfilled and whether a valid evaluation is possible based on the defined descriptors. For the validation concept, three essential questions must be answered: Which data are used as input parameters? Which method will be used to validate the model? How will the results of the validation process be evaluated? For the validation, techniques that can be objectified as far as possible should be applied.

3.1 Validation of the Computational Core Since the validation is mainly based on measured data, a test based on the comparison between the measured results and the initial data of the prediction will be performed. If necessary, the model parameters will then be adjusted. To facilitate validation, the SILVARSTAR project provides a separate tool to test the computational core using an input interface which will not be available to the end user.

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Input parameters for the prediction To perform a comparative test, a wide range of measurement data will be used to investigate different situations. Here, the FINE-2 partners will use existing measurement results. The focus will be to validate typical situations for the train categories of urban traffic, mixed traffic, and high-speed traffic. In addition, the FINE-2 partners performed an extensive measurement campaign by using a regional train on the Velim railway test circuit (Czech Republic) and tests in Germany by considering trams in two different situations. The results are currently being evaluated. Since a measurement of a specific situation is only an approximation of reality, the quality of the validation is significantly influenced by the quality of the measurements. Therefore, the measurement input data will be divided into different test scenarios of different quality level. The quality of the test scenario dependent on the measurement setup, on the number of available pass-by measurements (statistical relevance is given), on whether the measurements of the test scenario were carried out under the same conditions, whether the measurement as a whole is representative for future analyses and on how many input parameters for the prediction tool were recorded (e.g. train and track parameters). Therefore, a classification into low, medium, and high quality of the test scenario must be performed first. In general, the following test scenarios can be tested: • Determination of vibrations in the building (test of emission or transmission models) • Determination of vibrations in free field (test of emission or transmission models) • Determination of vibrations at the emission point (test of only the emission model) Each of these main scenarios can in turn be divided into several subgroups. These subgroups depend on the train type, the train speed and, of course, the terrain and ground properties. Validation method The validation will be performed by comparisons between measurement results and prediction results for the selected test scenarios. For these test scenarios, the thirdoctave vibration band spectra of the corresponding measurements are averaged and additionally the standard deviation for each frequency band of the third-octave spectrum is calculated. The range of the standard deviation σ of the measurements around the mean value represents the confidence interval. Then it will be checked whether the prediction lies within the confidence interval. If the prediction result lies outside the confidence interval, a model adjustment is carried out in a second step. Here, the model parameters that are subject to a (particularly) high level of uncertainty in the test scenario (because they are unknown or could be only determined to a limited extent) are adjusted until the prediction result lies as optimally as possible within the confidence interval. Subsequently, the input parameters are checked for plausibility and the deviations are evaluated based on the matches. A model adjustment is also checked if the predicted value lies within the confidence interval, but below the

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mean value. Since in principle an overestimation is preferable to an underestimation regarding the prediction reliability. The procedure is repeated for the three levels of accuracy. The comparison is made from accurate to inaccurate. So, the individual terms of Eq. (1) are replaced with each level by more numerical approaches of the prediction tool. The levels of accuracy of a prediction are divided as follows: • 1st level: All terms of the Eq. (1) are unknown and are replaced by model assumptions. This results in a medium to poor accuracy of the prediction. • 2nd level: Emission and the transfer function of the ground vibration propagation are measured but the transfer function from the ground into the building is not measured. A second possibility is that measured data must be re-calculated (e.g. because the train speed and also the emission data are changed due to upgrading the line). This leads to a medium accuracy of the prediction. • 3rd level: Emission, propagation and vibration at the receiver position are completely measured. This should lead to a good accuracy of the prediction. Evaluation of the validation results The following evaluation of the validation procedure is suggested, but the evaluation and weighting of the frequency ranges in particular still needs to be specified and discussed during the validation process. It has to be mentioned that there cannot be an absolute validity of models. The model should be useful, i.e. allows statements about a system with reasonable accuracy. A central question is, therefore, which differences between prediction and reality are tolerable. According to this, closeness to reality can be affirmed if the degree of deviation is below a certain limit. The degree of match should be between 0 and 1. It must also be taken into account that larger deviations are more tolerable for certain frequency ranges than for others. Especially for most situations in Germany, a high prediction accuracy is required in the frequency range (II) of 8 Hz ≤ f ≤ 80 Hz, since building ceilings tend to vibrate resonantly in this range. In the ranges (I) with < 8 Hz and (III) with > 80 Hz, deviations can rather be tolerated. This results in three frequency ranges (I), (II), (III). For each of the three ranges, it is now examined whether the prediction lies within or outside the confidence interval. If the prediction is outside, model fitting is used to move the prediction into the confidence interval. If this is not possible, the prediction is considered to be inaccurate and is assigned a value of 0. If the prediction is within the confidence interval and above the mean value, it is scored as 1. It is assumed that an overestimation offers in principle higher prediction certainties than an underestimation. Therefore, for an underestimation, the prediction is assigned a value of 0.6. If the significance in the frequency range is indifferent between over and underestimation, the prediction is evaluated with 0.8. The evaluations of the prediction are then weighted as follows: (I) * 0.15 + (II) * 0.7 + (III) * 0.15 = degree of match of the prediction with the measurement (Fig. 2). Since a sufficiently large number of train pass-by measurements is not available for all situations that can be represented by the prediction tool, it is not possible to draw unambiguous conclusions. Therefore, specifying a degree of confidence in the

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Fig. 2 Schematic representation of the suggested evaluation with the three frequency ranges (I), (II), (III) and the evaluation factors for the prediction (blue figures)

correctness of the tool is more useful. The confidence in the correctness of the result depends on the quality of the test scenario. As mentioned, this is divided into low, medium and high. This is important because it is difficult to make a statement about the correctness of the prediction, especially with test scenarios of low quality. With increasing data quality, the result of the validation can be also more trusted. In addition, a weighting must be carried out based on the level of accuracy of the prediction. Since it can be assumed that a purely numerical prediction is subject to higher uncertainties than one based on measured data. For each test scenario, validity is determined by the measurement/prediction match, confidence in correctness, and level of accuracy. The values for all test scenarios are then summarized in a table and represent the result of the validation, e.g. test scenario 1 {0.8; medium; 3}. For the same situations, only test scenarios with high quality should be used, if possible, in order to increase the confidence in the prediction. However, since for many situations only test scenarios with medium or low quality are available, the results of the match are subject to greater uncertainty.

3.2 Validation of the Whole Prediction Tool The first step is to formally check which of the requirements described in Sect. 2 of this paper or Deliverable 8.1 [4] have been implemented. A checklist is created for this purpose. Since the requirements should be understood as a guideline for the design of vibration tools, it is not necessary that all requirements are met. The requirements will be classified according to the MoSCoW-method (MoSCoW is an acronym for must-have, should-have, could-have, and won’t-have, each denoting a category of prioritization).

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On the basis of the previously examined test scenarios, those with high match, high confidence in correctness and accuracy level 2 or 3 are used in order to be able to carry out the validation of the tool. Afterwards, the scenarios will be modeled using the graphical interface and vibration evaluation as well as the defined descriptors. Then the initial situation is modified, i.e. changing the train operation forecast, shifting the track position, adding new railways, adding new buildings. Based on the changes, the response of the descriptors/vibrations is examined. In contrast to the computational core for which the methodology of the computation has been defined by SILVARSTAR, the process for the computation of the descriptors is described in the standards. Therefore, a computational check of the scenarios “by hand” can be performed here. Acknowledgements The FINE-2 project, with this paper and the described work, is linked, has received funding from the Shift2Rail Joint Undertaking under the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No. 881791, there we authors are grateful.

References 1. DIN 4150-2:1999 (1999) Erschütterungen im Bauwesen - Teil 2: Einwirkungen auf Menschen in Gebäuden, Beuth Verlag 2. VDI 3837:2013 (2013) Ground-borne vibration in the vicinity of at-grade rail systems. Beuth Verlag, Berlin 3. Degrande G, Lombaert G, Ntotsios E, Thompson D, Nélain B, Bouvet P, Grabau S, Blaul J, Nuber A (2021) Deliverable D1.1, state of the art and concept of the vibration prediction tool 4. Brick H, Stiebel D, Garburg R, Schleinzer G, Zandberg H, Faure B, Pfeil A, Thomas S, Guiral A, Oregui M (2020) Deliverable 8.1, specification of model requirements including descriptors for vibration evaluation 5. TÜV Rheinland Consulting GmbH: Rivas Project. http://www.rivas-project.eu/. Last accessed 09 Sept 2020 6. ISO 2631-1:1997 (1997) Mechanical vibration and shock—evaluation of human exposure to whole-body vibration—part 1: general requirements 7. ISO 2631-2:2003 (2003) Mechanical vibration and shock—evaluation of human exposure to whole body vibration—part 2: vibration in buildings (1 Hz to 80 Hz) 8. ISO/TS 14837-31:2017 (2017) Mechanical vibration—ground-borne noise and vibration arising from rail systems—part 31: guideline on field measurements for the evaluation of human exposure in buildings

Framework for Optimization of Multi-source Railway High Speed Noise Models Through Hybrid Methods Combining Acoustic Simulations and Close Perimetric Noise Measurements Gennaro Sica, Jaume Solé, Pierre Huguenet, and Oliver Bewes

Abstract The prediction of future noise levels of railway lines prior to their construction has evolved with the years. This evolution has reflected the fact that aerodynamic noise sources at high speed are not only placed at low height, but also in the upper parts of the train (Gautier et al. in High speed trains external noise: a review of measurements and source models for the TGV case up to 360 km/h, Seoul, 2008 [1]; Noh in J Rail Rapid Transit 228:307–322, 2014 [2]). It is common practice in environmental noise modelling to represent a train by multiple sources with speed relationships (Marshall et al in Derivation of sound emission source terms for high speed trains running at speeds in excess of 300 km/h. Springer, Berlin, Heidelberg, pp. 497–504, 2015 [5]). Careful estimation of the emission laws of these sources is critical for estimating the noise impact in the surroundings, particularly in presence of barriers or where buildings overlook the railway. Building on the results and conclusions previously reported by the authors in (Sica et al. in Pass-by noise assessment of high-speed units by means of acoustic measurements in a perimeter close to the train, Ghent, 2019 [1]), this work presents a framework for optimizing a multi-source railway noise model by combining accurate simulation with test data obtained with microphones close to the perimeter of the railway. Acoustic models to determine the screening of noise sources by the train body and other complex acoustic phenomena (i.e. directivity, diffusion and diffraction) have been coupled to numerical optimization tools, in order to improve accuracy of noise estimations of the multi-source railway noise model. Keywords Railway noise prediction · Pantograph · Rolling noise G. Sica (B) · O. Bewes HS2 Ltd., The Podium Euston, 1 Eversholt Street, London, NW1 2DN, UK e-mail: [email protected] J. Solé · P. Huguenet SENER Ingeniería y Sistemas, Noise and Vibration Technical Office, C/. Creu Casas I Sicart 86-88, Cerdanyola del Valles, 08290 Barcelona, Spain © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_8

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1 Methodology Environmental noise modelling methods represent the train with multiple sources each defined as a different function of speed according to a generic law A·log(SPEED) + B. A specific optimization framework has been proposed in this paper to improve prediction at the TSI/NTSN pass-by noise measurement position (25 m) by adjusting coefficients A and B in each source emission law. The optimization framework proposed in this work is based on the following elements: • Implementation of a test setup mixing close measurement points in a catenary portal together with several further measurement positions going up to 300 m away from track center, as described by the authors in previous work [3]. This is described in Sect. 2. • Preliminary data analysis including transversal noise emission maps. These maps are used to obtain directivity estimations for different noise sources in the model. This is described in Sect. 2. • Implementation of an supplementary noise model to represent screening of train body, diffusion, diffraction and directivity estimates. The model is adjusted to fit the experimental data obtained in the test setup described in [3]. This is described in Sect. 3. • Optimization of noise emission laws with respect to speed, for each individual noise source in the railway noise model, so that a good fit of the model to the test data is achieved. This is described in Sect. 4. Section 5 of the paper provides results for the application of the optimization framework to derive a 5-line source prediction model representative of a Siemens Velaro unit measured during the test campaign in [3].

2 Experimental Test Data 2.1 Test Setup As presented in reference [3], experimental data of high-speed railway noise have been obtained in the test site of Las Inviernas (SPAIN), belonging to the Spanish ADIF railway network. Noise data was collected both in near-field and far-field microphone positions, according to the setup shown in Fig. 1. Track decay rate and acoustic rail roughness were also measured, both within specifications in standard ISO 3095:2013. A total of 15 pass-by of a dedicated Siemens Velaro test unit at different speeds were recorded (3 pass-by for each reference speed of 250, 280, 300, 320 and 350 km/h). For each 3 pass-by, 2 were in normal pantograph configuration (raised) and one lowered just before the pass-by point. This approach was used to assess impact of pantograph, recess and other sources of aerodynamic

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Fig. 1 Scheme and view of the near and far field sensors installed (from [3])

noise. Pass-by of other units (Alstom TGV, Talgo, Velaro, CAF ATPRD) were also recorded during commercial operation at the site.

2.2 Preliminary Analysis The test set up described in the section above allowed the signal to be analysed in the time and frequency domain which provided initial estimation of the strength, directivity and other properties of the sources as described in [4]. From the microphones within the portal where pressures are known, it is possible to estimate transversal noise emission maps by applying symmetries and interpolating minimal curvature surfaces as shown in Fig. 2. Spectral directivity estimates can be obtained from the grid of interpolated data.

3 Noise Model 3.1 Equivalent Noise Source Terms A five noise source model was considered for the optimization framework. Original baseline speed dependencies laws relating train speed V with pass-by noise in terms of LpAeq are the following, for each noise source, from [5]: • R + 30·log10V for rolling noise 0.0 m above rail head; • B + 70·log10V for body aerodynamic noise 0.5 m above rail head; • S for starting noise (no speed dependency) 2.0 m above rail head;

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Fig. 2 Transversal noise emission maps of a train running at 350 km/h in the 5000 Hz octave band

• H + 70·log10V for upper level (pantograph recess, HVAC and other aerodynamic noise) 4.0 m above rail head; and • P + 70·log10V for raised pantograph aerodynamic noise 5.0 m above rail head. where RSEL, BSEL , SSEL , HSEL and PSEL are constant parameters and V is the train speed.

3.2 Position of Noise Sources In addition to the height of the noise sources the transversal position needs to be defined. Prediction methods such as the Dutch SRMII or CNOSSOS-EU assume all noise sources are aligned with track axis and the train body is not represented in the model. This is a reasonable assumption for environmental noise prediction concerned with predicting noise in the far-field. The approach in this paper uses measurements made in the near-field. This means that the effect of the train body on screening, diffraction and diffusion must be represented to enable better definition of the noise source levels and locations. Source positions and near-field positions used in this study are informed from the preliminary data analysis and are given in Fig. 3 (left).

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Fig. 3 Left, ODEON model used to reproduce the test setup from [3], with near-field microphone positions, train geometry and noise source positions. Right, ODEON model of the test setup, with propagation of pantograph noise represented as red balls following acoustic rays

3.3 Use of Predictive Model Based on Acoustic Ray-Tracing To accurately reproduce phenomena like train body screening, horizontal diffraction and diffusion, an acoustic model based on ray-tracing methods (as implemented in ODEON) was created, incorporating details of train geometry and track. Noise sources and receivers were introduced to compute the relationship between noise sources, near-field and far-field values. In addition to the diffraction and diffusion effects, noise sources are defined with a corresponding directivity pattern including pantograph derived using [4]. Figure 3 (right) shows train body screening effect in the propagation of pantograph noise. Direct contribution of the pantograph noise would be visible at the near-field microphones situated next to the wheels if train body screening was not considered. Noise transfer functions between each noise source and all the relevant microphones positions are calculated using the ODEON model. Transfer functions are an efficient way to obtain total noise at each microphone position: individual source contributions are added to obtain total noise at each position. Individual source adjustment is then possible, and total noise re-evaluated without recalculation of acoustic model. Accordingly, this approach is recommended for optimization methods.

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4 Optimization Method 4.1 Optimization of Noise Source Terms Based on Experimental Data Optimization of noise source terms is performed, following the 5 sources approach, and speed dependency law of A·log10(V ) + B, for a speed range from 250 up to 350 km/h. As the optimization process is based on nonlinear objectives, the algorithm followed is based on a non-linear evolutionary method which uses a genetic algorithm approach to find optimal solutions. It reduces the risk of stopping at local optimum values, implying a solution that may not be optimized globally. A two-step optimization process is followed. First optimizing with the near-field microphones and secondly with both far-field and near-field microphones. This twostep optimization process is an iterative approach: FIRST STEP Considering A·log10(V ) + B, A and B constants are first obtained with near-field data optimization, isolating specific near-field microphone data. The pantograph and upper aerodynamic noise sources are optimized with MIC1, MIC2, MIC3 and MIC4 data, while Rolling + Lower Body Aerodynamic + Start noise are optimized with MIC 5 and MIC 6. The range of possible values for A are defined depending on the noise source between 50 and 90 for aerodynamic noise and 10–40 for rolling noise. Start/Engine noise is constrained between 0 and 5. SECOND STEP Using the A and B values from the first step, the B constant of each source are tuned with far-field data optimization centered on MIC9 at 25 m. The optimization process starts with the initial A and B values from the first step, but only the B values are modified. Weighting coefficients are applied to both near-field and far-field data with the highest weighting at MIC9. Lower weightings are applied to near-field data to ensure the process is optimized for the MIC9 position whilst maintaining good correlation with nearfield microphones. The optimization is complete when the lowest possible value of the weighted mean square error between measurement and predictions at all microphones of interest for all speeds is obtained. Two scenarios have been considered in the optimization process: • Scenario A—Speed laws A are fixed according to the literature in [5] for all noise sources, while source levels B are optimized. • Scenario B—A and B are calculated as part of the optimization process for all noise sources.

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5 Results 5.1 Optimization Results Based on Different Speed Dependencies The optimization framework proposed in this paper is applied to the pass-by noise measurements of a Siemens Velaro Unit. Results of the optimization process are presented in Table 1 which also shows the A and B constants and correlation metrics. Comparison of predicted and measured noise levels at MIC9 are presented in Fig. 4. It can be seen that the agreement between measured and predicted levels is improved for Scenario B when both A and B constants are optimized. Table 1 Equivalent source terms for LpAeq indicator at MIC9 Noise source

LpAeq,tp Scenario A A

Scenario B B

· log10(V) +

A

B · log10(V) +

Rolling

30

58

28

Lower body

70

− 43

70

61

Start

0

110

5

Upper body

70

− 45

58

− 14

Pantograph

70

− 42

64

− 27

Correlation

0.60

− 43 95

0.26

Fig. 4 Comparison of experimental data with predicted results from optimized noise sources (Scenario B) for LpAeq, at MIC9

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Fig. 5 Comparison of noise source contribution as a function of speed, Scenario A (left) and Scenario B (right), at MIC9

The contribution of each noise source to the total LpAeq across the speed range is shown in Fig. 5. Scenario B leads to different conclusions regarding the importance of each noise source at high speeds. In Scenario B the optimization tends to an outcome where rolling noise is 2–3 dB lower at all speeds. This means that aerodynamic noise from the pantograph becomes the largest contributor to the total noise at 280 km/h for Scenario B rather than 310 km/h for Scenario A. At 360 km/h the pantograph is the largest contributor to the total noise in Scenario A, but in Scenario B the optimization tends to an outcome where pantograph and body aerodynamic noise are contributing equally to the total noise.

6 Conclusions A complete optimization procedure has been carried out to determine the noise emission laws (as function of level and train speed) corresponding to the different sources in a 5-source noise model of an existing high speed train. Optimization has been carried out for a specific Siemens Velaro train operating in Las Invernias, Spain, using a complete set of experimental noise emission data. Complex acoustic phenomena like train body screening, diffusion and diffraction have been represented using a ray-tracing model. The results produce speed laws and levels for a five source model of the train with a good level of correlation with experimental data. The results also indicate that full implementation of the optimization method (Scenario B) leads to different conclusions regarding the relative contribution of the different noise sources to the scenario when speed laws are set to generic terms found in literature (Scenario A). This shows that the characteristics will be highly dependent on the specific design of the train. Use of close perimeter noise measurements in

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the optimization process has enabled these characteristics to be better defined to some extent. A limitation of the approach is that it does not enable separation of the contributions of the different noise sources at each microphone. This will be particularly important for the lower noise sources at higher speeds where rolling noise and aerodynamic noise sources are providing comparable contributions to the total noise level. If the approach presented in this paper were supplemented with source separation approaches [6] this could lead to further improved characterization of a train.

References 1. Gautier P, Poisson F, Letourneaux F (2008) High speed trains external noise: a review of measurements and source models for the TGV case up to 360 km/h. In: Proceedings of the 8th world congress on railway research, Seoul 2. Noh H et al (2014) Investigation of noise in high speed trains. J Rail Rapid Transit 228(3):307– 322 3. Sica G, Solé J, Huguenet P (2019) Pass-by noise assessment of high-speed units by means of acoustic measurements in a perimeter close to the train. In: Proceedings of the 13th international workshop on railway noise, Ghent 4. Solé J, Huguenet P, Sica G (2019) Evolution of pantograph noise directivity at increasing speeds. In: Proceedings of Internoise, Madrid 5. Marshall T, Greer R, Fenech B (2015) Derivation of sound emission source terms for high speed trains running at speeds in excess of 300 km/h. In: Noise and vibration mitigation for rail transportation systems. notes on numerical fluid mechanics and multidisciplinary design, vol 126. Springer, Berlin, Heidelberg, pp 497–504 6. Arteaga IL et al (2022) The TRANSIT project: innovation towards train pass-by noise source characterization and separation tools. In: Proceedings of the 13th world congress on railway research, Birmingham

Noise Incentivisation for UK High Speed Train Procurement Gennaro Sica, Tom Marshall, Jon Sims, David Owen, and Oliver Bewes

Abstract The latest generation of high speed trains can be designed, constructed and operated with a lower noise emission that many existing trains. It is permissible to procure these trains for use in sensitive situations such as highly population regions where the noise impact could result in significant environmental impacts. To ensure that the cost of the noise control is proportionate to the benefit it provides, HS2 has developed a mechanism to incentivize pass-by noise in the Tender Evaluation of its fleet of high speed trains. The benefit has been assessed by estimating the monetized value of quieter trains operating on the new HS2 railway as well as the existing railway lines. This value was then used in the whole life value model developed for the Tender Evaluation to ensure train manufactures have a sufficient incentive to include state-of-the-art noise control measures in the design of the new trains. This approach has been successful in achieving the pass-by noise level set out as envisaged mitigation in the HS2 environmental assessments. The noise benefit of trains that are approximately 4 dB quieter than the national specification for interoperability will be experienced by approximately 320,000 people living near one thousand kilometers of railway. Keywords High speed rail · Procurement · Incentivisation

1 Introduction Railway transport is the most sustainable transport mode [1], however, noise has long been the main environmental challenge for railway stakeholders. Railway noise is controlled by local measures and by technical specifications for new trains. Specifying mitigation for the train ensures that noise is reduced at source and can avoid G. Sica (B) · O. Bewes High Speed Two (HS2) Ltd., 1 Eversholt Street, London, NW1 2DN, UK e-mail: [email protected] T. Marshall · J. Sims · D. Owen Arup, 63 St Thomas Street, Bristol, BS1 6JZ, UK © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_9

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increasing the carbon footprint from local measures such as taller noise barriers. The National Technical Specification Notice1 (NTSN): Rolling Stock—Noise (NOI) [2] is important to ensure noisy trains are phased out but does not always guarantee that the quietest possible technology is implemented. Measurements of existing high speed trains operating in the UK have shown that noise levels can be several decibels below the NTSN specifications [3]. HS2 Ltd. is developing a new high speed railway and procuring new high speed trains. This provides a unique opportunity to ensure the train, track and civil designs achieve the best possible noise reductions. Noise impact assessments performed for HS2 have assumed that HS2 trains will be approximately 4 dB below the NTSN pass-by noise specification. HS2 rolling stock procurement has specified pass-by noise to be as low as possible establishing an incentive mechanism with the aim to deliver trains quieter than the NTSN specifications. This incentive is based on a whole life value assessment of the noise impact from the new trains to ensure that rolling stock manufactures deliver the noise reduction necessary to achieve the railway’s capabilities. This assessment included over one thousand kilometers of railway track that the HS2 trains would be operating on which comprise of the full HS2 scheme connecting London, the West Midlands, Manchester and Leeds as well as the conventional rail network (West Coast Main Line and East Coast Main Line connecting Glasgow and Edinburgh). This paper describes the incentive mechanism used to procure quieter high speed trains for HS2.

1.1 Context Noise is the greatest environmental effect of railways in Western Europe [4]. Several activities involving many different players have been used to reduce the source of noise from rolling stock. The Technical Specifications for Interoperability (NTSN in Great Britain) have been implemented to remove the use of cast-iron brake blocks from new rolling stock and incentives in the form of charges or subsidies have been implemented to promote the ongoing activity of retrofitting the existing fleet of rolling stock to use quieter composite brake blocks. However, modern rolling stock designed to meet the challenging requirements of the transport sector can achieve a lower noise performance when operating on well-maintained low noise track. It is possible to select quiet rolling stock in the procurement process. However, the cost of low noise technology should be considered relative to the environmental benefit it provides.

1

NTSN NOI 2021 has the same technical requirements as the EU Commission Regulation on the technical specification for interoperability (TSI) relating to the subsystem ‘rolling stock – noise’.

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2 Methodology 2.1 HS2 Train Procurement The NTSN NOI defines limit values for passby noise. It is permissible for trains to be procured that are quieter than the NTSN specifications. This has been achieved on the latest high speed trains currently operating on High Speed 1 [3]. HS2 Ltd. has chosen to balance the train requirements by including an incentive rather than setting a mandatory requirement to achieve a fixed noise level lower than the NTSN specification values. This is because there was insufficient evidence to confirm that a lower level could be achieved by all rolling stock manufacturers without adding unreasonable costs. The incentive value is intended to ensure that noise control measures are applied by the train manufacturer to reduce noise as far as reasonably practicable. To develop an incentive regime for reducing noise from rolling stock the following elements should be considered: • Value for Money: a qualitative comparison of the health and environmental benefit [5] of the noise reduction provided compared to the long-life cost of the mitigation • Engineering and operational practicability: NTSN specification to be considered as upper limit and trade offs between operational specifications considered • Impacts on other environmental disciplines: (eg, the potential for worsened landscape, visual and carbon impacts associated with taller noise barriers) • Stakeholder engagement: brief evaluation of the responses received and reasons for selecting a particular noise mitigation option. In 2018, HS2 Ltd. Issued the Invitation to Tender that set out the Tender Evaluation process for the different types of requirements set in the HS2 Train Technical Specification (TTS) [6]. Within the TTS there are 3 types of requirements: • mandatory • scored; or • contributes to the whole-life value model. The pass-by noise requirement, reproduced in Fig. 1, was identified as a contributor to the whole life value model. The tenderer was required to submit a value for the tender evaluation which would then be included in the contract. Values submitted that are closer to the assumed pass by level used by HS2 in the environmental assessment are given a beneficial monetary value in the tender evaluation. Since the publication of the first national noise maps in Europe, policy makers have been investigating the monetary value of environmental noise. Hedonic pricing and willingness to pay techniques (revealed or stated preference methods) are used around the world to assess the impact of noise. The World Health Organization report on Burden of Disease from Environmental Noise published in 2011 [7] led to new techniques to monetize the impact of noise on health. The recommended methodology used recently in Europe to assess the external costs of transport assesses

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Fig. 1 Pass-by noise requirement as set out in the HS2 train technical specification (TTS)

annoyance using new evidence on annoyance costs and health based on the UK Government approach [8, 9]. In the UK, the original recommended method for valuing the impact of noise published by the Department for Transport was based on hedonic pricing of the Birmingham noise map exposure data. This was implemented for around 10 years within the Governments Transport Assessment Guidance (WebTAG) for use in policy and scheme appraisals. In 2014, the UK Government published guidance on the valuation of Environmental Noise [10]. This made a shift from quantifying the direct effect of noise on market prices for homes to monetize the impact of noise on health. The following year this approach was implemented in WebTAG. WebTAG has been used extensively to support decision making during the development of HS2 including: route option appraisals, environmental assessments and noise mitigation value assessments.

2.2 Noise Impact Estimate of HS2 Rolling Stock The airborne noise impact at residential properties due to the operation of the HS2 network was estimated using the results of detailed modelling of the railway design including envisaged mitigation that were summarised in the Phase Two Economic Case advice to DfT [11]. The airborne noise impact at residential properties due to conventional railway lines was estimated using Round 2 Environmental Noise Directive mapping data [12]. Using the WebTAG input for noise exposure levels equal or greater than 45dB day or 45dB night, there is estimated to be approximately 320,000 people that would experience either an increase in noise from the new railway or a decrease in noise from the new HS2 trains operating on the existing railway.

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3 Results A base case was defined to represent the sound source of HS2 trains at the NTSN pass-by noise limit when trains are tested on slab track. The resulting monetised benefit of 1, 2, 3, 4, 5, 6 and 10 dB quieter than the base case for the full mitigated high-speed railway combined with the existing conventional railway are presented in Fig. 2. The overall monetised difference between HS2 trains procured and operated at the loudest permissible level set by NTSN and HS2 trains procured and operated at the level assumed in the environmental assessments (approximately 4dB quieter) is estimated to be £80 million using the default settings in WebTAG 2015 [4]. The operation of the new HS2 railway will result in a noise impact on nearby residents. This has been reduced through careful consideration of all forms of effective noise mitigation measures including quieter trains, low noise track, noise barriers and landscape earthworks. The estimated health benefit of quieter HS2 trains is approximately equal to the entire residual health disbenefit of noise from HS2 trains on the entire new railway [13]. In December 2021 HS2 Ltd. Announced that Hitachi Alstom JV has been awarded the contracts to design, build and maintain a fleet of 54 state-of-the-art high speed trains that will operate on HS2. Following the award of the rolling stock contract, requirement TTS-178 has been updated to include an acceptance pass-by noise criterion which will be quieter than the current NTSN extrapolated at 360 km/h. Hitachi Alstom JV are now commencing a two-year design programme during which they will develop and share further information relating to the noise performance of the trains.

Fig. 2 Monetised benefit of HS2 rolling stock noise reduction

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4 Conclusions This paper has presented the noise incentivization approach developed by HS2 which has been used in the procurement of new rolling stock. As part of the train procurement, the tenderer was required to submit a value for a pass-by noise requirement for the tender evaluation which would then be included in the contract. Values submitted that are closer to the assumed pass by level used by HS2 in the environmental assessment are given a beneficial monetary value in the tender evaluation. This approach ensures that the cost associated with delivering the rolling stock noise control is proportionate to the benefit it provides to both people living near the new railway and also people living near the existing railway lines that these trains will operate on. The pass-by noise level has become a commitment by the train manufacturer to deliver a rolling stock with acoustics emission lower than the current NTSN limit extrapolated at 360 km/h. This provides confidence that the civil designs, including landscape earthworks and noise barriers, can achieve the environmental commitments of the project without the increased visual impacts, carbon and cost that could result from a need to design and build taller or additional noise barriers.

References 1. International Union of Railways, Sustainability/Noise and Vibration (2023). https://uic.org/sus tainability/noise-and-vibration/ 2. Department for Transport, The National Technical Specification Notice (NTSN) Rolling Stock—Noise (NOI) (2021) 3. Takano Y, Morita K, Mochida T (2011) Interior noise reduction of high-speed rolling stock in tunnels. Institute of Noise Control Engineering, Proceedings. InterNoise11, pp 2148–2154 4. Huebner P, Oertli J (2010) Railway noise in Europe, a 2010 report on the state of the art. International Union of Railways. https://uic.org/IMG/pdf/uic_railway_noise_the_state_of_the_art_ 2010.pdf 5. Department for Transport, Transport Analysis Guidance: WebTAG (or TAG) (2017) 6. High Speed Two (HS2) rolling stock: train technical specification revision P11, document no. HS2-HS2-RR-SPE-000-000007. https://www.gov.uk/government/publications/hs2rolling-stock-procurement 7. World Health Organization, Regional Office for Europe (2011) Burden of disease from environmental noise: quantification of healthy life years lost in Europe. World Health Organization, Regional Office for Europe. https://apps.who.int/iris/handle/10665/326424 8. Birchby et al. (2021) Methodology for external cost estimations WP8, task 8.1.1 [version 1, 29-04-2021], noise and emissions monitoring and radical mitigation (NEMO) EU horizon 2020 project. https://nemo-cities.eu/public_deliverables/ 9. Fiorello D, El Beyrouty K et al (2019) Handbook on the external costs of transport: version 2019-1.1. European Commission, directorate-general for mobility and transport, Essen, Publications Office. https://data.europa.eu/doi/10.2832/51388 10. Department for Environment, Food & Rural Affairs, Noise Pollution: Economic Analysis, 19 Dec 2014. https://www.gov.uk/guidance/noise-pollution-economic-analysis 11. High Speed Two (HS2) phase two—economic case advice for the department for transport, July 2017. https://www.gov.uk/government/publications/hs2-phase-two-economic-caseadvice-for-the-department-of-transport

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12. Department for Environment, Food and Rural Affairs, Environmental Noise Directive—Noise Mapping, Rail Noise—England Round 2, Open Government License 13. Full Business Case High Speed 2 Phase One April 2020 Department for Transport. https://ass ets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/939 905/full-business-case-hs2-phase-one.pdf

Analysis of the Uncertainty of High-Speed Rail Noise Predictions James Woodcock, Tom Marshall, Jon Sims, David Owen, Oliver Bewes, and Gennaro Sica

Abstract The effects of noise from future railway schemes are assessed using validated prediction methods that rely on multiple input parameters and assumptions. Generally, single values representing reasonable worst-case assumptions are selected for each input parameter. Variation in factors such as local meteorological conditions, receiver location and source characteristics means that there is uncertainty in the model inputs that, when propagated through the model, result in uncertainty in the model predictions. This paper presents an analysis to characterise and quantify the uncertainty of high-speed railway noise predictions via Monte Carlo simulation and global sensitivity analysis. The HS2 airborne noise prediction method is used as the basis of the study, along with elements of the CONCAWE method to take meteorological effects into account. Forty-eight generic scenarios representing different combinations of meteorological conditions, time of day, screening and receiver distances have been analysed for the LAeq and LAmax metrics. Output distributions representing the prediction uncertainty have been calculated for each scenario and are presented as boxplots. The results of the global sensitivity indicate that meteorological effects have the largest contribution to the prediction uncertainty. The aerodynamic source term parameters were found to be the most sensitive parameters related to the source. Keywords High speed rail · Prediction · Uncertainty

1 Introduction The effects of noise from future railway schemes are generally assessed using validated prediction methods developed by the national railway company, research institute, or Government department. These prediction methods are informed by local J. Woodcock (B) · T. Marshall · J. Sims · D. Owen Arup, 3 Piccadilly Place, Manchester, M1 3BN, UK e-mail: [email protected] O. Bewes · G. Sica High Speed Two (HS2) Ltd., 1 Eversholt Street, Euston, London, NW1 2DN, UK © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_10

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and national views on acoustical issues and their own set of regulations and policies which influence the development of the prediction standard. These standard methods include multiple input parameters and formulas that are typically fit to national data sets. Generally, the input parameters are assigned single values representing reasonable worst-case assumptions for the assessment that is being undertaken. Due to variation in factors such as local meteorological conditions, receiver location and source characteristics (e.g. rail roughness, temperature, pantograph geometry), the model inputs represent a point in a range of possible values. This input variation, when propagated through the model, results in uncertainty in the model predictions. As the outputs of prediction models are used to assess noise impacts, which ultimately inform the design of mitigation, prediction model uncertainty and the specification of input parameters has a material influence on the assessment and design of new rail schemes. As such, quantifying the uncertainty of railway noise predictions helps to understand the probability of achieving desired outcomes and identifies input sensitivity that can influence the design and assessment. HS2 Ltd. is developing a new high-speed railway in the UK. The effects of operational sound from HS2 have been assessed using a validated empirical prediction methodology [1]. As discussed above, knowledge of prediction model uncertainty helps to understand the probability of achieving desired outcomes and has a material effect on the design and assessment of new rail schemes. As such, HS2 Ltd. have undertaken a study of the uncertainty of high-speed rail predictions. The HS2 airborne noise prediction method forms the basis of the study, with elements of the CONCAWE [2] method incorporated to account for meteorological effects. Uncertainty has been characterised with respect to the variation the daytime and night-time LAeq,1h /LAmax metrics. The methodology used allows the quantification of the local uncertainty at a given receptor due to the model input parameters as well as the hourly variation in meteorological conditions. Although long-term weather trends can be predicted for a given receptor location, the analysis presented in this paper is focused on short term variations which cannot be reliably predicted. This paper presents an analysis to characterise and quantify the uncertainty of high-speed railway noise predictions via Monte-Carlo simulation (MCS) [3] and global sensitivity analysis (GSA) [4]. The remainder of this section sets out the context for the work. Section 2 outlines the methodology. Results are presented in Sect. 3. Finally, discussion and conclusions are provided in Sects. 4 and 5. Although this paper is focused on the uncertainty of the HS2 prediction method, the approach set out in the paper could be applied to characterise the uncertainty of any noise prediction method.

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2 Methodology 2.1 HS2 Airborne Noise Prediction Method The HS2 airborne noise prediction method is a validated methodology that allows the prediction of LAeq and LAmax levels from high-speed trains. A detailed technical description of the model can be found in [5]. The basis of the method is a multi-source model that incorporates five sources at different heights above track: rolling sound (0 m), body aerodynamic sound (0.5 m), starting sound (2 m), pantograph recess aerodynamic sound (4 m), and raised pantograph aerodynamic sound (5 m). Each of the sources in the model are characterised by a source term and a speed dependence that result in predictions of SEL and LAmax at a distance of 25 m from the track. To predict noise levels at different distances, the HS2 method models moderate downwind propagation conditions (or moderate ground-based temperature inversions) using empirically derived formulae that account for geometrical spreading, atmospheric absorption, soft ground attenuation, and attenuation due to reflective/absorptive noise barriers.

2.2 Monte-Carlo Simulation and Global Sensitivity Analysis Monte-Carlo simulation (MCS) is a commonly used method to characterise the uncertainty of prediction models [3]. The method consists of defining probability distributions that represent the uncertainty of the model inputs. These input probability distributions are sampled to generate multiple input parameter sets that are representative of the possible range of the input parameters. The model is then evaluated with each of the sampled input parameter sets to generate a distribution of model outputs. The uncertainty of the model can then be characterised as a probability distribution or as a statistical quantity, such as the standard deviation. The MCS was conducted using SALib (a sensitivity analysis library implemented in Python [6]) using the random permutation method [7]. Correlations between variables have been taken into account by defining the input distributions as copulas [8]. The guidance provided in Song et al. [9] for the required sample size for the random permutation method has been followed. This results in around 400,000 model runs for each of the scenarios investigated. Global sensitivity analysis (GSA) [4] provides a method to calculate sensitivity indices for each input parameter that quantify the contribution of each parameter to the overall model uncertainty. Sensitivity indices generally take on a value from 0 to 1 with 1 indicating that the parameter accounts for all the variance in the model output and 0 indicating that the parameter does not contribute to any of the model variance. Shapley effects have been used to determine sensitivity indices for each input parameter using the algorithm described in [9].

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Table 1 Input parameters considered in the Monte-Carlo simulation Input parameter

Distribution

Approach to set distribution

SEL and Lmax source term and Normal (correlational between Rolling/aero: statistical speed dependence terms taken into account with analysis of measured passby. couplas) Starting: Information from published literature [14] Meteorological effects

Probably of occurrence

Statistical analysis of meteorological data

Atmospheric absorption, ground absorption and barrier attenuation

Normal (correlational between Reported standard error ground and air terms taken into account with couplas)

Train speed

Normal

Statistical analysis of operational modelling

Traffic composition and Uniform proportion of services running at maximum speed

Consultation with subject matter experts (HS2 operational team)

Receiver position

Normal

Statistical analysis of a noise modelling

Distance attenuation

Uniform

Modelling of sum of finite line source (representing the train body) and two point sources (representing pantographs)

2.3 Development of Parameter Distributions This section provides a high-level description of the development of the input parameter distributions for the MCS. A detailed description of the probability distribution developed for each input parameter is beyond the scope of this paper. Table 1 summarises the input parameters considered in the MCS. Because the HS2 train does not yet exist and the precise characteristics of the different noise sources are not yet defined, uncertainty distributions for the different HS2 train noise sources are not currently defined. To address this, input distributions for the rolling and aerodynamic source term parameters have been determined through statistical analysis of 146 existing highspeed train passbys (including TGVA, TGV-POS, Eurostar ICE, Talgo and Velaro rolling stock from 1990-present). The HS2 train is being procured to achieve passby noise levels below the NTSN1 [10] passby limits. Considering the incentive to reduce noise in the HS2 train procurement [11] and the low noise track specification, passbys above the current NTSN limit were excluded from the dataset. Linear regression and bootstrapping [12] have been used to estimate distributions for the source term and speed dependence parameters. The

1

NTSN NOI 2021 has the same technical requirements as the EU Commission Regulation on the technical specification for interoperability (TSI) relating to the subsystem ‘rolling stock— noise.Query

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analysis was conducted in two speed regions to allow the estimation of parameters for the rolling and aerodynamic sources. The HS2 method models moderate downwind propagation and does not include corrections for other meteorological conditions. Several prediction methodologies exist that can take different meteorological conditions into account including the French national railway noise prediction method (NMPB: Nouvelle Méthode de Prévision du Bruit) [13] and the CONCAWE method [2]. The NMPM method includes a procedure to account for meteorological effects in long term noise predictions but does not provide a method to calculate an overall correction to the hourly LAeq /LAmax metrics that are used as the basis of the uncertainty analysis. The CONCAWE method provides empirical formulae for six categories of meteorological conditions that can be applied directly to the hourly LAeq /LAmax model predictions. Considering this, the CONCAWE method has been used to account for uncertainty due to local meteorological conditions. Hourly observations of wind speed, wind direction, cloud cover and solar radiation measured at a weather station close to the HS2 route in 2019 have been used to calculate the occurrence of the six CONCAWE meteorological categories over a 12-month period. This analysis has been conducted for receivers to the north-east and south-west of the source during the daytime and night-time periods. In the MCS, corrections for meteorological effects have been applied as an overall additive correction to the level calculated using the HS2 method. CONCAWE category 5 has been assumed to be representative of the moderate downwind propagation modelled in the HS2 method. Input distributions for other distance dependent propagation effects including atmospheric absorption, ground absorption, and barrier attenuation have been set using the standard error reported in the development of the original TNPM method [1]. Additional noise modelling has been undertaken to determine input distributions for the effect of geometric spreading and receiver position. Distributions for operational parameters including capabilities for speed, proportion of services running at maximum speed, train mix and flows were determined though a statistical analysis of HS2 operational modelling of services running to timetable and discussion with HS2 Ltd.

3 Results Monte Carlo simulations and a global sensitivity analysis have been conducted using the method set out in Sect. 2.2 and the parameter distributions set out in Sect. 2.3. Eight generic scenarios representing different screening (unscreened and with a 5.0 m absorptive barrier), receiver positions (nominally upwind and downwind respectively) and time periods (daytime and night-time) have been investigated at four receiver distances. Figures 1 and 2 present boxplots illustrating the calculated prediction uncertainty for the LAeq and LAmax metrics respectively. The whiskers of

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Fig. 1 Boxplots representing prediction uncertainty for the LAeq metric results are shown for no screening (left pane) and a 5.0 m absorptive barrier (right pane)

Fig. 2 Boxplots representing prediction uncertainty for the LAmax metric results are shown for no screening (left pane) and a 5.0 m absorptive barrier (right pane)

the boxplots represent the 2.5 and 97.5 percentiles, the boxes represent the upper and lower quartiles and the horizontal line represents the median. Figures 3 and 4 show the results of the global sensitivity analysis as Shapley effects for the LAeq and LAmax metrics respectively. The results are shown for a receiver to the north-east of the source—similar results were observed for receivers to the southwest. The bars represent the percentage of the total model variance accounted for by each of the input parameters. A higher value indicates a greater contribution to the model variance—it should be noted that a high sensitivity does not indicate that the parameter contributes more to the overall noise level.

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Fig. 3 Shapley effects for the LAeq metric. Results are shown for no screening (left pane) and a 5.0 m absorptive barrier (right pane)

Fig. 4 Shapley effects for the LAmax metric. Results are shown for no screening (left pane) and a 5.0 m absorptive barrier (right pane)

4 Discussion The results presented in Sect. 3 represent the overall prediction model uncertainty for the different scenarios modelled in the MCS. The overall model uncertainty has been quantified by the standard deviation of the resulting output distributions. The range of model uncertainty over the day/night periods and north-east/south-west receiver positions is shown in Table 2 for the screened and unscreened scenarios at the four receiver distances. The uncertainty generally increases with increasing distance from the source. Table 2 Standard deviation of the model output uncertainty Metric LAeq LAmax

Screening

Standard deviation (dB) 200 m

400 m

600 m

800 m

No screening

4.2–4.4

5.4–5.5

6.0–6.2

6.6–6.8

5.0 m barrier

5.0–5.1

5.7–5.9

6.0–6.2

6.1–6.3

No screening

4.4–4.5

5.4–5.6

6.1–6.2

6.5–6.7

5.0 m barrier

5.6–5.7

6.2–6.4

6.5–6.6

6.6–6.7

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The parameter sensitivity analysis shows that meteorological effects have the largest contribution to the model uncertainty across all scenarios for both the LAeq and LAmax metrics. This indicates that the most effective strategy to reduce the overall model uncertainty would be to take local and temporal variations of meteorological conditions into account. The body aerodynamic and pantograph source term parameters are the most sensitive parameters relating to the source. In the screened scenario, the pantograph source showed the largest sensitivity and had an influence similar to the meteorological effect parameter for the LAmax metric at 200m. As with the findings for meteorological effects, this result suggests that reducing the uncertainty of the aerodynamic source term parameters would be an effective strategy to reduce the overall model uncertainty. Operational parameters such as speed, flows and proportion of catch-up services do not significantly affect the overall uncertainty of the model results. In the unscreened cases, uncertainties associated with ground absorption and atmospheric absorption contribute appreciably to the overall model uncertainty, particularly at larger propagation distances. In the screened cases, the uncertainty associated with barrier attenuation is significant and the relative contributions of ground absorption and atmospheric absorption to the overall uncertainty are reduced.

5 Conclusions This paper has presented an analysis to characterise and quantify the uncertainty of high-speed railway noise predictions via Monte-Carlo simulation and global sensitivity analysis. From the analysis of the overall model uncertainty, it was found that the overall model uncertainty has a standard deviation of 4–7 dB depending on distance from the source, position of the receiver, screening and time of day. The global sensitivity analysis revealed that meteorological effects and aerodynamic source term parameters had the largest contribution to the model uncertainty across all scenarios. Considering this, reducing the uncertainty of the aerodynamic source term parameters and consideration of local meteorological conditions would be an effective strategy to reduce the overall model uncertainty.

References 1. Hood R, Williams P, Collins K, Greer RJ (1991) The calculation of train noise. In: Proceedings. Institute of Acoustics 2. Manning CJ (1981) The propagation of noise from petroleum and petrochemical complexes to neighbouring communities. CONCAWE, Den Haag 3. Couto PRG, Damasceno JC, Oliveira SP, Chan WK (2013) Monte Carlo simulations applied to uncertainty in measurement. In: Theory and applications of Monte Carlo simulations, pp 27–51

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4. Saltelli A, Tarantola S, Campolongo F, Ratto M (2004) Sensitivity analysis in practice: a guide to assessing scientific models. Wiley, New York 5. HS2 Ltd. (2013) Sound, noise and vibration: methodology, assumptions and assessment (routewide) (SV-001-000, ES 3.5.0.10) 6. SALib—sensitivity analysis library in python [online]. Available https://salib.readthedocs.io/ en/latest/. Accessed 11 Jan 2021 7. Iooss B, Prieur C (2019) Shapley effects for sensitivity analysis with correlated inputs: comparisons with Sobol’ indices, numerical estimation and applications. Int J Uncertainty Quantification 5(4) 8. Nelsen R (2007) An introduction to copulas. Springer Science & Business Media 9. Song E, Nelson J, Staum J (2016) Shapley effects for global sensitivity analysis: theory and computation. SIAM/ASA J Uncertainty Quantification 4:1060–1083 10. Department for Transport (2021) The national technical specification notice (NTSN) rolling stock—noise (NOI) 11. Sica G, Marshall T, Sims J, Owen D, Bewes O (2022) Noise incentivisation for UK high speed train procurement. In: Proceedings—IWRN14 12. Mooney C, Duvall R (1993) Bootstrapping: a nonparametric approach to statistical inference. Sage 13. SETRA (2009) Road noise prediction 2—noise propagation computation method including meteorological effects (NMPB 2008) 14. Lutzenberger S, Gutmann C, Reichart U (2015) State-of-the-art of the noise emission of railway cars. In: Noise and vibration mitigation for rail transportation systems, Berlin

Towards Rail Noise Identification and Localization Based on Deep Learning Rui Xue, Guohua Li, and Xiaoning Ma

Abstract Noise and vibration remain a major reason for sustainable railways. Furthermore, noise and vibration in railways are often related to defects or faults. It is essential to understand the source of noise and vibration to identify the issue behind it. However, the complexity of noise analysis is embodied with acoustic signals with overlaps, as is usually the case in rail systems with the urban environment, while seldom discussed in previous studies. Leveraging cutting-edge acoustic processing, this study proposes a novel method incorporating trendy contrastive learning and neural network structure to identify overlapping noises and capture their directions. The model is validated on both the public sound and the synthetic rail datasets. Model effects on various sound conditions are then discussed. Results show that the proposed method offers a new perspective to disentangle intertwined noises, shedding light on mitigation measures and thus a sustainable rail system. Keywords Noise identification · Railways · Deep learning

1 Introduction Acoustic analysis holds significant promise in sound identification through the assessment of pitch, energy, sound entropy, and spectral characteristics [1]. The proliferation of technology and the miniaturization of electronic devices have made acoustic measurement sensors widely accessible [2]. Acoustic signals find application in various railway scenarios, including defect detection [3] and noise mapping [4], with potential extensions to predictive maintenance and strategy development. Despite its potential, acoustic monitoring remains relatively underutilized in the railway sector, primarily due to the complex nature of real-world sound data, often consisting of multiple concurrent events and ambient noise. This complexity, as R. Xue (B) · G. Li · X. Ma China Academy of Railway Sciences Co. Ltd., Beijing 100081, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_11

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Fig. 1 Complex noise monitoring and localization in the rail sector

depicted in Fig. 1, poses challenges for noise monitoring and localization, especially in urban rail environments, a facet largely overlooked in previous studies, thus limiting acoustic applications in rail. Fortunately, advances in acoustic analysis, particularly in sound event localization and detection (SELD), offer a promising avenue to address overlapping sound events. However, numerous unresolved issues from prior research underscore the need for further exploration in this area. To address the challenge of simultaneous noise sources in rail systems, we introduce Corail, a novel deep learning-based approach. Corail employs contrastive learning to create signal representations for untangling overlapping noises, followed by a deep joint learning structure for their classification and localization. Leveraging state-of-the-art learning models, Corail unlocks new insights and solutions for a range of potential rail applications. This paper unfolds as follows: Sect. 2 reviews related work, Sect. 3 presents the methodology with a detailed framework description and evaluation metrics. Section 4 validates the model with a case study and finally the conclusion is in Sect. 5.

2 Related Work 2.1 Sound Event Localization and Detection Sound event localization and detection (SELD) represents a multi-task learning challenge that involves both sound type classification and direction of arrival (DOA) estimation [1]. This process, critical for applications in monitoring and robotics, has garnered substantial attention in the field of audio processing. Prior research has explored sound event detection and localization using signal processing techniques and tracking algorithms, such as the TRAMP algorithm [5]. Unfortunately, these feature-based solutions are hampered by the need for humandefined parameters, including window size, hop size, and filter bank type, which significantly impact model performance and adaptability across diverse scenarios. In recent years, deep learning-based methods have shown remarkable promise in sound event detection and localization [2]. These contemporary models demand

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fewer handcrafted features than conventional algorithms but still necessitate labeled training data. Many of these models incorporate two networks—one for sound event detection (SED) and the other for DOA estimation [6]. However, this dualnetwork approach increases system complexity and model size, posing challenges in terms of parameter optimization. Recently, the convolutional recurrent neural network (CRNN) model and its end-to-end trained variations have been introduced for SELD, allowing joint detection of sound events and DOA estimation [7]. Nonetheless, SELD remains challenging in acoustic environments characterized by varying impulse responses, ambient noise, and interference.

2.2 Acoustic Monitoring and Analysis in Railways Recent research in acoustic analysis within the railway domain has primarily concentrated on defect detection and noise mapping. When the train wheels contact the rail, any motion resulting from track surface irregularities creates vibration and distinct noise, differentiating this defect from regular rolling noise. Acoustic analysis thus proves invaluable for detecting rail surface defects. For example, a railway track fault detection system was developed to identify burnt wheels and elevated rails. Deep learning models, such as convolutional neural networks, have been applied to process MFCC data [3]. Another non-linear time-domain model, known as WERAN, was introduced to analyze axle box acceleration (ABA) and under-coach noise measurements, facilitating the identification of faults in the German railway network, with a primary focus on squats [8]. Acoustic analysis also plays a crucial role in assessing railway noise. Various countries have adopted diverse noise reduction strategies in railways, ranging from infrastructure-based measures to a combination of rolling stock modifications and noise barriers [4]. Projects like HARMONISE and IMAGINE have developed a universal framework for distinguishing different railway noise sources [9]. Despite previous research efforts, the potential applications of acoustic analysis in railways remain vast. Noise analysis complexity is amplified in railway systems in urban environments due to signal overlaps, a facet often overlooked in previous studies.

3 Methodology This approach, seen in Fig. 2, includes two phases, the first one of which is signal representation by contrastive learning, and the other is noise detection and localization through a neural network structure.

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Fig. 2 The framework of Corail

3.1 Signal Representation A general sound representation can be defined with class and location (directionof-arrival, DOA). Each sound example a, a ∈ RC×T can be represented as C-class T-frame activities, whose reference value of each activity is 1 when an event is active and 0 when inactive. Meanwhile, the sound localization R, R ∈ R3×C×T be Cartesian DOAs, three nodes corresponding to the location in x, y, and z axes, where the length of each Cartesian DOA is 1. Thus, the sound representation E can be formulated in Eq. (1). E ct = act Rct

(1)

where Ect refers to the sound representation of type C and time frame T, act , states the Boolean representation of sound activity, and Rct demonstrates the Cartesian DOA of the sound. Based on Eq. (1), the sound activity can be detected as described in Eq. (2) and Cartesian DOA can be obtained as Eq. (3) when the sound representation is learned in the trained model. act = E ct 

(2)

E ct E ct 

(3)

Rct =

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Acoustic embeddings are learned through multi-view pre-training neural networks with a contrastive loss. Contrastive learning aims to learn discriminative representations by pulling similar samples into close positions in the embedding space while pushing dis-similar ones far apart [10]. Sound class and DOA are selected as contrastive views considering that these two tasks require different features from acoustic signals. Sound identification mainly relies on time–frequency patterns while direction estimation focuses on the magnitude or phase differences between microphones. Therefore, the signal representation includes class embeddings and DOA embeddings. Each part iterates with a clustering algorithm, based on cosine similarity, and a convolutional recurrent neural network (CRNN) as the updated encoder. E t = Fθ (I t )

(4)

where I t is the input instance, E t represents the sound embedding, and Fθ indicates the convolutional recurrent neural network that works as the encoder model. L cn = −

c c+ N 1  ecos( E n , E n ) log c c+ c c− N n=1 ecos( E n ,E n ) + ecos( E n ,E n )

(5)

where cos refers to the cosine similarity, N states the number of sound instances c− E cn E c+ n , and E n are the learned embeddings of the noise representation, its positive sample and its negative sample. Here the positive sample means E c+ n shares the same belongs to a different class. sound type with E cn , while the negative one denotes E c− n The distance contrastive loss L dn can be defined in a similar way. Combining these two aspects, the optimized function of signal representation can be defined as follows.  1   λ · L cn + λˆ · L dn N · |C| n=1 c=1 N

L r ep =

C

(6)

where λ and λˆ are hyper-parameters, L cn and L dn stand for class contrastive loss and distance contrastive loss, respectively.

3.2 Noise Identification and Localization In the noise identification and localization phase, signal representations are taken as inputs of a jointly-trained CRNN structure to estimate outputs. Similar to the activity-coupled Cartesian direction of arrival representation (ACCDOA) model [11], we unify the sound detection and localization losses into a single regression loss to simplify the architecture in this part. The mean square error (MSE) is measured as a single loss function, shown in Eq. (7).

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L loc =

C T   1  M S E E ∗ct , E ct CT c t

(7)

where E ∗ct and E ct embody the ground truth and learned sound representations. MSE means the mean square error. Similarly, c denotes the sound class and c ∈ E, and t refers time frequency and t ∈ T . Therefore, the overall loss function comes with the sum of optimal equations from these two phases. L = L r ep + L loc

(8)

3.3 Evaluation Metrics The localization error (L E C D ), localization recall (L R C D ), location-dependent error rate (E R 20◦ ) and F-score (F20◦ ) were adopted for the evaluation. L E C D expresses the average angular distance between the predictive one and ground truth. L R C D tells the true positive rate of sound detection. E R 20◦ and F20◦ measure the error and precision rates of predictions that fall close enough with the ground truth (less than 20°). A good model should perform low L E C D , high L R C D , low E R 20◦ and high F20◦ .

4 Case Study 4.1 Datasets and Experiments The public spatial sound dataset, named TAU-NIGENS spatial sound events dataset, introduces localized interfering events that are naturally encountered in real environments [12]. Sampled at 24 kHz, the recordings are offered in two 4-channel spatial audio formats, signals of a tetrahedral microphone array (MIC) and firstorder Ambisonics (FOA). Multichannel ambient noise was collected in each room with the same recording setup and added to the event mixtures. Another dataset that is used to verify this model is generated with isolated sounds in rail. Five types and more than 4200 rail-related sound clips are collected, covering fans, gearboxes, pumps, slide rails, and valves. Each sound clip contains 10 s of single-channel 16-bit audio data sampled at 16 kHz. We compare the proposed method with a state-of-the-art baseline method, named SELDnet [7]. We train both models with multichannel log-mel spectrograms as inputs, together with acoustic intensity vectors for FOA, and generalized crosscorrelation sequences for the MIC. We set the sampling frequency to 24 kHz, and

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apply the short-term Fourier transform (STFT) with a configuration of 20 ms frame length and 10 ms frame hop. During the training process, we adopt a batch size of 32. In addition, we use Adam as the optimizer with a learning rate of 10−6 for 100 epochs. Cross-validation is used to select the best parameters.

4.2 Results and Discussion The model performance of Corail and SELDnet on both public and rail sound datasets are presented in Tables 1 and 2. The results show that the proposed method, Corail, brings large gains in detection and improves localization accuracy on both datasets, though this challenging task seem still has a long way to go, as intended. In general, the MIC dataset exhibits a worse performance than FOA in all cases. This fact may be attributed to the input features employed in the baseline for each format. GCC sequences for the MIC format may become very noisy in complex scenes with multiple simultaneous events, while the intensity vectors of the FOA format can potentially retain robustness due to their narrowband nature and sparsity of the sound signals in the time–frequency domain. We further undertake a comprehensive examination of the effects of our proposed model on segmented sound components. To provide clarity, we define the following key terms: (1) Targets: These are the sound events we aim to identify and track. Table 1 Overall performance on TAU-NIGENS FOA

MIC

L EC D

L RC D

E R 20◦

F20◦

L EC D

L RC D

E R 20◦

F20◦

Baseline

32.3°

45.2%

0.78

24.7%

38.6°

43.9%

0.83

20.2%

Corail

24.8°

46.3%

0.74

30.3%

37.8°

44.8%

0.71

22.4%

w/o class

25.2°

45.6%

0.77

26.7%

38.4°

43.6%

0.78

21.2%

w/o distance

26.6°

45.2%

0.76

24.9%

38.2°

44.2%

0.74

20.8%

Table 2 Overall performance on the synthetic rail dataset FOA

MIC

L EC D

L RC D

E R 20◦

F20◦

L EC D

L RC D

E R 20◦

F20◦

Baseline

32.1°

44.6%

0.77

24.8%

37.9°

37.9%

0.81

19.5%

Corail

29.1°

45.8%

0.76

27.9%

38.7°

44.6%

0.76

21.6%

w/o class

29.8°

44.6%

0.77

26.7%

38.4°

43.5%

0.78

20.2%

w/o distance

31.1°

45.1%

0.76

24.9%

38.2°

44.2%

0.80

21.2%

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Table 3 Further comparison on TAU-NIGENS FOA

MIC

L EC D

L RC D

E R 20◦

F20◦

Targets

20.1°

60.3%

0.55

Targets with ambience

22.4°

52.6%

0.56

Targets with interferers 26.7°

46.2%

Overall combinations

46.3%

24.8°

L EC D

L RC D

E R 20◦

F20◦

57.3% 22.0°

56.4%

0.59

52.6%

46.6% 22.8°

53.6%

0.62

33.9%

0.73

32.3% 38.6°

45.7%

0.73

24.6%

0.74

30.3% 37.8°

44.8%

0.71

22.4%

Table 4 Further comparison on the synthetic rail dataset FOA

MIC

L EC D

L RC D

E R 20◦

F20◦

L RC D

E R 20◦

F20◦

Targets

22.7°

58.4%

0.58

50.6% 24.2°

L EC D

52.6%

0.61

50.2%

Targets with ambience

23.1°

55.6%

0.62

45.9% 31.6°

49.8%

0.64

33.8%

Targets with interferers 30.2°

46.2%

0.73

29.6% 39.5°

49.1%

0.76

23.2%

Overall combinations

45.8%

0.76

27.9% 38.7°

44.6%

0.76

21.6%

29.1°

(2) Ambience: This signifies the background noise collected under the same settings, with noise levels scaled to create signal-to-noise ratios (SNRs) ranging from 6 to 30 dB. (3) Interferers: In this context, interferers represent other sound events that act as potential sources of interference, designed to challenge the model’s performance. A range of distinctive conditions are generated by blending sound elements, targets, targets with ambience, targets with interferers, and holistic combinations that faithfully emulate real-world acoustic scenarios. The model’s performance results on both datasets are presented in Tables 3 and 4. As anticipated, the model exhibits its most effective performance on clean target sounds compared to other conditions. Performance declines when dealing with sound combinations, whether target sounds with ambience or interference. Notably, the addition of ambient noise to target sounds has a subtle but discernible impact, indicating that background noise adversely affects model performance in practical scenarios. This slight effect may stem from the varying SNRs across the recordings and warrants further investigation in future research.

5 Conclusion This study introduces an innovative approach, merging trendy contrastive learning and neural network architecture to discern overlapping noises and pinpoint their origins, providing valuable insights into mitigation strategies for a sustainable rail

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system. The proposed model advances the development of well-designed SELD systems, with potential applications encompassing noise mapping, noise reduction strategy formulation, rail defect monitoring, and predictive track maintenance, among others.

References 1. Evers C, Löllmann HW, Mellmann H, Schmidt A, Barfuss H, Naylor PA, Kellermann W (2020) The LOCATA challenge: acoustic source localization and tracking. IEEE/ACM Trans Audio Speech Lang Process 28:1620–1643 2. Grumiaux PA, Kiti´c S, Girin L, Guérin A (2021) A survey of sound source localization with deep learning methods. arXiv preprint arXiv:2109.03465 3. Shafique R, Siddiqui HUR, Rustam F et al (2021) A novel approach to railway track faults detection using acoustic analysis. Sensors 21(18):6221 4. Oertli J (2008) Overview of railway noise control in Europe. J Acoust Soc Am 123(5):3258 5. Kiti´c S, Guérin A (2018) Tramp: tracking by a real-time ambisonic-based particle filter. arXiv preprint arXiv:1810.04080 6. Cao Y, Kong Q, Iqbal T, An F, Wang W, Plumbley MD (2019) Polyphonic sound event detection and localization using a two-stage strategy. arXiv preprint arXiv:1905.00268 7. Adavanne S, Politis A, Nikunen J, Virtanen T (2018) Sound event localization and detection of overlapping sources using convolutional recurrent neural networks. IEEE J Sel Top Sig Process 13(1):34–48 8. Pieringer A, Stangl M, Rothhämel J, Tielkes T (2021) Acoustic monitoring of rail faults in the German railway network. In: Noise and vibration mitigation for rail transportation systems. Springer, Cham, pp 242–250 9. Szwarc M, Kostek B, Kotus J, Szczodrak M, Czy˙zewski A (2011) Problems of railway noise—a case study. Int J Occup Saf Ergon 17(3):309–325 10. Tian Y, Sun C, Poole B, Krishnan D, Schmid C, Isola P (2020) What makes for good views for contrastive learning? Adv Neural Inf Process Syst 33:6827–6839 11. Shimada K, Koyama Y, Takahashi N, Takahashi S, Mitsufuji Y (2021) ACCDOA: activitycoupled Cartesian direction of arrival representation for sound event localization and detection. In: ICASSP 2021–2021 IEEE international conference on acoustics, speech and signal processing (ICASSP). IEEE, pp 915–919 12. Trowitzsch I, Taghia J, Kashef Y, Obermayer K (2019) The NIGENS general sound events database. arXiv preprint arXiv:1902.08314

Relationship Between Train Horn Sound Levels Tested at 25 m and Sound Levels Experienced at Distance by Track Workers Martin Toward, Marcus Wiseman, Michael Lower, and David Thompson

Abstract The factors that affect sound propagation and audibility of train horns were investigated. Sound levels from a static horn above a test track decayed by 6 dB per doubling of distance up to about 30 or 50 m. At greater distances the level decayed by approximately 12 dB per doubling of distance—significantly higher than would be expected from spherical spreading. The effective range of a horn was found to depend on its height—at 400 m, the sound level from a horn 2.5 m above the ground was about 10 dB higher than one at 0.5 m, despite levels at 25 m being the same. At two mainline sites, the mean attenuation rates beyond 90 m were around 9 and 11 dB per doubling of distance respectively. At the second site, horn sound levels were highly correlated with distance. At the first site, horn levels were poorly correlated, suggesting variability in propagation or source sound levels. Keywords Train horn · Sound propagation · Audibility

1 Introduction The current minimum and maximum sound levels for the warning horns of new classes of train in Great Britain are specified at 25 m from the train in EN 151532 [1] and Railway Group Standard GM/RT2131 [2]. Although sound levels from horns comply with the version of the standard in force when each train class enters service, the specified levels have changed over the years, and the Rail Safety and Standards Board (RSSB) has received reports from track workers that the horns of some newer trains are quieter and less audible than horns of older trains. This work was undertaken to determine horn sound levels in practice, and the various factors that affect sound propagation and the sound levels experienced by track workers at some distance down the track. M. Toward (B) · M. Wiseman · M. Lower · D. Thompson Institute of Sound and Vibration Research, University of Southampton, Southampton SO17 1BJ, UK e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_12

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2 Methodology In ‘static tests’, sound levels from a stationary, Trent KSJ-2 (370 Hz) horn, were measured at a railway test track near Tuxford. The sound levels were measured simultaneously at 5, 10, 25, 50, 100, 200, 400 and 800 m from the horn. The height of the horn was varied in 0.5 m steps from 0.5 to 3.0 m above the ballast. The tests were supplemented by modelling using CadnaA software. Figure 1 shows the spectrum of the horn which is rich in harmonics [3]. Figure 2 shows the static test site. The test track was straight to about 350 m, with a shallow curve beyond. ‘Dynamic tests’ were then carried out with in-service trains at two rural, mainline sites, shown in Fig. 3. At Site 1, near Didcot on the Great Western Main Line, the line speed was 200 km/ h and traffic was a mix of Class 800 bi-mode powered multiple unit passenger trains operating in overhead electric mode and some Class 66 diesel-hauled freight. These passenger trains were fitted with horns about 0.4 m above the rails (0.6 m above the ground). The horns of Class 66 locomotives are nearly 4 m above ground. Fig. 1 Spectrum of the Trent Instruments KSJ-2 horn, nominally 370 Hz

Fig. 2 a View of test track. b The horn mounted above the test track

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Fig. 3 Dynamic test sites. a Site 1 (Great Western Main Line; four track). b Site 2 (South West Main Line; double track)

Site 2, near Basingstoke on the South West Main Line, had a line speed of 160 km/ h and traffic was mainly Class 444/450 passenger third-rail electric multiple units and some Class 66 diesel-hauled freight. The electric passenger trains had horns close to the coupler, about, 1 m above the ground. Both sites were chosen because they were close to uncontrolled foot crossings with ‘whistle boards’ which ensured that horns would be sounded on approach. Horns at both sites had nominal fundamental frequencies of 311 and 370 Hz, the two tones generally in use in Britain. Measurements were made in February and March at Site 1 and in April 2021 at Site 2. Horn sound levels and ambient noise levels were measured with microphones at 7.5 m from the track centre ahead of the trains at a height of 1.5 m above the ground. The rail vibration was recorded synchronously using accelerometers and enabled the train speeds to be accurately determined. The position of each train when the horn was sounded could be calculated from the train speed, the speed of sound, and the time of arrival of the sound at the microphones. During both the static tests and the dynamic tests, panels of experienced track workers were asked to rate the audibility of the horns. These ratings were correlated against measured sound levels. Weather conditions, including wind speed and direction, were recorded.

3 Results 3.1 Static Tests The sound levels measured in the static tests are shown in Fig. 4. Each data point is an average of three runs. The sound levels from the horn decayed at 6 dB per doubling of distance (6 dB/dd), due to spherical spreading, but only up to a distance of about

144 Fig. 4 Sound levels at distances from 5 to 800 m from the horn in static tests, measured 1.5 m above the ground. The broken lines show −6 and −12.2 dB/dd

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Horn height above ground, m

Fig. 5 Sound levels at 200, 400 and 800 m relative to the level at 25 m

50 m for a horn mounted at a height of 1.5 m or above, and only up to about 30 m for a horn at a height of 0.5 m or 1 m. Beyond 50 m for the high-mounted horn, and beyond 30 m for the low-mounted horn, the sound level decayed at approximately 12 dB/dd. The ground surface may affect the attenuation rate, e.g. for slab track the decay at 6 dB/dd might extend to greater distances. This could be investigated in future tests. Figure 5 shows the variation in sound levels with the height of the horn. At 200 and 400 m, the sound level from a horn 2.5 m or 3 m above the ground was about 10 dB higher than the sound level from a horn only 0.5 m above the ground, although there was virtually no difference in the sound levels measured at 25 m. The effect of horn height is very important.

3.2 Modelling of Static Tests A noise model of the static site was used to compare predicted levels with the measured levels along the track. The calculation procedures in ISO 9613-2:1996 [4] were implemented using CadnaA software and a digital terrain model of the local topography. Receiver heights were 1.5 m above the ground, and the horn or source height was varied between 0.5 and 3.0 m above the ground. Attenuation of the ground and ground cover were modelled and meteorological conditions including

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wind speed and direction were matched to those on the day that the measurements were made. Although the horn sound levels predicted by the ISO 9613-2 model were roughly in agreement with measured levels when topology and weather conditions were accounted for, predicted sound levels were typically higher than those actually measured. The model overestimated sound levels at 200 and 400 m by approximately 5 dB for horn heights of 1.5 m or 3.0 m. The ISO model is a simple ‘broad-brush’ model often used in estimating noise levels in land-use planning and noise mapping and is best suited for use in meteorological conditions favourable to propagation, usually downwind. It is less suited to conditions prevailing during the static tests, with a light breeze of 4 m/s towards the source. In practice, propagation will vary and not always be favourable. While the measurements showed the horn height to have a large influence on the sound levels at 200 and 400 m, about 10 dB as shown in Fig. 5, the model showed a more modest effect of horn height. A horn at 3.0 m above the ground had a predicted level only 2 dB higher than the horn at 0.5 m at 200 m, and only 4 dB higher at 400 m.

3.3 Dynamic Tests The sound levels measured 1.5 m above the ground in the dynamic tests at Sites 1 and 2 are shown in Figs. 6 and 7 respectively. Both A- and C-weighted levels were measured but only the A-weighted levels are shown here. For comparison, the green crosses show the current maximum and minimum sound levels at 25 m, the levels in dB(A) are estimated by subtracting 2 dB from the C-weighted levels specified in GM/RT2131 [2]. In Fig. 6, the specified levels at 25 m are for trains travelling above 160 km/h. In Fig. 7, specified levels are for trains travelling at or below 160 km/h. Although Fig. 7 shows the current maximum and minimum horn levels at 25 m, the horns of the trains shown in this figure comply with an earlier standard for trains travelling at or below 160 km/h. This earlier standard specified higher sound levels. Fig. 6 Measured horn sound levels (L AFmax ) at Site 1 (Didcot)

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Fig. 7 Measured horn sound levels (L AFmax ) at Site 2 (Basingstoke)

At Site 1 the correlation of sound levels of the Class 800 horns with distance was poor, with a wide scatter in sound levels (R2 = 0.45 on Day 1; R2 = 0.55 on Day 2). The trend lines were −8.2 dB/dd on Day 1 in February, and −10.7 dB/dd on Day 2 in March. In contrast, at Site 2 the sound levels for the Class 444/450 horns were highly correlated with distance from the train (R2 = 0.90), and the slope of the trendline was −13.3 dB/dd. Although there may have been some differences in the sound propagation between the two days at Site 1, there was little wind on both days. It is possible that the wide scatter of results on each day could be caused by minute-to-minute variations in propagation but it could also indicate some variability in the sound levels from the horns at source. Two or three microphones were placed at various positions alongside the tracks at each test site, and in some cases the same horn sounding was recorded at two microphones. Because the position of each train was known when its horn was sounded, the sound attenuation rate could be calculated for individual horn blasts from the difference in sound levels between two microphones each at a known, but different, distance from the train. The distances from the train ranged from 90 to 450 m. The measured attenuation rates are shown in Fig. 8. The average attenuation rates at distances beyond 90 m were, as expected, usually higher than 6 dB/dd. At Site 1, the attenuation rate varied between 6.2 and 14.3 dB/ Fig. 8 Measured attenuation rates of individual horn soundings at distances greater than 90 m

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dd with a mean of 9.2 dB/dd. At Site 2, the attenuation rate varied from 8.5 to 12.5 dB/dd, with a mean of 10.7 dB/dd. As each attenuation rate was derived from measurements at two positions of the same horn, the measured attenuation rates do not depend on the absolute sound level output of each individual horn, provided that the horn sound levels are sufficiently above the background noise.

4 Audibility During the static and dynamic tests, experienced track workers whose hearing met the requirements for their job were asked to rate the sound levels of the horns they heard. In the static test, they were asked two questions; Q1: was the horn ‘clearly audible’ or ‘not clearly audible’ and Q2: was the horn (a) easy to hear, (b) difficult to hear, or (c) inaudible. In the dynamic tests track workers were asked Q2 above but were also asked to rate the horn sound levels on a five-point scale from ‘not audible’ to ‘clearly audible’. Two established methods were used to determine the minimum recommended levels for warning sounds. Both methods, (i) the Detectsound software [5] and (ii) the one-third octave band method, method (c), of ISO 7731 [6] calculate the masked threshold imposed by the background noise and then recommend that the components of the warning horn should exceed the masked threshold by a specified margin. During the static tests, the horn level at the workers’ location was controlled by varying their distance from the horn and by adjusting the air pressure that controlled the horn’s output. In the dynamic tests, the sound level could only be varied by positioning the track workers closer or farther from the whistle boards, but the train drivers also sounded their horns as soon as they spotted the track workers in the cess. This is standard practice, but also gave a wider range of horn sound levels for the track workers to rate. The track workers found the horn sound levels clearly audible when the horn levels were at or above the minimum predicted using either Detectsound software or method (c), of ISO 7731, with Detectsound being more consistent and accurate. Method (c) of ISO 7731 is, however, simpler and quicker in practice, and the better accuracy of Detectsound is outweighed in practical outdoor applications which are less well controlled than indoor environments. It was also noted that horn sound levels were ‘clearly audible’ to the track workers when the A-weighted horn level was 7 dB above the A-weighted background noise. However, this finding is based on limited data and may not be universally applicable. At Site 1 track workers commented that horns of the Class 800 trains were quieter than the horns of the Class 43 trains that they replaced. Class 43 trains no longer run at Site 1, so it was not possible to measure their horn sound levels for comparison. Also, at Site 1, the whistle boards are presumably positioned so that a horn should be audible at their associated foot crossing. Nevertheless, in 24% of the pass-bys, only half the subjects or fewer located at this crossing rated the horns as “clearly audible”.

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5 Conclusions Sound levels from a stationary train horn measured along the track decayed at 6 dB/ dd, but only up to 30 m or 50 m depending on the height of the horn above the ground. Beyond 30 m or 50 m, with ballasted track, the sound attenuated at about 12 dB/dd. At 200 and 400 m the sound level of a horn mounted 2.5 m or 3.0 m above the ground was about 10 dB higher than the sound level of the same horn at 0.5 m above the ground. The height of a horn is important; it will affect sound levels at long distances, but not at the standard test distance of 25 m specified in EN 15153-2. The fitting of horns close to the ground would best be avoided in future designs. The mean attenuation rates beyond 90 m for trains travelling at speed varied considerably. At Site 1, the attenuation rate for individual horn soundings varied between 6.2 and 14.3 dB/dd with a mean of 9.2 dB/dd. At Site 2, the attenuation rate varied from 8.5 to 12.5 dB/dd, with a mean of 10.7 dB/dd. Acknowledgements This work was undertaken for, and funded by, the Rail Safety and Standards Board as part of project T1205. Trent Instruments made horns available for the static testing.

References 1. European Committee for Standardization (CEN): EN 15153-2:2020 (2020) Railway applications—external visible and audible warning devices. Part 2: Warning horns for heavy rail, Brussels 2. RSSB: Railway Group Standard GM/RT2131 Issue 1 (2015) Audibility and visibility of trains. Rail Safety and Standards Board, London 3. Toward M, Lower M, Wiseman M, Thompson D, Ferraby P (2022) Sound propagation and audibility of train horns. In: Proceedings of Inter-noise 2022, Glasgow 4. International Organization for Standardization: ISO 9613-2:1996 (1996) Acoustics—attenuation of sound during propagation outdoors. Part 2: General method of calculation, Geneva, Switzerland 5. Zheng Y, Giguère C, Laroche C, Sabourin C (2003) Detectsound Version 2: a software tool for adjusting the level and spectrum of acoustic warning signals. Can Acoust 31(3):76–77 6. International Organization for Standardization. ISO 7731-2003 (2003) Ergonomics—danger signals for public and work areas—auditory danger signals, Geneva, Switzerland

Considerations for the Implementation of a Train Vibration Monitoring System in Subway Tunnels Shannon McKenna, Shankar Rajaram, James Tuman Nelson, and Hugh J. Saurenman

Abstract The Northgate Link extension of the Sound Transit Link Light Rail system starts at the southern end of the University of Washington (UW) Seattle campus and extends northward beneath the campus in twin-bore tunnels. To address UW concerns that train-generated ground vibration may negatively affect sensitive research, Sound Transit agreed to install a vibration monitoring system in the tunnels and use the measured tunnel vibration to identify any trains that generate vibration that might exceed negotiated limits. Prior to train operations, the relationships between the third octave vibration measured by the monitors within the tunnel and in the sensitive facilities were estimated using a shaker as a vibration source. This paper describes the verification phase of the project, where vibration from test-train operations was used to refine the estimates based on the shaker data. Keywords Groundborne vibration · Vibration monitoring · Vibration sensitive laboratories

S. McKenna (B) Cross-Spectrum Acoustics, 400 Corporate Pointe, Suite 300, Culver City, CA 90230, USA e-mail: [email protected] S. Rajaram Sound Transit, 401 S Jackson Street, Seattle, WA 98104, USA e-mail: [email protected] J. T. Nelson Wilson Ihrig & Associates, 5900 Hollis St, Suite T1, Emeryville, CA 94608, USA e-mail: [email protected] H. J. Saurenman ATS Consulting, 130 W Bonita Avenue, Sierra Madre, CA 91024, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_13

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1 Introduction Sound Transit’s Link light rail system in Seattle opened the Northgate Link extension in October 2021. This extension has a twin bore train tunnel passing under the University of Washington (UW) campus. To protect the research environment on campus, UW and Sound Transit entered into an agreement over two decades ago that requires the train-generated third octave vibration to not exceed specific vibration thresholds for several research buildings. To implement the agreed upon vibration thresholds, the agreement also requires a vibration monitoring system. During preliminary engineering, monitoring of tunnel structure vibration was determined to be most practicable compared to monitoring vibration in the various laboratories to avoid background vibration. A major challenge to implement the tunnel vibration monitoring system for UW was to determine the relationship between the third octave vibration measured on the tunnel bench by the permanent monitors and in the UW buildings located between 60 and 900 m away from the train tunnels. This relationship between tunnel and building vibration is referred to in this paper and in [1, 2] as vibration adjustment estimates (VAEs). The third octave vibration measured on the tunnel bench plus the third octave VAE provides an estimate of the third octave vibration inside the sensitive UW research facilities. After the subway tunnel was constructed, but before the track slab was installed, the VAEs were estimated by using an electrodynamic shaker mounted on the tunnel invert and geophones on the tunnel bench and in up to 12 buildings on the UW campus. These data were used to estimate the VAE’s for a point source in the tunnel, and an adjustment was used to estimate the line-source VAE’s to represent the distributed line source of the moving light-rail train. The measured data were extrapolated to determine the VAE’s at all 24 sensitive research buildings identified by UW. This process of VAE development is described in [2]. A verification phase of the VAE development was completed during test-train operations in Spring 2021. Train vibration data were collected on the tunnel invert and inside the same UW sensitive research buildings. The train vibration levels measured in the buildings were compared with the levels that were predicted using the VAEs and the vibration levels measured on the tunnel bench. The VAEs estimated with the shaker data were refined using the test-train data where there were discrepancies. Additionally, the verification phase included ambient vibration measurements at all 31 vibration monitoring positions in the tunnel. The ambient data were analyzed to determine the likelihood of non-train vibration at the tunnel monitoring positions falsely indicating an exceedance on the UW campus. This paper focuses on the data collected and lessons learned from the verification phase of the VAE development.

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2 Background In 2016, the University Link extension opened which reached the southern edge of the UW campus. A monitoring system comprising nine vibration monitors was installed in the tunnels within the University campus. An approach to estimate the relationship between those initial vibration monitoring sites in the light-rail tunnel and the vibration at the buildings on campus for the University Link was documented in 2016 [1]. The vibration attenuation estimates were defined as: V AE ∼ = Lv( f acilit y) − Lv(V M Sn )

(1)

where VAE is the third octave vibration adjustment estimate from monitor n to the research facility, Lv(VMS n ) is the measured vibration in the light-rail tunnel at monitor n, and Lv(Facility) is the estimate of the resulting vibration level at the research facility on the campus. Thus, the VAE is added to the tunnel vibration level to estimate the facility vibration level in decibels. The Northgate Link extension, which opened in October 2021, continued the University Link line north underneath the UW campus with 31 additional vibration monitors placed in the twin bore tunnels every 45 m between the UW station and the U District station. Beginning at the northern end of the UW Station is a 5 Hz floating slab track that extends about 1160 m before transitioning to standard track with resilient direct fixation fasteners [3]. The Northgate Link extension required that the VAE be developed from each of the 31 monitors to 24 buildings on the UW campus in 1/3 octave bands from 2 to 100 Hz. Improving the accuracy of the VAEs compared to the methodology for the University Link was critical because the Northgate Link would pass closer to sensitive research facilities. A three-phase approach was developed: • Phase 1—Exploratory Measurements: Testing equipment and measurement procedures between a few monitoring positions and buildings to develop a robust test plan for Phase 2. • Phase 2—Field Testing: Collect vibration propagation data between most of the 31 monitoring positions in the tunnel and more than 10 buildings across the UW campus. This phase was described in [2]. • Phase 3—Verification and Debugging: Measure vibration in the tunnel and UW buildings during pre-revenue and revenue service to verify the VAEs developed in Phase 2 and, where necessary, propose refinements to the VAEs. The VAE Verification Phase had two components: (1) vibration measurements during test train operations in both the Northgate Link tunnels and UW buildings and (2) Ambient vibration measurements in the tunnels to investigate the potential for false positives.

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3 Verification Phase Methodology 3.1 Vibration Measurements During Test Train Operations The goal of the vibration measurements during test train operations was to verify the VAE developed in Phase 2 by completing simultaneous vibration measurements in the tunnel and at the sensitive receiver buildings. A test train was made available for six nights. Due to the number of monitoring positions (31) and sensitive research buildings (24), it was not possible to measure at all locations at once. On each of the six nights of measurements, data were collected at six monitoring locations in the tunnel and at five locations within the sensitive research facilities. The following additional considerations were taken into account when developing the verification phase test plan: • The verification measurements were completed using a test train prior to beginning pre-revenue service and prior to installation of the permanent monitoring system to ensure that the VAE values were a best estimate and that issues with the monitoring system would not delay the start of pre-revenue or revenue service. • Measurements were completed at all 31 vibration monitoring positions. Establishing train-generated vibration levels at all 31 monitoring positions was important to identify any possibility of exceedance of the vibration limits. Data were not collected at all of the farthest vibration-sensitive buildings on the UW campus where it would be highly unlikely to measure train vibration above ambient levels, based on prior shaker testing results. • Geophones similar to those used for the permanent monitoring system were used to measure the vibration levels. • The data collected in the tunnels and the data collected in the UW buildings were recorded with independent data recorders that were synchronized to within 1-s. Precise time synchronization was not necessary because there was no need for time-series analyses. This significantly reduced the complexity of the field measurements from Phase 2 where precisely synchronized data were necessary to calculate accurate transfer mobilities using time-series analyses. • Sound Transit operates two different light-rail vehicles (Siemens and Kinkysharyo). Prior to the verification measurements, the Kinkysharyo vehicle was identified as likely to produce higher vibration levels, so that the Kinkysharyo vehicle was selected as the test train. • Data were collected at speeds from 40 to 72 kph to quantify the variability of train vibration levels with respect to speed. The planned operational speed in the tunnel is 56 kph. The minimum design speed assumption was 48 kph. A key component to the success of the verification phase measurements was that a test train was made available to the VAE team that could be operated exclusively for the purposes of the vibration measurements at the speeds that were planned. Extensive coordination between the UW, Sound Transit, the measurement team, and

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Sound Transit’s contractors working in the tunnels was also required to successfully execute the measurement plan.

3.2 Ambient Vibration Measurements in the Tunnels Ambient vibration data were measured to investigate the potential for “false positives”, or ambient vibration events that exceed the vibration limits on the tunnel bench when no trains were operating. The following ambient vibration data were collected: 1-h of data prior to test train operations at all 31 monitoring positions 24-h of ambient data at a total of 12 measurement positions spread throughout the two tunnels. The 24-h of ambient data were necessary to confirm ambient levels during daytime hours. The test train operations were completed overnight, when ambient vibration levels are typically at their lowest. Ambient measurements revealed that low frequency vibration transients occurred every few minutes that greatly complicated the measurements. These were determined to be seismic tremors related to the Cascadia subduction zone with spectral energy below about 6 Hz. Discrimination of train vibration from seismic vibration at 6.3 Hz and lower frequencies required careful identification of train passage times. Many of the low frequency vibration samples had to be discarded.

4 Verification Phase Measurement Results 4.1 Train Vibration in Tunnel Vibration data from the test trains were examined at all 31 vibration monitoring stations to observe variation in data between the different monitoring positions and different speeds. The following were observations from the vibration measured on the tunnel bench: • Some of the highest train vibration levels were measured near the station platforms as trains were accelerating out of the platform. One may not assume that the lowest vibration levels occur near the station platforms where trains are traveling at the lowest speeds, since the floating slab track does not extend into the station platform area. • The highest train vibration levels were measured at 5 Hz which is the design resonance frequency of the floating slab track. At the planned operating speed there was a variation of about 4 dB in the vibration levels at 5 Hz across the 26

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monitoring positions adjacent to the floating slab track. This includes locations where the train would be slowing down or speeding up near the station platform. • Vibration data were collected for train speeds of 40, 48, 56, 64, and 72 kph. At 5 Hz, vibration levels were usually highest at 40 kph. This is likely because the rotational frequency of the wheel at 40 kph was approximately equal to the resonance frequency of the floating slab track. Vibration measurements at all of the 31 monitoring positions and at different speeds were important to include in the verification test plan because train-generated vibration levels would not necessarily be lower during deceleration and acceleration near platforms or at lower speeds. These observations are not intuitive and helped the project to accurately assess the margin between the measured train vibration level at every position in the tunnel and the level at which vibration might exceed the thresholds. Ambient vibration measurements in the tunnel identified one portion of the tunnel with higher-than-average ambient levels because of an adjacent power plant that served the UW campus. The vibration levels from the power plant within the tunnel were not high enough to trigger exceedances at the vibration monitoring sites, however, it was established as possible source of “false exceedances” that could be investigated as a source if exceedances are detected that do not show a standard train vibration signature.

4.2 Train Vibration in Sensitive Research Buildings The goal of the train vibration measurements was to verify if the vibration levels in the sensitive research buildings on the UW campus were represented by the tunnel vibration levels plus the VAEs from Phase 2. Figure 1 shows the train vibration levels measured in Wilcox Hall during the test train measurements and the train vibration estimated in Wilcox Hall using the train vibration in the tunnel plus the VAEs. The ambient vibration (1-h Leq without trains) is shown with the dotted black line and the vibration limit is shown with the dashed red line. Key observations from the plot are: • The measured train vibration exceeds the ambient Leq at 5 Hz, which is the design resonance frequency of the floating slab track. At 5 Hz, there is high confidence in the measured train vibration level because it was consistent across a large sample of train evens. • At frequencies below 5 Hz, the ambient vibration, measured train vibration, and the expected train vibration using the Phase 2 VAE were all relatively similar in value. At these lower frequencies, refinements were made on a case-by-case for each building as indicated by the data. There was significant variation in the data at these frequencies, so careful evaluation of the data was necessary to determine

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Fig. 1 A comparison of the measured train vibration and the expected train vibration using the VAE at a UW sensitive building

if vibration levels were likely from trains or some other ambient source, later to be determined to be seismic. • At frequencies of 8 Hz and above, the predicted train vibration levels using the Phase 2 VAEs were more than 10 decibels below the ambient level. The train vibration levels at these frequencies were too far below the ambient levels to use the data to refine the Phase 2 VAE. However, the train vibration levels are also significantly below the vibration limits so that the data at these frequencies were not of high concern. The biggest challenge with determining how to refine the VAEs at 5 Hz and below based on the measured train vibration data was how to account for the influence of the ambient vibration. A “background correction” approach was developed to subtract out the ambient vibration from the measured test train vibration to arrive at a better estimate of the true train vibration in the building. In this approach, the ambient Leq measured when trains were not operating was decibel-subtracted from the measured train vibration in each 1/3 octave band. This background corrected value was used to arrive at a refined Phase 3 VAE that was equal to: V AEr e f ined = Lv( f acilit y, backgr ound corr ected)−Lv(V M Sn )

(2)

All refinements to the VAE using the train vibration data at 5 Hz resulted in lower VAE’s compared to those developed in Phase 2. The Phase 2 VAE’s were based on the point-source transfer mobilities (PSTMs) measured using a shaker in the tunnel,

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Fig. 2 A comparison of the VAE at 5 Hz assuming line-source transfer mobility (LSTM), pointsource transfer mobility (PSTM), and measured train vibration (Phase 3)

and incorporated an adjustment to account for the expectation that train vibration would more closely represent a vibration line-source. One explanation for why the Phase 2 VAE’s were overly conservative compared to the refined VAE’s using the train vibration data is that the point-to-line source adjustment was overly conservative. Figure 2 shows the VAE versus distance for the Phase 2 VAE with and without the point-source to line-source adjustment, as well as the refined VAE values at 10 of the buildings. At closer distances, the refined VAE falls somewhere between the line-source and point-source VAE. At the farthest distances, the refined VAE is closer to the point-source VAE. This is consistent with the expectation that as the distance from the tunnel to the sensitive building increases compared to the length of the train, the vibration propagation will behave more like that from a point source.

5 Conclusions The case-study presented in this paper shows that developing a relationship between the vibration measured in the tunnel and the vibration experienced in a sensitive laboratory facility is possible to support a vibration monitoring system permanently installed in the light-rail tunnel. When developing that relationship, referred to as a VAE in this case study, careful consideration of whether the vibration from the train will propagate as a point source or a line source is necessary.

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The development of the VAE was structured over three phases, with the first two phases completed prior to the installation of the floating slab track in the tunnel and the final phase completed during test train operations prior to revenue service. All three phases were critical to the successful development of the VAE. Phases 1 and 2 described in [2] were critical for measuring the vibration propagation transfer mobilities at all frequencies prior to the floating slab construction. During test-train operations in Phase 3, it was only possible to measure vibration from trains in the sensitive buildings at the resonance frequency of the floating slab. That data were used to refine the VAE at 5 Hz based on the observation that the Phase 2 VAE likely incorporated an overly conservative adjustment to account for line-source vibration propagation. When developing the monitoring system and vibration limits, careful consideration of the ambient vibration levels at both the facility and at the vibration monitoring point is necessary. At the facility, if there are common transient vibration events that exceed the vibration limits, confirmation that the train events do not exceed the ambient is difficult. Within the tunnel, ensuring that ambient vibration at the vibration monitoring point does not falsely flag train events as vibration exceedances is necessary.

References 1. Evans AL, Ono CG, Saurenman HJ (2018) Estimating adjustment factors to predict vibration at research facilities based on measurements in a subway tunnel. In: Anderson D et al (eds) Noise and vibration mitigation for rail transportation systems. Notes on numerical fluid mechanics and multidisciplinary design, vol 139. Springer, Cham. Proceedings of the 12th international workshop on railway noise, vol 139 of Notes on numerical fluid mechanics and multidisciplinary design, Terrigal, Australia, Sept 2016. Springer, Heidelberg, pp 607–618 2. Saurenman HJ, Della Neve Longo R, Nelson JT (2021) Predicting vibration in University of Washington research facilities up to 500 m from a light rail tunnel. In: Degrande G et al (eds) Noise and vibration mitigation for rail transportation systems. Notes on numerical fluid mechanics and multidisciplinary design, vol 150, Ghent, Belgium, Sept 2019. Springer Nature, Switzerland, pp 470–477 3. Rajaram S, Nelson JT (2019) High-performance floating slab track: design and construction improvements based on lessons learned from prototype slabs. Transp Res Rec J Transp Res Board, paper number: 19-04618

Design and Performance of a Comprehensive Vibration Monitoring System for Trains Under University of Washington Campus Shankar Rajaram, James Tuman Nelson, and Marc Pearlman

Abstract Seattle Sound Transit’s Link Light Rail extension to Northgate runs under the University of Washington (UW) campus in a twin bore tunnel system. The ground vibration produced by the trains is required to meet stringent vibration limits for 24 buildings. Vibration from each train passby is recorded by 40 vibration monitoring units installed in the tunnels. The monitoring units are designed to trigger warning alarms in case the train vibration levels approach the vibration limits and exceedance alarms if the limits are exceeded. These limits are based on building vibration limits with vibration adjustments based on field testing. Based on the frequency and location of the monitors, the warning alarm settings needed to be adjusted to minimize false alarms from background vibration. This paper presents the design of the monitoring system, the progression of the warning alarm setting adjustments, and the preliminary vibration trends from representative monitors. Keywords Vibration monitoring system · Train in zone · Background vibration · Vibration thresholds

1 Introduction Sound Transit’s Link Light Rail runs in a twin bore train tunnel system under the University of Washington (UW) Seattle campus that houses 24 vibration sensitive buildings. As part of the vibration agreement with UW, Sound Transit installed and maintains a permanent real time vibration monitoring system that demonstrates that S. Rajaram (B) Sound Transit, 401 S Jackson Street, Seattle, WA 98104, USA e-mail: [email protected] J. T. Nelson Wilson Ihrig & Associates, 5900 Hollis Street, Suite T1, Emeryville, CA 94608, USA M. Pearlman International Electronics Machines Corporation, 850 River Street, Troy, NY 12180, USA © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_14

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the stringent vibration limits for each of the UW buildings are not exceeded by train operations. Nine vibration monitoring system (VMS) units are installed at part of the University Link (U-Link) alignment in 2016 [1]. In 2021, the train tunnels were extended further through the UW campus as part of the Northgate Link Extension (NGLE) alignment. Sound Transit added 31 new VMS monitors in the tunnels. The 40 VMS monitors are located every 91.5 m (300 feet), with 20 monitors in each tunnel. The Master Implementation Agreement (MIA) between Sound Transit and UW requires that the vibration monitoring system should be reliable. As a result, each VMS monitor has two independent data loggers and geophones to provide redundancy. In case of malfunction of the primary data logger, the VMS monitor will automatically switch to the alternate data logger. This paper discusses the design of the vibration monitoring program, lessons learned from the first nine monitors, refinements to the NGLE system, and train identification algorithm for different track types. The paper also discusses examples of vibration trends due to rail and wheel degradation.

2 Methodology The train vibration data from the permanent VMS units were collected during prerevenue and revenue service at both U-Link and NGLE. The monitor data are used to identify vibration signatures of trains on tracks with high compliance direct fixation fasteners (HCDF), floating slab track (FST), and special trackwork with moveable point frogs and a double cross-over diamond. For each track type, one or two peak one third octave vibration frequencies are used to set alarm thresholds. The presence of a train adjacent to the vibration monitors is communicated to the VMS units through the train control network (TCN). The TCN uses the track circuit loops to identify that the train is in the “zone” of a specific VMS unit. The data logging is continuous, so that the background vibration data just before and after the presence of train in zone (TIZ) are available in the post-processing data to help distinguish false alarms from true train alarms. The nine vibration monitors on the U-Link section are adjacent to rails on HCDF tracks. The vibration signature of the trains on the HCDF tracks show a peak vibration at the track resonance frequency of about 40 Hz that is clearly above background vibration by at least 20 dB. This strong positive identification at 40 Hz helped to distinguish false positives at other frequencies such as 12, 16, and 20 Hz that might have been due to other sources such as pumps, traffic from an adjacent bridge, and episodic seismic tremors due to the Cascadia subduction zone. The train vibration signature on the floating slab section is positively identified at the fundamental resonance frequency of the 5 Hz FST. The vibration signature is accompanied by a secondary peak at around 63 Hz due to the track resonance. The rails of the FST are supported with standard resilient direct fixation fasteners of dynamic stiffness 34 MN/m spaced at 610 mm. The secondary peak is much more

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subtle due to the vibration reduction effect of the floating slabs at that frequency. However, the vibration at this 63 Hz frequency may increase due to deterioration of rail surface conditions between maintenance cycles. This peak is directly depends on rail grinding and wheel truing frequency. For example, if either the rail or the wheels have a dominant wavelength at 250 mm it would lead to sharp vibration peaks at 63 Hz for train speeds of 56 kph (35 mph). The FST is designed to provide substantial isolation at these frequencies to protect the UW laboratory vibration environments. Some of the lessons learned from University Link that are incorporated into the NGLE vibration monitoring system include the following: • Ability to identify up to 2 min of data before and after the presence of a train in the TIZ of the monitor. This feature allows efficient discrimination of train vibration from other sources, particularly at 5 Hz. The 5 Hz ambient vibration is much greater than the background vibration at 40 Hz, often greater than train related vibration at 5 Hz, and is highly correlated with episodic seismic tremors from the Cascadia subduction zone. • Connection of the monitors to the track circuit loops in the opposite tunnel so that correlation of data from multiple monitors can discriminate against potential external vibration sources affecting the measurements. • Performing advance trending capabilities using the human machine interface (HMI) from which extensive 1/3 octave band vibration data can be exported for each monitor over any 24-h period.

2.1 Background Vibration and Alarm Settings The data for the NGLE monitors indicate high background vibration activity between 2 and 6.3 Hz due to episodic seismic tremors from the Cascadia subduction zone. Based on about 6 months of revenue service train data, all monitor warning functions were turned off at frequencies at and below 4 Hz. Sound Transit and UW agreed that the vibration trends at these very low frequencies will be evaluated on an annual basis and that there is no need for alarming on a per train basis. At all third octave frequencies between 5 and 100 Hz, the alarms had two settings: one for warning and another for exceedance. The exceedance limit is the same as the MIA limit, but challenges remain with setting the warning limits. The warning limits were adjusted through trial and error as discussed in the next section.

3 Results This section discusses the performance of the vibration monitoring system during the first eight months since the opening of the NGLE for revenue service.

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3.1 Warnings and Exceedances The settings for warnings and exceedances were initially evaluated for a 3-month period between October and December of 2021 after revenue service opening. During this period, the alarm settings were set artificially high to suppress alarms and just evaluate the train vibration in relation to ambient vibration levels. The warning settings were adjusted in January 2022 as summarized in Table 1. A summary of average warnings and exceedances per day are shown in Table 2. As shown in Table 2, the number of warning and exceedance alarms was excessive, during the period between January and February 2022. Analysis showed that all alarms were due to some background source. An effort was made to reduce the false alarms without diluting the intended purpose of the monitoring system. All alarming functions were turned off for the 2–4 Hz 1/3 octave bands in March 2022. The warning settings were adjusted for 8–10 Hz 1/3 octave bands. Substantial number of warnings and alarms still occurred after adjustments in March. Analysis of the monitors with the most false alarms was performed for three oneweek periods between March and May. The results are summarized in Table 3. The analysis showed that the false alarms for non-train related windows were associated with 9 of the 40 monitors and were mostly at 8 Hz or 12.5 Hz. Based on this analysis, targeted revisions to the warning alarm settings were made at these frequencies in May as shown in Table 1. This revision reduced the number of warnings and alarms further but did not completely eliminate them. While the challenge to reduce the number of false alarms continues, the false alarms point out to the effectiveness of the floating slabs in reducing train vibration to levels that are comparable with or less than the ambient vibration. That is, discriminating between train vibration and ambient vibration is difficult due to the floating slab track isolation. Note that the MIA with the UW required that Sound Transit meet stringent laboratory vibration limits regardless of ambient vibration. Table 1 Summary of warning settings during different periods since the opening of NGLE Monitoring period

Warning settings compared to exceedance limit 2–4 Hz

5–6.3 Hz

8–10 Hz

12.5 Hz

16–100 Hz

Oct–Dec 2021

Turn off

Turn off

Turn off

Turn off

Turn off

Jan–Feb 2022

− 10 dB

− 10 dB

− 10 dB

− 10 dB

− 10 dB

Mar–Apr 2022

Turn off

− 5 dB

− 5 dB

− 10 dB

− 10 dB

May 2022

Turn off

− 0 dB

− 2 dB

− 7 dB

− 10 dB

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Table 2 Summary of average alarms per day during different periods since NGLE opening 1/3 octave band freq.

Jan–Feb 2022

Mar–Apr 2022a

May 2022b

Wb

Wb

Wb

Ec

Ec

Ec

2 Hz

18,125

45

0

0

0

0

2.5 Hz

20,000

38

0

0

0

0

3.15 Hz

74,910

255

0

0

0

0

4 Hz

19,242

21

0

0

0

0

5 Hz

28,518

0

32

1

16

0

1408

96

16

0

1

0

6.3 Hz 8 Hz

12,664

8

555

2

24

1

10 Hz

6007

20

610

21

80

19

12.5 Hz

5186

88

6369

20

1307

15

16 Hz

49

0

15

1

19

0

20 Hz

20

14

3

0

5

4

25 Hz

105

0

54

2

20

3

31.5 Hz

324

5

36

1

120

16

40 Hz

73

0

88

0

85

5

50 Hz

64

0

45

0

6

0

63 Hz

254

2

34

0

7

0

80 Hz

7

0

0

0

1

0

100 Hz

97

0

16

0

2

0

a All

alarms were turned off between 2 and 4 Hz from March 2022 = Warnings. The warning settings were progressively revised from Dec 2021 to May 2022 to make them less stringent c E = Exceedances. All exceedance alarms were determined to be due to background bW

4 Trend Analysis The change of vibration over the course of seven months was evaluated for four monitoring positions. One is at a tangent section of direct fixation track in the northbound tunnel where trains ascend a grade and decelerate into the UW Station double cross-over. The second is at a section of direct fixation track at a position north of the FST track, also in the northbound tunnel where trains negotiate a curve at 56 kph. The third and fourth are at sections of tunnel with FST. The data were analyzed by exporting a full day of continuous vibration data in 1-s increments of time for 2021-11-08 and 2027-06-07. Each sample is a running rms average of nominally 8 s derived from 16-s Fourier transforms and a Hamming window function with an overlap of fifteen to sixteen. The train-in-zone data were employed to identify time-of-passage of a train on the track adjacent to the monitor and exclude vibration from the adjacent tunnel. The ambient data were sampled before or after a train passage, also excluding data produced by trains in the opposite tunnel. In all cases,

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Table 3 Summary of monitors and frequencies with most non-train related vibration alarms Sensor cabinet

1/3-octave frequency band (Hz)

Location

Approximate % of total active TIZ alarms

N06-VCC-01

12.5

Wilcox Hall

N06-VCC-01

12.5

Roberts Hall 4%

N06-VCC-02

25

Wilcox Hall

N06-VCC-02

31.5

Wilcox Hall

N06-VCC-03

8

N06-VCC-03 N06-VCC-04

3/7/22–3/14/ 22

4/21/22–4/27/ 22

4/28/22–5/5/ 22

11%

12%

9%

3%

2%

< 1%

3%

< 1%

< 1%

2%

< 1%

Roberts Hall < 1%

< 1%

1%

12.5

Wilcox Hall

2%

2%

1%

10

Roberts Hall 1%

1%

2%

N06-VCC-04

12.5

Roberts Hall 7%

6%

7%

N06-VCC-04

12.5

Wilcox Hall

17%

18%

20%

N06-VCC-05

12.5

Mech Eng.

1%

1%

1%

N06-VCC-07

8

Mech Eng. Annex

23%

24%

36%

N06-VCC-09

8

Mech Eng. Annex

1%

1%

1%

N06-VCC-10

8

Mech Eng. Annex

5%

7%

8%

N06-VCC-25

40

Physics/ Astronomy

1%

2%

< 1%

the sampling duration for each train was the length of time that a train in zone flag was set. The third octave maximum levels obtained during the period were selected as the spectrum for averaging. The ambient data were sampled in similar fashion, using the same sampling duration as that used for the train, and the maximum ambient third octave levels occurring during that period were selected for averaging. The ambient data are maximum levels occurring between two and three minutes after or before each train passage, so that the number of ambient samples is the same as the number of train samples. In this way, the train maxima and ambient maxima are obtained with virtually parameters in terms of number of samples of maximum third octave levels for averaging and time period. Thus, a Student’s T test can be applied directly to determine significant differences (this was not done for this paper). The typical standard deviation of the third octave averages were typically 3–6 dB. The standard error of the mean is obtained as the standard deviation divided by the square root of the number of train passes (typically 130), resulting in a standard error of the mean of the order of a fraction of a decibel. Thus, any changes of more than a decibel over the course of the seven months is resolved with significant level of confidence.

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Fig. 1 Vibration levels measured at a tangent section of direct fixation track with HDCF in the northbound tunnel (N04-VCC-02) (left) and at standard direct fixation track N06-VCC-25 (right)

4.1 Tangent Standard Direct Fixation Track Third octave velocity levels measured on 2021-11-01 and 2022-06-07 are plotted in Fig. 1 (left). These data were collected at monitor N04-VCC-02 located in the northbound tunnel approximately 90 m south of the double cross-over box structure at the UW Station. The trains are ascending a grade, requiring tractive effort without braking. The data collected in 2021 contain substantial low frequency vibration at 5 Hz for both train vibration and ambient vibration, which is surprising, especially since this component of vibration is absent from the 2022-06-07 vibration. The reason for this is not known, except that episodic seismic tremors for the Cascadia subduction zone may have been active on 2021-11-01. Except for the 4, 5, and 6.3 Hz third octave bands, no change is apparent in the data over the seven-months beginning at revenue service startup. Also plotted are the mean plus two standard errors of the mean, here labeled as 2xSEM. The standard error of the mean is reduced considerably to a fraction of a decibel by the approximately 240 train samples that make up the means on both days. The standard deviations of the data sets are about three to six decibels. Third octave velocity levels measured on 2021-11-08 and 2022-06-07 for trains running on a curve of nominal radius 100 m north of the FST track are plotted in Fig. 1 (right). These data were collected at a section of track with high compliance direct fixation fasteners (HCDF) for train speeds of about 56 kph. These data exhibit almost no significant difference between vibration levels over almost the entire range of frequencies except for a slight decrease of 1 dB at 16 Hz and an increase of 1 to 2 dB at frequencies of 63–100 Hz. The peak in the third octave spectrum is at 40 Hz, which is the nominal track resonance frequency. The vibration at 40 Hz is slightly less after seven months of operation. Although not plotted, the standard errors of the means are a fraction of a decibel, based on approximately 130 samples for both days. Most interesting is that the vibration below 4 Hz is significantly higher than the ambient vibration.

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Fig. 2 Vibration levels measured at the floating slab section at N06-VCC-08 in the southbound tunnel (left) and N06-VCC-03 in the northbound tunnel (right)

Third octave vibration levels measured with monitor N06-VCC-08 on the southbound tunnel structure at the FST section are plotted in Fig. 2 (left). The train speed is approximately 56 kph with dynamic braking on the down-hill grade. The alignment is curved at this point, but at the beginning of the spiral. This location is actually under or very close to the mechanical plant for the UW campus, so that background vibration dominates the site. The prominent peak at 5 Hz is related to the FST resonance frequency. The peak at 31.6 Hz is present in the ambient vibration as well as train vibration and is likely due to UW mechanical plant equipment. The minor peak at 63 Hz might be related to the track resonance, but it also appears in the ambient data. From about 10 Hz up to 40 Hz the data recorded in 2021-11-08 are the same as the ambient vibration levels. Except for the peak at 31.6 Hz, the data recorded in 2022-06-07 are higher by 2–4 dB at frequencies at and above 20 Hz. The final example of third octave vibration level changes at the FST section of track is presented in Fig. 2 (right). These data were collected on 2021-11-08 and 2022-06-07 with monitor N06-VCC-03 located in the tunnel at a section of tangent track with slight grade. Trains are ascending the grade at a nominal speed of 56 kph. The peak at 5 Hz corresponds to the floating slab resonance frequency and is virtually unchanged over the seven intervening months. Vibration at 2, 2.5, and 3.16 Hz is clearly above the ambient by a few decibels but decreased by about one decibel over seven months. The vibration levels between 12.5 and 20 Hz increase by a decibel though the vibration levels from 10 to 40 Hz are basically at the ambient. The vibration reduction provided by the FST is such that the ambient dominates the vibration due to the trains at frequencies from 10 to 40 Hz. The levels increased significantly at 50 Hz and higher frequencies and are above the ambient. This increase is consistent with the increase at these frequencies at N06-VCC-25, indicated in Fig. 1 (right).

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5 Conclusions A comprehensive vibration monitoring system is installed in the train tunnels under the UW campus. The functionalities of the NGLE monitors were refined based on lessons-learned from the U-Link monitoring program. The identification of vibration alarms from trains and discrimination against ambient vibration are performed by the monitoring system using sophisticated software. The monitors allow discrimination of small changes of vibration over several months by statistical analysis of a substantial number of trains for any given day. The long-term trend of vibration data collected by the monitors provides a basis for scheduling maintenance intervention.

Reference 1. Rajaram S, Nelson JT, Saurenman HJ (2016) Design and performance of a permanent vibration monitoring system with exceedance alarms in train tunnels. In: Proceedings of the 12th international workshop on railway noise, vol 139 of Notes on numerical fluid mechanics and multidisciplinary design, Terrigal, Australia, Sept 2016. Springer, Heidelberg, pp 607–618

High-Speed Rail and Aerodynamic Noise

Numerical Simulation of the Aerodynamic Noise of the Leading Bogie of a High-Speed Train Yuan He, David Thompson, and Zhiwei Hu

Abstract Numerical simulations of the noise radiated by a train bogie under the leading car of a high-speed train are carried out using Computational Fluid Dynamics (CFD) and Computational Aeroacoustics (CAA). In order to reduce the grid size and increase the grid quality, a hybrid grid is used to discretize the computational domain. The Delayed Detached Eddy Simulation method with Spalart–Allmaras turbulence model is used to simulate the unsteady flow field. The aerodynamic results show that the shear layer detached from upstream of the bogie cavity is critical for the aerodynamic noise generation of the leading car. The time-varying surface pressure is collected during the unsteady simulation and then used as input for the far field noise calculation, which uses the Ffowcs Williams and Hawkings equation. The onethird octave noise spectra show broadband characteristics with the contribution from low frequencies being dominant. The results show that the bogie cavity contributes more to the sound power than the bogie itself. Keywords Train bogie · Aerodynamic noise · Numerical simulation

1 Introduction As the train speed increases, the aerodynamic noise becomes the dominant contributor to the overall noise [1]. Of the various aerodynamic noise source regions, such as the pantographs, gaps between coaches, and the wake region, the bogies are very important noise sources [1–5]. The bogie region, especially the leading one, is responsible for significant low-frequency noise, which is critical for the neighbouring urban Y. He (B) · D. Thompson Faculty of Engineering and Physical Sciences, Institute of Sound and Vibration Research, University of Southampton, Southampton SO17 1BJ, UK e-mail: [email protected] Z. Hu Aeronautics, Astronautics and Computational Engineering, Faculty of Engineering and Physical Sciences, University of Southampton, Southampton SO17 1BJ, UK © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_15

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areas because of its high transmission into buildings though the windows [6]. To study the characteristics of aerodynamic noise generated by the train bogie, scale model experiments have previously been carried out in a wind tunnel. Lauterbach et al. [7] tested a 1:25 train model in cryogenic wind tunnel to investigate the Reynolds number and Mach number dependence of the aerodynamic noise of the train. Two velocity-independent humps were identified in the spectra, the shape of which did not change significantly within the tested range of Mach number. Moreover, only a weak Reynolds number dependence of the noise of the first bogie was found and the speed power law exponent was approximately equal to 6 over a wide range of Reynolds number. Latorre Iglesias et al. [5] studied the aerodynamic noise from a 1/7 scaled bogie, and found that the noise contribution from low frequencies is dominant, which was also found by Lauterbach et al. [7]. Yamazaki et al. [8] also conducted some tests on a 1/7 scaled model in a wind tunnel. The aerodynamic noise of different configurations of the bogie, located in the cavity under the train model, was measured by a twodimensional microphone array installed at the wayside. The results showed that the wheelsets as well as the motor and the brake, which are exposed to the shear layer from the car body, significantly influence the aerodynamic noise of the bogie. Although many experiments have been conducted to investigate the characteristics of the bogie noise, its generation mechanism still needs to be further understood. Therefore, numerical methods have been used to study it. Due to the extremely complex geometry, only limited work has been carried out for simplified geometries. Zhu et al. [9] used a highly simplified bogie model, which only includes the wheelsets and a simplified frame, to simulate the aerodynamic noise of the train bogie. The bogie cavity was initially not included in the simulation and the results showed that the noise generated by the wheelsets is greater than that generated by the frame. The aerodynamic noise of a simplified bogie located inside a bogie cavity with and without a fairing was also studied by Zhu et al. [3]. It was found that the pressure fluctuation produced by the flow separation and the vortex shedding around the geometries are the main contributors to the aerodynamic noise. The fairing can shield the flow unsteadiness inside the bogie cavity and reduce the pressure fluctuation outside the cavity, leading to a reduction of the far field noise. To ensure the simulated flow is close to the practical flow, a bogie with most of its components in a simplified cavity was used in the numerical simulation by He et al. [10]. A hybrid grid system was used to discretize the computational domain and the mesh quality and quantity were well controlled. The results showed that the rear part of the bogie model has greater noise source than the front part while the noise contribution from the cavity is dominant. In this paper, to facilitate a feasible numerical method, the scale of the model has been reduced and the hybrid computational grid, which is explored by He et al. [10], is further developed and successfully applied for simulations of a bogie under a leading car. In the discretization of the computational domain, most of the features of the bogie are retained, while the number of grid elements is reduced to an acceptable level by removing small bogie features. The noise source distribution on the bogie and car body surface and the noise spectra are calculated.

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2 Grid Strategy and Numerical Setup Figure 1 shows dimensions of the computational domain, defined in terms of the height of the train H, which is about 3.8 m. As shown in Fig. 1a, the simulation model includes the front part of the leading car body and a bogie in the cavity. To reduce the computational cost, the model size is reduced to 1/12 and the incident flow speed is 10 m/s, which is about 1/10 of the full speed. This gives a Reynolds number of 2.1 × 105 , based on the inlet velocity and the height of the scaled car body. To minimize the influence from the domain boundaries, including the upstream velocity inlet boundary and the symmetry boundaries at the top and two sides, they are set at a sufficient distance from the car body. Because the rear part of the car body is truncated, the outlet plane, at which a zero pressure outlet boundary condition is specified, is located at about 5.6H away from the train nose. In addition, the ground is specified as a moving wall to reproduce the condition of a real train pass-by. To discretize the complex domain, a hybrid mesh used in [10] is further developed. ANSYS ICEM 19.1 and Fluent 14.8 are used to generate the hybrid mesh, which uses a structured hexahedral mesh close to the boundary surfaces and an unstructured polyhedral mesh far from the surfaces. When generating the structured mesh of the car body, to get a good connection with the unstructured grid, the ratio of the edges of the surface cells should not exceed 3. The grid size on the train nose and the cowcatcher is refined compared with that of the rear part of the car body. The expansion ratio of the boundary layer grid is about 1.1 and the height of the first boundary layer cells is small enough to make the non-dimensional grid size y+ smaller than 1 on both the bogie surface and the car body surface. The minimum ‘Equiangle skewness’ of the grid of the car body in ANSYS ICEM is 0.4 and the minimum ‘Determinate’ is 0.7. Figure 2 shows the volume grid distribution on three slices. Particular attention was paid to the volume grid refinement at the train nose and the bogie cavity region. Several refinement boxes are specified, wrapping around the train nose, the cowcatcher, and the bogie cavity region.

(a) the side view of the model

Fig. 1 Computational domain dimensions

(b) the full computational domain

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(a) Slice at X=0 and the local enlarged view

(b) Slice at Y=0.02 m though centres of wheels and the local enlarged view

(c) Slice at Z=0.066 and the local enlarged view Fig. 2 Mesh distribution on slices

The Delayed Detached Eddy Simulation (DDES) method with Spalart–Allmaras turbulence model is used in the simulation of the unsteady flow field, using the software OpenFOAM 2.4.0. For a CFD simulation with complex geometry, the DDES can well balance the prediction accuracy and the computational cost [11, 12]. To achieve calculation stability and accurate results at the same time, a second-order Total Variation Diminishing (TVD) interpolation scheme is adopted for the divergence term. The Gauss linear interpolation scheme, which requires a grid with high quality and uniform distribution, is applied for the convection term. A second order implicit temporal scheme, which is called “backward” time marching in OpenFOAM, is selected. The time step is about 2 × 10–5 s, ensuring the maximum CourantFriedrichs-Lewy number (CFL) < 5. The total number of cells in the model is about 36.4 million. The total non-dimensional time t* is nearly 25, corresponding to a physical time of 4.3 s (t* = tU 0 /L, where t is the physical time, U0 is the free stream

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velocity and L is the car body length). The computational wall-time is approximately 650 h with 640 processors on the Iridis5 cluster at the University of Southampton.

3 Aerodynamic Results The data collection is started when the simulation becomes statistically steady, at a non-dimensional time t* of about 3.5; it is stopped when the collected force coefficients achieve statistical convergence. Figure 3 depicts the three-dimensional (3D) streamlines. In Fig. 3a, it can be noted that the incoming flow is separated into three streams at the front face of the cowcatcher. Two of them flow towards the side surface of the cowcatcher and the other separates at the front edge of the cowcatcher and forms a separation bubble behind it. At the side surface, as shown in Fig. 3b, the streamline close to the rear part of the cavity bends towards the inside of the cavity and some flow even gets into it, which forms a recirculation at the rear part of the cavity, as shown in Fig. 3c. Some of the flow at the side surface of the cowcatcher enters the cavity through its front lip and forms another recirculating vortex nearby. Figure 4 visualizes the instantaneous flow structure represented by the iso-surfaces of the normalized second invariant of the velocity gradient (Q criterion, the second invariant of the velocity gradient) at a value of 12; this is based on Q/(U0 /H)2 , where U0 is the free stream velocity and H is the height of the car body. The isosurfaces are coloured by the normalized streamwise velocity U/U0 . Figure 4a shows the vortices, which originate from the front area of the cowcatcher, at the bottom of the model. The bogie components are immersed in the highly turbulent wake and face a complex incoming flow. In addition, it is noted that, compared with the flow developed around the bogie, the vortices dissipate rapidly after the rear of the bogie cavity. It is believed that the rear wall impedes the further development of the wake; some of it impinges on the wall and largely deforms, and subsequently enters the cavity [13]. This turbulent flow invasion may cause high pressure fluctuations at the upper part of the cavity and the bogie.

(a) bottom

(b) side

(c) vortex entering the cavity

Fig. 3 Time-averaged 3D streamlines for flow over the leading car

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(a) bottom view

(b) side view

Fig. 4 Flow structures represented by the normalised second invariant of the velocity gradient Q/(U0 /H)2 , coloured by the ratio of the streamwise velocity to the free stream velocity

The mechanism of the generation of the dipole noise is the presence of solid boundaries, which creates or augments noisy flow features such as unsteady separation and vortex shedding [14] or impingement. The pressure on the solid surfaces is collected during the simulation. When the focus is on the far field noise, the rate of change of pressure dp/dt can be used to assess the sound source strength [15]. To show the noise source regions on the model surface, dp/dt is calculated and expressed in decibels. Figure 5 displays the contours of dp/dt on the surface. It can be observed that the bottom of the model, including the cowcatcher and the bottom of the bogie components, has very strong noise sources. The reason is, as shown in Fig. 4a, this area has a very strong interaction with the highly turbulent wake separated from the front edge of the cowcatcher. Another area with strong noise source is the side components, such as the lateral dampers, the vertical dampers, and the side parts of the bolster. This area is mainly affected by the shear layer detached from the two side edges of the cavity, as shown in Fig. 4b. The lateral dampers, which directly face the detached shear layer, are almost all covered by the strongest noise source. Moreover, the rear surface of the cavity also has a strong noise source distribution because the turbulent flow from upstream is impeded. Fig. 5 Surface contours of the pressure rate of change dp/dt

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4 Aeroacoustic Results The collected time-varying surface pressure is used as input to the Ffowcs Williams and Hawkings equation to predict the far field noise. After determining the sound pressure level (SPL) of the simulation model at reduced scale, the results are converted to full scale. Figure 6 shows the 1/3 octave noise spectra of the bogie, the car body and their summation at a side receiver 20 m away (full scale) from the centre of the bogie. The ground was not considered in the calculation. The spectra are broadband with no tonal peaks. The noise spectrum of the car body is greater than that of the bogie at all frequencies. Moreover, it is noted that the spectra have a broad peak around 100 Hz and the noise is dominated by low frequencies. Similar conclusions can be found in the experiments of Latorre Iglesias et al. [5] and Lauterbach et al. [16]. To understand better the noise contribution from different components, the sound power level (SWL) emitted by each component is investigated. A sphere with 20 m radius, which encloses the model, is almost uniformly divided into 486 segments with a receiver at the centre of each. The SWL is obtained by integrating over the whole sphere: ⎛ SW L = 10 log10 ⎝

 S

⎞ pr2ms ⎠ ds / Wref ρc

(1)

where pr ms is the RMS acoustic pressure, ρ is the density, c is sound speed, S is the surface of the sphere and Wref is the reference sound power, 10–12 W. Figure 7 shows the proportion of sound power emitted by the various components. The car body was divided into four parts, including train nose, cowcatcher, bogie cavity, and rear car body, whereas the bogie is compared as an integrity. The sound power generated by the surfaces of the bogie cavity is 134 dB, which is the highest component. According to the noise source distribution shown in Fig. 5, the rear part of the cavity is the key area that contributes the highest sound power. In addition, Fig. 6 One-third octave noise spectra at full scale for a speed of 400 km/h and distance 20 m

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Fig. 7 Sound power proportion of components

the ground beneath the vehicle generates 133.5 dB, which is similar to the cavity. The sound power generated by the ground is due to the jet flow generated at the gap between the bottom of the cowcatcher and the ground. The sound power emitted by the whole bogie (131.3 dB) is very similar to that from the train nose. Although, as shown in Fig. 5, there are strong noise source regions on the cowcatcher and the rear part of the car body, their sound power contribution is the smallest, because the area of the total surface with strong noise source is smaller than that of the other components.

5 Conclusions Numerical simulations have been carried out to calculate the unsteady flow field and noise of a train bogie under a leading vehicle. The bogie model retains most of the components to ensure the simulated flow is close to the practical flow. The aerodynamic results show that the detached shear layer from upstream has a great influence on the noise generation of the downstream components. The aeroacoustic results show that the noise spectrum is dominated by low frequencies. The sound power level generated by the bogie cavity is around 3 dB greater than that of the bogie. Acknowledgements The work described here has been supported by the Ministry of Science and Technology of China under the National Key R&D Programme grant 2016YFE0205200, ‘Joint research into key technologies for controlling noise and vibration of high-speed railways under extremely complicated conditions’. All simulations were carried out on Iridis4 supercomputer at the University of Southampton.

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References 1. Thompson DJ, Latorre Iglesias E, Liu X et al (2015) Recent developments in the prediction and control of aerodynamic noise from high-speed trains. Int J Rail Transp 3(3):119–150 2. Liu X, Zhang J, Thompson DJ et al (2021) Aerodynamic noise of high-speed train pantographs: comparisons between field measurements and an updated component-based prediction model. Appl Acoust 175:107791 3. Zhu J, Hu Z, Thompson D (2018) The flow and flow-induced noise behaviour of a simplified high-speed train bogie in the cavity with and without a fairing. Proc Inst Mech Eng Part F J Rail Rapid Transit 232(3):759–773 4. Nagakura K (2006) Localization of aerodynamic noise sources of Shinkansen trains. J Sound Vib 293(3):547–556 5. Latorre Iglesias E, Thompson DJ, Smith M et al (2017) Anechoic wind tunnel tests on highspeed train bogie aerodynamic noise. Int J Rail Transp 5(2):87–109 6. Minelli G, Yao HD, Andersson N et al (2020) An aeroacoustic study of the flow surrounding the front of a simplified ICE3 high-speed train model. Appl Acoust 160:107125 7. Lauterbach A, Ehrenfried K, Loose S et al (2012) Microphone array wind tunnel measurements of Reynolds number effects in high-speed train aeroacoustics. Int J Aeroacoustics 11(3–4):411– 446 8. Yamazaki N, Uda T, Kitagawa T et al (2019) Influence of bogie components on aerodynamic bogie noise generated from Shinkansen trains. Q Rep RTRI 60(3):202–207 9. Zhu J, Hu Z, Thompson DJ (2016) Flow behaviour and aeroacoustic characteristics of a simplified high-speed train bogie. Proc Inst Mech Eng Part F J Rail Rapid Transit 230(7):1642–1658 10. He Y, Thompson D, Hu Z (2021) Numerical investigation of flow-induced noise around a high-speed train Bogie in a simplified cavity. In: International conference on rail transportation, Chengdu, pp 65–72 11. Spalart PR (2000) Strategies for turbulence modelling and simulations. Int J Heat Fluid Flow 21(3):252–263 12. Spalart PR, Deck S, Shur ML et al (2006) A new version of detached-eddy simulation, resistant to ambiguous grid densities. Theoret Comput Fluid Dyn 20(3):181 13. Zhu J (2015) Aerodynamic noise of high-speed train bogies. PhD thesis, University of Southampton 14. Wang M, Freund JB, Lele SK (2005) Computational prediction of flow-generated sound. Annu Rev Fluid Mech 38(1):483–512 15. Curle N (1955) The influence of solid boundaries upon aerodynamic sound. Proc R Soc Lond A 231(1187):505–514 16. Lauterbach A, Ehrenfried K, Kröber S et al (2010) Microphone array measurements on highspeed trains in wind tunnels. In: Berlin beamforming conference. Citeseer

Prediction of the Aerodynamic Sound Power Level of a High Speed Train Bogie Based on Unsteady FW-H Simulation Martin Rissmann, Romain Leneveu, Claire Chaufour, Alexandre Clauzet, and Fabrice Aubin

Abstract Aerodynamic noise is generated by interaction of the air flow with an object and by the turbulent flow itself. In railways it becomes a significant noise source for speeds above 250 kph and major areas of noise generation on (high speed) trains are the train head, the leading and second bogie, the pantograph and the gaps between coaches. This paper presents a numerical simulation approach based on CFD/CAA techniques aiming to estimate equivalent sources for aerodynamic noise of different components of SNCF’s TGV high speed trains. The approach is based on an unsteady DES flow simulation combined with the Ffowcs-Williams and Hawkins (FW-H) analogy for the acoustic part. In order to develop the method a symmetric and full model are implemented and the leading bogie was selected as an application case. Results of this simulation, in terms of sound power and directivity, are already used by SNCF noise experts in order to estimate pass-by noise levels of TGV high speed trains. In the future other noise source will be simulated and mitigation devices such as deflectors will be tested numerically. Keywords Aeroacoustics · High speed train · FW-H

1 Introduction Railway noise is largely dominated by rolling noise. However, above 250–300 kph and beyond, the aerodynamic noise becomes a significant additional source, which can even become the dominant noise source. It is characterized by an evolution with speed following 60–80 log laws and its tonal components and broadband character in the low and mid-frequency range [1]. The noise is generated by interaction of the M. Rissmann (B) · R. Leneveu Vibratec, Railway Business Unit, 28 Chemin du Petit Bois, 69130 Ecully Cedex, France e-mail: [email protected] C. Chaufour · A. Clauzet · F. Aubin SNCF Voyageurs—SNCF Materiel Ingénierie du Matériel—Centre d’Ingénierie du Materiel, 4, Allée des Gémeaux, 72100 Le Mans, France © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_16

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air flow with the train surfaces and by the turbulent flow itself (turbulent boundary layer, un-steady wake, etc.). It is well known from several publications [2–7] that the major aerodynamic noise sources are the train head, the leading and second bogie, the pantograph and the gap between trailers. For SNCF the main goal is to be able to estimate aerodynamic noise sources in order to include them in exterior noise emission predictions at train level (including rolling and equipment noise sources) for typical EMU running at 200 kph and more. Further-more once the noise emission of the whole train is simulated, SNCF is able to define the source term for the CNOSSOS noise assessment method (European parliament directive 2002/49/CE).

2 Methodology SNCF uses STARCCM+ for different aerodynamic simulations. Therefore in this study, this tool is used for the prediction of the aerodynamic sound power of the leading bogie. The prediction approach is based on an unsteady DES aerodynamic flow simulation combined with the Ffowcs-Williams and Hawkins (FW-H) analogy for far-field acoustic prediction. To ensure a correct implementation of the approach in STARCCM+ the well-known reference case of flow noise around a tandem cylinder was reproduced before modelling the TGV train: Satisfying agreement with the simulated and measured reference case was obtained [8].

2.1 Setup Figure 1 shows the computation domain with the TGV train’s head: the nose is placed far from the inlet boundary condition such that the flow field develops properly. The bogie geometry is modelled in detail including suspension elements, brake discs, motors and gearboxes. After the first bogie the train’s geometry is simplified by extruding its section up to the outlet boundary condition. Furthermore, two numerical models are created: A first model comprises a symmetry plane along the center axis of the train to save computation time. This hypothesis is acceptable with regard to the objective of the project. A second model takes into account the full train geometry. Both models have a trimmed mesh with a base size of 0.56 m, which is refined towards the bogie area, where a cell size of 8.4 mm is reached, see Fig. 2. More details about the mesh parameters and the boundary conditions are given in Tables 1 and 2. The chosen mesh resolution allows to solve turbulence (local turbulent fluctuations compared to mesh size) up to 500 Hz (symmetric model), respectively 1000 Hz for the acoustic part (at least 20 elements per wavelength). For the full model turbulence is resolved up to 800 Hz and acoustics up to 2000 Hz.

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Downstream: Outlet Fluid: Symmetry Downstream: Ground Upstream: Inlet

Z Y

X

Fig. 1 Computation domain and boundaries—X = longitudinal, Y = lateral, Z = vertical

Fig. 2 Computation mesh in a horizontal plane 1.5 m above ground—full model

Table 1 Mesh parameters Parameter

Symmetric model

Full geometry

Domain length (X)

20 m upstream extension + 37.75 m + 40 m downstream extension

Domain width (Y)

10 m

30 m

Domain height (Z)

25 m

30 m

Total number of cells

36 millions

167 millions

Boundary layers

6

10

1st layer thickness

2e−5 m

Boundary layer thickness

4.4 mm

2.2 FW-H The sound pressure at far-field receivers is predicted using the FW-H acoustic analogy with Farrassat’s Formulation 1A. Two FW-H source regions are defined: The first

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Boundary

Value

Inlet

Velocity inlet 320 km/h

Outlet

Pressure outlet

Ground

Wall—no slip

Sides

Symmetry

Y=0

Symmetry

Fig. 3 Left: Impermeable FW-H surface—right: permeable FW-H surface

one, so called impermeable surface, takes into account the skin of the bogie, which corresponds to free-field radiation, see Fig. 3 left. The second one, is a so-called permeable surface allowing to take into account acoustic interaction in the bogie cavity, see Fig. 3 right. The back surface in downstream direction of this FW-H source is not considered in the evaluation since it is known that artificial, spurious signals might appear [9]. The mesh size in the permeable FW-H is 8.4 mm for both models, which makes this region computationally expensive. FW-H volume terms (quadrupole noise), which take into account nonlinearities in the flow and are computationally expensive, are not considered.

2.3 Numerical Resolution The numerical resolution of the problem consists of three steps: First the flow field is initialized with a steady RANS model. Then, in the second step, the unsteady flow field, resolved by a DES model, is initiated in order to develop the turbulent flow before activating in the third step the FW-H model with a smaller time step, see details in Tables 3 and 4. For the symmetric model, pressure signals at virtual microphone positions are recorded at a frequency of 5.1 kHz starting from 0.6 s physical time. The chosen approach for the symmetric model is aggressive since only one flow flush between the train nose and the end of the bogie zone (estimated time 0.09 s) is considered

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Table 3 Physical time section and time steps Parameter

Symmetric model

Full model

Physical time flow initialization (s)

0–0.5

0–1.4

Time step initialization (s)

1e−3

1e−3

Physical time FW-H resolution (s)

0.5–0.75

1.4–1.75

Time step FW-H (s)

6.5e−5

4e−5

Table 4 Model and solver parameters Parameter

Value

Turbulence

K-omega SST

Gas

Ideal gas

Solver

Segregated flow and fluid temperature

Numerical scheme

2nd order implicit

Iterations per times step

Min. 5–max. 10

before starting signal recording. This choice is made in order to meet the major aim of the project which consisted in implementing the complete approach up to the equivalent noise source. For the full model, a less aggressive approach was chosen.

2.4 Post-Processing For each virtual microphone pressure signals are either recorded directly (FW-H on the fly) or in a post-FW-H approach for a duration of 0.125 s (symmetric model). For the later, the necessary flow field data is exported during the computation run. This approach has the advantage that microphone positions do not have to be defined before-hand. The equivalent acoustic source of the bogie is described by the sound power and directivity which are both determined using a virtual microphone array, see Fig. 4. The sound power is obtained from the mean pressure of 40 microphones arranged regularly on a hemisphere around the bogie center (ISO 3745 standard). For the symmetric model, the pressure signals from the modelled side are mirrored to the non-modelled, symmetric side. Furthermore, ground effects are not considered.

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Fig. 4 Virtual microphone array used to determine the equivalent acoustic source of the bogie

3 Results 3.1 Flow Field The aerodynamic part of the model is validated by comparing the drag force to previously obtained results of a numerical simulation with Powerflow [10]. A good agreement is observed such that the model is validated from this point of view. Furthermore the drag force is compared between the different model implementations as shown in Fig. 5: A good agreement is observed; the main effects on drag such as the impact of the nose and bogie are well reproduced by all models. A snapshot of the instantaneous velocity field in the bogie area, see Fig. 6, reveals the turbulent nature of the flow: First the flow is slowed down up to the stagnation point at the nose, before being accelerated below and along the car body. Strong flow-structure interaction, mainly observed at the axle box of the first wheelset and the longitudinal damper, causes formation of turbulent eddies combined with strong velocity gradients. Aerodynamic noise sources are related to instantaneous pressure fluctuations p' = p − p¯ as shown in Fig. 7. The main fluctuations in the shown plane are located at the previously identified regions of strong flow-structure interaction, see Fig. 6: Fig. 5 Comparison of drag forces between RANS and instantaneous DES results for the symmetric and full model

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flow direction

Fig. 6 Instantaneous velocity magnitude in a horizontal plane 1.5 m above ground—full model

Fig. 7 Instantaneous pressure fluctuations p' in a horizontal plane 1.5 m above ground—full model

The axle box of the first wheelset and the longitudinal damper are both elements that protrude above the car body envelope.

3.2 Acoustics Currently, acoustic results are only available for the symmetric model: Fig. 8 shows the sound power spectra of the two FW-H source regions: taking into account the bogie cavity (permeable region) leads to a 5 dB lower noise level. Furthermore the spectra reveal two emerging third octave bands at 250 and 500 Hz third octave band, which are probably related to flow-structure interaction in the region of the axle box and longitudinal damper (see Figs. 6 and 7). Both bands were previously observed

188 Fig. 8 Sound power—full line: impermeable FW-H source—dashed line: permeable FW-H source—symmetric model

M. Rissmann et al. 5 dB

Fig. 9 Horizontal directivity (dB) in the 250 Hz band of the symmetric model—left: impermeable FW-H source surface—right: permeable FW-H source surface—symmetric model

by SNCF in numerical simulations and measurement campaigns, so the results of this work can be trusted. Figure 9 shows the directivity patterns in horizontal direction of both FW-H sources in the 250 Hz third octave band. The directivity from the modelled side is mirrored to the non-modelled side. The leading bogie has a dipole radiation characteristic in the horizontal plane.

4 Conclusions In this work a numerical simulation approach based on CFD/CAA techniques is developed to predict aerodynamic noise of different components of SNCF’s TGV high speed trains. The approach is applied to estimate an equivalent acoustic source for the first, leading bogie. First acoustic results, obtained with a symmetric, computationally less expensive model are presented. The results reveal that the leading bogie has a dipole characteristic with emerging frequencies in the 250 and 500 Hz third octave band, which was also observed in previous works by SNCF. Using two

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different FW-H source zones allows to show that the bogie cavity acts as an acoustic screen and influences the source directivity. In a next step, the results will be compared to the full model which has also a higher resolution. This allows to see if the computationally less expense symmetric approach is sufficient to estimate an equivalent acoustic source for the aerodynamic noise. In addition to that the aerodynamic noise will be compared to rolling noise, which is another major railway noise source. In the future the suggested approach will allow SNCF to estimate other aerodynamic noise sources such as the pantograph recess, the inter coach gap and the second bogie for example. Also, the impact of noise mitigation devices such as flow deflectors can be quantified before actual prototype tests. Finally, the results from this work are already used by SNCF noise experts in order to predict the exterior noise emission of TGV high speed trains.

References 1. Thompson D (2008) Railway noise and vibration: mechanisms, modelling and means of control. Elsevier 2. Mellet C, Létourneaux F, Poisson F, Talotte C (2006) High speed train noise emission: latest investigation of the aerodynamic/rolling noise contribution. J Sound Vib 293(3–5):535–546 3. Poisson F (2013) Railway noise generated by high-speed trains. In: Proceedings of the 11th international workshop on railway noise. Uddevalla 4. Zhang J et al (2018) Source contribution analysis for exterior noise of a high-speed train: experiments and simulations. Shock Vib 2018:1–13 5. Li C, Chen Y, Xie S, Li X, Wang Y, Gao Y (2021) Evaluation on aerodynamic noise of high speed trains with different streamlined heads by LES/FW-H/APE method. In: Noise and vibration mitigation for rail transportation systems. Springer, pp 57–65 6. Minelli G, Yao HD, Andersson N, Höstmad P, Forssén J, Krajnovi´c S (2020) An aeroacoustic study of the flow surrounding the front of a simplified ICE3 high-speed train model. Appl Acoust 160:107–125 7. Iglesias EL, Thompson DJ, Smith MG (2015) Component-based model for aerodynamic noise of high-speed trains. In: Noise and vibration mitigation for rail transportation systems. Springer, pp 481–488 8. Lockard D (2011) Summary of the tandem cylinder solutions from the benchmark problems for airframe noise computations-I workshop. In: 49th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, p 353 9. Lopes LV et al (2017) Identification of spurious signals from permeable Ffowcs-Williams and Hawkings surfaces. In: American Helicopter Society (AHS) international annual forum and technology display, no. NF1676L-25336 10. Masson E, Paradot N, Allain E (2010) The numerical prediction of the aerodynamic noise of the TGV POS high-speed train power car. In: Proceedings of the 10th international workshop on railway noise, Nagahama

Optimization of Window Pattern of Tunnel Hood Installed at Long Slab Track Tunnel for Reducing Micro-Pressure Waves Shinya Nakamura, Tokuzo Miyachi, Takashi Fukuda, and Masanobu Iida

Abstract Micro-pressure waves (MPWs) associated with high-speed railways can cause serious environmental problems. The magnitude of the MPWs is proportional to the pressure gradient of the compression wave at the tunnel exit. A compression wave is generated when a train enters a tunnel, and it propagates towards the exit. For a long slab track tunnel, the pressure gradient of the generated compression wave increases during propagation owing to nonlinear effects. The nonlinear effects primarily depend on the pressure gradient of the compression wave at the entrance. Therefore, tunnel hoods are installed in long slab track tunnels in Japan to reduce the pressure gradient. Recently, a rapid numerical method has been developed to calculate the generation and propagation of compression waves based on the nonlinear acoustic theory, which enables optimization of the window pattern of the hoods by considering the propagation of the compression wave for long tunnels. In this study, the window patterns for short and long slab track tunnels were optimized, and the optimum window patterns (OWPs) are shown to be dependent on the tunnel length. Keywords Pressure wave · Micro-pressure wave · High-speed train · Tunnel entrance hood · Slab-track

1 Introduction Micro-pressure waves [1] (MPWs) radiate outward from high-speed railway tunnels, potentially causing audible noise. The waveforms of MPWs are proportional to those of the pressure gradient of compression waves at the exit of a tunnel having propagated from the entrance of the tunnel. Generally, the compression waves steepen in slab track tunnels, and the maximum values of the pressure gradients increase because of the nonlinear effect. The steepening becomes significant when the pressure gradient of the compression wave at the tunnel entrance (called an initial wave) is S. Nakamura (B) · T. Miyachi · T. Fukuda · M. Iida Railway Technical Research Institute, 2-8-38 Hikari-cho, Kokubunji-shi, Tokyo 185-8540, Japan e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_17

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large. The maximum values of micro-pressure waves tend to be large around portals of long slab-track tunnels. Countermeasures to MPWs reduce the maximum pressure gradient of initial waves to suppress the nonlinear effect during propagation. Therefore, Japanese railway engineers have examined optimizing tunnel hoods [1] and profiles of train noses [2], while some studies are reported the countermeasures in a tunnel [3, 4]. Accordingly, in past studies, the maximum pressure gradient at the tunnel entrance was chosen as an objective function of optimizing. However, to be exact, the maximum value of MPW is proportional to that at the exit. Miyachi et al. [5, 6, 7] reported that the propagation characteristics, particularly the steepening of compression waves, depend not only on the maximum pressure gradient of the compression wave but also on its waveform at the tunnel entrance. Therefore, it is necessary to consider the propagation characteristics in hood optimization. Railway Technical Research Institute (RTRI) and DB Systemtechnik [8, 9] have developed a numerical technique to theoretically and numerically investigate the propagation of compression waves in slab-track tunnels. The technique can be used to calculate a compression waveform at the exit of a tunnel using that at the entrance in a short time. Moreover, Howe et al. [10, 11] developed an acoustic procedure to compute a compression waveform at the tunnel entrance by considering a train and hood configurations. Here, the hood configuration constitutes a pattern of windows installed on side walls (or a roof) of the tunnel hood. Combining these two techniques enables to optimize the hood configuration, taking the propagation characteristics into consideration. Generally, the maximum pressure gradients at the entrance and exit are approximately the same in short tunnels; for instance, less than 1 km in length. Therefore, the optimum window pattern minimizes the maximum pressure gradient at the entrance. However, for long slab-track-tunnels, the optimum window pattern differs from that for short tunnels because the pattern need to minimize the maximum pressure gradient at the exit, not at the entrance. This study optimizes the window pattern for short and long slab-track-tunnels and demonstrates that the optimum window pattern depends on the tunnel length.

2 Methodology 2.1 Simulation for the Initial Wave Generation with a Hood The tunnel hood is considered as an entrance countermeasure. Generally, windows are provided on the side of the hood. The window size, number, train nose, train speed, etc., affect the performance of a hood. In this study, we consider an optimization problem to investigate “window pattern minimizing micro-pressure wave.” In this analysis, the basic specifications of the train and the hood are fixed on the initial wave generation. The window pattern for minimizing micro-pressure wave is defined as

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OWP (x) at a tunnel length x. It indicates that the optimum window pattern depends on x. The peak value of the MPW is approximately proportional to the maximum pressure gradient of the compression wave at the tunnel exit. Here, β is defined as follows, ( ) β(x) = (

∂p ∂t max, EX OWP(x)

)

(1)

∂p ∂t max, EX OWP(x=0)

where p: pressure, x: propagating distance (tunnel length), t: time, EX: tunnel exit conditions. Here, β represents the micro-pressure wave ratio when the window pattern changes from OWP (x = 0) to OWP (x). As described above, OWP (x = 0) is the design guideline in many existing hoods. The specifications of the train and hood are listed in Table 1. Figure 1 illustrates the window conditions of the hood. The windows are on the far-side from the train running at offset position from the tunnel center. Tunnel hoods with lengths of 20, 30, and 40 m were assumed in this study. The 20 m, 30 m, and 40 m hoods have six, nine, and twelve windows, respectively. Opening or closing each window generates 26 = 64, 29 = 512, and 212 = 4096 window patterns for hood lengths of 20 m, 30 m, and 40 m, respectively. These window patterns (WP) are represented by binary numbers, where open window is “1” and close window is “0”, which are displayed from the hood entrance. For example, “WP = 111111” is a pattern in which all windows are open, and “WP = 000001” is a pattern in which all windows are closed except the nearest window to the main tunnel. The compression waveform for each window pattern at the entrance was calculated using the method by Howe et al. [7, 8]. An example of calculating the waveform at entrance is shown in Fig. 2. The pressure rise Δp of the compression wavefront at the tunnel entrance when the train enters is given in Eq. (2). The Eq. (2) neglects the effects of friction on the side of the train and tunnel and is independent of the window pattern. Table 1 Specifications of the tunnel hood and train Hood Train

Cross-sectional area ratio of the hood to the tunnel

1.4

Hood length L (m)

20, 30, 40

Cross-sectional area ratio of the train to the tunnel R

0.189

Train speed U (km/h)

320

Length of the train nosel(m) Cross-sectional area of the train

15 (m2 )

12

Shape of the Train nose

Ellipse

Train offset (m)

2.16

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Fig. 1 Windows of hood (far-side)

Fig. 2 Waveforms of ∂p/∂t at entrance (20 m hood)

Δp =

1 − (1 − R)2 1 ) ( ρ0 U 2 2 (1 − M) M + (1 − R)2

(2)

Here, U: train speed, ρ 0 : atmospheric density, R: cross-sectional area ratio of the train to the tunnel, M: train Mach number. From the conditions of Eq. (2), the pressure gradient waveform at the tunnel entrance by OWP (x = 0) is a trapezoidal form having a constant section of the waveform gradient, which is shown in Fig. 2 as “OWP (x = 0) = 010111”.

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2.2 Simulation for Wave Propagation for Long Slab-Track Tunnels The simulation of the compression wave propagating through the tunnel follows the following spatial evolution equations [3−6]. ∂p ∂ 1/2 p ∂p = ┌p − αp − 2β 1/2 ∂x ∂t ∂t ∂ 1/2 p 1 =√ 1/2 ∂t π

{t 0

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Each quantity is made dimensionless by atmospheric pressure, atmospheric sound speed, and tunnel hydraulic diameter. Moreover, α and β represent empirical parameters (α = 2 × 10–4 , β = 5.5 × 10–4 , [5]). The calculation conditions are listed in Table 2. Generally, Shinkansen tunnels have small branches called “short side branches.” Here, the short side branches were installed as indicated in Fig. 3, and the pressure waveform before and after the short side branch was obtained from one-dimensional acoustic analysis [5]. Table 2 Simulation parameters of the tunnel Cross-sectional area of the tunnel A (m2 )

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Fig. 3 Short side branches in the tunnel

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3 Results The calculation results are presented in Figs. 4, 5, 6 and 7. Figure 4 illustrates the maximum pressure gradients for each tunnel length when 0, 20, 30, and 40 m hoods are installed. Note that the calculation results of OWP (x = 0) or “no hood” exhibit change in the maximum pressure gradient of the compression wave which has the same initial waveform. However, the calculation results of OWP (x) have different initial waveforms for each distance, e.g. OWP (x = 0) = 010111, OWP (x = 5.5 km) = 000011 for 20 m hoods. From Fig. 4, when the window pattern was set to OWP (x = 0) (conventional method), the maximum pressure gradient at the exit is approximately 50% in a short tunnel and approximately 30% in a tunnel that is approximately 2 km in length compared to the case without a hood. From Fig. 5, for example, when a 40 m hood is installed in a 9 km tunnel, β = 0.4, the maximum pressure gradient at tunnel exit for OWP (x = 9 km) is reduced to almost 40% from that for OWP (x = 0) of the conventional method.

Fig. 4 (∂p/∂t)max,EX versus x

Fig. 5 β (x) versus x

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Fig. 6 Waveforms of ∂p/∂t (40 m hood)

Fig. 7 Pressure gradients of Max 1 and Max 2 of OWP (x) for 40 m hood

Figure 6 illustrates pressure gradient waveforms for OWP 40 m hood. Figure 7 depicts variation of the maximum values of pressure gradients with tunnel length. Here, Max 1 and Max 2 denote the maximum values of pressure gradients at the entrance for t < 0.975 s and t > 0.975 s, respectively, of OWP (x) for 40 m hood. For OWP(x = 0), the waveform is a trapezoidal shape to reduce the peak value as its integration keeps the constant shown in Eq. (2). Moreover, Max 1 is almost the same as Max 2 of OWP (x) with x < 3 km, as shown in Fig. 7. For x > 3 km, , Max 1 of OWP (x) increase with tunnel length. For x > 5 km, , Max 1 of OWP (x) is clearly larger than Max 2 of OWP (x). Furthermore, for OWP (x = 5.5 km) (Fig. 2) or OWP (x = 7.5 km) (Fig. 6a), the pressure gradient waveforms at the entrance are downward to the right. This tendency is consistent with the results already reported

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in the reference 0 and 0. Further research is required to quantitatively explain the tendency and the propagation characteristics.

4 Conclusion Numerical calculations were performed to investigate the optimum window pattern of tunnel hoods for long slab-track tunnels. Two numerical methods were combined, where one is for a wave generated at the entrance by a train entering a tunnel with a hood with windows and the other is for the wave propagation through a slabtrack tunnel. The results revealed that the optimum window patterns are different for short and long slab-track tunnels. The hoods with the optimum window patterns make initial waveforms trapezoidal and downward to the right for short and long slab-track tunnels, respectively. The tendency can be observed more clearly for long tunnels over 5 km in length.

References 1. Ozawa S (1978) Reduction of micro-pressure wave radiated from tunnel exit by hood at tunnel entrance. Q Rep RTRI 19(2):77–83 2. Iida M et al (1996) Optimization of train nose shape for reducing impulsive pressure wave from tunnel exit. Trans Japan Soc Mech Eng Ser B 62(596):1428–1435 (in Japanese) 3. Tielkes T et al (2008) Measures to counteract micro-pressure waves radiating from tunnel exits of DB’s new Nuremberg-Ingolstadt high speed line, noise and vibration mitigation for rail transportation systems. Notes Numer Fluid Mech Multidisc Des 99:40–47 4. Liu F et al (2021) Influence of air chambers on wavefront steepening in railway tunnels. Tunn Undergr Space Technol 117:104120 5. Miyachi T et al (2013) A new simple equation governing distortion of compression wave propagating through Shinkansen tunnel with slab tracks. J Fluid Sci Technol 8(3):462–475 6. Miyachi T et al (2016) Propagation characteristics of tunnel compression waves with multiple peaks in the waveform of the pressure gradient: part 1: field measurements and mathematical model. Proc Inst Mech Eng Part F J Rail Rapid Transit 230(4):1297–1308 7. Miyachi T et al (2016) Propagation characteristics of tunnel compression waves with multiple peaks in the waveform of the pressure gradient: part 2: theoretical and numerical analyses. Proc Inst Mech Eng Part F J Rail Rapid Transit 230(4):1309–1317. https://doi.org/10.1177/095440 9715602728 8. Miyachi T et al (2016) Numerical simulation of compression wave propagation in German slab-track tunnels. In: Proceedings of 12th world congress on railway research 9. Hieke M et al (2016) Field measurements of Micro-pressure wave mitigations of German new high-speed line Erfurt-Halle/Leipzig. In: Proceedings of 12th world congress on railway research 10. Howe MS et al (2006) Rapid calculation of the compression wave generated by a train entering a tunnel with a vented hood. J Sound Vib 297:267–292 11. Miyachi T (2019) Non-linear acoustic analysis of the pressure rise of the compression wave generated by a train entering a tunnel. J Sound Vib 458:365–375

Component-Based Model to Predict Aerodynamic Noise from High-Speed Train Bogies Tatsuya Tonai, Eduardo Latorre Iglesias, Toki Uda, Toshiki Kitagawa, Jorge Muñoz Paniagua, and Javier García García

Abstract Aerodynamic noise becomes a significant source of railway noise at speeds above 300 km/h. The bogie of a high-speed train area is one of the most relevant aerodynamic noise sources. Semi-empirical component-based models have been used for bogie aerodynamic noise prediction because they allow fast and cheap calculations compared with numerical methods. A semi-empirical component-based model to predict high-speed train bogie aerodynamic noise is being developed based on an existing model already used to predict pantograph noise. Thus, noise tests were conducted in the Railway Technical Research Institute’s anechoic wind tunnel placed in Kunitachi for different flow speeds using simple shape-representing simplified bogie components and a simplified 1/5 scale bogie placed inside a cavity. The noise spectra radiated by a cube at different vertical positions and by two cubes in tandem are presented. These are used to adjust the empirical constants of the prediction model and assess the low-frequency interaction noise correction. The noise radiated by the complete simplified bogie and without some components are also presented, including the contribution of each bogie component to the overall noise. Keywords Aerodynamic noise · Bogie · Prediction model · Wind tunnel tests

T. Tonai (B) · T. Uda Railway Technical Research Institute, 2-8-38 Hikari-cho, Kokubunji-shi, Tokyo 185-8540, Japan e-mail: [email protected] E. Latorre Iglesias · T. Kitagawa ETSIST, Universidad Politécnica de Madrid, C/Nikolas Tesla s/n (Campus Sur), 28031 Madrid, Spain J. Muñoz Paniagua · J. García García ETSII, Universidad Politécnica de Madrid, C/José Gutiérrez Abascal, 2, 28006 Madrid, Spain © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_18

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1 Introduction Aerodynamic noise becomes a significant source of railway noise at speeds above 300 km/h, typical of high-speed trains. Aerodynamic noise is produced by the interaction of the incoming airflow with different components or areas of the train. Affirmatively, the bogie area has been identified as one of the most relevant [1]. Thus, understanding how this noise is produced is crucial to quantify and accurately predict it in order to assess its impact on the environment and to evaluate noise countermeasures. Recently, numerical simulations have attracted interest in predicting railway aerodynamic noise. In the case of train bogies, examples of using Delayed DetachedEddy Simulation (DDES) for calculating the noise generated by a simplified bogie [2] and the noise reduction achieved using side skirts [3] exist. These studies show that numerical simulations are a vital tool for bogie area aerodynamic noise prediction; however, the required computational cost and time may be too high due to the large computational domain, complex geometry, and wide range of wavelengths involved in the calculations. As an alternative, component-based semi-empirical models can be used as a quick engineering calculation tool that could satisfy the requirements of a real project. This approach has already been applied to predict the aerodynamic noise generated by high-speed train pantograph, obtaining good results compared with wind tunnels [4] and field tests [5]. A first attempt to apply a component-based approach for predicting the aerodynamic noise produced by a high-speed train bogie is found in [6]. In this case, the component-based model used to predict pantograph noise is applied to the bogie case with few modifications. For example, the normalized spectra were adjusted using experimental data obtained in anechoic wind tunnel noise measurements with simple geometries representing the bogie components; in addition, a correction term was added to account for the low-frequency noise produced by the interaction of the incoming turbulence and the bogie components. However, the work done so far seems insufficient as the low-frequency noise, for the case when the bogie is installed in the bogie cavity, remains underpredicted. Noise tests were performed in the anechoic wind tunnel using different test configurations, including a cavity: in an attempt to continue building the prediction model. The obtained results are presented in this study as follows: some insights into the semi-empirical component-based model are presented in Sect. 2. The experimental setup is shown in Sect. 3 and the obtained results are presented in Sect. 4. Section 5 shows the implications of the obtained results for the prediction model and finally, conclusions are drawn.

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2 Existing Component-Based Prediction Models The component-based prediction model assumes that the aerodynamic noise produced by a high-speed train bogie can be obtained as the incoherent sum of the noise generated by its components. The mean-square-sound pressure spectrum radiated by an assembly of bodies exposed to an incoming flow can be obtained as follows [6]:  2 2 ρ0 c0  Mi6 ηi Si Fi ( f ) Dradi (ψ, φ) p2 ( f ) = 16 (1 − Mi cos(θ ))4 Ri2 i   E( f ) 1+C E0 ( f )

(1)

where ρ0 is the air density, c0 is the speed of sound, f is the frequency, M = U/c0 is the Mach number, U is the incident flow speed, R is the distance between the component and the receiver, and S is the bogie component’s total surface area. The index i represents the number of bogie components. Some correction terms are amplification included, such as the directivity function, Dradi (ψ, φ), the convective  

factor, (1−Mi cos(θ ))4 , and the interaction noise correction 1 + C EE(0 (ff)) , which accounts for the low-frequency interaction noise produced by turbulence generated upstream of the components interacting with themselves. E( f ) is the spectrum of the incident turbulent energy, E 0 ( f ) is the reference turbulent spectrum used to make the incident turbulent-noise correction term nondimensional and C is a constant used to fit the function to empirical/numerical data. The parameter, ηi , controls the amplitude and Fi ( f ) defines the noise spectrum shape of each component. In [6], the amplitude constant, ηi , and the shape of the empirical functions, Fi ( f ), were used to fit the noise spectra of a cube, a disc (representing a train wheel), and two different rectangular cuboids (representing the train motor and gearbox) measured in an anechoic wind tunnel at different flow speeds. The aerodynamic noise produced by those simple geometries had a distinguishable peak whose frequency depended on the flow speed. The chosen function, Fi ( f ), to represent the peak noise is [6]: ap1 Fp ( f ) =  2 ( f 0 / f )2 − ( f / f 0 )2 + ap2

(2)

where ap1 and ap2 are empirical constants used to modify the width of the function and f 0 is the peak frequency. The function in Eq. (2) provides a haystack-like spectrum shape that accurately fits the typical vortex shedding noise spectrum. Figure 1a shows the measured and fitted noise spectra of a cube at an airflow speed of 31.5 m/s. The model’s overall noise is the result of the energetic sum of peak and broadband noise functions. It had good consistency, except at low and high frequencies due to background noise. Figure 1b shows the difference between measurements and predictions using a 1/

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Fig. 1 a Simple cube: measured noise spectrum and fitted normalized function (from [6]), flow speed: 31.5 m/s. b Noise difference between predictions and measurements for a 1/10-scale simplified motor bogie alone and inside a cavity. Frequency scale as measured (results obtained using the data of [6]). Flow speed: 50 m/s

10 scale simplified motor bogie, alone and inside a cavity [6]. The results obtained using the existing component-based model are good for a bogie alone, but the model tends to underpredict the noise at low frequencies (below 1 kHz) when the bogie is placed inside a cavity. This inconsistency could be because the bogie components are partially shielded by the bogie cavity, which is a situation not considered in the existing prediction model. Another reason could be the noise produced by the interaction between the flow separated in the upstream bogie cavity step and the bogie components or among the bogie components themselves. Thus, the correction term in Eq. (1) must be properly adjusted. Therefore, new anechoic wind tunnel tests were performed. The used experimental setup and the obtained results are presented in Sects. 3 and 4.

3 Experimental Setup at an Anechoic Wind Tunnel Aerodynamic noise from a 1/5-scaled cavity model was measured using a single microphone at the RTRI’s anechoic wind tunnel placed at Railway Technology Research Institute (RTRI) in Kunitachi, Japan. Figure 2 shows the experimental setup. The model was constructed with 15-mm-thick plates that simulate the ground and the two-dimensional bogie cavity of a train. The cavity length and height were 800 and 160 mm, respectively, and the distance between the ground plate and the underside of the car body was 80 mm, based on Shinkansen’s dimensions. Although the car body and ground are actually in relative motion, the use of a moving ground was discarded to avoid increasing the background noise. The upstream ground plate is 1 m into the nozzle to reduce noise radiated from the tip of the ground plate. Further, the cavity’s rear edge was rounded to a radius of 60 mm to minimize cavity noise. The microphone was positioned so that the sound receiving point was x = 650 mm (the center of cavity length), y = 1250 mm (1250 mm away from the center

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Fig. 2 1/5 scaled cavity model and experimental setup

of nozzle width), z = 0 mm (height of the underside of the car body), and the orientation matched the y direction. Figure 2 shows the coordinate axis and its origin. The inflow velocity was 250 km/h, which was measured using a pitot tube at (x, y, z) = (0, 0, 40) mm. Figure 3 shows the three configurations considered inside the cavity. Figure 3a shows the “single cube” configuration. A cube (D = 150 mm on each side) was fixed in the cavity using a circular support (diameter of 20 mm) and was mounted so that one of its faces was directly opposite the x-direction. The circular support’s center axis was placed 1 D from the upstream wall (x = 400 mm) on the cavity center line (y = 0). The z-position of the top of the cube was varied from 0 to 60 mm at 15 mm steps to assess the effect on the noise of its vertical position inside the cavity. Particularly, the condition at 30 mm was used as a “reference.” Fig. 3b the shows “double cubes in tandem” configuration that adds another identical cube and support to the “reference.” The central axis of the added support was on the cavity center (y = 0), and the distance between the two cubes varied from 1.5 D to 3.5 D at 1 D steps. Figure 3c shows the 1/5 scale “simplified bogie” configuration, which comprises a bogie frame, two wheelsets, two motors, and two gearboxes, each of which can be removed. The contribution of each component (in this case, the gearboxes, and motors) to aerodynamic noise from the bogie was evaluated based on the following four bogie conditions: the bogie with all components (SB), the bogie with motor and gearbox upstream only (SB front components), the bogie with motor and gearbox downstream only (SB rear components), and the bogie without motor and gearbox (SB no components).

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Fig. 3 Configurations inside the cavity: a “single cube,” b “double cubes in tandem,” and c “simplified bogie”

4 Experimental Results In this section, comparisons of the sound pressure level (SPL) in the three configurations shown in Sect. 3 are presented. The frequencies presented are multiplied by 1/5 to convert to the actual scale. Figure 4 compares the SPL at the different heights of the cube in the “single cube” configuration. The noise increases as the z-position of the top of the cube increases, that is, as the area exposed to airflow on the surface of the cube increases. The noise increase is similar for all frequency bands except for the 160 Hz band. Figure 5 shows the SPL at the “double cubes in tandem” configuration. The figure also shows the “single cube” reference. Compared to the case with a single cube, the relative noise is greater at lower frequencies when two cubes are inside the cavity and conversely, is closer to 0 dB at higher frequencies. This is because the backward cube is in a flow that is delayed by the upstream cube, and its contribution to the

Fig. 4 Experimental result of the “single cube” configuration: a SPL and b Relative SPL between reference and others at each 1/3 octave band. BGN means the noise with no cube condition

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overall sound should be smaller than that of the upstream cube. However, the noise increases by more than 3 dB at lower frequencies. This is due to a noise amplification mechanism at the “double cube in tandem” configuration. Figure 6 shows the SPL at the “simplified bogie” configuration. The bogie conditions had little effect noise difference. The front components add noise between 0.5 and 1.5 dB to relative SPL across all frequency bands. However, the noise in the frequency range of 200–500 Hz is increased when the rear components are added. When all components are attached, the results are similar to those with only the front components, except for the frequency range.

Fig. 5 Experimental result of the “double cubes in tandem” configuration: a SPL and b relative SPL between reference and others at each 1/3 octave band

Fig. 6 Experimental result of the “simplified bogie” configuration: a SPL and b Relative SPL between “SB no components” and others at each 1/3 octave band

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5 Modification of the Component-Based Model Section 4 shows that any distinguished peak related to vortex shedding cannot be observed in the noise spectra of a cube or a simplified bogie inside a cavity. Thus, the normalized spectrum function shown in Eq. (2) does not fit the measured noise spectra well. The noise in the bogie area appears to be generated by the turbulence produced by the upstream cavity step or the bogie components themselves, and its spectral shape resembles that of the typical turbulence spectrum. An alternative function, F( f n ), for improving the fit is selected and expressed in Eq. (3):    F( f n ) = 4/ 1 + 4π 2 f nav

(3)

where f n = f de /U∞ is the normalized frequency, de is the length scale (in this case, 150 mm is chosen since it is the characteristic dimension of the cube), U∞ is the mainstream flow speed (250 km/h), and a value of av = 1.2 is chosen to fit the experimental data. Equation (3) is calculated in narrowband and subsequently converted to 1/3 octaves, Fo ( f ). Then, two additional corrections are applied to obtain the normalized spectrum function, Fp ( f ), to be substituted in Eq. (1) and presented as follows:   N Fp ( f i ) = 1/ Fo ( f i )ap Fo ( f i )ap i=1

(4)

where the first term is used to force the sum of Fp ( f ) over frequency to be unity and an exponent ap = 7.1 is chosen to increase the slope decay by an octave of the function and to improve fitting with the experiments. The obtained normalized spectrum function, Fp ( f ), is substituted in Eq. (1), with the cube surface area, S = 0.135 m2 , the amplitude constant, η = 0.07, and R = 1.25 m. Figure 7a shows the results obtained in which the adjusted noise spectrum (adjustment made “by eye”) is compared with the measured noise spectrum for a single cube in a cavity. Although the peaks obtained in the measurements are not followed by the normalized spectrum curve, the difference between the measured (90.5 dB) and predicted (90.3 dB) overall noise is only 0.2 dB. The correction factor that considers the low-frequency interaction noise included in Eq. (1) is reviewed using the data obtained from the measurements with the “double cubes in tandem” configuration. Since the turbulence spectrum was not measured in this wind tunnel test, the measured noise spectra were used instead. Thus, as a reference spectrum, E 0 ( f ), the noise measured with only one cube is selected, and as turbulence spectrum, E( f ), the noise measured with the “double cubes in tandem” is chosen. Figure 7b shows the results after adding the interaction noise correction with a value of C = 0.25 to the noise measured with one cube. The corrected noise spectrum is similar to that measured with the “double cubes in tandem” configuration separated by a distance of 2.5 D, with small differences in the peak at 50 Hz and in high frequencies.

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Fig. 7 a Normalized spectrum adjusted to the measured noise with one cube in a cavity; flow speed of 250 km/h. b Comparison between the noise made by one cube in a cavity without and with the interaction noise correction and the noise made by two cubes in tandem, 250 km/h

6 Conclusions Aerodynamic noise from a cube, double cubes in tandem, and a 1/5-scaled simplified bogie placed in a cavity was measured using a single microphone at the RTRI’s anechoic wind tunnel to develop a component-based model of aerodynamic noise from a bogie area. For a “single cube” configuration, the noise increased as the area exposed to airflow on the surface of the cube increased for all frequency bands, except for the 160 Hz band. For the “double cubes in tandem” configuration, the noise increase was greater at lower frequencies than expected due to the interaction between the cubes. From the “simplified bogie” configuration, the front components (motors and gearboxes) added noise across all frequency bands and the rear components only added the noise between 200 and 500 Hz. Based on the test results, an improved equation is proposed to model the noise spectra from bogie components and the applied interaction noise correction is revised.

References 1. Mellet C et al (2006) High speed train noise emission: latest investigation of the aerodynamic/ rolling noise contribution. J Sound Vib 293(3–5):535–546 2. Zhu J et al (2016) Flow behaviour and aeroacoustic characteristics of a simplified high-speed train bogie. Proc Inst Mech Eng Part F J Rail Rapid Transit 230(7):1642–1658 3. Zhu J et al (2018) The flow and flow-induced noise behaviour of a simplified high-speed train bogie in the cavity with and without a fairing. Proc Inst Mech Eng Part F J Rail Rapid Transit 232(8):759–773 4. Latorre Iglesias E et al (2017) Component-based model to predict aerodynamic noise from high-speed train pantographs. J Sound Vib 394:280–305

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5. Liu X et al (2021) Aerodynamic noise of high-speed train pantographs: comparisons between field measurements and an updated component-based prediction model. Appl Acoust 175:107791 6. Latorre Iglesias E (2015) Component-based model to predict aerodynamic noise from high-speed trains. PhD. thesis, University of Southampton

Reduction of Aerodynamic Noise Emitted from Pantograph by Applying Multi-Segmented Smooth Profile Pantograph Head and Low Noise Pantograph Head Support Takeshi Mitsumoji, Takayuki Usuda, Shigeyuki Kobayashi, Kyohei Nagao, Yuki Amano, and Yusuke Wakabayashi

Abstract Reducing aerodynamic noise emitted from a pantograph head and its support, which are the pantographs’ dominant aerodynamic noise sources, is among the key environmental challenges facing the further acceleration of high-speed trains. This paper shows three aerodynamic noise reduction strategies applicable to actual trains: applying multi-segmented smooth-profile pantograph head, shape improvement of the pantograph head support, and covering of the pantograph head support with a layer of porous material. Wind tunnel tests confirmed that aerodynamic noise can be reduced by 2.7 dB compared to pantographs in current use by applying these strategies. Keywords Pantograph head · Aerodynamic noise · Porous material

1 Introduction Japan has strict environmental quality standards for noise along the Shinkansen highspeed train route, which runs through densely populated areas. Therefore, reduction of wayside noise caused by Shinkansen trains is necessary to protect the environment along the railway lines. Since the power of aerodynamic noise grows as the 6th to 8th power of train speed, aerodynamic noise dominates the wayside noise of high-speed train. Among the various parts of the Shinkansen train that emit aerodynamic noise, the pantograph is one of the dominant aerodynamic noise sources, particularly the T. Mitsumoji (B) · T. Usuda · S. Kobayashi · K. Nagao · Y. Amano Railway Technical Research Institute, 2-8-38, Hikari-cho, Kokubunji-shi, Tokyo, Japan e-mail: [email protected] Y. Wakabayashi Advanced Railway System Development Center, R&D Center of JR East Group, East Japan Railway Company, 2-479 Nisshin-cho, Kita-ku, Saitama-shi, Saitama, Japan © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_19

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Horn

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Fig. 1 Shape of high-speed pantograph and pantograph head: a high-speed pantograph; b currently used pantograph head cross-section; c smooth-profile pantograph head cross-section

pantograph head and its support (see Fig. 1a). Because the shape of the pantograph head is important for stabilizing lift force characteristics, a cross-sectional shape similar to a rectangle, as shown in Fig. 1b is currently used, making it impractical to smooth the cross-sectional shape to reduce aerodynamic noise. A former study applied an optimization technique with the help of CFD analysis, under the assumption of one-directional operation, to propose a smooth-profile pantograph head (see Fig. 1c) that achieves both aerodynamic noise reduction and stabilization of lift force characteristics [1]. Other studies showed that reducing aerodynamic noise requires improving the cross-sectional shape of the pantograph head and mitigating the flow interference between the pantograph head and its support [2, 3]. Accordingly, these former studies have proposed a method of relocating the pantograph head to a position for its support that weakens flow interference [4] and a method of applying an open-cell-type porous material layer to the pantograph head support [5]. Based on these studies, the present research develops three aerodynamic noise reduction strategies further applicable to actual trains: applying multi-segmented smooth-profile pantograph head, improving the pantograph head support, and covering the pantograph head support with a layer of porous material. We performed wind tunnel tests to evaluate the aerodynamic noise reduction effects. This study premises that only one pantograph in the knuckle-forward direction is used for one trainset as in the E5 series Shinkansen. Train speed to consider is up to 100 m/s (360 km/h) and target of overall noise level reduction is set at 3 dB, which corresponding to the same noise level at 88.9 m/s (320 km/h) train operation under the assumption of 6th power law.

2 Wind Tunnel Test Aerodynamic noise measurement was carried out in RTRI’s large-scale low-noise wind tunnel, with a nozzle size of 3 m × 2.5 m and a maximum flow speed of 111 m/ s (400 km/h). Figure 2 shows the wind tunnel test setup. An actual Shinkansen pantograph was installed in an open-type test section. An omnidirectional microphone for aerodynamic noise measurement was set laterally and downward from

Reduction of Aerodynamic Noise Emitted from Pantograph … Fig. 2 Implementation of wind tunnel test

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the pantograph as shown in Fig. 2, and a 1/3-octave band analysis with A-weighting was undertaken. Within the omnidirectional microphone setup, the microphone position in the streamwise direction was set at the center of two insulators supporting the pantograph, which corresponds to 0.356 m upstream from the pantograph head center. The microphone position in the horizontal and vertical directions perpendicular to streamwise direction were set 2.616 m downward from the top of the pantograph head and 5 m laterally from the center of the pantograph head, which corresponds to the centerline of the nozzle. In addition, in some tests, a microphone array was installed 2.5 m above the pantograph head for noise source detection. The wind speed U 0 was set at 100 m/s (360 km/h). The Reynolds number based on the thickness of the pantograph head is 4.2 × 105 . We conducted a test without the pantograph head (hereinafter referred to as the condition “without pantograph head”) to account for background noise. The results from this test are described together below, with the aerodynamic noise measurement results.

3 Multi-Segmented Smooth-Profile Pantograph Head 3.1 Overview Figure 3 shows a schematic diagram of a multi-segmented smooth-profile pantograph head. This pantograph head is designed to reduce aerodynamic noise, stabilize lift force characteristics, and achieve high current collection performance [6]. In the multi-segmented smooth-profile pantograph head, the pantograph head is divided into nine elements in the lateral direction. Of these, the seven central are free to move up and down to some extent while maintaining the cross-sectional shape regarding the core (see Fig. 3a). The lift force characteristics are stabilized by avoiding changes

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Divided into 9 segments

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Glass epoxy 131mm

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(b)

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Fig. 3 Schematic diagram of multi-segmented smooth-profile pantograph head: a overview; b cross-section; c appearance

in the cross-sectional shape of the pantograph head due to the operation of the suspension mechanism. In addition, current collection performance is enhanced by using a C/C composite for the contact strip and glass epoxy for the pantograph head element to reduce the mass. This pantograph head differs from previous studies [7] in that “the pantograph head including the contact strip” is divided rather than “only the contact strip” to stabilize lift force characteristics and in that the significantly smooth profile cross-sectional shape is applied to reduce aerodynamic noise. The cross-sectional shape of the pantograph head (see Fig. 3b) is based on the smooth-profile pantograph head in Fig. 1c; however, the cross-sectional dimensions have been expanded due to the built-in suspension mechanism. Furthermore, a notch is provided in the leading edge portion on the upper surface to stabilize the lift force characteristics. In addition, one through-hole with cross-sectional dimensions of 5 mm × 17 mm is provided for each pantograph head element in order to reduce aerodynamic noise. A sliding test has confirmed that the multi-segmented smooth-profile pantograph head has good current collection performance. In this paper, we describe the following improvements to reduce aerodynamic noise: in Sect. 3.2, improvements to the shape of the pantograph head edge and horn; in Sect. 3.3, reductions in aerodynamic noise from the gaps between pantograph head elements. Both are new improvements specific to this kind of pantograph head compared to the previous study [7].

3.2 The Shape of the Pantograph Head Edge and Horn Figure 4 shows the noise source detection results. As shown in Fig. 4a, both edges of the initially developed multi-segmented smooth-profile pantograph head are short type, with lengths of 135 mm, and are equipped with a circular cross-section horn (Case 1-1). We confirmed that substantial aerodynamic noise was emitted from these parts. Therefore, expecting turbulence reduction, each edge is extended by 50% to 203 mm (Case 1-2), and the cross-sectional shape of the horn is changed from circular to oval (Case 1-3). As shown in Fig. 4b–d, it is confirmed that the aerodynamic noise is reduced by each of these changes independently. Finally, we confirmed the noise level could be reduced by a total of 0.8 dB by combining the long edge with the oval

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horn (Case 1-4). Based on these results, we selected the shape shown in Fig. 4d for the pantograph head edge and horn of the multi-segmented smooth-profile pantograph head.

3.3 Aerodynamic Noise from the Gaps Between Pantograph Head Elements The multi-segmented smooth-profile pantograph head possesses gaps of 2–4 mm between laterally adjacent elements so that each element can move up and down independently. Figure 5 shows the dependence of the aerodynamic noise on the opening condition of the gap. Based on this figure, the noise level when all the gaps are opened (Case 2-1; Fig. 5a upper left) is 0.8 dB higher, over a wide frequency band above 1 kHz, than when all the gaps are fully closed (Case 2-2; Fig. 5b upper right). In order to reduce aerodynamic noise emitted from the gaps while maintaining a movability of suspension mechanism, we installed a fur material to the inner wall of each gap along the front and bottom of the pantograph head (Case 2-3; see Fig. 5b bottom). As seen in Fig. 5a, this strategy reduced the gap-emitted aerodynamic noise at frequencies above 1 kHz while reducing the overall noise level by 0.5 dB compared to the case in which all gaps were fully opened. Based on these results, we selected the configuration in Case 2-3 to reduce the aerodynamic noise emitted from the gaps between the segments of the smooth-profile pantograph head.

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4 Low Noise Pantograph Head Support 4.1 Overview In this chapter, we propose two strategies to reduce the aerodynamic noise generated by the pantograph head support: in Sect. 4.2, an improved pantograph head support which relocates pantograph head to an appropriate position; in Sect. 4.3, a pantograph head support whose external layer consists of a porous material.

4.2 Improved Pantograph Head Support Past studies have shown that aerodynamic noise can be reduced by relocating the pantograph head to an appropriate position [4]. Figure 6a and b show visualized vortex structure obtained by CFD analysis when the pantograph head position was 144 mm upstream from its standard position in current use. This figure confirms that the vortex generation by the pantograph head support is weakened by relocating the pantograph head. Based on these results, we developed an improved pantograph head support (see Fig. 6c) that considered the pantograph’s mechanical mechanism and strength. Sliding tests confirmed that this improved pantograph head support meets mechanical strength requirements while maintaining the current collection performance to the extent of standard support.

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4.3 Pantograph Head Support Cover with Porous Material as an External Layer Past studies have shown that applying an open-cell-type porous material to the surface of an object can reduce aerodynamic noise [5]. These studies have also clarified that the mechanism of noise reduction is not sound absorption but rather stabilization of the flow field by spontaneous inflow and outflow on the surface of the porous material. It is essential to use a metal porous material of sufficient mechanical strength to withstand working conditions in actual trains (see Fig. 7a). In methods used in previous studies, the porous material was applied to the entire surface of the member, as shown in Fig. 7b. However, it was difficult to apply the metal porous material along the complicated curved surface in the present context. Therefore, as a novel application method, we flush-mounted the porous material only along with the areas where an aerodynamic noise reduction effect could be obtained (see Fig. 7c). Furthermore, in manufacturing a pantograph head support cover with a metal porous material for an actual train, it is important to limit the processing of the metal porous material as much as possible, for example, to manipulations such as surface flattening. According to some wind tunnel test results, it is confirmed that the corner portion of the upper surface of the support cover is an important region to consider in the context of porous material-based reduction of aerodynamic noise from the pantograph head support. Based on these considerations, we developed a pantograph head

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support cover with porous material as an external layer as shown in Fig. 7d. For this cover, we widened the existing current pantograph head support cover by 10 mm in the lateral direction. We applied a metal porous material with a thickness of 10 mm and an average hole diameter of 1.9 mm to the side of the cover, including the corners, with uniform thickness.

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Figure 8 shows the aerodynamic noise measurement results for the three strategies developed in this research, applied step by step to an actual pantograph. Compared to the pantograph in current use (Case 4-1), Case 4-2, with a multi-segmented smoothprofile pantograph head, showed a significantly reduced noise level in the frequency band above 630 Hz, and the overall noise level was reduced by 1.9 dB. In Case 4-3, we built upon Case 4-2 by adding a layer of porous material to the pantograph head support cover, and Case 4-4 by adding an improved pantograph head support. These further reduced the noise level in the frequency band above 630 Hz and a further ~ 0.5 dB reduction in the overall noise level. Finally, Case 4-5, which combined all three strategies, showed the lowest noise level in the frequency band above 630 Hz and a 2.7 dB overall noise level reduction regarding the pantograph in current use. These results demonstrate that this study’s aerodynamic noise reduction strategies for the pantograph head and its support can effectively reduce aerodynamic noise.

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6 Conclusions We developed three strategies to reduce the aerodynamic noise of the pantograph head and its support, premising knuckle-forward directional operation: applying multi-segmented smooth-profile pantograph head, improving the pantograph head support, and covering the pantograph head support with a layer of porous material. Wind tunnel tests at the wind speed of 100 m/s confirmed the aerodynamic noise reduction effect of each of these strategies as follows. (1) By applying multi-segmented smooth-profile pantograph head, the overall noise level is reduced by 1.9 dB compared to the pantograph in current use. (2) A further ~ 0.5 dB reduction in the overall noise level can be achieved by applying an improved pantograph head support to the multi-segmented smoothprofile pantograph head. A similar alternative reduction can be achieved by covering the pantograph head support with a layer of porous material. (3) Compared to the pantograph in current use, an overall noise level reduction of 2.7 dB is obtained by simultaneously applying all three strategies: applying multi-segmented smooth-profile pantograph head, improving the pantograph head support, and covering of the pantograph head support with a layer of porous material. Our future plans to improve upon the aerodynamic noise reduction strategies developed in this research include further reducing aerodynamic noise at least 3 dB and stabilizing lift force characteristics. We also plan to verify the current collection performance at high-speed range above 300 km/h on our new test bench, high-speed pantograph test equipment.

References 1. Ikeda M, Suzuki M, Yoshida K (2006) Study on optimization of Panhead shape possessing low noise and stable aerodynamic characteristics. Q Rep RTRI 47(2):72–77 2. Ikeda M, Mitsumoji T (2009) Numerical estimation of aerodynamic interference between Panhead and articulated frame. Q Rep RTRI 50(4):227–232 3. Ikeda M, Mitsumoji T, Sueki T, Takaishi T (2010) Aerodynamic noise reduction in pantographs by shape-smoothing of the Panhead and Its support and by use of porous material in surface coverings. Q Rep RTRI 51(4):220–226 4. Mitsumoji T, Sato Y, Yamazaki N, Uda T, Wakabayashi Y (2016) Reduction of aerodynamic noise emitted from pantograph by appropriate aerodynamic interference around pantograph head support. In: Proceedings of the 12th international workshop on railway noise 5. Sueki T, Ikeda M, Takaishi T, Kurita T, Yamada H (2008) Application of porous material to reduce aerodynamic noise caused by a high-speed pantograph. In: 37th international congress and exposition on noise control engineering 6. Usuda T, Mitsumoji T, Nagao K, Isono T, Hirakawa H (2020) The current collection performance of multi-segment pantograph head. In: The 15th international conference on motion and vibration 7. Saito M, Mizushima F, Wakabayashi Y, Kurita T, Nakajima S, Hirasawa T (2019) Development of new low-noise pantograph for high-speed trains. In: Proceedings of the 13th international workshop on railway noise

Influence of Flow Disturbing Grooves Underneath the Cowcatcher on Aerodynamic Noise Generated Around a High-Speed Train Bogie J. Y. Zhu, Y. Z. Wang, G. D. Cheng, Y. Y. Yuan, and Y. H. Lu

Abstract The influence of the flow disturbing grooves underneath a cowcatcher on the flow and aerodynamic noise performance around a high-speed train bogie is investigated based on acoustic analogy method. Results show that the parallel grooves set on the rear end of cowcatcher bottom surface, interfere with the forming and shedding of the large-scale vortices generated at the rear rim of cowcatcher as well as the leading edge of the bogie cavity where the flow separation and flow interaction between the wake and the geometries are mitigated. Thus, the wall pressure fluctuations on the solid surfaces of cowcatcher and bogie areas are decreased and the flow-induced noise is reduced. Based on the semi-anechoic wind tunnel experimental measurements on the scaled high-speed train nose car model with the flow disturbing method applied underneath the cowcatcher, it is found that the far-field noise at the location opposite to the bogie region is reduced around 0.5 dB(A) and the noise source area around the bogie cavity is decreased with the sound amplitude level reduced up to 1 dB(A) under 20 kHz. This demonstrates that the aerodynamic noise is reduced effectively and verifies the noise reduction effect calculated from the numerical simulation. Keywords High-speed train · Cowcatcher · Aerodynamic noise · Flow disturbing

This work was supported by National Natural Science Foundation of China (51875411). J. Y. Zhu (B) · Y. Z. Wang · G. D. Cheng · Y. Y. Yuan · Y. H. Lu Institute of Rail Transit, Tongji University, Shanghai 201804, China e-mail: [email protected] Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Shanghai 201804, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_20

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1 Introduction It is well accepted that the aerodynamic noise introduced by the flow passing over them becomes important as the running speed increases above 300 km/h for highspeed trains [1, 2]. Generally, field tests and wind tunnel experiments were used to study the aerodynamic noise produced from the bogie area of high-speed train. Kurita et al. [3] found that using fairing and sound-absorbing materials in the bogie areas of a high-speed train would reduce the generation and radiation of aerodynamic noise produced in this area through the field tests performed on the Shinkansen lines. Lauterbach et al. [4] used microphone arrays to identify the aerodynamic noise source in the bogie area and compared the effects of different noise reduction methods. The noise source maps of a leading car from the ICE3 (inter city express) model between wind tunnel and full scale tests matched well. Results showed that the aerodynamic noise produced from the bogie section was dominant in the frequency below 5 kHz and could be characterised by cavity mode excitation. As a strong tonal source, the pantograph was the dominant sound source for frequencies above 5 kHz. The Mach number dependence was around power law exponent of 6. Iglesias et al. [5] studied the aerodynamic noise from a train bogie based on a scale train model in the anechoic wind tunnel. It was found that the local inflow speed had a significant influence on the noise generation and the bogie components exposed to the flow produced large noise. For different bogie configurations, the noise spectrum was broadband and the overall sound pressure level (OASPL) presented a speed exponent about 6.5. With the improvement of the computation ability, numerical simulation methods have been used to study the characteristics of the aerodynamic noise generated around the high-speed train and its main components. Tan et al. [6] used the large eddy simulation (LES) and acoustic analogy method to simulate the vortices generated from the pantograph tail of high-speed train and investigate the frequency characteristics and sound directivity of the radiated aerodynamic noise, providing the theoretical guidance for the low-noise design and optimization of the main components of the pantograph. Zhu et al. [7] studied the influence of bogie cavity on flow and aerodynamic noise performance of bogie based on acoustic analogy method. Results showed that the bogie cavity changed the flow characteristics and sound directivity of the bogie structure. The dipole noise generated by the surface pressure fluctuation of bogie geometries was the main sound source of the aerodynamic noise. Li et al. [8] investigated the aerodynamic noise behaviour of flow passing the simplified leading car and nose car scale models of a high-speed train. It was found that the volume dipole source was much stronger than the volume quadrupole source and became the dominant sound source of the near-field quadrupole noise. The flow was separated significantly in the regions of the nose, bogies, bogie cavities, and train tail of the leading car where the pressure fluctuations were generated largely upon the wall surfaces, resulting in a dipole noise source of high levels. The noise contribution from the leading bogie and bogie cavity was larger than that from the other components, demonstrating that the flow generated around the bogie region was the dominant aerodynamic sound source. Thus the flow-induced noise produced around the train

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leading car would be controlled effectively through mitigating the flow separation and flow interaction occurring around the leading bogie and bogie cavity. Due to the complexity of high-speed train structure, most of previous studies investigated the frequency characteristics and sound directivity of aerodynamic noise through numerical and experimental methods. The research on the aerodynamic noise control was limited to the approaches of installing fairings outside the bogie cavity and optimizing the shape of various components of the pantograph [1, 6, 9]. In order to further study the aerodynamic noise control methods of the high-speed train, a new flow control approach is introduced to reduce the aerodynamic noise in the bogie areas through setting a series of grooves at the rear part of the cowcatcher bottom surface to disturb the flow developing around the leading edge of the bogie cavity. The influence of flow control on the aerodynamic performance and aerodynamic noise characteristics of the flow field in the cowcatcher and bogie areas of train nose is compared based on numerical simulation and wind tunnel measurements. Thus, the mechanism of aerodynamic noise reduction in the bogie region using the cowcatcher with dented bottom surface underneath (named “dented cowcatcher” for simplicity as follows) is revealed to guide the low noise design and optimization of the key regions of high-speed train.

2 Numerical Method In principal, aerodynamic noise generation and propagation can be described by compressible Navier–Stokes (N–S) equations. However, this will lead to high computational cost. By contrast, a two-step hybrid approach uses less computational resources and becomes practical for the industrial applications. In hybrid methods, near-field sound source is solved by the N-S equations and the far-field noise is calculated through an acoustic analogy using the equivalent noise sources obtained from unsteady flow field [10]. In order to cope with a moving source problem, the Ffowcs Williams-Hawkings (FW-H) acoustic analogy method was employed for flow-induced noise prediction. Considering the effects of source motion, the FW-H equation [11] is written as ∂ 2 [H ( f )ρ] − c02 ∇ 2 [H ( f )ρ] ∂t 2  ∂ ∂2  ∂ = [Qδ( f )] − Ti j H ( f ) [Fi δ( f )] + ∂t ∂ xi ∂ xi x j

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Mach number flow, the noise radiation of the quadrupole sources resulting from the fluctuating stresses of the fluid outside the integration surface is typically small and may be neglected. The hybrid approach has been successfully used for aerodynamic noise prediction on the pantographs, the bogies of high-speed train and the landing gear of aircraft [6–10].

3 Simulation Setup In order to reduce the computational cost, the current study is performed initially based on a simplified model of bogie region with cowcatcher at 1:10 scale (see Fig. 1). Figure 1a shows a simplified model of the bogie area with a conventional cowcatcher and Fig. 1b shows the bogie region with a dented cowcatcher of four grooves underneath. Each groove has the width of 15 mm and an interval of 20 mm with the adjacent groove based on the parameter studies. The depth of the grooves is 5 mm. The bogie structure is simplified with the main components of wheelset and frame and its dimensions are displayed in [12, 13]. Half of the geometries are applied for simulation to make use of the symmetrical structure of the train where the influence of the three-dimensional flow on the carbody longitudinal central plane is expected to be small [12, 13]. The boundary conditions applied are as follows: the upstream inlet flow is represented as a steady uniform flow (U0 = 30 m/s) with a low turbulence intensity less than 0.5%. The inflow speed being simulated is lower than the wind tunnel measurements introduced below for the sake of saving the computational resources used for a large numerical simulation with boundary layer solved. The top and side boundaries are specified as zero-shear slip walls. In order to simulate the actual situation of a moving train running on a stationary ground in the numerical wind tunnel case, the wheelset surfaces are set as moving no-slip walls and the ground is defined as a no-slip wall moving with the inflow velocity. All the other solid surfaces are defined as stationary no-slip walls and a pressure outlet with zero gauge pressure is imposed at the downstream exit boundary. In order to capture the small flow fluctuations which are responsible for introducing the aerodynamic noise, the flow field needs to be simulated correctly and thus the boundary layer in the near-wall areas is solved to obtain the detail flow behaviour.

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Based on the grid convergence study for a cylinder case [12, 13], a fully structured mesh is generated around the geometries (see Fig. 2) with resolutions similar to the cylinder baseline grids. The distance from the solid surfaces to the first grid point is set as 1×10−5 m and stretched with a growth ratio of 1.1 in the wall-normal direction with 38 layers within the boundary layer region. This yields a maximum value of y + (the dimensionless first-cell spacing) less than 1. This grid generation strategy results in the structured meshes in the computation domain with a total number of grid points of 30.3 million for the conventional cowcatcher case and 31.0 million for the dented cowcatcher case. Simulations are run with a physical timestep size of 5 × 10−6 s which gives an adequate temporal resolution for implicit time marching scheme used with a Courant-Friedrichs-Lewy (CFL) number of less than 1 within most part of the computational domain. The same mesh topology and numerical schemes were employed for the wheelset and bogie cases in which good agreements were achieved between noise predictions and experimental measurements for the far-field noise radiation [12, 13].

4 Aerodynamic Results In order to understand the flow behaviour around the cowcatcher and its influence on the aerodynamic noise generated from the bogie region, the calculation results of the instantaneous iso-surfaces of Q-criterion and the wall pressure fluctuations are compared for the two cases of the conventional and dented cowcatchers respectively. The turbulent vortical structures of the flow field produced around the bogie areas of two cowcatcher cases are shown in Fig. 3. They are represented by the iso-surfaces of normalized Q-criterion value of 20 (based on Q/[(U∞ /D)2 ], where Q is the second invariant of the velocity gradient, U∞ is the freestream velocity and D the wheel diameter). It can be found that the flow separated at the leading edge of the bogie cavity acts mutually with the geometries inside the bogie cavity. Large-scale coherent vortices are formed outside the bogie cavity and a great number of irregular turbulence vortices with smaller scales are generated within the bogie

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cavity. These complex vortex structures interplay with each other and are convected downstream along the carbody, consequently impinging strongly on the rear edges and walls of the bogie cavity. Compared with the conventional cowcatcher case, the vortices are produced more uniformly with a lower velocity amplitude and the large-scale coherent vortices are reduced remarkably in the dented cowcatcher case. This is due to the parallel grooves structure settled at the rear end underneath the cowcatcher changing the flow generated around it, restraining the shear layer development and mitigating the flow mutual interfering around the bogie cavity. The power spectral density (PSD) of the instantaneous normalized streamwise velocity coefficient (Ux /U∞ ) at the probe located between the bogie cavity leading edge and the upstream wheel inner surface is presented in Fig. 4. It shows that the spectrum amplitude of the dented cowcatcher case is generally lower than the conventional cowcatcher case in the frequency range below 140 Hz and becomes quite similar between them above 140 Hz. Moreover, Fig. 5 displays the PSD of the drag coefficient of the bogie, of which the spectrum amplitude is decreased greatly for the dented cowcatcher case in the low frequency range below 50 Hz. These results demonstrate that the large-scale vortex structures are broken down by the dented configurations settled on the cowcatcher bottom surface, leading to a reduction of the incident flow speed impinging on the bogie structure, and thus the aerodynamic forces produced from the interaction between the flow and the bogie components are mitigated. This will reduce potentially the dipole noise induced by the pressure fluctuation on the solid walls. As a source term, the wall surface pressure is applied for far-field noise prediction through acoustic analogy method at low Mach numbers. In order to identify the potential noise sourceregions, Fig.  6 displays the wall fluctuating pressure level in 2 2 decibels (L p = 10log p / pr e f , where p  2 is the mean-square fluctuating pressure and pr e f is the reference acoustic pressure 20 μPa) on the solid surfaces around the bogie cavity region. Results show that a high pressure fluctuation occurs on the downstream half part of the geometries for both cases. Compared with the conventional cowcatcher case, the wall surfaces with strong pressure fluctuation are reduced noticeably, especially around the regions of upstream wheelset and the front half part of the bogie cavity. This is due to the flow interaction occurring around the bogie and bogie cavity is mitigated by the concaved structures of the dented cowcatcher as discussed earlier. Therefore, the dipole sound source formed by the wall pressure fluctuation can be reduced effectively and the less aerodynamic noise may be generated around the bogie region when the dented cowcatcher is applied under the train nose.

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5 Aeroacoustic Results When the transient flow field has become statistically steady, the FW-H acoustic analogy method is used to predict the far-field noise based on the near-field unsteady flow data. The sound spectra and directivities of the aerodynamic noise generated by the train model with conventional and dented cowcatchers are investigated and compared. The noise reduction effect through passive flow control method is verified against the semi-anechoic wind tunnel experiments. The length of the time signal of 0.52 s of the flow data is used as input to the FW-H method for noise prediction after the flow has become statistically steady. Figure 7 compares the far-field noise spectra of the conventional cowcatcher case and dented

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cowcatcher case based on the numerical simulations on the half train model. The receiver is located 2.5 m away and 0.35 m above the bogie center. Results show that the OASPL of the radiated noise in the frequency range below 1 kHz for the case of dented cowcatcher is 68.6 dB which is 0.5 dB lower than the case of conventional cowcatcher (OASPL of 69.1 dB). The reason is that the parallel grooves installed underneath the rear end of the cowcatcher, disturb the forming and developing of the vortices generated around the regions at the rear rim of the cowcatcher and the leading edge of the bogie cavity where the turbulence intensity and the transportation speed of the flow are decreased, and consequently the flow separation and flow interaction are mitigated and the aerodynamic noise is reduced. The experimental measurements of the aerodynamic noise produced by the highspeed train nose car model with different types of cowcatchers are conducted in Shanghai Automotive Wind Tunnel Center (SAWTC) at Tongji University. The wind tunnel is equipped with an open-jet and a semi-anechoic chamber except for the ground. The nozzle area is 27 m2 and the test section is 15 m long with a static pressure gradient less than 0.001/m. The wind tunnel background noise is less than 61 dB(A) at the wind speed of 160 km/h. The high-speed train nose car model at 1:3 scale (shown in Fig. 8) used for wind tunnel tests has the dimensions of 5.8 m (length), 1.1 m (width), and 1.4 m (height), respectively. The blockage ratio of the train nose car model is less than 5%. In order to avoid the aerodynamic noise produced by the flow separating at the train tail, the rear section of the train model is streamlined. The train model is fixed on the support floor in the test section of the wind tunnel and located precisely along the nozzle longitudinal centerline. The connections between the carbody and the floor are covered by airfoils to reduce flow interfering. In the experimental measurements, the conventional cowcatcher (Fig. 9a) with a smooth surface underneath and the dented cowcatcher (Fig. 9b) with the grooves

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Fig. 8 High-speed train nose car model in the wind tunnel

distributed at the rear end of the cowcatcher bottom surface are installed respectively under the train nose. The flow speed is 250 km/h with the turbulence intensity in the jet core less than 0.5%. The experimental data are collected for 10 s with a sampling frequency of 48 kHz. The spectral analysis of the receiver signals in the time domain is performed by fast Fourier transform (FFT) to obtain the noise spectrum and OASPL at the receivers. The far-field receivers are situated in a plane parallel to the longitudinal centerplane of the train model with a distance of 6 m and distributed in sequence along the inflow direction at the height of 0.6 m from the ground, as sketched in Fig. 10. The receiver 1 is located from the bogie center laterally and has a gap of 0.67 m with receiver 2 and a distance of 1.77 m with receiver 3 longitudinally. Figure 11 compares the far-field noise 1/3 octave spectra of receiver 2 for the two cowcatcher cases. It can be seen that compared with the conventional cowcatcher case, the spectrum level is lower for the dented cowcatcher case in the frequency range between 100 and 1300 Hz. Due to the aerodynamic noise introduced by the interplaying of the flow with the solid walls of the grooves set in the cowcatcher bottom surface, the spectrum level is higher for the dented cowcatcher case above 1300 Hz whereas the amplitude of the sound pressure level (SPL) is much lower than the frequency range from 400 to 1000 Hz. The OASPL in the frequency range below 20 kHz for the dented cowcatcher case is 86.6 dB(A), about 0.4 dB(A) lower than the conventional cowcatcher case with the OASPL of 87.0 dB(A). For receivers 1 and 3, the noise reduction of around 0.5 dB(A) is achieved for the dented cowcatcher case. Therefore, the experimental measurements verifies the numerical calculation in that the noise reduction effect can be achieved by installing the dented cowcatcher under the high-speed train nose car. In order to obtain the sound source distribution around the bogie region, a 120channel planar spiral array with dimensions of 1.8 m*1.8 m (length*width) is set out-of-flow with a distance of 5.8 m from train model centerline and opposite to the bogie cavity, as shown in Fig. 8. In the sound source identification measurements, the sound pressure signals acquired by the microphone array have a certain delay depending on their spatial angle. Through reconstructing the sound source signals

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Fig. 9 Cowcatcher models Fig. 10 Distribution of far-field receivers

(a) side view

(b) front view Fig. 11 Noise spectra (receiver 2)

85

SPL (dBA)

75

65

55

45 50

Conventional cowcatcher Cowcatcher with grooves underneath

100

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(a) case of conventional cowcatcher

(b) case of cowcatcher with grooves underneath

Fig. 12 Noise source maps of train nose car model at 250 km/h

at each space angle by enhancing the signals produced from the sound source direction and weakening the signals generated from other directions, the sound source localization can be performed. For the two cowcatcher cases, the sound source distribution measured by the microphone array is presented in Fig. 12. Results show that compared to the conventional cowcatcher case, the noise source area of the bogie region of the train nose car model installed with the dented cowcatcher is decreased remarkably with the amplitude level about 1 dB(A) lower under 20 kHz. Thus a fairly good noise reduction effect has been achieved in the train bogie region with the grooves distributed in parallel at the rear region of the cowcatcher bottom surface. When the microphone array is moved forward along the inflow direction to the position opposite to the train tail, the main noise source obtained still comes from the bogie region of the train model at different frequencies. This demonstrates that the bogie region is the dominant aerodynamic noise source of the scaled train model and the train tail is reasonably streamlined to control the noise introduced by the flow separation occurring at the train rear section.

6 Conclusion The influence of the grooves set underneath the cowcatcher on the flow and flowinduced noise in the bogie region of a high-speed train is investigated based on the numerical simulations and wind tunnel measurements. The simulation results show that compared with the cowcatcher with smooth bottom surface, the parallel grooves underneath the cowcatcher can mitigate the flow interaction between the cowcatcher wake and the components inside the bogie cavity by producing the flow disturbing. Consequently the aerodynamic noise produced by the wall pressure fluctuations is reduced through weakening the flow separation around the geometries. According to the wind tunnel measurements on the nose car scale model of high-speed train, the noise reduction around the bogie and rear bogie cavity regions at the trackside

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direction reaches 0.5 dB(A) and the noise source area around the bogie is shrunk noticeably with noise level up to 1 dB(A) lower under 20 kHz after the dented cowcatcher is applied under the train nose, resulting in an effective noise reduction effect. Therefore, the numerical simulation on the simplified model of bogie region with cowcatcher and experimental measurements on a high-speed train nose car model demonstrate that the grooves applied in the rear region of the cowcatcher bottom surface can inhibit the flow separation at the leading edge of the bogie cavity and interfere with the vortex shedding and flow developing around this region, leading to the reduction of the flow-induced noise generated around the region of a highspeed train bogie. Note that the numerical investigations on the train nose car models with different cowcatchers used in the wind tunnel experiments are in progress. For the high-speed train in reality, the grooves with various configurations such as rectangular, square, rhombic and circular shapes can be set underneath the cowcatcher for flow disturbing at the region around the bogie cavity leading edge based on the parameter design and structure optimization to effectively reduce the noise generated around the bogie cavity and front wheelset.

References 1. Thompson DJ, Iglesias EL, Liu XW, Zhu JY, Hu ZW (2015) Recent developments in the prediction and control of aerodynamic noise from high-speed trains. Int J Rail Transp 3(3):119– 150 2. Talotte C, Gautier PE, Thompson DJ, Hanson C (2003) Identification, modelling and reduction potential of railway noise sources: a critical survey. J Sound Vib 267:447–468 3. Kurita T, Wakabayashi Y, Yamada H, Horiuchi M (2011) Reduction of wayside noise from Shinkansen high-speed trains. J Mech Syst Transp Logist 4(1):1–12 4. Lauterbach A, Ehrenfried K, Loose S, Wagner C (2012) Microphone array wind tunnel measurements of Reynolds number effects in high-speed train aeroacoustics. Int J Aeroacoust 11:411–446 5. Iglesias EL, Thompson DJ, Smith M, Kitagawa T, Yamazaki N (2017) Anechoic wind tunnel tests on high-speed train bogie aerodynamic noise. Int J Rail Transp 5(2):87–109 6. Tan XM, Yang ZG, Tan XM, Wu XL, Zhang J (2018) Vortex structures and aeroacoustic performance of the flow field of the pantograph. J Sound Vib 432:17–32 7. Zhu JY, Hu ZW, Thompson DJ (2018) The flow and flow-induced noise behaviour of a simplified high-speed train bogie in a cavity with and without a fairing. Proc Inst Mech Eng Part F J Rail Rapid Transit 232(3):759–773 8. Li CW, Zhu JY, Hu ZW, Lei ZY, Zhu YM (2022) Investigation on aerodynamic noise generated from the simplified high-speed train leading cars. Int J Aeroacoust 21(3&4):218–238 9. Zhu JY, Zhang Q, Xu FF, Liu LY, Sheng XZ (2021) Review on aerodynamic noise research of high-speed train. J Traffic Transp Eng 21(3):39–56 10. Wang M, Freund JB, Lele SK (2006) Computational prediction of flow-generated sound. Annu Rev Fluid Mech 38:483–512 11. Ffowcs-Williams JE, Hawkings DL (1969) Sound radiation from turbulence and surfaces in arbitrary motion. Philos Trans R Soc Lond 342:264–321

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12. Zhu JY, Hu ZW, Thompson DJ (2016) Flow behaviour and aeroacoustic characteristics of a simplified high-speed train bogie. Proc Inst Mech Eng Part F J Rail Rapid Transit 230(7):1642– 1658 13. Zhu JY (2015) Aerodynamic noise of high-speed train bogies. University of Southampton, Southampton

Boundary Condition and Equivalent Mass-Spring-Damper System for a Truncated Railway Track X. Sheng and Y. Peng

Abstract To deal with vehicle/track interaction in the time domain, the infinitely long railway track often has to be truncated, generating a finite track model. The ends of the rail in the model are normally simply supported. To account for high-frequency vibration, high train speed and the presence of multiple carriages, the track model must be long, demanding too much computational effort. Means is required to shorten the track model. Aiming at this, the track is divided into three parts, a left semi-infinite part, a middle part (the track model) and a right semi-infinite part. The left and right parts are assumed to be two semi-infinite periodic tracks. The semi-infinite periodic track is replaced with an equivalent mass-spring-damper system. The mass-springdamper system is determined in such a way that it provides the same receptance to the track model as the semi-infinite periodic track. The receptance of the semi-infinite periodic track is calculated from the response of the two semi-infinite periodic tracks joined together as an infinite periodic structure subject to specific harmonic loads. Keywords Track model · Semi-infinite track · Equivalent mass-spring-damper system

1 Introduction Many issues frustrating the railway industry require vehicle/track interaction analysis at high frequencies. In many cases, a time-domain method has to be employed, requiring truncating the infinitely long track [1, 2] with the ends of the rail being normally hinged. For modern high-speed railways, the length of the track model can X. Sheng (B) School of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai 201620, China e-mail: [email protected] Y. Peng State Key Laboratory of Rail Transit Vehicle System, Southwest Jiaotong University, Chengdu 610031, Sichuan, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_21

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be very long. This is because: (1) high-speed railway slab tracks normally have a vibration decay rate as low as 0.5 dB/m for frequencies above few hundred hertz [3]. At these frequencies, a distance of about 40 m is required for vibration to decay 20 dB. To make wave reflections from the ends of the track model insignificant, wheelsets must be at least 40 m away from the ends; (2) the low vibration decay rate will also enhance interaction between neighbouring wheelsets via the rail. Ideally the entire train should be considered so that rail-induced interaction between all the wheelsets can be fully taken into account. However, by doing so a too large model may be generated. A compromised approach is to consider just three carriages and only the time-histories of various quantities for the middle carriage are taken. The distance between the two most separated wheelsets of the three carriages is about 75 m for a typical high-speed train; (3) to calculate time-histories of 1 second, the train has travelled about 111 m at 400 km/h; (4) these time-histories are generated through solving a set of ordinary differential equations of the vehicle/track system numerically with pre-defined initial displacements and velocities at t = 0. The initial displacements and velocities are normally set to zero. In other words, in the simulation the weights of the vehicles are placed on the track instantaneously at t = 0, generating an impulsive response for the vehicle/track system [4]. Due to damping in the vehicle/ track system, this impulsive response will eventually become negligible after the train has travelled a certain distance. This distance increases with train speed. Thus, by adding up all the lengths or distances estimated above, the track model should be at least as long as 266 m (= 40 + 75 + 111 + 40). Ideally the track should be treated to be infinitely long and this is possible if the track is a periodic structure. In fact, based on the periodic structure theory, dynamics has been modelled for a ballasted track [5, 6], a ballasted track with rail dampers [7], a slab track [8] and a ballasted track with the rail modelled using the 2.5D FEM [9]. Based on these periodic track models, several methods have been developed for wheel/rail interaction, working either in the frequency domain [10] or in the time domain [11–13]. In these methods, the wheel is allowed to move, and even rotate [13], at the train speed along the track. Periodicity always breaks down for a constructed track due to various reasons. In such cases, the periodic structure theory-based methods may be inapplicable, and a finite track model has to be used. If the ends of the track model have boundary conditions which are close to those provided by a semi-infinite track, the length of the track model can be shortened. This paper presents derivation of such boundary conditions. In the derivation, the track is divided into three parts, a left semi-infinite part, a middle part (the track model) and a right semi-infinite part. The left and right parts are assumed to be periodic in the track direction. The boundary condition for the track model may be represented by the receptance matrix of the semi-infinite track at the interface. This receptance matrix is calculated from the response of the two semi-infinite tracks joined together as an infinitely long periodic structure subject to specific harmonic loads. A mass-spring-damper system is determined based on the receptance matrix and attached to the track model, so that the response of the track model to given excitations can be solved conveniently using the conventional finite element method.

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The paper is organised as below. Calculation of the response of an infinitely long periodic track to specific harmonic loads is briefly described in Sect. 2. The receptance matrix of the semi-infinite track is derived in Sect. 3. Results for the receptance matrix and the equivalent mass-damper-spring system are produced in Sect. 4. The paper is concluded in Sect. 5. It should be noted that the current conference paper has been largely extended after IWRN14 and published in JSV [14].

2 Responses of a Periodic Track to Harmonic Loads The track (Fig.1) consists of two rails, rail fastener systems, track slabs, a layer of concrete–asphalt mortar and a concrete base. The concrete base is approximated to be rigid. The length of the slab is denoted by L. The track is idealised to be periodic with the period being L. The jth, where j = −∞, · · · , −1, 0, 1, 2, · · · + ∞, bay is located within [ j L , ( j + 1)L]. It is assumed that in each bay there are S rail fasteners connecting the rail and the slab. The sth fastener in the 0th bay is installed at x = xs , where 0 ≤ xs < L. For vertical vibration of the rail up to about 3000 Hz, the Timoshenko beam theory can be employed to the rail. Therefore, the differential equation of the rail subject to a vertical harmonic force and a harmonic torque (Fig. 1) is given by ∂ 2w ∂ψ ∂ 2w − κ AG + κ AG ∂t 2 ∂x2 ∂x S ∞ ∑ ∑ δ(x − xs − j L)F js (t) = δ(x − x0 )F0 eiωt +

ρA

(1)

j=−∞ s=1

ρI

y

∂ 2ψ ∂w ∂ 2ψ − E I 2 − κ AG + κ AGψ 2 ∂t ∂x ∂x

x x0 z

F0eiωt M0eiωt

Rail Fastener Slab CA layer Concrete base

kP kC L

Fig. 1. A sketch of the slab high-speed railway track and the coordinate system

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= δ(x − x0 )M0 eiωt +

∞ ∑ S ∑

δ(x − xs − j L)M js (t)

(2)

j=−∞ s=1

where w denotes the vertical displacement (directed downwards) of the rail and ψ is the rotation angle (directed clockwise) of the cross-section of the rail due to bending moment only; x 0 is the location of the force and torque; F js (t) represents the vertical force (directed downwards) applied to the rail by the sth fastener within the jth slab and M js (t) (directed clockwise) is the torque exerted on the rail by that fastener; ρ, E, G, A, I and κ are, respectively, density, Young’s modulus, shear modulus, crosssectional area, bending moment of inertia and shear coefficient of the rail; and finally, F 0 , M 0 and ω are the amplitudes and angular frequency of the loads. By letting {

[ } [ ] ] w 00 A0 ,M =ρ , , K 0 = κ AG ψ 01 0 I } [ [ { ] ] 0 1 κ AG 0 F0 K 1 = κ AG , K2 = , p0 = M0 −1 0 0 EI

q=

(3)

it can be shown that [8] [

1 ∞ ' ∫ [ D(β, ω)]−1 eiβ x dβ 2π −∞ ∞ ( ∑ )]−1 ( ) 1 −i2π j (x ' +x0 )/L ∞ [ ( ∫ D βj, ω − e + C β j [ A(β)]−1 2π L −∞ j=−∞ )] ' B(β)[ D(β, ω)]−1 eiβ x dβ p0 ei ωt

q(x, t) =

(4)

where x ' = x − x0 , β j = β − 2π j/L and D(β, ω) = −ω2 M + K 0 + iβ K 1 + β 2 K 2

(5)

] ( ) [ C β j = e−iβ j x1 U · · · e−iβ j x S U

(6)

[ ]T B(β) = eiβ x1 U · · · eiβx S U

(7)

A(β) = ( Ar s (β))r,s=1,···S ⎛ ⎛ ⎞ ⎞ ∞ ∑ [ ( )] 1 −1 D βj, ω = ⎝U T ⎝ eiβ j (xr −xs ) ⎠U + H r s (ω)⎠ L j=−∞

r,s=1,···S

(8)

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U is the 2×2-unit matrix and H sr (ω) is a matrix formed by the receptances seen by the rail and associated with the rth and sth fasteners within a slab.

3 Receptance Matrix of a Semi-periodic Track Now the infinite track is cut into two semi-infinite tracks at the junction of the −1th and 0th slabs (i.e., at x = 0, see Fig. 2). Consider the right one. At the end of the iωt ˜ and a harmonic bending moment semi-infinite track a harmonic shear force Q(ω)e iωt ˜ M(ω)e are applied and the amplitudes of the vertical displacement and rotation ˜ and ψ(ω). It can be written out that ˜ angle of that end are denoted by w(ω) {

˜ w(ω) ˜ ψ(ω)

}

[

α11 (ω) α12 (ω) = α21 (ω) α22 (ω)

]{

˜ Q(ω) ˜ M(ω)

} (9)

where αi j (ω) (α12 (ω) = α21 (ω)) is the receptance of the semi-infinite track at the end. To determine these receptances, a unit vertical harmonic load is applied on the rail above the junction between the −1th and 0th slabs. The amplitudes of the vertical displacement and rotation angle of the rail at the loading point are denoted by w˜ 1 (ω) and ψ˜ 1 (ω), and those of the shear force and bending moment are denoted by Q˜ 1 (ω) and M˜ 1 (ω). It is evident that ψ˜ 1 (ω) = 0 and Q˜ 1 (ω) = 0.5. Then a harmonic torque (in clockwise) is applied. The amplitudes of the vertical displacement and rotation angle of the rail at the aforementioned cross-section are denoted by w˜ 2 (ω) and ψ˜ 2 (ω), and those of the shear force and bending moment are denoted by Q˜ 2 (ω) and M˜ 2 (ω). It is evident that w˜ 2 (ω) = 0 and M˜ 2 (ω) = 0.5. Thus, according to Eq. (9), [

] [ ][ ] w˜ 1 (ω) 0 α11 (ω) α12 (ω) 0.5 Q˜ 2 (ω) = 0 ψ˜ 2 (ω) α21 (ω) α22 (ω) M˜ 1 (ω) 0.5

Bending moment eiωt

Shear force f

Rail Fastener Slab CA layer Fig. 2. Shear force and bending moment on the rail cross-section

(10)

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The shear force and bending moment of the rail appearing in Eq. (10) are related to the displacement of the rail via the following equations ( ) ∂ψ1 x0+ , t , = −E I ( ∂x ( ) ) ( + ) ( + ) ∂w2 x0+ , t Q 2 x0 , t = −κ AG − ψ2 x0 , t ∂x (

M1 x0+ , t

)

(11)

The derivatives appearing in Eq. (11) can be determined numerically based on ψ 1 (x) and w2 (x). From Eqs. (4), (11) and (12), the receptance matrix can be worked out.

4 Results Results are produced for track parameters listed in Ref. [8] with the railpad stiffness and loss factor being adjusted to 5.44×107 N/m and 0.1. The sleeper spacing is 0.65 m. For Eq. (4), wavenumber β is within [−78.5, 78.5] rad/m at a spacing of 2π× 0.0025 rad/m. The index j is from −20 to 20. Frequency ranges from 3 to 3000 Hz at a resolution of 6 Hz.

4.1 Receptances of the Semi-infinite Track The magnitudes of the receptances of the semi-infinite track are shown in Fig. 3. It can be seen that, at about 183 Hz (denoted by ωn1 ), all the receptances have a peak. This is because the rail in the semi-infinite track has repeated modes at this frequency. The first one is a mode in which the rail vibrates vertically on the railpad stiffness. The second one is a mode in which the rail pitches on the railpad stiffness. It is well known that, an infinitely long periodic track has pinned-pinned frequencies. For the track parameters, the first and second pinned-pinned frequencies are around 940 and 2577 Hz. Characteristics also exhist at these frequencies for the semi-infinite track, as shown in Fig. 3. At the first pinned-pinned frequency, |α 11 | exhibits a peak while |α 22 | has a dip. This is because at this frequency the track has a characteristic mode (the pinned-pinned mode) in which the mid-span (between two neighbouring sleepers) cross-section of the rail, on which there is bending moment but no shear force, vibrates vertically. At the second pinned-pinned frequency, |α 11 | exhibits a dip while |α 22 | shows a peak. This is because of another charateristic mode (the second pinned-pinned mode) of the track; in this mode the mid-span cross-section of the rail, on which there is shear force but no bending moment, only rotates.

239

Magnitude of the receptance

Boundary Condition and Equivalent Mass-Spring-Damper System …

183

940 980

2577 2607

Frequency (Hz) Fig. 3. Semi-track receptance. —, |α 11 | (m/N); – –, |α 12 | (rad/N); –·–, |α 22 | (rad/(N·m))

4.2 The Equivalent Mass-Spring-Damper System The equivalent mass-spring-damper system is shown in Fig. 4. It is formed by a number of N rigid bars hinged together. The mass, length and moment of inertia about the mass centre of the jth bar are denoted by mj , L j and J j . The bars are supported by vertical springs and dampers. The stiffnesses of the springs at the ends of the jth bar are identical and denoted by k j while the dampers are allowed to have different damping coefficients with clj for the left damper and crj for the right. A rotational spring k ϕ j and a rotational damper cϕ j connect the right end of the jth bar and the left end of the ( j+1)th bar, where j = 1, 2, …, N − 1. It can be shown that, when 2 , k j = 0.5m j ωn1

m1 k1

J j = 0.25m j L 2j

kφ1, cφ1 J1

cl1

Fig. 4. The equivalent mass-spring-damper system

(12)

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the first two modal frequencies of the system are identical to ωn1 , leaving m1 , L 1 , cl1 , cr1 , k ϕ 1 , cϕ j …, mN , L N , clN , crN are to be determined. The number of unknowns is 6N − 2. ˜ iωt and a harmonic torque Me ˜ i ωt are applied Now a vertical harmonic force Qe to the first rigid bar at the left end. The vertical displacement of the left end of the first bar is denoted by w1 (t) = w˜ 1 ei ωt and the rotation angle of the jth bar is denoted by ϕ j (t) = ϕ˜ j ei ωt . The equivalent system has N+1 degrees of freedom defined by w1 (t), ϕ1 (t), · · · ϕ N (t). The receptance at the left end of the first bar can be worked out. By equating the receptance to that of the semi-track at a number, M, of preselected frequencies (M must be equal to, or greater than, N), a set of 6M nonlinear equations are formed from which the 6N − 2 parameters of the equivalent system can be determined. The determined parameters of the equivalent system are listed in Table 1 for N = 5 and the pre-selected frequencies are 3, 15, 87, 117, 183, 207, 333, 597, 897 Hz (M = 9). The receptance of the equivalent system and that of the semi-track are compared in Fig. 5. They match very well apart from frequencies around the pinned-pinned frequency. Table 1. Parameters of the equivalent system No. of bar

1

2

3

4

5

m (kg)

10.080

0.000

67.013

0.000

257.134

J (kg·m2 )

0.021

0.000

3.104

0.000

0.917

L (m)

0.091

0.329

0.430

0.181

0.119

k (N/m)

0.666×107

0.000

4.430×107

0.000

16.998×107

cl (N·s/m)

0.000

0.206×103

2.876×103

0.000

0.000

cr (N·s/m)

0.206×103

2.876×103

0.000

0.000

102.930×103

k ϕ (N·m/rad)

2.099×107

cϕ (N·m·s/rad)

0.321×103 2.882×103 0.529×103 0.792×103

0.288×107

Amplitude of the receptance

(a)

Frequency (Hz)

0.061×107

(b)

Phase of the receptance (rad)

1.275×107

Frequency (Hz)

Fig. 5. The magnitude (a) and phase (b) of the semi-infinite track (—) and the equivalent system (- - -). Black: α 11 (m/N); green: α 12 (rad/N); red: α 22 (rad/(N·m))

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5 Conclusion A railway track can be divided into three parts, a left semi-infinite part, a middle part, and a right semi-infinite part. The left and right parts are assumed to be periodic. For the middle part to be modelled using FEM, the left and right parts should be replaced with an equivalent mass-spring-damper system. This paper proposes a method to determine the equivalent system. Firstly, the receptance of the semi-infinitely long periodic track are calculated based on the responses of the entire track subject to a harmonic force and torque. The equivalent system is then determined by equating the receptance of the system to that of the semi-track at pre-selected frequencies. Acknowledgement This work has been funded by China’s NSFC (U1834201).

References 1. Knothe K, Grassie SL (1993) Modelling of railway track and vehicle/track interaction at high frequencies. Veh Syst Dyn 22:209–262 2. Nielsen JCO, Igeland A (1995) Vertical dynamic interaction between train and track–influence of wheel and track imperfections. J Sound Vib 185:825–839 3. Feng D, Thompson DJ, Zhu Y, Liu X (2014) Vibration properties of slab track installed on a viaduct. Proc IMechE Part F: J Rail Rapid Transit 1–18 4. Zhao X, Wen Z, Wang H, Jin X, Zhu M (2014) Modelling of high-speed wheel-rail rolling contact on a corrugated rail and corrugation development. J Zhejiang Univ Sci A 15(12):946– 963 5. Sheng X, Jones CJC, Thompson DJ (2005) Responses of infinite periodic structures to moving or stationary harmonic loads. J Sound Vib 282:125–149 6. Mazilu T (2007) Green’s functions for analysis of dynamic response of wheel/rail to vertical excitation. J Sound Vib 306:31–58 7. Sheng X (2015) Generalization of the Fourier transform-based method for calculating the response of a periodic railway track subject to a moving harmonic load. J Mod Trans 23:12–29 8. Sheng X, Zhong T, Li Y (2017) Vibration and sound radiation of slab high-speed railway tracks subject to a moving harmonic load. J Sound Vib 395:160–186 9. Zhang X, Thompson DJ, Li Q, Kostovasilis DM, Toward GR, Squicciarini G, Ryue J (2019) A model of a discretely supported railway track based on a 2.5D finite element approach. J Sound Vib 438:153–174 10. Sheng X, Li M, Jones CJC, Thompson DJ (2007) Using the Fourier-series approach to study interactions between moving wheels and a periodically supported rail. J Sound Vib 303:873– 894 11. Mazilu T, Dumitriu M, Tudorache C, Sebe¸sAn M (2011) Using the Green’s functions method to study wheelset/ballasted track vertical interaction. Math Comput Model 54(1–2):261–279 12. Sheng X, Xiao X, Zhang S (2016) The time domain moving Green function of a railway track and its application to wheel–rail interactions. J Sound Vib 377:133–154 13. Zhang S, Cheng G, Sheng X, Thompson DJ (2020) Dynamic wheel-rail interaction at high speed based on time-domain moving Green’s functions. J Sound Vib 488:115632 14. Sheng X, He Y, Yue S, Thompson DJ (2023) Receptance of a semi-infinite periodic railway track and an equivalent multi-rigid body system for use in truncated track models. J Sound Vib 559:117783

A Method for Predicting the Aerodynamic Pass-By Noise Based on FW-H Equation Without Using Sliding Mesh or Overset Mesh Shumin Zhang, Jiawei Shi, and Xiaozhen Sheng

Abstract The classical FW-H equation is a common method to predict the far field aerodynamic noise, which has been integrated into many CFD software. However, when using CFD software to predict aerodynamic pass-by noise of the train, a sliding mesh or overset mesh has to be used to simulate the train motion, generating interfaces between the moving region and other stationary regions. The existence of such interfaces may have a negative effect on calculation accuracy. In this paper, a method based on the FW-H equation without using sliding mesh or overset mesh is proposed to predict sound generated at a fixed far-field point by an object moving uniformly in the space. In order to verify the effectiveness of this method, taking a stationary cylinder as an example, results of this method are compared with STAR-CCM+ , and then the far-field pass-by noise of the cylinder moving at 50 m/s is calculated. Keywords Aerodynamic noise · Pass-by noise · FW-H equation · Cylinder

1 Introduction Noise pollution is the main impact of high-speed train operation on the surrounding environment. According to the field tests and numerical studies, when the train speed exceeds 300 km/h, the aerodynamic noise will gradually exceed the wheel-rail noise and become the main source of train noise [1, 2]. Nowadays, the operation speed of high-speed train in many countries have reached 300 km/h, and higher speed train S. Zhang (B) School of Railway Rolling Stock, Shandong Polytechnic, Jinan 250104, Shandong, China e-mail: [email protected] J. Shi State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, Sichuan, China X. Sheng School of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai 201620, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_22

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are also being developed. In order to meet the requirements of the relevant environmental laws and regulations, aerodynamic noise control has become an important consideration during the design process of high-speed trains [3–5]. Early studies on aerodynamic noise of high-speed trains were mainly through field test and wind tunnel test. These tests can help to determine the main location of the noise sources and grasp the characteristics of those sources and far-field noise [6–9]. However, from the point view of the product development, it is uneconomical to rely only on the test. This is because once a prototype train is produced, huge cost will be taken to solve the noise problem by field test. On the other hand, wind tunnel testing is generally expensive, and the results of a scaled model may can’t accurately reflected the noise level of a real train. In recent years, with the rapid development of computing technologies, computational fluid dynamics (CFD) have been gradually applied to aerodynamic noise prediction. Compared with the test, numerical simulation can obtain more detailed flow field information, and the mechanism of the aerodynamic noise can be better understood. More importantly, numerical simulation can help to predict and improve the aeroacoustic performance of the train in the early stage of design, so as to avoid the risk of solving noise problems in the later stage of vehicle development. The theoretical description of the sound generated by the interaction between a moving object and the fluid is FW-H equation, proposed by Ffowcs Williams and Hawkings [10]. Its far-field integral solution under subsonic condition is given by Farassat [11] and has been integrated into many CFD softwares, which is the most commonly used method to predict the far-field aerodynamic noise. However, when using CFD software to predict the train aerodynamic noise, the train and the measuring point are considered to be stationary, and the wind blows towards the train at a certain speed, just like the wind tunnel mode. By doing this, the Doppler effect caused by the movement of the sound source will be ignored. In order to predict the aerodynamic pass-by noise, sliding mesh or overset mesh method must be used to simulate the movement of the train. In this process, the computational domain is divided into a moving domain and a stationary domain, and the flow field data are transmitted by interpolation through a so called interface between the moving domain and the stationary domain. At present, these technologies are mainly used to calculate the aerodynamic force and the pressure wave when the train crossing each other or passing through the tunnel [12]. But for aerodynamic noise, more accurate and detailed flow field simulation is needed, and the existence of the interface between the moving domain and the stationary domain may have a great negative effect on calculation accuracy. In this paper, a method is proposed to predict aerodynamic pass-by noise, which can avoid the use of the interface. Firstly, the sound source data of the object surface is obtained through the flow field simulation in the wind tunnel mode. Then the aerodynamic pass-by noise is calculated based on Farssat_1A formula according to the movement of the object and the relative position between the measuring point and the object. Thus, the use of interface can be effectively avoided. The method is verified by a classical cylinder case. Firstly, the effectiveness of the far-field noise prediction program is verified by a stationary cylinder, and then far-field aerodynamic

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pass-by noise generated by a cylinder moving at a speed of 50 m/s through a fixed measuring point is calculated.

2 Methodology The FW-H equation describes the sound produced by the interaction between a moving object and fluid, shown as the following equation:    1 ∂2   p H ( f ) + ∇ 2 p H ( f ) 2 ∂t 2 c0   ∂2  ∂  ∂ = [ρ0 vn |∇ f |δ( f )] − pi j nˆ j |∇ f |δ( f ) + Ti j H ( f ) ∂t ∂ xi ∂ xi ∂ x j

(1)

where, c0 is the speed of sound, t is the time, p  is the sound pressure, xi is the component of the Cartesian coordinate, f = 0 is the equation of the sound source surface. H (·) is Heaviside function, ρ0 is the density of the fluid at the undisturbed region, Pi j = ( p − p0 )δi j − σi j is the stress tensor, ∇ is Nabla operator, vn is the normal velocity component of the sound source surface, Ti j is Lighthill stress tensor. FW-H equation is directly derived from N-S equation after introducing the generalized function. It is an accurate description of the sound generated by the interaction between moving object and fluid. However, solving FW-H equation directly is difficult, but from the perspective of Lighthill acoustic analogy, if the right side of Eq. (1) are regarded as the noise source (monopole source, dipole source and quatrupole source respectively), then Eq. (1) is a typical wave equation, and its far-field solution can be obtained by using the Green’s function in classical acoustics. For far-field noise prediction under the subsonic condition (the quatrupole source can be ignored), the most widely used form of acoustic analogy solution of the FW-H equation is Farassat_1A formula, as shown in Eq. (2). p  = pT (x, t) + p L (x, t)    ρ0 v˙n 1 = dS 4π r (1 − Mar )2 ret f =0 

  ρ0 vn r Mai rˆi + c0 Mar − c0 Ma 2 1 + dS 4π r 2 (1 − Mar )3 f =0

 

l˙i rˆi r (1 − Mar )2



 

ret

lr − li Mai 2 r (1 − Mar )2 f =0 f =0    lr (r Mai rˆi + c0 Mar − c0 Ma 2 ) 1 dS + 4πc0 r 2 (1 − Mar )3 ret 1 + 4πc0

f =0

1 dS + 4π ret

 dS ret

(2)

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where, pT (x, t) and p L (x, t) are the sound pressure generated by the monopole source and the dipole source, respectively. r is the distance between emitting point and receiving point, rˆi is the unit vector in the direction from the emitting point to the receiving point, Mai is the component of the Mach number in xi direction, Mar is the component of the Mach number in ri direction; li = Pi j n j ; f = 0 under the integral sign means that the integral is performed on the object surface, and the subscript ret means that the variables in brackets adopt the delay time determined by the delay time equation. Farassat_1A formula has been integrated into many CFD software, and become the most commonly method for predicting the far-field aerodynamic noise. However, when predicting aerodynamic noise of the train using CFD software, the wind tunnel mode is usually used, that is, the train and the measuring point remain stationary, and the wind blows towards the train at a certain speed. In this case, the velocity of the object surface is zero, and Eq. (2) is simplified to Curle’s equation [13]. Compared with the train passing through a fixed far-field point, this method ignores the Doppler effect caused by the movement of the sound source. To realize the pass-by noise prediction, a sliding mesh or overset mesh need to be used to simulate the motion of the train. When using the sliding mesh or overset mesh, the computational domain is divided into a moving domain and a stationary domain and the flow field data between them are transmitted by interpolation through a so called interface. For aerodynamic noise prediction, accurately flow field data is needed, so the existence of the interface may have a great impact on the computational accuracy. Therefore, this paper presents a new method to calculate the pass-by noise. Firstly, the fluctuating pressure (sound source data) of the object surface is obtained by the unsteady flow field simulation with a wind tunnel mode. According to the relativity of motion, the fluctuating pressure obtained can be considered the same as that of the object moving in the still air. After obtaining the fluctuating pressure of the object surface, the aerodynamic pass-by noise can be calculated by Eq. (2), comprehensively considering the movement of the object and the relative position between the measuring point and the object. This method is also consistent with the idea of acoustic analogy, that is, the solution of the sound source and the calculation of the sound propagation are independent. Compared with the existing methods, this method has two advantages. One is to use the wind tunnel mode to obtain the near-field fluctuating pressure as the sound source data, which avoids the error caused by using the interface. The other is if that after completing the unsteady flow field calculation, the stored sound source data can be used repeatedly for the pass-by noise calculation at different far-field measuring points, which can significantly reducing the time required for unsteady flow field simulation.

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3 Results As a check of the method, the aerodynamic noise generated by a finite cylinder is considered. According to the description of the methodology in Sect. 2, the calculation is divided into two parts. First, the unsteady flow field is simulated to obtain the sound source data of the object surface. In this paper, the unsteady flow field of the cylinder is simulated by STAR-CCM+ . After obtaining the fluctuating pressure (sound source data) of the cylinder surface, the movement of the cylinder and the relative position between the sound source and the measurement point are applied, and then using Farassat_1A formula to calculate the pass-by noise. The time delay between the receiving time and the emitting time is considered by the “Advanced time method” proposed by Casalino [14]. This part of the calculation is realized by MATLAB. The diameter of the cylinder is 10 mm and the spanwise length is 31.4 mm. As mentioned above, the unsteady flow field is simulated in the wind tunnel mode. The incoming flow velocity is 50 m/s, and the computing domain is shown in Fig. 1a. The trimmed volume mesh is used to discretize the computing domain. The total number of grids is about 3.5 million and the grid distribution is shown in Fig. 1b. Simulation of the unsteady flow field uses DES method based on SST k-w turbulence model, and the time step is 0.0001 s. The surface fluctuating pressure starts after the transient calculation reaches statistical stability, and the sampling time is 0.6 s.

3.1 A Stationary Cylinder In order to verify the accuracy of the MATLAB program developed in this paper, the far-field noise generated by a stationary cylinder is compared with the result calculated by the FW-H equation module in STAR-CCM+ (the moving speed of

(a) The computing domain

(b) The grid distribution

Fig. 1 The computing domain and grid distribution of the cylinder

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Fig. 2 Schematic diagram of relative position of the stationary cylinder and the far-field point

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the cylinder is set to 0 in the sound propagation calculation program). The far-field measuring point is located at (0, 0.1, 0) m, just above the cylinder, as shown in Fig. 2. Figure 3a shows the comparison between the sound pressure generated by the stationary cylinder at (0, 0.1, 0) m calculated by MATLAB program and STARCCM+ in time domain. Figure 3b further gives the comparison of the frequency spectrum. It can be seen that both the time domain and frequency domain results agree well with each other, which verifies the effectiveness of the program. In Fig. 3b, it can be clearly seen that there is a peak at 480 Hz, corresponding to the Strouhal number of about 0.19, close to 0.2. This peak frequency is caused by the periodic vortex shedding formed when the air flows pass through the cylinder.

3.2 A Moving Cylinder The far-field noise generated by a cylinder moving at 50 m/s pass through a farfield measurement point is calculated in this section. The schematic diagram of the movement direction and its relative position with the far-field point is shown in Fig. 4. Figure 5a shows the sound pressure at the far-field point in time history. It can be seen that sound pressure increases when the sound source moves close to the measuring

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Fig. 4 Schematic diagram of relative position of the moving cylinder and the far-field point

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Fig. 5 Aerodynamic pass-by noise at point (13, 0.5, 0) m

point and decreases gradually when the sound source moves away. Figure 5b gives the frequency spectrum of sound pressure. It can be seen that two peaks are generated at 417 and 562 Hz, which is close to the frequency shift caused by Doppler effect. Those two frequencies are consistent with the frequency shift determined by Eq. (3) [15]. f1 = f0

c0 , c0 + V

f2 = f0

c0 c0 − V

(3)

where f 0 is the frequency without Doppler effect, v is the velocity of the source, f 1 and f 2 are the frequencies after frequency shift. It is worth noting that, despite the frequency shift, the peak at 480 Hz still exists, the magnitude of this peak may be related to the relative distance between the measurement point and the cylinder.

4 Conclusion In this paper, a method for predicting aerodynamic pass-by noise is proposed. By using this method, the sound source data (pressure fluctuation) on the object surface is firstly obtained through unsteady flow field simulation with wind tunnel mode,

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and then the pass-by noise is calculated through Farassat_1A formula based on the movement of the object and the relative position between the measuring point and the object. By doing so, the negative effect of the interface on calculation accuracy when using sliding mesh or overset mesh to simulate the train’s movement can be effectively avoided. The method is preliminary verified by the cylinder case, and the authors have been calculated the aerodynamic pass-by noise generated by a pantograph based on the method proposed in this paper, and results are agree well with STAR-CCM+ for the stationary case, and further results will show in our next paper.

References 1. Thompson DJ (2009) Railway noise and vibration: mechanisms, modelling and means of control, 1st edn. Elsevier, Amsterdam, Netherlands 2. Li M, Zhong S, Deng T et al (2021) Analysis of source contribution to pass-by noise for a moving high-speed train based on microphone array measurement. Measurement 174:109058 3. Kurita T, Wakabayashi Y, Yamada H et al (2011) Reduction of wayside noise from Shinkansen high-speed trains. J Mech Syst Transp Logistics 4(1):1–12 4. Kurita T (2011) Development of external-noise reduction technologies for Shinkansen highspeed trains. J Environ Eng 6(4):805–819 5. Thompson DJ, Iglesias EL, Liu X et al (2015) Recent developments in the prediction and control of aerodynamic noise from high-speed trains. Int J Rail Transp 3(3):119–150 6. Nagakura K (2006) Localization of aerodynamic noise sources of Shinkansen trains. J Sound Vib 293(3–5):547–556 7. Mellet C, Létourneaux F, Poisson F et al (2006) High speed train noise emission: latest investigation of the aerodynamic/rolling noise contribution. J Sound Vib 293(3–5):535–546 8. He B, Xiao X, Zhou Q et al (2014) Investigation into external noise of a high-speed train at different speeds. J Zhejiang Univ Sci A 15(12):1019–1033 9. Zhang J, Xiao X, Wang D et al (2018) Source contribution analysis for exterior noise of a high-speed train: experiments and simulations. Shock Vib 2018 10. Ffowcs Williams JE, Hawkings DL (1969) Sound generation by turbulence and surfaces in arbitrary motion. Philos Trans Royal Soc London. Series A, Math Phys Sci 264(1151):321–342 11. Farassat F (2007) Derivation of formulations 1 and 1A of Farassat. NASA Technical Report, United States 12. Niu J, Sui Y, Yu Q et al (2020) Aerodynamics of railway train/tunnel system: a review of recent research. Energy Built Environ 1(4) 13. Curle N (1955) The influence of solid boundaries upon aerodynamic sound. Proc Royal Soc A 231(1187):505–514 14. Casalino D (2003) An advanced time approach for acoustic analogy prediction. J Sound Vib 261(4):583–612 15. Rienstra SW, Hirschberg A (2006) An introduction to acoustics. Eindhoven University of Technology

Wheel Out-of-Round and Polygonalisation

Influence of Running Speed on the Development of Metro Wheel Polygon Rang Zhang, Weiming Wang, Gang Shen, and Jiangyu Xiao

Abstract This paper makes a more in-depth study on the relationship between vehicle running speed and the development of wheel polygon when the wheel has an initial polygon. Firstly, in order to highlight the research focus and ignore the secondary factors, the vertical coupling vibration model of vehicle and track is reasonably equivalent simplified, and the wheel polygon vertical vibration model is established. Then, in order to obtain the variation of wheel longitudinal creep wear on the wheel circumference and the development trend of wheel polygon, the mathematical model of wheel/rail longitudinal creep wear under alternating normal force is established. By calculating the wear power of each point on the wheel circumference at different speeds, the phase relationship between the wear power distribution curve and the wheel radial jump curve is obtained. The simulation results show that, speed can change the distribution of wear power on the wheel circumference, and have a certain impact on the amplitude and phase of wear power. According to the phase relationship, the corresponding speed range can be obtained, and the train running in this speed range can inhibit the deterioration of the initial polygon. Keywords Metro vehicle · Wheel rail wear · Wheel polygon · Running speed

1 Introduction The irregular circumferential wear of metro train or EMU train wheels is called wheel out-of-roundness. If it presents periodicity, it is called wheel polygon, which is a common defect form of wheels along the circumferential direction. This form generally exists in Metro and high-speed trains in service [1]. In engineering, the R. Zhang (B) · W. Wang · G. Shen Institute of Rail Transit, Tongji University, Cao’an Road 4800, Shanghai 201804, China e-mail: [email protected] J. Xiao Department of Industrial Systems Engineering, National University of Singapore, Lower Kent Ridge Road, Queenstown, Singapore © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_23

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wheel polygon leads to strong vibration of the frame, resulting in a lot of economic losses and potential dangers. At present, more and more test data show that speed is also one of the important factors affecting the development of wheel polygon [2, 3], but few references in literature theoretically explain the effect of speed on the development of wheel polygon. By establishing a wheel rail vertical vibration model, the influence of vehicle running speed on the development of wheel polygon was analyzed in this paper, under the condition of constant acceleration and when there is regular polygon wear on the circumference of the wheel set.

2 Computational Model 2.1 Equivalent Simplification of Model Figure 1 shows the vehicle/track vertical coupling dynamic model. In order to highlight the main characteristics of the problem studied, it is necessary to reasonably simplify the complex vehicle/track vertical coupling dynamic model. When the wheel has initial polygon, the wheel radius changes, resulting in the change of the normal force between the wheel and rail. Considering that the vertical vibration of the front and rear wheelset of the same bogie is basically uncoupled, the model can be simplified to a single wheelset, a local steel rail and its lower floating plate structure (see Fig. 2). In addition, since the sprung mass is much larger than the wheel set mass, the sprung mass displacement is relatively small in high-frequency vibration and can be approximately regarded as static, so it is further simplified into a fixed coupling vibration model of single wheelset (see Fig. 3). And the following assumptions are made: (a) The rail is a smooth ideal rail; (b) The vertical displacement of the wheelset and rail is caused by the normal force between wheel and rail; (c) The wheel radial jump is caused by the wheel polygon; (d) The stiffness and damping parameters are constants; (e) The wheel speed is constant. Take the static equilibrium position of the system as the origin of the body coordinate system for modelling. According to the Newtonian mechanical equilibrium equation, it can be seen that: {

Mw Z¨ w + C1 Z˙ w + K 1 Z w = ΔF Mr Z¨ r + C2 Z˙ r + K 2 Z r = −ΔF

(1)

If the wheel has an initial polygon, the actual radius of the tread contact point is R = R(t). Therefore, the track vertical displacement changes with time as Z r = Z w −R(t) Add the two formulas in Formula 1 to obtain

(2)

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Fig. 1 Vehicle/track vertical coupling dynamic model Fig. 2 Simplified equivalent model

Mw Z¨ w + Mr Z¨ r + C1 Z˙ w + C2 Z˙ r + K 1 Z w + K 2 Z r = 0

(3)

Formulas (2) and (3) are combined to solve the equations, as shown in Formula (4) (Mw + Mr ) Z¨ w + (C1 + C2 ) Z˙ w + (K 1 + K 2 )Z w ¨ + C2 R(t) ˙ + K 2 R(t) = Mr R(t)

(4)

By combining Formulas (1) and (4), the dynamic additional normal force ΔF between wheel and rail can be obtained.

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Fig. 3 Fixed coupling vibration model

2.2 Longitudinal Creep Wear Model of Wheel/Rail Under Alternating Normal Force When the wheel has an initial polygon or the geometric irregularity of the rail surface reaches a certain range, the alternation of normal force between wheel and rail will occur. To explore the development of wheel polygon under long-term operation, it is necessary to establish the longitudinal creep wear model of wheel/rail under alternating normal force. Figures 4 and 5 shows the calculation model of wheel/rail creep force/creep rate. According to Hertz contact theory, when there is a normal force N acting between the two objects, deformation will occur near the contact point. When the size of the contact area is much smaller than the radius of curvature of the ellipsoid at the contact point, an elliptical contact spot will be formed. When the wheel rolls on the rail, there is relative sliding between the particle pairs in contact on the wheel/rail contact spot, which is called creep. According to the definition of creep rate, that is, the ratio of the relative speed difference between the two rolling elements at the contact point to the average speed, the calculation formula is as follows. ξx = where v1x = ω1r1 , v2x = ω2 r2 , v =

v1x − v2x v

(v1x +v2x ) . 2

(5)

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Fig. 4 Contact calculation diagram

Fig. 5 Creep force/creep rate curve

For wheel/rail contact, the coordinate system is established with the center of wheel/rail contact ellipse as the origin, and the three-dimensional creep rate of wheel/ rail surface is as follows. ⎧ v−ωr ⎨ ξ1 = v 0 0 (6) ξ = v−ωr cos δ ⎩ 2 ωδ ξ3 = v where, ξ1 ,ξ2 and ξ3 are longitudinal creep rate, lateral creep rate and spin creep rate, respectively.v is the vehicle forward speed.ω is the wheelset rotation speed.r0 is the nominal rolling circle radius.δ is the wheel/rail contact angle.

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According to Kalker linear theory [4], the calculation method of wheel/rail longitudinal creep force, lateral creep force and rotational creep force couple within the linear range can be obtained, as shown in Formula (7). ⎧ ⎨ T1 = − f 11 ξ1 T = − f 22 ξ2 − f 23 ξ3 ⎩ 2 M3 = f 23 ξ2 − f 33 ξ3

(7)

where f 11 is the longitudinal creep coefficient, f 11 = GabC11 . f 22 is the lateral creep coefficient, f 22 = GabC22 . f 23 is the spin/lateral creep coefficient, f 23 = 3 G(ab) 2 C23 . f 33 is the spin creep coefficient, f 33 = G(ab)2 C33 . a and b are the major and minor axis radii of the contact spot ellipse, respectively. G is the combined shear rigidity modulus of wheel and rail materials. Ci j is the dimensionless Kalker coefficient. The tangential resultant force of the contact spot is shown in Formula (8). TL(R) =

/

Tx2L(R) + Ty2L(R)

(8)

where, Tx L(R) is the longitudinal creep force, Ty L(R) is the lateral creep force. The reduced creep force is shown in Formula (9). ' TL(R) =

⎧ ⎨ μN ⎩

[( L(R)

TL(R) μN L(R)

)

−

1 3

(

TL(R) μN L(R)

)2

+

1 27

(

TL(R) μN L(R)

)3 ]

TL(R) ≤ 3μN

(9)

TL(R) > 3μN

μN L(R)

where μ is the wheel/rail friction coefficient, N L(R) is the normal force. The reduction factor is defined as shown in Formula (10) ε L(R) =

' TL(R)

TL(R)

(10)

The corrected actual tangential creep force and spin creep moment are shown in Formula (11) ⎧ ' ⎪ ⎨ Tx L(R) = ε · Tx L(R) (11) Ty' L(R) = ε · Ty L(R) ⎪ ⎩ M' z L(R) = ε · Mz L(R) In the straight-line operation condition, the change of lateral creep and spin creep of the wheel set is very small [5], so it is not considered. The saturation limit of creep force will change with the change of normal force between wheel and rail. According to the range of different normal forces of the train, the relationship curve between creep force and creep rate under different normal

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Fig. 6 Creep force/creep rate curve under different normal force

forces can be obtained. According to the creep rate/creep force curves under different normal forces, a three-dimensional numerical table can be formulated (see Fig. 6). The X/Y coordinate is the normal force/creep force, respectively, and the Z coordinate is the creep rate. If the creep force and normal force during wheel braking or traction are known, the creep rate at different positions during wheel rolling can be interpolated. The calculation method of wheel wear power is the sum of the product of creep force and creep speed, as shown in formula (12). Pr = Tx Vx + Ty Vy + Tz Vz

(12)

By omitting the lateral creep and spin creep, it is further written as Pr = ξx Tx · V

(13)

In Zobory wear model [6], the calculation of radial wear is shown in Formula (14). Δr =

k Pr ρbv

(14)

where k is the wear coefficient, ρ is the wheel material density, b is the axial radius of contact spot, v is wheel forward speed. Considering that the wear amount of each circle is very small, the wheel wear can be calculated every N circles as a cycle, that is, the wheel diameter is updated every N circles, so as to obtain the development of wheel out of roundness.

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3 Influence of Speed on the Development of Wheel Polygon Based on the above wheel/rail equivalent vertical dynamic model and the longitudinal creep wear model under alternating normal force, the influence of running speed on the development of wheel polygon is explored. Input the eighth-order initial polygon simulation signal, and its mathematical expression is shown in Formula (15). R(t) = A sin(nω0 t + ϕ)

(15)

where A = 0.01 mm, indicating the amplitude of wheel polygon; n = 8, indicating the order of the polygon; ω0 = 42.27 rad/s, indicating the angular speed of wheel rotation, ϕ = 0, indicating the included angle between wheel rotation angle and polar axis. Figures 7 and 8 show the changes of the normal force and wear power at various points on the wheel circumference at different speeds. It can be seen that when the speed is 44 km/h, the normal force on the wheel circumference changes sharply, and the difference between the maximum wear power and the minimum wear power become larger, mainly because the polygon excitation frequency is close to the natural frequency of the system, resulting in resonance. It can be seen from Fig. 8 that the resonance of the system will also lead to rapid increase and drastic changes in the wear power at each point of the wheel circumference, which will not be conducive to the improvement of wheel out of roundness. Therefore, from the perspective of amplitude, 44 km/h is an important critical speed. Next, the development of wheel polygon with speed is analyzed from the perspective of phase angle. Firstly, the included angle between the wheel circumferential radial jump peak and the wear power peak is defined as the speed phase angle β (see Fig. 9). When the speed phase angle is close to 0 or the integral multiple of Fig. 7 Normal force

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Fig. 8 Wear power

the amplitude change period of the radial jump, the wear power at the crest position of the wheel radial jump is the largest and the wear power at the trough position is the smallest. Therefore, under long-term operation, the wheel polygon condition will be improved and the wheel will tend to be round and smooth. When the speed phase angle is close to half or odd times of the amplitude change period of the radial jump, the wear power at the crest position of wheel diameter jump is the smallest, the wear power at the trough position is the largest, and the wheel out of roundness will gradually deteriorate. Therefore, the safety area is defined when the velocity/phase angle is 0, and the danger area is defined when the velocity phase angle is π 8 rad (half period). The variation of velocity phase angle under different velocities is obtained, as shown in Fig. 10. When the running speed is 1–9 km/h, the speed phase angle is in the danger area, and considering the normal operation of the train, this speed range is Fig. 9 Speed phase angle

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Fig. 10 Speed phase angle

not analyzed. With the increase of the running speed of the vehicle, the speed phase angle rapidly develops to near 0° and reaches the safety area. When the vehicle runs under the working condition of 10–40 km/h for a long time, the wheel polygon will be improved. When the speed reaches 44 km/h, the wheel phase angle quickly transits to the danger area, causing rapid wear and polygon deterioration, which makes the wheel more out of round. With the increase of speed, the speed phase angle fluctuates near the danger area, although the wear rate decreases when the resonance point is exceeded, the polygon still tends to deteriorate due to the existence of velocity phase angle.

4 Conclusion Speed can change the distribution of wear power on the wheel circumference, and have a certain impact on the amplitude and phase of wear power. The simulation analysis shows that when the speed is in the range of 10–40 km/h, the speed phase angle is in the safe area, and the initial wheel polygon will be restrained under the long-term operation of the vehicle. When the vehicle speed reaches 44 km/h, the external excitation frequency is close to the natural frequency of the system, which causes resonance, so that the wear power increases rapidly and changes dramatically. At the same time, the speed phase angle rapidly enters the danger area, and the wheel polygon tends to deteriorate.

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When designing a new vehicle, the safety area of speed phase angle can be expanded by setting reasonable vehicle parameters, so as to avoid the deterioration of the initial polygon. In addition, during the service of the vehicle, the reasonable running speed is set to ensure that the speed is in the safe area, and the wheel polygon is further improved, so as to achieve the effect of “similar turning repair”.

References 1. Yang XX (2015) Preliminary study on formation mechanism of wheel polygon of type a metro vehicle. Master’s thesis, Southwest Jiaotong University 2. Liu BL, Li ZS, Chen L, Zhu J, Guan KK (2019) Regularity and cause analysis of wheel set non roundness of metro vehicles. Mod Urban Rail Transit 2019(7):22–29 3. Cai WB, Chi MR, Wu XW, Sun JF, Zhou YB, Wen ZF, Liang SY (2021) A long-term tracking test of high-speed train with wheel polygonal wear. Veh Syst Dyn 59(11):1735–1758 4. Kalker J (1970) Transient phenomena in two elastic cylinders rolling over each other with dry friction. J Appl Mech 137(3):677–688 5. Jin XS (2006) Wheel/rail creep theory and its experimental study, 1st edn. Southwest Jiaotong University Press, Chengdu China 6. Ren L, Shi HL (2018) Railway vehicle system dynamics and its application, 1st edn. Southwest Jiaotong University Press, Chengdu China

Rail Roughness, Corrugation and Grinding

Cause Analysis of Metro Rail Corrugation Based on Mode Coupling Resonance Zhiqiang Wang and Zhenyu Lei

Abstract Based on the actual situation of metro line, a three-dimensional wheel-rail contact finite element model was established. Then, the stability of wheel-rail system was analyzed by using the complex eigenvalue method, the relationship between the modal coupling characteristics of wheel-rail system and the rail corrugation was discussed, according to the unstable frequencies and vibration modes, and the cause of rail corrugation was revealed. Finally, the influence of the wheel-rail friction coefficient on the stability of the system was investigated by using the equivalent damping ratio. The results show that the modal coupling resonance is the main reason for the instability of wheel-rail system, and for promoting the formation of rail corrugation. The increase of the friction coefficient will increase the instability of wheel-rail system in proportion. Therefore, in the actual metro operation process, properly reducing the wheel-rail friction coefficient can effectively inhibit the occurrence probability of rail corrugation on the premise of considering the traction and braking demands of vehicles. Keywords Metro · Rail corrugation · Finite element method · Complex eigenvalue · Coupling resonance

1 Introduction Rail corrugation is one of the most common track structural diseases on metro lines, which is characterized by periodic uneven wear of rail surface in the longitudinal direction. The existence of rail corrugation will cause high-frequency wheel-rail vibration, resulting in fatigue damage of vehicle and rail components and reducing passenger comfort. Meanwhile, the abnormal noise induced by rail corrugation will also adversely affect the living environment along the line [1]. Rail corrugation has a history of more than 120 years since it was reported in 1895. The research on rail Z. Wang (B) · Z. Lei Institute of Rail Transit, Tongji University, Shanghai 201804, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_24

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corrugation is also deepening and refining, but it is still unable to effectively prevent and control its formation and development [2]. Rail grinding is a commonly used corrugation treatment measure, but its economy is not high, and it cannot fundamentally eliminate rail corrugation [3]. Therefore, it has always been an important research topic in the railway industry to recognize the causes of rail corrugation and find out economic and effective treatment measures. There are many factors affecting rail corrugation, and all aspects related to wheelrail/vehicle-track system have become the starting points of rail corrugation research. The simplified numerical models are first applied to the study of rail corrugation. In Ref. [4], the generation mechanism of rail corrugation was successfully determined by using the corrugation formation model considering the creep characteristics of wheel-rail interface. In Ref. [5], a mathematical model was established to simulate the rail as an infinite beam and the bogie as a two-point mass, and the formation mechanism of rail corrugation was analyzed. It was considered that the rail deformation wave was the result of the mutual interference of the deformation waves under the two-point excitation, in other words, the interference was considered to be the basic mechanism of the formation of rail corrugation. Further, in Ref. [6], a linear wheel-rail model was developed to explain the formation of short-wavelength corrugation on the straight track, and also illustrate how wheel-rail parameters affect the development trend of rail corrugation. In Ref. [7], the influence of wheel-rail lateral force on the formation of inner rail short-wavelength corrugation and the effect of inner rail lubrication on reducing lateral force and preventing the formation of corrugation were analyzed. A time-domain prediction method of rail corrugation considering three-dimensional train-track interaction was proposed in Ref. [8]. The calculation showed that the high corrugation growth rate at a specific wavelength corresponded to the specific excitation mode of train-track coupling system. By establishing a nonlinear freight vehicle-track model on the curve track, Ref. [9] investigated the rail corrugation caused by the wheel-rail stickslip self-excitation vibration. The results indicated that the frequencies of wheel stick-slip process were composed of the combined effect of fundamental frequency, double fundamental frequency and triple fundamental frequency, and formed the wavelengths of rail corrugation under different conditions. Recently, the finite element method and complete numerical modeling method are gradually used to analyze the corrugation problem. In Ref. [10], the stability of wheel-rail system was studied by using the finite element complex eigenvalue method, and the friction coupling between wheel-rail interface was proposed as the mechanism of rail corrugation. In Ref. [11], aiming at a special rail corrugation phenomenon in Beijing metro, through field investigation and measurement, it was found that the dynamic train-track interaction at the main frequency was the cause of rail corrugation. In view of the abnormal rail corrugation phenomenon on the straight track with Cologne egg fasteners, the complex modal method and transient dynamic method were used in Ref. [12] and it was concluded that the low rail support stiffness was the main reason for this kind of corrugation. In Refs. [13–15], the multi-body dynamic theory and finite element method were used comprehensively to analyze the formation mechanism and development characteristics of rail corrugation and

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corresponding control measures were put forward. In Refs. [16–18], the influence parameters of rail corrugation were studied in detail, which provided guidance for restraining the occurrence and development of rail corrugation. According to the literature investigation, the formation of rail corrugation is closely related to the vibration characteristics of wheel-rail/vehicle-track system, but the specific vibration mechanism has not been determined. In view of this, this paper analyzes the cause of rail corrugation on a measured line from the perspective of wheel-rail vibration. Firstly, based on the actual situation of the metro line, a three-dimensional wheel-rail contact finite element model is established. Then, the stability of wheel-rail system is analyzed by using the complex eigenvalue method, and the relationship between mode coupling characteristics of wheel-rail system and rail corrugation is discussed according to the unstable frequencies and vibration modes, and then the cause of rail corrugation is revealed.

2 Methodology According to the line actual situation in Ref. [14], this paper further improves the three-dimensional finite element model of the wheelset-track system. The system model mainly includes a wheelset, two rails, a track slab and several spring-damper connecting elements. The wheel and rail surfaces are frictionally coupled tangentially by the penalty function, the friction coefficient is set as 0.3, and the normal direction is connected by the “hard” contact. The rail and track slab are connected by the spring-damper elements to simulate the fastener part, and the track slab is connected with the foundation through the spring-damper elements to simulate the supporting effect of the foundation. The wheel tread profile is the LM wear type, the rail type is CHN60, the rail cant is 1/40, the fastener type is Cologne egg fastener with a spacing of 0.6 m, the cross-section size of track slab is 2700 × 300 mm, the curve radius of track is 350 m, the gauge is 1435 mm, the total length of track is 36 m, and symmetrical constraints are imposed on both ends of the track. The established finite element model is shown in Fig. 1, and the relevant track structure parameters are shown in Table 1 of Ref. [14].

3 Results Based on the complex modal theory, the stability of the above wheelset-track system is analyzed by using the complex eigenvalue method. By identifying and extracting the unstable frequencies and vibration modes, the relationship between mode coupling characteristics of wheel-rail system and rail corrugation is studied to explain the cause of rail corrugation.

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Fig. 1 Finite element model of wheelset-track system

3.1 Complex Eigenvalue Method The complex eigenvalue analysis method is used to calculate the complex modes of structures, and it is a method to accurately predict the stability of the system from the perspective of frequency domain [2, 19]. In complex eigenvalue analysis, when the friction coupling is considered, the equation of motion of the system at the equilibrium position can be abbreviated as: M f x¨ + C f x˙ + K f x = 0

(1)

where, M f , C f and K f are the mass matrix, damping matrix and stiffness matrix of the system respectively. Because M f , C f and K f are all asymmetric matrices at this point, the eigenvalues of Eq. (1) may be greater than 0, that is, the system may be unstable. The corresponding eigenvalue equation can be written as: (λ2 M f + λC f + K f ) y = 0

(2)

where, λ is the eigenvalue of the system; y is the eigenvector of the system. The general solution of the above eigenvalue equation can be written as follows: x(t) =

n  i=1

ϕi exp((αi + ωi j)t) =

n 

ϕi exp λi t

(3)

i=1

where, t is the time; λi is the i-order eigenvalue of the system, λi = αi + ωi j. The real part αi of the eigenvalue represents the stability of the system. If the real part

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of the eigenvalue is greater than 0, the displacement amplitude of the system will increase exponentially, which means that the system will have unstable vibration. The imaginary part ωi of the eigenvalue represents the circular frequency of a particular mode. Therefore, in the complex eigenvalue analysis, the real part of the eigenvalue can be used to predict the stability of the system, so as to study the problem of rail corrugation.

3.2 Stability Analysis By setting the frequency domain analysis range as 20 ~ 1200 Hz and performing complex eigenvalue analysis (considering the friction effect caused by the wheel-rail relative slip from the previous analysis step) on the model, all vibration modes and corresponding frequencies in this range can be obtained. The unstable modes, i.e., the modes with the real parts greater than 0, are shown in Fig. 2 (only two modes), and the corresponding frequencies are 382.04 and 382.36 Hz respectively. It can be seen from Fig. 2 that the unstable vibration modes corresponding to frequencies 382.04 and 382.36 Hz are the bending vibration of the inner wheel, but the shapes of the vibration modes are completely different. Because the frequencies corresponding to the above two vibration modes are very close, they are easy to couple, and the different shapes of the two vibration modes will cause the phase Fig. 2 Unstable mode diagrams

(a) 382.04 Hz

(b) 382.36 Hz

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change in the motion process, so that one vibration mode drives the other. At this time, the friction force will provide energy for the system, so that the system becomes no longer stable [20]. Therefore, the mode coupling resonance is the main cause of system instability, and further induces the formation of rail corrugation. At the same time, the calculation results show that the unstable vibration modes are the bending vibration of the inner wheel, indicating that the inner rail is more prone to corrugation than the outer rail, which is consistent with the line actual situation, and also verifies the effectiveness of the model. From the above analysis, it can be seen that the wheel-rail friction plays a key role in the process of modal coupling resonance. Therefore, the influence of friction coefficient (one of the main factors determining friction) on the stability of the system will be mainly studied below. The friction coefficient is set to vary from 0.1 to 0.8 with a change interval of 0.1, and the system instability frequency and the real part of the corresponding complex eigenvalue under each friction coefficient condition are calculated respectively. Meanwhile, in order to clearly describe the degree of instability of the system, the equivalent damping ratio ζ [21] of the system is introduced to measure the occurrence tendency of unstable vibration, as shown in Eq. (4). If the equivalent damping ratio is negative, it indicates that the system is unstable at this time, and the smaller the value is, the more likely the corresponding unstable vibration is to occur. The variation of equivalent damping ratio with friction coefficient is shown in Fig. 3. ζ =

−2Re(λ) |Im(λ)|

(4)

where, Re(λ) represents the real part of λ and Im(λ) represents the imaginary part of λ. It can be seen from Fig. 3 that, with the increase of friction coefficient, the equivalent damping ratios corresponding to the two coupling frequencies are both negative -8.302

equivalent damping ratio (10-4)

Fig. 3 Variation diagram of equivalent damping ratios

382.04 Hz 382.36 Hz -8.303

-8.304

-8.305

-8.306 0.0

0.1

0.2

0.3

0.4

0.5

0.6

friction coefficient

0.7

0.8

0.9

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and gradually decrease, and the decrease trend presents a linear form, which indicates that the increase of friction coefficient will promote the instability degree of wheelrail system to increase proportionally, and then induce rail corrugation. Therefore, in the actual process of metro operation, on the premise of considering the traction and braking requirements of vehicles, appropriately reducing the wheel-rail friction coefficient can effectively suppress the occurrence probability of rail corrugation.

4 Conclusion Based on the actual situation of metro line, through the establishment of three- dimensional wheel-rail contact finite element model and complex eigenvalue analysis, it is found that mode coupling resonance is the main reason for the instability of wheelrail system, and for promoting the formation of rail corrugation. The increase of friction coefficient will lead to a linear increase in the instability degree of wheelrail system. Therefore, in the actual metro operation process, under the premise of considering the requirements of vehicle traction and braking, appropriately reducing the wheel-rail friction coefficient can effectively suppress the occurrence probability of rail corrugation. The friction effect induced by the wheel-rail relative slip has a crucial impact on the stability of the system, i.e., the formation of rail corrugation. That is to say, wheelrail relative slip is one of the preconditions for the occurrence of rail corrugation on the line. Acknowledgements This study was supported by the National Natural Science Foundation of China (11772230).

References 1. Wang ZQ, Lei ZY (2021) Analysis of influence factors of rail corrugation in small radius curve track. Mech Sci 12(1):31–40 2. Cui XL, Qi W, Du ZX, Dong RX, Zhong JK (2021) Generation mechanism and suppression method for the abnormal phenomenon of rail corrugation in the curve interval of a mountain city metro. J Vib Shock 40(14):228–236 3. Beshbichi OE, Wan C, Bruni S, Kassa E (2020) Complex eigenvalue analysis and parameters analysis to investigate the formation of railhead corrugation in sharp curves. Wear 450–451(15), 203150 4. Matsumoto A, Sato Y, Tanimoto M, Qi K (1996) Study on the formation mechanism of rail corrugation on curved track. Veh Syst Dyn 25(S):450–465 5. Manabe K (2000) A hypothesis on a wavelength fixing mechanism of rail corrugation. Proc Inst Mech Eng Part F-J Rail Rapid Transit 214(1):21–26 6. Muller S, Knothe K (2000) Numerical simulation of the formation of short pitch corrugation. Zeitschrift fur Angewandte Mathematik und Mechanik 80(S1):53–56

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7. Ishida M, Moto T, Takikawa M (2002) The effect of lateral creepage force on rail corrugation on low rail at sharp curves. Wear 253(1–2):172–177 8. Andersson C, Johansson A (2004) Prediction of rail corrugation generated by three-dimensional wheel-rail interaction. Wear 257(3–4):423–434 9. Sun YQ, Simson S (2007) Nonlinear three-dimensional wagon-track model for the investigation of rail corrugation initiation on curved track. Veh Syst Dyn 45(2):113–132 10. Chen GX, Zhou ZR, Ouyang H, Jin XS, Zhu MH, Liu QY (2010) A finite element study on rail corrugation based on saturated creep force-induced self-excited vibration of a wheelset-track system. J Sound Vib 329(22):4643–4655 11. Zhang HG, Liu WN, Liu WF, Wu ZZ (2014) Study on the cause and treatment of rail corrugation for Beijing metro. Wear 317(1–2):120–128 12. Cui XL, Chen GX, Yang HG, Zhang Q, Ouyang H, Zhu MH (2016) Study on rail corrugation of a metro tangential track with Cologne-egg type fasteners. Veh Syst Dyn 54(3):353–369 13. Wang ZQ, Lei ZY (2020) Causes and development characteristics of corrugation on tangential track of metro. J Vibroeng 22(8):1814–1825 14. Wang ZQ, Lei ZY (2020) Rail corrugation characteristics in small radius curve section of Cologne-egg fasteners. J Mech Sci Technol 34(11):4499–4511 15. Lei ZY, Wang ZQ (2020) Generation mechanism and development characteristics of rail corrugation of Cologne egg fastener track in metro. KSCE J Civ Eng 24(6):1763–1774 16. Cui XL, Huang B, Chen GX (2021) Research on multi-parameter fitting of fastener structures to suppress wheel-rail friction self-excited vibration. J Southwest Jiaotong Univ 56(1):68–74 17. Wu BW, Chen GX, Lv JZ, Zhu Q, Kang X (2020) Generation mechanism and remedy method of rail corrugation at a sharp curved metro track with vanguard fasteners. J Low Freq Noise Vib Active Control 39(2):368–381 18. Wang ZQ, Lei ZY (2021) Parameter influences on rail corrugation of metro tangential track. Int J Struct Stab Dyn 21(3):2150034 19. AbuBakar AR, Ouyang H (2006) Complex eigenvalue analysis and dynamic transient analysis in predicting disc brake squeal. Int J Veh Noise Vib 2(2):143–155 20. Meehan PA (2020) Prediction of wheel squeal noise under mode coupling. J Sound Vib 465:115025 21. Cui XL, Qian WJ, Zhang Q, Yang HG, Chen GX, Zhu MH (2016) Forming mechanism of rail corrugation of a straight track section supported by Cologne-egg fasteners. J Vib Shock 35(13):114–118, 152

Use of Flexible Wheelset Model, Comb Filter and Track Identification to Derive Rail Roughness from Axle-Box Acceleration in the Presence of Wheel Roughness Tobias D. Carrigan and James P. Talbot

Abstract Axle-box accelerometers fitted to in-service vehicles are a cost-effective way of monitoring rail roughness that can supplant the use of manual trolleys and dedicated measurement trains. Unlike the latter, accelerometers measure the vibration caused by roughness rather than the roughness itself, and so require processing to derive the levels of roughness. This is challenging due to variations in track stiffness, vibration coupling between wheels, and the presence of wheel roughness. This paper describes the derivation of rail roughness from axle-box acceleration (ABA) using a frequency-domain technique based on a vehicle-track model comprising multiple flexible wheelsets on two rails. The model is continuously updated by identifying variations in track stiffness from the P2 resonance peak in the ABA measurements. Furthermore, the effect of wheel roughness is removed from ABA by using a comb filter. The new methods are evaluated using measurements of ABA and rail roughness from the London Underground. The results demonstrate the derivation of narrowband roughness spectra within 10 dB of conventional measurements across most of the 40–1000 mm wavelength range, even with variations in track stiffness. Keywords Axle-box acceleration (ABA) · Rail roughness · Rail corrugation · Wheel roughness · Track stiffness

T. D. Carrigan (B) · J. P. Talbot Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK e-mail: [email protected] J. P. Talbot e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_25

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1 Introduction The use of axle-box accelerometers is being investigated by many railway operators as a means of continuously monitoring track condition. The accelerometers measure the vertical vibration of the axle box as excited by irregularities on the running surfaces of the wheel and track. A variety of techniques can be employed to analyse axle-box acceleration (ABA) measurements in order to detect corrugation and short track defects [1]. However, ABA alone cannot quantify rail roughness in absolute terms because it is dependent on the dynamic properties of the vehicle and track. The use of a frequency-response function (FRF) is investigated as part of a signal processing procedure to derive rail roughness spectra from ABA. Previous attempts to derive rail roughness by means of an experimentally calibrated FRF were affected by variations in track stiffness [2]. It was therefore proposed to use a parametric FRF calculated from a dynamic vehicle–track model along with a method to continuously update the track stiffness parameter in the FRF as the vehicle travels along the track [3]. Such identification of track stiffness is achieved by fitting the FRF to the P2 resonance peak in the ABA spectrum, as described in Sect. 3. It is relatively straightforward to model the track, but the dynamic response of the wheelset–axle-box assembly has proven to be more challenging to accurately model. Because of this, Tufano et al. [4] devised a method to measure the vehicle’s FRF and use this alongside the FRF of a track model to derive roughness from ABA. This paper investigates the effect of the wheelset dynamics on ABA by means of an analytical model of the wheelset. A parametric FRF is derived incorporating multiple flexible wheelsets on two rails and compared with that of rigid wheels on a single rail. The models and roughness derivation procedure are outlined in Sect. 2 and, along with the track stiffness identification method, are evaluated using ABA data recorded on a section of the London Underground. The results are presented alongside conventional measurements of rail roughness in Sect. 5. A further issue is the presence of wheel roughness, and a new method is described in Sect. 4 to remove the effect of wheel roughness from ABA by means of a comb filter, and is demonstrated on the measurement data in Sect. 5.

2 Deriving Roughness Spectra from Axle-Box Acceleration Random process theory is used to derive rail roughness spectra from ABA in the form of power spectral density (PSD) functions. For a single wheel, S yy (ω) = |H (ω)|2 Sx x (ω)

(1)

where S yy (ω) is the PSD of the axle box’s vertical displacement (ABD), which is calculated from ABA by Saa (ω) = ω4 S yy (ω); Sx x (ω) is the PSD of rail roughness as seen by the moving vehicle; H (ω) is the frequency response function from roughness

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to axle-box displacement (ABD); and ω is the angular frequency. Translating from the frequency domain to the wavenumber (γ ) domain, according to vehicle speed v, and rearranging, gives the required PSD of rail roughness in the fixed reference frame: ( ) Sx x γ = ωv = vSx x (ω) =

v |H (ω)|2

S yy (ω)

(2)

For multiple wheelsets on two rails, the cross-PSD of ABD between wheels j and k is defined, assuming random phase in the rail roughness between wheelsets and omitting “(ω)” for brevity: ) ( S y j yk ≈ Q jk L L Sx L x L + 2R Q jk L R Sx L x R + Q jk R R Sx R x R ,

(3)

Q jk L L = A j1 Ak1 + A j3 Ak3 + . . . , Q jk L R = A j1 Ak2 + A j3 Ak4 + . . . , Q jk R R = A j2 Ak2 + A j4 Ak4 + . . . where Amn is the transfer function from the roughness at wheel m to ABD at wheel n, the subscript ‘L’ denotes the left rail and ‘R’ the right rail. Odd-numbered wheels are on the left and even-numbered on the right. The transfer functions are elements of a transfer matrix, }−1 { A(ω) = Hca (ω) Hw (ω) + Hr (ω) + k −1 , H I

(4)

defined in terms of the cross-receptance matrices between the wheel treads Hw (ω) and rail contact points Hr (ω), the wheel-rail contact stiffness k H , and the crossreceptances from the wheel treads to the accelerometers Hca (ω). These matrices are determined from the vehicle-track models in Fig. 1 in terms of the parameters in Table 1.

Fig. 1 Vehicle-track models: flexible wheelsets on two rails (side and front view) and rigid wheels on one rail (side view only)

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Table 1 Vehicle and track parameters used in the underlying models Parameter

Value

Parameter

Vehicle

Value

Flexible wheelset model

Suspension stiffness k1

1.59 MN m–1

Wheel mass spacing lw

1.48 m

Suspension damping c1

3.0 kN s m–1

Wheel contact spacing lc

1.50 m

Contact stiffness k H

900 MN m–1

Axle box spacing lab

1.82 m

Rigid wheel model Unsprung mass m w1

Axle diameter: 400 kg

Rail

… between wheels dax

0.15 m

… wheel to axle box dae

0.09 m

Cross-sectional area A

7.17 × 10−3

Axle box mass m ab

50 kg

Density of steel ρ

7850 kg m−3

Axle box inertia Jab

0.245 kg m2

Young’s modulus E

207 GPa

Axle box rot. damping cθab

0.5 kN s rad–1

2nd moment of area I

2.35 × 10−5 m4

Accelerometer offset z aba

0.15 m

Shear modulus G

81 GPa

Wheel mass m w

222 kg

Shear coefficient κ

0.34

Wheel hub inertia Jwh

0.05 kg m2

Wheel rim inertia Jwr

10.7 kg m2

m2

Track foundation Stiffness per length k f '

(See Table 2)

Wheel rim rot. damping cθ wr

5.0 kN s rad–1

Loss factor η f

0.50

Hub-to-rim rot. stiff. kθ w,wr

6.0 MN rad–1

Table 2 Track stiffness identified from ABA using rigid and flexible wheelset models Track section

Vehicle speed (m/ s)

Wheel roughness removed?

ABA-identified track stiffness k f ' (MN m−2 ) Rigid wheel model Flexible wheelset model

A B

13.6–14.2 15.8–16.2

No

245

225

Yes

323

279

No

15.6

15.4

Yes

16.62

16.72

In the flexible wheelset model, each wheelset comprises an axle, modelled as an Euler beam of mass per unit length m ax ' = ρπ (dax /2)2 and bending stiffness E Iax = Eπ (dax /2)4 /4, where dax is the axle diameter, on which four masses representing the wheels and axle boxes are attached. The outer sections of axle towards the axle boxes are of a different diameter dae to that of the inner section between the wheels, dax , and hence have different mass and bending stiffness. The axle is discretised into 7 elements approximated by Hermitian cubic polynomials. The axle boxes each have mass m ab , inertia Jab , vertical suspension stiffness k1 , vertical damping c1 and rotational damping cθab . The accelerometers are offset outward from the centres of the axle boxes by distance z aba . Each wheel is split into two rotational degrees of freedom—a hub of inertia Jwh and a rim of inertia Jwr —joined by rotational stiffness

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kθw,wr in order to model the first out-of-plane bending mode of the wheel disc. The rim is subjected to rotational damping cθwr by the rolling wheel-rail contact. The wheel’s radial stiffness is greater than the wheel-rail contact stiffness so this is not included in the model and the rim moves with the hub in the vertical direction with a total mass of m w . The track is modelled as two independent infinitely-long Timoshenko beams on elastic foundations, representing two rails directly fastened via railpads to a concrete tunnel invert as is common in metro systems. The equations for the receptance matrices are given in Ref. [5], for a single wheelset, and are expanded here to represent multiple wheelsets. It is possible to derive the roughness PSDs for the individual rails from the PSDs and cross-PSD of ABA by rearranging a system of three equations, i.e., Eq. (3) for S y1 y1 , S y2 y2 and S y1 y2 . Theoretically, this would compensate for the vibration coupling between wheels, but achieving this requires both the vehicle model and ABA PSDs to be sufficiently accurate. This is not presently achieved, so Eq. (3) is simplified to S y1 y1 ≈ Q 11L L Sx L x L , S y2 y2 ≈ Q 22R R Sx R x R ,

(5)

and hence, in Eq. (2), |H (ω)|2 = Q 11L L = Q 22R R (by symmetry). Since the coupling between rails [ is not accounted for, ] the energy mean of the left and right rail PSDs, Sx x (γ ) = Sx L x L (γ ) + Sx R x R (γ ) /2, is presented in Sect. 5. The flexible wheelset model is compared to a simpler model comprising multiple rigid wheel-suspension units of mass m w1 on a single rail. The overall FRF in this case is |H (ω)|2 = |A11 |2 + |A12 |2 + |A13 |2 + . . ., with the receptance matrices in Eq. (4) instead representing rigid wheels on a single rail. To compute the PSD of ABA Saa (ω), the modified Welch’s method presented in Ref. [6] is used. This method splits the track section of interest, which is 62 m long, into 30 segments of length 4 m, overlapped by 50%, and aligns the time-domain ABA signal with the segment boundaries according to vehicle position measurements. The portions of signal that fall within each segment are Hann-windowed and their periodograms (square-magnitude fast-Fourier transforms) Saa (ω) are taken with the appropriate scaling applied. These periodograms are then converted into wavenumber-domain roughness periodograms Sx x (γ ) using Eq. (2), given the average vehicle speed in their respective segments, and then averaged together to produce the final roughness spectrum. Applying Eq. (2) to the individual segments minimises the error introduced by variations in vehicle speed within the section of track.

3 Identifying Track Stiffness Variations in track stiffness strongly influence ABA and occur due to wear, environmental conditions and changes in the track structure along the track. Here, a method is presented to derive the stiffness by identifying the P2 resonance peak in the ABA

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spectrum and fitting the same resonance in the FRF to this peak. The method is implemented in the technical computing software, MATLAB. Firstly, the ABA PSD is calculated over the track section of interest. To locate the P2 resonance peak, MATLAB’s findpeaks function is used to find the first peak in the PSD with a minimum peak separation of 60 Hz and prominence of at least 5 dB above the local minima between it and any higher peaks. A portion of the ABA PSD extending 12 dB down either side from the peak but limited to a frequency range of 0.6–1.8 times the peak’s frequency is isolated for the curve fitting. To perform the curve fitting itself, MATLAB’s fminsearch function is used to numerically minimize the sum-squares of the difference between the square-root of the ABA PSD and the weighted magnitude of the FRF aω|H (ω)| by optimising the track support stiffness k f ' as well as a multiplier a that accounts for the level of the underlying roughness. Once the curve-fitting is complete, the FRF with the resulting best-fit estimate of stiffness k f ' is used to derive the roughness spectrum from ABA. This method relies on the clear appearance of the P2 resonance in the ABA spectrum and can be affected by peaks in the underlying roughness, such as P2 corrugation, that are adjacent to the P2 resonance. This can occur when the vehicle’s speed profile differs from usual on the section of track such that the corrugation is not aligned with the resonance. It is therefore preferable to analyse multiple ABA measurements from the same section of track and identify those that have a clear P2 resonance peak to derive the track stiffness for that section. It is possible, particularly at higher vehicle speeds, that a peak of the sleeper-passing frequency or its harmonics may appear near the P2 resonance. In such cases, it may be necessary to suppress these peaks according to calculations of the sleeper-passing frequency, knowing the vehicle speed and sleeper spacing.

4 Removing Wheel Roughness Wheel and rail roughness are inherently combined in the ABA measurement. Wheel roughness is periodic with wheel rotation, which means that it contributes a series of discrete, equally-spaced peaks in the derived roughness spectrum that correspond to successive orders of wheel rotation, whereas rail roughness tends to be continuous over frequency. The wheel roughness component can therefore be either extracted from ABA using a peak comb filter or removed using a notch comb filter. Previously, the use of the synchronous average (a form of peak comb filter) was investigated in Ref. [3] to identify the wheel roughness component in the ABA signal, which was then subtracted to obtain the rail roughness component. The ABA signal needs to be interpolated to the rotation of the wheel so that the peaks in the filter are aligned with the orders of rotation. The synchronous average has a particularly narrow bandwidth and therefore requires precise measurements of wheel rotation that are sampled synchronously with the accelerometers. Instead, the use of a wider-bandwidth notch comb filter relaxes these requirements and extracts the rail component directly. This enables the use of wheel rotation (tachometer) measurements sampled independently

Use of Flexible Wheelset Model, Comb Filter and Track Identification …

ABA Sample rate: 25.6 kHz

Anti-alias filter

Interpolate ABA to wheel rotation (fixed samples per revolution)

Tachometer Sample rate: 25 Hz Resolution: 200 CPR

31-point moving average

Upsample to 25.6 kHz by cubic interpolation

281

Notch comb filter

Interpolate back to time domain

Filtered ABA

Fig. 2 Flowchart for removing wheel roughness from ABA using a notch comb filter

of the accelerometers at a lower sample rate, as is the case for the data considered here. However, this comes with the increased risk of filtering out periodic rail roughness components, such as grinding patterns and well-formed corrugation, that coincide with one of the orders of wheel rotation. The flowchart in Fig. 2 shows the present wheel roughness removal method. This interpolates the ABA signal to the wheel rotation data before applying a 4th-order zero-phase Butterworth notch comb filter with a 3 dB stopband width of 1/8 of a cycle per wheel revolution. The number of notches in the filter is equal to the number of samples per revolution so that the notches are at successive orders of wheel rotation. Finally, the filtered ABA signal is interpolated back into the time domain for the track stiffness and roughness derivation methods.

5 Results London Underground Ltd routinely record vibration levels using in-service trains fitted with axle-box accelerometers on both sides of one undriven wheelset. These continuously measure ABA, speed, and other parameters as they travel around the network. This paper considers ABA data acquired from two 62 m sections of the Victoria line, where conventional measurements of rail roughness were also taken using a corrugation analysis trolley (CAT) for comparison with those derived from ABA. The conventional measurements are processed through spike-removal and wheel-curvature filters according to EN 15610 [7]. The track stiffness and roughness derivation methods are tested on the ABA measured on the two track sections, A and B, with the rigid wheel and flexible wheelset models described in Sect. 2. A total of four wheels/wheelsets are employed in the models, spaced apart by 2.05, 4.474 and 2.05 m, respectively, and the accelerometers are on the first wheelset. Track section A is fitted with standard clip fasteners with 10 mm studded railpads, whereas section B has resilient Pandrol Vanguard fasteners.

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Figure 3 plots the ABA PSDs together with the portions of FRF fitted to their P2 resonance peaks. The track stiffness estimates are listed in Table 2 and the ABAderived roughness PSDs are plotted in Fig. 4 alongside those from conventional roughness measurements. The track stiffness derivation appears to work well in section A, with the estimates lying in the expected range. In section B, these are twice the expected value of 8 MN m−2 . This is likely due to the P2 resonance in section B, which, in general, tends to be less clear in data acquired on resiliently mounted track. The roughness derivation is therefore performed here with a prescribed stiffness of 8 MN m−2 . The instrumented wheelset on the ATMS train appears to be affected by a level of wheel roughness that exceeds the rail roughness in section A in the middle wavelengths but not the much higher rail roughness in section B. Comparison of the thick and thin lines in Fig. 4 shows the effectiveness and selectivity of the notch comb filter in removing the wheel roughness. Furthermore, compared to the rigid wheel model, the flexible wheelset model improves the agreement between the ABA-derived and

Fig. 3 ABA PSDs recorded on track sections A (left) and B (right), together with the fitted FRFs used to identify track stiffness for the flexible wheelset (thick solid) and rigid wheel (thick dotted) models. Black: ABA with wheel roughness removed. Green/grey: original ABA

Fig. 4 ABA-derived roughness PSDs, energy-averaged on both rails of track sections A (left) and B (right), using the flexible wheelset (thick black, from ABA with wheel roughness removed; thin black, original ABA) and rigid wheel (thin green, from original ABA) models, together with the conventionally-measured roughness PSD (black dashed). The track stiffnesses given in Table 2 are used to derive roughness for track section A only; section B uses k f ' = 8.0 MN m−2

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conventionally measured roughness PSDs so that they are within 10 dB across most of the 30–1000 mm wavelength range. Improvement to this accuracy may be achieved by further refining the vehicle model or by measuring or calibrating the vehicle receptances whilst retaining an analytical track model that can be adjusted with changes in track properties.

6 Conclusions Accounting for the flexible wheelset dynamics and variations in track stiffness, together with removing the influence of wheel roughness, has enabled the derivation of narrow-band rail roughness spectra from axle-box acceleration (ABA) that are accurate to within 10 dB at most of the wavelengths between 30 mm and 1 m. This may be sufficiently accurate for some applications, where the objective is to monitor solely for changes in roughness, but greater absolute accuracy is desirable. To this end, further improvements are currently being sought by analysing additional track sections from a larger dataset. It is hoped that such improvements will contribute to realising the aim of developing an autonomous ABA-based system that continuously ‘maps’ rail roughness, enabling more efficient and proactive scheduling of rail maintenance.

References 1. Salvador P et al (2016) Axlebox accelerations: their acquisition and time-frequency characterisation for railway track monitoring purposes. Measurement 82(3):301–312 2. Bongini E, Grassie SL, Saxon MJ (2012) ‘Noise mapping’ of a railway network: validation and use of a system based on measurement of axlebox vibration. In: Maeda T et al (eds) Noise and vibration mitigation, NNFM 118. Springer, Tokyo, pp 505–513 3. Carrigan TD, Talbot JP (2021) Extracting information from axle-box accelerometers: on the derivation of rail roughness spectra in the presence of wheel roughness. In: Degrande G et al (eds) Noise and vibration mitigation, NNFM 150. Springer, Cham, pp 286–294 4. Tufano AR et al (2021) Numerical and experimental analysis of transfer functions for on-board indirect measurements of rail acoustic roughness. In: Degrande G et al (eds) Noise and vibration mitigation, NNFM 150. Springer, Cham, pp 286–294 5. Carrigan TD, Talbot JP (2022) Addressing challenges in measuring rail roughness using axle-box accelerometers on trains. In: Proceeding 28th international congress sound vibration, Singapore 6. Carrigan TD, Fidler PRA, Talbot JP (2019) On the derivation of rail roughness spectra from axle-box vibration: development of a new technique. In: Proceeding international conference on smart infrastructure and construction. Cambridge, UK 7. EN 15610:2009 (2009) Railway applications—noise emission—rail roughness measurement related to rolling noise generation. CEN, Brussels

Analysis of the Mechanism of Rail Corrugation by Using Temperature Dependent Friction Coefficient Kuikui Ma and Xinwen Yang

Abstract In order to investigate the mechanism of rail corrugation on small radius curves, a three-dimensional wheelset-track thermal-mechanical coupling finite element (FE) model was developed. Friction coefficients are modeled in consideration of the wheel-rail contact temperature effects. The dynamic response of the wheelset-track system is investigated by transient analysis on a curved track with a radius of 350 m. The results show that the wheelset-track coupling dynamic system exhibits lateral stick-slip motion on the wheelset-low rail. The wheel-rail lateral creepages have obvious periodic fluctuations with dominated frequencies of 410 and 1045 Hz, In addition, The dominated frequencies of the wheel lateral vibration velocity on contact point as well as the dominated frequencies of lateral force are similar to dominated frequencies of the creep force. During a stick-slip process, the maximum temperature of the wheel-rail contact patch temperature increases with the creepages. The percentage of sliding region within the contact patch increases from 77.1 to 100%. The stick-slip vibration of the wheelset-low rail may lead to the occurrence of rail corrugation, which corresponds to wavelengths of 40.6 and 15.9 mm. Keywords Rail corrugation · Stick-slip process · Friction coefficients · Temperature

K. Ma · X. Yang (B) Shanghai Key Laboratory of Rail Infrastructure Durability and System Safety, Tongji University, Shanghai 201804, China e-mail: [email protected] The Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, Shanghai 201804, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_26

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1 Introduction Rail corrugation is a common problem in railway transportation. As the capacity of railway transportation increases, it is getting more and more attention from researchers. Corrugation is one kind of rail injury damage, manifested as a periodic unevenness of the rail surface, thus increasing the wheel-rail forces, making the vehicle, track coupling system a series of problems [1]. Under the action of corrugation, the noise and vibration of the wheel and rail increase, and also may lead to the fasteners and axle box fracture, which brings challenges to the safe operation of the railway. In order to mitigate the corrugation problem, railway operators often have to pay a large cost for regular grinding of the corrugated rail. Research on corrugation has been ongoing for more than 100 years, dating back to 1805 when corrugation was reported on the Midland Line in England [2]. The formation mechanism of rail corrugation is the fundamental problem of rail corrugation research, which helps to propose effective control means for rail corrugation. Various theories have been proposed to explain the rail corrugation mechanism based on the characteristics and formation process of rail corrugation [3]. In the process of research, researchers are also more and more inclined to find the common problem of rail corrugation formation mechanism, among which, there is a class of rail corrugation that is attracting more and more attention, that is, in the small radius curves of the subway, more than 90% of the section of rail corrugation occurs, which is called the common and deterministic (CD) phenomenon of rail corrugation [4]. Based on the key factor of small radius curves, Chen et al. [5] pointed out that the corrugation on small radius curves is caused by the frictional self-excited vibration of the wheel-rail system, the instability of the wheel-rail system will lead to the occurrence of vibration consistent with the unstable frequency. On the small radius curves, for the unstable vibration of the wheel-rail system, it is generally believed that there are two factors, one is the unstable mode coupling instability of the wheel-rail due to the friction force, and the other is the negative slope type instability of the friction coefficient [6]. It can be seen that the wheel-rail friction coefficient is an important parameter affecting the instability of the wheelrail system. Frictional heat generation phenomenon exists in both rolling and sliding contact processes of wheel tracks. The temperature In wheel-rail contact patch is easy to make the wheel-rail friction coefficient change, thus accelerating the rail surface wear. In particular, it should be noted that the coupled thermal-mechanical analysis of all wheel-rail contact uses the Coulomb friction model with a constant friction coefficient, while the actual rolling and sliding contact friction coefficients are not constant, but are related to the relative sliding speed and temperature of the wheel-rail contact [7]. Therefore, in this paper, the temperature-dependent friction coefficient is taken into account, a finite element model of small radius curves wheel-rail is established, and a transient thermal-mechanical coupling analysis method is carried out to obtain the dynamic response of the wheel-rail system, and the wavelength fixing mechanism of rail corrugation is analyzed by established model.

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Carbody

Front bogie

Wheelset 1 Wheelset 2

Rear bogie

Wheelset 3 Wheelset 4

Track

Fig. 1 The metro vehicle-track coupling dynamic model

Table 1 The quasistatic position parameters of the guiding wheelset (wheelset 1) Parameters

Lateral displacement (mm)

Yaw angle (rad)

Roll angle (rad)

Value

9.24

0.00441

0.000593

2 Wheelset-Track Coupling System Modelling 2.1 Dynamics Model of the Metro Vehicle-Track System In order to obtain the contact position between the wheelset and rails when the metro vehicle is running on a small radius curved track, a corresponding vehicletrack system dynamics model was built using UM software, as shown in Fig. 1, and the specific vehicle parameters were referenced from Ref. [8]. In this vehicletrack system dynamics model, the vehicle model is a simplified model of a B-type metro vehicle, consisting of a car body, two bogies, and four wheelsets. The vehicle dynamics response of the vehicle passed the R350 curved track were calculated, where the wheelset position was determined by the lateral displacement, the yaw angle, and the roll angle. The quasistatic position parameters of the guiding wheelset (wheelset 1)extracted at the midpoint of the curve are shown in Table 1.

2.2 Friction Coefficient Bucher et al. [9] used a combination of molecular dynamics simulations and laboratory tests to study the friction coefficient between wheels and rails, and found that the dynamic friction coefficient between wheel and rail can be expressed as a function of the variables k 1 , k 2 : μ = f (k1 , k2 ) = μ0 + μ1

k1 1 + μ2 1 + bk1 1 + ck2

(1)

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where μ0 , μ1 , μ2 , b, and c are constants of 0.15, 0.0442, 0.3243, 0.195, and 0.00212, respectively, here k 1 and k 2 are related to factors such as normal pressure, relative sliding velocity, and temperature. k1 =

σE σ v2 E , k2 = 2 σb σb

(2)

where ρ is the density of wheel-rail material; E is the elastic modulus of wheel-rail material; σ b is the tensile strength; σ is the normal stress. Considering the influence of wheel-rail contact friction temperature rise on the elastic modulus E and tensile strength σ b of wheel-rail material, the Formula (2) can be rewritten as follows [10]: k1 =

σ E(θ ) σ ω2 E(θ ) , k2 = 2 σb (θ ) σb (θ )

(3)

where θ is the temperature of the temperature field generated by the frictional heat between the wheels and rails.

2.3 Dynamics Model of the Wheelset-Track System According to the finite element theory and the wheel-rail contact position obtained in Sect. 2.1, a wheelset-track coupling finite element model is established. As shown in Fig. 2, the model includes wheelset, rails, fasteners, and mass above the suspension and slab. The wheelset is the guiding wheelset, and the tread profile of the wheel is LM profile. The type of rail is 60 kg/m. In addition, no irregularity on the rail is accounted for in the simulation. As shown in Fig. 3, to consider the effect of the thermal-mechanical coupling effect, the wheelset and rails are discretized using C3D8RT elements. Ignoring the 12.5m

Wheelset

2.4m

High rail V=60km/h

Low rail

Slab

Fig. 2 Overview of the 3D wheelset-track coupling model

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thermal-mechanical coupling effect of the slab, the C3D8R element is used for discretization. The mass above the suspension is simulated using mass elements, and firstly suspension and fasteners are simulated using CONN3D elements that can consider the stiffness and damping in three directions. For wheel-rail contact, a “hard” contact algorithm is used in the normal direction to allow wheel-rail separation, and a penalty contact algorithm is used in the tangential direction, applying a friction coefficient model that takes into account the temperature as described in Sect. 2.2. The friction coefficient model is implemented using VFRIC [1], a subroutine interface provided by ABAQUS/Explicit. As shown in Fig. 4, to take into account the calculation efficiency and accuracy, the model length is 12.5 m, and the dynamic relaxation zone (A-B section) of corresponding to the length of three sleeper bays and the solution zone (B-C section) of one span rail sleeper length are set [11]. The initial position of the wheelset is set according to Table 1. Model parameters are cited from Ref. [12]. Mass above the Suspension

Mass above the Suspension

Primary suspension

Primary suspension

Fig. 3 Firstly suspension and mass above the suspension Mass above the Suspension Fasteners （Springs and dampers） Primary suspension

1.875m

A

0.625m

B

C

Fig. 4 The dynamic relaxation zone and the solution zone

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(b)

0.4 0.3

0.1

0.2

0.4

0.1 0.0

406Hz

-0.2

Lateral velocity(m/s)

Lateral velocity(m/s)

-0.1

0.3

-0.3 0.0180

0.0182

0.0184

0.0186

0.0188

0.0190

0.0192

0.0194

0.0196

0.2 0.1 0.0 -0.1

0.01

1053Hz

0.001

1E-4

1E-5

-0.2 -0.3 0.0000

0.0075

0.0150

0.0225

0.0300

t(s)

0.0375

1E-6

10

100

1000

Frequency(Hz)

Fig. 5 Lateral vibration velocity: a velocity data; b frequency spectrum of velocity data

3 Result and Discussion 3.1 Result The dynamic response of the wheelset-track coupling system is calculated based on the finite element model, and because rail corrugation on the small radius curves generally occurs on the low rail [13], the dynamic response results on the wheelsetlow rail are analyzed in this paper. As shown in Fig. 5a, at the wheel-rail contact point, the lateral vibration velocity of the wheel has obvious periodic fluctuations, ranging from −0.2 to 0.3 m/s. From the frequency domain, as shown in Fig. 5b, the dominant frequencies of the lateral vibration velocity are 406 and 1053 Hz. As shown in Fig. 6, the wheelset-low rail lateral creep force also has obvious periodic fluctuation, ranging from −5 to −17.5 kN, the dominant frequencies of the lateral creep force are 410 and 1406 Hz. The results of the wheel-rail lateral dynamic response indicate that the wheelset-track system has a self-excited vibration on the low wheelset-low rail without irregularity on the rail.

3.2 Contact Temperature and Stick/Slip Region Distribution As shown in Fig. 7, the wheel-rail lateral creepage is given in Fig. 7a, which can be seen lateral creepages occur with obvious periodic fluctuations, and the dominant frequencies can be seen in Fig. 7b at 410 and 1045 Hz. In Fig. 7a, the wheel-rail creepage occupying the four different moments from t 1 to t 4 is shown in Table 2. To analyze the wheel-rail contact temperature rise and the distribution of the stick/ slip region, as shown in Fig. 8, for the temperature on the wheel-rail contact patch, it can be seen that the temperatures of t 1 ~ t 4 are 168, 205, 255, and 316 °C, with the

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10

(b)

5

100

-5

Lateral creep force(kN)

Lateral creep force(m/s)

0

5

-10

-15

291

0.0180

0.0182

0.0184

0.0186

0.0188

0.0190

0.0192

0.0194

0.0196

0 -5 -10

1046Hz 410Hz

10 1 0.1 0.01

-15 -20 0.0000

0.0075

0.0150

0.0225

0.0300

0.001

0.0375

10

100

1000

Frequency(Hz)

t(s)

Fig. 6 Lateral creep force: a creep force data; b frequency spectrum of creep force data (a) 0.012

(b)

0.008

t1 t2 0.01850

0.01855

t3

0.01860

0.01

t4 0.01865

0.01870

0.01875

Lateral creepage

Lateral creepages

0.010

0.1

0.01880

0.006 0.004 0.002

0.001

410Hz

1045Hz

1E-4 1E-5 1E-6 1E-7

0.000 0.1500

0.1575

0.1650

0.1725

0.1800

0.1875

1E-8

10

t(s)

100

1000

Frequency(Hz)

Fig. 7 Lateral creepage. a creepage data; b frequency spectrum of creepage data

Table 2 The times and corresponding creepages Time

t1

t2

t3

T4

Creepage

0.0015

0.0036

0.0052

0.0068

creepage rises, the wheel-rail contact patch within the maximum temperature is rising trend. From the stick/slip region distribution on contact patch, as shown in Fig. 9, the percentage of sliding region increases with the creepage, and the percentage of sliding area in four moments are 77.1, 85.6, 92.8, and 100%. Therefore, the motion of the wheel on the low rail is a typical stick-slip vibration process.

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Fig. 8 Temperature on contact patch: t 1 ~ t 4

Fig. 9 Stick/slip distribution on contact patch and tangential stress: t 1 ~ t 4

3.3 Rail Corrugation Wavelength Fixing Mechanism According to the viewpoint of rail corrugation caused by wheel-rail stick-slip vibration, The period of the corrugation coincides with the period of the stick-slip vibration [14]. Therefore, The relationship between wavelength λ of corrugation and frequency f can be expressed by Formula (4): λ=

v f

(4)

where v is the speed of the vehicle. Thus, the wavelength of rail corrugation corresponding to the dominant frequencies of stick-slip vibration is shown in the Table 3. Table 3 The rail corrugation wavelength corresponding to stick-slip vibration

Frequency (Hz)

410

1045

Wavelength (mm)

40.6

15.9

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4 Conclusion In this paper, the wheel-rail friction model considering temperature is applied to the small radius curved wheelset-track coupling model, the transient analysis is used to calculate the wheelset rolling/slipping process, and the fixed wavelength mechanism of rail corrugation is analyzed, and the following conclusions can be drawn. (1) On the small radius curves, the lateral frictional self-excited vibration occurs to the wheel on the low railt, the lateral vibration velocity of the low wheel has obvious periodic fluctuations with dominated frequencies of 406 and 1053 Hz. The lateral creep force between the wheelset-low rail is likewise periodic fluctuations with dominated frequencies of 410 and 1046 Hz. (2) The wheel-rail lateral creepages has obvious periodic fluctuations with dominated frequencies of 410 and 1045 Hz, and the maximum temperature of the wheel-rail contact patch temperature increases with the creepages from 168 ~ 205°C. From the stick/slip region distribution, with the increase of creepage, the percentage of sliding region within the contact patch increases from 77.1 to 100%. Therefore, the motion of the wheel on the low rail is a typical stick-slip vibration process. (3) According to the viewpoint of stick-slip vibration causing rail corrugation, the possible corrugation wavelength of the low rail can be derived as 40.6 mm as well as 15.9 mm. Acknowledgements The Authors heartfelt acknowledge the research project supported by the National Natural Science Foundation of China (No. 52178436,51778484).

References 1. Qinghua G, Bin Z, Jiayang X et al (2021) Review on basic characteristics, formation mechanisms, and treatment measures of rail corrugation in metro systems. J Traffic Transp Eng 21(1):316–337 (in Chinese) 2. Haarmann A (1913) Die Baustoffe der Spurbahnen: Stahl and Eisen, vol 1. Kisling, Berlin, Germany, pp 1–12 (in German) 3. Cui X, Chen G et al (2016) Study on rail corrugation of a metro tangential track with Cologneegg type fasteners. Veh Syst Dyn 54:353–369 4. Grassie SL (2009) Rail corrugation: characteristics, causes, and treatments. Proc Inst Mech Eng Part F: J Rail Rapid Transit 5. Chen G, Zhou ZR, Ouyang H et al (2010) A finite element study on rail corrugation based on saturated creep force-induced self-excited vibration of a wheel-set-track system. J Sound Vib 329(22):46–55 6. Ding B, Squicciarini G, Thompson D et al (2018) An assessment of mode-coupling and falling-friction mechanisms in railway curve squeal through a simplified approach. J Sound Vib 423:126–140 7. Zhu Y, Olofsson U (2014) An adhesion model for wheel–rail contact at the micro level using measured 3d surfaces. Wear 314(1–2):162–170

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8. Qi Y, Dai H, Wu P et al (2021) RSFT-RBF-PSO: a railway wheel Profile optimisation procedure and its application to a metro vehicle. Veh Syst Dyn 1–21 9. Bucher F, Dmihrifv AI, Ertz M et al (2006) Muti-scale simulation of dry friction in wheel/rail contact. Wear 261(7):87–88 10. Qian X, Hai Z, Chengguo W et al (2013) Thermal mechanical coupling analysis of wheel rail rolling and sliding contacts under functional friction coefficient. Chin Railway Sci 34(4):60–65 (in Chinese) 11. Zhao X, Wen Z, Wang F et al (2014) Modeling of high-speed wheel-rail rolling contact on a corrugated rail and corrugation development. J Zhejiang Univ-Sci A 15(12):946–963 12. Cui X, Chen G, Zhao J et al (2017) Field investigation and numerical study of the rail corrugation caused by frictional self-excited vibration. Wear 376–377:1919–1929 13. Huang Z (2007) Theoretical modelling of railway curve squeal. University of Southampton 14. Deng X, Ni YQ, Liu X (2022) Numerical analysis of transient wheel-rail rolling/slipping contact behaviours. J Tribol 1–15

Wheel and Rail Noise

Determination of Acoustic Properties of Railway Ballast Xianying Zhang, Giacomo Squicciarini, Hongseok Jeong, and David Thompson

Abstract As a porous material, railway ballast has absorptive properties that are important for the noise produced by the railway system. To understand its acoustic behaviour, measurements are presented on 1:5 scale ballast. Following direct measurements of the flow resistivity and porosity, transfer function methods are used in a vertical impedance tube to determine the surface impedance and absorption coefficient of different depths of ballast. The complex wavenumber is determined through transfer function measurements within the medium in the vertical tube. The Johnson-Champoux-Allard model for porous materials is fitted to these measurements, allowing determination of the remaining parameters, thermal and viscous characteristic lengths and tortuosity. The parameters are finally adopted to predict the diffuse field absorption coefficient of the scale ballast and full-size ballast. These are compared with measurements, showing acceptable agreement. Keywords Ballast properties · Acoustic absorption · Sound propagation

X. Zhang (B) Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, Shanghai 201804, China e-mail: [email protected] Shanghai Key Laboratory of Rail Infrastructure Durability and System Safety, Tongji University, Shanghai 201804, China X. Zhang · G. Squicciarini · D. Thompson Institute of Sound and Vibration Research, University of Southampton, Southampton SO17 1BJ, UK H. Jeong Korea Research Institute of Ships and Ocean Engineering, Daejeon 34103, South Korea © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_27

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1 Introduction The ballast, a layer of coarse stones, supports the track vertically and provides lateral stability. Due to the gaps between the stones, it behaves as a porous acoustic material, with absorptive properties, which is beneficial in reducing the railway rolling noise. The absorption coefficient of ballast was measured in a reverberation chamber by Kaye et al. as early as 1940 [1]. Measurements were more recently made of the flow resistivity and porosity of ballast by Attenborough et al. [2]. The acoustic properties of ballast were also investigated by Broadbent et al. [3] in terms of the diffuse field absorption coefficient and the excess attenuation for propagation over a layer of ballast. Heutschi considered ballast as an extended reaction medium by using an electrical transmission line model [4]. The present authors conducted an experimental and analytical study on the absorption of 1:5 scale ballast [5], and showed that this scale ballast could represent the acoustic features of the full-scale ballast at the corresponding scale frequencies. The aim of the current work is to present a comprehensive investigation of the acoustic properties of railway ballast, by extending the preliminary results in [5] and finding suitable parameters for use in the phenomenological model of JohnsonChampoux-Allard [6–8]. A granular material can be considered as an equivalent continuum provided that the wavelength is much ‘greater than the particle size [7]. For typical ballast dimensions of 50 mm this suggests such a model could be used up to 5 kHz at full scale. An impedance tube is used to determine the normal incidence absorption coefficient and surface impedance for different depths of ballast. Additionally, the complex wavenumber inside the ballast is determined. By fitting the model to these measurements, the appropriate parameters are obtained. Finally, the diffuse field absorption coefficients of the scale ballast and full-scale ballast based on these parameters are compared with measurements.

2 Johnson-Champoux-Allard Model for Porous Materials The Johnson-Champoux-Allard (JCA) model for porous materials [6–8] is used here to represent the ballast. This allows for sound propagation within the ballast (extended reaction). According to this phenomenological representation of ballast, the effective density is given by: ) ( / σfΩ qρ0 4iq 2 ηρ0 ω ρe = 1+ 2 2 2 1+ Ω iωρ0 q σfɅ Ω

(1)

where σf is the flow resistivity, q and Ω are the tortuosity and the porosity of the porous material, while ρ 0 and η are the density and viscosity of the air. Ʌ is the viscous characteristic length which can be approximated as a function of other parameters for

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some specific shapes of the pores but has not been determined a priori for materials like ballast. The effective or dynamic bulk modulus of material is Ke =

[ γ − (γ − 1) 1 +

γ P0 /Ω 8η iɅ'2 N p ωρ0

/

1+

iɅ'2 N p ωρ0 16η

]−1

(2)

where the ratio of specific heats γ = 1.4, the atmospheric pressure P0 = 1.013 × 105 Pa and N p = 0.709 is the Prandtl number. The thermal characteristic length Ʌ' is given approximately as Ʌ' ≈ 2Ʌ for fibrous materials or Ʌ' ≈ Ʌ for identical cylindrical pores [7]. The ratio between the two characteristic lengths is however not defined a priori for a material like ballast. The characteristic impedance and wavenumber are given by zc =

√

√ K e ρe , kwe = ω ρe /K e

(3)

The surface normal impedance of a rigidly-backed layer of the porous material with thickness l can be calculated as z n = −iz c cot(kwe l)

(4)

From this, the angle-dependent absorption coefficient can be determined and hence the random incidence absorption coefficient is obtained by using Paris’ formula [9].

3 Measurements of Porosity and Flow Resistivity Measurements of the flow resistivity and porosity of 1:5 scale ballast presented in [5] are summarised. The ballast samples were obtained by passing granite railway ballast through different sizes of sieve to achieve the correct scale gradation, see Fig. 1a. The flow resistivity was measured according to ISO 9053: 1991 [10] for two thicknesses, 30 and 60 cm. Figure 1b shows the corresponding measured results; there is little difference between the results for these two thicknesses. The mean value of the flow resistivity for the scale ballast is determined as 280 Pa s/m2 , which is close to the value of 200 Pa s/m2 obtained by Attenborough et al. [2] for full-scale ballast. The porosity of this 1:5 scale ballast was determined by filling a bucket with ballast and adding a known volume of water until it was flush with the surface of the ballast. The porosity of the ballast was determined as 0.463 ± 0.006, which is close to the value of 0.491 given in [2] for full-scale ballast.

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Flow resistivity, Pa.s/m 2

400 60cm 30cm

350

300

250

200

2

3

4

5

Flow velocity, mm/s

Fig. 1 a Gradation of 1:5 scale ballast. b Measured flow resistivity for the scale ballast

4 Acoustic Characterization of Ballast in an Impedance Tube Measurements were performed using a bespoke impedance tube to determine the wavenumber, the surface impedance and the absorption coefficient of the 1:5 scale ballast. The tube was mounted vertically, as shown in Fig. 2, with a sound source fitted at the top, and was filled to different depths with ballast. The diameter of the tube is 100 mm which is sufficient to ensure plane wave propagation up to 2 kHz.

Fig. 2 Measurement set up. a microphone arrangement for measurements inside ballast; b arrangement for transfer function method for impedance tube; c experimental set-up for the vertical impedance tube; d the positions of the microphones used in the tube; e the ballast tested in the impedance tube

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4.1 Wavenumber and Characteristic Impedance To estimate the wavenumber, the tube was filled with ballast. Four microphones, inserted through holes in the side at 10 cm intervals, were used to measure the sound pressure within the ballast, as shown in Fig. 2a. These were expressed as transfer functions, using the first microphone as a reference. To estimate the complex wavenumber for sound propagation inside the ballast, a least-squares fit was used between the measured transfer functions and those from an equivalent analytical model as H1 j =

e−ikb x j + eikb x j e−ikb x1 + eikb x1

(5)

where x1 and x j denote the distances of the corresponding microphones from the bottom of the tube (see Fig. 2a) and kb is the wavenumber. The values of kb estimated from this procedure are presented in Fig. 3a with continuous lines. The quality of agreement between the measured transfer functions and the analytical ones (not shown here) was used to verify the convergence of the curve fit algorithm. The measured wavenumbers were in turn used to determine the values for the input parameters required in the JCA model. To this end, a second curve fitting procedure was implemented with the aim of minimizing the difference between the measured and analytical complex wavenumbers. The flow resistivity and porosity were fixed at their directly measured values. The parameters that could be updated in the minimization procedure were therefore the tortuosity and the two characteristic lengths. The values obtained as a result of the minimization procedure are shown in Table 1 and the wavenumbers obtained with these optimized parameters are shown in Fig. 3a with dashed lines. The agreement between the measurements and the model is

Fig. 3 a Wavenumber; b characteristic impedance of 1:5 scale ballast shown, relative to the values for air

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very satisfactory. The characteristic impedance calculated with the analytical model is shown in Fig. 3b. A sensitivity analysis has been performed for the results in Table 1. Wavenumbers and characteristic impedance have been calculated for random variations of the input parameters following the ranges outlined in the last column of Table 1. The results are summarized in Fig. 4a and show the amount of variability that can be expected for the ranges assumed in Table 1 and for a combination of changes to all the parameters. Changes to porosity and flow resistivity alone have a small effect on the wavenumbers and impedance (see Fig. 4b) while changes in tortuosity can results in larger variation of the real part of these quantities, see Fig. 4c. Figure 4d shows that the variation in characteristic lengths has a larger effect in the lower frequency range while their influence gradually decreases becoming less important above 1 kHz. Overall, the effect of changes in tortuosity alone is comparable to all the parameters combined. Table 1 Scaled ballast properties for JCA model Variable

Value

Units

Description

Variation for Fig. 4

Ω

0.46

–

Porosity—measured directly

± 5%

q

1.5

–

Tortuosity—from curve fit

1.2–1.8

σf

280

Pa

Flow resistivity—measured directly

± 5%

Ʌ

840

μm

Viscous length—from curve fit

± 30%

Ʌ'

840

μm

Thermal length—from curve fit

± 3%

s/m2

Fig. 4 Effect of variations in input parameters on wavenumber and characteristic impedance. a combination of all variations in Table 1; b variation of porosity and flow resistivity; c variation of tortuosity only d variation of characteristic lengths

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Fig. 5 Acoustic surface impedance under normal incidence and for different thicknesses of ballast. Comparisons between measurements and predictions with JCA model

4.2 Surface Impedance and Absorption Coefficient The same apparatus has been adapted to measure the absorption coefficient and the surface impedance following the classical transfer function procedure for impedance tube measurements [11]. The set-up for this measurement is depicted in Fig. 2b. Five different depths of ballast were considered, from 0.07 to 0.035 m in steps of 0.07 m. These same quantities were also calculated with the parameters of Table 1. The surface impedance is shown in Fig. 5 while the absorption coefficient is in Fig. 6 for three example thickness. The good agreement between measurements and predictions confirms that the JCA model, with the parameters obtained from curve fitting the measured wavenumbers, constitutes a suitable approach to represent the acoustic properties of the scaled ballast in this range.

5 Diffuse Field Absorption Coefficient One-third octave band measurements of the diffuse field absorption coefficient of full-scale ballast and the 1:5 scale ballast are available from previous research [3, 5], each for two thicknesses. The JCA model is used with the parameters in Table 1 to predict the absorption coefficient of the 1:5 scale ballast, which is compared with the measured data from [5] in Fig. 7. The prediction by using the nominal parameters is denoted by the thicker black line. The changes of the prediction caused by the variations of the parameters in the last column in Table 1 are also shown. For frequencies below 2 kHz the agreement between the measured data and the predictions is satisfactory for both thicknesses. This frequency range is the one that was adopted for characterisation of the wavenumbers in Sect. 4 before the occurrence

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Fig. 6 Absorption coefficient under normal incidence and for different thicknesses of ballast. Comparisons between measurements and predictions with JCA model

of higher order modes in the tube. For frequencies above 2 kHz the predictions tend to underestimate the measured diffuse field absorption coefficient and this will require further investigation. For the full-scale ballast, both the viscous and thermal characteristic lengths of the 1:5 scale ballast in Table 1 are multiplied by 5. The flow resistivity is set to 200 Pa s/m2 as measured for full scale ballast in [2] but a value of 280 Pa s/m2 would give similar results. The other parameters are left unchanged. The predicted results are compared with the measurement results from [3] in Fig. 8. These results for the full-scale ballast broadly confirm the observations made for the scaled one. At lower frequencies the agreement between the model and the measurements is more satisfactory than at higher frequencies, where the model tends to underestimate the measurements. This suggests that the parameters obtained from the impedance tube measurements need to be adjusted for use at higher frequencies. 1

0.03 m

0.8

Absorption coefficient

Absorption coefficient

1

0.6 0.4 0.2 0 2 10

10

3

Frequency, Hz

10

4

0.06 m

0.8 0.6 0.4 0.2 0 2 10

10

3

10

4

Frequency, Hz

Fig. 7 Absorption coefficient in diffuse field for different thicknesses of the 1:5 scale ballast. Comparisons between measurements (◯) and predictions (–) with JCA model

Determination of Acoustic Properties of Railway Ballast 1

0.17 m

0.8

Absorption coefficient

Absorption coefficient

1

0.6 0.4 0.2 0 2 10

10

3

Frequency, Hz

305 0.33 m

0.8 0.6 0.4 0.2 0 2 10

10

3

Frequency, Hz

Fig. 8 Absorption coefficient in diffuse field for different thicknesses of the full-scale ballast. Comparisons between measurements (◯) and predictions (–) with JCA model

6 Conclusions Impedance tube measurements are used to obtain the surface impedance and absorption coefficient of different depths of 1:5 scale ballast. The complex wavenumber is determined through transfer function measurements within the medium. The JCA model is fitted to these measurements, using the flow resistivity and porosity obtained by non-acoustical measurements and adjusting the remaining parameters. These parameters are finally adopted to predict the diffuse field absorption coefficient of the scale ballast and full-size ballast, showing acceptable agreement with measurements. The results presented confirm that the flow resistivity and porosity directly measured in the laboratory can be used in phenomenological models for sound propagation through ballast but further investigation is needed to improve the results at high frequency. Acknowledgements The work described here has been supported by the National Natural Science Foundation of China (NSFC) under the grant 12104341.

References 1. Kaye GWC, Evans EJ (1940) The sound absorbing properties of some common outdoor materials. Proc Phys Soc 52:371–379 2. Attenborough K, Boulanger P, Qin Q, Jones R (2005) Predicted influence of ballast and porous concrete on rail noise. In: Internoise 2005. INCE, Rio de Janeiro, Brazil 3. Broadbent RA, Thompson DJ, Jones CJC (2009) The acoustic properties of railway ballast. In: EURONOISE 2009. Institute of Acoustics, Edinburgh 4. Heutschi K (2009) Sound propagation over ballast surfaces. Acta Acust Acust 95:1006–1012 5. Zhang X, Thompson D, Jeong H, Squicciarini G (2017) The effects of ballast on the sound radiation from railway track. J Sound Vib 399:137–150 6. Johnson DL, Koplik J, Dashen R (1987) Theory of dynamic permeability and tortuosity in fluid-saturated porous media. J Fluid Mech 176:379–402

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7. Allard JF, Atalla N (2009) Propagation of sound in porous media: modelling sound absorbing materials. Wiley, Chichester 8. Champoux Y, Allard J-F (1991) Dynamic tortuosity and bulk modulus in air-saturated porous media. J Appl Phys 70:1975–1979 9. Thompson D (2015) Noise control, chapter 5. In: Fahy F, Thompson D (eds) Fundamentals of sound and vibration. CRC Press, Boca Raton, FL, USA 10. ISO 9053 (1991) Acoustics—Materials for acoustical applications—Determination of airflow resistance. International Standards Organization 11. BS EN ISO 10534-2 (2001) Determination of sound absorption coefficient and impedance in impedance tubes: Part 2 Transfer function method. British Standards Institution

Rolling Noise on Curved Track: An Efficient Time Domain Model Including Coupling Between the Two Wheels and Rails Jiawei Wang, David Thompson, and Giacomo Squicciarini

Abstract High levels of vibration and noise usually arise when a railway vehicle negotiates a tight curve. The rolling noise radiated by the vibration of the wheel and rail is generally greater than on straight track. Although models of rolling noise on straight track are well established, much less attention has been given to curved track. The present study introduces a computationally efficient time-domain simulation model that is applied to curved track. To model the track a moving Green’s function approach is used but for the wheel, due to its low damping, the impulse response is quite long so a state-space approach is preferred. The current study introduces a novel combination of these two approaches. Additionally, the presence of steady lateral creepage during curving introduces a cross term between the vertical and lateral dynamics in the wheel/rail contact. Moreover, coupling between the two rails through the sleepers and between the two wheels through the axle are considered. The study indicates a significant influence of the lateral contact position and the effect of the steady creepage on the rolling noise in a curve. The inclusion of the coupling between the two sides of the wheel-rail system modifies the results at low frequency. Keywords Wheel/rail interaction · Time domain · Contact model · Sound radiation · Vertical/lateral coupling · Rails/wheels coupling

1 Introduction When a railway vehicle negotiates a tight curve, high levels of vibration and noise usually arise. The rolling noise radiated by the vibration of the wheel and rail is generally more severe than on straight track. Compared with the well-established models of rolling noise on straight track, curved track has received much less attention. J. Wang (B) · D. Thompson · G. Squicciarini Institute of Sound and Vibration Research, University of Southampton, Southampton SO17 1BJ, UK e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_28

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When negotiating a sharp curve, the leading wheelset of each bogie exhibits a significant yaw angle relative to the running direction, which results in a longitudinal and lateral sliding velocity at the wheel-rail contact. The sliding velocity normalized by the running speed is called the creepage and gives rise to a creep force. Unsteady creep forces can also lead to curve squeal noise but that is beyond the scope of the current work. In addition, in a curve the wheel/rail contact point moves towards the wheel flange on the outer (high) rail side and towards the field side on the inner (low) rail side. Vibration and rolling noise on tangent track have been studied for a long time. Remington [1] developed early theoretical models of rolling noise. Thompson [2] extended Remington’s theory and developed the model into a computer program called TWINS [3, 4]. The sources of rolling noise and the importance of the surface roughness in railway noise have been thoroughly investigated by using TWINS. For curved track, Torstensson et al. [5] simulated wheel/track interaction on small radius curves. A time-domain model was used to simulate the low-frequency vehicle dynamics due to curving and vehicle-track dynamics up to at least 200 Hz. The structural flexibility of the wheelsets and track was accounted for by using the finite element method. Time-domain Green’s function is also a sufficient method to deal with interactions between wheels and track [6]. Zhang et al. [7] extended this method based on time-domain moving Green’s functions to include the flexibility and rotation of the wheelset. This approach was employed to calculate wheel/rail interaction forces at high speed. The frequency content of the high-speed wheel/rail forces was shown for a number of typical excitation cases. The effects of wheelset rotation and multiple wheelsets were also investigated. But curved track is not considered here. The present study introduces a time-domain simulation model for rolling noise that is applied to curved track. To model the track, a moving Green’s function approach is used [7]. However, to model the wheel, due to its low damping, the impulse response is quite long so a state-space approach is preferred. The current study introduces a novel combination of these two approaches. Additionally, the presence of steady lateral creepage during curving introduces a cross term between the vertical and lateral dynamics in the wheel/rail contact [2]. Thus, the vertical/lateral coupling is also included in the current simulation. Moreover, coupling between the two rails through the sleepers and between the two wheels through the axle is considered. The investigations allow the influence of these coupling terms on the vibration and noise level to be determined.

2 Time-Domain Simulation Model In the current study, a time-domain vehicle-track interaction model is used. Timedomain models can consider the effect of the discrete sleeper spacing. However, they are computationally expensive due to the requirements for the fine spatial and time discretization. Nevertheless, with the advances in computers this limitation can be overcome and it is becoming possible to perform realistic time domain analysis.

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Fig. 1 The structure of the simulation model

There are two main methods used for time domain analysis. A modal system such as the wheel can be represented efficiently using a state-space method but it is difficult to apply this to the track. Alternatively, pre-calculated moving Green’s functions [7] are used to represent railway track and used in a convolution integral. This is efficient for the track but for the wheel the Green’s functions have to be very long due to the low damping. In the present work, therefore, these two approaches are combined. The overall structure of the model is shown in Fig. 1. The steady-state curving behaviour is calculated based on the formulation of Wickens [8]; this gives the lateral contact position, normal load and steady creepages. A non-Hertzian non-steady-state 3D wheel-rail contact model based on Kalker’s variational theory [9] is applied to obtain the stress distributions and to calculate the interaction forces in the contact. The calculated contact forces are applied as input to the calculation of the wheel and rail response at the following time steps. To calculate the rolling noise, the vertical and lateral contact forces are converted to the frequency domain and combined with a sound radiation model in a post-processing step. The sound radiation from the wheel and track is calculated by using TWINS [3].

2.1 Wheelset and Rail Receptances The wheelset is based on a modern electric multiple unit train. The wheel has a straight web and a diameter of 0.84 m; the axle is also included in the model. A finite element (FE) axi-symmetric model is produced by using the software ANSYS. A modal analysis is performed to determine the modal parameters (natural frequencies and mode shapes). The modal damping ratios ζ are based on the approximate values proposed by Thompson [10]. The point receptances for the nominal contact point of the wheel are presented in Fig. 2a, obtained using modal summation. In the time domain model, the response is calculated using a state-space approach in modal coordinates. The track consists of a UIC60 rail which is discretely supported on rail pads, sleepers and ballast. The rail is modelled by an improved semi-analytical method

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(a) Wheel receptances

(b) Track receptances of one rail

Fig. 2 Wheelset and track receptances

including bending and torsion, presented by Kostovasilis et al. [11], and the sleepers are modelled as flexible beams based on the approach presented by Thompson [10]. These are connected to the rail by a series of springs which represent the rail pads. The vertical stiffness of the rail pads is 90 MN/m, and 45 MN/m for lateral stiffness; the sleeper spacing is 0.65 m. The overall receptances of the track system are obtained by the approach adopted by Zhang et al. [12]. In order to ensure the waves generated are sufficiently attenuated at the ends of the finite supported region, 121 rail supports are used in the longitudinal direction to represent the infinite supported rail. When the excitation is given on the rail top surface, reaction forces at the discrete support positions can be obtained by the receptances of the discrete supports. If the discrete rail supports are considered to be replaced by corresponding reaction forces at the discrete support positions, then the rail can be considered as an infinite structure with many point forces acting on it. Due to the curving behaviour, the wheel/rail contact position has a lateral offset from the nominal contact point on the railhead. The vertical, lateral and cross receptances above a sleeper at the wheel/rail contact point for a 7.5 mm lateral offset on the railhead are presented in Fig. 2b.

2.2 Coupling Between Rails and Wheels In practice, the wheelset which consists of two wheels is running on a pair of rails. Here, the coupling between the rails through the sleepers and the coupling between the wheels through the axle are considered. The wheel-rail contact conditions are different on the high rail and low rail. Thus, the wheel-rail contacts on the high rail and low rail need to be considered separately and simultaneously in the time domain model. The contact positions of the two wheel-rail contacts are obtained from the steady-state curving model. According to the steady-state yaw angle of the wheelset and the gauge distance, the relative positions of the two wheel-rail contacts in the longitudinal direction can also be determined.

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(a) Vertical direction

311

(b) Lateral direction

Fig. 3 Comparison between point receptance of the low rail and transfer receptance between two rails with excitation at the high rail and response at the low rail in two directions

To account for coupling between the two rails through the sleepers, the rail transfer receptances are calculated to give the response on one rail due to excitation on the other. These are compared with the point receptances in Fig. 3.

2.3 Time-Domain Calculation The moving Green’s functions of the track are obtained from these receptances by applying an inverse Fourier transform. For each time step in the Green’s functions the rail transfer receptances are calculated at a distance corresponding to the distance travelled in that time and these are assembled into a moving Green’s function. The wheel and rail displacements in the current time step are determined by convolving the contact forces with the point response obtained from the state-space matrices of the wheelset and the moving Green’s functions of the track. Vertical and lateral forces on both sides of the wheel-rail system are included simultaneously.

2.4 Sound Radiation from the Wheel and Rail The sound radiation is calculated in a post-processing step, after the force timehistories are obtained. The forces are converted to the frequency domain and applied in the TWINS model to calculate the wheel and track vibration and their noise radiation. The frequency resolution is 0.2 Hz which ensures sufficient resolution around the wheel resonances. It is essential that the wheel modal basis used in TWINS corresponds exactly to that used in the time domain simulations.

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3 Curving Results 3.1 Effect of Curve Radii on Steady Parameters The steady-state contact parameters of the vehicle negotiating a curved track are obtained in advance by a steady curving model for curved track. The steady contact parameters include the normal loads on the two rails, the lateral wheel/rail contact positions, yaw angle, and steady creepages in the two wheel/rail contacts at high and low rails. The time-domain interaction model is then used with these contact positions and creepages. The discretely supported track system and the wheel model described in Sect. 2.1 are applied in the interaction model. Since the steady lateral offset increases as the curve radii reduce, Fig. 4 shows the wheel/rail contact position against the lateral offset and the creepages against curve radii. For tangent track, the steady creepages are set to be zero and wheel/rail contact is centered at the nominal point on the surfaces.

3.2 Effect of Curve Radii on Rolling Noise A curved track with radius of 300 m is firstly considered here. The operational velocity of the vehicle negotiating the curve is 72 km/h (20 m/s). The static friction coefficient is 0.3. The calculation time is long enough for the wheel/rail contact to reach steady-state before introducing the roughness. The roughness spectrum used is a broadband roughness corresponding to the limit curve from ISO 3095-2013 [13]. The wheel/rail interaction forces obtained in the presence of the roughness are plotted as one-third octave spectra for comparison. To reveal the difference in interaction forces between tangent and curved tracks, the results of these two cases are compared in Fig. 5a.

(a) Creepage against curve radius

(b) Offset against curve radius

Fig. 4 Effects of curve radius on steady parameters when curving

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(a) Curved track and tangent trac k

313

(b) Curved track with coupling and without coupling

Fig. 5 Interaction force comparison

Several important frequencies can be identified in the 1/3 octave spectra of the interaction forces in Fig. 5a. The peak at around 90 Hz is the P2 resonance (the vehicle unsprung mass bouncing on the track stiffness). The 200–300 Hz frequency range is dominated by the track receptance which contains the resonance frequency of the rail mass on the rail pad stiffness, seen as a dip in the interaction force. The vertical interaction forces of the two cases show little difference except around 20 Hz, associated with rigid body modes of the wheelset. For the tightly curved track, the steady lateral creepage is large enough to make the lateral interaction force reach saturation. Since a constant friction coefficient was applied, the saturation value is equal to vertical interaction force multiplied by the friction coefficient. Thus, the lateral interaction force of the tightly curved track shows mainly the characteristics of the vertical wheel/rail dynamics. For the tangent track, only the dynamic lateral creepage is considered and the interaction force is mainly related to the characteristics of the lateral wheel/rail dynamics. A significant effect is seen in the vertical interaction force at 20 Hz due to the vertical-lateral coupling. To investigate the effects on the interaction forces of the coupling between the two wheels and rails, Fig. 5b shows the force spectra for the curved track with and without this coupling. The coupling mainly introduces differences in the frequency range around the P2 resonance and the 200–300 Hz frequency range. Figure 6a compares the total sound pressure spectrum of the low side of the tangent track and curved track with 300 m curve radius; for the curved track, results are shown with or without considering the coupling between the two wheels and rails. These results include the sound radiated by the wheel, sleepers, vertical and lateral vibration of the track. It’s found that the rolling noise level between 100 and 1250 Hz of the curved track is higher than that of the tangent track. The effect of the coupling between the two wheels and rails is mainly found in the range 80–300 Hz, similar to the contact force. Figure 6b shows results for different curve radii. The sound pressure level decreases between 100 and 1250 Hz as the curve radius increases. As the curve radius is increased, the steady-state wheel/rail contact position shifts back to the nominal position and the steady lateral creepage value becomes lower. Consequently,

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(a) Curved track and tangent track

(b) Curved track with different radii

Fig. 6 Total sound radiation level Fig. 7 A-weighted SPL of each component

the sound radiated by the lateral vibration of the track are reduced. The A-weighted sound pressure level of each component against curve radius are shown in Fig. 7. The overall A-weighted sound pressure at low frequencies is dominated by the track. When the curve radius is large enough, the results become very similar to the tangent track case.

4 Conclusions A new time-domain wheel/rail interaction model has been presented, which simulates the wheel/rail interaction due to the wheel/rail surface roughness. The wheel is represented by a state-space model and the track by pre-calculated Green’s functions. The interaction forces and rolling noise are affected by the lateral contact position and

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by the effect of the steady creepage. For different curve radii, the lateral interaction force is affected much more than the vertical one. The lateral force further affects the wheelset and track response in the lateral direction, which results in changes in the rolling noise level. The rolling noise increases between 100 and 1250 Hz as the curve radius reduces. The inclusion of the coupling between the two wheels and rails, was also found to influence the contact force and rolling noise between 80 and 300 Hz but does not have a significant effect on the overall level.

References 1. Remington PJ (1988) Wheel/rail rolling noise: What do we know? What don’t we know? Where do we go from here? J Sound Vib 120:203–226 2. Thompson DJ (1993) Wheel-rail noise generation, Part IV: Contact zone and results. J Sound Vib 161:447–466 3. Thompson DJ, Hemsworth B, Vincent N (1996) Experimental validation of the TWINS prediction program for rolling noise, Part 1: description of the model and method. J Sound Vib 193:123–135 4. Thompson DJ, Fodiman P, Mahe H (1996) Experimental validation of the TWINS prediction program for rolling noise, Part 2: results. J Sound Vib 193:137–147 5. Torstensson PT, Nielson JCO (2010) Simulation of dynamic vehicle-track interaction on small radius curves. Veh Syst Dyn 49:1711–1732 6. Pieringer A, Kropp W, Nielson JCO (2008) A time domain model for wheel/rail interaction aiming to include non-linear contact stiffness and tangential friction. Notes on numerical fluid mechanics and multidisciplinary design, vol 99, pp 285–291 7. Zhang S, Cheng G, Sheng X, Thompson DJ (2020) Dynamic wheel-rail interaction at high speed based on time-domain moving Green’s functions. J Sound Vib 488:115632 8. Wickens AH (2003) Fundamentals of rail vehicle dynamics—guidance and stability. Swets & Zeitlinger 9. Kalker JJ (1990) Three-dimensional elastic bodies in rolling contact. Kluwer Academic, Dordrecht 10. Thompson DJ (2009) Railway noise and vibration: mechanisms, modelling and means of control. Elsevier, Oxford, UK 11. Kostovasilis D, Thompson DJ, Hussein MFM (2017) A semi-analytical beam model for the vibration of railway tracks. J Sound Vib 393:321–337 12. Zhang X, Thompson DJ, Li Q, Kostovasilis D, Toward MGR, Squicciarini G, Ryue J (2019) A model of a discretely supported railway track based on a 2.5D finite element approach. J Sound Vib 438:153–174 13. Acoustics—Railway applications—Measurement of noise emitted by railbound vehicles. ISO 3095-2013. International Standards Organization, Geneva

P2 Resonance Analysis of Multiple Wheels Interacting with a Railway Track Qinghua Guan, Changlong Li, Zefeng Wen, and Xuesong Jin

Abstract P2 resonance affects irregular wear of wheel and rail profiles, which are the main source of noise and vibration in railway operations. The vibrations of multiple wheels and track coupled systems are investigated, and the natural frequencies and mode shapes are determined by solving the characteristic equation with Green’s function and Laplace transform. The proposed method provides the basis for further studies on irregular wear of contact surfaces, such as rail corrugation and wheel outof-roundness, and for measures to mitigate ground vibration in railway operations. Keywords P2 resonance · Railway track · Multiple wheels · Green’s function · Laplace transform

1 Introduction P2 resonance is the predominant response at the wheel–rail interface in the coupled system of vehicle and track. It can be triggered by any impact excitation at the wheel– rail interface, e.g., rail joints, rail corrugation, wheel out-of-roundness, as well as other local defects on the rolling contact surface [1]. P2 resonance can lead to rail corrugation and wheel polygonal wear [2–5]. According to Grassie’s classification of rail corrugation, there are three types of rail corrugation associated with P2 resonance [2]. Surface irregularities on the profiles of rail and wheel also contribute greatly to the vibration of the vehicle–track coupled system, which not only lead to serious noise and vibration problems, but also to structural failures of the vehicle and track system. Moreover, the frequency range of P2 resonance for a typical railway vehicle and track is about 40–80 Hz [6], which is the dominant frequency range of ground vibration affecting the lives of local residents [7–12]. Q. Guan (B) · C. Li · Z. Wen · X. Jin State Key Laboratory of Rail Transit Vehicle System, Southwest Jiaotong University, No. 111, First Section, North of Second Ring Road, Chengdu 610031, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_29

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Therefore, it is important to determine the P2 resonance frequency in the design of railway vehicles and tracks to reduce the irregular wear of contact surfaces and the negative effects of associated noise and vibration. The authors have proposed a method to calculate the P2 resonance frequency for a single wheel on an elastically supported rail [6]. In the present study, the interactions between multiple wheels on a rail are considered to investigate the P2 resonance behaviour of the coupled system of track and multiple wheels.

2 Mathematic Models of the Interaction Between Multiple Wheels and Railway Track 2.1 Governing Equations The model of a railway track interacting with multiple wheels is shown in Fig. 1. The rail is considered as an Euler–Bernoulli beam resting on a Winkler foundation, where an effective stiffness is used to represent the elasticity of the support system, including the fastening system and the trackbed. Wu and Thompson pointed out that although a train contains many wheelsets running on the rail, the effect of one wheel on the interaction caused by another wheel can be neglected if the wheels are farther than about 10 m apart [13, 14]. The numerical experiments performed by Nielsen et al. have shown that the effects from the boundary conditions are negligible when the length of the track model is large enough [15]. The equations of motion of the coupled multiple unsprung masses and track system can be expressed as follows P1eiωt

P2eiωt

M1

M2

P3eiωt

M3 kH

kf

x1

x2

x3

l

y Fig. 1 Schematic model of a railway track with multiple wheels

EI, mr

x

P2 Resonance Analysis of Multiple Wheels Interacting with a Railway …

 ∂ 2 y(x, t) ∂ 4 y(x, t) + m + k f y(x, t) = Fi (t)δ(x − xi ) r 4 2 ∂x ∂t i=1

319

n

EI

Mi y¨i (t) + k H [yi − y(xi , t)] = Pi (t)

(1) (2)

where EI is the bending stiffness of the rail, mr is the effective rail mass per unit length, k f is the equivalent stiffness per unit length of the track structure, δ is the Dirac delta function, F i is the contact force between the ith wheel and the rail, Pi is the external force on wheel i, M i is the mass of wheel i, k H is the linearized Hertzian contact stiffness and can be determined according to [16], x i is the distance of wheel i measured from the origin of the rail. The contact forces between each wheel and the rail can be expressed as follows Fi (t) = k H [yi − y(xi , t)] = −Mi y¨i (t) + Pi (t)

(3)

2.2 Free Vibration Analysis For the free vibration analysis, the external forces Pi on each wheel are assumed to be zero, and substituting Eq. (3) into Eqs. (1) and (2) yields EI

n  ∂ 2 y(x, t) ∂ 4 y(x, t) + m + k y(x, t) = − Mi y¨i (t)δ(x − xi ) r f ∂x4 ∂t 2 i=1

Mi y¨i (t) + k H yi = k H y(xi , t)

(4) (5)

Using the separation of variables, the responses of the rail and wheels can be written as follows   y(x, t) = Y (x) sin α 2 t (6)   yi (t) = Bi Yi (x) sin α 2 t where Y (x) is the eigenmode function to be determined, α 2 is the unknown natural frequency, the magnification factor Bi can be determined based on Eq. (5) Bi =

βi4 kH = k H − α 4 Mi βi4 − α 4

(7)

where βi4 is the natural frequency of wheel i on contact stiffness, and βi4 = k H /M i . If α < β i , Bi > 0 and the wheel mass moves farther than the rail, the rail and the wheel

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are in phase, so the wheel behaves like a mass-like force to the beam. On the other hand, if α > β i , Bi < 0, the wheel mass behaves like a spring force. Substituting Eq. (6) into Eq. (4), we obtain Y  − λ4 Y =

n  α 4 Mi i=1

EI

Bi Y (xi )δ(x − xi )

(8)

where λ4 = (mr α 4 − k f )/EI, and α 4 = (EIλ4 + k f )/mr . The cut-off frequency of the rail beam on Winkler’s foundation is αc2 =  1/2 k f /m r . If the natural frequency is greater than the cut-off frequency, i.e., α > α c , then λ4 is a positive value, there are two evanescent waves and two propagating waves travelling in opposite directions. On the other hand, if α < α c , the solutions of λ are four complex values, thus all waves are evanescent.

2.3 Characteristic Equation Applying the Laplace transform to Eq. (8) yields s 3 Y (0) + s 2 Y  (0) + sY  (0) + Y  (0)  Mi α 4 Bi Y (xi )e−sxi + s 4 − λ4 EI s 4 − λ4 i=1 n

(Y ) =

(9)

Using the inverse Laplace transform, the mode shape Y (x) can be determined from the above equation as Y (x) =

n  Mi α 4 Bi Y (xi )G(x; xi , λ) EI i=1

(10)

where G(x; x i , λ) is the Green’s function of the vibrating rail beam defined as the bending displacement due to a concentrated unit force acting on x i and whose frequency is related to λ. G(x; x i , λ) is given by G(x; xi , λ) = A sin λx + B cos λx + C sinh λx + D cosh λx   + 1/2λ3 [sinh λ(x − xi ) − sin λ(x − xi )]u(x − xi )

(11)

where A, B, C and D are the coefficients dependent on the boundary conditions, u is the unit step function. If the boundary conditions at both ends are considered as simple supports, the coefficients in Eq. (11) can be determined as 

B = D = 0, λ(l−xi ) λ(l−xi ) , C = − sinh A = sin 2λ3 sin λl 2λ3 sinh λl

(12)

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Based on the conditions that the displacements at the excitation positions satisfy Eq. (10), one obtains  n     Mi α 4 δi j − Bi G x j ; xi , λ Y (xi ) = 0 EI i

(13)

where δ ij is the Kronecker delta function. The characteristic equation of the coupled system of multi-wheels and track can be derived by the determinant of the coefficient matrix of Eq. (13). Since the Green’s function G(x; x i , λ) contains the trigonometric and hyperbolic functions, the characteristic function is a transcendental equation that has infinite number of solutions for the eigenvalues αn4 . Once the eigenfrequencies of the coupled system are determined, the eigenmodes of the combined system can be derived as Yr (x) =

n  Mi α 4 Bi Yr (xi )G(x; xi , λ) EI i=1

(14)

Figure 2 illustrates the graphical solution of the natural frequencies of the combined system of a railway track with a single wheel. It can be seen from Fig. 2 that the intersection points of the two curves represent the natural frequencies of the combined track and wheel system. The lowest natural frequency of the combined system moves to a value lower than the first natural frequency of the railway track system. Below the natural frequency of the wheel on contact stiffness, each natural frequency of the combined system is lower than that of the track system alone. Above the natural frequency of the wheel oscillator, all natural frequencies of the combined system are higher than those of the track 30

Track Wheel

Receptances

20 10 0 -10 30

51.6 Hz 100 Frequency (α2/2π) /Hz

1000

Fig. 2 Graphic illustration of the natural frequencies of the combined system of a railway track and a wheel

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system. These phenomena were addressed by Rayleigh who investigated the effects of additional mass and stiffness on a dynamic system.

2.4 Vibration Analysis of the Coupled Multi-wheels and Track System The following section illustrates the vibration behaviour of the railway track interacting with multiple wheels representing real cases of railway vehicles. The initial parameters for the track and the wheels are given in Table 1. Figure 3 shows the eigenmodes of a rail interacting with two identical wheels at the P2 resonance frequencies for two types of track substructure, representing respectively a soft fastening system and a stiff fastening system. It is clear that there are two P2 resonance frequencies with different eigenmodes when two wheels contact the rail. For the soft railway track where the pad stiffness is 35 MN/m and the equivalent stiffness of the track bed for half the sleeper is 70 MN/m, the lower P2 resonance frequency is 50.91 Hz when two wheels move in phase, and the higher one is 52.75 Hz when two wheels move out of phase. For the stiffer track, where the pad stiffness is 350 MN/m and the track substructure is the same as the previous one, the lower P2 resonance frequency is 71.22 Hz, and the higher one is 73.00 Hz. The difference between the soft track stiffness and stiff track stiffness is that in the stiffer track, the two wheels move out of phase at the lower P2 resonance frequency but in phase at the higher P2 resonance frequency. Comparing with the P2 resonance frequencies of the two types of track, it can be found that the stiffer the track foundation the higher the frequencies of the P2 resonances. However, the two P2 resonance frequencies are close to each other for both track types. Figure 4 shows the mode shapes of the coupled system of the track with four wheels, of which two wheels have a lower mass and represent the trailer bogie, while the two heavier wheels represent the motor bogie. It can be seen that there are two lower and two higher natural frequencies at the P2 resonances, the first two Table 1 Parameters for the coupled track and wheels system Symbols

Designation

Value

mr

Mass per unit length of rail

60–120 kg/m

kf

Equivalent stiffness of track foundation per unit length

97.22 (38.89) MN/m2

EI

Bending stiffness of rail

6.63 × 106 N m2

kH

Linearized Hertz contact stiffness

1.028 × 109 N/m

Mi

Unsprung mass per wheel

550 (750) kg

L

Track length

25 m

2b0

Axle spacing

2m

2c0

Distance between the second wheel and third wheel

4m

kf = 38.89 MN/m2

In phase

0.0 0.5

15

20

25 Mode shape Y

1.0 f P2_1 = 50.91 Hz 1.5 0 5 10 2 Out of phase 1 0 -1 -2

fP2_2 = 52.75 Hz 0

5

10 15 Track position x /m

20

2 Out of phase 1 0 -1 -2 fP2_1 = 71.22 Hz 0 5 10 -0.5 In phase

323

Mode shape Y

-0.5

Mode shape Y

Mode shape Y

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25

kf = 97.22 MN/m2

15

20

25

15

20

25

0.0 0.5

1.0 f P2_2 = 73.00 Hz 1.5 0 5 10

Track position x /m

(a) Soft fastening system

(b) Stiff fastening system

Fig. 3 Mode shapes of the two P2 resonances for a railway track interacting with two wheels -1.5

kf = 38.89 MN/m2

-1.0

63.33 Hz

71.22 Hz

-0.5

Mode shape Y

Mode shape Y

-1.5

0.0 0.5 73.01 Hz

1.0 1.5

0

5

61.67 Hz 10

kf = 97.22 MN/m2

-1.0

71.22 Hz

61.67 Hz

-0.5 0.0 73.01 Hz

0.5

63.33 Hz

1.0

15

20

25

0

5

10

15

20

Track position x /m

Track position x /m

(a) Soft fastening system

(b) Stiff fastening system

25

Fig. 4 Mode shapes of the four P2 resonances for a railway track interacting with four wheels

depending on the heavier wheels and the last two on the lighter wheels. For both the two lighter wheels and the two heavier wheels, the influence of the two adjacent wheels is significant, however, the interaction between the motor bogie and the trailer bogie is insignificant as can be seen in Fig. 4. The receptances of the coupled system of the track with a trailer bogie and a motor bogie are calculated according to the method in [17], and shown in Fig. 5. It can be seen that when the excitation acts on the wheels of the trailer bogie, the dominant P2 responses of all wheels and the corresponding contact positions on the rail are at the two higher P2 resonance frequencies. At the two lower P2 resonance frequencies, the rail under the motor bogie exhibits relatively pronounced P2 resonances, while the rail under the trailer bogie exhibits no resonances at these frequencies.

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Fig. 5 Recepances of the couple system of a railway track and four wheels

3 Conclusions The vibrations of the coupled system of a railway track interacting with multiple wheels are investigated based on Green’s function. The main conclusions are as follows: (1) The addition of wheels on the track causes the lowest natural frequency of the coupled system to shift to a lower value compared to that of the track-only system. (2) There are n P2 resonance frequencies of the coupled system of a track with n wheels on it. These P2 resonance frequencies are close to each other but have different mode shapes. The mode shapes corresponding to the P2 resonance frequencies depend on the system characteristics of the track and the wheels. (3) The interaction between the wheels of a bogie is significant. Although the interaction between adjacent bogies is less significant, the vibrations at P2 resonances still transfer energy to the adjacent bogie at least to some extent provided that the distance between two bogies is not too large. The present study helps to provide insight into the interaction between multiple wheels and its effects on the dynamics of the vehicle–track coupled system. The influences of P2 resonance on irregular wear of wheel and rail profiles as well as on ground vibrations can be investigated based on the developed method. Acknowledgements This work was supported by the National Natural Science Foundation of China (U21A20167), the Sichuan Science and Technology Program (2023NSFSC0399) and the Scientific Research Foundation of the State Key Laboratory of Traction Power of Southwest Jiaotong University (2020TPL-T02).

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References 1. Nielsen JCO, Pieringer A, Thompson DJ, Torstensson PT (2016) Wheel–rail impact loads, noise and vibration: a review of excitation mechanisms, prediction methods and mitigation measures. In: Degrande G (ed) Noise and vibration mitigation for rail transportation systems (Proceedings of the 13th international workshop on railway noise (IWRN13)). Notes on numerical fluid mechanics and multidisciplinary design, vol 150. Springer, Cham, pp 3–40 2. Grassie SL (2009) Rail corrugation: characteristics, causes, and treatments. Proc IMechE Part F: J Rail Rapid Transit 223(6):581–596 3. Nielsen JCO, Lunden R, Johansson A, Vernersson T (2003) Train–track interaction and mechanisms of irregular wear on wheel and rail surfaces. Veh Syst Dyn 40(1–3):3–54 4. Jin X, Wu L, Fang J, Zhong S, Ling L (2012) An investigation into the mechanism of the polygonal wear of metro train wheels and its effect on the dynamic behaviour of a wheel/rail system. Veh Syst Dyn 50(12):1817–1834 5. Tao G, Wen Z, Jin X, Yang X (2020) Polygonisation of railway wheels: a critical review. Railway Eng Sci 28(4):317–345 6. Guan Q, Zhou Y, Li W, Wen Z, Jin X (2019) Study on the P2 resonance frequency of vehicle track system. J Mech Eng 55(8):118–127 7. Nielsen JCO, Mirza A, Cervello S, Huber P, Muller R, Nelain B, Ruest P (2015) Reducing train-induced ground-borne vibration by vehicle design and maintenance. Int J Rail Transp 3(1):17–39 8. Sheng X (2019) A review on modelling ground vibrations generated by underground trains. Int J Rail Transp 7(4):241–261 9. Sheng X, Jones CJC, Thompson DJ (2004) A theoretical study on the influence of the track on train-induced ground vibration. J Sound Vib 272:909–936 10. Kouroussis G, Connolly DP, Verlinden O (2014) Railway-induced ground vibrations—review of vehicle effects. Int J Rail Transp 2(2):69–110 11. Auersch L (2020) Simple and fast prediction of train-induced track forces, ground and building vibrations. Railway Eng Sci 28(3):232–250 12. Auersch L (2015) Force and ground vibration reduction of railway tracks with elastic elements. J Vib Control 21(11):2246–2258 13. Wu TX, Thompson DJ (1999) The effects of local preload on the foundation stiffness and vertical vibration of railway track. J Sound Vib 219(5):881–904 14. Wu TX, Thompson DJ (2001) Vibration analysis of railway track with multiple wheels on the rail. J Sound Vib 239(1):69–97 15. Nielsen JCO, Egeland A (1995) Vertical dynamic interaction between train and track—influence of wheel and track imperfections. J Sound Vib 187(5):825–839 16. Guan Q, Zhao X, Wen Z, Jin X (2021) Calculation method of Hertz normal contact stiffness. J Southw Jiaotong Univ 56(4):883–888 17. Bergman LA, Nicholson JW (1985) Forced vibration of a damped combined linear system. ASME J Vib Acoust Stress Reliab Des 107(3):275–281

Quantifying Rolling Noise Reduction by Improvements to Wheel-Rail Interface Management Peeter Vesik, Briony Croft, Mark Reimer, and Donald Eadie

Abstract Vancouver SkyTrain noise has historically been highly variable. Corrugation in both curve and tangent track has been a maintenance challenge since the system opened, with changing rail surface condition between maintenance cycles resulting in up to 26 dBA variation in rolling noise emissions. This paper describes the outcomes from pilot studies and investigations to quantify the potential rolling noise reduction achievable by modifications to wheel-rail interface conditions, including harder rail steel; acoustic rail grinding and top of rail friction modifiers. The study demonstrates that reducing the cyclic variation in rolling noise is feasible. The objective is to optimize maintenance practices and wheel/rail interface conditions to keep train passby noise emissions within 5 dB of the best case (minimum) noise at all times. Keywords Rolling noise · Corrugation · Friction modifier · Wheel-rail interface · Rail grinding

P. Vesik (B) British Columbia Rapid Transit Company, 6800 14th Avenue, Burnaby, BC V3N 4S7, Canada e-mail: [email protected] B. Croft Acoustic Studio, Unit 27 43-53 Bridge Road, Stanmore, NSW 2048, Australia M. Reimer Advanced Rail Management, Winnipeg, Canada B. Croft · M. Reimer Sahaya Consulting, Winnipeg, Canada D. Eadie Don Eadie Consulting, Mayne Island, British Columbia, Canada © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_30

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1 Background This investigation was initiated in response to noise concerns raised by residents living near the Vancouver SkyTrain. Increasing numbers of complaints over several years led to completion of a noise study quantifying the issue in 2018 [1]. A 2020 noise survey identified that changing rail surface condition between track maintenance cycles can result in up to a 26 dBA variation in rolling noise emissions [2]. This paper summarises pilot studies and investigations of wheel-rail interface improvements targeting noise, following on from the 2018 study. Excessive SkyTrain noise due to corrugation first became an issue shortly after operations commenced in 1986. Early investigations by Kalousek and Johnson [3] identified misaligned wheelsets and conformal wheel/rail contact as contributing to the problem. Rectifying the misaligned wheels, adjustments to rail profiles and solid stick friction modifier applied to the wheel tread were found to be effective solutions. SkyTrain was the first system in the world to employ tread friction modifiers. However, maintaining the system has remained an ongoing challenge. The increase in noise complaints observed since 2010 has been attributed to increasing operational demand alongside competing maintenance priorities and cost pressures. Increased traffic requires increasing focus on management of rail condition and the wheel-rail interface [4]. This paper quantifies the potential rolling noise reduction achievable by modifications to wheel-rail interface conditions, specifically harder rail steel; acoustic rail grinding and top of rail friction modifiers (TORFM). More details on the study and recommendations for improvements to wheel rail interface management can be found in [5].

2 Harder Rail Steel A wide range of different rail steels are in use on the SkyTrain network. This mix is the result of the phased construction of the system, increases in the hardness of specified “standard strength” rail over three decades, and pre-existing use of harder rail than the minimum specified in some areas. At the time of original system construction, the standard specification was a minimum Brinell Hardness of 248 HB. This has increased to 310 HB minimum. Premium strength rail is minimum 370 HB.

2.1 Methodology The noise benefit of harder rail steels was investigated based on in-car rolling noise levels measured around the network in a dedicated test train without passengers on a weekly basis over two years. Trains are automated with very consistent speeds

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up to a maximum of 80 km/h. Test train noise levels were linked to unique track section identifiers and hence matched to specific locations with different rail grades. The analysis excluded areas with switches, stations, tunnels, and any areas with train speeds less than 70 km/h. In total, around 55 km of track was used in the analysis. The influence of any measurement outliers in the dataset was minimized by examining the difference between the 10th percentile “best case” and 90th percentile “worst case” measured noise level for each track section over the two years. Examples of outliers were the test train running slow in a particular section of track on a particular day, or noise from on-train announcements. The influence of train numbers and maintenance practices were considered by reviewing the traffic tonnage per grinding interval.

2.2 Results The analysis showed that best case in-car rolling noise levels occur on recently ground track at around 75–78 dBA. These minimum noise levels were similar everywhere, regardless of the rail hardness, age, brand, or location, indicating that the post-grind rail surface finish was very similar across the system. Differences between varying levels of rail hardness were found when comparing the range of noise levels throughout the grinding maintenance cycle at each location. Noise levels were separately analyzed for tangents and curves, however, both types of geometry had similar performance for both best and worst case noise. It is noted that the rolling stock has steerable wheelsets, effectively eliminating curve squeal and flanging noise so that rolling noise is the dominant issue. Unlike many rail transit systems the SkyTrain does not tend to experience more corrugation growth on curves than on tangent track. Areas with the softest rails were found to typically show an 8–10 dBA increase in in-car rolling noise level throughout the grinding cycle. These areas often require grinding every three months to address corrugation. The hardest rail areas showed a smaller 5 dBA increase in in-car rolling noise throughout the grinding cycle. These areas typically require grinding much less often, only every year or two years. Using harder premium steel for rail replacement in areas still using original standard hardness rails is therefore expected to result in annual average noise level reductions of up to 4–6 dB as shown in Table 1. Table 1 Average long term noise benefit of harder rail steel, relative to historical standard Rail grade

Minimum hardness (HB)

Noise reduction (dBA)

Historical standard (original system construction)

248

–

Current standard

310

2–4

Intermediate

350

3–5

High strength

370

4–6

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Areas with harder rail steel require less frequent grinding maintenance, up to 8 times less (from quarterly to every two years). The harder rail steel not only increases rail life, it therefore also frees up grinding capacity to address specific problem areas with softer rail in the short term, potentially providing an additional noise benefit. The capital cost increase to the rail replacement program of using premium strength rail in place of standard rail was calculated to be less than 0.5%. In the long term, grinding program cost savings are possible as the proportion of harder rail on the network increases with ongoing rail replacement projects.

2.3 Propensity for Surface Defects Surface defects such as spalls and shelling create localized increased impact noise levels as the wheel interacts with the defect. SkyTrain historical maintenance records were analysed to understand the number of defect repairs (rail plugs or surface welding) per kilometer of track, compared with years in service and rail hardness. No correlation was found between rail hardness and the resistance to surface defects, rather particular batches of rail were more defect-prone. It was concluded that steel quality and manufacturing processes are also factors in tendency for formation of surface defects, emphasizing the importance of rail quality control and metallurgical analysis to minimise system noise long term, in addition to carefully planned maintenance programs.

2.4 Benefits and Risks of Harder Rail Steel A common concern when increasing rail hardness is increased wheel wear, as the rail becomes the harder component in the wheel rail interface. The effects of varying rail and wheel hardness has been studied previously by Steele and Reiff [6], with recent studies by Lewis et al. [7]. If rail hardness is increased but is less than the hardness of the wheel, rail wear reduces, but wheel wear will increase. As rail hardness surpasses wheel hardness, further increase to the rail hardness will still reduce wear of the rail, but wear of the wheel remains constant. Regardless of whether the rail or wheel is harder, increasing rail hardness alone will reduce overall wear on the system. The specification for the SkyTrain rolling stock wheels is a Brinell Hardness range of 321–363 HB for the rim of the wheel. Qualification tests demonstrate the wheels received are closer to the higher side of the limit. There is not a significant amount of data or regular measurements of tread hardness for “in-service” wheels, but most indications suggest the hardness stays within the specified range. This is harder than the softest existing rail steel, and comparable to the rail hardness on the newest (2016) extension to the system, in the range of 330–355 HB. This extension is serviced exclusively by a particular rolling stock type. After over five years of

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operation on harder rails than the rest of the fleet, there are no signs of increased wheel wear on these trains. Other concerns raised about harder rail steel were weldability, more persistent residual grinding induced roughness, rolling contact fatigue and crack development, and cold weather performance. Examination of these issues did not identify any risks to increasing rail hardness. Some areas of high strength rail have been in use on SkyTrain since 2009 without observed negative effects.

3 Acoustic Rail Grinding SkyTrain completes about 130 km of maintenance grinding annually to improve rail surface condition and correct the rail profile following wear. Even if there are no visible defects or rail profile corrections required, regular grinding of all rails is a necessary maintenance activity required to avoid rolling contact fatigue. If track is corrugated, rail grinding also reduces roughness, corrugation and noise. Some areas of the network require grinding as frequently as four times a year, others only once every two years. The residual grinding surface finish (periodic scratches on rail) can possibly initiate corrugation formation and can increase noise directly if the track was not corrugated before grinding. Figure 1 shows examples of grinding surface finish illustrating the rougher, more scratched finish left by coarser grinding stones. The objective of acoustic grinding is to improve the surface finish after grinding, with the goal of reducing corrugation growth and limiting noise caused by the residual post-grinding surface finish. Achieving an improved surface finish after grinding is particularly important with harder rail steels, since with harder rail the residual grinding marks do not wear away for some time (months).

3.1 Methodology Acoustic rail grinding was trialed at eight different test sites with six of the eight sites split into adjacent standard and acoustic grinding zones. The selected sites included

Fig. 1 Post-grinding surface finish, coarse stones (left) and fine stones (right)

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different rail grades and areas prone to corrugation development. After either standard or acoustic grinding, all sites were monitored by repeated measurements of rail roughness using a Corrugation Analysis Trolley (CAT) over a period of approximately nine months. Rail roughness was used as a proxy for noise, expressed as overall (broadband) root mean square (RMS) amplitude averaged over both rails. Rail roughness and noise are directly correlated, and this parameter is dominated by corrugation growth at wavelengths in the key range of interest for rolling noise.

3.2 Results Example results are presented in Fig. 2 showing the change in roughness with increasing rail traffic after grinding at the softest and hardest rail steel sites. To enable direct comparison between sites, the results show traffic volumes accumulated over time expressed as Million Gross Tonnes (MGT). Results from other sites are omitted for clarity but can be found in [5]. Softer rail steel (260 HB) was prone to more rapid increases in corrugation and roughness with accumulated tonnage, regardless of the grinding approach. The steepest lines in Fig. 2 indicate rapid roughness growth on soft rail after acoustic grinding, and less roughness growth after standard grinding. Harder rail steel (380 HB example shown) was less prone to increase in corrugation and rail roughness over time than softer rail. Areas with harder rail steel saw relatively minimal roughness growth after acoustic grinding, relative to standard grinding.

Fig. 2 Rail roughness growth with increasing traffic after acoustic and standard grinding at two soft (260 HB) and one hard (380 HB) rail sites

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The acoustic grinding pilot study identified that acoustic grinding is not beneficial in areas with softer rail steels, since these areas see rapid roughness growth regardless of the grinding technique. Acoustic grinding was found to be beneficial in areas with the hardest rail steel. For medium hardness rail a combination grinding approach was recommended, depending on the initial rail condition and noise sensitivity of the area.

4 Top of Rail Friction Modifiers A proof-of-concept pilot study was undertaken to investigate the potential for friction modifiers to improve rail condition, reduce roughness and corrugation growth rates and hence to reduce noise on the SkyTrain system. Despite SkyTrain’s previous experience of TORFM, no controlled studies had been done on the system to quantify the rolling noise benefits of friction management. Previous studies [8–10] of TORFM have addressed the effect on rail roughness in curves, but there is no prior data on roughness effects in tangent track. In addition previous studies have not directly addressed the effect of TORFM on roughness generated wheel rail noise.

4.1 Methodology The TORFM pilot study involved an initial “dry rail” data collection over 8 months to establish the rate of noise increase and roughness growth immediately following maintenance rail grinding, without TORFM. Identical locations were then used to repeat all measurements immediately following another maintenance grind but with TORFM applied via a wayside applicator. Comparability of initial roughness following grinding was verified by CAT measurements. The TORFM measurements commenced as close as possible to the same time of year of the “dry” measurements, to minimise climate effects on the results. Noise, rail roughness and rail friction were measured periodically on a curve and on a tangent track section. The applicator was immediately before the curve, with the tangent measurement point 250 m downstream. Noise data was collected for at least 15 train passbys in each set, at elevated track height, 8 m from the guideway in the tangent and 13 m from the guideway in the curve.

4.2 Results Figure 3 shows the effect of TORFM on wayside noise expressed as the increase in passby LAFmax over time as roughness grows. In both cases the first measurement

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Fig. 3 Effect of TORFM on wayside LAmax noise levels over time—curve and tangent sites

was within two weeks of rail grinding. Two months later, passby noise levels in the baseline dry rail case increased by 5 dB or more at both sites. With TORFM the rate of noise increase halved at the tangent site—a 5 dB noise increase occurred over approximately 4 months. At the curved site, with TORFM the increase in noise over 6 months was only 2 dB. Although passby noise levels did increase gradually with TORFM applied at the tangent site, it is evident that TORFM reduced the rate of roughness and noise growth compared to the dry rail scenario, particularly in the first few months after grinding. At the curved site, perhaps due to the close proximity to the TORFM applicator, noise levels with TORFM applied appeared to stabilise around 2 dB above the initial post-grind noise level. This is a very small increase in the context of an area where 6–10 dBA noise increases were observed in a few months of the baseline dry rail tests. Figure 4 shows an example of the rail roughness data collected in support of the study. This figure shows the change in roughness along a single line in the running band of one rail at the tangent track test site over time. The lowest roughness levels (typically the lightest roughness line) were measured soon after rail grinding, with roughness steadily increasing over time. On this rail, roughness (corrugation) in the 50 mm wavelength band grew by over 15 dB in approximately 6 months in the dry rail scenario. Growth was observed in the 31.5 mm wavelength band, although this had a higher initial level (this initial peak is residual grinding induced roughness). With TORFM added, the growth in the 50 mm wavelength band was reduced to around 5 dB in the corresponding time period.

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Fig. 4 Example effect of TORFM on rail roughness over time with a dry rail and b TORFM. Tangent track, left rail. Light to dark lines reflect increasing time after grinding. Dotted line is ISO 3095:2013 reference spectrum

5 Conclusion The study has demonstrated that reducing the cyclic variation in rolling noise emissions is feasible by improving management of conditions in the wheel-rail interface. The objective for SkyTrain is to optimise maintenance practices to always keep train passby noise emissions within 5 dB of the best case (minimum) noise. This would represent a significant improvement in amenity for neighbouring residents.

References 1. SLR Consulting (Canada) Ltd (2018) SkyTrain Noise Study Vancouver Noise Report and Maps. https://www.translink.ca/-/media/translink/documents/plans-and-projects/skytrainnoise-study/skytrain-noise-report-20181128.pdf 2. Croft BE, Miller A, Kupper A (2021) Maintenance effects on rolling noise—metro and light rail. In: Proceedings of Acoustics. Wollongong, NSW, Australia 3. Kalousek J, Johnson KL (1992) An investigation of short pitch wheel and rail corrugations on the Vancouver mass transit system. Proc Inst Mech Eng Part F: J Rail Rapid Transit 206:127–135 4. Tuzik R (2022) SkyTrain: moving from reactive to preventive rail maintenance toward a state of good repair. Mass Transit Mag 5. SLR Consulting (Canada) Ltd (2021) SkyTrain Noise Mitigation Study Phase 2 Recommendation Report and Implementation Plan. https://www.translink.ca/-/media/translink/documents/ plans-and-projects/skytrain-noise-study/skytrain-noise-study-phase-two-technical-report.pdf 6. Steele R, Reiff R (1982) Rail—it’s behaviour and relationship to total system wear. In: Proceedings of the 2nd heavy haul conference, Colorado, Springs, USA 7. Lewis R, Christoforou P, Wang WJ, Beagles A, Burstow M, Lewis SR (2019) Investigation of the influence of rail hardness on the wear of rail and wheel materials under dry conditions (ICRI wear mapping project). Wear 430–431:383–392 8. Eadie DT, Santoro M, Oldknow K, Oka Y (2008) Field studies of the effect of friction modifiers on short pitch corrugation generation in curves. Wear 265(9):1212–1221

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9. Eadie DT, Santoro M (2004) Top-of-rail friction control for curve noise mitigation and corrugation rate reduction. J Sound Vib 293(3) 10. Eadie DT, Kalousek J, Chiddick KS (2002) The role of high positive friction (HPF) modifier in the control of short pitch corrugations and related phenomena. Wear 253(1–2):185–192

Research and Analysis on Disc Brake Noise of High Speed Trains Wensheng Xue, Chaogang Yu, Wenliang Zhu, and Peiwen Chen

Abstract Based on the self-excited vibration theory of mode coupling, the disc brake of trains is analyzed and studied as a whole, and a simplified model of brake disc and brake pad is established. By using ABAQUS complex eigenvalue analysis method, the relationship between system friction coefficient, braking speed, pressure, elastic modulus and contact rigidity is comprehensively considered and the friction noise of disc brake system is predicted by finite element method. The simulation results show that brake scream is more likely to occur at high friction coefficient, low speed and high pressure. Changing the elastic modulus and contact stiffness of brake disc will also affect the generation of brake scream, but there is no specific law, which depends on the coupling of system modes. It can be seen that the theoretical simulation of self-excited vibration based on mode coupling can be used to carry out cooperative analysis and study considering the matching of parameters. This idea provides a design direction for reducing braking noise. Keywords Modal coupling · Disc brakes · Complex eigenvalue simulation analysis · Brake scream

1 Introduction Over the past decade, China’s high-speed railway has achieved leapfrog development. At present, the built high-speed railway has a mileage of about 40,000 km, accounting for about 70% of the world. It plays an important role in the development of China and the world economy. Nowadays, with the gradual improvement of people’s living standards, noise pollution of high-speed trains has become the focus of attention. Disc braking is one of the most important braking modes for high-speed trains at present. The disc braking system is prone to generate braking friction noise when W. Xue · C. Yu · W. Zhu (B) · P. Chen School of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_31

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working, and the sound pressure sometimes reaches 100–120 dB. In disc braking, vibration and noise caused by friction is a subject with depth and difficulty in the field of mechanics. The hotspot of research has not been reduced for many years. In foreign, Aronov has tested that several structural vibration modes occur simultaneously when braking noise occurs [1]. Hoffmann et al. put forward a model of single mass and two degrees of freedom to explain the principle of mode coupling and system instability caused by friction. Liles GD introduces the friction coupling between brake disc and brake block of disc brake as an asymmetric term into the stiffness matrix of system equation, and characterizes the divergence of system vibration by its complex characteristic root with positive real part [2]. Triches Junior M. et al. discussed the influence of changing the properties of brake material and applying muffler on brake noise by analyzing the complex eigenvalues of the brake finite element model [3]. In recent years, theoretical analysis of brake noise has also made great progress and achieved good results in China. Zhang et al. found that changes in elastic modulus do not alter the free and constrained mode shapes [4]. But the square of the modal frequency is positively proportional to the elastic modulus. Qiao et al. obtained the characteristic frequencies of disc brake of trains are 256.78, 3904.07 and 4320.38 Hz by establishing the finite element model of disc brake [5]. Wen et al. studied the stability of brake system by full model direct complex eigenvalue analysis method [6]. Based on the simplified model of high-speed brake disc, Zhang et al. obtained by complex eigenvalue simulation analysis that brake scream is more likely to occur at low speed, high pressure, negative slope of friction coefficient velocity curve and high friction factor [7]. These research results provide ideas for optimizing brake system [8]. In this paper, the mechanism of brake scream caused by modal coupling selfexcitation vibration of train brake system is studied by finite element simulation with ABAQUS. The influence of various parameters (friction coefficient, braking speed, pressure, brake disc elastic modulus and contact rigidity, etc.) on disc braking noise is quantitatively analyzed [9, 10]. This can provide a design direction for reducing braking noise.

2 Train Disc Brake Prediction Model 2.1 Motion Equation Analysis of Friction System This paper applies the prediction friction noise method which is commonly used internationally—complex eigenvalue analysis. The ABAQUS simulation was set to use the Lanczos eigenvalue solver [11–15]. The resulting data were subjected to frictional noise analysis. Consider the friction between the brake pan and the friction plate when the system is braked. The kinetic equations of the system are as follows:

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[M]{u'' } + [C]{u' } + [K]{u} = {Ff }

339

(1)

where M, C and K are the mass matrix, damping matrix and stiffness matrix of the system respectively, and u is the displacement vector of the degree of freedom of the system. Ff is the contact friction between the brake disc and the friction plate. It is expressed as the relative displacement of the nodes between the contact surfaces. {Ff } = [Kf ]{u}

(2)

The matrix that links friction to joint displacement is called friction stiffness matrix, or simply friction matrix. By combining Eqs. (1) and (2), the frictional force in Eq. (1) is moved from the right to the left and can be written in the form of second-order homogeneous linear differential equation as follows: { } { } [M] u'' + [C] u' + [K − Kf ]{u} = {0}

(3)

As shown in Eq. (3), the stiffness coupling of the system caused by friction, the stiffness matrix of the system is asymmetric, and the characteristic matrix is asymmetric. Some of the eigenvalues solved are complex number, i.e., the modal frequencies and modes of the system are complex number, as follows: u = {ϕ}est

(4)

Differentiate it and bring it into Eq. (3) to obtain the following equation: ( ) [M]s2 + [C]s + [K − Kf ] {ϕ} = {0}

(5)

where ϕ and s are the characteristic vector and the characteristic value respectively. Unlike the symmetric mass matrix and stiffness matrix caused by inertial and elastic forces in the system, the friction matrix K caused by friction force is asymmetric. It will cause the stiffness matrix of the system to be asymmetric. λi = βi + iωi

(6)

where β and ω are the real part of its eigenvalue which represents the damping coefficient of the system and the imaginary part which represents the damping natural frequency of the system respectively. When the real part of complex eigenvalue is positive, the system vibration will be enlarged and developed into strong self-excited vibration. And the larger the real part, the more unstable the system and the greater the braking noise. Therefore, the complex eigenvalue data obtained by ABAQUS simulation is analyzed. By comparing the impact of changes in various parameters on disc brake noise, research and analysis were conducted.

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2.2 Finite Element Model of Friction Noise of Train Brake System According to the actual train disc brake structure (Fig. 1), the modal analysis of finite element simulation model is established by ABAQUS. Generally, lumped mass model and finite element model are used to predict brake friction noise. The former can only be analyzed qualitatively, which is difficult to get the quantitative frequency and vibration mode of friction noise. The latter can predict the frequency and vibration mode of friction noise quantitatively. Therefore, the finite element prediction model of full-size disc brake system is chosen to built. Figure 2 is a three-dimensional model of each component and assembly of the disc brake established in Proe software. Then, the finite element prediction model of the disc brake system processed by ABAQUS. In this model, actual data of brake discs and friction plates are used. The Fig. 1 Physical diagram of disc brake on train

Fig. 2 Finite element analysis model for disc brake of train

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connection between the brake pad and brake disc friction material is simulated using Surf-to-Surf Contact.

3 Finite Element Complex Eigenvalue Analysis of Brake System The brake discs and friction plates used in this study are defined as isotropic. The corresponding material parameters are shown in Table 1. Based on the above finite element model and component material parameters, the braking noise of the braking system is analyzed using the single factor Control variates and the two factor Control variates.

3.1 Effect of Friction Coefficient and Brake Speed on Brake Scream Figure 3a shows the effect of different friction coefficients on the positive real part of a complex eigenvalue. Due to the free choice of brake disc and friction plate materials for disc brakes, we choose μ = 0.2, μ = 0.3, μ = 0.4, μ = 0.5, μ = 0.6 (generally, the friction coefficient is not greater than 1). During the analysis process, under the conditions of maintaining a stable braking pressure (P = 3 MPa), a constant sliding speed (20 rad/s), and a contact stiffness of 15,000 N/mm, the system changes the friction coefficient from μ = 0.2 to 0.6. Figure 3b shows the effect of various sliding speeds on the positive real part of complex eigenvalues. During the analysis process, the system maintains a stable braking pressure (P = 0.5 MPa), a constant friction coefficient (μ = 0.4) and contact stiffness 15,000 N/mm. We change the sliding speed to increase it from 20 to 200 rad/ s (using a standard motor car wheel diameter of 920 mm, the corresponding driving speed is increased from 33.2 to 332 km/h). By analyzing the simulation results in Fig. 3a, we can obtain that the positive real value of the eigenvalues increases significantly with the increase of the friction coefficient. This means that a larger coefficient of friction increases system instability, which in turn makes it easier for the brake system to scream. The higher positive real part values near 2000 and 5700 Hz indicate that brake screaming may most likely Table 1 Materials parameters of brake disc and pad

Parameters part

Brake disc

Brake pads

Elastic modulus (MPa)

140,000

250,000

Poisson’s ration

0.23

0.25

Density (g/cm3 )

7.0

6.5

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(a) friction coefficient

(b) brake speed

Fig. 3 Effect of friction coefficient and brake speed on positive real part of complex eigenvalue

occur at these two frequencies. The friction coefficient has the most significant impact on the positive real part value near 2000 Hz. It can be seen from Fig. 3b that the real part of the eigenvalues decreases as the rotational speed increases. This indicates that low rotational speeds exacerbate the tendency for brake screaming, making the system more unstable, while high rotational speeds are relatively stable. The positive real part value is the largest (i.e. brake scream is most likely to occur) near 2000 Hz. The relative sliding speed around this frequency may have the most significant impact on brake screaming.

3.2 Effect of Brake Pressure on Brake Scream Figure 4a shows the effect of brake pressure on the positive real part of the complex eigenvalue. We choose brake pressure of 0.5 MPa, 1 MPa, 2 MPa, 3 MPa and 5 MPa respectively. During the simulation analysis, the sliding speed (20 rad/s), the constant friction coefficient (μ = 0.6) and contact stiffness (15,000 N/mm) are maintained, while changing brake pressure from 0.5 to 5 MPa. Figure 4b shows the effect of different contact stiffnesses on the positive real part of the complex eigenvalue. During the simulation analysis, we change the contact stiffness of the system from 2000 to 15,000 N/mm gradually, while the brake pressure (P = 3 MPa), sliding speed (20 rad/s) and constant coefficient of friction (μ = 0.6) are maintained. By analyzing the simulation results in Fig. 4a, we can obtain that the positive real part values of all complex eigenvalues increase with increasing braking pressure. This means that higher brake pressure makes the brake system unstable and thus more prone to brake screaming or higher brake noise. The maximum positive real part value is around 2000 Hz, which indicates that brake scream is most likely to occur at this frequency. At the same time, the change of positive real part value is

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(a) brake pressure

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(b) contact stiffness

Fig. 4 Effect of brake pressure and disc modulus on real part of complex eigenvalue

most obvious around 2500 Hz. It shows that brake pressure has the most obvious effect on brake scream near this frequency. It can be seen from Fig. 4b that there is no uniform rule for the influence of contact stiffness on the real part of the eigenvalue. The general trend is that in low frequency areas, the smaller the contact stiffness, the more unstable the system and the more likely it is to experience brake screaming. In high frequency areas, the greater the contact stiffness, the more unstable the system and the more likely it is to scream. It can be observed that the contact stiffness near 2000 Hz and 5700 kHz has a significant influence on the positive real part of the eigenvalue. Therefore, the contact stiffness near these two frequencies has the greatest effect on brake scream.

3.3 Effect of Brake Scream on Changes in Elastic Modulus and Contact Stiffness We select the two sets of data for analyzing the maximum and minimum elastic modulus and contact stiffness. The first group: elastic modulus 168,000 MPa, contact stiffness 15,000 N/mm; Group 2: Elastic modulus: 112,000 MPa, contact stiffness: 2000 N/mm. Simulation analysis results in Table 2. The analysis table shows that the first group is more stable than the second. The first group not only had a lower brake scream, but also had a lower likelihood. The different combinations might trigger different situations.

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The first group

The second group

Frequency

Real part

Frequency

1120.13

16.6141

1153.86

1364.22

3.08652

Real part 2.81221

1558.36

83.1974

1392.88

15.6087

1774.73

33.5721

1658.13

11.4071

2851.93

10.2718

1998.68

2.30816

4298.83

2238.12

3.34708

5232

19.458

5944.93

72.3105

2259.45

11.0631

4.36712

4 Discussion and Analysis From the five previous simulation results, it can be seen that the influence of friction coefficient, braking speed and pressure on braking noise has certain regularity. Brake screaming is more likely happen at high friction, low speed and high pressure. In addition, the brake system is most prone to generate brake scream at 2000 Hz and mode coupling near 2000 Hz. Therefore, when selecting materials during the design process, the difference between this mode frequency and other component frequencies should be maximized to avoid mode coupling as much as possible. The sixth group of simulation results change the two parameters of elastic modulus and contact stiffness. When the single-control contact stiffness is 15,000 N/mm, the brake system is at 1700 Hz as shown in Fig. 4, and the corresponding real complex eigenvalue value is close to 50. When the dual-control contact stiffness is 15,000 N/mm, the brake system is shown in Table 2 and the corresponding real value of complex eigenvalue is 33.57. The larger the real part is, the more likely it is to induce brake scream. It can be seen that the matching of each parameter can be studied by means of theoretical simulation of self-excited vibration based on mode coupling. This provides a design direction for reducing braking noise.

5 Conclusion and Prospect This paper draws a conclusion through ABAQUS simulation analysis: (1) Brake screaming is most likely to occur at low speed, high pressure, and high friction factor. (2) The possibility of brake screaming is related to the mode coupling self-excited vibration mechanism of the braking system composed of brake discs and friction plates. By changing its own characteristic parameters, the possibility of inducing brake scream is different. Moreover, the occurrence of brake screaming has a certain randomness.

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(3) In future research, the better group can be selected through analysis and comparison with different system parameters. Similarly, in the research and design of structures, various factors are comprehensively considered to control their modal coupling self-excited vibration mechanism to achieve an ideal state. Acknowledgements This research was funded by Natural Science Foundation of China (Grant Nos. 52072266 and U1534205).

References 1. Aronov V, Kalpakjian S, D’Souza AF, Shareef I (1984) Interactions among friction, wear, and system stiffness—Part 2: Vibrations induced by dry friction. J Tribol 106(1):59–64 2. Liles GD (1989) Analysis of disc brake squeal using finite element methods. Training 10–30 3. Trichês Júnior M, Gerges SNY, Jordan R (2008) Analysis of brake squeal noise using the finite element method: a parametric study. Appl Acoust 69(2):147–162 4. Zhang LJ, Tang CJ, Pang M, Meng DJ (2013) Simulation analysis of the effect of brake disc elastic modulus on brake squeal. J Autom Eng 3(05):313–323 (in Chinese) 5. Qiao QF, Yang WD, Zhu Q, Chen GX (2021) Mechanism and control method of railway disc brake noise. J Southw Jiaotong Univ 56(01):62–67 (in Chinese) 6. Wu W, Chen GX, Dai HY, Zeng J (2007) Finite element complex eigenvalue analysis of disc brake noise of railway vehicles. Southw Jiaotong Univ (in Chinese) 7. Zhang EY, Wang SW, Sun YD, Wei J (2018) Simulation and experimental study of the main influencing factors of high-speed braking acoustic noise. Mech Strength 40(04):923–929 (in Chinese) 8. Zhou ZQ, Wang DS, Gao SY, Liu B (2017) Research progress on the mechanism and control method of brake friction noise generation. Noise Vib Control 37(05):1–5 (in Chinese) 9. Lorang X, Foy-Margiocchi F, Nguyen QS, Gautier PE (2006) TGV disc brake squeal. J Sound Vib 293:735–746 10. Butlin T, Woodhouse J (2011) A systematic experimental study of squeal initiation. J Sound Vib 330:5077–5095 11. Zhan B, Sun T, Shen YW, Yu JH (2021) Improvement of the braking squeal problem of a disc brake based on complex characteristic value analysis. Vib Shock 40(05):108–112+135. (in Chinese) 12. Liu P, Zheng H, Cai C, Wang YY (2007) Analysis of disc brake squeal using the complex eigenvalue method. Appl Acoust 68:603–615 13. Brunetti J, Massi F, D’Ambrogio W, Berthier Y (2016) A new instability index for unstable mode selection in squeal prediction by complex eigenvalue analysis. J Sound Vib 377:106–122 14. Li JX, Mo JL, Wang DW, Zhu ZY (2017) The effect of braking force on brake squealing noise and wear characteristics. Lubr Seal 42(03):49–53 (in Chinese) 15. Zhong YQ, Yang J (2018) Disc brake noise analysis. Mech Eng Autom 03:155–157

The Effect of Wheel Rotation on the Rolling Noise Predictions Christopher Knuth, Giacomo Squicciarini, and David Thompson

Abstract The effect of the wheel rotation on its sound radiation in rolling noise predictions is investigated. The wheel response is modelled using a finite element model that can account for the different effects introduced by rotation and together with TWINS the radiated sound power is determined. Noise and vibration data are compared over a range of typical train speeds, between a stationary wheel, a rotating wheel where rotation is replaced by a moving load, and a rotating wheel that also includes the inertial forces. Compared with the most complete model, differences in the wheel sound power level of up to 6 dB in one-third octave bands are found if the stationary wheel is used instead. The differences remain below 2 dB for speeds up to 500 km/h if the rotation is approximated with a moving load. In terms of the total A-weighted sound power level of the wheel, the stationary wheel underestimates the noise by up to 3 dB, while the differences are less than 1 dB for a moving load. Generally, the differences introduced by the approximate representations of the wheel rotation are smaller than the uncertainties that are inevitable in rolling noise predictions. The results show that in rolling noise predictions for usual train speeds the wheel rotation is sufficiently well approximated by a moving load, which is the method implemented in TWINS. Keywords Rolling noise · Wheel rotation · Moving load · Sound radiation

1 Introduction Rolling noise is one of the most important sources of noise in railways and is caused by the excitation of the wheel and the track from their combined surface roughness [1]. One of the most commonly used rolling noise prediction models is TWINS [2, C. Knuth (B) · G. Squicciarini · D. Thompson Institute of Sound and Vibration Research, University of Southampton, Southampton SO17 1BJ, UK e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_32

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3], which requires models of the wheel and track vibration, their noise radiation and the roughness as an input. For modelling the wheel vibration, finite element models are commonly used that treat it as a stationary structure, which is an incomplete representation in case of a moving train. The classic approach to account for the wheel rotation that is used in TWINS is to replace the rotation with a moving load, that rotates around the wheel circumference at the same angular velocity [4]. This causes the wheel modes to be split into two co- and counter-rotating waves that, when viewed from the excitation point, are shifted in frequency by ±nΩ/2π , where n is the number of nodal diameters and Ω the angular velocity. However, this approach neglects the gyroscopic and centrifugal effects. In recent years, finite element models that include the inertial forces in the equation of motion of a rotating structure have been developed [5–7]. The kinematics can be defined in a non-rotating (Eulerian) or rotating (Lagrangian) frame of reference. For the interaction of the rolling wheel with the track, the non-rotating frame is preferred. Baeza et al. [5, 6] used Eulerian coordinates to establish an equation of motion of the rotating wheelset directly in a non-rotating reference frame that can be solved with the finite element method. Sheng et al. [7] developed a model in which the kinematics of the rotating wheelset were defined in a rotating frame and converted the response to the non-rotating frame by applying a transformation. This was implemented using axisymmetric finite elements. The moving load is an attractive simplification of the effect of wheel rotation, but according to [7, 8], a fully rotating model should be implemented for correct modelling of rolling noise at high train speeds. In this work, the effect of the wheel rotation on the prediction of the radiated sound power of rolling noise is investigated to quantify the differences caused by the various modelling approximations for a wide range of train speeds.

2 Methodology 2.1 Model of the Rotating Railway Wheel In this study, an axisymmetric finite element model that adopts the Eulerian approach of Baeza et al. [5, 6] has been implemented for modelling the rotating railway wheelset. Additionally, a geometric stiffness matrix can be included, as proposed in [9]. For more information, the reader is referred to the references. The model has been validated against a 3D model of a rotating wheel in the commercial software COMSOL Multiphysics. The equation of motion (EOM) of the rotating structure can be written as ( )) ( Mu¨ + (2ΩG + D)u˙ + K + Ω2 Kg − C u = Ω2 fc + f

(1)

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where M is the mass, D the damping, and K the stiffness matrix of the stationary wheel, u is the displacement vector and f is the force vector. The additional terms are due to the rotation at angular velocity Ω and can be described as follows. The matrix G accounts for the gyroscopic effects due to the inertial Coriolis forces. Matrix C contains terms that alter the stiffness of the structure, such as spin softening due to the inertial centrifugal force. In the non-rotating frame, a frequency shift of ±nΩ/2π is added to the rotating waves by the definition of G and C. The geometric stiffness matrix Kg adds stress-stiffening in the presence of the constant centrifugal force f c . Although f c is included on the right-hand side, it does not contribute to harmonic vibration at an angular frequency ω and is only non-zero for n = 0 nodal diameters. In the axisymmetric model, the displacements are written as a Fourier series of spatial harmonics n in the circumferential direction θ as u(r, z, θ ) =

∞ ∑

un (r, z)einθ ,

(2)

n=−∞

which allows the EOM to be solved for each harmonic separately. The solutions consist of co- and counter rotating waves (for n /= 0).

2.2 Modelling the Sound Radiation of the Wheel The wheel model is coupled with TWINS to calculate its radiated sound power. An analytical track model of a UIC60 rail with continuous support is adopted [1]. The vertical pad stiffness is 250 MN/m per rail with a loss factor of 0.2 and the half sleeper is modelled as a rigid mass of 140 kg supported by a ballast stiffness of 200 MN/m with a loss factor of 1.0. These values are converted to equivalent continuous ones using a sleeper spacing of 0.6 m. The wheel-track interaction and the wheel response are obtained in a non-rotating frame. The roughness spectrum is based on the ISO 3095:2013 limit curve [10]. To determine the overall wheel sound power, the spatially averaged wheel velocities for each nodal diameter (combination of the harmonics −n and +n) are combined with the approximate wheel radiation efficiencies from [11]. Mobilities from different wheel models are used to investigate the importance of including the rotation. They correspond to a stationary wheel, and rotating wheels in which the rotation is either replaced by a moving load or fully accounted for by the Eulerian approach.

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3 Results 3.1 Effect of the Rotation on the Wheel Modes and Frequency Response To illustrate the effect of wheel rotation, the frequency response is considered first. For this, a wheel with a straight web and radius of 0.43 m is adopted, see Fig. 1. It is constrained at the hub to replace the axle and the rigid body motion of the full wheelset is added separately. Three different cases are shown: a stationary wheel, a rotating wheel, in which the rotation is replaced by a moving load [4], and the rotating wheel based on the Eulerian approach including the inertial forces. The driving point mobilities are compared in Fig. 1 for a radial force and train speed of 300 km/h, i.e. Ω = 194 rad/s or 31 Hz. When the wheel rotation is included, resonances with n /= 0 split into two peaks with a reduced height compared with the stationary case. With the moving load, the frequency split is exactly ±nΩ/2π for all modes. The split is different for some resonances in the Eulerian model due to the gyroscopic and centrifugal effects, see for example the peaks around 2.1 kHz. The phenomena are explained in more detail below. The impact of the gyroscopic and centrifugal effects on the split of the natural frequencies, if observed in the non-rotating reference frame, is illustrated in Fig. 2 for the nodal diameters n = 1 and n = 2. The gyroscopic effect splits the frequencies of the two modes in proportion to Ω. Thus, the rotating waves can no longer form a standing wave, as in the stationary wheel. Axial modes are well approximated by the moving load with ±nΩ/2π , as they barely generate Coriolis forces. The Coriolis acceleration, determined by the cross product of the angular velocity vector with the ˙ v, ˙ w) ˙ T = 2Ω(−v, ˙ u, ˙ 0)T , is zero for the axial w, ˙ but velocity vector 2(0, 0, Ω)T ×(u, non-zero for the radial u˙ and circumferential v˙ velocity components. The frequency shift of a radial mode can be reduced by up to ±Ω/2π when compared with the moving load if it generates considerable Coriolis forces. Since modes have coupled

Fig. 1 Driving point mobility of the wheel for radial excitation and a velocity of 300 km/h; —, stationary wheel; · · · , rotating wheel (moving load); – – –, rotating wheel (Eulerian model)

The Effect of Wheel Rotation on the Rolling Noise Predictions Fig. 2 Frequency shift of the wheel modes in the non-rotating frame of reference for the nodal diameters a n = 1 b n = 2; —, stationary wheel; —, rotating wheel (moving load); – – –, rotating radial modes (Eulerian model); · · · , rotating axial modes (Eulerian model); – · –, rotating circumferential modes (Eulerian model)

351

(a)

(b)

radial/axial motion, the Coriolis shift is neither zero nor reaches ∓Ω/2π . Consequently, the overall frequency shift is between ±(n − 1)Ω/2π and ±nΩ/2π for radial modes. Circumferential modes are increased in frequency compared with the moving load, due to the different direction of the Coriolis force. Thus, the frequency shift of circumferential modes lies between ±nΩ/2π and ±(n + 1)Ω/2π. For larger n, the same trends can be observed. Additionally, the centrifugal effect shifts both modes equally towards higher (stress-stiffening), or lower (spin softening) frequencies, in proportion to Ω2 . Stressstiffening is larger for axial modes, as it increases the bending stiffness of the web. The centrifugal effects are small compared with the gyroscopic effects at usual train speeds [7].

3.2 Radiated Sound Power of the Rotating Wheel The sound power radiated by the wheel has been calculated for train speeds from 10 to 500 km/h in steps of 10 km/h. The sound power level (SWL) of an example wheel with a straight web is shown in Fig. 3 in one-third octave bands for a roughness input that is based on the ISO 3095 limit curve [10] with suitable contact filter. Spectra are shown for speeds of 80, 160 and 250 km/h, together with 500 km/h (Ω = 323 rad/ s) to see the continuing trend at higher speeds. Results are shown for the stationary

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Fig. 3 Sound power level of the wheel for train speeds of 80, 160, 250 and 500 km/h with ISO 3095 roughness; —, stationary wheel; · · · , rotating wheel (moving load); – – –, rotating wheel (Eulerian model)

wheel, the rotating wheel using the moving load approximation and the Eulerian model without the stress-stiffening term. As expected, the sound power increases with increasing speed. Below 400 Hz, the three models agree well. Above this frequency, there are differences of up to 6 dB between the stationary wheel and the rotating models, especially in the region below 2 kHz, where the wheel has fewer resonances. The differences increase as the train speed increases. Above 2 kHz, the difference reduces to about 3 dB. In most frequency bands the stationary wheel underestimates the noise compared with the two rotating wheel models. The differences between the Eulerian model and the moving load approximation remain much smaller than 1 dB at the lower speeds, but at 500 km/h they can be as high as 2 dB in some bands. The stationary wheel response consists of standing waves, as the rotating waves with harmonics ±n coincide in frequency and combine coherently. Consequently, the wheel response, calculated as the spatially averaged velocity over the wheel circumference, is smaller than the rotating case. In the rotating case the responses of the harmonics +n and −n are calculated separately and added incoherently, as the two waves have their resonance at different frequencies. The total A-weighted SWL of the wheel can be calculated from these spectra and is found to increase with the train speed V by approximately 30 log10 V between 50 and 500 km/h. The differences in these total A-weighted SWL of the wheel relative to those for the Eulerian model are plotted against train speed in Fig. 4. As well as the wheel with a straight web considered above, results are also shown for a wheel with a curved web with a radius of 0.42 m. If the stationary wheel model is used, the total SWL is underestimated by up to 3 dB, compared with the Eulerian model, which agrees with [8]. At very low speeds (< 40 km/h), the difference is around 1–2 dB. Above 100 km/h, the stationary model gives slightly better agreement for the wheel with straight web. If the rotation is approximated with a moving load, the differences remain much smaller than 1 dB for all the train speeds considered. Above 400 km/h the moving load

The Effect of Wheel Rotation on the Rolling Noise Predictions Fig. 4 Difference of total A-weighted wheel sound power level between the Eulerian model and rotation approximations with increasing train speed of a wheel with a straight web and b curved web; —, stationary wheel; · · · , rotating wheel (moving load); – – –, Eulerian without Coriolis force; —, Eulerian without centrifugal force; – · –, Eulerian with stress-stiffening

353

(a)

(b)

shows an increase up to around 0.6 dB for the wheel with the curved web, which is not seen for the wheel with a straight web. Results are also shown for variants of the Eulerian model: one that includes the additional geometric stress-stiffening, which was omitted in the previous results, another without the Coriolis force and a third without the inertial centrifugal force. Adding stress-stiffening or suppressing the centrifugal force changes the total SWL by less than 0.2 dB for the two tested wheels. Excluding the Coriolis force has a similar effect to using the moving load, since the remaining centrifugal terms in the equation of motion are negligible. The results have also been calculated using a measured roughness spectrum, but are not shown here. While the SWL spectra were different from those in Fig. 3, the relative differences in total SWL were found to be very similar to the ones shown in Fig. 4.

3.3 Comparison of the Response in a Non-Rotating and Rotating Frame In TWINS the wheel response, and consequently its sound radiation, is calculated in a rotating frame of reference. The rotating frame was preferred in TWINS to allow

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(b) (a) Fig. 5 Comparison of results obtained in a different frame of reference a velocity at web and contact position for a wheel at 300 km/h and b difference in total A-weighted SWL of the wheel; —, non-rotating frame; – – –, rotating frame

comparisons with measured data from accelerometers fixed to the rotating wheel [4]. In the present work, a non-rotating frame is used, which seems more appropriate for noise calculations. Figure 5a shows the mean square velocity averaged around the circumferential direction for the straight-webbed wheel at a speed of 300 km/h. Results are given for the axial direction at the middle of the web and the radial direction at the contact point. In Fig. 5b the differences in the total A-weighted SWL of the wheel are shown against speed. When calculating the wheel response in a rotating frame with the moving load, the resonance peaks in the response are no longer split [4]. Hence, the one-third octave band results differ from those in the non-rotating frame. The spectral differences in the velocity can be as high as 8 dB, but are generally lower, especially at frequencies above 2 kHz, which are most important for the wheel contribution to the noise. The trends are similar for other speeds and similar relative differences occur in the SWL spectra. The overall A-weighted SWL differs by less than 0.5 dB if the rotating rather than the non-rotating frame is used to calculate the noise radiated from the wheel. The level difference is again smaller than the uncertainty in rolling noise predictions.

4 Conclusions The effect of the rotation of a railway wheel on its sound radiation has been investigated using numerical wheel models that represent the rotation with different levels of approximation combined with the TWINS model. Three wheel models were implemented: (i) a stationary wheel, (ii) a rotating wheel in which the rotation is replaced by a moving load, and (iii) a rotating wheel that also includes the inertial forces and geometric stiffening effects.

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Spectral differences of up to 6 dB are found in the SWL spectra when not fully accounting for the rotation. The overall A-weighted SWL is underestimated by up to 3 dB if the rotation is completely neglected. If the rotation is represented by a moving load the differences in SWL are smaller than 1 dB. The impact of the inertial forces on the overall SWL is marginal and in all cases much less than 1 dB. Hence, the moving load model is a sufficient representation of the rotation at normal train speeds. The impact of the inertial forces cannot be easily generalized, as the additional change of the resonances depends on the speed of the wheel and its geometry. The differences found when approximating the rotation with a moving load are smaller than the uncertainty of rolling noise predictions [3], e.g. due to the variability of measured roughness [12]. If the wheel response is calculated in a rotating, rather than a non-rotating frame of reference, similar differences are found. Altogether, the study has shown that the approximations made in the TWINS model [2–4] have only a marginal effect on the noise predicted from the wheel even at very high speeds.

References 1. Thompson DJ (2009) Railway noise and vibration: mechanisms, modelling and means of control, 1st edn. Elsevier, Amsterdam 2. Thompson DJ, Hemsworth B, Vincent N (1996) Experimental validation of the TWINS prediction program for rolling noise, Part 1: description of the model and method. J Sound Vib 193(1):123–135 3. Thompson DJ, Fodiman P, Mahé H (1996) Experimental validation of the TWINS prediction program for rolling noise, Part 2: results. J Sound Vib 193(1):137–147 4. Thompson DJ (1993) Wheel rail noise generation, Part V: Inclusion of wheel rotation. J Sound Vib 161(3):467–482 5. Baeza L, Giner-Navarro J, Thompson DJ, Monterde J (2019) Eulerian models of the rotating flexible wheelset for high frequency railway dynamics. J Sound Vib 449:300–314 6. Baeza L, Giner-Navarro J, Thompson DJ (2020) Reply to Discussion on ‘Eulerian models of the rotating flexible wheelset for high frequency railway dynamics’ [J. Sound Vib. 449 (2019) 300–314]. J Sound Vib 489:115665 7. Sheng X, Liu YX, Zhou X (2016) The response of a high-speed train wheel to a harmonic wheel-rail force. J Phys: Conf Ser 744:012145 8. Cheng G, He Y, Han J, Sheng X, Thompson DJ (2021) An investigation into the effects of modelling assumptions on sound power radiated from a high-speed train wheelset. J Sound Vib 495:115910 9. Genta G (2005) Dynamics of rotating systems, 1st edn. Springer, New York 10. ISO 3095:2013 Acoustics—Railway applications—Measurement of noise emitted by railbound vehicles 11. Thompson DJ, Jones CJC (2002) Sound radiation from a vibrating railway wheel. J Sound Vib 253(2):401–419 12. Squicciarini G, Toward MGR, Thompson DJ, Jones CJC (2015) Statistical description of wheel roughness. In: Nielsen J et al (eds) Noise and vibration mitigation for rail transportation systems. Notes on numerical fluid mechanics and multidisciplinary design, vol 126. Springer, Berlin, Heidelberg

Improved Methods for the Separation of Track and Wheel Noise Components During a Train Pass-By David Thompson, Dong Zhao, Ester Cierco, Erwin Jansen, and Michael Dittrich

Abstract Experimental techniques are described that aim to allow the wheel and track components of rolling noise to be separated from pass-by measurements. These are based on Advanced Transfer Path Analysis, Pass-by Analysis, and a method based on the TWINS model. Improvements to these methods and their experimental validation using field tests are described. Initial comparisons are made for two test cases, a metro train running at 60 km/h and a regional train running at 80 km/h. The three methods agree reasonably well in terms of overall trends. The largest differences are found at low frequencies where the two experimental methods give similar levels for sleeper and rail vertical components whereas the TWINS model gives a larger distinction between them. Keywords Rolling noise · Source separation · Pass-by tests

1 Introduction Mainline trains in Europe must satisfy noise certification tests defined in the Technical Specification for Interoperability (TSI) Noise [1] and ISO 3095 [2]. The need to carry out the tests on a compliant track (with low roughness and high track decay rate) poses very restrictive limitations on the tracks that can be used, complicating the certification process in terms of time and costs. This requirement could be relaxed or even eliminated if the track and vehicle contributions could be identified separately. D. Thompson (B) · D. Zhao Institute of Sound and Vibration Research, University of Southampton, Southampton SO17 1BJ, UK e-mail: [email protected] E. Cierco Ingeniería para el Control del Ruido SL, Berruguete 52, 08035 Barcelona, Spain E. Jansen · M. Dittrich TNO Acoustics and Sonar, Oude Waalsdorperweg 63, 2597 AK The Hague, The Netherlands © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_33

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In the previous project Roll2Rail, experimental techniques to obtain the contributions of vehicle and track to rolling noise were developed and assessed [3]. The most promising techniques for quantifying the track component were Advanced Transfer Path Analysis (ATPA), Pass-by Analysis (PBA), and a method based on the TWINS model. For the wheel component, however, none of the methods tested (PBA-based methods or beamforming) achieved sufficient accuracy compared with a TWINS-based method. This paper describes improvements to these methods and their experimental validation using field tests. The aim is to separate the track from the wheel contributions, and if possible to separate the track into rail vertical, rail lateral and sleeper components. The frequency range should be extended to cover 100–8000 Hz.

2 Separation Methods 2.1 Method Based on Pass-By Analysis The PBA method [4] uses accelerometers on the rail and a microphone at the trackside to separate the total equivalent roughness excitation from the roughness-to-noise transfer function. Track decay rates are also extracted. This method is enhanced in the current work by the addition of measurements of static vehicle and track transfer functions. For these, reciprocal measurements are preferred. Whereas in the direct method, the track or wheel is excited by an impact hammer and the pressure at the wayside microphone position is measured together with the force (see Fig. 1a), in the reciprocal method a sound source of known volume velocity is placed at the microphone position (see Fig. 1b) and the resulting vibration is measured. Both methods yield a transfer function of the form p/F, where p is pressure at the receiver and F is force. They are then converted to the form p/r , where r is the roughness spectrum and the index i indicates vertical or lateral directions:  p r

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Fig. 1 Experimental set-up. a Impact measurements on the track; b sound sources used for reciprocal measurements

2.2 Advanced Transfer Path Analysis Method The ATPA method [6] is based on extensive transfer function measurements of the track, preferably with the vehicle present; these are combined with operational measurements of noise and track accelerations. The transfer functions take the form of transmissibilities (ratios of acceleration at different points) so there is no need to measure the applied force. A matrix operation allows the ‘direct transfer functions’ D Tk→M to be obtained which express the sound pressure at a receiver point M due to vibration in one ‘sub-system’ k when the response of all other ‘sub-systems’ is blocked [6]. There is no need to lift the wheel from the track. By combining these direct transfer functions with the measured acceleration spectra during the train passage ak , the total noise at location M can be decomposed into the components associated with each sub-system pM =

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2.3 TWINS-Based Method The TWINS model [7] is a series of engineering models for rolling noise that has been validated against extensive field experiments. It can be used to identify the separate wheel and track components. Moreover, as the parts of the model used to calculate the noise radiation are considered to be more reliable than the vibration prediction [8], the uncertainty in the estimates can be reduced by combining the model with vibration measurements obtained during a train pass-by. In the present work, updated models of the track radiation have also been introduced [9] and the effect of the vehicle on the sound radiation from the rail is included using boundary element models [5, 10]. To apply TWINS to source separation involves the following steps [3]: (1) The input parameters for the track are chosen to give the best possible fit to static measurements of track mobility and decay rate; the natural frequencies and damping of the wheels are measured and used to ensure good agreement with a finite element model of the wheel. The wheel and rail roughness spectra are also measured directly. Measured decay rates are used in the predictions. (2) The predicted rail and sleeper vibration is compared with measurements during train passages and the predicted noise from each component is adjusted in accordance with the difference between them. It is important that none of these adjustments is too large, i.e. that the TWINS model gives as good an agreement as possible with the measurements of vibration and noise before applying any adjustments. This requires experience and engineering judgement. As both test sites (see below) were fitted with stiff rail pads it was found to be necessary to use a discretely supported track model in the TWINS calculations. The average over five contact positions within half a sleeper span is used to estimate the noise during the train passage.

3 Field Tests Field measurements are used to verify and compare the methods. Selected results are presented here from two campaigns. The first is on a metro train running at 60 km/h on a metre gauge line in Northern Spain. The second is on a regional train running at 80 km/h at a test site at Velim in the Czech Republic; this site was fitted with rail dampers, visible in Fig. 1. In both cases the measurements focus on unpowered bogies for which the noise was dominated by rolling noise. Results are determined as the average over the passage of two half-vehicles with the test bogies at the centre. Rail roughness and track decay rates were measured at each test site using standard direct methods. Wheel roughness of the test bogies was also measured and modal identification of the wheels was carried out to verify the finite element modelling used in TWINS. Rail and sleeper accelerations and pass-by noise were measured during train passages. The various transfer functions described above were obtained, both

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with and without the train present. Wheel and track transfer functions were obtained with the wheels resting on the track as it was not permitted to jack the vehicle up on site. This had an adverse effect on the PBA wheel estimates.

4 Results The results are presented in the form of the components of noise from the track and wheel vibration relative to the total noise. In most cases the microphone position was at 7.5 m from the track centre and 1.2 m above the rail head. However, for the ATPA method the estimates are based on measurements at 3.5 m from the track and 0.5 m above the rail head as the transfer functions at 7.5 m were affected by background noise especially at low frequency.

4.1 Site 1: Metro Train at 60 km/h At the first test site, the transfer function measurements required for PBA separation were not carried out, so results are only shown here for ATPA and TWINS. Moreover, the instrumentation used for ATPA only allowed a maximum frequency of 5000 Hz at this site. Figure 2 shows the contributions of each component (rail vertical, lateral, sleeper and wheel) relative to the overall noise spectrum obtained from these two methods. As typically found [7, 8], the TWINS results indicate that the noise is dominated by the sleepers at low frequencies, the rail in the mid-frequency region and the wheel at high frequencies. Due to the stiff rail pads, the vertical track decay rate is high and consequently the contribution from the vertical vibration is small below 1000 Hz; the lateral contribution is larger for frequencies up to 1600 Hz. The stiff pads also

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mean that the sleeper is strongly coupled to the rail over a wide frequency range and, due to its larger area, it radiates significant noise up to 1600 Hz. The ATPA results show similar trends, especially for the lateral rail contribution. The wheel contribution is estimated by ‘subtraction’ (the difference between the measured total and the sum of the reconstructed components) which is known to be a less reliable method; nevertheless, it agrees reasonably well with the TWINS estimate. Results below -10 dB have been capped at this level. The main difference compared with TWINS is seen at low frequencies, where the sleeper contribution is up to 10 dB smaller than the TWINS estimate and the rail vertical contribution is 15–20 dB larger than that from TWINS. These two components are strongly coupled together by the stiff rail pads and it appears that the experimental method cannot easily separate them with the current test setup. At high frequencies both rail components are larger than the results from TWINS. The larger contribution from the rail was also found in [3] and is believed to be due to the neglect of rail cross-sectional deformation in the TWINS model. The estimates of the total noise contributions radiated by the track and wheel are compared in Fig. 3. Generally good agreement is seen between the two methods.

4.2 Site 2: Regional Train at 80 km/h For test site 2, Fig. 4 shows the contributions of each component relative to the overall noise spectrum. The overall trends from the TWINS model in Fig. 4a are similar to those in Fig. 2a for the first site. This site again has stiff rail pads and additionally is fitted with rail dampers. The sleeper noise is dominant up to 250 Hz and remains important up to 2 kHz. Of the rail components, the lateral direction is more important up to 1250 Hz and the vertical direction for 1600–2500 Hz. The wheel is mainly important above 2 kHz.

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The PBA method gives similar trends except that the sleeper component is lower at low frequency and the rail vertical component is higher at both low and high frequencies. As for site 1 these trends are also found with the ATPA method. The wheel noise estimate from ATPA is not shown below 250 Hz as the transfer function measurements were less reliable at these frequencies due to low signal to noise ratio. The total noise spectra for the track are compared in Fig. 5a and for the wheel in Fig. 5b. These show generally good agreement apart from below 250 Hz, where the wheel contribution predicted by TWINS is much lower than PBA (possibly because the wheel could not be lifted). Above 4 kHz the ATPA method gives a much higher track noise estimate and hence a lower wheel noise estimate than the other methods. The contributions of each source to the overall A-weighted sound level are shown in Fig. 6. The two methods used at site 1, TWINS and ATPA, agree well apart from the higher rail vertical and lower sleeper found by ATPA. This trend is found again for site 2 but with larger differences. PBA and TWINS results mostly agree quite well.

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5 Discussion and Conclusions Three methods for separating components of rolling noise during train pass-bys have been compared. ATPA is a purely experimental method, the TWINS-based method is based on theoretical models and the PBA-method, although experimental, relies on the TWINS framework to some extent. The three methods agree reasonably well in terms of overall trends. The largest differences are found at low frequencies where the two experimental methods give similar levels for sleeper and rail vertical components whereas the TWINS model gives a larger distinction between them. Further development and analysis are continuing to understand reasons for differences. Various possible simplifications will be considered, e.g. in the numbers of measurement transducers and static measurements required for the ATPA method. Acknowledgements This work has been supported by the TRANSIT project (funded by EU Horizon 2020 and the Europe’s Rail Joint Undertaking under grant agreement 881771). The contents

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of this paper only reflect the authors’ views; the JU is not responsible for any use that may be made of the information contained in the paper. The field tests have been carried out in collaboration with the FINE-2 project which provided the trains and track access.

References 1. Commission Regulation (EU) No 1304/2014 of 26 November 2014 on the technical specification for interoperability relating to the subsystem ‘rolling stock—noise’ 2. EN ISO 3095: 2013 Acoustics—railway applications—measurement of noise emitted by railbound vehicles 3. Thompson D et al (2018) Assessment of measurement-based methods for separating wheel and track contributions to railway rolling noise. Appl Acoust 140:48–62 4. Janssens MHA et al (2006) Railway noise measurement method for pass-by noise, total effective roughness, transfer functions and track spatial decay. J Sound Vib 293:1007–1028 5. Thompson D, Dittrich M, Jansen H, Zhao D, Cierco E (2022) Track and vehicle separation and transposition techniques including theoretical description and proposal for full scale validation test campaign. TRANSIT Deliverable D3.2, January 2022 6. Magrans FX (1981) Method of measuring transmission paths. J Sound Vib 74:321–330 7. Thompson DJ, Hemsworth B, Vincent N (1996) Experimental validation of the TWINS prediction program for rolling noise, part 1: description of the model and method. J Sound Vib 193:123–135 8. Thompson DJ, Fodiman P, Mahé H (1996) Experimental validation of the TWINS prediction program for rolling noise, part 2: results. J Sound Vib 193:137–147 9. Zhang X, Thompson D, Quaranta E, Squicciarini G (2019) An engineering model for the prediction of the sound radiation from a railway track. J Sound Vib 461:114921 10. Zhao D, Thompson D, Ntotsios E, Cierco E, Jansen H (2024) The influence of the vehicle body on the sound radiation from the rail. In: X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, p 8

Experimental Study on Modal Damping Ratios of a Ring Damped Wheel Mounted with Different Damper Types and Preloads Shuoqiao Zhong, Xin Zhou, Kun Wu, and Xiaozhen Sheng

Abstract Ring damped wheels have been widely applied on metro vehicles. However, mechanisms by which vibration and sound radiation are reduced with the ring damper have not been fully understood. The optimization of damper is much concerned in academic and industrial fields. This study conducts a series of tests in lab to study the influence of preload and the damper types, on the effect of vibration reduction. The preload is changed by inserting plug-pages between the two ends of the ring, and the damper types include ring, ring attached with rubber layer, and ring attached with rubber layer and additional mass. Through analyzing the vibration characteristics, it is found that the damping ratios of the axial and radial wheel modes change to different degree, making some difference in the overall vibration level. Keywords Ring-damped wheels · Experimental study · Damper type · Preload

1 Introduction Ring damped wheels have been widely applied on metro vehicles. However, mechanisms by which vibration and sound radiation are reduced with the ring damper have not been fully understood, although experiments and modelling simulation have been performed to study the influence of key parameters on the ability of a ring damped wheel to control wheel vibration. In terms of simulation, the friction between the ring and wheel is the main and difficult point, and is always simplified to some extent. These simplifications may make the simulation results far different from reality [1, 2]. In terms of experimental study, the effect of some parameters (such as the number of ring dampers, diameter of ring damper) on wheel vibration and sound radiation have been studied [3–5]. S. Zhong (B) · X. Zhou · K. Wu · X. Sheng School of Urban Rail Transportation, Shanghai University of Engineering Science, No. 333 Longteng Road, District Songjiang, Shanghai, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_34

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Besides those key parameters, the effect of which on vibration reduction by changing values of damping ratios has already been investigated, the authors of this paper find that damping ratio changes when using the three damper types, that is, only ring, ring attached with rubber layer, and ring attached with rubber layer and additional mass, which is to be analyzed in this study. In this study, the description of the test in lab is given in Sect. 2. There are two series of tests conducted, respectively, aimed to study the influence of selection of damper inserted into the wheel and the influence of preload on the ring’s circumference. Vibration characteristics of the test results from the series are abstracted in Sect. 3, such as the overall vibration level, the spectra of acceleration receptance and damping ratios of wheels’ dominating modes. Section 4 presents the conclusion of this study.

2 Tests in Lab The ring-damped wheel is supported by using a wooden rod going through the wheel center, of which the two ends are supported on two steel frames, as given in Fig. 1a. Four accelerometers are mounted on the wheel, as seen in Fig. 1b, one on wheel tread (P1 ), one on the side of wheel rim (P2 ), and two on the wheel web (P3 and P4 ). The points marked with A and B are respectively the hammer-hitting position in axial and radial directions. The hammer is a device installed with a sensor to record its impact on the wheel. By superposing plug pages into the spring inserted between the ends of the ring, the preload along the ring’s circumference gradually changes, as given in Fig. 1c. The performance of the four types of dampers in reducing vibration is studied, which are, respectively mounted on one side or both sides of the wheel. Among the four types, two are steel ring but not in the same overall length (shown in Fig. 2a), one is steel ring with additional rubber layer (shown in Fig. 2b) and one is steel ring with additional rubber layer and additional mass sticked on the rubber layer (shown

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3 Test Result Analysis 3.1 The Effect of Preload on the Ring’s Circumference The preload value changes with the thickness of plug pages inserted into the groove. By gradually superposing the plug-pages, their thickness increases by the increment of 1 mm from 0 up to 8 mm. The vibration of the wheel with single T1 ring with no pin (the pin can be seen in Fig. 2) and the normal wheel (with no ring dampers) is measured. Figure 3 gives the overall vibration levels of these cases, in which the tick label “none” of the horizontal axis indicates the ring-damped wheel with the pin but no plug page.

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Compared with the normal wheel vibration, the vibration in both axial and radial direction of the single T1 ring-damped wheel has been sharply decreased, as given in Fig. 3a, b. For the ring-damped wheel, the preload on the ring circumference changing with the increasing thickness of the plug pages, affects the vibration reduction amplitude. The vibration level of “rim” and “web” in Fig. 3a, respectively, are calculated with the acceleration measured at P2 and P4, the same as that in Fig. 6a. The vibration at P4 is smaller than that at P2, meaning the closer to the wheel center the axial vibration becomes weaker, because the hammer hit on the rim. Besides, it finds that when the thickness of the plug pages falls in the range of 0–4 mm, the single ring damper has better performance in alleviating vibration. In particular, the case 0 mm (the ring only inserted with pin but no plug pages) has the largest decreasing amplitude in the vibration on the web relative to the rim. In Fig. 3b, the best effect in reducing the radial vibration appears when the thickness of the plug pages falls in the range of 0–4 mm. Figure 4 shows the spectra of receptance of the accelerations under axial and radial excitation, helping to check the details of the wheel’s vibration in frequency domain. Three cases (single T1 ring with no pin, the plug page thickness of 0 and 8 mm) are taken as examples for a general view of the difference made by the preload. The receptance of the axial acceleration near the point P2 under the axial excitation by using the hammer is given in Fig. 4a. It is easy to find that after plugging the pin and plug pages the axial vibration decreases a lot. As we know, the wheel’s curve squeal generates dominantly due to the axial mode resonance. Then the peaks corresponding to the axial modes are marked. The shapes of the peaks corresponding to the same axial mode are not the same, indicating the changes of the damping ratio of the same axial mode. The damping ratio of the radial mode also changes, as given in Fig. 4b. The influence of preload on damping ratios, as indicated in Fig. 4, is directly presented by listing the value of damping ratios in all the cases in Fig. 5. For the single ring damped wheel with no pin, almost all the axial modes listed in Fig. 5a, have much larger damping ratios than the other cases with bigger preload. After inserting the pin and increasing the thickness of the plug pages, the damping ratios of the axial modes increase at different rates. Besides, it shows that the axial modes with higher frequencies have smaller damping ratios than those with relatively lower frequencies. While, for the radial modes, the increasing preload leads to a generally increasing trend for the damping ratio. During the process of the increasing trend, the damping ratios of the modes (r, 2) (r, 3) and (r, 4) see some fluctuation.

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T3 and T4. And for each type of the damper, the single and double dampers are, respectively, mounted on the wheel to analyze their effect of vibration reduction. The overall vibration level of the wheel in axial and radial directions drops a lot after the wheel is mounted with the dampers of any type, no matter it has single or double dampers, as given in Fig. 6a, b. And by comparing the results by using the single and double dampers, it comes that the double-damper wheel can reduce the vibration in axial direction to a lower level than the single-damper wheel. For the point at wheel’s rim, T2 and T3 damper seem to have a better performance in vibration reduction than the other two types. While, for the wheel core, double-T1-damper wheel gets the lowest axial vibration level. Also, for the double-T1-damper wheel the decreasing difference in the vibration transferred from rim to web is relatively larger.

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As seen in Fig. 6b, double-damper wheel works better than the single-damper wheel, except for T3 damper. So Fig. 7 shows the detailed spectrum of the radial vibration for the single- and double-T3 damper wheels. For frequency above 4000 Hz, the double-damper wheel has lower vibration. Figure 8 shows the spectra of receptance of accelerations under axial and radial excitation. Three cases (the normal wheel, single T1 damper wheel with no pin and double T1 damper wheel with no pin) are taken as examples for a general view of the difference made by the number of damper. It is easy to find that the axial and radial vibration decreases to some extent after plugging single or double damper. The damping ratios of axial and radial modes should have some changes. Figure 9 compares the damping ratios of the modes of single- and double-damper wheel for the four types. It shows that for most of the cases the double-damper wheel has much higher damping ratios than the single-damper wheel for both axial and radial modes. The features of the damping ratios corresponding to those, as seen in Fig. 9, can explain the features of the overall vibration level.

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4 Conclusion This study analyzes the influence of pre-load on the ring’s circumference and the influence of the type of damper inserted into the wheel by conducting two series of tests. Based on the analysis of the vibration characteristics of the wheels, it comes that the damping ratios of the axial modes increase at different rates and for the radial modes, the increasing preload makes the damping ratio in a generally growing trend. The damper types ring, ring attached with rubber layer and ring attached with rubber layer and additional mass lead to the wheel vibration reduction to different degrees. The values of damping ratios do make difference in the effect of vibration alleviation, and the further study on the optimization of damper type needs to combine with the simulation tool. Acknowledgements This work has been supported by the National Natural Science Foundation of China (U1834201), the National Key Research and Development Program of China (2017YFB1201103-08) and Sichuan Provincial Science and Technology Program (2020YJ0034).

References 1. Lopez I (1998) Theoretical and experimental analysis of ring damped railway wheels. University of Navarra 2. Brunel JF, Dufrenoy P, Charley J, Demilly F (2010) Analysis of the attenuation of railway squeal noise by preloaded rings inserted in wheels. J Acoust Soc Am 127:1300–1306 3. Zhang Y (2012) Experiment study on the vibration and sound radiation characteristics of subway ring damped low-noise wheel. Southwest Jiaotong University 4. Liu Y (2016) Experimental study on vibration and acoustic radiation characteristics of railway wheel with damping ring. Southwest Jiaotong University 5. Liu M, Zhou X, Han J, Du J, Xiao X (2018) Influence of the number of metal damping rings on noise reduction of the wheels in urban rail traffic. In: Noise and vibration control

The Influence of the Vehicle Body on the Sound Radiation from the Rail Dong Zhao, David Thompson, Evangelos Ntotsios, Ester Cierco, and Erwin Jansen

Abstract Numerical models and vibro-acoustic measurements are used to assess the effect of reflections from the underside of a railway vehicle on the sound radiation from the rail. A 2D boundary element model is used in which the rail vibrates uniformly in either vertical or lateral directions; various different shapes of vehicle body are introduced into the model. Measurements are performed on a 1:5 scale model and on a full-size track with and without a metro vehicle. The presence of the vehicle primarily affects the sound pressure from the vertical vibration of the rail, with negligible effect for the lateral vibration. The vehicle body reflects the sound back down towards the track where it is partly absorbed by the ballast, reducing the sound power. Nevertheless, the sound pressure at the trackside is increased by 0–5 dB and in some frequency bands by up to 9 dB. Finally, it is shown that the sound radiation in the presence of the vehicle can be approximated reasonably well with simple line source formulae. Keywords Rolling noise · Sound radiation · Reflections · Boundary element

1 Introduction Generally, in modelling rolling noise, which is radiated by vibration of the wheels and track [1], the presence of the vehicle on the sound radiation is neglected. In practice, the sound radiated by the rail is reflected and scattered by the train body located above it. As a result, the radiated sound may be altered to some extent, depending D. Zhao (B) · D. Thompson · E. Ntotsios Institute of Sound and Vibration Research, University of Southampton, Southampton SO17 1BJ, UK e-mail: [email protected] E. Cierco Ingeniería para el Control del Ruido SL, Berruguete 52, 08035 Barcelona, Spain E. Jansen TNO Acoustics and Sonar, Oude Waalsdorperweg 63, 2597 AK The Hague, The Netherlands © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_35

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on the geometry and the type of track. Moreover, measurement methods to separate wheel and track noise are being developed in which it is desirable to measure the track vibro-acoustic transfer functions without the vehicle present [2, 3]. Corrections may therefore be needed to allow for the effect of the vehicle. The aim of this work is to quantify the influence of the vehicle body on the vibroacoustic transfer functions for different situations, including various generic train bodies and typical tracks. The findings can be used to support suitable adjustments for the prediction or measurement of track noise without the need for the vehicle to be present.

2 Numerical Model The two-dimensional (2D) boundary element method (BEM) is used, making use of an in-house software WANDS (wave number domain software). The rail is assumed to vibrate uniformly over its cross-section; a unit velocity is applied in either the vertical or lateral direction. An engineering approach is used to account for the acoustic effect of the periodic support of a ballasted track [4]. This separates the cases of the rail ‘above ballast’ and ‘attached to sleeper’ into two 2D calculations. These are then combined, based on a weighted average of the results from the two cases. The absorptive effect of the ballast is simulated by applying an impedance to the boundary elements based on the Delany-Bazley model. The further effect of reflections from the ground adjacent to the track is taken into account by adding the pressure at an image receiver. The track geometry used is shown in Fig. 1. Figure 2 shows the sound pressure level for a unit vertical or lateral velocity, with or without a rigid ground. Compared with typical results for a point source, the effect of the ground is reduced by shielding at the ballast shoulder and tends to zero at high frequency. This 2D model will be used below in combination with various vehicles.

Fig. 1 Geometry used for BEM model of track

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Fig. 2 Sound pressure from the rail for unit velocity at 7.5 m from track centreline and different heights, with and without rigid ground. a Vertical rail vibration; b lateral rail vibration

3 Comparison with Measured Results 3.1 Scale Model Tests Laboratory measurements have been carried out on a 1:5 scale model of a ballasted track with a mock-up of a vehicle body (see Fig. 3). A reciprocal method is used to determine the transfer function from a point force on the rail to the sound pressure at the scaled positions shown in Fig. 1 [6]. The results are presented as the level difference (or insertion loss) of these transfer functions, with and without the vehicle present. In Fig. 4 the measured results are compared with predictions from the BEM model and plotted against frequencies corresponding to full scale. For the lateral direction

Fig. 3 Scale models studied in the measurements. a Ballasted track and vehicle body; b crosssection of model for normal vehicle height

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Fig. 4 Level differences due to presence of the vehicle from measurements and BEM calculations for 1:5 scale model metro train (near rail) at the receiver position of (1.5, 0.24) m; frequencies shown are for full scale. a Vertical vibration; b lateral vibration

the vehicle has negligible effect on the sound pressure level in both the measured and predicted results. For the vertical direction it gives a slight increase above 500 Hz and there is a stronger increase around 300 Hz in the predictions. The measurements are not shown at low frequencies as they were affected by background noise.

3.2 Full Scale Tests Transfer function measurements were carried out at Metro de Madrid (MdM) [5] using both direct and reciprocal methods. In the direct method the track was excited with an impact hammer (Fig. 5a) and the force on the rail and resulting sound pressure at the trackside were measured. In the reciprocal method an omnidirectional sound source with known volume velocity was used at the trackside and the rail response was measured with an accelerometer. Two sound sources, shown in Fig. 5b, were used to cover low and high frequency ranges. As the vehicle geometry is not invariant along its length, several different crosssections of the vehicle are introduced above the ground in the BEM model, as shown in Fig. 6. Figure 7 compares the measured and predicted level differences for the microphone position at 7.5 m from the track and 1.2 m height above the rail. Three measurements are included, one direct measurement and two reciprocal ones at different positions. BEM calculations are shown for the three different cross-sections of the vehicle shown in Fig. 6 but these produce similar results. For the lateral rail vibration, the predicted results are again close to 0 dB and the measurements above 300 Hz are between 0 and + 2 dB. For the vertical direction there is more variation with frequency and between the different measurements. The predicted sound pressure is increased in most frequency bands by 0–5 dB, but this

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Fig. 5 Photos of the static measurements at MdM. a Impact hammer; b high frequency (left) and low frequency (right) sound sources exciting the track with train in position

Fig. 6 Vehicle models used to represent MdM vehicle in the 2D BE model. a Section A, with fairings and no equipment; b Section B, with equipment; c Section C, with equipment

tendency is not seen for the measurements. Instead, the measured sound pressure in some frequency bands can be reduced by 5 dB or more or increased by up to 9 dB.

3.3 Different Vehicle Shapes Results have been calculated for full-size models with different train geometries, including those shown in Fig. 3 (‘Model’), Fig. 6 (A, B and C), a high-speed train with a lower floor profile (HS) and two other models [5] (here labelled D and E). It should be noted that in each case in this section the sleeper spacing is set to 0.6 m,

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Fig. 7 The level differences due to presence of vehicle from the measurements and BEM calculations for a metro train (near rail) at the receiver position of (7.5, 1.2) m. a Vertical vibration; b lateral vibration

whereas it is set to 1 m in the previous section, as in the measurements. The effect of the different vehicle profiles on the sound power radiated from the rail is shown in Fig. 8. The sound power radiated from the rail is calculated by integrating the sound intensity at a radius of 15 m from the centre of the track for angles spaced 5° apart. For the vertical direction a consistent reduction of 2–6 dB is found above 200 Hz which can be attributed to the reflection of sound downwards towards the ballast. For the lateral direction the reduction in sound power level is 0–2 dB. Figure 9a shows the level difference in sound pressure due to the introduction of the vehicle for vertical vibration with no ground (or highly absorptive ground). Despite the reduction in sound power, there is an increase in the sound pressure level, at most frequencies by 0–5 dB and in some frequency bands by up to 10 dB; in other bands below 300 Hz there are reductions. The largest increases occur in the vicinity of the dip in the spectrum without the train, around 250–500 Hz (see Fig. 2a). There are differences between the various train designs but they each have the same trend.

Fig. 8 Change in sound power level due to presence of vehicle calculated using BEM for different train profiles for a vertical rail vibration; b lateral rail vibration

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Fig. 9 Level differences due to presence of vehicle calculated using BEM for different train profiles for vertical vibration of near rail at the receiver position of (7.5, 1.2) m. a Without ground; b with rigid ground

The train body makes little difference to the radiation from the lateral rail vibration (not shown). The corresponding results in the presence of a rigid ground are shown in Fig. 9b. The ground is located 0.74 m below the top of rail. As seen in Fig. 2, for the case without the train, the introduction of the ground leads to only small changes in the sound pressure due to vertical rail vibration. However, in the presence of the train the sound pressure level is increased as sound is reflected first from the underside of the train and then from the ground to the receiver. For the lateral direction the introduction of the train body again has little effect (not shown).

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bringing the result closer to 0 dB in the mid and high frequency regions. Consequently, the line source estimates can be used reliably in the presence of the vehicle. Although the level at the mid frequency dip is increased, it remains at around – 5 dB. For the lateral direction, the train has very little effect and the result remains close to 0 dB. Figure 11 shows the corresponding results with a rigid ground. For the vertical direction the changes due to inclusion of the ground are small, but for frequencies above 250 Hz they nevertheless have the effect of bringing the estimates closer to 0 dB. For the lateral direction, the effect of the ground reflection can be seen in the peaks and dips but these are not affected by the presence of the vehicle.

Fig. 10 Sound pressure from the rail, at 7.5 m from track centreline, normalised by sound calculated for line source—with no ground. a Vertical vibration; b lateral vibration

Fig. 11 Sound pressure from the rail, at 7.5 m from track centreline, normalised by sound calculated for line source—with rigid ground. a Vertical vibration; b lateral vibration

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4 Conclusion The sound radiated by the rail towards the ground is found to be strongly attenuated by shielding due to the ballast shoulder. As a result, the ground reflection is considerably reduced compared with conventional estimates, especially for the vertical rail vibration. The presence of the vehicle primarily affects the sound pressure from the vertical vibration of the rail whereas the effect is negligible for the lateral vibration. The vehicle body reflects the sound back towards the ballast. Absorption by the ballast then leads to a reduction in the radiated sound power but the sound pressure at the trackside is increased at most frequencies by 0–5 dB and in some frequency bands by up to 9 dB. To assess the effect of the vehicle in a particular situation, the 2D BE method can be used; alternatively, simple line source formulae give reasonably good results for the radiation including the vehicle. Acknowledgements The work described here has been supported by the TRANSIT project (funded by EU Horizon 2020 and the Europe’s Rail Joint Undertaking under grant agreement 881771). The contents of this paper only reflect the authors’ views; the Joint Undertaking is not responsible for any use that may be made of the information contained in the paper.

References 1. Thompson D (2009) Railway noise and vibration: mechanisms, modelling and means of control. Elsevier, Oxford 2. Thompson D, Zhao D, Cierco E, Jansen H, Dittrich M (2022) Improved methods for the separation of track and wheel noise components during a train pass-by. In: IWRN14 3. Thompson D et al (2018) Assessment of measurement-based methods for separating wheel and track contributions to railway rolling noise. Appl Acoust 140:48–62 4. Zhang X, Thompson D, Quaranta E, Squicciarini G (2019) An engineering model for the prediction of the sound radiation from a railway track. J Sound Vib 461:114921 5. Thompson D, Dittrich M, Jansen H, Zhao D, Cierco E (2022) Track and vehicle separation and transposition techniques including theoretical description and proposal for full scale validation test campaign. TRANSIT Deliverable D3.2, January 2022 6. Zhang X, Jeong H, Thompson D, Squicciarini G (2021) Experimental study of noise mitigation measures on a slab track. Appl Acoust 172:107630 7. Thompson DJ, Hemsworth B, Vincent N (1996) Experimental validation of the TWINS prediction program for rolling noise, part 1: description of the model and method. J Sound Vib 193:123–135

Noise Sensitivity Analysis of a Two-Stage Baseplate Fastening System Evangelos Ntotsios, Boniface Hima, David Thompson, Giacomo Squicciarini, and David Herron

Abstract A study is presented into the sensitivity of rolling noise to design changes in a two-stage baseplate rail fastening system. The focus is on the influence on the rolling noise of three parameters of the fastening system: the stiffnesses of the railpad and the baseplate pad and the thickness of the baseplate that determines its mass and sound radiation ratio. The TWINS model is adapted by introducing the baseplate vibration and sound radiation using results from an experimentally verified 2.5D finite element model. Based on the simulations, an optimum railpad stiffness is identified of around 500 MN/m, based on a baseplate pad stiffness value of 80 MN/ m. The thickness of the baseplate has only a small effect on the total rolling noise. Keywords Rolling noise · Baseplate rail fastener · Sound radiation

1 Introduction There are several commercially available two-stage baseplate designs, each of which consists of a metal baseplate between two elastic pads: the railpad, which is usually stiffer, and the baseplate pad, which is softer and is placed under the baseplate. To minimize vibration transmission to the foundation and the ground the overall stiffness should be kept as low as possible. This is mainly governed by the stiffness of the lower pad. On the other hand, the stiffness of the railpad and the mass of the baseplate affect the track decay rates (TDRs) and thereby the rail component of rolling noise. Moreover, the flexural modes of vibration of the baseplate and the size of the radiating surface affect the sound radiation efficiency and thereby the baseplate radiated noise. E. Ntotsios (B) · B. Hima · D. Thompson · G. Squicciarini Institute of Sound and Vibration Research, University of Southampton, Southampton SO17 1BJ, UK e-mail: [email protected] D. Herron Pandrol, 63 Station Road, Addlestone KT15 2AR, Surrey, UK © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_36

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The overall rolling noise can be calculated as a combination of the noise radiated by the train wheels, the rails and the vibrating components of the track; for the case of a slab track with a two-stage fastening system these are the baseplates and the slab. The design of the fastening system will influence the wheel radiated noise only at low frequencies (i.e. below 1 kHz) and not at higher frequencies where the wheel contribution to the overall noise is significant [1]. Moreover, as the baseplate pad usually has a low stiffness, the sound radiation from the slab will be negligible. Thus, the influence of the two-stage fastening design is important principally for the noise radiation from the rail and the baseplates. The aim of this work is to quantify the influence on the rolling noise of three design parameters of the two-stage fastening system: the stiffnesses of the baseplate pad and the railpad and the thickness of the baseplate. For this, a computational strategy is used that represents the track using an experimentally validated 2.5D finite element (FE) model including the flexural response and radiation efficiency of the baseplates. These results are then used in combination with the TWINS model [2] to calculate the wheel-rail interaction forces and the wheel, rail and baseplate vibration and noise. The results can be used to identify baseplate fastening designs that minimise the noise.

2 Methodology Separate numerical models are used for the rail and baseplate vibration in the frequency domain. The free infinite rail is represented by a 2.5D FE model whereas the metal baseplates and the lower pad are represented by a 3D FE model in Comsol. This is used to obtain a mobility matrix corresponding to nine positions beneath the rail pad (in a 3 × 3 arrangement). The rail is coupled to a large number of these baseplates, through discrete springs representing the railpads, using the method from [3]. The coupled track model is used to predict the rail mobilities and TDRs, and also the interaction forces between the railpads and the baseplates. These railpad forces are then introduced in the FE model of the baseplate to determine the velocities (due to a unit point load on the rail) at the FE nodes of the baseplate. The radiation ratio and radiated power of the multiple baseplates are calculated by applying the Rayleigh integral method to the predicted velocities of the baseplates. The predicted rail point mobilities and TDRs from the coupled model are introduced into TWINS to calculate the wheel-rail interaction forces and the wheel and rail vibration and noise considering the wheel/rail roughness. On the other hand, the baseplate noise is determined by combining the wheel-rail forces with the results from the numerical track model. The overall track rolling noise due to the train passage is quantified as the sum of the sound power radiated by the rails and the baseplates for a 20 m section of the track.

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Fig. 1 Two-stage baseplate rail fastening system. a At the test track; b baseplate geometry; c baseplate 3D FE model

3 Comparison with Measured Results 3.1 Model Parameters The two-stage baseplate design considered in this work consists of a cast-iron baseplate with a railpad above it and baseplate pad beneath it (Fig. 1a). The detailed baseplate geometry can be seen in Fig. 1b. The baseplate has length 0.404 m and width 0.206 m, and it has a mass of 6.3 kg. The thickness of the plate body is 15 mm. Figure 1c shows the FE model from which it can be seen that some of the detail of the clipping area was omitted; nevertheless, the vibration modes, in the frequency range of interest, were validated against measurements on a free baseplate. The baseplate pad is represented by a layer of springs with hysteretic damping. From comparison with experiments, the vertical and lateral stiffness and damping loss factor were set to 80 MN/m and 60 MN/m and 0.12 respectively. In the track model, the rail is UIC60 and is discretely supported by 121 rail fasteners with 0.65 m spacing. The vertical stiffness used for the railpads was obtained from measurements for a selection of railpads [4]. The lateral railpad stiffness is assumed as 25% of the value used for the vertical stiffness.

3.2 Mobility Measurements at the Test Track Measurements of rail and baseplate mobility were made on a non-operational slab track located at the National College for Advanced Transport and Infrastructure at Doncaster, UK. The tests were performed on a 20 m section of track fitted with UIC60 rail on Pandrol two-stage rail fasteners for a selection of railpads with different stiffness. The measured rail and baseplate mobilities were then compared with the predictions from the numerical model using railpad stiffnesses obtained from [4]. Figure 2 compares the measured and predicted rail vertical responses for the case of a railpad with 310 MN/m vertical stiffness. A good agreement can be seen for both the driving point mobility and the TDR. The oscillations seen in the measured mobility are due to reflections from the end of the finite rail of the test track. Similar good agreement was found for the other railpads tested (not shown).

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Fig. 2 Comparison between rail measurements and predictions from the numerical model. a Rail driving point mobility magnitude and b one-third octave TDR

3.3 Baseplate Sound Radiation Measurements A 6 m section of half-width slab track fitted with 8 two-stage baseplates (Fig. 3a) was installed in the reverberation chamber (Fig. 3b). The track was fitted with a 6 m UIC60 rail using railpads with 310 MN/m vertical stiffness and baseplate pads similar to the ones installed on the test track at Doncaster. Noise and vibration tests were conducted to validate the predictions from the numerical model. To determine the radiation ratio σ , spatially-averaged mobilities were measured by impact hammer tests, and a reciprocity method was used to determine the sound power for a unit force [5]. The structure is excited by acoustic excitation from a known sound source and the resulting vibration of the structure is measured (Fig. 3b). Figure 4a shows the measured and predicted baseplate vibration response. These results are for a single baseplate without the presence of the rail. A good agreement is found in the frequency range below 1 kHz. Above 1 kHz, there are differences between the frequencies of measured and predicted vibration modes, probably due to the geometric simplifications used for the 3D FE model; however, the general trend of the predicted velocities agrees with the measured one. The radiation ratio is shown in Fig. 4b. The predicted results are calculated using the Rayleigh integral method with the predicted surface-averaged squared velocity

Fig. 3 Slab track test section. a Dimensions; b in the reverberation chamber

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Fig. 4 Comparison between baseplate measurements and predictions. a Spatially averaged meansquared mobility and b one-third octave radiation index (10 log10 σ )

from Fig. 4a. The measured results below 300 Hz are believed to be affected by the radiation contribution of the slab (which had a thickness of only 0.2 m) and possibly the room floor, which are not included in the numerical model. A good agreement can be seen between the measured and the predicted results for frequencies above 300 Hz. With the rail fitted on the slab track, the spatially averaged mobility of the rail and the baseplates were measured for excitation on the rail above the fourth baseplate. Figure 5a shows the ratio of the squared vibration of the baseplates to that of the rail. A good agreement is obtained between 160 and 2500 Hz. For frequencies outside this range, the measured values are higher than the predicted ones; the reason for these differences is unknown although simplifications in the model of the baseplate and the railpad may play a role. Figure 5b shows the sound power from the track for a unit force. In the predictions, it is assumed that the radiated sound power from the rail and the baseplates can be

Fig. 5 Comparison between rail and baseplate measurements and predictions. a Spatially averaged transmissibility of the baseplates relative to the rail and b sound power due to a unit force on the railhead

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treated as uncorrelated. The rail radiation is determined from the spatially averaged vibration calculated using the numerical track model combined with the radiation ratio from [6]. The baseplate sound radiation is calculated by using the radiation ratio calculated from the Rayleigh integral for 8 baseplates excited by the rail. The measured and predicted results show good agreement above 800 Hz. Between 315 and 630 Hz, the measured sound power levels are lower than the predicted ones, but the difference is less than 10 dB. These differences are probably due to modelling and parametric uncertainty that affect the predicted results.

4 Noise Sensitivity Analysis To investigate the effect of the baseplate design parameters, the radiated sound power during a train passage was calculated by using the proposed approach. Results were obtained for different values of baseplate pad stiffness, railpad stiffness and baseplate thickness. For the TWINS calculations, the wheel is from a modern multiple unit train, with a diameter of 0.84 m and a straight web. The train speed is 120 km/h and measured rail roughness data used is from a typical ballasted track. Figures 6, 7 and 8 show the predicted TDRs, and total track sound power, i.e., from the rail and baseplates. The wheel noise is not shown but is around 103.4 dBA in all cases. Figure 6 compares the predictions for different values of the baseplate pad stiffness (given in the legend) and a constant railpad stiffness of 310 MN/m. When increasing the baseplate pad stiffness, the TDR is increased at frequencies below 500 Hz, but is less affected at higher frequencies. Below 500 Hz the baseplate radiation efficiency, not shown here, decreases when the lower pad stiffness is increased. These differences in the TDRs and the baseplate radiation ratio affect the track radiated power, shown in Fig. 6b, at frequencies below 500 Hz. A smaller influence (less than 4 dB) can be seen in the frequency range 500–1600 Hz. Nevertheless, the overall A-weighted sound power remains almost unaffected, with differences of less than 1.5 dB. In Fig. 7, the railpad stiffness is varied, while the baseplate pad stiffness is kept constant at 80 MN/m. When the railpad stiffness is increased, the TDR in Fig. 7a is increased at frequencies below 500 Hz and at higher frequencies, above 1.25 kHz. This reduces the average rail vibration and thus the radiated track sound power; however, above 1 kHz the baseplate vibration (not shown) is increased with stiffer railpads. For the highest values of railpad stiffness, the baseplate vibration becomes significant and its sound radiation in the frequency range 1.6–2.5 kHz dominates the track radiated sound, as can be seen by the higher levels in Fig. 7b. Therefore, the overall A-weighted track sound power has a minimum for a railpad stiffness of 528 MN/m, for which it is about 4 dB lower than for the softest pad and 1 dB lower than for the stiffest one. Finally, in Fig. 8, results are given for different thicknesses of the baseplate; these are for a baseplate pad stiffness of 80 MN/m and railpad of 310 MN/m. Below 1.25 kHz the TDR increases when the baseplate thickness (and hence mass) is

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Fig. 6 One third octave comparison between predictions for different baseplate pad stiffness. a TDR and b track radiated sound power (unweighted)

Fig. 7 One third octave comparison between predictions for different railpad stiffness. a TDR and b track radiated sound power (unweighted)

Fig. 8 One third octave comparison between predictions for different baseplate thickness. a TDR and b track radiated sound power (unweighted)

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increased; above 1.6 kHz, the effect on the TDR is reversed. However, over much of the frequency range the radiation ratio of the baseplates (not shown) increases as the thickness is increased, by up to 4 dB below 1 kHz for this range of parameters. Consequently, at low frequencies, below 500 Hz, there is little change in the track radiated power in Fig. 8b. Between 500 and 1250 Hz, the track sound power is reduced as the thickness is increased. The largest level difference between the thinnest and thickest baseplate is about 6 dB, which occurs at 800 Hz where the sound power has its maximum. In the frequency range 1.25–3.15 kHz, the increase of the baseplate thickness leads to an increase in the track sound power. However, the overall A-weighted track sound power level remains almost unchanged, with differences of less than 2 dB between the lowest and highest predicted values.

5 Conclusion The effect of the various parameters of a two-stage baseplate on the rolling noise has been explored. It is concluded that the thickness (and mass) of the baseplate has only a small effect on the overall noise which would not justify the increase in material and cost of a heavier baseplate. The stiffness of the baseplate pad has only a small effect on the total rolling noise from the track; however, a low stiffness is important to control the vibration transmission to the foundation and the ground. The railpad stiffness has the greatest effect on the noise, with variations in the track noise level of up to 4 dB. A stiff railpad can help to control the noise from the rail by increasing the TDR, but this occurs at the expense of increased noise from the baseplate itself. An optimum railpad stiffness is identified of around 500 MN/m, based on a baseplate pad stiffness value of 80 MN/m. Acknowledgements The authors gratefully acknowledge Pandrol for providing the rail-fastening system, railpads and organizing the measurement at the test track. The work described here has been supported by the EPSRC under the programme grant EP/M025276/1, ‘The science and analytical tools to design long life, low noise railway track systems (Track to the Future)’.

References 1. Thompson D (2009) Railway noise and vibration mechanisms, modelling and means of control. Elsevier, Oxford 2. Thompson D, Hemsworth B, Vincent N (1996) Experimental validation of the TWINS prediction program for rolling noise, part 1: description of the model and method. J Sound Vib 193(1):123– 135 3. Zhang X, Thompson D, Li Q, Kostovasilis D, Toward M, Squicciarini G, Ryue J (2019) A model of a discretely supported railway track based on a 2.5 D finite element approach. J Sound Vibr 438:153–174 4. Hima B, Thompson D, Squicciarini G, Ntotsios E, Herron D (2021) Estimation of track decay rates and noise based on laboratory measurements on a baseplate fastening system. In: Degrande

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G et al (eds) Noise and vibration mitigation for rail transportation systems. Proceedings of the 13th international workshop on railway noise, Ghent, Belgium, Sept 2019. Notes on numerical fluid mechanics and multidisciplinary design, vol 150. Springer Nature Switzerland, pp 621–628 5. Squicciarini G, Putra A, Thompson D, Zhang X, Salim MA (2015) Use of a reciprocity technique to measure the radiation efficiency of a vibrating structure. Appl Acoust 89:107–121 6. Zhang X, Thompson D, Quaranta E, Squicciarini G (2019) An engineering model for the prediction of the sound radiation from a railway track. J Sound Vib 461:114921

Study on the Wide-Frequency Tuned Mass Damper Inhibiting Rail Corrugation and Noise in Floating Slab Track Xuejun Yin, Xiaotang Xu, Huichao Li, Qian’an Wang, and Yunfeng Gao

Abstract In order to solve the rail corrugation in the curved section of the steel spring floating slab track in Qingdao metro, a new type wide-frequency tuned mass damper (WTMD) was developed, which integrated the labyrinth restraint damping plate and TMD’s technology. The track tests of the rail corrugation, rail vibration, interior noise, trackside noise were conducted before and after the WTMDs installation. After the study, the following three conclusions can be drawn: (1) Three times corrugation track tests show that the corrugation develops slowly at 1 month and 4.5 months after the installation of WTMD, and the corrugation is invisible. (2) After installing WTMD, the vertical and lateral vibration of the rail are 10% of the original, and the total rail vibration level will be reduced by 8.1 dB and 10.7 dB respectively. (3) The trackside noise, the passenger interior noise and the driver interior equivalent A-weighted noise overall levels decrease by 9.0, 7.7, and 5.8 dBA, after the WTMDs installation. It can be seen that, the installation of WTMDs can effectively reduce the rail vibration, inhibit the rail corrugation, and also play a good role in reducing the trackside noise and the interior noise. Keywords Tuned mass damper · Rail corrugation · Vibration · Noise · Floating slab track

X. Yin · X. Xu · H. Li · Q. Wang Qingdao Create Environment Control Technology Co., Ltd., Qingdao 266101, P R China X. Xu (B) Civil Engineering, Southwest Jiaotong University, Chengdu 610031, P R China e-mail: [email protected] Y. Gao GERB (Qingdao) Vibration Control Co., Ltd., Qingdao 266108, P R China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_37

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1 Introduction With the rapid development of urban rail transit in worldwide, because of the largescale construction of subways in various cities, they are also faced with some new problems, such as fastener fracture, primary spring fracture, excessive interior and exterior noise caused by rail corrugation [1, 2], which will not only increase the maintenance cost of the track system, but also affect the safety of the vehicle. In recent years, scholars at home and abroad have done a lot of research on the rail corrugation treatment. Egana found that changing the friction coefficient and hardness of rail surface could improve the rail corrugation state, but there were some hidden dangers to vehicle safety by lubricating [3]. Grassie studied the generation and development of rail corrugation by changing the train traction force. But there are few studies on rail corrugation in curve section of steel spring floating slab track so far. In the process of metro construction, due to various factors, most lines generally have a curve section with a radius of less than 600 m. And the rail corrugation mainly appears in the curve section [4], which belongs to short-pitch corrugation, whose wave depth ranges from 88 to160 µm and the wave length ranges from 12.5 to 40 mm [5, 6]. In order to solve the rail corrugation in the curved section of the steel spring floating slab track in Qingdao metro, the wide-frequency tuned mass damper (WTMD) is developed. The track tests of the rail Corrugation, rail vibration, interior noise, trackside noise are conducted before and after the WTMDs installation. It can be seen that, the installation of WTMDs can effectively reduce the rail vibration, inhibit the rail corrugation, and also play a good role in reducing the trackside noise and the interior noise.

2 Design Principle It is well known that the tuned mass damper (TMD) can reduce the vibration amplitude of the original system by adding the mass element, the elastic element and the damping element to form a subsystems to the original system. The principle schematic diagram is shown in Fig. 1. According to the relationship between the amplitude amplification factor and the tuning frequency ratio, it can be seen that the original single-peak vibration of the main system is transformed into two reduced peaks vibration, thus achieving a good vibration reduction effect. When evaluating the vibration acceleration of the main structure, the tuning frequency ratio and damping ratio can be calculated according to the following

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Fig. 1 The vibration of main system of the TMD

formulas. µ = m T M D /m M

(1)

f T M D = f /(1 + µ)

(2)

/ Dopt =

3µ 8(1 + µ/2)

(3)

where µ refers to the mass ratio between the mass of the TMD and the mass of the main system, m T M D refers to the mass of the TMD, m M refers to the mass of the main system, f T M D refers to the optimal natural frequency of the TMD, f refers to the natural frequency of the main system, Dopt refers to the optimal damping ratio. In order to solve the rail corrugation in the curved section of the steel spring floating slab track in Qingdao metro, based on the above principles, the wide-frequency tuned mass damper (WTMD) is developed, which is composed of the labyrinth restraint damping plate, the tuned mass damper and the elastic clip. And the tuned mass damper is composed of the mass element and the damping material. The structure of the WTMD is showed in Fig. 2a. The picture of the WTMD installation is showed in Fig. 2b.

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Fig. 2 WTMD: a structure; b installation

3 Track Test In order to study the effect of the developed WTMD on inhibiting the corrugation and noise, systematic track tests are carried out on the rail vibration, the trackside noise, the passenger room interior noise, the driver room interior noise and the rail corrugation level before and after the rail grinding and the WTMD installation, according to GB10070-88, GB10071-88, GB 14892-2006, and ISO 3095-2013 [7– 10]. The tests’ timetable is shown in Table 1. Before the WTMDs installation, the first rail corrugation test finds that there are serious corrugations, as shown in Fig. 3d, on the inner rail, with the main wavelength 25 and 40 mm, which are 19.5 and 23.2 dB exceeding the standard in ISO 3095:2013, as shown in Fig. 4. The rail corrugations present as severe exceedance. The roughness level (L r ) is given by the following equation: ( L r = 10 × log

r R2 M S r02

) (4)

where the L r is the roughness level in dB, the r R M S is the root mean square roughness in µm, and the r0 is the reference roughness (1 µm). Table 1 Track tests’ timetable Time

Test contents

Dec. 15–17, 2020

Tests of rail vibration, interior noise, trackside noise

Dec. 16, 2020

Rail corrugation test (First test)

Dec. 20–27, 2020

WTMD installation

Dec. 29–31, 2020

Tests of rail vibration, interior noise, trackside noise

Jan. 20, 2021

Rail grinding

Feb. 21, 2021

Rail corrugation test (Second test)

Jun. 11, 2021

Rail corrugation test (Third test)

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Fig. 3 Pictures of the three times track tests of the rail corrugation: a first test-outer rail, b second test-inner rail, c third test-outer rail, d first test-inner rail, e second test-outer rail, f third test-inner rail

The second rail corrugation tests are carried out one month after the rail grinding, with WTMDs. The test results show that the o exceedance values at the typical wavelengths of 25 and 40 mm are 9.4 and 9.8 dB. The rail corrugations present as mild exceedance, as shown in Fig. 3b, e. The third rail corrugation tests are carried out 4.5 months after the rail grinding, with WTMDs. The test results show that the exceedance values at the typical wavelengths of 25 and 40 mm are 6.3 and 6.6 dB. The rail corrugations also present as mild exceedance, as shown in Fig. 3c, f. In addition, compared with the previous first rail corrugation tests, it is found that rail grinding can significantly reduce the rail surface roughness level. The comparison of the last two rail corrugation tests show that the rail surface roughness levels are similar due to the installation of WTMDs, and the development of the rail corrugation is effectively inhibited. In addition, according to Fig. 3b, c, e, f. The rail surface is in good condition, and no visible rail corrugation is developed.

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Fig. 4 Rail roughness level

(a) Lateral

(b) Vertical

Fig. 5 The rail vibration acceleration before and after WTMD installation

Figure 5 is a time domain comparison diagram of inner rail vibrations before and after the WTMD installation. It can be seen that the rail vibration accelerations are significantly reduced after WTMD installation, which are reduced from 300 to 18 g in lateral and from 500 to 45 g in vertical.

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180

Acceleration level in dB

175

Before installation After installation

170 165 160 155 150 145 140 135

Frequency/Hz

(b) Vertical

(a) Lateral Fig. 6 Rail vibration level

Figure 6 is a 1/3 octave rail vibration acceleration level spectrum diagram. In Fig. 6, the acceleration level (VL) is defined by the formula 5. Where the ai is the vibration acceleration in m/s2 , and a0 is the reference value (10−6 m/s2 ). After analysis, it can be found that the maximum lateral and vertical vibration levels of the rail appear at 800 Hz. After installing WTMDs, the lateral and vertical vibration levels are reduced by 13.7 dB and 9.8 dB, respectively, and the total vibration levels of the rail lateral and vertical vibration accelerations are reduced by 10.7 and 8.1 dB. V L = 20 × log

ai a0

(5)

Finally, the trackside noise, the passenger room interior noise and the driver room interior noise are tested before and after the WTMDs installation, as shown in Fig. 7. The analysis results show that, the trackside noise, the passenger interior noise and the driver interior equivalent A-weighted noise overall levels decreased by 9.0, 7.7, and 5.8 dBA, after the WTMDs installation. Thus, the WTMDs also have significant noise reduction effect.

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Frequency/Hz

(a) Trackside noise

Frequency/Hz

(b) Passenger room interior noise

(c) Driver room interior noise Fig. 7 Noise overall levels

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4 Conclusion The following conclusions can be obtained through the above track tests: Firstly, the rail has a good surface condition without visible rail corrugation, within 5 months of the WTMDs installation. Secondly, the total vibration levels of the rail lateral and vertical vibration accelerations are reduced by 10.7 and 8.1 dB, after the WTMDs installation. Thirdly, the trackside noise is reduced by 9.0 dBA, the passenger room noise is reduced by 7.7 dBA, the driver room noise is reduced by 5.8 dBA, after the WTMDs installation. It can be seen that, the installation of WTMDs can effectively reduce the rail vibration, inhibit the rail corrugation, and also play a good role in reducing the trackside noise and the interior noise.

References 1. Ling L, Li W, Shang HX, Xiao XB, Wen ZF, Jin XS (2014) Experimental and numerical investigation of the effect of rail corrugation on the behavior of rail fastenings. Veh Syst Dyn 52(9):1211–1231 2. Yin XJ, Liu XL, Liu YQ, Liang ZD (2017) Application of rail dampers to rail corrugation noise control. In: Noise and vibration control, vol 37(6), pp 190–198 3. Egana JI, Vinolas J, Negrete NG (2005) Effect of liquid high positive friction (HPF) modifier on wheel-rail contact and rail corrugation. Tribol Int 38(8):769–774 4. Grassie SL, Elkins JA (2005) Tractive effort, curving and surface damage of rails Part 1. Forces exerted on the rails. Wear 258(7–8):1235–1244 5. Grassie SL (2009) Rail corrugation: characteristics, causes, and treatments. Proc Inst Mech Eng Part F J Rail Rapid Transit 223:581–596 6. Jin XS, Li X, Li W, Wen ZF (2016) Review of rail corrugation progress. J Southwest Jiaotong Univ 51(2):264–273 7. GB10070-88 (1988) Standard of environmental vibration in urban area. State Bureau of Environmental Protection, Beijing, China (in Chinese) 8. GB10071-88 (1988) Measurement method of environmental vibration of urban area. State Bureau of Environmental Protection, Beijing, China (in Chinese) 9. GB 14892-2006 (2006) Noise limit and measurement for train of urban rail transit. National Standardization Management Committee, Beijing, China (in Chinese) 10. ISO 3095-2013 (2013) Acoustics-railway applications-measurement of noise emitted by railbound vehicles. International Organization for Standardization, Geneva, Switzerland

A Program for Predicting Wheel/Rail Rolling Noise from High-Speed Slab Railway Cheng Gong, Sheng Xiaozhen, Zhang Shuming, and Feng Qingsong

Abstract Wheel/rail rolling noise is considered to be one of the most important sources of railway noise, even for high-speed railways. In order to accurately predict wheel-rail noise, representative prediction program has been developed and applied. The authors have also developed a wheel/rail rolling noise prediction program, taking more account of characteristics of high-speed slab railway tracks, having sufficient computational efficiency to handle engineering problems. This paper introduces the calculation methods, operation mechanism and characteristics of this program. Typical results are given and compared with measurement. Keywords Wheel-rail rolling noise · High-speed railway · Prediction program

1 Introduction Wheel/rail rolling noise is considered to be one of the most important sources of railway noise, even for high-speed railways. In order to accurately predict wheel/ rail noise, an iconic prediction Program has been developed [1] and applied [2]. In the Program, a set of prediction sub-models in the frequency domain is built. In subsequent versions, the Program has improved some of these models, such as using an correction 2D-BEM to calculate the acoustic radiation efficiency of rail, such as C. Gong (B) · F. Qingsong State Key Laboratory of Performance Monitoring and Protecting of Rail Transit Infrastructure, East China Jiaotong University, Nanchang 330013, China e-mail: [email protected] S. Xiaozhen School of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai 201620, China Shanghai Engineering Research Centre for Vibration and Noise Control Technologies in Railway Transportation, Shanghai 201620, China Z. Shuming School of Railway, Shandong Polytechnic, Shandong 250104, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_38

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modeling rail sleeper as elastomer, considering the coherence of rail and rail sleeper sound radiation [4], and considering the sound absorption of ballast [5], making the model more realistic. The frequency domain method has a great computational efficiency advantage for dealing with rolling noise as a steady-state wheel-rail interaction problem, and it can deal with complex engineering problems quickly and accurately, and later many other rolling noise prediction Program is also based on this theory. With the rapid increase of computer calculation speed, some time domain models or Program have also been applied to calculate the high frequency vibration in rolling noise calculation. In order to achieve the calculation accuracy of high frequency vibration, the time domain model requires more degrees of freedom and more complex processing, which can handle the noise caused by railroad impact, but has no advantage in calculating rolling noise. The authors have also developed a wheel/rail rolling noise prediction Program, taking more account of characteristics of high-speed slab railway tracks, having sufficient computational efficiency to handle engineering problems. This paper introduces the calculation methods, operation mechanism and characteristics of this Program. Typical results are given and compared with measurement.

2 Description of the Program The basic calculation method of the Program is elaborated in Ref. [3], and on the basis of this prediction method the prediction Program has been further developed.

2.1 Inputs and Outputs (1) Inputs Track parameters: rail type, vertical and lateral stiffness of fastener pad, vertical and lateral loss factor of fastener pad, length, width and thickness of the track slab, number of fasteners for one slab, vertical stiffness and loss factor of the concrete–asphalt layer under slab, acoustic geometry boundary, rail roughness. Vehicle parameters: finite element mesh information for wheelset profile, boundary node, mass of axle box and rotary arm, mass of half bogie frame, the moment of inertia in roll of half bogie frame, stiffness between axle and axle box, loss factor between axle and axle box, primary vertical stiffness of steel spring, Primary vertical damping coefficient of hydraulic damper, stiffness of the rubber bushings, loss factor of the rubber bushings, transverse distance between two primary suspensions, wheel roughness.

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(2) Outputs: Sound pressure level of fixed field points with defined coordinates, the radiated sound power of wheelsets, rails and track plates at the moving coordinate system with the vehicle.

2.2 Program Features The Program has the following features that allow it to take into account more complex factors: (1) The vibration response of the wheelset due to vertical and lateral unit harmonic load is calculated by the finite element method and Fourier series, and the acoustic radiation power of the wheelset is obtained by the axisymmetric boundary element method, which only needs to discretize the two-dimensional profile of the wheelset. This methodology largely reduces the matrix dimension, improves the calculation speed, and can consider the high-speed rotation of the wheelset [8]. (2) The sound radiation of the wheelset due to the vertical and lateral forces at the left and right wheel/rail contact point is considered. Since these four forces are coherent with each other, the radiated sound power components of these four forces acting individually and coherently, which are unique for any wheelset, are obtained in Program. So if the track structure or roughness are changed, it is no need to repeat the calculation of sound radiation of unchanging wheelset that takes a long time-consuming, improving the efficiency of the calculation. (3) The superstructure of the wheelset (axle box, swivel arm, primary vertical suspension and bogie frame) is considered [9]. (4) Periodic discrete supports of track plates and fasteners to the rail and the high speed movement of wheel/rail forces are fully considered when calculating track vibration. (5) Using the 2.5-dimensional boundary element method to directly predict field sound pressure, rather than converting rail radiation to line sources (need to use BEM to obtain the acoustic radiation efficiency). Boundaries include the actual surface of the rail, track slab and the car body, and others such as sound barriers, bridge decks. In the sound field, the radiation of the wheelset is equivalent to a point source, which means that the above-defined acoustic boundaries can affect the sound waves radiated by the wheelset, but cannot affect the sound power radiated by the wheelset. (6) In the above-defined sound field, the field point sound pressure due to unit radiated sound power of wheelset, unit rail vibration and different normalized slab vibration modes for different wave numbers are calculated separately to obtain the sound transfer function for different sound sources. This means that this transfer function can be reused to improve the computational efficiency if the acoustic boundary is not changed.

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(7) In the wheel/rail interaction part, parametric excitation, incoherence of left and right wheel/rail roughness and incoherence of wheel/rail roughness under front and rear wheelsets are considered.

2.3 Ways to Improve Computational Efficiency Using the above calculation method, there will be several aspects that will greatly affect the calculation efficiency. (1) This program uses the axisymmetric BEM to calculate the radiation of the rotating wheelsets, and the degree of freedom in the BEM solution process is three times the number of cross-sectional boundary nodes using this method. (2) This program uses the method given in the Ref [7]. to calculate the track vibration. Since the periodic discrete support of the track has to be considered, the vibration response under different period coefficient j needs to be calculated, and in addition, the lateral vibration of the track needs to be calculated, so the whole track vibration calculation process is also slow. (3) This program uses 2.5-D BEM to calculate the track acoustic radiation, while the rail, track plate, car body and other acoustic surface boundary are put together in the boundary integral equation, although the calculation efficiency is higher than the 3-D BEM modeling calculation, but its calculation efficiency is much lower than the traditional calculation method that usually only consider the rail, track plate or ballast surface acoustic boundary. In order to overcome the above three problems so that the program can have enough computational efficiency to solve engineering problems, the program does the following: Since the calculation of the above three parts takes a lot of time, it is required to avoid the repeated calculation of these three parts, so it is necessary to decouple these three parts from other parts of the program and form three independent calculation structures, whose positions in the program are shown in Fig. 1. Since the wheelset needs to be applied to the combined action of four forces, the radiated sound power of the wheelset can be written as: WW

[ ] ⎞ PV ,L (Ω) p V m,L (r ' , y ' , Ω)+PH,L (Ω) p H m,L (r ' , y ' , Ω) ' , y ' , Ω)+P ' , y ' , Ω) ⎟ ⎜ Re +PV ,R (Ω) p (r (Ω) p (r H,R V m,R H m,R ⎜ [ ] ⎟ ⎟ ⎜ PV ,L (Ω)υ V m,L (r ' , y ' , Ω) + PH,L (Ω)υ H m,L (r ' , y ' , Ω) ⎟ ⎜ ∞ { ⎜ Re ⎟ . ∑ +PV ,R (Ω)υ V m,R (r ' , y ' , Ω) + PH,R (Ω)υ H m,R (r ' , y ' , Ω) ⎜ [ ]⎟ = 2π ⎟r d┌ ⎜ ' ' ' ' ⎟ ⎜ PV ,L (Ω) p V m,L (r , y , Ω) + PH,L (Ω) p H m,L (r , y , Ω) m=−∞ ┌ ⎜ +Im ⎟ ⎜ (r ' , y ' , Ω) + PH,L (Ω) p H m,R (r ' , y ' , Ω) ⎟ ⎜ [ +PV,R (Ω) p V m,R ] ⎟ ' ' ' ' ⎠ ⎝ P (Ω)υ V m,L (r , y , Ω) + PH,L (Ω) p H m,L (r , y , Ω) Im V ,L +PV ,R (Ω)υ V m,R (r ' , y ' , Ω) + PH,R (Ω) p H m,R (r ' , y ' , Ω) ⎛

(1)

where, the subscript V and H respectively denotes vertical and lateral direction, the subscript L and R denotes left and right wheel/rail contact point respectively,

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(b)

Fig. 1 Comparison of predicted and measured noises of equivalent A-weighted sound pressure level at a 7.5 m and b 25 m measuring point

the subscript m denotes circumferential coefficient, P denotes wheel-track force magnitude, p and υ respectively denotes sound pressure magnitude and normal velocity magnitude of wheelset surface. Then PV,L denotes the vertical wheel-track force acting on the left wheel, and p V m,L denotes the m-order sound pressure of wheelset surface subject to unit vertical force at left wheel-rail contact point. Note that if only the left-hand side of the vertical roughness is given as input, these four wheel-rail forces are coherent, so Eq. (1) can be written as: | |2 | |2 WW = | PV,L (Ω)| WV,L (Ω) + | PH,L (Ω)| W H,L (Ω) | |2 | |2 + | PV,R (Ω)| WV,R (ω) + | PH,R (Ω)| W H,R (Ω) ( [ ] [ ] ) Re PV ,L (Ω) Re PH,L (Ω) [ ] [ ] WV H,L L1 (Ω) + +Im PV,L (Ω) Im PH,L (Ω) ( [ ] [ ] ) Re PV ,L (Ω) Im PH,L (Ω) [ ] [ ] WV H,L L2 (Ω) + −Re PH,L (Ω) Im PV ,L (Ω) ( [ ] [ ] ) Re PV ,R (Ω) Re PH,R (Ω) [ ] [ ] WV H,R R1 (Ω) + +Im PV,R (Ω) Im PH,R (Ω) ( [ ] [ ] ) Re PV ,R (Ω) Im PH,R (Ω) [ ] [ ] WV H,R R1 (Ω) + −Re PH,R (Ω) Im PV,R (Ω) ( [ ] [ ] ) Re PV ,L (Ω) Re PV,R (Ω) [ ] [ ] WV V,L R1 (Ω) + +Im PV,L (Ω) Im PV,R (Ω) ( [ ] [ ] ) Re PV ,L (Ω) Im PV,R (Ω) [ ] [ ] WV V,L R2 (Ω) + −Re PV,R (Ω) Im PV ,L (Ω)

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[ ] [ ] ) Re PV,L (Ω) Re PH,R (Ω) [ ] [ ] WV H,L R1 (Ω) + +Im PV,L (Ω) Im PH,R (Ω) ( [ ] [ ] ) Re PV,L (Ω) Im PH,R (Ω) [ ] [ ] WV H,L R2 (Ω) + −Re PH,R (Ω) Im PV ,L (Ω) ( [ ] [ ] ) Re PH,L (Ω) Re PV ,R (Ω) [ ] [ ] W H V,L R1 (Ω) + +Im PH,L (Ω) Im PV,R (Ω) ( [ ] [ ] ) Re PH,L (Ω) Im PV ,R (Ω) [ ] [ ] W H V,L R2 (Ω) + −Re PV,R (Ω) Im PH,L (Ω) ( [ ] [ ] ) Re PH,L (ω) Re PH,R (ω) [ ] [ ] W H H,L R1 (Ω) + +Im PH,L (ω) Im PH,R (ω) ( [ ] [ ] ) Re PH,L (Ω) Im PH,R (Ω) [ ] [ ] W H H,L R2 (Ω), + −Re PH,R (Ω) Im PH,L (Ω) (

(2)

where, the variables WV ,L (ω), W H,L (ω), WV,R (ω), W H,R (ω), etc. are only related to the wheelset, the superstructure of the wheelset and the rotation speed, have nothing to do with the parameters of roughness and track structure, so only these variables need to be calculated to achieve the decoupling of the wheelset vibration acoustic radiation and other parts. (1) According to the Ref. [7], the vibration of the left rail, as an example, can be written as: ⎛ ⎞ {∞ ∑ ∞ D ( ) ∑ ( ' ) 1 d ' d ⎝ e - iβx0 qv (β j )eiβ j x dβ j ⎠ei(Ω− jΩ0 )t , (3) qv x , t = PV,L (Ω) 2π j=−∞ d=1 −∞

where, superscript d denotes d-th wheelset, x ' is the coordinate in the direction of the track under the moving coordinate system with the vehicle, j is period coefficient, β j = β − 2πj/L, β is wavenumber, qv is the vibration magnitude of the rail at different wave numbers. qv is only related to the parameters of the track, and it can be known from Eq. (3) that only qv needs to be calculated to achieve the decoupling of track vibrations and other parts. (2) Since the rail is considered as beam in the vibration calculations and the geometric acoustic boundaries of the rails are to be considered in the acoustic radiation calculations, this means that the vertical surface vibration velocities of the rails in any cross section are equal, and the surface node vertical velocity for different wavenumber υR (β) = 1 are defined, then the normal velocity is NυR (β), where N converts the vertical velocity response into the normal velocity response. Taking NυR (β) into the 2.5D acoustic integral equation, the sound pressure at the rail surface and the spatial field point P0 (β) can be obtained.

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Taking into account Eq. (3), the field point sound pressure under the moving coordinate system due to wheel-rail forces P(β) can be written as: ⎛ ⎞ ) {∞ ∑ ∞ D ( ) ( ∑ ( ) iβ x ' ( ' ) 1 - iβ x0d d j ⎝ P x , t = PV,L (Ω) e qv (β j )P0 β j e dβ j ⎠ei Ω− jΩ0 t . 2π p=−∞

(4)

−∞ d=1

Obviously, P0 (β) is only related to the geometry of the acoustic boundary and the surface material impedance. Therefore, only P0 (β) needs to be calculated to decouple the acoustic transfer part from the rest of the program.

3 An Example Application of the Program Input a group of measured wheel-rail roughness into the prediction program, and compare the prediction results with the test results of standard points in the section where the measured roughness data comes from. The measured point is located at 1.2 m above the rail surface and 7.5 m, 25 m from the track center line. The vehicle operating speed range for the comparison is 160–350 km/h. The vehicle type is Chinese standard rolling stock, and the track type is CRTS-II ballastless track, the parameters of both can be found in the Ref. [6]. The comparison results are shown in Fig. 1. The measured and predicted values of the equivalent A-weighted sound pressure level are given in Fig. 1, and the fitted curves in the figure are fitted using the following equation. S P L = a log10 (V /160) + b

(5)

The value a represents the rate of increase of SPL with speed. As can be seen from Fig. 1, the SPL difference between the tested and predicted results is within 2 dB, and the trend of the two with speed is also relatively close, although the predicted values only include wheel-rail noise. To further discuss the reasonableness of the predicted results, Fig. 2 gives a comparison of the test results and the predicted results in the frequency domain at speed 160 and 350 km/h. The observation point is at 25 m from the track center line. As can be seen from Fig. 2, at a speed of 160 km/h, the band of 400 Hz is a clear dividing line, and when the frequency is higher than this frequency, the difference between the measured and predicted results is small, while as the speed rises, the difference begins to become significantly larger in the band of 400 and 500 Hz, and at a speed of 350 km/h, the difference between the two has changed from 0.7 and 0.9 dB(A) to 4.5 and 2.6 dB(A). In addition, the difference becomes larger in the lower frequency band. Figure 3 compares the fitting coefficients of predicted and measured sound pressure levels with speed for different frequency bands. As can be seen from the figure,

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(a)

(b)

Fig. 2 Comparison of predicted and measured 1/3 octave SPL at 25 m measuring point. a 160 km/ h; b 350 km/h

the fit coefficients a of the predicted and measured values in the range of 315–2000 Hz are in good agreement, and this frequency band is also the most important source of noise outside the vehicle; above 2000 Hz the trend is the same, but there are some differences between them. To explain this difference, it is first necessary to clarify why a increases with increasing frequency. Contact filtering will mainly filter the roughness corresponding to the high frequency band above 1000 Hz, and as the speed increases, the wavelength of the roughness corresponding to the fixed frequency will become longer, resulting in the contact filtering effect corresponding to the fixed frequency will weaken as the speed increases, and the higher the frequency the more significant this weaken effect is, resulting in a will increase with the increase of frequency. The existing contact filtering theory is based on the assumption of statics, and the contact filtering will obviously change under high-speed conditions. Therefore, this paper argues that the difference between the predicted and measured values comes from the applicability of the prediction model of contact filtering. The measured a-values are much higher than the predicted a-values at frequencies below 315 Hz, and here it is judged that the measured sound pressure in this frequency band is mainly contributed by other sources except wheel-rail noise. The above analysis can show that the prediction results of this program are relatively accurate.

4 Parts that Need Further Improvement (1) In the program, the vibration of the rail in the vertical and lateral directions are simulated as a single Timoshenko beam and a combined beams, respectively, without considering the coupling of vertical and transverse directions. Therefore, more accurate results can be obtained theoretically by using a 2.5D FEM with discrete support, and the relevant derivation has been given in the Ref. [7], which can also be well implemented in the program, but in the actual calculation

A Program for Predicting Wheel/Rail Rolling Noise from High-Speed …

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Fig. 3 The fit coefficients of the predicted and measured results

is faced with the computational inefficiency. The difficulties are mainly reflected in two aspects: (a) the increase of the degrees of freedom of vibration calculation; (b) the calculation of the acoustic transmission part of Part C cannot be decoupled from the vibration part, which makes it necessary to repeat the calculation for each acoustic transmission. Therefore, the program needs to further improve the 2.5D finite element method so that the vibration can be transformed into a superposition of multiple free waves (similar to modal superposition), so that only the cross-sectional vibration patterns of different free waves need to be calculated when calculating the vibration. (2) In the program, the noise radiation of the wheelset is simplified as a monopole source, but in TWINS program radial and axial vibrations are modeled as bipolar and monopole source, respectively, so the program needs to further differentiate the radiated sound power from radial and axial vibrations to improve the radiated noise calculation of the wheelset. Acknowledgements This work is funded by Natural Science Foundation Project of Jiangxi Province (20232BAB214095) and Science and Technology Research Project of Jiangxi Provincial Education Department (GJJ210644).

References 1. Track Wheel Interaction Noise Program (TWINS) User Manual (1996) 2. Thompson DJ, Fodiman P, Mahe H (1996) Experimental validation of the TWINS prediction program for rolling noise, Part II: results. J Sound Vib 193(1):137–147 3. Zhang XY, Squicciarinni G, Thompson DJ (2016) Sound radiation of a railway rail in close proximity to the ground. J Sound Vib 362:111–124 4. Zhang XY, Thompson DJ, Squicciarinni G (2016) Sound radiation of railway sleepers. J Sound Vib 369:178–194

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5. Zhang XY, Thompson DJ, Squicciarinni G, Jeong H (2017) The effects of ballast on the sound radiation from railway track. J Sound Vib 399:137–150 6. Sheng X, Cheng G, Thompson DJ (2020) Modelling wheel/rail rolling noise for a high-speed train running along an infinitely long periodic slab track. J Acoust Soc Am 148(1):174–190 7. Sheng X, Zhong T, Liu Y (2017) Vibration and sound radiation of slab high-speed railway tracks subject to a moving harmonic load. J Sound Vib 395:160–186 8. Sheng X, Liu Y, Zhou X (2016) The response of a high-speed train wheel to a harmonic wheel-rail force. J Phys Conf Ser 744:012145 9. Cheng G, He HP, Han J, Sheng X (2020) An investigation into the effects of modelling assumptions on sound power radiated from a high-speed train wheelset. J Sound Vib 495:115910

Strong Rail Damper Development Wilson Ho, Ron Wong, Max Yiu, Ghazaleh Soltanieh, Marco Ip, and Yi-Qing Ni

Abstract Rail dampers typically provide 3–4 dB(A) noise reduction, but occasionally 5–10 dB(A) for lightly damped rails on soft fasteners (Ho et al. in Noise and vibration mitigation for rail transportation systems. Springer, pp 89–96, 2012; Thompson et al. in Appl Acoust 68:43–57, 2007; Lo et al. in Noise and vibration mitigation for rail transportation systems. Springer, pp 638–645, 2019; Ho et al. in Noise and vibration mitigation for rail transportation systems. Springer, pp 654–661, 2019; Ho et al. in Noise reduction effect by rail damper on single rail, 2021 [1–5]). For retrofit applications, rail dampers often perform below their capacities due to poor connection at the rubber/metal interface due to uncontrollable rusted surface and rail profile tolerance. The rubber/metal interface is soft to maximize the contact area, but is not so soft that it becomes an isolator rather than a vibration absorber. Rigid Contact TMD (RCTMD) rail damper uses metal-to-metal mounting plates (Ho et al. in Noise and vibration mitigation for rail transportation systems. Springer, pp 89–96, 2012; Lo et al. in Noise and vibration mitigation for rail transportation systems. Springer, pp 638–645, 2019; Ho et al. in Noise and vibration mitigation for rail transportation systems. Springer, pp 654–661, 2019; Ho et al. in Noise reduction effect by rail damper on single rail, 2021; Ho et al. in Tuned mass damper design optimization using FEA, 2014; Tam et al. in Noise and vibration mitigation for rail transportation systems. Springer, pp 585–593, 2016; Ho et al. in Tuned mass damper for rail noise and corrugation control. Proceeding of acoustics, 2012; Ho and Wong in Tuned mass damper for rail noise and corrugation control. Proceeding of the 5th cross-strait acoustical conferences, 2012; Ho et al. in Reducing rail corrugation growth by tuned mass damper, 2013; Ho et al. in Analytical study on railway corrugation growth control by tuned mass damper, 2014; Ho et al. in Suppression of corrugation growth by rail damper, 2021; Ho et al. in Groundborne noise reduction by rail damper effect W. Ho (B) · R. Wong · M. Yiu Jabez Innovation Limited, Unit 601, Block A, Shatin Industrial Centre, Sha Tin, N.T., Hong Kong SAR, China e-mail: [email protected] G. Soltanieh · M. Ip · Y.-Q. Ni Hong Kong Polytechnic University, Hong Kong Branch of National Rail Transit Electrification and Automation Engineering Technology Research Center, Hong Kong SAR, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_39

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on P2 resonance 2021; Ho et al. in TMD tunable for railway groundborne noise control, 2021 [1, 3–14]) that repositions the rubber/metal interface into a flat surface aligned perpendicular to the rails for tolerance control. Multiple RCTMDs increase the rubber/metal interface area. With multi-frequency tunable TMD customized for individual rails at curve, it reduces corrugation growth rate by 50–90% (Ho et al. in Noise and vibration mitigation for rail transportation systems. Springer, pp 89–96, 2012; Ho et al. in Noise reduction effect by rail damper on single rail, 2021; Ho et al. in Proceeding of acoustics, 2012; Ho and Wong, Proceeding of the 5th crossstrait acoustical conferences, 2012; Ho et al. in Reducing rail corrugation growth by tuned mass damper, 2013; Ho et al. in Analytical study on railway corrugation growth control by tuned mass damper, 2014; Ho et al. in Suppression of corrugation growth by rail damper, 2021 [1, 5, 8–12]), and all curve track corrugations are suppressed. Single-frequency RCTMD (550 Hz, lateral pin-pin resonance) achieved the – 4 dB(A) project requirement with 1 RCTMD per space on low rail, where RCTMD is short-length design for fitting 2 RCTMDs per space for contingency (Ho et al. in Noise reduction effect by rail damper on single rail, 2021 [5]). When RCTMD is tuned to rail P2 resonance (47 Hz), the concrete floor vibration level is reduced by 6–8 dB(A) (Ho et al. in Groundborne noise reduction by rail damper effect on P2 resonance 2021; Ho et al. in TMD tunable for railway groundborne noise control, 2021 [13, 14]) under a laboratory setting with a 6.3 m rail sitting on resilient fasteners (~17 kN/mm) with a ~ 450 kg steel block to simulate the weight of a half wheelset on rail. It is a potential retrofit measure to mitigate railway groundborne noise caused P2 resonance. Around the world, train speed restrictions are occasionally adopted to reduce noise. Such speed restrictions will be unnecessary when reliable dampers performances are shown to the railway operators. Keywords Retrofit mitigations · Rail Damper · Groundborne noise · Corrugation

1 Rail Dampers as Retrofit Railway Noise Mitigations Railway noise and vibration often cause dissatisfaction and complaints in residential area. Rail dampers, as retrofit solution to noise issues, have been developed in many countries, such as SilentTrack, Vossloh, Schey & Veith and STRAIL [15–19]. Rail dampers often perform below their capacities due to poor connection to the rail in retrofit applications. A good connection at the rubber/metal interface is difficult to achieve due to uncontrollable rusted surfaces and rail profile tolerances. To cater such situation, a soft rubber/metal interface is needed to maximize the contact area. However, a soft interface would also act as a vibration isolator in addition to vibration absorber which could diminish their damping effect. Therefore, the actual interface cannot be too soft (Fig. 1).

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Fig. 1 Commonly use rail dampers. Left: SilentTrack [15]. Right: Schey & Veith [16]

1.1 Rail Interface by Rigid-Contact Tuned Mass Damper (RCTMD) In contrast, RCTMD use a rigid mounting plate to provide strong mounting force (withstand ~ 1 ton pulling force) to connect the rail to heavy TMD oscillators [7–10]. Its performance is summarized in Table 1. Over the past decade, various versions of RCTMD have been developed for different rail conditions. They all share basically the same principles: (i) Rigid-Contact Interface by metal-to-metal direct contact at the interface (ii) Tuned Mass Damper using shear stiffness of resilient layer (Not compression stiffness) (iii) Each TMD oscillator responses to vertical and lateral vibration at same tuned frequency (iv) Easily tunable for individual site and rail to maximize damping effect.

1.2 3-point Contact Mounting Plate In Fig. 2, the latest version of RCTMD uses 3-point-contact mounting plates rearrange the rubber/metal interface onto a flat surface that aligned perpendicularly to the rails for tolerance control. The 3-point-contact points at rail web, foot tip and rail underside provide stable and rigid mounting interface for transmitting strong damping force.

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Table 1 Noise and vibration reduction of RCTMD Site

Vib reduction at peak freq., dB(A)

Noise reduction, dB(A)

Remark

Hong Kong, 2010 [1]

11.4 (V), 13.5 (L)

3.5

Microphone at walkway in curve tunnel ~ 300 m radius with booted sleepers

Hong Kong, 2016

11.6 (V), 16.2 (L)

4.7

NSR at 25 m from the rail

Hong Kong, 2017

8.1 (V), 19.1 (L)

7

5 years long-term noise reduction

Zurich, 2018 [3]

21.2 (V), 13.5 (L)

3.7–4.2

Light rail, asymmetric grooved rail

London (test), 2019

9.9 (V), 5.4 (L)

1.7*

Microphone inside tunnel at ~ 2.5 m from high rail and ~ 1.1 m low rail

Hong Kong, 2020 [4, 5]

10.1 (V), 21.5 (L)

6.4–8.6** (Saloon Noise)

Single installation on LR and ¼ installation on HR

* The

London test was initially used only for vibration tests. 5 dampers were installed on high rail and no damper on low rail. The noise reduction of 1.7 dB(A) was mainly contributed by ~ 4 dB reduction at 800 Hz and ~ 3 dB at 630 Hz, which are clearly in spectrum and repeatable in all passby data **Saloon noise reduction of 6.4–8.6 dB(A) refers to 2–4 months after grinding as a result of vibration absorption (~4.5 dB(A)) and corrugation growth reduction (~2–4 dB(A)) by RCTMD, where the corrugation growth rate was slow down by 90% (V) for vertical, (L) for lateral

Fig. 2 Latest version of RCTMD (left). RCTMD installed in site (right)

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1.3 Precise Rubber/Metal Interface for Vertical and Lateral TMD The rubber/metal interface is where vibration energy is mainly dissipated for all rail dampers. Slight mismatch at the interface would reduce the effective stiffness, shift down TMD resonance frequency and result in missing the required damping region. Relocating the rubber/metal interface from rail surface to mounting plates, which also aligns vertically, can easily control the contact quality. Resilient layers are placed on both sides of the mounting plate to couple with the cylindrical oscillators. Each oscillator provides TMD effect, which can response to vertical and lateral rail vibrations at the same tuned frequency.

1.4 Easily Tunable for Individual Site to Maximize Damping Effect Multiple mounting plates increase the number of rubber/metal interface. It allows multi-frequency tuning customized for individual sites. Resilient material at the rubber/metal interface are custom-made (stiffness and thickness) for tunable frequency between 300 and 1500 Hz.

1.5 Modular Design The length of the latest RCTMD is between 100 and 150 mm, and the specific length can be customized according to individual sites. One to three sets of RCTMD can be installed in the rail space between 2 fasteners. Generally, standard installation (1 RCTMD per space) is more than sufficient to make the rail quieter than other noise sources. In many cases, half installation (1 RCTMD per 2 spaces) is sufficient to provide 3 dB(A) noise reduction if cost saving is needed [4].

2 Site Data of Damper Performance RCTMD has shown superior noise and vibration reduction, as well as corrugation growth suppression [1, 4, 5, 10, 12], but it does not provide good Track Decay Rate (TDR). It is believed that TDR measurements using hammer excitation can only measure the immediate viscous damping effect but underrates TMD reactive damping force. TMD takes milliseconds to generate reactive damping force as a response to rail vibration. To illustrate, the RCTMD performance of 2 projects (London 2019 and Hong Kong 2020) are discussed below.

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2.1 Vibration and Noise Reduction Figure 3 shows the vibration and noise spectrum in London test. The track has a curvature of 400 m. The rail type is UIC-56E1 sitting on very soft baseplates (stiffness may be lower than 10 kN/mm). A short section of high rail was installed with 5 sets of RCTMDs while no damper was installed on low rail. Vibration resonance peaks at ~ 400 and 800 Hz are reduced by ~ 10 dB. Tunnel noise peak at 800 Hz was reduced by ~ 4 dB, and 1.7 dB(A) overall reduction at microphone ~ 1.1 m from the low rail and ~ 2.5 m from the high rail (microphone cannot be placed next to the high rail due to safety concern). In Hong Kong 2020 project, a 200 m track has a curvature of 300 m with UIC-60 rail siting on resilient fasteners (< 20 kN/mm). A short-length RCTMD was designed for fitting 2 RCTMDs per the spacing between fasteners, and tuned to 550 Hz to reduce lateral pin-pin resonance and suppress corrugation growth at low rail. The 200 m track is capable to accommodate more than 1300 RCTMDs for contingency if higher noise reduction is required. The – 4 dB(A) project requirement was already achieved by damper standard installation on low rail only (1 RCTMD per space). In order to fulfill the project requirement of “dampers installed on both rails”, the high rail was also installed with 1 RCTMD per 4 spacings. Total of ~ 460 RCTMDs were installed on the 200 m track which is only ~ 1/3 of capacity of this track. Figure 4 shows the relative vibration of rail web, foot tip and under rail of the lower rail, and the saloon noise level before and after installation of RCTMD. The index ‘a’ and ‘b’ refers to the 2nd and 4th month of the grinding cycle. Saloon noise reduction of 6.4–8.6 dB(A) was achieved at 2–4 months after grinding as a result of vibration absorption (~4.5 dB(A)) and corrugation growth reduction (~2–4 dB(A)) by RCTMD, where the corrugation growth rate was slow down by 90% [5].

Fig. 3 Vibration and noise spectrum for London (2019) 5 m trial

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Fig. 4 Vibration and noise spectrum for Hong Kong 2020 project. *The index ‘a’ and ‘b’ refers to the 2nd and 4th month of the grinding cycle

2.2 Suppression of Corrugation Growth The RCTMD has been shown to suppress corrugation growth [5, 8–12]. In the Hong Kong 2020 project, roughness data are measured for the 2 grinding cycles. In Fig. 5, the rail roughness has dominant peaks at 332 and 528 Hz, where the 528 Hz peak corrugation is associated with lateral pin-pin resonance. The 528 Hz corrugation has a growth rate of ~ 1.2 µm/month before the installation of RCTMD, which is reduced by 90%, to 0.12 µm/month after the installation of RCTMD. The corrugation spectrum (332–665 Hz, roughly within ± 20% TMD tuned frequency), also shows a growth rate reduction of 50–90%. This study has demonstrated the severity of lateral pin-pin resonance in developing rail corrugation, and how the rail dampers can suppress the corrugation growth with strong TMD force by adopting rigid mounting interface.

2.3 Track Decay Rate (TDR)—Vibration Decay in Distance In Fig. 6, RCTMD improves the TDR in 315–630 Hz significantly for both vertical and lateral directions after single RCTMD installation on the low rail. The TSI target is satisfied in lateral TDR but not in vertical TDR at 630 Hz and below. Further improvement with 2 RCTMDs per space can be retrofitted if required. On the other hand, TDR may not be a good indicator of noise and vibration damping performance for a continuous vibration source of wheel/rail interaction since the

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Fig. 5 Rail roughness measurement for lower rail before and after installation of dampers

Fig. 6 Vertical and lateral TDR before and after single RCTMD installation on low rail

current TDR measures the decay of impulse vibrations, not continuous vibrations. TMD mechanism provides amplified damping force with a 90° phase lag oscillation to counteract continuous vibrations excitation, but is not suitable for impulse vibrations because the TMD reactive damping force has not yet been generated in the first vibration impulse.

2.4 Vibration Decay Rate in Time In addition to standard TDR analysis, vibration decay rate in time domain provides another perspective to analyze the damping characteristics of rail/fasteners system.

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Fig. 7 Vibration time history of passby, with and without dampers

Figure 7 shows the 500 Hz (1/3 Octave) vibration time history. The 16 peaks correspond to moments when 16 bogies are running on the measurement point, while the 8 troughs correspond to moment when middle points of 8 train cars are above the measurement point. With RCTMD installed, rail vibrations were reduced by ~ 10 dB at the peaks, and ~ 30 dB at the troughs, resulting a ~ 13 dB average reduction. Vibration decay is rapid when the excitation source is few meters away. Rail vibration is localized at the bogie locations, and vibration accumulation from multiple wheels is ceased. Figure 8 is enlargement of a half second (14.6–15.1 s) in Fig. 7. It shows the vibration decay after excitation by the last bogie. Hammer impact rail vibration time history is also included for easy comparison. Without RCTMD, there are some fluctuations due to accumulation of vibration reflections from fasteners, which slows down the decay significantly. Using RCTMD to stop accumulation of small vibration reflections from fasteners, rail pin-pin resonance is difficult to develop. Moreover, the vibration decay has an initial drop of ~ 15 dB before any vibration reflection from fasteners. This initial drop is increased to ~ 50 dB by RCTMD, where vibration reflections from fasteners are mostly eliminated. It should be noted that RCTMD is able to stop accumulation of rail vibration of atomic scale magnitude (~0.1 nm rms displacement).

3 Potential Retrofit Mitigation for Groundborne Noise RCTMD is able to be tuned to very low frequency to match P2 resonance of a rail. In a laboratory experiment, a 6.3 m rail sitting on high resilient fasteners at 0.6 m spacing, with a 450 kg steel block placed on a rail running surface to simulate the

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Fig. 8 Vibration time history of passby, with and without dampers

mass of a half wheelset, the P2 resonance (~47 Hz) at the laboratory concrete floor is reduced by 6–8 dB [13, 14]. It is a potential retrofit measure to mitigate railway groundborne noise caused P2 resonance.

4 Conclusion For retrofitting rail dampers to rusted rails, RCTMD uses 3-point-contact mounting plates to provide rigid interface that facilitates efficient transmission and dissipation of rail vibration by TMD mechanism, independent of the uncontrolled conditions of the rusted rail surface. The mounting plates align vertically, for relocating the rubber/ metal interface to a flat vertical surface for easy control of the effective stiffness for TMD mechanism. The 3-point contact at rail web, foot tip and rail underneath provide stable and rigid retrofit mounting. Multiple RCTMDs can be fitted into single sleeper-to-sleeper spacing to allow double installation of rail damper when stronger damping is required. With multifrequency TMD customized for individual sites, it provides best fit TMD damping for individual sites. In addition to noise and vibration reduction, RCTMD also reduces corrugation growth rate at curved track by 50–90% [5, 8–14]. The corrugation suppression is particularly effective at rails sitting on resilient fasteners. In laboratory experiment of railway P2 resonance groundborne noise, RCTMD reduced rail vibration as well as floor vibration by 6–8 dB [13, 14], when the TMD is tuned to P2 resonance. It is a potential retrofit measure to mitigate railway groundborne noise.

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References 1. Ho W, Wong B, England D (2012) Tuned mass damper for rail noise control. In: Noise and vibration mitigation for rail transportation systems. Springer, pp 89–96 2. Thompson DJ, Jones CJC, Waters TP, Farrington D (2007) A tuned damping device for reducing noise from railway track. Appl Acoust 68(1):43–57 3. Lo S, Ho W, Cheung C (2019) Rail damper composed of tuned mass damper and constrained layer adopted in non-symmetric rail. In: Noise and vibration mitigation for rail transportation systems, vol 150. Springer, pp 638–645 4. Ho W, Cheung C, Cheng M, Lin L (2019) Half Installation of rail dampers. In: Noise and vibration mitigation for rail transportation systems, vol 150. Springer, pp 654–661 5. Ho W, Soltanieh G, Wong P, Wong W, Ip M, Tse D (2021) Noise reduction effect by rail damper on single rail. In: Proceeding of the ICSV 27, July 2021 6. Ho W, Wong B, Tam P, Cai T (2014) Tuned mass damper design optimization using FEA. In: The 21st international congress on sound and vibration (ICSV22) 7. Tam P, Leung D, Mak C, Ho W, Cai T (2016) Development of orthogonal resilient materials for Tuned Mass Damper. In: Noise and vibration mitigation for rail transportation systems, vol 139. Springer, pp 585–593 8. Ho W, Wong B, England D, Pang A (2012) Tuned mass damper for rail noise and corrugation control. In: Proceeding of acoustics 9. Ho W, Wong B (2012) Tuned mass damper for rail noise and corrugation control. In: Proceeding of the 5th cross-strait acoustical conferences 10. Ho W, Wong B, Tsui D, Kong C (2013) Reducing rail corrugation growth by tuned mass damper. In: Proceedings of 11th international workshop on railway noise (IWRN11) 11. Ho W, Ting C, Wong B (2014) Analytical study on railway corrugation growth control by tuned mass damper. In: Proceeding of 21th international congress on sound and vibration 12. Ho W, Tse D, Wong P, Wong W, Ip M, Soltanieh G (2021) Suppression of corrugation growth by rail damper. In: Proceeding of the ICSV 27, July 2021 13. Ho W, Ip M, Soltanieh G, Wong W, Tse D (2021) Groundborne noise reduction by rail damper effect on P2 resonance. In: Proceeding of the ICSV 27, July 2021 14. Ho W, Soltanieh G, Wong W (2021) TMD tunable for railway groundborne noise control. In: Proceeding of the internoise 2021, Aug 2021 15. SilentTrack (2014) Reducing railway noise, TATA STEEL—Product brochure 16. Vossloh Fastening Systems Rail web damping Presentation SZDC (2010) 17. STRAILastic_A. The noise-absorber system—Product brochure 18. Scossa-Romano E, Oertli J (2012) Rail dampers, acoustic rail grinding, low height noise barriers. A report on the state of the art. Prepared for International Union of Railways 19. Reducing Railway Noise Pollution. Study, European Parliament. Directorate General for Internal Policies Policy Department B: Structural and Cohesion Policies Transport and Tourism (2012)

Inclined Plane TMD with Independent Vertical and Lateral Frequency Vibration Control Marco Ip, Yi-Qing Ni, Ghazaleh Soltanieh, Wilson Ho, and Max Yiu

Abstract Rail damper is a retrofit solution for excessive noise and vibration from the rail. Rigid Contact Tuned Mass Rail Damper (RCTMD), a new type of rail damper, can be tuned to rail resonance frequency for specific site requirements to address noise issues stemming from rail courrgation, rail pin-pin resonance (vertical and lateral directions) and P2 resonance. Current RCTMD could only be tuned to one frequency per oscillator. Multi-frequency vibration reduction requires extra oscillators. If additional oscillators are required, the project would become more costly, heavier, space consuming, and less overall damping efficient, which would have negative implications to the manufacturers and the users. This paper aims to develop a tuned mass damper that could simultaneously be tuned to both rail vertical and lateral pin-pin resonance ( ~550Hz and ~1000Hz, respectively) at the same oscillator. Preliminary laboratory tests are performed with the patented inclined plane tuned mass damper. Vertical-to-lateral resonance frequency ratio of 1.2 is achieved. Further improvement will be made to achieve the target ~1000Hz and ~550Hz in vertical and lateral direction. Keywords Rail vibration mitigation · Rail damper · Tuned mass damping

M. Ip (B) · Y.-Q. Ni · G. Soltanieh The Hong Kong Polytechnic University, Hong Kong Branch of National Rail Transit Electrification and Automation Engineering Technology Research Center, Hong Kong SAR, China e-mail: [email protected] W. Ho Wilson Acoustics Limited, Unit 601, Block A, Shatin Industrial Centre, Sha Tin, N.T., Hong Kong SAR, China M. Yiu Jabez Innovation Limited, Unit 106, Block A, Shatin Industrial Centre, Sha Tin, N.T., Hong Kong SAR, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_40

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1 Background The dominant rail air-borne noise radiates from rail vibration at its pin-pin resonance frequency of vertical and lateral directions. The vertical pin-pin resonance frequency of the UIC60 rail on ~ 600 mm fastener spacing, vertical and lateral pin-pin resonance are ~ 1000 Hz and ~ 550 Hz, respectively [1]. The lateral pin-pin resonance contributes to the formation of rail surface corrugation in a curved track [2]. The surface corrugation causes curve-squeal when the train is passing the sharply curved track. Tuned mass damper (TMD) is commonly used as a retrofit solution to railway noise and vibration [3, 4]. This type of TMD could be tuned to the either vertical or lateral resonance frequency for each oscillator to fulfill individual site requirements. Extra oscillator is required for other targeted resonance frequencies (Fig. 1). If additional oscillators are required, the project would become more costly, heavier, space consuming, and less overall damping efficient, which would have negative implications to the manufacturers and the users. Rubber isolators mechanical analysis model with deformation for seismic isolated structure is well studied in the last 40 years. In compliance with the incompressibility of rubber. Lindley [5] conducted a model for rubber isolator’s vertical stiffness. Koh and Kelly [6] developed a mechanical analysis model for rubber bearings under deformation. Liu and He [7] provided a complete study on vertical stiffness and deformation of rubber isolators in compression and compression-shear states. The analysis of stiffness and hence frequencies of rubber resilient material undergo compression and shear deformation for TMD will follow the approach as above. To mitigate the distinctive vertical and lateral frequencies with one oscillator, a new tuned mass damper (TMD) design is trial. By elevating the rubber resilient layer with certain angle from propagation plane of rail, both the offset compression stiffness Kv and lateral stiffness KH are contributed to the stiffness against vertical vibration and therefore provides two tuning frequencies in vertical and lateral directions at the same time (Fig. 2).

Front view

Side view

Fig. 1 a Current TMD configuration with resilient layer pressure distribute uniformly (front view). b Current TMD configuration with resilient layer pressure distribute uniformly (side view)

Fig. 2 a Proposed TMD configuration with resilient layer having different compression with inclined plate (front view). b Proposed TMD configuration with resilient layer have different compression with inclined plate (side view)

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2 Effective Stiffness Evaluation of Resilient Plate 2.1 Resilient Layer Under Pure Vertical Compression Consider the variation of rubber elastomer’s bulk change which is affected by perpendicular compression load on rubber itself. In accordance with incompressibility assumption of rubber, the vertical stiffness K v of a rubber with Tr = ntr as the total thickness of rubber with n-layers under pure vertical compression is: K vo =

Ec A ntr

(1)

where E c is the compression modulus (1/E c ≈ 1/6G S 2 + 4/3K ) by Chalhoub et al. [6]; G is the shear modulus; K is the bulk modulus; S is the shape factor for circular pad (S = (Do − Di )/4tr ); D is the rubber elastomer’s diameter; A is the contact area.

2.2 Impact on Vertical Stiffness Under Lateral Displacement To resemble the derivation of expression for the reduction in vertical and lateral displacement and subsequently the amended vertical stiffness of rubber elastomer under the exertion of both vertical load and lateral force, an illustrative two-spring mechanical model introduced by Koh and Kelly is shown in the following. The two-spring mechanical model in Fig. 3 is introduced by Koh and Kelly [8] a composition of a linear spring with stiffness K H , rotational spring with stiffness K θ , a rigid column on a supporting pin under perpendicular load P, and lateral force F H . With those force acting on the rubber elastomer, the rubber elastomer experiences vertical deformation and lateral offset δv and Δ respectively through geometry relation with height h and deformation of linear spring s. Δ = s cos(θ) + h sin(θ)

(2)

δv = s sin(θ) + h[1 − cos(θ)]

(3)

which is further approximated to the following relations by assuming sin(θ) ≈ θ under small rotation and expanding cos(θ) with Taylor series up to the second term in the relation of δv , Δ = s + hθ δv = sθ +

hθ2 2

(4)

(5)

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P

Δ

δv

FH θ y'

Rigid

h s x'

y

KH

x

Pin

Kθ

Fig. 3 2 spring model undergoes vertical and lateral offset

Also, the equilibrium equations of force and moment under small rotations can be presented as ∑ Fx ' : −Pθ + K H s = FH

(6)

∑ M pin : (K θ − Ph)θ − Ps = FH h

(7)

To obtain the expression of rotational spring K θ , Euler buckling load of a column (PE = π 2 E Is / h 2 ) is applied such that K θ = PE h. Also, with K H = G A/ h, the equilibrium equations can be expressed as: GA + P G A(PE − P) − P 2

(8)

s PE = FH h G A(PE − P) − P 2

(9)

θ = FH

With subjecting FH by substituting (8) and (9) into (5), δv can be expressed as: δv =

Δ2 (G A + P)(G A + P + 2PE ) 2h (G A + P + PE )2

(10)

The expression could be further simplified by reasonably assuming G A 94 dBA LAmax and > 104 dBA LAmax event categories. The choice of the noise thresholds used for these categories is arbitrary though consistent with previous studies undertaken in NSW. Further categorization of high noise events (exceeding > 94 dBA LAmax (Up) and > 100 dBA LAmax (Down)) is provided in Table 3. All presented results are compared between the monitoring years (2021 and 2022) to highlight the changes in measured noise levels and the incidences of squeal, flanging and other noise in the study area. The results highlight some interesting and noticeable differences between the monitoring years: • In 2022, at all measured locations, a significant drop in noise levels occurs across the central four days of the monitoring period. This coincides with the Easter long weekend and is consistent between the Up and Down tracks. • Some tracks and sites also show significant differences between the loudest and quietest 24-h periods. The comparative measurements in 2022 allow for a forensic analysis of factors contributing to these changes. • High noise events (flanging and other) marginally decrease on the Up track at Site A while squeal marginally increases. On the Down track, squeal and flanging increase while lower frequency (corrugation induced) noise significantly decreases. • High noise events across all categories increase at Site B. The distribution is similar between the categories, with a slightly higher overall increase in high noise events on the Down track. • High noise events at Site C Up track have significantly decreased, with a large reduction in flanging. On the Down track, there is a slight reduction in flanging events as well.

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Table 2 High noise classification Year/ site

Up track trains only

Down track trains only

Total

> 94 dBA LAmax

> 104 dBA LAmax

> 114 dBA LAmax

% high noise (%)

Total

> 100 dBA LAmax

> 110 dBA LAmax

> 120 dBA LAmax

% high noise (%)

2021 A

1185

184

1

0

16

1149

645

3

0

56

2022 A

1637

217

10

0

13

1641

542

60

0

33

−2

Change A

− 23

2021 B

1190

148

0

0

12

1155

76

10

0

7

2022 B

1589

430

7

0

27

1591

471

39

2

30

+ 15

Change B

+ 23

2021 C

1266

825

8

0

65

1229

247

8

0

20

2022 C

1630

392

1

0

24

1632

210

4

0

13

Change C

− 41

−7

Note The change values are calculated based on the raw, non-rounded values and therefore, may appear to be off by 1%

The reasons for these differences and changes (including the four ‘quieter days’ across the 2022 monitoring period) are further investigated below.

5 Investigation of Factors Common to All Sites 5.1 Train Set, Fleet Mix and Passenger Loading Train set, fleet mix and passenger loadings were similar across the two monitoring periods and between days within the monitoring periods. Therefore, these were not considered to provide an explanation for the large differences between the years or between the quieter and louder days.

5.2 Unique Consists While overall fleet and train set mix was similar, it was noted that in 2021 only two of the seven monitoring days were during weekends (slightly lower train volumes)

+5

15

+8

−2

12

27

Change A

2021 B

2022 B

16

−7

24

− 41

2021 C

2022 C

Change C

23

+ 15

65

Change B

7

8

13

3

16

2022 A

> 94 dBA With squeal LAma (%) (%)

Up track trains only

2021 A

Year/site

Table 3 High noise categorization

− 24

23

47

+8

18

11

−2

12

14

With flanging (%)

− 10

1

10

+5

7

2

−2

2

3

With sig. ≤ 1 kHz component (%)

−3

2

5

0

1

1

−3

1

4

Above threshold, not in other bins (%)

−7

13

20

23

30

7

− 23

33

56

> 100 dBA LAma (%)

+1

4

2

+9

14

4

+8

11

3

With squeal (%)

Down track trains only

−1

9

10

+ 12

15

3

+5

26

20

With flanging (%)

0

7

7

+5

6

1

− 34

16

50

With sig. ≤ 1 kHz component (%)

+2

3

1

+ 12

15

3

0

9

9

Above threshold, not in other bins (%)

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while in 2022, the quieter four days coincided with the Easter long weekend (i.e. trains were running to weekend train timetables/lower volumes). Unique train consists (leading-trailing wagons) were extracted from passby data at one location (Down track at Site A). Of the 542 high noise events on the Down track, 348 happened in the first three days while 73 happened over the next four days. The number of unique consists involved in these high noise events reduced from 112 (first three days) to 40 (Easter long weekend). The high noise events were mapped to consists which operated across both the initial three days and the Easter long weekend to assess if the reductions in noise levels were due to certain consists not operating over the quieter period. The comparison found that high noise events were independent of consists—the same consists which had a high percentage of high noise events during the first three days were significantly quieter over the Easter long weekend. Therefore, the reduction in noise levels across the four quieter days could not be attributed to changes in consists.

5.3 Meteorology Relative humidity and temperature data over the monitoring periods was overlaid, as both periods started on a Tuesday in the same month one year apart. The data was similar and was not considered to account for the large differences observed across the days in 2022.

5.4 Train Speeds Train speeds were extracted from passby durations, with a slight clip to account for the rise and fall times. These were considered to be a reasonable approximation of the exact train speeds. The relationship between speed and passby LAmax noise levels at all sites is shown in Fig. 2. Similar trends are also present for LAeq noise levels- shown for Site C in Fig. 2. The 2021 data is shown in color while the 2022 data is overlaid in black. Theoretical curve balance speeds are shown as red lines on the plots. Noise levels appear to be strongly correlated with speed. At some locations and tracks, noise levels increase significantly below balance speed (i.e. cant excess conditions). This has been previously discussed in literature elsewhere and is attributed to a more acute Angle of Attack under these conditions. However, at other locations, the transition point appears to be significantly above the balance speed. Furthermore, At Site A (Up and Down track) and Site C (Down track), the shape of the transition appears to be sharper than at the other locations. For the purposes of quantifying the change in noise levels associated with this transition, these transition speeds are referred to as ‘threshold speeds’. The following threshold speeds have been chosen:

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Fig. 2 Speed (kph) versus LAmax trends at all sites and speed (kph) versus LAeq (site C, bottom right)

• Site A: 46/47 kph (Up/Dn track). Both speeds are significantly above balance speeds • Site B: 38/37 kph (Up/Dn track). Both speeds are equal to the balance speed • Site C: 46/40 (Up/Dn track). Speeds on the Up track are higher than the balance speed while speeds on the Down track are equal to the balance speed. Linear averages of maximum noise levels have been calculated for passbys below and above the threshold speed. The results are shown in Fig. 3 and indicate that, with high percentages of passbys below the threshold speed, average maximum levels for these passbys also increase, indicating tendencies towards greater flanging or squeal events.

Fig. 3 Percentage of passbys below threshold speed versus average maximum passby noise level for these passbys, dBA

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Furthermore, average maximum noise levels above and below the threshold speeds were compared. An example is shown in Table 4. The quieter monitoring periods aligns with a significantly lower number of passbys below threshold speeds. At some sites and tracks, average maximum noise levels from passbys below threshold speeds is up to 7 dB higher than passbys above threshold speeds. These results highlight that while the severity of the high noise squeal and flanging events may be probabilistic, at this site there is a greater probability of encountering these events at lower speeds.

5.5 Rail Friction Friction measurements were undertaken in 2021 and not repeated in 2022. Based on electronic data feeds, both Top of Rail friction modifiers and gauge face lubricators were operating normally throughout the monitoring period except at one location (Site A Up track) on the first day of the 2022 monitoring period. The significantly higher levels (95 dBA, refer to Table 4 results for 12/04/2022), even for passbys above the threshold speed (when compared to the 2021 data) may be due to this reason.

5.6 Rail Roughness The effect of rail roughness is noticeable in the percentage of high noise events with significant frequency components below 1 kHz. At Site A, on the Down track, no difference between levels above and below the threshold speed was found in 2021. This is attributed to the high noise events mostly comprising of corrugation induced noise. Significant reductions in peak 50 mm roughness wavelength on the near (Down, low) rail in 2022 were attributed as the cause for reducing the percentage of high noise events associated with this category. At other locations, roughness levels have also slightly improved though the effects are difficult to isolate from changes to rail profiles as well.

5.7 Rail Profiles Rail profiles are designed to suit the wheel profiles and the rolling stock navigating the track. Rail grinding templates, provided in Australian Rail Standards [5] have been designed to improve wheel and rail interaction and contact band widths. The templates used in the study area are H1 for high rail, ML1 for low rails, and MT for tangent rails. For passenger traffic, the grinding templates are designed to provide low and tangent rails with a contact band width of 18–30 mm, and conformal contact

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Table 4 Site A up track—daily comparison 2021 versus 2022 Day

Average speed, kph

Passbys below (≤) threshold speed

LAmax , passby linear average, dBA

Difference

Raw

Percentage of total on track (%)

Speeds ≤ threshold

Speeds > threshold

27/04/ 2021

48

36

22

92

89

+3

28/04/ 2021

49

35

19

91

89

+3

29/04/ 2021

49

34

19

93

90

+4

30/04/ 2021

48

40

21

93

90

+3

01/05/ 2021

48

35

24

92

90

+2

02/05/ 2021

48

30

20

93

91

+3

03/05/ 2021

48

40

23

93

90

+3

12/04/ 2022

47

51

28

94

95

0

13/04/ 2022

47

36

25

91

90

0

14/04/ 2022

51

19

10

90

87

+2

15/04/ 2022

54

1

1

82

83

See note

16/04/ 2022

54

2

1

80

84

See note

17/04/ 2022

56

3

2

85

84

See note

18/04/ 2022

58

1

1

86

83

See note

19/04/ 2022

56

9

5

86

84

See note

20/04/ 2022

54

14

7

89

85

+4

21/04/ 2022

50

35

22

91

87

+4

Note Differences not calculated for these days as too few passbys (< 10) below threshold speed

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Fig. 4 Wheel-rail contact—site B down track high rail (2021 left and 2022 right)

on the gauge corner extending from 0 to 10 mm from the centreline to the field side. The grinding templates were overlayed on the measured 2021 and 2022 MiniProf rail profiles where it was observed that high rails were generally non-conformal and low rails generally conformal. Non-conformal high rails can result in variations in wheel contact points (producing two-point contact) which can lead to plastic flow, non-effective gauge corner lubrication, higher lateral forces, higher top of rail creep forces and higher gauge face wear rates. Typical worn wheel profile data in the area was provided by government agencies and is considered to be representative of passbys operating in the area. Comparisons of overall noise levels were undertaken for periods with similar average speeds and percentage of passbys below threshold speeds to isolate the effect of changes in roughness and rail profiles. Where this was possible (such as at Site B), the increase in curving noise was attributed to profile non-compliance and grinding facets on the high rail. This is shown in Fig. 4. Generally, the contact gap between the wheel and the rail appears to be larger in the 2022 measurement with a large grinding facet between two points of contact; one on the gauge face (at the plastic flow lip) and one high on the gauge corner.

6 Conclusion A longitudinal study investigating the frequency of squeal, flanging and other noise events at three interconnected sharp passenger curves in New South Wales, Australia has been undertaken. By undertaking measurements of common variables 12 months apart, it was possible to isolate the effects of individual variables on curve noise events at this site. The results, perhaps surprisingly, indicate a noticeable influence of speed—where the incidences of curving noise events significantly increase when passby speeds fall below a threshold speed. At some locations, this threshold speed is equal to the balance speed of the curve while at other locations it is significantly higher. These trends (slower speeds leading to louder noise events) are opposite to what would be typically expected in an environment without curving noise—i.e. an increase in

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rolling noise with speed. The reasons for these trends are not entirely clear though may relate to conformal wheel-rail contact at the gauge corner of the high rail at higher speeds. At locations where the speed effect can be reasonably isolated and quarantined, comparisons between monitoring years highlight the benefits of conformity with recommended rail profile templates and improved roughness.

References 1. Thompson D (2008) Railway noise and vibration, 1st edn. Elsevier Science, Oxford, UK 2. Thompson DJ, Squicciarini G, Ding B, Baeza L (2018) A state-of-the-art review of curve squeal noise: phenomena, mechanisms, modelling and mitigation. In: Noise and vibration mitigation for rail transportation systems. Notes on numerical fluid mechanics and multidisciplinary design, vol 139. Springer, Cham 3. Grassie SL (2009) Rail corrugation: characteristics, causes, and treatments. Proc Inst Mech Eng Part F J Rail Rapid Transit 43(3):199–220 4. Bullen R, Jiang J (2010) Algorithms for detection of rail wheel squeal. In: 20th international congress on acoustics 2010, ICA 2010—incorporating proceedings of the 2010 annual conference of the Australian Acoustical Society, 3, 2212–2216 5. TMC 225—Rail Grinding (2013) Transport for NSW, version 2.5

Estimation of Vibration Limit Cycles from Wheel/Rail Mobilities for the Prediction of Curve Squeal Noise Olivier Chiello, Rita Tufano, and Martin Rissmann

Abstract A novel method for the approximate estimation of curve squeal sound levels is proposed. The method directly targets the stationary regime by using wheel/ rail mobilities at contact instead of modal characteristics of the structures. The condensation allows a more general description of the dynamics of the structures, in particular the behavior of the rail for which a modal representation is not very suitable. The method is first validated in the case of a reduced modal description of the system by comparing results to a reference cycle obtained by numerical integration in the time domain. It is then applied to realistic cases for which the wheel/ rail mobilities are obtained from more elaborated models. The model can be used to carry out parametric studies allowing to design squeal noise mitigation solutions. Keywords Curve squeal · Instability · Self-sustained vibrations · Power balance

1 Introduction Since Rudd [1], most of the works in the literature agree to attribute the generation of wheel/rail squeal noise in curves to the high lateral slip imposed in the curve and to the resulting instabilities [2]. In squeal models, the occurrence of the phenomenon is thus generally studied through a stability analysis based on the linearization of the contact forces. Two families of methods are used: those leading to a generalized eigenvalue system via a modal description of the system [3] and those describing the wheel/rail interaction at the contact’s degrees of freedom using their respective mobilities (Nyquist criterion) [4]. Despite its undeniable interest, stability analysis does not allow the prediction of the amplitudes of the nonlinear self-sustained vibrations resulting from instabilities. O. Chiello (B) Univ Gustave Eiffel, CEREMA, Univ Lyon, UMRAE, F-69675 Lyon, France e-mail: [email protected] R. Tufano · M. Rissmann Vibratec, Railway Business Unit, 28 Chemin du Petit Bois, 69131 Ecully Cedex, France © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_44

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These nonlinear vibrations are most often calculated using a numerical integration of the dynamic equations of the system in the time domain, by using either a modal description [3] or a contact condensation from the wheel/rail impulse responses [5]. The possible stationary regimes or “limit cycles” obtained are then re-expressed in the frequency domain. A disadvantage is that the integration has to be carried out over a sufficiently long period of time for the transient regime to stabilize. Some authors have proposed simplified methods allowing a direct computation of stationary regimes [1, 6, 7]. These methods are mainly based on the assumption of mono-harmonic limit cycles. Unfortunately, they are limited to a reduced modal description of the system dynamics. In this paper, a more general method using wheel/rail mobilities is proposed to determine approximate limit cycles.

2 Proposed Approach The pass-by of a guided vehicle at speed V in a curve of small radius is considered. The key parameter is the angle of attack α which designates the misalignment of the wheel axis with the rolling direction tangent to the rail. The resulting lateral slip of the wheel on the rail head is given by Vt ≈ αV . The interaction of a single wheel with the rail is considered and the flange contact is disregarded. The wheel/rail interaction is point-like and reduced to two degrees of freedom, normal and tangential. The wheel and the rail are described by their point and cross contact mobilities YW tt , YW nn , Ywtn , Y Rtt , Y Rnn and Y Rtn in the frequency domain where subscripts W , R, n and t stand for wheel, rail, normal and tangential degree of freedom. These mobilities can be determined using various types of models.

2.1 Contact and Friction Laws The contact is modelled by Hertz’s normal stiffness k H and Mindlin’s tangential stiffness ξ k H leading to normal and tangential point mobilities YCnn = j ωk −1 H and YCtt = j ωξ k −1 (see for instance rolling noise models [8]) while a non-linear friction/ H creep law is considered relating the total friction force f t acting at the wheel/rail interface to the wheel/rail creep s and the normal contact force f n : f t (s, f n ) = μ(s, f n ) f n with s = (Vt + Δvt )/V

(1)

where μ denotes the non-linear dynamic friction coefficient and Δvt = vW t − v Rt − vCt stands for the relative instantaneous tangential velocity at the wheel/rail interface. In this paper, the choice was made for a non-linear creep law of Shen-Hedrick-Elkins type [2, 4], combined with a heuristic velocity-weakening friction coefficient, but this choice does not restrict the generality of Eq. (1).

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2.2 Stability Analysis A stability analysis is first performed using the Nyquist criterion as proposed by De Beer et al. [4]. For small oscillations around the quasi-static equilibrium characterized by normal load N , lateral creep s ≈ α and quasi-static friction force T = μ(α, N )N , the dynamic part of the friction force can be linearized. Considering furthermore harmonic variations of the oscillations such that Δvt = Δvt eiωt , f t − T = f t eiωt and f n − N = f n eiωt , the wheel, rail and contact mobilities can be used to express the normal and tangential coupling between the components in the frequency domain: Δ

Δ

Δ

Δ

Δ

Δ

Δ

Δ

Ynn f n + Ynt f t = 0 and Ytn f n + Ytt f t = Δvt

(2)

where Ynn = YW nn + Y Rnn + YCnn , Ytt = YW tt + Y Rtt + YCtt and Ynt = Ytn = YW nt + Y Rnt are the total contact mobilities. A complex equation f t = H (ω) f t is obtained for the friction force, where closed-loop transfer function H (ω) is given in [4] as a function of total contact mobilities. According to the Nyquist criterion, oscillations are unstable for pulsations ω such that I(H (ω)) = 0 and R(H (ω)) > 1. This technique is useful to find the pulsations where instabilities may occur and initiate self-sustained vibrations but does not give any information on the amplitude of these vibrations. Δ

Δ

2.3 Power Balance for Non-linear Harmonic Cycles Considering larger oscillations around the quasi-static equilibrium, the friction force can no longer be linearized and in most cases the frequency domain is not appropriate to describe the response of the structure. Nevertheless, a mono-harmonic response of the structure at pulsation ωi for which the system is unstable, such that ) ( is assumed Δvt (t) = R Δvt eiωi t . With this assumption the power dissipated in the system can be evaluated analytically with linear harmonic techniques [i.e. from Eq. (2)] since the behavior in the structure remains linear: |2 | ) |Δvt | (( )−1 ) 1 ( ∗ −1 R Ytt − Ytn Ynn (3) Ynt Wdis = R Δvt f t = 2 2 Δ

Δ

Δ

However, for the evaluation of the injected power a time integration over the cycle has to be performed since the friction force is non-linear:

Winj

1 = T

{T Δvt (t)μ(s(t), f n (t)) f n (t)dt 0

(4)

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(( ) ( ) )−1 where s(t) = α + V1 R Δvt ei ωi t and f n (t) = N +R Ytn − Ytt Ynt−1 Ynn Δvt eiωi t is directly expressed as a function of Δvt (t) from Eq. (2). The ntegral (4) may be computed numerically for a given value of amplitude Δvt . It is important to note that, unlike dissipated power Wdis , injected power Winj is not | |2 proportional to |Δvt | so that the power balance may vary with Δvt and differ from the linear case (see ref. [9] in this case). The search for stationary self-sustained vibrations thus amounts to find Δvt such that: Δ

Δ

Δ

Δ

Δ

Δ

( ) ( ) Winj Δvt = Wdis Δvt Δ

Δ

(5) Δ

which consists in solving a nonlinear algebraic equation on Δvt .

2.4 From the Amplitude of the Cycle to the Radiated Sound Power Δ

Δ

In cases where a solution is found to Eq. (5), complex magnitudes f t and f n of the tangent and normal forces acting at the wheel/rail interface at unstable pulsation ωi are calculated using Eq. (2). The sound power radiated by the wheel is finally estimated from contact forces by a “rolling noise” type method based on analytical radiation factors [8].

3 Validation for a Reduced Wheel/Rail Model The method was tested on the reduced model proposed in [10] and shown in Fig. 1. The wheel and rail are each modelled by a mass-spring-damper system tuned to a particular mode. Angle θ is related to the ratio of the normal and tangential contributions of the wheel mode. For the rail, only the normal dynamics are considered. For the wheel, parameters have been adjusted to the axial mode 0L4 of the wheel modelled in Sect. 4. For the rail, the reduction to one mode is not very realistic: the parameters were simply chosen to obtain the same normal mobility (modulus and phase) as the model used in Sect. 4 at the natural frequency of the wheel mode (1850 Hz).

3.1 Expression of Contact Mobilities and Stability Analysis For such a system, the contact mobilities are simply written: Ynn = YW sin θ 2 + Y R + j ωk −1 H

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Fig. 1 Schematic of the reduced model used for the validation of the method

Ytt = YW cos θ 2 Ynt = YW sin θ cos θ with ) ( YW = j ω −MW ω2 + j ωMC W + K W and ( ) Y R = j ω −M R ω2 + j ωMC R + K R

(6)

Closed-loop transfer function H (ω) can be easily computed from these mobilities, and linearized form of creep/friction law f t (s, f n ) as described in [4, 9]. With the tuned parameters, the Nyquist criterion shows that the system is unstable at a frequency close to the natural frequency of the wheel mode.

3.2 Numerical Integration in the Time-Domain In order to obtain a reference solution, a numerical integration of the nonlinear equations corresponding to the reduced model (see [7] for instance) has been performed in the time domain. A small initial tangential velocity of 10−3 m/s has been used to accelerate the development of the self-sustained vibrations from the quasi-static equilibrium. The evolution of the tangential velocity over the whole integration time (1 s) is given on the left of Fig. 2. On the right, only the five last milliseconds are

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Fig. 2 Solution obtained by numerical integration in the time-domain

plotted. A transient increase due to instability is observed, followed by the establishment of a quasi-harmonic periodic stationary oscillation at a fundamental frequency of 1847 Hz and an amplitude of 0.0585 m/s.

3.3 Results Obtained with the Proposed Approach Non-linear Eq. (5) is then solved at the frequency where instability occurs, from contact mobilities given in Eq. (6) and non-linear form of creep/friction law f t (s, f n ), leading to a solution Δvt = 0.0585 m/s. This result is remarkably good as it corresponds to an error of less than 0.02% compared to the reference value obtained with the numerical integration. Details of the variations of the injected and dissipated powers (normalized by | | |Δvt |2 ) are plotted on Fig. 3 as a function of Δvt . The figure highlights the difference between the linear domain (amplitudes Δvt < 0.05 m/s) where the normalized powers are both constant and the non-linear domain (higher amplitudes Δvt > 0.05 m/s) where the normalized injected power decreases with the amplitude of the cycle until it reaches the normalized dissipated power at the solution value. Δ

Δ

Δ

Δ

Δ

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Fig. 3 Power balance as a function of the cycle amplitude for the reduced model

4 Results Obtained with More Elaborated Models 4.1 Components Models and Input Data The method is tested in a realistic case of a metro wheel rolling in a curve at speed V = 30 km/h and angle of attack α = 11 mrad. At this angle of attack and for the chosen friction parameters, the friction/creep curve is decreasing which reflects a potential source of instability. A normal load N = 51 kN is considered. The wheel is a steel monobloc wheel with a diameter of 86 cm. It is first modelled by the Finite Element Method considering clamped boundary conditions at the axle axis. Contact mobilities are computed by modal superposition from 37 normal modes obtained with the Finite Element model in the frequency range 0–6250 Hz. Damping factors of 0.01% are chosen for most of modes above 400 Hz. A classical “Rodel” model (infinite Timoshenko beam with uniform elastic support [8]) is chosen for the rail lying on monobloc concrete sleepers through elastic rail pads of medium stiffness. Contact mobilities are computed analytically from rail and support parameters. The stability analysis performed by using the Nyquist criterion highlights 9 frequencies where instabilities may occur. They correspond for the most part to the natural frequencies of axial wheel modes without nodal circles. These modes are known to play an important role in the generation of curve squeal.

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Fig. 4 Radiated sound power for each unstable mode

4.2 Non-linear Harmonic Cycles and Radiated Sound Power Non-linear Eq. (5) is solved for each frequency where instability may occur. For each of them an amplitude Δvt is found, leading to a balance between the injected and dissipated powers. The corresponding radiated sound powers are given in Fig. 4. It can be observed that the amplitudes are quite similar for all modes. Even though this simple model cannot predict which mode(s) or set of modes will actually be present in the solution, computed sound powers provide a first estimation of the squeal noise potentially emitted by the system for one given unstable mode. The levels obtained for the 0L0 and 0L1 modes are however questionable, as these modes are generally not found in field measurements. The single wheel model used here is probably not sufficient to fully understand the dynamics of these low-frequency modes, due to the potential influence of bending axle modes on the wheel mobility. Δ

4.3 Effect of Wheel Damping The effect of wheel damping is studied to illustrate possible parametric studies with the simplified approach. Figure 5 shows the results obtained for the mode 0L4 with damping factors of 0.02, 0.05 and 0.1% compared with a nominal damping factor of 0.01%. It is important to note that a critical damping factor of 0.11% is sufficient to stabilize the mode. It can be observed that the amplitude of the cycle as well as the

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Fig. 5 Influence of damping on radiated sound power (mode 0L4)

radiated power are very little sensitive to the damping factor except near the critical damping, which reflects a strongly non-linear behavior.

5 Conclusion A novel method for the approximate estimation of curve squeal levels is proposed, directly targeting the non-linear stationary regime and using wheel/rail mobilities at contact instead of modal characteristics of the structures. As for the stability analysis or the time integration, the condensation at contact allows a more general and more functional description of the dynamics of the structures, in particular the behaviour of the rail for which a modal representation is not very suited. The method is applied to a realistic case for which the wheel and rail mobilities are obtained from elaborated models. It proves to be very efficient and adapted to parametric studies aiming to design curve squeal noise mitigation solutions.

References 1. Rudd MJ (1976) Wheel/rail noise—part II: wheel squeal. J Sound Vib 46:381–394 2. Thompson DJ, Squicciarini G, Ding B, Baeza L (2018) A state-of-the-art review of curve squeal noise: phenomena, mechanisms, modelling and mitigation. In: Anderson D et al (eds) Noise and vibration mitigation for rail transportation systems. Notes on numerical fluid mechanics and multidisciplinary design, 139, 3–41. Springer, Cham

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3. Chiello O, Ayasse J-B, Vincent N, Koch J-R (2006) Curve squeal of urban rolling stock—part 3: theoretical model. J Sound Vib 293:710–727 4. De Beer FG, Janssens MHA, Kooijman PP (2003) Squeal noise of rail-bound vehicles influenced by lateral contact position. J Sound Vib 67:497–507 5. Pieringer A (2014) A numerical investigation of curve squeal in the case of constant wheel/rail friction. J Sound Vib 333:4295–4313 6. Meehan PA, Liu X (2018) Modelling and mitigation of wheel squeal noise amplitude. J Sound Vib 413:144–158 7. Meehan PA (2020) Prediction of wheel squeal noise under mode coupling. J Sound Vib 465:115025 8. Thompson DJ (2009) Railway noise and vibration: mechanisms, modelling and means of control. Elsevier 9. Chiello O, Tufano R, Rissmann M (2022) Modelling of wheel/rail squeal noise in curves from mono-harmonic vibratory limit cycles. In: InterNoise 2022, Glasgow, UK 10. Ding B, Squicciarini G, Thompson DJA (2019) Effect of rail dynamics on curve squeal under constant friction conditions. J Sound Vib 442:183–199

Survey of Curve Squeal Occurrence for an Entire Metro System Olle Eriksson, Peter T. Torstensson, Astrid Pieringer, Rickard Nilsson, ´ Martin Höjer, Matthias Asplund, and Anna Swierkoska

Abstract The current work presents a statistical analysis based on data collected during approximately 1.5 years of regular operation by two vehicles equipped with an on-board noise monitoring system on the Stockholm metro. Data covers 379,776 passages through 143 curves with radii up to 1000 m. Binary logistic regression is used to investigate the importance of curve radius, vehicle speed, relative humidity, air temperature, rail grinding and vehicle individual on curve squeal. Curve squeal occurrence shows an inverse proportionality with respect to curve radius. This trend is particularly pronounced for curve radii below 600 m. The two vehicles accounted for in the study show differences in propensity to generate squeal. The influence of temperature and relative humidity, and their interaction, on curve squeal is described by an estimated response surface. Results show the occurrence of curve squeal to increase after rail grinding. No strong relationship between curve squeal occurrence and vehicle speed is identified. Keywords Curve squeal · Noise monitoring · Statistical analysis · Binary logistic regression

O. Eriksson · P. T. Torstensson (B) Swedish National Road and Transport Research Institute (VTI), Linköping, Sweden e-mail: [email protected] A. Pieringer Department of Architecture and Civil Engineering, Division of Applied Acoustics/CHARMEC, Chalmers University of Technology, Gothenburg, Sweden R. Nilsson Stockholm Public Transport (SL), Stockholm, Sweden M. Höjer Tyréns Solutions AB, Stockholm, Sweden M. Asplund Swedish Transport Administration (Trafikverket), Borlänge, Sweden ´ A. Swierkoska Sie´c Badawcza Łukasiewicz, Railway Vehicles Institute “TABOR”, Pozna´n, Poland © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_45

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1 Introduction Railway curve squeal with large magnitude tonal noise components in the frequency range up to 10 kHz is a major cause of annoyance that still lacks a satisfying solution [1]. The development of self-sustained unstable vibrations has traditionally been attributed to a friction coefficient that is “falling” for increasing wheel–rail contact sliding velocities [2]. Later this theory has been supplemented by studies that instead focus on “mode coupling” as the governing mechanism for curve squeal [3, 4]. This illustrates gaps in the current understanding of the problem that motivate further studies. Jiang et al. investigated the importance of angle of attack (AOA), vehicle speed, rail lubrication and rail grinding using data collected by a wayside condition monitoring system during three years of mixed traffic through a 300 m radius curve in Sydney [5]. Freight trains equipped with three-piece bogies were found to be responsible for the squeal generation in the curve. In the studied curve, high-pitch squeal was predominantly radiated by the outer wheel–high rail contact [6]. Curve squeal occurred almost exclusively for AOA over 10 mrad [5]. A weak increasing trend between squeal occurrence and vehicle speed was found (at a rate of 1.5% for vehicle speed span 17–65 km/h) [5]. Rail grinding was performed twice during the studied period. At both occasions a significant increase in rate of curve squeal was observed (by comparison of squeal occurrence during the first months after and before the rail grinding) [5]. The rail grinding was observed to generate wide facets at the gauge corner of the high rail preventing lubrication to reach important contact areas. Moreover, it is discussed that the steering performance of bogies may have been further deteriorated by the resulting two-point contact at the high rail. Long-term wayside monitoring of several 200 m radius curves in south Australia has shown temperature and relative humidity to strongly influence the occurrence of wheel squeal and flanging noise [7]. More specifically, squeal noise was found to become more prevalent with increasing relative humidity. Subsequent experimental studies by Liu and Meehan using a twin-disc in a controlled environment confirmed this observation [8]. Effective squeal noise mitigation using water is reported by several contributions in literature. A trial at Barnt Green, UK, showed a reduction of squeal occurrence from 14 to 2.5% of passing wheel axles by application of a mist spray system [9]. The current work has used the MSc dissertation by Swierkoska [10] as starting point. Measurement data obtained during long-term noise monitoring of metro trains in regular traffic forms the basis for a statistical analysis that searches empirical evidence for the importance of selected variables on curve squeal occurrence. In addition, the results demonstrate knowledge gaps associated with the stochasticity of real operative and environmental conditions.

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2 Methodology The onboard condition monitoring system used at the Stockholm metro is presented in [11]. Microphones are mounted close to wheel–rail contacts behind the leading bogie of the leading car or in front of the trailing bogie of the trailing car (depending on the travelling direction) of a Bombardier C20 trainset. Curve squeal is detected in time steps of 250 ms as cases during curving when the radiated noise from the inner wheel exceeds that of the outer wheel by at least 3 dB(A). In the current work, 0.5 s (2 samples) of continuous squeal is taken as criteria to identify squealing curve passages. Data from two vehicles that have operated in regular traffic on the green line between January 2019 and November 2021 are used. The green line is approximately 41 km long, has three routes and 49 stations. All curves (including transition curves) of the green line with radius below 1000 m are accounted for. In total the data contain 143 curves and 379,776 vehicle passages. 367,306 passages remain after removing passages with vehicle stop, unreliable speed data or incorrect coding of curve squeal. This data pre-processing has not meant that any curve is excluded from the analysis. The statistical analysis is performed by binary logistic regression with a logit link function and curve squeal as dependent variable [12]. Coefficients in logistic regression are expressed in terms of the natural logarithm of the explanatory variables’ effect on odds. Odds represent the probability that an event occurs divided by the probability that it does not occur. An empiric estimate of the odds for curve squeal is the number of passages with curve squeal divided by the number of passages free of curve squeal. The logistic regression enables to estimate the effect of the explanatory variables adjusted for the effects of other possible explanatory variables. The following explanatory variables are accounted for in the current work; vehicle individual, rail grinding, vehicle speed, air temperature and relative humidity. Additionally, several variable interactions have been included, for more details see Sect. 3.1. Air temperature and relative humidity are obtained from metrological data measured each hour at the weather station located at Bromma airport in Stockholm. The air temperature and relative humidity at a specific time of a vehicle passage is calculated by interpolation. Vehicle speed is assessed by introducing a factor with three levels corresponding to constant speed, acceleration and retardation. For curves that have been ground, the explanatory variable “rail grinding” is introduced. More details on how this variable is implemented in the analysis is found in Sect. 3.1.

3 Results 3.1 Regression Analysis The regression analysis was able to estimate coefficients of explanatory variables for 122 curves. Each curve is analysed separately generating a set of estimated coefficients. Figure 1a shows the distribution of the estimated intercepts expressed as log

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odds. It shows that curve squeal has a generally higher probability for smaller radius curves but also that this effect levels off at around 600 m radius. Curve radius is not introduced as a separate explanatory variable in the analysis but the tilt in the distribution shown in Fig. 1a demonstrate that shorter radius covary with higher squeal probability. Also, results obtained for curves outdoors and in tunnels are observed in one common cloud which suggest the impact of location to be unimportant. Figure 1b shows the estimated coefficient related to vehicle individual. A negative coefficient is noticed for most curves indicating that vehicle 2 has lower squeal probability than vehicle 1. This relation however becomes more uncertain at longer curve radii. The root-cause (e.g. turning of wheels, wheel dampers, etc.) of this observed difference in squealing propensity between vehicles is not further investigated as part of the current work. For curves that were ground during the studied period a dummy variable is introduced. In the analysis, squeal occurrence for vehicle passages performed before/ after grinding is treated separately. The resulting coefficients are found in Fig. 1c.

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The cloud is centered above 0 which indicates an increased probability for curve squeal after rail grinding. The root cause being for example deteriorated steering capability due to reduced rolling radius difference or the removal of rail surface roughness is not further investigated as part of the current work. Potential impact by other maintenance measures conducted in the current curves during the studied period have not been regarded in the analysis. Figure 1d presents estimated coefficients for the relation between probability of curve squeal and average vehicle speed. The figure also outlines results from significance tests. The cloud is approximately centered around zero, meaning that the analysis does not show a general relation between vehicle speed and curve squeal. The results from a simultaneous assessment of all curves using regression analysis would become difficult to interpret including a large set of variable interactions. Regression analysis is typically ill-prepared for treating individual curves as samples from a distribution. Instead, in the formal analysis presented here, coefficients in Fig. 1 are treated as individual observations. There is a significant (p < 0.001) slope in a linear regression based on the results in Fig. 1a. A t-test based on Fig. 1b confirms that the effect of vehicle individual is significant (p < 0.001). With respect to rail grinding shown Fig. 1c, its effect on squeal occurrence is significant at level p = 0.017. The effect of average speed on curve squeal occurrence is insignificant (p = 0.413), see Fig. 1d. Figure 2a, b show the regression coefficients for temperature and relative humidity, respectively. Both are negative for most curves indicating that the probability for curve squeal decreases with increasing temperature (if humidity is 0%) and increasing humidity (if temperature is 0 °C). The interaction between temperature and humidity has an estimated coefficient different from 0 in most curves as shown in Fig. 2c, meaning that the combined effect of a change in temperature and humidity cannot be found by adding their main estimated effects shown in Fig. 2a, b, respectively. Because the interaction is positive in most curves, it counteracts the negative main effects if both temperature and relative humidity increase. Treating the coefficients in Fig. 2a–c as samples and analysing with t-test, all three tests were significant (p < 0.001 in all cases). The estimated combined effect of temperature and humidity on the log odds for curve squeal is shown by the contour plot in Fig. 2d. The estimated coefficients (main effects) of temperature and relative humidity are the slopes of the surface along the directions of the axes represented by the arrows. The dotted level curves represent the log odds compared to a reference point, the black bullet, which is chosen to be the average temperature and relative humidity in the data. The gray scale background shows number of vehicle passages (dark color indicates a large number of vehicle passages while white color means that no vehicle passage has been recorded for the current combination of temperature and relative humidity). At temperatures over 10 °C the occurrence of curve squeal is noticed to increase with increasing relative humidity. This is in correspondence with results in [7, 8]. However, at temperatures below 10 °C, the opposite trend with respect to relative humidity is noticed. These results need further verification by future work.

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Some additional explanatory variables were also tested before the final model was selected. Interaction between vehicle individual and relative humidity was not found. Interaction between vehicle individual and temperature may be present and was included in the model but results were unclear and left for future studies. In addition to average speed mentioned above, also average speed squared was tested as it could indicate the existence of an ideal speed with lower propensity of curve squeal. Moreover, vehicle speed was analysed categorised into three types (accelerating, constant and braking) but results did not indicate a significant relation to probability of curve squeal.

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Fig. 3 Squeal occurrence as dependent on longitudinal coordinate and vehicle speed. Results are shown for a 213 m radius curve located between stations Gamla stan and T-centralen on the green line at the Stockholm metro. a Vehicle 1 and b vehicle 2

3.2 Squeal-Free Track Section Figure 3 presents an interesting observation contained in the comprehensive dataset used for the current study. Squeal occurrence for both vehicles as dependent on vehicle speed and longitudinal coordinate in a 213 m radius curve located in a tunnel is shown. Figure 3a, b are based on 2596 and 2041 vehicle passages, respectively. Observe the locally low squeal occurrence between approximate longitudinal coordinates 1345–1355 m. This behavior is noticed for a large variation in vehicle speed and is therefore believed to be associated with local properties of the track infrastructure. At the time of writing, these observations are under investigation. Future additional field measurements are planned to confirm their existence and to contribute with more information on local properties of the track superstructure. The similar results obtained from both vehicles is deemed as a sufficient justification to report the results at this early stage.

4 Conclusions The main contribution by the current work is the large number of curves accounted for in the analysis. This contrasts with the majority of existing literature that focus on conditions in few selected curves. In that respect, the current work demonstrates the large differences in propensity to generate curve squeal between curve individuals. The main conclusions from the current study are summarised below: • For curve radii below approximately 600 m, the occurrence of curve squeal shows a strong invers proportionality with respect to curve radius. At larger curve radii this relation is noticed to become weaker.

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• The occurrence of curve squeal for the two studied vehicles differs significantly. Both vehicles have operated on the same metro line and during the approximate same time period. • The occurrence of curve squeal increases after rail grinding. These results need further verification by future work. • No significant relationship between curve squeal occurrence and vehicle speed is found. • Curve squeal occurrence shows a complex influence from air temperature and relative humidity. At temperatures over 10 ºC the occurrence of curve squeal increases with increasing relative humidity. This is in correspondence with results in [7, 8]. However, at temperatures below 10 ºC, the opposite trend with respect to relative humidity is noticed. These results need further verification by future work. Acknowledgements The current work has been funded by the Swedish Transport Administration in the project “Curve squeal—Influence of track design and maintenance status” (TRV 2020/49829).

References 1. Thompson DJ, Squicciarini G, Ding B, Baeza L (2018) A state-of-the-art review of curve squeal noise: Phenomena, mechanisms, modelling and mitigation. In: Noise and vibration mitigation for rail transportation systems, notes on numerical fluid mechanics and multidisciplinary design 139 2. Rudd MJ (1976) Wheel/rail noise—part II: wheel squeal. J Sound Vib 46(3):381–394 3. Glocker C, Cataldi-Spinola E, Leine RI (2009) Curve squealing of trains: measurement, modelling and simulation. J Sound Vib 324(1):365–386 4. Pieringer A (2014) A numerical investigation of curve squeal in the case of constant wheel/rail friction. J Sound Vibr 333(18) 5. Jiang J, Hanson D, Dowdell B (2008) Wheel squeal: insights from wayside condition monitoring. In: Schulte-Wening B et al (eds) Noise and vibration mitigation for rail transportation systems, notes on numerical fluid mechanics and multidisciplinary design 139 6. Jiang J, Dwight R, Anderson D (2012) Field verification of curving noise mechanisms. In: Maeda T et al (eds) Noise and vibration mitigation for rail transportation systems, notes on numerical fluid mechanics and multidisciplinary design 118 7. Anderson D, Wheatley N (2008) Mitigation of wheel squeal and flanging noise on the Australian rail network. In: Schulte-Wening B et al (eds) Noise and vibration mitigation for rail transportation systems, notes on numerical fluid mechanics and multidisciplinary design 139 8. Liu X, Meehan PA (2014) Investigation of the effect of relative humidity on lateral force in rolling contact and curve squeal. Wear 310:12–19 9. Oertli J (2005) Combatting curve squeal, phase II, final report. UIC 10. Swierkoska A (2019) Curve squeal on the Stockholm metro—statistical analysis based on data collected by an onboard monitoring system. M.Sc. thesis, Chalmers University of Technology, Göteborg, Sweden 11. Höjer M, Almgren M (2015) Monitoring system for track roughness. EuroNoise 2015, Maastricht, the Netherlands 12. Collett D (1991) Modelling binary data, 1st edn. Chapman and Hall/CRC, New York

Transient Modelling of Curve Squeal Considering Varying Contact Conditions Astrid Pieringer, Peter Torstensson, Jannik Theyssen, and Wolfgang Kropp

Abstract Modelling railway curve squeal poses a challenge since the phenomenon is non-linear, transient and complex. This work focusses on the transient effects of varying contact parameters on curve squeal. A previously developed high-frequency tool for the simulation of curve squeal in the time domain during quasi-static curving is extended to account for transient curving and connected to a software for the lowfrequency vehicle dynamics. An application of the model demonstrates that timevarying contact parameters such as contact position, lateral creepage, and friction coefficient can lead to an on- and offset of squeal. The history of the wheel/rail dynamics can also have an influence on the occurrence of squeal and the selection of the squeal frequency. Keywords Curve squeal · Wheel/rail interaction · Transient curving · Instability · Time domain

1 Introduction Curve squeal is an intense tonal noise emitted by railway vehicles negotiating tight curves. This type of noise is commonly attributed to self-excited vibrations of the railway wheel caused by a large lateral creepage of the wheel tyre on the top of the rail during ‘imperfect’ curving [1]. Squeal is known to be a threshold problem occurring above a certain value of the lateral creepage and the friction coefficient. The lateral contact position on the wheel and the rail, which is responsible for the degree of coupling between vertical and lateral dynamics, has also shown to influence squeal occurrence [2]. In [3], this coupling between lateral and vertical directions was identified as the driving mechanism for building up self-excited vibrations in the situation of a squealing test rig. During curving, both lateral creepage and conA. Pieringer (B) · J. Theyssen · W. Kropp Applied Acoustics/CHARMEC, Chalmers University of Technology, Göteborg, Sweden e-mail: [email protected] P. Torstensson Swedish National Road and Transport Research Institute (VTI), Göteborg, Sweden © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_46

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tact position will vary due to vehicle dynamics, and the latter also due to varying wear of the rail profile along the curve, although creepage and contact position can be assumed to be approximately constant in the circular part of the curve. Local friction conditions may vary along the curve. Squeal also needs some time to build up and might consequently not become audible if the conditions for instability are not fulfilled long enough. Furthermore, discrete defects on the rail might disturb the build-up of squeal. These described effects of transient curving on the occurrence of squeal have so far only scarcely been investigated and considered in modelling. Modelling curve squeal poses a challenge since the phenomenon is non-linear and transient, and high-frequency wheel/rail interaction during curving is complex. Frequency-domain models require a linearization of the mechanical system and are in general computationally efficient but can, by their nature, not consider timevarying effects. These models can only predict the onset of squeal in the linear regime assuming steady-state conditions. Time-domain models, which have the capability to include the non-linear and transient processes in the contact zone, can not only predict which modes are prone to squeal, but also the ultimate squeal amplitudes (i.e. the limit cycle). Keeping the computational effort in time-domain models manageable, generally necessitates, however, to simplify the wheel/rail system and/or the curving process. Recent time-domain models with detailed wheel and track description, and a transient contact model assume quasi-static curving [2, 4], while the model in [5] included the variation of the contact position and creepage but used a steady-state contact model. In this work, the previously developed model WERAN for the simulation of curve squeal in the time domain [2] is extended from quasi-static to transient curving. After a presentation of the model and its extension in Sect. 2, the functioning of the extended model is demonstrated, and the influence of transient curving on squeal occurrence is investigated. First, the influence of time-varying contact parameters is researched separately and systematically in Sect. 3. Second, a realistic curving scenario from Stockholm metro is considered in Sect. 4. Contact positions and creepages are pre-calculated with a vehicle dynamics programme and used as input to WERAN to assess the occurrence of squeal.

2 Methodology The time-domain model WERAN (WhEel/RAil Noise) for wheel/rail interaction and noise combines pre-calculated impulse response functions (Green’s functions) for track and wheel dynamics with an implementation of Kalker’s variational method for transient rolling contact [6]. The model includes the coupling between vertical and lateral dynamics of wheel and track and considers squeal in the case of a constant friction coefficient. Longitudinal dynamics is not included. The track is modelled with Waveguide Finite Elements [7], while a standard Finite Element Model is used for the wheel.

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The longitudinal motion of the contact point along the rail .x(t) with train speed v is included by using moving Green’s functions .giRj (x(τ ), x(t)) [2]. The function R . gi j (x(τ ), x(t)) gives the displacement response of the rail in. j-direction at the contact point at .x(t) at time .t for an excitation of the rail with a unit force in .i-direction at the contact point that was at .x(τ ) at time .τ . The moving Green’s functions can also be described as containing, for each point of excitation on the rail, the displacement response of the rail in the contact point, which moves away from the excitation with train speed .v. The lateral and vertical displacements of the track at the contact point, R R .ξ2 (x(t)) and .ξ3 (x(t)), are calculated by convolving the lateral and vertical contact forces . F2 and . F3 with the moving Green’s functions .

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curve of radius .120 m that is entered through a transition curve of .50 m length. The track superstructure includes continuously welded BV50 rails (50 kg/m) with inclination 1:40 mounted via Pandrol pads to monoblock sleepers on ballast subgrade. The current curve is operated exclusively by so-called C20 trains manufactured by Bombardier Transportation. Trains at the Stockholm metro use S1002 wheel profiles. The vehicle speed in the current curve is approximately 30 km/h. In WERAN, the vehicle is represented by a single flexible C20 metro wheel with a radius of 390 mm, which is modelled using a commercial finite element software. A rigid constraint is applied at the inner edge of the hub, where the wheel would be connected to the axle. With this undamped FE model, the eigenfrequencies and eigenmodes have been calculated up to 7 kHz. The eigenmodes of the wheel were assigned a modal damping value using the approximate values proposed by Thompson [9]. From this modal basis, the Green’s functions of the wheelset were calculated. The track model consists of one continuously supported rail of type BV50 and is built with waveguide finite elements using an inhouse software [7]. Track receptances calculated for various combinations of excitation and response points on the rail are used to construct the moving Green’s functions of the track. The material data of the wheel and track are given in [2]. The static preload . P is .54 kN, and the longitudinal .Δx and lateral spatial resolution .Δy are .0.33 mm and .1.0 mm, respectively. The prescribed lateral creepage can be modified in each time step. Longitudinal creepage and spin creepage have been neglected in this study.

3 Systematic Variation of Contact Parameters In this section, the extended version of WERAN is used to study the influence of time-varying contact parameters on the occurrence of squeal. The train speed is .30 km/h. The relative lateral wheel/rail displacement .Δywr , the lateral creepage .η and the friction coefficient .μ are varied sinusoidally, one parameter at the time as specified in Figs. 1, 2 and 3. When these parameters are kept constant their nominal values are: .Δywr = −15 mm, .η = −0.01 and .μ = 0.3. The nominal value of .Δywr corresponds to a contact position on the field side of the wheel tread, see Fig. 4. A negative lateral creepage corresponds to an underradial position of the wheelset, which is typical for the leading wheelset of a bogie in a tight curve. The results of the simulations are shown in Figs. 1, 2 and 3 in terms of the spectrogram of the lateral contact force. It is clearly seen that squeal is a threshold problem. It occurs for a contact position towards the field side on the wheel tread/rail head, larger (negative) lateral creepage and larger friction coefficient but stops below a certain threshold of these parameters. When squeal builds up several competing squeal frequencies can be present (see Fig. 2) but when the limit cycle is reached, i.e. stick/slip locks in, only one squeal frequency and its overtones exist (e.g. from .20 m in Fig. 2). Figure 3 demonstrates that the occurrence of squeal and the selection of the squeal frequency can depend on the history of wheel and rail dynamics. The first time the friction threshold for squeal is reached in the sinusoidal variation (at about .15 m),

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Fig. 1 Wheel/rail interaction for systematic variation of the contact position: imposed relative lateral wheel/rail displacement .Δywr (—) and corresponding contact positions on wheel (– –) and rail (–.·) (upper). Spectrogram of the lateral contact force (lower)

Fig. 2 Wheel/rail interaction for systematic variation of the lateral creepage: imposed lateral creepage .η (upper). Spectrogram of the lateral contact force (lower)

squeal occurs at 433 Hz, the second time (at about .42 m) at 1141 Hz. The history at the first time is different due to the initial conditions of the simulation which consist in increasing normal force and lateral creepage smoothly from zero to their desired value during the first .2 m of the simulation. The two occurring squeal frequencies correspond to the axial mode of the wheel with two respectively three nodal diameters (and zero nodal circles). Figure 3 also suggests that squeal has to stop before it can switch to a new squeal frequency involving a new limit cycle.

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Fig. 3 Wheel/rail interaction for systematic variation of the friction coefficient: imposed friction coefficient .μ (upper). Spectrogram of the lateral contact force (lower) 20

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4 Realistic Curving Scenario The proposed procedure for transient modelling of curve squeal is applied to a realistic curving scenario. A model that has been previously developed in the commercial software SIMPACK is used [11, 12] to simulate the low-frequency vehicle dynamics in the 120 m radius curve on Stockholm metro described in Sect. 2. The result of this simulation is then used as an input to WERAN. The SIMPACK model includes a generic vehicle model modified to have properties that correspond to the leading car of a C20 train. Wheelset structural flexibility is accounted for by modelling flexible C20 wheel axles using finite elements [12]. In SIMPACK these are introduced as modal representations where all eigenmodes and corresponding eigenfrequencies up to 500 Hz are retained. The track is modelled by mass-spring-damper systems of seven degrees-of-freedoms that are co-following

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Fig. 5 Results of the vehicle dynamics simulation for the leading inner wheel in the leading bogie in the transition curve (0–50 m) and the subsequent circular curve: Lateral contact position (left) on the wheel (—) and on the rail (– –) and lateral creepage (right) for train speed 30 km/h (upper) and 40 km/h (lower) and the track gauges 1435 mm (black), 1440 mm (dark grey) and 1445 mm (light grey)

with each wheelset. The parameters of the track model have been calibrated towards receptance measured on the 120 m radius curve using an instrumented hammer [12]. The time series of the contact positions on wheel and rail, and of the lateral creepage on the leading inner wheel in the leading bogie of the C20 car obtained from SIMPACK are used as input to the squeal simulation in WERAN. Simulations are carried out with a train speed of 30 and 40 km/h and three different track gauges: 1435, 1440 and 1445 mm. The input to WERAN is given in Fig. 5 and the result in terms of the lateral contact force is exemplified in Fig. 6 and Table 1. For higher train speed and larger track gauge, the contact position moves more to the field side of the wheel tread. The lateral creepage increases linearly in the transition curve (0–50 m) and reaches then a similarly high steady-state value in the circular curve in all six cases. The squeal results look also similar in all cases. Squeal develops from about the middle of the transition curve at a frequency of 431 Hz. The squeal amplitude increases as long as the lateral creepage increases and is then approximately constant in the circular curve. The final level of the lateral contact force differs slightly in the different cases, see Table 1. The level increases slightly with train speed and track gauge. Persistent squeal occurs in all six cases in the circular curve. This is due to the fact that the contact parameters are in a range where squeal is expected and do not change during the passage of the circular curve. In reality, squeal can be intermittent also in the circular curve or may not occur at all. There are parameters not modelled here or assumed constant that have an influence on squeal and may change in space and time. Among those are the rail profile and the friction coefficient. Corrugation on the rail head may also influence the wheel/rail contact position and flange contact on the outer wheel may have an influence on the instability at the inner wheel.

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Fig. 6 Spectrogram of the lateral contact force calculated with WERAN based on contact positions and lateral creepage obtained from SIMPACK for a train speed of 30 km/h and track gauge of .1435 mm, see Fig. 5 Table 1 Total lateral contact force level during squeal in the circular curve for the different combinations of train speed and track gauge 1435 mm 1440 mm 1445 mm 1435 mm 1440 mm 1445 mm 30 km/h

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5 Conclusions The main contribution of this work is the extension of a detailed time-domain model for curve squeal to allow for transient curving. An application of the model for systematically varied contact parameters demonstrated that time-varying contact parameters such as contact position, lateral creepage, and friction coefficient can lead to on- and offset of squeal. The history of the wheel/rail dynamics can also have an influence on the occurrence of squeal and the selection of the squeal frequency. Although such transient effects were not observed when simulating a realistic curving scenario based on pre-calculated low-frequency dynamics, this is expected to change when allowing for varying rail geometry (profile, corrugation) or varying friction along the curve. Acknowledgements The current study is part of the ongoing activities in CHARMEC – Chalmers Railway Mechanics. It has been funded by the EU’s Horizon 2020 research and innovation programme in the project In2Track3 under grant agreement no 101012456 and by the Swedish Transport Administration in the project “Curve squeal—Influence of track design and maintenance status” (TRV 2020/49829).

References 1. Thompson DJ, Squicciarini G, Ding B, Baeza L (2018) A state-of-the-art review of curve squeal noise: phenomena, mechanisms, modelling and mitigation. In: Anderson D et al (eds) Noise and vibration mitigation for rail transportation systems. NNFM, vol 139. Springer, Cham

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2. Pieringer A (2014) A numerical investigation of curve squeal in the case of constant wheel/rail friction. J Sound Vib 333(18):4295–4313 3. Kropp W, Theyssen J, Pieringer A (2021) The application of dither to mitigate curve squeal. J Sound Vib 514:116433 4. Giner-Navarro J, Martínez-Casas J, Denia FD, Baeza L (2018) Study of railway curve squeal in the time domain using a high-frequency vehicle/track interaction model. J Sound Vib 431:177– 191 5. Périard FJ (1998) Wheel-rail noise generation: curve squealing by trams. PhD thesis, TU Delft 6. Kalker JJ (1990) Three-dimensional elastic bodies in rolling contact. Kluwer Academic Publishers, Dordrecht, Boston, London 7. Theyssen J, Pieringer A, Kropp W (2021) The influence of track parameters on the sound radiation from slab tracks. In: Degrande G et al (eds) Noise and vibration mitigation for rail transportation systems. NNFM, vol 150. Springer, Cham, pp 90–97 8. Torstensson PT, Nielsen JCO (2009) Monitoring of rail corrugation growth due to irregular wear on a railway metro curve. Wear 267(1–4):556–561 9. Thompson D (2009) Railway noise and vibration: mechanisms, modelling and means of control. Elsevier, Oxford, UK 10. DEsolver (2009) GENSYS users manual 11. SIMPACK rail. https://www.3ds.com/products-services/simulia/training/course-descriptions/ simpack-rail/. Accessed 31 May 2022 12. Carlberger A, Torstensson PT, Nielsen JCO, Frid A (2018) An iterative methodology for the prediction of dynamic vehicle-track interaction and long-term periodic rail wear. Proc Inst Mech Eng Part F: J Rail Rapid Transit 232(6):1718–1730

Predictive Modelling of Curve Squeal Occurrence in Tramways: Influence of Wheel/Rail Double Contact Points Federico Castellini, Leonardo Faccini, Egidio Di Gialleonardo, Stefano Alfi, Roberto Corradi, and Giacomo Squicciarini

Abstract The prediction of curve squeal is one of the most challenging problems especially in tramway applications, where the negotiation of very sharp curves often involves the presence of multiple contact points at wheel/rail interface. Curve squeal is generally attributed to the self-excited vibration of the wheel/rail system, which may occur due to the negative slope of the friction coefficient or due to the modecoupling mechanism. The frequencies involved are usually the ones corresponding to the wheel modes of vibration, resulting in a strong, tonal and very annoying noise emission. Its occurrence is strictly related to the wheel/rail contact conditions, such as creepages, contact angle and friction coefficient. The purpose of this paper is to assess the role of the presence of double contact points at wheel/rail interface. The investigation is performed through a multibody simulation in time-domain and a frequency-domain predictive model capable to reproduce the linearized wheel/rail dynamics including the presence of multiple contact points between the wheel and the rail. It is shown how the presence of flange contact can alter the overall wheel/ rail coupled system mobility, modifying the curve squeal occurrence as well as the wheel modes involved in the phenomenon. Keywords Curve squeal · Self-excited vibrations · Tramways

F. Castellini (B) · L. Faccini · E. Di Gialleonardo · S. Alfi · R. Corradi Department of Mechanical Engineering, Politecnico di Milano, Via Giuseppe La Masa 1, 20156 Milano, Italy e-mail: [email protected] G. Squicciarini ISVR, University of Southampton, Southampton SO17 1BJ, UK © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_47

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1 Introduction The continuous growth in the mobility demand and the stricter urban regulations concerning the environmental noise resulting from the operation of railway vehicles require reliable predictive tools, to support engineers in the design of new vehicles and in the development of effective mitigation solutions. Curve squeal noise is a loud tonal noise, which often occurs when a railway vehicle negotiates a tight curve. A literature review of the several experimental and numerical researches developed to investigate and predict the mechanism behind this annoying phenomenon is presented by Thompson [1]. The wheel/rail self-excited vibration caused by falling friction mechanism [2] and mode-coupling [3] have been investigated. Curve squeal simulation can be performed relying on frequency or time-domain models. Adopting a frequency-domain approach, the wheel/rail dynamics is linearized about a steady state curving condition and a stability analysis is carried out to detect the possible unstable frequencies at which curve squeal is expected to occur [4]. Concerning tramway applications, experimental campaigns have been performed by the Department of Mechanical Engineering of Politecnico di Milano, in which the noise emission of a reference tramcar negotiating a set of reference curves has been measured, also analyzing the effect of different friction conditions [5, 6]. The present work aims at assessing the effect on curve squeal occurrence of multiple contact points at wheel/rail interface, that can be typically found on the leading outer wheel (tread and flange contacts) but also on the leading inner wheel, in which a contact between the flange back of the wheel and the check rail can develop. This unconventional contact condition is more likely to develop in tight tramway curves because of the large value of the angle of attack between the leading inner wheel and the rail (the inner wheel flange back tends to move towards the check rail while turning) but also due to the additional displacement associated to the flexibility of the resilient wheel when subjected to significant lateral forces.

2 Methodology The curve squeal predictive model adopted in this work is based on the frequencydomain model proposed by Huang [4] and updated by Squicciarini [7] to include the possible presence of multiple contact points between wheel and rail. The curve squeal prediction procedure involves a vehicle dynamics simulation in time-domain and a stability analysis of the wheel/rail coupled system in frequency-domain. The wheel and rail dynamics are described through their mobilities and coupled by means of the contact model, as shown in Fig. 1. Several curve squeal simulations are performed, randomly varying the model inputs to simulate the statistical variability of the real contact conditions.

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2.1 Wheel/Rail Coupled Model Including Multiple Contact Points The wheel/rail interaction is described by an Hertzian spring which introduces the linearized contact dynamics between the two bodies [2]. The wheel/rail sliding velocity (Eq. 1), which represents the wheel/rail relative vibration, is defined in longitudinal (1), transversal (2), and normal (3) direction as well as for spin rotation (6): ⎤ ⎡ r V1 V1s s ⎥ r ⎢ ⎢ V 2 ⎥ = ⎢ V2 Vs = ⎢ ⎣ Vs ⎦ ⎣ Vr 3 3 V6s V6r ⎡

⎤ ⎡ c V1w V1 ⎥ ⎢ Vw ⎥ ⎢ Vc ⎥−⎢ 2 ⎥+⎢ 2 ⎦ ⎣ Vw ⎦ ⎣ Vc 3 3 V6w V6c ⎤

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s V1 [Y 11 ] [Y 12 ] F 1 = (3) V 2s [Y 21 ] [Y 22 ] F 2 where [Y mn ] is the system mobility matrix containing the point and cross contribution of the m, n = 1, 2 contact points. Thus, the generic term Yi j,mn consists in the system complex dynamic sliding velocity of the m-th contact point in the i-th direction as the results of applying a unitary dynamic force in the n-th contact point in the j-th direction. Assuming that the total sliding velocity in normal direction V3,n for the generic contact point n is null (wheel and rail remain always in contact) and defining

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Fig. 2 Wheel-rail self-excited loop in frequency domain [4]

the following quantities:   n = 1, 2 d nT = Y13,1n Y23,1n Y63,1n Y13,2n Y23,2n Y63,2n a nT = bnT



Y31,n1 Y32,n1 Y33,nn Y33,nn

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where [C] is obtained by removing the rows and the columns of the matrix [Y ] related to the normal direction. By including in Eq. 7 the linearized relation between contact forces and creepages, a self-excited loop describing the wheel/rail coupled system is obtained [2, 4, 7]: F = ([H 1 ][E] + [H 2 ])F

(8)

where the matrix [H 1 ] and [H 2 ] contain respectively the effect of the friction coefficient with respect to a fluctuation in creepages and in the normal load. The stability of the Multi-Input Multi-Output (MIMO) system (see Fig. 2) is analyzed through the Generalized Nyquist Criterion [8]. The self-excited loop may become unstable due to mode-coupling (i.e. dynamic coupling between axial and radial directions) or due to falling friction mechanism, which is introduced through the heuristic formula adopted in [4, 7].

2.2 Wheel, Rail and Contact Dynamics The wheel natural frequencies and mode shapes are collected through a finite element model, while damping ratios are estimated experimentally. Wheel mobility in different directions is obtained through modal superposition approach (Eq. 9):

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Fig. 3 Wheel mobility in radial (a) and axial (b) directions: comparison between FEM (orange hyphen) and experimental results (blue hyphen)

Yikw (ω) =

∑ n



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where ωn is the natural circular-frequency of mode n, ξn is the damping and mn is the modal mass. The numerator collects the mode shapes φin and φkn associated to mode n and the degrees of freedom i, k. The wheel model is validated by means of comparison with the results of an experimental modal analysis of the wheel. The experimental and numerical point mobilities of the wheel in radial (a) and axial (b) directions are shown in Fig. 3. Similarly to the wheel model validation, the parameters of the analytical model adopted to describe the track dynamics [2, 9] are calibrated in order to fit the experimental mobilities obtained through an impact test carried out on the track in the reference site, consisting in an embedded rail system with 62R1 profile. The rail model is formulated neglecting the coupling between the lateral and the vertical dynamics, thus assuming that the wheel/rail contact forces are applied along the rail principal axes of inertia.

3 Curve Squeal Simulation Curve squeal occurrence prediction is performed by simulating a tramcar with independently rotating wheels (IRW) negotiating a 24 m radius curve at 10 km/h. The effect of multiple wheel/rail contact on curve squeal occurrence is investigated by comparing the results obtained considering a single wheel/rail contact point and the ones including the presence of multiple contacts. A set of 200 simulations is performed for each analyzed case, varying randomly the model inputs (creepages, falling friction coefficients, normal load, contact position, contact plane angle, etc.). This approach allows accounting for the statistical variability of the contact parameters. According to past research, the most critical situation in terms of curve squeal

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Fig. 4 Contact forces computed through multibody simulation on the inner wheel in normal (blue right arrow) and transversal (orange right arrow) directions: tread (I) and flange back (II) contact points

(a)

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occurrence is found to be on the leading inner wheel of the bogie [1]. Experimental campaigns have been performed on the reference vehicle [5, 6], highlighting the presence of simultaneous wheel/rail contact on the wheel tread and on the wheel flange back. The experimental results are also confirmed by the vehicle multibody simulations [10]. The steady state contact forces on the inner front wheel are reported in Fig. 4. The multibody simulation allows to reproduce an accurate contact condition, by including the possible presence of simultaneous multi-Hertzian contact patches, due to the local deformation of wheel and rail. However, a single contact case (a) is first obtained, by assuming that the forces are exchanged only in the geometrical contact point. Then, a more realistic condition is studied, including the possible simultaneous presence of multiple wheel/rail contacts (b), as reported in [11, 12]. Despite the limited loading of the back flange contact point (1.8 kN) with respect to the tread one (31.5 kN), its effect on the wheel/rail coupled dynamics and on curve squeal seems to be quite remarkable. The results of curve squeal prediction considering single (a) and double contact (b) models are reported in Fig. 5 and compared with the sound pressure level measured in the reference site (c). Unstable cases are collected through orange dots “•” on the wheel axial and radial point mobility. It is interesting how the instability of the system around 550 Hz seems to be completely absent in the double contact point simulations. This is also confirmed by the experimental SPL measurements (c). The reason for this result has been attributed to the physical constraint imposed by the flange back to the wheel in lateral direction, which reduces the coupled system mobility in this direction. Thus, being the system dynamics around 550 Hz governed by the wheel axial mode with 2 ND, the presence of the flange back contact limits the overall axial mobility of the system, preventing the possible self-excitation of the wheel in correspondence to this frequency. In the double contact case (b) the highest curve squeal occurrence is predicted in correspondence to the wheel modes characterized by both axial and radial vibration. This is the case of the 3 ND axial (1273 Hz) and radial (1423 Hz) modes and the 4ND of the radial (2230 Hz) and axial modes (2479 Hz). The frequency shift between wheel natural frequencies and unstable ones, observed both numerically and experimentally, may be attributed to two main reasons. First, the wheel/rail coupled mobility ([E]) is different with respect to the one of the wheel alone. Furthermore,

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system instability may be the result of mode-coupling mechanism, which is usually featured by a frequency shift between the natural frequencies of the modes involved and the unstable ones. Thus, the same simulations presented in Fig. 5 are repeated, suppressing the falling friction mechanism, to highlight the mode-coupling contribution only in the system instability. No unstable cases are obtained in the single-contact point simulation, while the double-contact points results are collected in Fig. 6. The simulation results suggest that the presence of multiple contact between wheel and rail favors the occurrence of mode-coupling type of instability. This evidence

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can be explained by the presence of wheel/rail transversal forces oriented towards the radial direction, thus promoting the coupling between wheel axial and radial modes. The results presented in [5], confirmed by the current numerical simulations (see Fig. 5), reveal how a different loading condition on the flange back of the inner wheel determines different modes of vibration involved in the curve squeal phenomenon. In fact, the measurements performed on two similar curves highlight a dominant noise emission around 530 Hz in the first site and around 1560 Hz in the second one, in which the flange back contact was proved to be much more loaded. These numerical and experimental evidences confirm that a reliable curve squeal predictive model should include the possible presence of multiple contact point between wheel and rail.

4 Conclusions The curve squeal prediction of a tramcar negotiating a 24 m radius curve is presented including the presence of double contact points between wheel and rail. The tramcar dynamic behavior during the curve negotiation is obtained through a multibody simulation. The steady state curving conditions are the input of the curve squeal predictive tool, that consider the wheel/rail coupled dynamics in the longitudinal, transversal and vertical directions. A stability analysis about the steady state curving condition is carried out to detect the unstable frequencies at which the curve squeal noise is expected to occur. A set of simulations for each analyzed case is performed to account for the statistical variability of the wheel/rail contact conditions. A comparison between curve squeal prediction considering a single contact point model and double contact condition is presented. The analysis suggests that the presence of a flange-back contact condition alters the wheel/rail coupled dynamics, decreasing the system overall mobility in lateral direction and the squeal occurrence probability in correspondence of the wheel axial mode with 2 nodal diameters (535 Hz). Moreover, the flange contact condition seems to favor the coupling between the lateral and radial direction, increasing the possibility to excite wheel mode shapes with a relevant radial modal deflection. The predicted behavior is similar to the one observed experimentally, including the measured frequency shift typical of mode-coupling mechanisms.

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References 1. Thompson DJ, Squicciarini G, Ding B, Baeza L (2018) A state-of-the-art review of curve squeal noise: phenomena, mechanisms, modelling and mitigation. Notes on Numerical Fluid Mechanics and Multidisciplinary Design 139:3–41 2. Thompson D (2008) Railway noise and vibration: mechanisms, modelling and means of control. Elsevier 3. Ding B, Squicciarini G, Thompson D, Corradi R (2018) An assessment of mode-coupling and falling-friction mechanisms in railway curve squeal through a simplified approach. J Sound Vib 423:126–140 4. Huang Z (2007) Theoretical modelling of railway curve squeal. PhD thesis, University of Southampton 5. Corradi R, Facchinetti A, Manzoni S, Vanali M (2006) Effects of track parameters and environmental conditions on tramcar induced squeal noise. ISMA2006: International Conference on Noise and Vibration Engineering, pp. 3745–3759 6. Corradi R, Crosio P, Manzoni S, Squicciarini G (2011) Experimental investigation on squeal noise in tramway sharp curves. In: Proceedings of the 8th international conference on structural dynamics, EURODYN 2011, pp. 3214–3221 7. Squicciarini G, Usberti S, Barbera A, Corradi R, Thompson D (2015) Curve squeal in the presence of two wheel/rail contact points. Notes on Numerical Fluid Mechanics and Multidisciplinary Design 126:603–610 8. MacFarlane A, Postlethwaite I (1977) The generalized Nyquist stability criterion and multivariable root loci. Int J Control 25:81–127 9. Wu T, Thompson D (1999) Analysis of lateral vibration behavior of railway track at high frequencies using a continuously supported multiple beam model. J Acoust Soc Am 106:1369– 1376 10. Belforte P, Cheli F, Corradi R, Facchinetti A (2003) Software for the numerical simulation of tramcar vehicle dynamics. Heavy Veh Syst - Int J Veh Des 10:48–69 11. Pascal JP, Sauvagemen G (1993) The available methods to calculate the wheel/rail forces in non Hertzian contact patches and rail damaging. Veh Syst Dyn 22:263–275 12. Bruni S, Collina A, Diana G, Vanolo P (2000) Lateral dynamics of a railway vehicle in tangent track and curve: tests and simulation. Veh Syst Dyn 33:464–477

Experimental Study on Curve Squeal Noise with a Running Train Yasuhiro Shimizu, Takeshi Sueki, Tsugutoshi Kawaguchi, Toshiki Kitagawa, Hiroyuki Kanemoto, and Masahito Kuzuta

Abstract Field tests were conducted at the Railway Technical Research Institute to clarify the mechanism of curve squeal noise. Simultaneous measurements of noise and vibration on the track side and onboard revealed the following results: (1) curve squeal noise is generated at frequencies closely related to the wheel resonance, (2) squeal noise does not necessarily occur on all curves, (3) the intensity of the squeal significantly depends on the conditions of the wheel and rail surfaces, and (4) the vibration of the leading wheel on the inner rail of the curved sections is the dominant noise source. The vibration generated by the roughness of the wheels and rails was estimated based on the measured roughness and its vibration characteristics obtained by hammering tests. The results show that the contribution of the vibrations caused by roughness is quite small near the natural frequency of the wheels, at which the squeal is dominant. Keywords Railway noise · Wheel/rail noise · Wheel vibration · Rail vibration

1 Introduction Curve squeal noise is a source of railway noise, in which a tonal noise is emitted by a moving train on curved rails. To understand the generation mechanisms of the squeal noise and develop measures to reduce it, it is necessary to investigate the curve squeal noise generated by train wheels and railway tracks and associated vibrations while a train is running. A previous study [1] reported that curve squeal noise is generated from the inner leading wheels of a train. However, the contributions of wheels and rail vibrations to curve squeal noise have not been investigated in detail. In this study, curve squeal noise and its associated vibrations were measured through field tests at two curved rail sections to determine the characteristics of the curve squeal noise generated during train passages. These tests involved simultaneous Y. Shimizu (B) · T. Sueki · T. Kawaguchi · T. Kitagawa · H. Kanemoto · M. Kuzuta Railway Technical Research Institute, 2-8-38 Hikari-Cho, Kokubunji-Shi, Tokyo 185-8540, Japan e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_48

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measurements of noise and vibrations on the trackside and onboard. Based on the results obtained from the tests, we identified the dominant source of squeal noise. These results could then be used to clarify the characteristics of curve squeal noise.

2 Outline of the Field Tests 2.1 Test Vehicle and Test Sections Field tests were conducted on the test line at the Railway Technical Research Institute (Figs. 1 and 2). The test train comprised one 20-m long trailer vehicle and one locomotive. The train runs on a maximum velocity of approximately 30 km/h. The leading wheels of the target bogie have a straight web and are called the “C-type wheels” in Japan. The trailing wheels have a double-curved web and are called “NAtype corrugated wheels” in Japan. The test measurements were conducted on one straight and two curved track sections. The specifications of each section are given below: Curve 1: Radius = 230 m, Cant = 105 mm, Slack = 20 mm. Curve 2: Radius = 160 m, Cant = 105 mm, Slack = 20 mm. The railhead surfaces were dry or wet, and the train traveled in one direction (Figs. 1 and 2).

2.2 Hammering Tests The track at the test sections and the wheels of the target bogie were excited using an impulse hammer to measure their vibration characteristics. Figure 3 shows all excitation points. The wheel vibrations were measured using accelerometers installed on the webs and tires of both wheels in the same straight line. The tread and tires

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were excited at 7.5° intervals within a 180° range. The excitation was conducted from the points on the extension of the line connecting the center of the axle and the accelerometers. During the measurements of the rail vibrations, the rail heads were excited in the vertical and horizontal directions.

2.3 Trackside Measurements Accelerometers and microphones were installed on Curves 1 and 2 (Figs. 2 and 4b). The figures show the installation positions of the sensors on the curved sections. The arrows on Fig. 4 indicate the installation positions of the accelerometers and the direction in which the vibrations were measured.

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2.4 Onboard Measurements Accelerometers were installed on the leading wheels (Fig. 4a). In addition, microphones were installed close to the leading wheels (Figs. 1 and 4). The vibrations obtained at VS7 as well as the noise obtained at S2 are discussed in this study. Signals from the accelerometers installed on the leading wheels were transmitted to the car via slip rings in the axle boxes. The maximum measured frequency of the leading wheel vibration and noise was approximately 20 kHz. On the trailing wheels, only the accelerometers VT1 and VT2 were installed in the same position as VS3 and VS7.

2.5 Roughness Measurements The profiles of the wheel tread and rail surface were obtained using a probe. The wheel-tread roughness was measured at 0.5-mm intervals in the circumferential direction at multiple locations in the axle direction. The rail roughness of the curved and straight sections was measured over a 1 m length at lateral positions spaced 1 mm apart. The measured roughness data were analyzed using the maximum entropy method (MEM) [2]. Using this method, the roughness of long wavelengths can be estimated with high accuracy. The results of the MEM analysis were summarized into level values with a reference value of 1 µm.

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Fig. 5 Frequency responses obtained using the impulse excitation test

3 Results and Discussion 3.1 Hammering Tests Figure 5 shows the accelerance (vibration acceleration per unit force) of the inner leading wheel (VS7) and that of the inner rail of the curved sections (VRL2) obtained during the impact excitation tests. The results of the leading wheels show several peaks at different frequencies, e.g., 1.1, 2.0, 2.4, and 3.0 kHz (Fig. 5a). The peaks were obtained at the same frequencies in both excitation directions, but they vary in their magnitudes. By hammering the wheels at 7.5° intervals, the mode shapes of these peaks were identified. Among them, the peaks observed at 1.1, 2.0, and 3.0 kHz correspond to the 0-nodal circle out-of-plane vibration modes of the C-Type straight wheel with nodal diameters of 3, 4, and 5, respectively. The 2.4-kHz peak corresponds to the 1-nodal axial vibration mode with a 2-nodal diameter. Several other peaks also correspond to the out-of-plane vibration modes. Peaks such as those observed at 1.4, 2.0, and 2.9 kHz are shown in the trailing wheel results (VT2, not shown in this paper). These peaks correspond to the out-of-plane vibration modes for the NA-type wheels [3]. On the other hand, no clear peak was observed in the vibration of the rail in any direction in both curves (Fig. 5b).

3.2 Trackside Measurements Figure 6 shows the frequency spectra of the lateral vibration (VRH2/VRL2) and noise at points close to the tracks (SHC/SLC) when the train was traveling at approximately 30 km/h on Curves 1 and 2 under dry conditions. The figure also shows the noise collected from the microphone installed on the straight section. In case of Curve 1,

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Fig. 6 Noise and vibrations of the studied rails

no sharp peaks were observed in the rail vibration during the passage of the leading or trailing wheels (Fig. 6a). In addition, the noise near the rail on Curve 1 (Fig. 6b) was similar to that on the straight section, and it is considered that no squeal noise was generated. In Curve 2, sharp peaks were observed in the rail vibration spectra at 2.0 and 4.0 kHz (Fig. 6c). These peaks were more noticeable when the leading wheels were passing through the curve compared to when the trailing wheels were passing, and the peaks on the inner side were larger than those on the outer one. These results combined with the onboard measurement results discussed in the next section indicated that the squeal noise on the inner-rail side was the loudest when the leading wheel was passing. These frequencies match the natural frequencies of the wheel measured by the hammering test. It is thought that the sharp peaks observed only at 2.0 and 4.0 kHz are due to the high excitation force at those frequencies. In contrast, no clear frequency peak was observed in the rail vibrations (Fig. 5c). Therefore, these vibrations are considered to be generated by the wheels. The peaks observed in the noise spectra near the rail have almost the same frequencies as the vibrations of the rail (Fig. 6d). However, the difference between the inner and outer peak magnitude was less than that between their vibration results. This is thought to be because the noise on the outer side includes that generated from the inner side.

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The reason for the difference in the generation of the squeal noise between Curve 1 and Curve 2 is not clear. However, this may be due to differences in contact conditions resulting from different track conditions, such as the radius of the curvature.

3.3 Onboard Measurements As shown in the previous section, the squeal noise was generated when the leading wheel on the inner-rail side passed through Curve 2. In this section, these results are further discussed. In the dry state (Fig. 7a), peaks were observed in the wheel vibration results at different frequencies such as 1.1, 2.0, 2.4, and 3.0 kHz. As shown in the hammering test results, the dominant frequencies of the squeal noise correspond to the out-ofplane vibration modes of the wheel. In addition, the vibration of the wheel shows the maximum peak at 2.0 kHz. This tendency is consistent with the results of the trackside measurements. In the result of the noise near the wheels (Fig. 7b), peaks were also observed at different frequencies such as 1.1, 2.0, and 3.0 kHz. They match the prominent peaks in the wheel vibration. However, not all these frequency peaks occur in the rail vibrations or noise. The cause of this is currently unknown and requires further investigation. Under wet conditions, the peak of the wheel vibration observed at 2.0 kHz was lower, on the other hand, the peak at 1.1 kHz was slightly larger than those observed under dry conditions. This was also the case in the noise spectra, which may be attributed to the change in the friction between the wheels and rails due to the presence of water. In the trailing wheel vibrations (not shown in this paper), peaks were also observed at frequencies corresponded to the out-of-plane vibration mode of the wheel. As with the trackside measurement results, vibrations generated when the trailing wheel passed through the curve were smaller than those generated by the leading wheel (measured from the opposite side of the wheel flange).

Fig. 7 Noise and vibration from the inner leading wheel at curve 2

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Fig. 8 Averaged roughness of wheel treads and rail surfaces

The roughness of the rails and wheel is averaged over several measurement lines in the transverse direction (Fig. 8). The horizontal axis of the figure represents the spatial frequency, which is the inverse of the wavelength. The figure indicates that both wheels have slightly large roughness around 50 m−1 . The average roughness of the wheels on both sides is approximately the same. In both Curves 1 and 2, almost equal roughness levels of 10 m−1 and higher were measured for both rails. The roughness in the straight section is greater than that in either curve (10 m−1 or higher). Figure 9 shows the estimated vibrations caused by the roughness of the rails and wheels assuming a train speed of 33 km/h. Each vibration velocity amplitude can be obtained using Eq. (1): vw =

iωr Yw iωr Yr , vr = Yw + Yr Yw + Yr

(1)

where iωr is the roughness velocity amplitude. Y w and Y r are the wheel and rail mobilities (vibration velocity per unit force), respectively. Here, the mobility of the contact spring, Y c , is negligible. In the figure, the estimated vibrations near the natural frequency of the wheel (where squeal is predominant) are quite smaller than the measured vibrations and are comparable to those of the straight sections. This indicates that the contribution from the vibration caused by roughness to the squeal noise is very small, i.e., roughness has little direct effect on squeal generation.

4 Conclusions Field tests were conducted to investigate curve squeal noise of trains using a test train. Based on the measurements obtained from these tests, the characteristics of curve squeal noise are summarized as follows:

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Fig. 9 Estimated vibrations generated by roughness

• The vibrations and noise of the inner leading wheels of the train are greater than those of the other wheels. • The dominant frequencies of curve squeal noise obtained in the field tests conducted in this study correspond to the axial natural frequencies of the wheel. • The prominent frequencies of the vibration and noise of the wheel may not always be observed as a curve squeal noise on the ground. • The roughness of the rails and wheels do not directly affect the generation of squeal noise.

References 1. Thompson DJ (2009) Railway noise and vibration: mechanisms, modeling and means of control, Elsevier Ltd. 2. Hino M (1977) [Spectrum analysis] Supekutoru Kaiseki. Asakura Publishing Co., Ltd, pp 86–88 in Japanese 3. Kitagawa T et al (2003) Application and validation of the TWINS model for Japanese railways. ISVR Techn Memorandum 919:220

Interior Noise

A Study on Vibration Transmission in the Suspension/bogie System of a High-Speed Train Mingyue Wang and Xiaozhen Sheng

Abstract Vibration transmitted to a car body through the wheelset, bogie and suspension system is one of the main sources generating interior noise for a highspeed train. In order to derive measures for controlling train interior noise, it is necessary to determine the high-frequency (up to about 1000 Hz) operational forces in the suspension/bogie system and to quantify vibration powers input for each force to the car body. These operational forces can be estimated if sufficient measured vibration data of the bogie frame are available. However, since the number of the forces is large, and the number of sensors which can be installed is limited, measured vibration data are often insufficient to determine the forces and the associated vibration powers. To overcome this difficulty, an approach making use of response reconstruction is developed in this paper. Firstly, a time-domain response reconstruction method based on empirical wavelet transform is applied so that, although measurement is performed for a limited number of locations, responses of the frame at other locations can be reconstructed, giving sufficient response data for force identification. Secondly, with the measured and reconstructed responses, forces are identified using regularization techniques developed for inverse problems. Finally, a power-transfer path analysis is attempted to rank the vibration transmission paths between the bogie system and the car body. Keywords High-Speed train · Transfer path analysis · Load identification · Dynamic response reconstruction

M. Wang (B) State Key Laboratory of Traction Power, Southwest Jiaotong University, Cheng-du, Sichuan, China e-mail: [email protected] X. Sheng School of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai 201620, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_49

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1 Introduction Train interior noise is mainly contributed via two transfer paths. One is airborne through which noise outside the train excites the car body to vibrate and the vibration radiates sound inside the train, generating a part of interior noise. The other path is structure-borne through which the other part of interior noise is generated by car body vibration which is transmitted structurally through the wheelset, primary suspensions, bogie frames and secondary suspensions. In order to derive measures for controlling structure-borne train interior noise, it is necessary to determine the highfrequency (up to 1000 Hz) operational forces in the suspension/bogie system and to quantify vibration powers input by each force to the car body. These operational forces can be estimated if sufficient measured vibration data of the bogie/bolster are available. However, since the number of the forces is large, and the number of sensors which can be installed is limited, measured vibration data are often insufficient to determine the forces and the associated vibration powers. This paper proposes an approach to tackle this problem and to analyze vibration transmission in the suspension/bogie system of a high-speed train. Response reconstruction is to use measurement data at a limited number of locations to get as much response information as possible, in case of measurement is not performed for a sufficient number of locations due to various reasons. Recent studies have proposed several types of dynamic response reconstruction methods. The most common method is based on the transmissibility concept [1–4], and the unknown responses are reconstructed using the known responses and the transmissibility matrix in the frequency domain. This method requires the knowledge of excitation locations and a sufficient number of measurement responses. The second type is developed from modal theory [5–7] and has been extended to be based on empirical mode decomposition (EMD) and structural finite element modeling (FEM) [8, 9]. The time-domain signals at unmeasured locations are reconstructed by summarizing the reconstructed modal responses, which derived from EMD-obtained intrinsic mode functions (IMFs) and FE-calculated transmission ratios. The quality of the reconstruction is largely limited by issues in EMD, such as mode mixing, sensitive to measurement noise, etc. Meanwhile, more advanced state estimation methods based on Karman filtering techniques [10–12] are also developed for response reconstruction. The filtering technique-based state estimation methods still work on the condition that the number of measurements is larger than the total number of external excitations. It turns out that, when the number of measurement locations is limited, the EMDbased method is most often applied, although, as already pointed out, the EMDbased method has its own weaknesses. Therefore, this paper introduce the empirical wavelet transform (EWT) [13, 14], which can overcome the shortcomings of EMD in vibration response decomposition, combined with transfer matrix, to reconstruct response in the time-domain, especially for complex engineering structures such as the bogie described above.

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According to the classical transfer path analysis (TPA) approach [15, 16], estimation of the interface forces is a vital step, and frequency response function (FRF) matrix inversions are commonly involved. To obtain the FRFs experimentally, the bogie system must be disassembled and a large number of FRF measurements have to be performed on the bogie frame. They are troublesome and time-consuming. Alternatively, the required FRFs may be produced by the finite element method. However, inversion operation of a FRF matrix may give rise to large errors because the condition number of the FRF matrix is considerably high, especially at and near the structural resonances. It is well known that, force identification, as an inverse problem, is usually ill-posed and difficult to find an accurate solution. In this regard, the regularization techniques, such as Tikhonov regularization, truncated singular value decomposition (TSVD) and L1-regularized are utilized to increase the inversion stability. With the identified forces, mechanical powers transmitted or received by the bogie frame/bolster may be estimated and ranked, providing a structural vibration transfer path analysis for the high-speed train. The paper is structured as follows. The approach is formulated in Sect. 2. The bogie and its finite element model and an in-situ test are described in Sect. 3. An analysis on the vibration response data of the test is also presented in this section. Other results, including reconstructed responses, identified forces and powers flowing to, or out from, the bogie system, are accommodated in Sect. 4. And finally, the paper is concluded in Sect. 5.

2 The Approach The main purpose of this paper is to determine the operational forces on and vibration powers to the bogie system. Firstly, in case of that directly measured responses are too few to determine the forces and powers, the response reconstruction technique is used to generate vibration data for locations where vibrations have not been measured. Secondly, the time-domain operational forces applied to the bogie system are identified using regularization techniques based on the measured and reconstructed responses and the frequency response functions. Finally, with the identified forces, mechanical powers transmitted or received by the suspension/bogie system are then estimated and ranked, providing a structural vibration transfer path analysis for the high-speed train. Response reconstruction. In view of limitations in the number and installation positions of sensors on the bogie system, a time-domain response reconstruction based on empirical wavelet transform is performed. Empirical wavelet transform is used to decompose each measured response signal into a number of mono-components. Structural responses at unmeasured locations are reconstructed from those monocomponents and dynamic properties derived from the finite element model of the bogie frame, as in Ref. [17].

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Operational force identification. With the FE model, FRFs can be generated. The operational forces can be obtained from a sufficient number of operational responses by a frequency response function (FRF) matrix of the structure. Since the FRF matrix is often ill-conditioned, especially at or near the structural resonance frequencies, direct inversion of the FRF matrix may give rise to large errors. To overcome this difficulty, regularization techniques are utilized to increase the inversion stability. Power exchange. Elements between the bogie frame and the car body will transmit different vibration powers from the bogie to the car body. In an attempt to investigate the vibration transmission characteristics of the bogie, the powers are estimated and ranked, providing a structural vibration transfer path analysis.

3 In-Situ Test, FE Model and Data Analysis 3.1 The Layout of the Measurement Points on the Bogie System The test was performed on a typical Chinese high-speed train. The train runs along a newly built ballastless track at a maximum speed of 350 km/h. The bogie used in this study is from the trailer bogie located under the driver’s cab and is shown in Fig. 1. It can be observed that the carbody is connected to the bogie by a bolster, which is fixed under the carbody. Ideally, a measurement point should be as close to an excitation source as possible and at the same time, not located at a modal node of the structure. Limited by the measurement environment, only 10 vibration acceleration sensors with 24 channels were arranged on the bogie frame. Similarly, only 6 vibration measurement points with 12 channels were arranged on the bolster. The layout of the measurement points on the bogie frame and the bolster is depicted in Fig. 2 with the measured points indicated by symbol “⊗”. Fig. 1 A trailer bogie of the high-speed train

A Study on Vibration Transmission in the Suspension/bogie System … 1B3

(a)

527 1C6

(b)

1B9

1B4 1B5

1C4 1B7 1B8 1B2

1B1

1C2

1B6

1C1

1C5 1B10

1C3

Fig. 2 Finite element model and the layout of measurement points a bogie frame, b bolster

Measurement points 1B1, 1B2, 1B3 and 1B4 are just above the axle-box spring seat (where 1B indicates it is the first bogie); 1B5 and 1B6 are near the air spring seats; 1B7 and 1B8 are above the traction rod seat; 1B9 and 1B10 are above the antiroll torsion bar seats. Besides, 1C1 and 1C2 are just above the left traction rod seat of the bolster; 1C3 and 1C4 are near the left antiroll torsion bar of the bolster; 1C5 and 1C6 are located on car body just above the bolster.

3.2 The FE Model and Modal Analysis The bogie frame is an H-shaped and welded structure but is not completely symmetric. It is made of weather-resistant steel. The material density is 7800 kg/ m3 and Young’s modulus is 2.061011 Pa. The bolster is made of cast aluminium alloy, with material density is 2700 kg/m3 and Young’s modulus is 7.11010 Pa. Figure 2 shows the finite element model of the bogie frame and bolster used in this paper. Since the technique of response reconstruction used in this paper requires the modal shapes of the nodes, the accuracy of the FE model is verified by the operational modal analysis (OMA), which is carried out using LMS Test. Lab based on the acceleration of the bogie frame and bolster measured in the test.

3.3 Test Data Analysis As a train runs along a track, dynamic wheel/rail forces are induced due to wheel/rail irregularities. Vibration data are sampled at a sampling frequency of 5000 Hz, although for train interior noise, frequencies concerned are from 20 to 800 Hz. Figure 3 shows the frequency spectrum of the vertical vibration acceleration measured at an axle box, the bogie frame and the car body in bogie area with the train running at 121, 156, 221 and 323 km/h along the subgrade section. It can be seen that, the spectra have a modulation characteristics. The fundamental characteristic frequencies are, respectively, 11.60, 14.34, 21.97 and 31.13 Hz, equal to the corresponding rotating frequencies of the wheel which has a diameter of

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Fig. 3 The spectrum of the vibration acceleration in bogie area

920 mm. This indicates that one of the rotating wheels creates periodically impulsive excitations to the bogie.

4 Vibration Transmission in the Suspension/Bogie System As analyzed in Sect. 3.3, the rotating wheels create periodically impulsive excitations to the bogie. Subject to such excitations, natural modes of the bogie will be excited and the response spectrum has peaks not only at the modal frequencies, but also at wheel rotating frequency and its harmonics. To separate the modal frequencies from the excitation frequencies, a time-history is divided into sections (sub-time periods), so that each section contains a single impulse event only. For a given sub-time period, the bogie frame/bolster is excited by a single impulse excitation and the response can be calculated to be a sum of modal responses. These modal responses are a set of mono-components each only containing a single mode

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Fig. 4 Measured and reconstructed response at location 1C3Y. a time-history; b spectrum. (The red dotted line represents the reconstructed response; the black solid line represents the measured response)

of the bogie frame/bolster. Then, the corresponding component in the to-be reconstructed response is predicted using the associated transfer matrix derived from the shape of that mode, as explained in Sect. 2. To check the accuracy of the response reconstruction method, responses are reconstructed for certain locations at which the responses are actually measured. Comparison is shown in Fig. 4 with good agreement. Noise in measured data is may be the major factor, which contributes to the difference between the reconstructed and measured responses. To determine the operational forces, it is necessary to reconstruct the dynamic response of the bogie frame and bolster at the forcing dofs, using the same procedure. Then, the operational forces can be obtained from a sufficient number of operational responses. Having worked out the forces and the responses at the loading degrees of freedom, powers done by the connection elements in the primary and secondary suspensions to the bogie frame, and the secondary suspensions to the car body can be estimated (Fig. 5). Elements in the primary suspension are always inputting powers to the bogie frame with the vertical damper and the axle box spring being the main contributors. Powers flow to the carbody mainly through the secondary transverse damper and the antiroll torsion rod.

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Fig. 5 The overall powers (0–800 Hz) flowing to, or out of a bogie frame; b bolster

5 Conclusion This paper demonstrates that the time-domain responses of the bogie frame and bolster at force locations can be reconstructed from responses measured at other locations. With the reconstructed responses, forces applied to, and vibration powers transmitted by, the bogie frame and bolster can be estimated, providing structural vibration transfer path analysis for the high-speed train. Acknowledgements This work is funded by the National Natural Science Foundation of China (U1834201, U1934203).

References 1. Ribeiro AMR, Silva JMM, Maia NMM (2000) On the generalization of the transmissibility concept. Mech Syst Signal Process 14(1):29–35 2. Law SS, Li J, Ding Y (2010) Structural response reconstruction with transmissibility concept in frequency domain. Mech Syst Signal Process 25(3):952–968 3. Law SS, Li J, Ding Y (2012) Substructure damage identification based on response reconstruction in frequency domain and model updating. Eng Struct 41(8):270–284 4. Li J, Law SS (2011) Substructural response reconstruction in wavelet domain. J Appl Mech 78(4):041010-1–041010-10 5. Kammer DC (1997) Estimation of structural response using remote sensor locations. J Guid Control Dyn 20(3):501–508 6. Zhang XH, Zhu S, Xu YL, Hong XJ (2011) Integrated optimal placement of displacement transducers and strain gauges for better estimation of structural response. Int J Struct Stab Dyn 11(3):581–602 7. Zhang XH, Xu YL, Zhu S, Zhan S (2014) Dual-type sensor placement for multi-scale response reconstruction. Mechatronics 24(4):376–384 8. He JJ, Guan XF, Liu Y (2012) Structural response reconstruction based on empirical mode decomposition in time domain. Mech Syst Signal Process 28(1):348–366

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9. Wan ZM, Li SD, Huang QB, Wang T (2014) Structural response reconstruction based on the modal superposition method in the presence of closely spaced modes. Mech Syst Signal Process 42(1):14–30 10. Zhu SY, Zhang XH, Xu YL, Zhan S (2013) Multi-type sensor placement for multi-scale response reconstruction. Adv Struct Eng 16(10):1779–1797 11. Xu YL, Zhang XH, Zhu SY, Zhan S (2016) Multi-type sensor placement and response reconstruction for structural health monitoring of long-span suspension bridges. Sci Bull 61(4):313–329 12. Zhang CD, Xu YL (2016) Optimal multi-type sensor placement for response and excitation reconstruction. J Sound Vib 360(1):112–128 13. Gilles J (2013) Empirical wavelet transform. IEEE Trans Signal Process 61(16):3999–4010 14. Gilles J, Heal K (2014) A parameterless scale-space approach to find meaningful modes in histograms—application to image and spectrum segmentation. Int J Wavelet Multiresolution Inf Process 12(6):1450044 15. Seijs M, Klerk DD, Rixen DJ (2016) General framework for transfer path analysis: history, theory and classification of techniques. Mech Syst Signal Process 68–69(2):217–244 16. Oktav A, Yilmaz C, Anlas G (2017) Transfer path analysis: current practice, trade-offs and consideration of damping. Mech Syst Signal Process 85(2):760–772 17. Wang MY, Sheng XZ (2022) Combining empirical wavelet transform and transfer matrix or modal superposition to reconstruct responses of structures subject to typical excitations. Mech Syst Signal Process 163(15):108162

Bi-objective Sound Transmission Loss Optimal Design of Double Panels Using a Genetic Algorithm Y. M. Zhang, Y. Zhao, D. Yao, Y. Li, X. B. Xiao, K. C. Zuo, and W. J. Pan

Abstract This paper presents a bi-objective optimization of double panels for simultaneously minimizing mass while maximizing the weighted sound transmission loss (STL). Firstly, the acoustic model of double panels is introduced based on the wave propagation method and modal superposition method. Secondly, the optimization problem is formulated as a bi-objective programming model, and a solution algorithm based on the non-dominated sorting genetic algorithm II (NSGA-II) is provided to solve the proposed model. Finally, taking a standard window structure on a high speed train as a reference structure, an optimization calculation based on nondominated sorting genetic algorithm II (NSGA-II) is carried out to get the Pareto front solutions. The fitting formula of the mass and weighted STL (Rw ) under the Pareto front solution is obtained, which provides a reference for the design and selection of Rw under different masses. The frequency sound insulation characteristics and its STL mechanism of the optimized double panel are further analyzed, which shed some light on the lightweight design of double panel structures. Relative optimization method can also be applied to airplane’s window design. Keywords Double panel · Transmission · Lightweight · Pareto Front

Y. M. Zhang (B) · Y. Zhao · D. Yao · W. J. Pan Civil Aviation Flight, University of China, 46 Nanchang Road, Guanghan, Sichuan, P.R. China e-mail: [email protected] Y. M. Zhang · Y. Zhao · D. Yao · K. C. Zuo Key Laboratory of Aerodynamic Noise Control, China Aerodynamics Research and Development Center, Mianyang Sichuan 621000, China Y. Li · X. B. Xiao Southwest Jiaotong University, 111 Second Ring Road, Chendu, Sichuan, P.R. China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_50

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1 Introduction Double panels are one of the main components of the transportation vehicles, including high-speed train, airplane, marine and automotive. Windows, for example, are usually formed with double panels to strengthen their acoustic performance. Improvement of the window’s Sound Transmission Loss (STL) can reduce the interior noise from this transmission path [1]. On the STL improvement research of double panels, there are studies on the improvement of sound insulation by adding mass to the double panel [2], filling the cavity with sound-absorbing materials [3], and installing Magnetic-Linked Stiffness [4]. However, for the window structure, due to its sightseeing performance, adding additional materials on the structure is limited. Ideally, its STL can be optimized from the structure itself. The wave propagation method is one of the most effective and common methods to simulate the STL of double panels [5]. The authors’ previous study of windows’ acoustic properties including the vibration measurement and STL simulation of highspeed window has been given for a high-speed train at running speed of 250 km/h [6]. The motivations in this study focus on exploring the optimization of minimizing panel mass and maximizing sound insulation performance. Among the multi-objective optimization for minimum weight (or mass) and maximum acoustic transmission loss of panel structures, genetic algorithm (GA) approaches were used to study the optimization of symmetric laminated composite cylindrical shells by Shojaeifard [7] and sandwich panel by Wang et al. [8]. The non-dominated sorting genetic algorithm II (NSGA-II) is an improved version of NSGA, which has been widely used to solve multi-objective optimization. Among lightweight STL optimization of panel structures, Xu et al. [9] has applied it in the optimization of sandwich panels and Zhou et al. [10] optimized the double-walled panel with poroelastic lining in the core for minimum weight and maximum acoustic transmission loss based on NSGA-II. NSGA-II is chosen as the optimization method here. This paper is organized as follows. In Sect. 2, the STL model of double panels based on wave propagation method and modal superposition method is introduced. In Sect. 3, the optimization objective function and constraints are given. The optimal solution is the maximum Rw and the minimum mass, while the thickness of each panel and air gap of double panel are set as design parameters. In Sect. 4, a window on a high-speed train is chosen as a reference double panels structure to be optimized.

2 STL Model of Double Panels The STL model of a double panel is built based on the wave propagation and modal superposition method [5, 6]. A schematic view of the window is shown in Fig. 1. For simplicity, simply supported boundary conditions are used for panels.

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Fig. 1 Schematic of sound transmission through a rectangular simply supported double panel window partition: a global view; b side view

(a)

(b)

For a plane harmonic sound wave, its acoustic potential is given by ϕ(x, y, z; t) = I e− j (kx x+k y y+kz z−ωt )

(1)

√ where I is the sound amplitude; j = −1, ω is the angular frequency, k 0 is the acoustic wavenumber in air, c0 is the sound speed in air, and k x , k y , and k z are the wavenumber components in the x, y, and z directions respectively. The equations of motion of panel 1 and panel 2 are: Di ∇ 4 wi + Mi

∂ 2 wi − j ωρ0 (ϕi − ϕi+1 ) = 0, (i = 1, 2) ∂t 2

(2)

where index i = 1, 2 represents panel 1 or 2, wi is the displacement of the panel, ρ0 is the air density, M i is panel surface density, Di is the flexural rigidity of the panels. Based on the modal superposition method, the transverse displacements of the two panels can be written as w1 (x, y, t) =

∑

φmn (x, y)q1,mn (t), w2 (x, y, t) =

m,n

∑

φmn (x, y)q2,mn (t)

(3)

m,n

where φmn and qi,mn are the modal shape function and modal displacements amplitude under simply supported boundary conditions respectively. The velocity potential for each fluid domain, namely ϕ1 , ϕ2 , ϕ3 , can be described as the superposition of positive and negative waves in the z direction, which can be further expressed in terms of the panel modal shape functions as ϕ1 (x, y, z; t) =

∑

Imn φmn e− j(kz z−ωt) +

m,n

ϕ2 (x, y, z; t) =

∑

ϕ3 (x, y, z; t) =

m,n

βmn φmn e− j(−kz z−ωt)

m,n

εmn φmn e

− j(k z z−ωt)

m,n

∑

∑

+

∑ m,n

ξmn φmn e− j(kz z−ωt)

ζmn φmn e− j(−kz z−ωt)

(4)

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Where Imn , βmn , εmn , ζmn and ξmn can be determined by applying the orthogonality condition of the modal shape function by Fourier transform:

-λmn

4 = ab

{ b {a 0

-λe− j (kx x+k y y ) sin

mπ x nπ y sin d xd y a b

(5)

0

Combining the above equations with the velocity compatibility equations at the air-panel interface, we can obtain the parameters Imn , βmn , and ζmn . The sound power transmission coefficient and the diffuse incidence sound field be expressed as { π/2 { ϕlim ∑∞ ∑∞ 2 τ (ϕ, θ ) sin(ϕ) cos(ϕ)dθ dϕ m=1 n=1 |ξmn | 0 τ (ϕ, θ ) = ∑∞ ∑∞ , τdiff = 0 { π/2 { ϕlim 2 sin(ϕ) cos(ϕ)dθ dϕ m=1 n=1 |Imn + βmn | 0 0 (6) where ϕ lim is the limiting angle defining the diffuseness. Here the limiting incident angle is 78° [5]. The sound transmission loss is given as STL = 10lg(1/τ ).

3 Optimization Methodology The optimization method is NSGA-II and the optimization objective function and constraints are: [ Maximize: Rw (b) Objective Minimize: M(b) Subject to bid ≤ bi ≤ bit

(7)

M = ab(ρ1 h 1 + ρ2 h 2 + ρ0 H )

(8)

where

The optimal solution is the maximum Rw and the minimum mass M. The weighted STL, Rw , is determined according to ISO 717-1 [11]. The bid and bit are the lower and upper bounds of the ith design parameter, as shown in Tables 1 and 2. Table 1 Parameters of window’ physical system Length

Width

Thickness of glass

Thickness of air cavity

Glass Young’s modulus

Glass density

Glass Poisson’s ratio

a

b

h1 = h2

H

E1 = E2

ρ1 = ρ2

υ1 = υ2

0.009 m

5.5 ×

1.4 m

0.82 m

0.005 m

1010

Pa

2500

kg/m3

0.24

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Table 2 Window’s dimensions and material parameters Thickness of glass (m) Thickness of air cavity (m)

bi

Lower bound (bid )

Upper bound (bit )

h1

0.0025

0.01

h2

0.0025

0.01

H

0.0045

0.018

4 Simulation Results and Discussions 4.1 Reference Structure The theoretical model is applied to simulate the STL of the high-speed train window. The materials, dimensions, and boundaries of the structure are consistent with those in reference [6], as shown in Table 1.

4.2 Optimization Parameters The mass M and weighted reverberation sound transmission loss Rw of the window structure are taken as the optimization objectives based on NSGA-II optimization algorithm. The optimization parameter is the thickness of the two panels of the double-panel cavity structure h1 , h2 and cavity thickness H. Its lower limit and upper limit are set as half and 2 times the reference condition value respectively, as shown in Table 2.

4.3 Optimization Results Figure 2 indicates the nonlinear relationship between the Rw and mass resulting from more than 200 cases during optimization. Overall, as the mass increases, Rw increases, but for the same mass, there are different Rw cases. Except for the standard window reference case (red square), all other points are the output results of the optimization process. For the convenience of analysis, these points are divided into several categories: the green five-pointed star is the point identified as the optimum by the algorithm, and the mass and weighted sound insulation are 14.4 kg and 29.4 dB respectively, the red cases are Pareto Front. The remaining cases are marked as black round points. The mass and Rw of the optimal solution are smaller than the reference case, which may not meet the requirements of the actual engineering for structural strength, etc., but the red point cases of the Pareto Front provides us a selectable area of better cases.

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Fig. 2 Mass and Rw relationship results

Fit of red point cases Rw= 22.098+0.618 m-0.005 m2

40

Rw (dB)

38 36 34 same mass

32 same Rw

Reference Case (28.7 kg, 31.7 dB)

30 Optimized Case (14.4 kg, 29.4 dB)

28

10

15

20

25

30

35

40

45

50

55

Mass (kg)

Therefore, a relatively optimal structure can be selected according to the comprehensive consideration of sound insulation and mass. To find the optimized relationship between mass and Rw , a second-order polynomial fitting was performed on the optimal cases in red points, and the result is shown by the red line in the figure. The red point cases with equal Rw and equal mass compared to the reference window were selected respectively, as shown in Table 3. To identify the mechanisms of “resonance” frequency dips of STL, the typical frequencies of the “Mass-AirMass” resonance, f MAM , “coincidence frequency”, f co , are given as Eqs. (9) and (10). Where mp1 and mp2 are the mass per unit area and s' equals (ρ0 c02 )/H . Compared to the mass 28.7 kg of the reference window, the mass of the optimal case with the same Rw is 18.3 kg, which is 63.8% of the reference window. The double plate thicknesses in this case are 0.0034 m and 0.0030 m respectively, and the cavity thickness is 0.018 m. Another optimal case chosen has the same mass as the reference window structure and the Rw is 35.5 dB, which is 3.8 dB higher than 31.7 dB according to standard window. Its cavity thickness is 0.018 m. The diffuse field sound insulation in one-third octave and narrow band are given in Fig. 3. Table 3 Typical 2 cases on the Pareto front (a = 1.4 m, b = 0.82 m) Thickness of glass (m)

Thickness of Mass air cavity (kg) (m)

Rw (dB)

f MAM,ϕ0° (Hz)

f co,ϕ90° (Hz)

h1

h2

H

M

Reference case

0.005

0.005

0.009

28.7

31.7

254

2685, 2685

Same Rw

0.0034

0.0030

0.0180

18.3

31.7

229

3932, 4542

Same mass 0.0067

0.0033

0.0180

28.7

35.5

190

2014, 4029

Panel 1, 2

Bi-objective Sound Transmission Loss Optimal Design of Double … 80

80 h1 (m) h2 (m) H (m) M (kg) Rw (dB) 0.0050, 0.0050, 0.0090, 28.7, 31.7 (Reference Case) 0.0034, 0.0030, 0.0180, 18.3, 31.7 (Same Rw) 0.0067, 0.0033, 0.0180, 28.7, 35.5 (Same Mass)

70

60

50 Rw 31.7 Rw 35.5

40

50 40

30

30

20

20

100

200

400

800

1600

h1 (m) h2 (m) H (m) M (kg) Rw (dB) 0.0050, 0.0050, 0.0090, 28.7, 31.7 (Reference Case) 0.0034, 0.0030, 0.0180, 18.3, 31.7 (Same Rw) 0.0067, 0.0033, 0.0180, 28.7, 35.5 (Same Mass)

70

STL (dB)

STL (dB)

60

10

539

3150

10

102

1/3 Octave Centre Frequency (Hz)

(a)

103

Frequency (Hz)

(b)

Fig. 3 Diffuse field STL. a One-third octave, b narrow band

/

f M AM,ϕ0

s'(m p1 + m p2 ) π f M AM,ϕ0 , 0 ≤ϕ< , f M AM,ϕ = m p1 m p2 cos(ϕ) 2 } { ) ( c2 12ρ 1 − ν 2 1 f co,ϕ90 π 2, f = 0 , 0 ks 2 4π/ks , |k| ≤ ks

(12)

/ where |k| = k x2 + k 2y . The cross-spectrum density in Eq. (10) can be approximated using a rectangular rule, truncating and regularly sampling the wavenumber space. ext

Sff

Ny Nx ∑ 1 ∑ ≈ S pp (k, ω)U ∗ (k)U (k)e−ik(xn −xm ) δk x δk y 4π 2 i=1 j=1

(13)

where δk x and δk y represent the wavenumber discretisation size in the spanwise and streamwise directions, respectively. The step length of wavenumber √ √ discretisation is set as 0.25 rad/m for both δk x and δk y . N x = N y = 4.8 max( ω ρh/D) represents the total number of grid points in the spanwise and streamwise directions [7].

2.2 FE-SEA Model The hybrid FE-SEA method developed by Shorter and Langley et al. [10, 11] is reviewed. The response of the statistical subsystem is related to the direct field due to acoustic radiation from the deterministic boundary. The reverberation field is formed

Vibroacoustic of Extruded Panels Excited by a Turbulent Boundary Layer

587

as wave reflections occur on the statistical boundary of the statistical subsystem. As a result, blocked pressures acting on the coupling surface are produced. The governing equation of the coupled system can be written as (Dd + Ddir )q = f ext + frev

(14)

where q, fext and frev denote the displacements, external force vector, and generalised forces induced by reverberant waves, respectively; Dd is the dynamic stiffness matrix of the panel. Dd = K + i ωC − ω2 M

(15)

where K, C and M are the stiffness, damping, and mass matrices, respectively; Ddir is the direct-field dynamic stiffness matrix of the statistical subsystem. If the dynamic stiffness matrix and nodal forces are prescribed, the displacement response of the panel can be calculated as q = (Dd + Ddir )−1 (fext + frev )

(16)

Its cross-spectral matrix becomes ( ) rev Sqq = qqH = (Dd + Ddir )−1 Sext (Dd + Ddir )−H ff + Sff

(17)

where Sext f f is a cross-spectral matrix of external nodal forces induced by external loads; Srev f f represents a cross-spectral matrix of the blocked reverberant forces. The radiated sound pressure can be related to the structural displacement using the dynamic stiffness matrix of the direct radiation field Prad =

} ω 1 { Re −iωDdir qqH = Sqq Im{Ddir } 2 2

(18)

where Ddir is a direct-field dynamic stiffness matrix. The finite panel’s transmission loss (TL) can be calculated using T L = 10 log10

Pinc Prad

(19)

where aerodynamic excitation produce the equivalent incident power in the TBL. The pressure blocked by the panel is two times the incident pressure. The equivalent incident power is expressed as Pinc =

ϕ(ω) A 8ρ0 c0

where A denotes the surface area of the panel.

(20)

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3 Numerical Results 3.1 Validation of Numerical Results Numerical examples of an extruded panels are presented in this section to demonstrate the usefulness of the proposed hybrid method. The extruded panel is simply supported, with the material and surrounding fluid properties in Table 1. Figure 1 shows that the sound transmission loss of the extruded panel was calculated using the hybrid model; the calculation results are shown in Fig. 2. The equivalent nodal forces calculated in analysis of the extruded panel can be directly applied to the different shapes of the extruded panel without recalculating the equivalent nodal forces as long as the in-plane dimensions, mesh size of the structure, and calculation frequencies are the same. It provides a basis for acoustic optimization design of profile structure. Table 1 Parameters of extruded panel and fluid Extruded panel

Fluid

Fig. 1 The hybrid model

Parameters

Value

Length

1m

Width

1m

Height

0.04 m

Elastic modulus

70 GPa

Poisson’s ratio

0.3

Density

2700 kg/m2

Damping loss factor

0.005

Inflow velocity

350 km/h

Kinematic viscosity

1.5 × 10–5 m2 /s

Friction velocity

1.85 m/s

Boundary layer thickness

0.0046 m

Shear stress at the wall

4.39 N/m2

Vibroacoustic of Extruded Panels Excited by a Turbulent Boundary Layer 100

Hybrid model UWPWs

90 80

Transmission Loss (dB)

Fig. 2 The TL obtained by different methods

589

70 60 50 40 30 20

400

800

1200

1600

2000

2400

2800

3200

Frequency (Hz)

3.2 Influence of Train Speed During train operation, the flow of the fluid outside it will form a TBL excitation on the surface of the train body. The magnitude of the excitation is closely related to the train operation speed. Taking the current high-speed train operation speed as an example (mainly within 250–600 km/h), the influence of the extruded profiles under different vehicle speeds is explored. Based on the calculation results in Fig. 3, it is found that the TL decreases with the increase in the train running speed. A simple train running speed correction model can be developed to predict the TL of extruded profiles at different speeds. T L aim = T L ref − 25 log10 (vaim /vref ) (vaim ≥ vref )

100 250 km/h 300 km/h 350 km/h 400 km/h 600 km/h

90 80

Transmission Loss (dB)

Fig. 3 Influence of train speed on TL

(21)

70 60 50 40 30 20

400

800

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1600

2000

Frequency (Hz)

2400

2800

3200

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where T L aim and vaim respectively represent the train running speed and TL of extruded profiles at the target speed. T L ref and vref respectively represent the train running speed and TL of extruded profiles at the reference speed. Therefore, the TL of extruded profiles depends on the train speed when all other parameters remain unchanged.

3.3 Influence of Empirical Models TBL excitation is random excitation. A single model cannot accurately represent the external turbulence excitation of different vehicles. Additionally, the TBL excitation model can vary with train speed. Three cross-spectral models were considered to explore the influence of varying incentive models on the structure of sound transmission loss: (1) Corcos model, (2) Mellen model, and (3) Generalized Corcos model. The structure parameters of the profiles remained unchanged, and the train speed was fixed at 350 km/h. Figure 4 illustrates the impact of three TBL excitation models on the sound transmission loss of extruded profiles. The TL of the extruded profiles was consistent under the Corcos model and the Generalized Corcos model. However, under the Mellen model, the TL was the same as the other models only under 1800 Hz. Above 1800 Hz, the Mellen model had greater TL but with consistent alternating peaks and troughs. 100 Generalized Corcos model Mellen model Corcos model

90

Transmission Loss (dB)

Fig. 4 Influence of TBL model on TL

80 70 60 50 40 30 20

400

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1200

1600

2000

Frequency (Hz)

2400

2800

3200

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4 Conclusions This study proposes a hybrid model to investigate the vibroacoustic characteristics of flat panels under the effect of TBL. The hybrid model combines TBL’s wavenumber domain model with FE-SEA to expand its application range. The priority is to determine the generalized forces caused by the wall pressure of TBL utilizing wavelets. By solving fluid–structure coupling equations in the spectral domain, the structural response can be found once the external load of the finite element panel model is established. Although this paper utilizes a semi-empirical model to describe TBL excitation in high-speed train cars, it is necessary to choose an appropriate model for outside TBL excitation where complexities may exist, and parameters should be modified for better prediction accuracy.

References 1. Arguillat B, Ricot D, Bailly C et al (2010) Measured wavenumber: frequency spectrum associated with acoustic and aerodynamic wall pressure fluctuations. J Acoust Soc Am 128(4):1647–1655. https://doi.org/10.1121/1.3478780 2. Olivier R, Stephane M, Thomas P et al (2013) Measurement of the wavenumber-frequency spectrum of wall pressure fluctuations: spiral-shaped rotative arrays with pinhole-mounted quarter inch microphones. In: 19th AIAA/CEAS aeroacoustics conference (AIAA). Université De Sherbrooke. https://doi.org/10.13140/2.1.1382.0166 3. Shorter P, Blanchet D, Cotoni V (2012) Modeling interior noise due to fluctuating surface pressures from exterior flows. 2012. https://doi.org/10.4271/2012-01-1551 4. Chen L, Macgillivray IR (2014) Prediction of trailing-edge noise based on reynolds-averaged navier-stokes solution. AIAA J 52(12):2673–2682. https://doi.org/10.2514/1.J052827 5. Miller TS, Gallman JM, Moeller MJ (2015) Review of turbulent boundary layer models for acoustic analysis. 2015:1739–1754. https://doi.org/10.2514/1.C031405 6. Hekmati A, Ricot D, Druault P (2013) Numerical synthesis of aeroacoustic wall pressure fields over a flat plate: Generation, transmission and radiation analyses. J Sound Vib 332(13):3163– 3176. https://doi.org/10.1016/j.jsv.2013.01.019 7. Maxit L (2016) Simulation of the pressure field beneath a turbulent boundary layer using realizations of uncorrelated wall plane waves. J Acoust Soc America 140(2):1268. https://doi. org/10.1121/1.4960516 8. Langley RS (2007) Numerical evaluation of the acoustic radiation from planar structures with general baffle conditions using wavelets. J Acoust Soc Am 121(2):766. https://doi.org/10.1121/ 1.2405125 9. Shorter PJ, Langley RS (2005) On the reciprocity relationship between direct field radiation and diffuse reverberant loading. J Acoust Soc Am 117(1):85. https://doi.org/10.1121/1.181 0271 10. Vergote K, Genechten BV, Vandepitte D et al (2011) On the analysis of vibro-acoustic systems in the mid-frequency range using a hybrid deterministic-statistical approach. Comput Struct 89(11–12):868–877. https://doi.org/10.1121/1.3478780 11. Shorter PJ, Langley RS (2005) Vibro-acoustic analysis of complex systems. J Sound Vib 288(3):669–699. https://doi.org/10.1016/j.jsv.2005.07.010

Structure-Borne Noise and Ground-Borne Vibration

The Influence of a Building on the Ground-Borne Vibration from Railways in Its Vicinity Xiangyu Qu, David Thompson, Evangelos Ntotsios, and Giacomo Squicciarini

Abstract A finite element numerical model and a semi-analytical model are used to analyse the influence of buildings on ground vibration from underground railways. The insertion loss of a building with four types of foundations is examined using a 3D finite element model. Additionally, a semi-analytical model is built to analyse the vibration of the ground with the influence of a building with a pile foundation. This model is divided into two parts: a finite element model that represents the building as a column-shell structure and a semi-analytical model that simulates the infinite free-field ground. The foundations can amplify or attenuate the ground vibration in different frequency regions. For an example case, both models give similar insertion loss results due to a building in the transmission path, although there are differences due to the modelling assumptions. The findings suggest that when predicting the ground surface response induced by an underground railway, the surrounding buildings should be included in the calculations to get more accurate results. Keywords Railways · Ground vibration · Finite element model · Semi-analytical model · Soil-structure interaction

1 Introduction Train-induced ground vibration from underground railways can cause disturbance to local residents through feelable vibration or ground-borne noise [1]. Many numerical [2, 3] and semi-analytical models [4] have been developed to study the problem. To obtain calculation results conveniently and quickly, it is usual to predict the vibration of the ground in free-field conditions, and to combine this with building transfer functions. This means that the impact of the presence of other building foundations between the vibration source (track) and the receiver position is neglected. In reality, X. Qu (B) · D. Thompson · E. Ntotsios · G. Squicciarini Institute of Sound and Vibration Research, University of Southampton, Southampton SO17 1BJ, UK e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_56

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between the track and the target buildings (i.e., the buildings for which predictions are made), or around the target buildings, there may be many other buildings. The presence of these buildings can have an impact on the ground vibration. Therefore, to improve the accuracy of ground vibration predictions, the influence of these surrounding buildings should be investigated. A variety of technical methods are used to analyse the role of soil-building interaction. In [5] the effects of piled and raft foundations on the vibration level transmitted into structures near railway tunnels are evaluated using a simple analytical model. The sub-modelling technique [6] has been developed based on a dynamic stiffness matrix of the soil coupled to the receptance matrix of the building. The soil-pile interaction was ensured at a series of coupled nodes between the soil and the piles. In [7] a subdomain formulation was used to predict the free-field vibration due to pile driving. In [8] the boundary element method is applied to investigate the effects of a group of buildings on ground vibration. Results from numerical simulations and measurements are presented in [9] in terms of the coupling loss, which is well-adapted for use with the empirical method. In [10] a simplified building-soil coupled model in the time domain is introduced by using simplified spring elements to represent the soil-structure interaction. In this paper, two different models are used to investigate the impact of a building on the ground response in its vicinity. These are a 3D time domain finite element (FE) numerical model, and a semi-analytical frequency domain model. The effect of introducing the building is expressed as an insertion loss to evaluate the influence of the building on the ground vibration and the two models are compared.

2 Time-Domain 3D Numerical Model 2.1 Model Description To compare the ground vibration with and without a structure, a 3D finite element model was created in ABAQUS, which consists of a tunnel in layered soil and a four-storey building. Infinite elements are placed at the boundaries of the model to suppress wave reflections. A separate model of a train passing over a section of track is used to generate a set of force time histories at the fastener locations which are then applied to the base of the tunnel in the FE model. A sketch of the two models is shown in Fig. 1. The fasteners and elastic supports are represented by spring and damper elements. The elastic supports are utilised to approximate the flexibility of the tunnel and soil. Both models operate in the time domain. For the building, four different foundation types are evaluated (strip, raft, pile, and box), depicted in Fig. 2. The 8 m deep pile and 4.8 m deep box foundations are deep foundations, whereas the strip and raft foundations are shallow foundations, with depth 2.4 m.

The Influence of a Building on the Ground-Borne Vibration …

597

Fig. 1 The numerical FE models with sub-models: a 2D train-track model used to generate fastener support forces and b 3D tunnel-soil-building model

Fig. 2 Different foundation types modelled in ABAQUS: a strip foundation; b raft foundation; c pile foundation and d box foundation

Each span in the building is 6.6 m wide, the thickness of the wall is 0.6 m and the height of each storey is 3 m. The parameters of the materials in this model are listed in Table 1. The soil parameters are related to Beijing Metro line 5 [11]. Rayleigh damping is used for each material. The Rayleigh damping is proportional to a linear combination of mass and stiffness. The Rayleigh damping coefficient for mass, α = 0.248, and the coefficient of stiffness β = 7.86 × 10–5 . Table 1 The parameters used for each soil layer and the concrete [11] Materials Density (kg/ Young’s Poisson’s Height (m) Shear wave Compressional m3 ) modulus (N/ ratio velocity (m/ wave m2 ) s) velocity (m/s) 1850

1.31 × 108

0.344

5.0

162

333

Layer 2

2030

4.75 ×

108

0.319

15.7

298

578

Layer 3

2150

6.98 × 108

0.268

33.0

358

636

Concrete

2500

3.60 × 1010

0.28

–

–

–

Layer 1

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2.2 Results To assess the impact of different buildings and foundations, the vibration of the ground surface is shown in the form of an insertion loss (IL) relative to the free-field case. This is determined at a grid of 640 receiver points, shown in Fig. 3a, which is used to produce contour plots of the IL. In addition, the IL is plotted at 8 points located along a line passing through the centre of the building. These receiver points are shown in Fig. 3b; e.g., N25 denotes a point at a distance of 25 m from the tunnel centreline. Insertion loss results in the 50 Hz one-third octave band are shown in Fig. 4. This indicates that there can be areas of attenuation or amplification behind the structure. In Fig. 4a, which shows results for the piled foundation, there are several zones of high positive IL close to the building column locations, indicating that vibration has been reduced by the presence of the structure and foundation. However, behind and in front of the building there are zones in which the vibration is increased (behind the building this was initially an area of low vibration amplitude). Figure 4b compares the four foundation types at 50 Hz. At this frequency the IL is largest at locations directly beneath the structure. The IL is larger for the deep foundations than for the shallow foundations. However, the vibration behind the structure is increased more by the shallow foundations than by the deep foundations. The IL spectra for the four different foundations at N15 (beneath the building) and N30 (behind the building) are shown in Fig. 5. At the receiver point N15, at low frequencies, the insertion loss is close to zero. The vibration is attenuated in the regions 6.3–16 Hz and 32–80 Hz (the IL value is positive). Deep foundations have a greater impact on the vibration than shallow foundations. The IL values at N30 vary in a smaller range than those at N15. There is amplification in the region 10–16 Hz for all cases. Apart from the box foundation, all foundations have a vibration mitigation effect on the ground at this position behind the building at 40–50 Hz.

Fig. 3 The receiver points at the ground surface: a receiver points used to plot contours and b line of receiver points

The Influence of a Building on the Ground-Borne Vibration … Insertion loss (dB)

36

-10

12.0

31

9.0

26

6.0

599

-8

Strip Raft Pile Box

-6

3.0

Tunnel

22

0.0

17

-3.0 12

Insertion loss (dB)

-4 -2 0 2 4 6 8 10

-6.0

12

7 -9.0 2

14 16

-12.0

0 4

8

12

17

21

26

30

35

N0

N5

N10

39

N15

N20

N25

N30

N35

N40

Receiver points

Distance away from tunnel (m)

(a)

(b)

Fig. 4 The insertion loss at 50 Hz: a contour of IL in dB for pile foundation (building location in red) and b IL on centreline of building (building location in yellow zone and tunnel position marked in red line) 20

10

5

Frequency (Hz)

(a)

63 80

32 40 50

20 25

8

63 80

32 40 50

20 25

8

10 12 .5 16

-10 4

-10 5 6.3

-5

2 2.5 3.1 5

-5

10 12 .5 16

0

4

Insertion loss (dB)

0

Strip-N30 Raft-N30 Pile-N30 Box-N30

1 1.2 5 1.6

5

1 1.2 5 1.6

Insertion loss (dB)

10

15

5 6.3

Strip-N15 Raft-N15 Pile-N15 Box-N15

15

2 2.5 3.1 5

20

Frequency (Hz)

(b)

Fig. 5 Insertion loss spectra of four different foundation types at positions a N15 and b N30

3 Frequency Domain Semi-Analytical Model 3.1 Methodology To create a model that can be used for parametric study, a semi-analytical traintrack-tunnel model is coupled with a ground vibration model based on a frequencywavenumber domain dynamic stiffness matrix (DSM) method, using the method of [12, 13]. This is connected to a simple finite element building model, created using the Stabil Matlab toolbox [14]. The coupling method uses the sub-modelling approach in the frequency domain described in [5, 6]. The modelling approach is shown schematically in Fig. 6.

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Fig. 6 Semi-analytical model sketch

As shown in Fig. 6, the overall displacement at a receiver point (x 0 , y0 , z0 ) generated by the underground railway may be separated into two parts: the ground response caused by the train loads transmitted through the free field, uˆ 0 (x0 , y0 , z 0 , ω), and the response caused by the equivalent forces at the coupled nodes of the building. It can be written as u(x ˆ 0 , y0 , z 0 , ω) =

n 

Hˆ G (xc,k − x0 , yc,k − y0 , z c,k − z 0 , ω)

k=1

ˆ c,k , yc,k , z c,k , ω) + uˆ 0 (x0 , y0 , z 0 , ω) F(x

(1)

ˆ c,k , yc,k , z c,k , ω) is the where Hˆ G denotes the Green’s function of the soil, and F(x equivalent reaction force at coupled node k, with Cartesian coordinates (x c,k , yc,k , zc,k ). As it is assumed that the displacement of the soil is equal to the displacement of the foundation at the coupled nodes, the displacement of the coupled nodes is obtained as  −1 ˆ g (ω) = I + H ˆ s0 (ω) ˆ G (ω)K ˆ  b (ω) U U   −1 ˆ G (ω) K ˆ gg (ω) − K ˆ gi (ω)K ˆ ii (ω)−1 K ˆ ig (ω) ˆ s0 (ω) = I+H U

(2)

ˆ  b (ω) is the reduced dynamic stiffness matrix of the building model. It can where K ˆ ii , K ˆ ig , be obtained from the full matrix by partitioning it into four sub-matrices K ˆ gi and K ˆ gg , where the subscript i indicates the internal nodes of the building, and g K ˆ s0 (ω) =uˆ 0 (xc,k , yc,k , z c,k , ω), indicates nodes of the building coupled to the ground. U the displacement at the coupled node positions induced by the train load in the tunnel ˆ G (ω) is the soil transfer receptance without any building in the transmission path. H matrix for the coupled node positions, which can be denoted as

The Influence of a Building on the Ground-Borne Vibration …

⎡ˆ ˆ 12 (ω) · · · H ˆ 1k (ω) ⎤ H11 (ω) H ⎢H ˆ 21 (ω) H ˆ 22 (ω) · · · H ˆ 2k (ω) ⎥ ⎥ ˆ G (ω) = ⎢ H ⎢ . . .. ⎥ . .. .. ⎣ .. . ⎦ ˆ l1 (ω) H ˆ l2 (ω) · · · H ˆ lk (ω) H

601

(3)

ˆ lk (ω) indicates the displacement at coupled node l due to a unit force at where H coupled node k. It can be calculated from the Green’s function of the soil. After the displacements of the coupling points are calculated, the equivalent forces acting at the coupled nodes are calculated using   ˆ ig (ω) U ˆ  b (ω)U ˆ g (ω) = K ˆ gg (ω) − K ˆ gi (ω)K ˆ ii (ω)−1 K ˆ g (ω) Fˆ g (ω) = K

(4)

In summary, the displacement response of the ground receiver point can be calculated as the sum of the components due to the train excitation and due to the reactions at the building.

3.2 Results and Comparison For simplicity, it is assumed that the piles are located directly beneath the building columns. To allow comparison, a similar arrangement is used in both the timedomain FE model and the frequency-domain semi-analytical model. Moreover, in this section, the soil is represented by a homogeneous half space instead of the layered soil used previously. The main dimensions of the model, including the location of the selected receiver point, are shown in Fig. 7a. The insertion loss at this point calculated from these two models is shown in Fig. 7b. The overall shape of the IL is similar in both results, although there are differences in the numerical values. Due to differences in the modelling assumptions, it is unavoidable that there are differences in some frequency bands. The semi-analytical model can estimate the effect of buildings on the vibration of the ground surface in the frequency domain and provide calculation results faster than the FE model. It can provide a suitable method for further investigation into the impact of the building and the source separately. However, this modelling approach is less flexible than the FE approach in terms of the foundation shapes it can consider. If there are too many coupled nodes, it will affect the calculation efficiency.

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Semi analytical model Time domain model

Insertion loss (dB)

1.5 1 0.5 0 -0.5 -1 -1.5 -2 -2.5 -3 1.251.6 2 2.5 3.15 4

5 6.3 8 10 12.5 16 20 25 32 40 50 63 80

Frequency (Hz)

(a)

(b)

Fig. 7 a Position of source and receiver point and b comparison between IL of the two models

4 Conclusions The presence of buildings between the railway and the target receiver point will influence the train-induced ground vibration. Results from numerical and semi-analytical models are presented to assess this effect. The numerical model can consider more details, which means different kinds of foundation shape can be considered. The semi-analytical model can calculate the influence of the buildings quickly and efficiently but is less flexible. For an example case, both models give similar insertion loss results due to a building in the transmission path, although there are differences due to the modelling assumptions. The foundations can amplify or attenuate the ground vibration in different frequency regions. When predicting the ground surface response due to underground railways, the effects of neighbouring buildings should be included in the calculations to get more accurate results. Further investigation using this semi-analytical model can show the impact of the building and the source separately.

References 1. Thompson D, Kouroussis G, Ntotsios E (2019) Modelling, simulation and evaluation of ground vibration caused by rail vehicles. Veh Syst Dyn 57(7):936–983 2. Kouroussis G, Connolly D, Alexandrou G, Vogiatzis K (2015) Railway ground vibrations induced by wheel and rail singular defects. Veh Syst Dyn 53(10):1500–1519 3. Yang J, Zhu S, Zhai W, Kouroussis G, Wang Y, Wang K, Lan K, Xu F (2019) Prediction and mitigation of train-induced vibrations of large-scale building constructed on subway tunnel. Sci Total Environ 668:485–499 4. Xia H, Cao Y, De Roeck G (2010) Theoretical modeling and characteristic analysis of movingtrain induced ground vibrations. J Sound Vib 329(7):819–832 5. Kuo K, Jones S, Hunt H, Hussein M (2008) Applications of PiP: Vibration of embedded foundations near a railway tunnel. In: 7th European conference on structural dynamics (EURODYN), pp 7–9

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6. Hussein M, Hunt H, Kuo K, Costa P (2013) The use of sub-modelling technique to calculate vibration in buildings from underground railways. Proc Inst Mech Eng Part F J Rail Rapid Trans 229(3):303–314 7. Masoumi H, Degrande G (2008) Numerical modeling of free field vibrations due to pile driving using a dynamic soil-structure interaction formulation. J Comput Appl Math 215(2):503–511 8. Coulier P, François S, Lombaert G, Degrande G (2013) Application of hierarchical matrices to boundary element methods for elastodynamics based on Green’s functions for a horizontally layered halfspace. Eng Anal Bound Elem 37(12):1745–1758 9. Kuo K, Papadopoulos M, Lombaert G, Degrande G (2019) The coupling loss of a building subject to railway induced vibrations: numerical modelling and experimental measurements. J Sound Vib 442:459–481 10. López-Mendoza D, Connolly D, Romero A, Kouroussis G, Galvín P (2020) A transfer function method to predict building vibration and its application to railway defects. Constr Build Mater 232:117217 11. Xia H (2013) Traffic induced environmental vibrations and controls: theory and application. Nova Publication, New York 12. Hussein M, François S, Schevenels M, Hunt H, Talbot J, Degrande G (2014) The fictitious force method for efficient calculation of vibration from a tunnel embedded in a multi-layered half-space. J Sound Vib 333:6996–7018 13. Ntotsios E, Thompson D, Hussein M (2017) The effect of track load correlation on ground-borne vibration from railways. J Sound Vib 402:142–163 14. François S, Schevenels M, Dooms D, Jansen M, Wambacq J, Lombaert G, Degrande G, De Roeck G (2021) Stabil: an educational Matlab toolbox for static and dynamic structural analysis. Comput Appl Eng Educ 29(5):1372–1389

Prediction of Ground Vibration Induced by a High-Speed Train Moving Along a Track Supported by a Pile-Plank Structure Yuhao Peng, Jianfei Lu, and Xiaozhen Sheng

Abstract Piles are commonly applied to the construction of high-speed railways at grade for many purposes including controlling train-induced ground vibration. The piles are inserted into the ground periodically in the track direction, making the track/pile/ground system very complicated. The most frequently used method to analyze this kind of structure is to establish a three-dimensional finite element model at a very high computational cost. Based on the fictitious pile method, this paper develops a semi-analytical model, in which the track/pile/ground system is divided into a 2.5D track/ground system and a system of an infinite number of periodically arranged fictitious piles, to investigate the effect of the pile-plank structure on ground vibration. The two systems become equivalent to the original track/pile/ ground system when they are coupled using the displacement continuity condition. Making use of the periodicity of the track/pile/ground system, the model works in the Floquet wavenumber domain and only a single cell of the periodic structure is required to analyze. The results show that the pile-plank structure reduces as well as increases, depending on frequency, train-induced ground vibration. Keywords Ground vibration · Pile-plank structure · Fictitious pile method · Moving load

Y. Peng (B) State Key Laboratory of Rail Transit Vehicle System, Southwest Jiaotong University, Chengdu, Sichuan, China e-mail: [email protected] J. Lu Department of Civil Engineering, Jiangsu University, Zhenjiang, Jiangsu, China X. Sheng School of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_57

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1 Introduction Train-induced ground vibration has long been concerned by academia and industry. Many researchers have developed different prediction models, in pursuit of understanding the generation mechanisms and developing mitigation measures. Sheng et al. [1] used the transfer matrix method to predict train-induced ground vibration, in which the ground is simplified as a horizontally layered structure. To consider more complex ground geometry, Yang and Hung [2] established a 2.5D finite/infinite element model, allowing the track/ground system to have an arbitrarily shaped crosssection. It is well known that both the transfer matrix method and the 2.5D FEM have high computational efficiency, but they require the structure to be uniform longitudinally, although in reality, the track/ground system is periodic due to the segmentation of the track slabs and discrete support of the fasteners. Several researchers, e.g., Degrande et al. [3] and Peng et al. [4], have developed methods/models which take into account the periodicity of the track/ground system. It is a common engineering practice to use piles or a pile-plank structure in the subgrade of a high-speed railway to control frost heave, settlement and ground vibration. Examples include the Schnellfahrstrecke Nürnberg–Ingolstadt–München in Germany, the Channel Tunnel Link in the UK/France and Wuhan-Guangzhou railway and Suining-Chongqing railway in China [5]. With the piles or the pile-plank structure, the track/ground system becomes much more complicated. The methods in Refs. [1, 2], although very efficient, can no longer be applied. Alternative methods have to be used. To analyze the effect of the piles on ground vibration, Thach et al. [6] built a three-dimensional finite model using ABAQUS. However, the model is very large, having more than 16 million degrees of freedom. Recently, the authors [7] of the current paper proposed a semi-analytical model for a high-speed track enhanced with a pile-plank structure based on the fictitious pile method. According to the fictitious pile method [8], the pile-plank enhanced track/ground system can be divided into a 2.5D track/ground system in combination with periodically arranged fictitious piles so that the 2.5D approach can be applied. The two separated systems (the 2.5D track/ground system and the fictitious piles) become equivalent to the original track/pile/ground structure when they are coupled using the displacement continuity condition between them. Therefore, the actual ground response is that of the 2.5D track/ground system due to the external loads and the interaction forces between the 2.5D track/ground system and fictitious piles. The current paper is to introduce the methodology in Ref. [7] and show typical results. The paper is organized as follows. The pile-plank structure-supported track/ ground system and the methodology of the semi-analytical model are introduced in Sect. 2. In Sect. 3, ground response is produced and compared for the track/ground system with and without pile enhancement. Finally in Sect. 4, the paper is concluded.

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2 Methodology As depicted in Fig. 1, the ballastless slab track rests on the pile-plank structure. The piles go through the embankment and are inserted into the ground. They are periodically arranged along the track direction (Fig. 1c), forming a periodic track/ pile/ground structure with the period being L. Within each cell, there are two piles supporting the plank and the track system. According to the fictitious pile method [7], the layered ground with the periodic pile-plank structure can be divided into a 2.5D track/ground system and the fictitious piles interacting with each other. In fact, the separation of the track/pile/ground system is essentially to decompose the original pile into two coupled piles, as shown in Fig. 1a, b. For each pile (assumed to vibrate vertically like a bar) in the original track/pile/ground system, the governing equation of the pile in frequency domain can be written as −ρp Aω2 uˆ (p) (z) = E p A

∂ 2 uˆ (p) (z) + fˆg (z), ∂z 2

(1)

where ρp , E p , A denote density, Young’s modulus and cross-sectional area of the original pile. uˆ (p) (z) is the vertical displacement of the original pile at frequency ω (in rad/s). fˆg (z) denotes the forces acting on the pile from the surrounding soils and the plank. The original pile can be decomposed into two piles interacting with each other. The one is embedded in the ground (termed soil pile and drawn in dotted line in Fig. 1a) and its material properties are the same as those of the surrounding soil, making the ground become homogenous in the track direction (2.5D structure). The other one is the fictitious pile interacting with the soil pile, as shown in Fig. 1b. Consequently, the governing equations of these two piles are written as

(a) 2.5D track/ground system

(b) Fictitious piles

Fig. 1 A sketch of the pile-plank structure with layered ground

(c) Periodic pile-plank/ground

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−ρs Aω2 uˆ (s) (z) = E s A

∂ 2 uˆ (s) (z) − fˆItr (z) + fˆg (z), ∂ z2

(2)

∂ 2 uˆ (f) (z) + fˆItr (z), ∂z 2

(3)

−ρf Aω2 uˆ (f) (z) = E f A

where uˆ (s) (z) and uˆ (f) (z) stand for the displacements of two decomposed piles. The subscripts ‘s’ and ‘f’ indicate the soil pile and the fictitious pile. fˆItr (z) denotes the interaction forces between them, i.e., N1 j , q1 j , N2 j , q2 j indicated in Fig. 1 acting along the pile or at pile ends. The displacements of two separated piles are forced to be identical, i.e., uˆ (s) (z) = uˆ (f) (z).

(4)

Based on Eq. (4), the addition of Eqs. (2) and (3) is −(ρf + ρs )Aω2 uˆ (f) (z) = (E f + E s )A

∂ 2 uˆ (f) (z) + fˆg (z). ∂z 2

(5)

Comparing Eq. (1) with Eq. (5), the two coupled piles are dynamically equivalent to the original pile if satisfying ρp = ρf + ρs ,

(6a)

Ep = Ef + Es.

(6b)

Furthermore, the fictitious piles can be separated from the original track/pile/ ground system and the soil piles left in the ground have the same material properties as the surrounding soil. It makes the track/ground system become a 2.5D structure interacting with the fictitious piles, which are periodically arranged in the track direction. Therefore, the ground response is equivalent to addition of those due to the external load P(t) and interaction forces between the 2.5D track/ground system and fictitious piles, i.e., N1 j and N2 j at pile ends and q1 j , q2 j along the pile (see Fig. 1). From the analysis above, the governing equation in the frequency domain (at spectral frequency ω) of the βth fictitious pile in the jth cell is qˆβ j (z) = −

∂ Nˆ β j (z) − ρf (z)Aω2 uˆ (f) β j (z), ∂z

(7)

and the vertical displacement of the fictitious pile can be expressed as uˆ (f) β j (z)

z = 0

1 Nˆ β j (η)dη + uˆ (f) β j (0), E f (η) A

(8)

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where β = 1, 2 and j = −∞, …, 0, …, ∞. E f and ρf are Young’s modulus and density of the fictitious pile given by Eqs. (6a) and (6b), which are depth-dependent if the ground is horizontally layered. For the 2.5D track/ground system in Fig. 1a, the vertical strain along the αth pile axis in the ith cell due to the external load and interaction forces is expressed as (ex) εˆ αi (z) = εˆ αi (z) +

−

2 ∞    β=1 j=−∞

L 2 ∞  p   β=1 j=−∞ 0

(G) (G) ˆ Nˆ β j (0)ˆεαi,β εαi,β j (z, 0) − Nβ j (L p )ˆ j (z, L p )



(G) qˆβ j (ξ )ˆεαi,β j (z, ξ )dξ,

α = 1, 2; j = −∞, . . . , 0, . . . , +∞

(9)

(ex) where εˆ αi (z) is the vertical strain of the 2.5D structure due to the external train load (G) at depth z along the axis of the αth pile in the ith cell; εˆ αi,β j (z, ξ ) is termed the vertical strain fundamental solution of the 2.5D structure (similar to Green’s function) with response at depth z along the αth pile axis in the ith cell due to a unit patch load at ξ of the βth pile axis in the jth cell. The displacement at (x, y, z) of the 2.5D track/ground system can also be expressed as

u(x, ˆ y, z) = uˆ (ex) (x, y, z) −

L 2 ∞  p   β=1 j=−∞ 0

+

2 

∞ 

β=1 j=−∞



qˆβ j (ξ )uˆ β(G) j (x, y, z, ξ )dξ

 (G) ˆ Nˆ β j (0)uˆ β(G) (x, y, z, 0) − N (L ) u ˆ (x, y, z, L ) βj p βj p , j (10)

where uˆ β(G) j (x, y, z, ξ ) is the vertical displacement fundamental solution of the 2.5D track/ground structure at position (x, y, z) due to a unit vertical patch load at depth ξ along the axis of the βth pile in the jth cell, and uˆ (ex) (x, y, z) is the vertical displacement at position (x, y, z) due to the external train load. The strain and displacement fundamental solutions are always calculated in advance [9]. The displacement continuity condition between the 2.5D track/ground system and fictitious piles along the pile axes (similar to Eq. (4)) can be alternatively expressed as (f) εˆ αi (z) = εˆ αi (z), u(i ˆ L , yα , 0) = uˆ (f) αi (0).

(11)

Inserting Eqs. (7) and (8) into Eqs. (9) and (10) and considering Eq. (11), the Fredholm integral equations of the second kind can be established. Due to the periodicity

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of the track/pile/ground system, the integral equations are always transformed into the wavenumber domain based on the Floquet transform, i.e., (G) 2  p  ∂ ε˜ˆ α,β (z, ξ, κ) N˜ˆ α (z, κ) ˜ ˜ (G) ˆ ˆ N β (ξ, κ) + N α (z, κ)ε (z) + dξ E f (z) A ∂ξ β=1 L

0

−

2 

L p

2  (f) (a) N˜ˆ β (ξ, κ) ˜ (b) u˜ˆ β (0, κ)κ˜ˆ α,β (z, κ) κˆ α,β (z,ξ, κ)dξ − E f (ξ ) β=1

β=1 0 (ex) = ε˜ˆ α (z, κ),

(12)

L L (G) 2  p 2  p ˜   ∂ u˜ˆ α,β (0, ξ, κ) Nˆ β (ξ, κ) ˜ (b) ˜ ˆ ˆ α,β (0, ξ, κ)dξ dξ − N β (ξ, κ) ∂ξ E (ξ ) f β=1 β=1 0

−

2 

0

(f) ˜ˆ (a) (0, κ) + u˜ˆ (f) (0, κ) = u˜ˆ (ex) (0, κ). uˆ˜ β (0, κ) α α α,β

(13)

β=1

In Eqs. (12) and (13), κ is the Floquet wavenumber. The displacement at pile top ˜uˆ (f) (0, κ) and the axial force N˜ˆ β (ξ, κ) are unknown while the other terms can always α be calculated in advance. Firstly, the trapezoidal quadrature is used to calculate the integrals in Eqs. (12) and (13) with the integral points being ξ 1 , ξ 2 , …, ξ M and then z is forced to be identical to these integral points to establish a set of linear algebraic (f) equations. The unknowns uˆ˜ α (0, κ) and N˜ˆ β (ξ, κ) can therefore be worked out. With (f) the calculated u˜ˆ (0, κ) and N˜ˆ (ξ, κ), assembling Eqs. (7), (8) and (10), the ground β

α

displacement can be finally obtained [7] (G) 2  p  ∂ u˜ˆ β (x (e) , y, z, ξ, κ) ˜ ˆ dξ N β (ξ, κ) ∂ξ β=1 L

˜ˆ (e) , y, z, κ) = u˜ˆ (ex) (x (e) , y, z, κ) − u(x

0

+

L 2  p  β=1 0

+

2 

N˜ˆ β (ξ, κ) ˜ (b) (e) ˆ β (x , y, z, ξ, κ)dξ E p (ξ )

(f) ˜ˆ (a) (x (e) , y, z, κ), u˜ˆ β (0, κ) β

(14)

β=1

where − L2 ≤ x (e) ≤ L2 . The ground spectral response is given by performing the ˜ˆ (e) , y, z, κ). inverse Floquet transform on u(x

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3 Results Results are presented on the effect of the pile-plank structure on train-induced ground vibration. The parameters of the track and pile-plank structure are listed in Tables 1 and 2 while those of the layered ground are given in Table 3. In what follows, ground vibration induced by a high-speed train with eight vehicles running at 100 m/s are predicted and compared with that without pile enhancement (i.e., the material properties of the pile are set to be identical to the surrounding soil). The train parameters are taken from Ref. [9] while the irregularity spectrum is the German spectrum for train speed beyond 250 km/h [10]. The piles can transmit the train load to deeper positions, as shown in Fig. 2, which gives the ground displacement along the axis of symmetry of the structure (z-axis in Fig. 1a) at spectral frequency f = 10 Hz. The displacement within 0 m ≤ z ≤ 4 m of the ground is much decreased by the piles while it is increased for z ≥ 14 m.

Table 1 Parameters of the rail and rail pad

Mass of the rail beam per unit length

60 kg/m

Bending stiffness of the rail beam

6.4 × 106 N m2

Loss factor of the rail beam

0.01

Vertical stiffness of the rail pad

4 × 107 N/m

Loss factor of the rail pad

0.2

Table 2 Parameters of the track and pile-plank structure Structure component

Thickness (m)

Width (m)

Density (kg/m3 )

Young’s modulus (MPa)

Poisson ratio

Track slab

0.21

2.5

2500

36,500

0.18

SCC layer

0.1

2.5

2500

34,000

0.18

Bed plate

0.3

3.1

2500

34,000

0.18

Plank

0.8

10

2500

32,500

0.18

Pile

17 (length)

1.25 (dia.)

2500

30,000

–

Table 3 The parameters of the embankment and layered ground Layer

Thickness (m)

Density (kg/m3 )

Young’s modulus (MPa)

Poisson ratio

Loss factor

P-wave speed (m/s)

S-wave speed (m/s)

Embankment

2.8

1900

120

0.30

0.1

291.6

155.9

Layer 1

1

1800

80

0.35

0.1

267.1

128.3

Layer 2

12

1820

40

0.35

0.1

187.8

Layer 3

7

2000

532

0.30

0.1

598.4

90.22 319.9

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Fig. 2 Vertical displacement of the ground along the z-axis at spectral frequency f = 10 Hz

Figure 3 compares the acceleration spectra of the ground at x = 0, z = 0, y = 10 m and 30 m for the track/ground structure with or without pile enhancement. The comparisons are shown only for spectral frequencies up to 50 Hz, since the model in Ref. [7] is to be improved for higher frequencies. From Fig. 3 it can be seen that in general, the pile-plank structure exhibits vibration reduction effect for most of the frequencies analyzed here, especially for the peak frequencies shown in Fig. 3, but it still increases vibration at some frequencies such as 12.5 and 45 Hz (Fig. 3b).

(a)

(b)

Fig. 3 Acceleration spectra of the ground at x = 0, z = 0, a y = 10 m and b y = 30 m

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4 Conclusions In this paper, a model based on the fictitious pile method is presented to predict the ground vibration induced by a high-speed train moving along the track supported by a pile-plank structure. The fictitious pile method is employed to deal with the pile-soil interaction by dividing the periodic track/pile/ground structure into a 2.5D track/ground system and an infinite number of periodically arranged fictitious piles, making the 2.5D finite element method employable. The 2.5D track/ground system and fictitious piles are equivalent to the original system by using the displacement compatibility condition between them. The results show that the pile-plank structure has vibration reduction effect at most of the analyzed frequencies, but it also increases the vibration at some frequencies. Work is still underway to make the model working at high frequencies. Acknowledgements This work is funded by the National Natural Science Foundation of China (U1834201 and U1934203) and the National Key R&D Program of China (2016YFE0205200).

References 1. Sheng X, Jones C, Petyt M (1975) Ground vibration generated by a load moving along a railway track. J Sound Vib 228(1):129–156 2. Yang Y, Hung H (2001) A 2.5D finite/infinite element approach for modelling visco-elastic bodies subjected to moving loads. Int J Numer Methods Eng 51:1317–1336 3. Degrande G, Clouteau D, Othman R, Arnst M, Chebli H, Klein R, Chatterjee P, Janssens B (2006) A numerical model for ground-borne vibrations from underground railway traffic based on a periodic finite element-boundary element formulation. J Sound Vib 293(3–5):645–666 4. Peng Y, Cheng G, Sheng X (2020) Modelling track and ground vibrations for a slab ballastless track as an infinitely long periodic structure subject to a moving harmonic load. J Sound Vibr 489 5. Wang F (2011) The application status and research of pile-plank structure in high-speed railway. Railway Stand Des 55(6):27–32 (in Chinese) 6. Thach P, Liu H, Kong G (2013) Vibration analysis of pile-supported embankments under high-speed train passage. Soil Dyn Earthq Eng 55:92–99 7. Peng Y, Lu J, Sheng X, Yang J (2022) Modelling ground vibration from a high-speed railway track resting on a periodic pile-plank structure-enhanced embankment. J Sound Vibr 539 8. Lu J, Jeng D, Wan J (2014) A new model for the vibration isolation via pile rows consisting of infinite number of piles. Int J Numer Anal Meth Geomech 37(15):2394–2426 9. Yao Y, Li G, Wu G, Zhang Z, Tang J (2019) Suspension parameters optimum of high-speed train bogie for hunting stability robustness. Int J Rail Trans 8:195–214 10. Zhai W (2020) Vehicle-track coupled dynamics. Science Press, Beijing

Train Ground-Borne Vibration Control Measures and Validation Tests to Meet Stringent Vibration Thresholds for University of Washington Research Labs Shankar Rajaram, James Tuman Nelson, and Thomas Bergen

Abstract Seattle Sound Transit’s Link Light Rail extension to Northgate runs under the University of Washington (UW) campus that is home to world-class research facilities with vibration-sensitive equipment. Sound Transit has installed 1150 m of 5 Hz floating slab track in each of the twin bore tunnels. The train vibration is required to meet stringent vibration limits for 24 buildings over the 2–100-Hz third octave bands. Prior to opening of the new extension for revenue service, detailed compliance verification tests were performed for worst-case operating scenarios. Based on these tests, the vibration limits were amended at four sensitive buildings for the 5-Hz third octave band frequency. This paper presents the results of the compliance tests, performance of the floating slabs, and the determination of allowed train speeds under the UW campus. Keywords Floating slab track · Force density level · Compliance tests

1 Introduction Sound Transit’s Link Light Rail extension to Northgate includes a twin bore train tunnel system running under the University of Washington (UW) campus that houses 24 vibration-sensitive research buildings. Each of these buildings has stringent vibration thresholds for the 2 Hz through 100 Hz one third octave bands, based on a Master Implementation Agreement (MIA) between Sound Transit and UW implemented in S. Rajaram (B) Sound Transit, 401 S Jackson Street, Seattle, WA 98104, USA e-mail: [email protected] J. T. Nelson Wilson Ihrig & Associates, 5900 Hollis Street, Suite T1, Emeryville, CA 94608, USA T. Bergen Wilson Ihrig & Associates, 155 NE 100th Street, Suite 115, Seattle, WA 98125, USA © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_58

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2007 and subsequent amendments in 2014 and 2021. The MIA vibration limits are based on ambient rms vibration levels inside the research laboratories that ranged between 12 and 42 dB (re 50 nm/s) (The velocity level in VdB re 1 micro-in/s used by the US FTA is 6 dB higher than the velocity level in dB re 50 nm/s as used in this paper and standardized by the ISO. We are avoiding the use of “VdB” in favor of “dB” to avoid confusion). The distances of the buildings from the tunnels range from 0 ft to 700 m horizontal. Light rail vehicle (LRV) trains and track need to conform to these thresholds to avoid monetary liquidated damages. The tunnel is about 27– 37 m below grade at the heart of the campus. The track is on a 4% grade and has a curve with radius 250 m. The design analysis showed that a floating slab track (FST) installed in the Northgate tunnels would require a vibration reduction performance of 25 decibels or more between 50 and 100 Hz, and substantial vibration reduction between 25 and 50 Hz. The 5-Hz FST was installed for a track length of ~ 1160 m in each tunnel. Premium head-hardened rails meeting the EN 13674-1 ‘Class A’ standards for rail straightness were installed on the floating slabs to minimize rail undulations from the manufacturing process and wear. The flash butt welds for the rails were used to meet the EN 14587-1 2007 (Class 3) standards with some minor modifications. Before revenue service started, detailed vibration testing was performed at various train speeds with dedicated test trains under controlled conditions to verify that the MIA thresholds will not be exceeded after train service begins. The testing was performed using the Series 1 (Kinkisharyo) LRVs and Series 2 (Siemens) LRVs. This paper discusses the performance of the 5 Hz floating slab track system, the results of the detailed vibration compliance tests, how the test results helped to optimize train speeds and inform the need for minor amendments to the thresholds at four buildings.

2 Methodology The FST is based on the prototype floating slab system installed in the University Link tunnel and tested in 2016 [1]. The fabrication and installation of the Northgate Link floating slabs incorporated lessons-learned from the University Link prototype slabs [2]. The performance of the floating slab was characterized by its insertion loss. The floating slab insertion loss was measured using an instrumented force hammer to excite each slab while measuring its vibration response. The insertion loss from train passes were verified using a 2-car test train at multiple speeds and measuring the response on the tunnel bench. Vibration responses were measured at 14 representative buildings for compliance verification. Two types of light rail vehicles (LRV) with resilient wheels were tested at various speeds ranging from 24 to 72 kph. Kinkisharyo (KI) LRVs were about 10 years old, and Siemens LRVs were only a few months old at the time of testing. To satisfy MIA requirements, two Kinkysharyo test trains were operated between the University District Station (UDS) and the University of Washington Station (UWS).

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The worst-case vibration created by the two trains passing each other in opposite directions was simulated by running both trains simultaneously in the same direction in their separate tunnels. Thus, on any given test run, one train was run in the opposite direction of travel from the normal direction while the other was run in the normal direction. This is nominally equivalent to having the two trains pass each other continuously at every point along the alignment rather than at a discrete point. The maximum expected difference between a single train and two trains operating simultaneously is three decibels relative to the single train/tunnel that produces the maximum level, notwithstanding differences between tunnels and trains. The vibration from the tunnel closest to a receiver is normally higher than the vibration from the more distant tunnel due to propagation distances and energy spreading.

2.1 Background Vibration and Train Position A train traveling at 48 kph requires about 90 s to traverse the 1160-m section of FST. Thus, the rise and fall of train vibration was expected to occur over this period of time with maximum levels occurring over a period of 8–45 s when the train was closest to the building. However, identifying the trains at many of the buildings was challenging due to the high vibration reduction provided by the FST at high frequencies and the presence of substantial low frequency transient vibration in the 2–6.3 Hz third octave bands. As a result, there was a need to correlate tunnel vibration levels with building vibration levels, especially at buildings in the middle of the campus with very low MIA limits, rather than simply take the maximum measured third octave band levels occurring during each run. These buildings were at an approximate center of curvature of the track, so that the vibration exposure was longer than for buildings close to the track. Short background samples of durations approximately 20–60 s were taken from the longer samples to avoid low frequency transient phenomena and achieve a realistic estimate of background vibration. The background third octave band spectrum was determined for each building by energy averaging the ambient maximum levels occurring without anomalous transient events. Each of the vibration samples recorded during a train run was analyzed with a running energy average of eight seconds duration for each second. The maximum third octave band levels were determined on an individual third octave basis. For long samples of 45 s, the maximum third octave at one frequency may occur at an entirely different time than the maximum third octave at another frequency. For short samples of 10–20 s, the time differences between maximum levels of individual third octaves were generally of the order of a few seconds. Typical vibration events observed during train runs were generally inconsistent for long samples due to low frequency background vibration transients. Observed transient vibration events at 2.5, 3.16 and 6.3 Hz, generally involved a few seconds to perhaps 20 s and occurred at times that could not be correlated with train position and further occurred during non-operation of the trains. Considering that vibration

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from trains tends to be very consistent from run to run for the same direction and speed, time domain train vibration levels that were influenced by transients were deemed as outliers and discarded. Many or all of these low frequency transients have been subsequently associated with seismic tremors produced by the Cascadia subduction zone near Seattle, and these transients were generally more significant than the vibration due to the trains at these frequencies. These transients occurred every few minutes. The background vibration energy was subtracted from the total vibration energy due to both train and ambient sources in each third octave band to estimate the vibration level due just to the train. This is practical if the train sample is at least 0.5 dB above the ambient. In this case, the estimated train level would be 9.6 dB below the train sample level. If the ambient level is higher than the train sample, the result is not defined. If the estimated net vibration due to the train is less than the level of train vibration and ambient vibration, or undefined, the train vibration level is assumed to be at most 10 dB below the vibration level occurring during train passage. The result is a conservative estimate of train vibration energy that may still be an over-estimate. At buildings within 100 m of the tunnels, the passby exposure duration was shorter than at more distant buildings by roughly 10–20 s. These close-range buildings include Wilcox Hall, Roberts Hall, More Hall, Mechanical Engineering, and Mechanical Engineering Annex. At these buildings, the train vibration at 5 Hz was easily discernable above the ambient vibration, notwithstanding seismic tremors, and the measured levels were consistent for each train passage at 40 kph. The 5 Hz vibration levels at other speeds were generally lower compared to those for 40 kph. The vibration levels for the trains were similar to the ambient vibration levels at other buildings. For a given speed and direction of travel, vibration levels for train samples that did not include large positive deviations from the mean were energy averaged and plotted with the backgrounds. The tunnel bench vibration at 5 Hz was usually a good indicator of train passage.

3 Results This section discusses the results of the FST tests and the compliance verification tests.

3.1 Floating Slab Insertion Loss The Force Density Level (FDL) was measured at two tunnel locations near crosspassages CP23 at the middle of the curve and CP24 further north at the end of the curve spiral. These tests involved measuring the Line Source Response (LSR or LSTM) from the southbound tunnel to the adjacent northbound tunnel and combining these data with vibration measured during test train passage. The LSR tests were conducted

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with a reciprocity procedure involving excitation of the northbound tunnel bench with a hammer and load cell while recording the vibration response at the invert under the floating slab. Thus, the FDL applies to the combined vehicle and floating slab track. The vehicle passby vibration measurements were conducted with a Kinkisharyo vehicle at various speeds ranging from 32 to 72 kph in 8 kph increments. The FDL’s for the Kinkisharyo vehicle at CP23 and CP24 are shown on the left and right plots, respectively, in Fig. 1. All test speeds are represented, ranging from 32 kph to the maximum design speed of 72 kph. The “ambient” is the background vibration with the LSR subtracted in the same fashion as that used for the FDL. The ambient represents the “noise floor” of the measurement. The FDL’s at both locations are very similar, as may be expected. The FDL’s at both locations are not significantly above the equivalent ambient levels at frequencies between 12.5 and 20 Hz for all speeds. The FDL’s are virtually at the background levels between 8 and 40 Hz for the lowest speed and at the background levels between 12.5 and 31.6 Hz for speeds of 40 and 48 kph. The FDLs at 50–100 Hz increase monotonously with train speed and are highest at Cross Passage 23 near the center of the curve. Most significant is the FDL at 5 Hz, which is well above the measurement background at all speeds, and particularly at speeds of 40, 56, 64, and 72 kph. The wheel rotation frequency is approximately 5 Hz at 40 kph, and the ground surface vibration at 5 Hz was particularly prominent for 40 kph trains, suggesting that the slabs are vibrating in phase at the design resonance of the floating slab track, which is supported by theory (Most remarkable is the almost equivalent results for the FDL’s at these two tunnel locations, indicating the robustness of the estimation procedure for force density levels based on measured transfer functions and velocity levels). The FDL’s for the Kinkisharyo vehicle are compared with FDL’s measured for the same vehicle in twin-bore tunnels at Beacon Hill for trains speeds of 48 and 56 kph. Figure 2 applies to CP 23 and CP 24. The FDLs for the Kinkisharyo vehicle were obtained at a section of curved track of similar radius as that of the Northgate UW curve and with direct fixation fasteners identical to those used for the floating slab 60 1/3 OCTAVE FDL - DB RE N2/M

1/3 OCTAVE FDL - DB RE N 2/M

60 50 40 30 20 10 0 -10

50 40 30 20 10 0 -10

4 32 KPH 64 KPH

8

16 31.5 FREQUENCY - HZ 40 KPH 72 KPH

48 KPH AMBIENT

63

125 56 KPH

4 32 KPH 64 KPH

8

16 31.5 63 FREQUENCY - HZ 40 KPH 48 KPH 72 KPH AMBIENT

125 56 KPH

Fig. 1 FDL for Kinkisharyo vehicle on 5 Hz floating slab track at a curve CP23 (left) and at a curve spiral CP24 (right)

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1/3 OCTAVE FDL - DB RE N2/M

1/3 OCTAVE FDL - DB RE 1N2/M

60 50 40 30 20 10 0

50 40 30 20 10 0 -10

-10 4

8

16 31.5 FREQUENCY - HZ

48 KPH CP23 FS 48 KPH DF CURVE

63

125

56 KPH CP23 FS 56 KPH DF CURVE

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8

16 31.5 FREQUENCY - HZ

48 KPH CP24 FS 48 KPH DF CURVE

63

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56 KPH CP24 FS 56 KPH DF CURVE

Fig. 2 Comparison of floating slab FDL at a curve (CP 23) and at a curve spiral (CP 24) with Beacon Hill curve FDL (2009)

track at Northgate. The dynamic stiffness of the floating slab direct fixation fasteners was about 35 MN/m, with a nominal pitch of 610 mm. However, the fastener pitch at the Beacon Hill tunnel was 762 mm, longer than that at the Northgate floating slab, so that the rail support modulus at Beacon Hill was 20% lower than at Northgate. The Beacon Hill data were collected in 2009 at the beginning of revenue service before the rails experienced significant wear, similar to wear conditions at Northgate. The spectra exhibit a broad peak due to the primary suspension resonance at about 8 Hz and a high peak at about 63 Hz, which is the track resonance frequency. The peak at 20 Hz is attributed to the curving characteristics of the center trucks based on previous studies. Except for the different fastener pitch and the floating slab track, the two test sites are essentially similar, notwithstanding variations in rail and vehicle conditions. Figure 3 illustrates the third octave vibration level differences between the Northgate floating slab track and the Beacon Hill tunnel track. We are hesitant to call this an insertion gain as the differences may depend on track and wheel condition, but the results suggest a vibration reduction roughly comparable with that expected for a very efficient single-degree-of-freedom isolator. The attenuation rate is about 12 dB per octave, except for the slight increase of vibration attenuation at 25 Hz. If the background energy were subtracted from the Northgate FDLs, the vibration reductions in the mid-frequency bands would have been greater than those represented in Fig. 3. However, subsequent measurements of the FDL spectra for tangent track in the Beacon Hill tunnel in 2012 after repetitive finish grinding of the rails indicated a substantial reduction of the FDL in the 50–80 Hz range. Using this later FDL as a reference would indicate less vibration reduction than that shown in Fig. 3. The change of the FDL at Northgate after three or four years of service and additional finish grinding of the rails is yet to be seen.

Train Ground-Borne Vibration Control Measures and Validation Tests … Fig. 3 Floating slab FDL relative to direct fixation curved track at Beacon Hill (2009)

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0 -10 -20 -30 -40 -50 -60 4

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GAIN 48 KPH

16 31.5 FREQUENCY - HZ GAIN 56 KPH

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GAIN AVERAGE

3.2 Compliance of Train Vibration The floating slab insertion loss measurements showed that the 5 Hz amplification was higher than for the prototype floating slabs [1], however the insertion loss at 63 and 80 Hz was more than 40 decibels. As a result, the primary frequency of concern for exceeding the vibration thresholds at the sensitive buildings was 5 Hz. The measured train vibration at Wilcox building is shown in Fig. 4 and indicates that:

40 30 20 10 0 2

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MIA THRESHOLD AMBIENT MEAN 40KPH-LMAX

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16 31.5 FREQUENCY - HZ

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1. At 40 and 56 kph train speeds, the 5 Hz peaks are sharp and prominently higher than at 32 and 48 kph. 2. The 5 Hz peaks at 40 kph are 5–8 decibels greater than the peaks at 56 kph for both KI and Siemens trains. This is attributed to potential coincidence effect of the floating slab resonance frequency and the wheel rotation frequency at 40 kph, combined with high longitudinal phase velocity of the slab track vibration at 5 Hz. At 40 kph, the 5 Hz results for KI cars are surprising as the vibration levels are 3–5 decibels higher compared to the Siemens cars. Several potential reasons are explored to explain the higher 5 Hz vibration for KI cars at 40 kph. 40 30 20 10 0 2

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8

16 31.5 FREQUENCY - HZ

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125

AMBIENT MAXIMUM 32KPH-LMAX 48KPH-LMAX

Fig. 4 Measured train vibration levels versus speed at Wilcox Hall: KI (left) and Siemens (right)

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1/3 OCT VEL LEVEL - dB RE 50E-9M/S

622 40 30 20 10 0 2

4

8

16 31.5 63 125 FREQUENCY - HZ MIA THRESHOLD AMBIENT LMAX AMBIENT MEAN 32KPH-LMAX 40KPH-LMAX 48KPH-LMAX

Fig. 5 Measured KI train vibration levels at Mechanical Engineering (left) and Mechanical Engineering Annex (right)

The radial stiffness of the Bochum 2000 resilient wheels used on the Siemens vehicles is approximately twice that of the original Bochum 84 resilient wheels, with the result that the Siemens vehicle wheels are likely to exhibit less runout than the KI wheels or because the Siemens wheels were still relatively new. More detailed verification tests were conducted using just the KI test cars as these cars represented the worst-case conditions. The detailed tests showed that the four buildings that were closest to the train tunnels experienced train vibration that was within 1 dB of the allowed limits at 56 kph and in fact exceeded the MIA limits at 40 kph train speed. As a result, the MIA limits had to be amended for Wilcox, Roberts, Mechanical Engineering and Mechanical Engineering Annex at 5 Hz. The acute case was at the Annex building where the limit was revised by 8–35 dB (re 50 nm/ s). The testing also helped determine that the maximum operating speed should be limited to 56 kph, although the track design would have allowed up to 72 kph. This adjustment was to needed to reduce the risk of vibration exceedance between vehicle maintenance cycles. In addition, the use of 40 kph as emergency speed was revised to 32 kph under the UW campus to avoid the potential for exceedance from a KI train operating at 40 kph. Figure 5 shows the measured train vibration at Mechanical Engineering and Mechanical Engineering Annex buildings after the MIA limit was revised at 5 Hz. The 5 Hz vibration level at Mechanical Engineering Annex for 40 kph was 35 dB (re 50 nm/s). Ambient transient vibration due to seismic tremors actually exceeded these levels at many times.

4 Conclusions The vibration isolation performance of the Northgate Link 5 Hz floating slab track system was above 40 dB at 63 and 80 Hz. The trains running on this vibration isolated track did not exceed design limits at any of the research labs on the UW campus under

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normal operation. A potential coincidence effect between the floating slab resonance frequency and the wheel rotation frequency at 5 Hz was observed at the ground surface, possibly due to in-phase motion of the discontinuous floating slabs at design resonance. This effect was particularly pronounced for the older KI LRVs with less stiff wheels and more usage compared to the Siemens LRV wheels. However, the effect was not observed in the FDL, suggesting that source-receiver distance is a factor affecting the significance of a coincidence effect. The train speeds for normal operations under the university campus were optimized and the MIA limits were amended at 5 Hz for four closest buildings based on the verification test results.

References 1. Nelson JT, Watry DL, Amato MA, Faner PG, Kaddatz SE, Bergen TF (2016) Sound transit prototype high performance low frequency floating slab testing and evaluation. In: Proceedings of the 12th international workshop on railway noise, volume 139 of notes on numerical fluid mechanics and multidisciplinary design, Terrigal, Australia, Sept 2016. Springer, Heidelberg, New York, Dordrecht, London, pp 607–618 2. Rajaram S, Nelson JT (2019) High-performance floating slab track: design and construction improvements based on lessons learned from prototype slabs. Transp Res Rec 2673(1):300–309

Design and Implementation of Measures to Reduce the Vibration Levels of Metro Trains Wout Schwanen and Jacco de Regt

Abstract Since November 2012 there has been a local increase of vibration levels at the metro system in Amsterdam. At this location, the vibration levels have increased by more than 10 dB with a strong component around 80 Hz. At other locations in the same area, no increase of vibration levels is found. A combination of pass-by measurements and ARRoW measurements, vibration measurements on a moving train, revealed the root cause of the high vibration levels. The track was heavily corrugated with excitation of the resonance of the unspring mass on the track stiffness due to an impact when driving over a joint in the track. Two measures were taken: (1) replacement of the joint and (2) grinding of the track. After these measures were taken, the pass-by vibration measurements were repeated. The results show a strong decrease of the measured vibration levels and have proven that the measures have been very effective. Keywords Vibrations measures · Measurements · Metro

1 Introduction Since November 2012, the number of complaints about vibrations due to the metro system in Amsterdam increased, mainly for one specific area in the vicinity of a metro station. Measurements in the station showed an increase of vibration levels of more than 10 dB at one specific location since the start of the operation in the early 1980s while at other locations, the vibrations levels did not increase. So, there is a local increase of vibrations. A study was conducted to find the cause of this increase and to design measures to reduce the vibration. W. Schwanen (B) M+P, Wolfskamerweg 47, 5262 ES Vught, The Netherlands e-mail: [email protected] J. de Regt Gemeente Amsterdam, Metro en Tram, Entrada 600, 1114 AA Amsterdam, The Netherlands © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_59

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2 Problem Description 2.1 Increase of Vibration Levels Figure 1 shows the results of pass-by measurements at two locations in the metro station, location 1 on the south side of the metro station and location 2 on the north side of the metro station. The measurements were performed in the early 1980s and repeated in April 2014 as part of the investigation after the complaints increased. For location 1 (left side figure), there is an increase of the vibration levels between the measurements in 2014 and in 1980 for frequencies above 63 Hz with a clear peak around 80 Hz. This increase in vibration levels is not present in the results for location 2 (right side figure). Secondly, there is a frequency shift in the results for the peak. For both locations, the frequency for the peak shifts from 63 to 80 Hz. The cause of this frequency shift is not exactly clear but is most likely caused by changes in the stiffness of the track during previous maintenance. The differences in vibration levels for the lowest frequency range at location 2 is not exactly clear but might be caused with the limited accuracy of the previous measurements due to low number of measured pass-by’s in the early 1980s. Figure 2 shows the vibration levels for four different train types at location 1 for both tracks. The results reveal clear differences between the tracks but also between the different train types. First, we notice higher vibration levels for the trains of the types 2 and 5 than for trains 1 and 4. This holds for both tracks. Secondly, we observe higher vibration levels at track 1 than at track 2 for the train types 2 and 5. Both train types yield a clear peak in the 80 Hz third octave band for track 1. This peak is not visible at track 2 for the same train types. For train types 1 and 4 there is no clear difference in vibration levels between both tracks.

Fig. 1 Measurement vibration levels in 1980 and 2014. Left: location with a significant increase in vibration levels. Right: location without significant increase in vibration levels

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Fig. 2 Measured vibration levels at location 1 for the different train types per track

2.2 Hypothesis Based upon the previous measurement results and the properties of the trains and the track it seems most likely that the increase of the vibration levels is caused by an impact in the track, which excites the so called P2-resonance. The P2-resonance (or loaded track resonance) is associated to the resonance of the vehicle as an unsprung mass on the track stiffness [1]. The cause of the impact is unknown and more detailed experiments are needed to test the hypothesis.

3 Experimental Setup 3.1 Goal of the Experiments The goal of the experiments is to determine the root cause of the high vibration levels around 80 Hz at location 1 and to design dedicated measures to reduce the vibration levels. Therefore, a combination of on-board and pass-by vibration measurements was conducted. This method was chosen as the track around location 1 has various joints and is situated in a curve. Earlier maintenance on one of the joints did not lead to the desired result and a more detailed investigation was required.

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Fig. 3 Schematic representation of ARRoW on the metro vehicle. Accelerometers a1 and a2 are on the running bogie, a3 and a4 are on the motor bogie

3.2 Measurement Set-Up The ARRoW system [2, 3] was installed on a metro vehicle of ‘type 5’. For this purpose, ARRoW consists of four accelerometers and an optical sensor to measure speed and position of the vehicle during the measurements. The accelerometers were mounted on two different bogies on the axle boxes: two on the motor bogie (a3 and a4) and two on a running bogie (a1 and a2). Both bogies have a different mass and thus the P2-resonance will occur at slightly different frequencies. On each bogie an accelerometer was mounted on both sides of the vehicle to be able to distinguish between the rails. The set-up is schematically depicted in Fig. 3. The measurements were conducted on both tracks at various vehicle speeds and in two driving directions to determine the effect of all variables. A total of 16 measurement runs were performed. Simultaneously, pass-by measurements at location 1 were conducted to determine the representativity of the on-board measurements and to compare the vibration levels with previous results. After implementing measures to reduce the vibration levels, the measurements at location 1 have been repeated to determine the effect of the measures.

4 Results 4.1 Representativity of the Measurements The pass-by measurements with the measurement train are recorded at location 1. The resulting vibration spectra are compared with the vibration spectra measured at the same location during earlier experiments. The results, shown in Fig. 4, are very similar to previously recorded vibration levels. Hence, the measurements conducted with the measurement train are representative for normal operation conditions.

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Fig. 4 Recorded pass-by’s with the measurement train in comparison to previous recorded vibration levels at location 1 for track 1

4.2 ARRoW-Measurements Figure 5 shows a typical result of the ARRoW-measurements. The upper diagram shows the vibrations levels as function of the position of the track. The lower diagram shows the corresponding vehicle speed. There are clear variations in vibration levels along the track, which are not caused by variation in vehicle speed: around 0.8 km the vibration levels increase with decreasing speed. Between 1.0 and 1.2 km we observe differences between both rails, as the levels for channels a2 and a4 are higher than the levels for the channels a1 and a3. A more detailed result of the vibration levels between 1.0 and 1.2 km is given in Fig. 6. It shows the vibration spectra for the running bogie (diagram on the left side) and the motor bogie (diagram on the right side). The results show a clear impulse around 1.07 km, corresponding with the location of a joint in track 1. The impulse causes a peak in the vibration levels around 80 Hz. Looking into more detail reveals that the frequency of the peak around 80 Hz differs for both bogies. The peak for the running bogie occurs above 80 Hz and just below 80 Hz for the motor bogie. This is as expected as the unsprung mass of the running bogie is smaller than the unsprung mass of the motor bogie. Influence of vehicle speed The measurements were performed at constant speed and under normal operation conditions. The results for both measurement runs are depicted in Fig. 7. It shows the vibration spectra for channel a4 only, but this result is typical for the other channels. The results in Fig. 7 show differences and similarities. Between 1 and 1.2 km roughly two effects can be distinguished. First, we notice a clear speed dependency. At constant speed the maximum vibration levels occur around 75 Hz. Under normal operation conditions, there is also a peak in the vibration levels around 75 Hz but there is also a second peak shifting to higher frequencies as the speed increases.

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Fig. 5 Vibration level as function of position along the track

Fig. 6 Vibration spectra as function of position along the track. Left: running bogie. Right: motor bogie

4.3 Interpretation of the Results One joint in track 1causes an impulse which causes the high vibration levels around 80 Hz. The exact frequency of the peak is different for the motor bogie and the running bogie. For the latter, the peak occurs at a higher frequency, 83 Hz for the running bogie versus 73 Hz for the motor bogie. This is as expected since the motor bogie has a higher mass than the running bogie. The ratio of the frequencies of the peaks is equal to the square root of the unsprung masses of both bogies. This is a clear indication that the P2-resonance is excited.

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Fig. 7 Vibration spectra as function of the position along the track. Left: measurement at constant speed. Right: measurement at the speed under operational conditions

In addition, the measured vibration spectra have a strong dependency on the travelling speed. That indicates corrugation of the track. The corrugation and the P2-resonance can coincide at the same frequency.

5 Vibration Measures The following measures were taken to reduce the vibration levels: • The joint in track 1 has been replaced • Both tracks were ground to remove the corrugation. After implementing the measures, the vibration measurements at location 1 (the location with the high levels) were repeated. The results show a clear decrease of the vibration levels in the relevant frequency range before and after the measures. For track 1, replacement of the joint led to a significant decrease of the peak at 80 Hz. The joint in track 2 has not been replaced yet (Fig. 8).

6 Conclusions and Recommendations A combination of pass-by and on-board vibration measurements was used to determine the root cause of increased vibration levels and to implement measures to reduce the vibrations. The measurements revealed that most likely the P2-resonance was excited by an ES-joint in track 1. In addition, corrugation caused high vibration levels. Therefore, the joint was replaced, and the track was ground to remove the corrugation. The measurements before and after showed a significant reduction of the measured vibration levels.

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Fig. 8 Vibration levels before and after measures were taken. Left: track 1. Right: track 2

This case study illustrates the power of combining onboard and on-site measurements to identify and tackle vibration problems on railway tracks.

References 1. Guan Q, Zhou Y, Li W, Wen Z, Jin X (2019) Study on the P2 resonance frequency of vehicle track system. J Mech Eng 55(8):118–127 2. Kuijpers AHWM, Schwanen W, Bongini E (2012) Indirect rail roughness measurements: the ARRoW system within the LECAV project. Notes Numer Fluid Mech Multidisc Des 118(2012):563–570 3. Schwanen W, Kuijpers AHWM (2016) Early rail defect detection using sound measurements. In: Third international conference on railway technology: research, development and maintenance, Railways 2016, paper 170, Cagliari, Italy

Simulation and Analysis on Ground Vibrations of Pile-Net Composite Subgrade Under High-Speed Train Loadings Guangyun Gao , Jianlong Geng , Junwei Bi , and Yuanyang You

Abstract The pile-net composite subgrade is a widely adopted construction for high-speed railway in China. This study employs a 3D finite element method (FEM) model to investigate the influences of soil type and pile-net composite subgrade design parameters on ground vibrations induced by high-speed trains moving on such composite foundations. The model comprise the track, embankment, geogrid, pile caps and piles. The results reveal that the ground vibrations exhibit a decreasing trend with the increasing distance from the track center under different soil types, and the attenuation rate of ground vibrations in softer soil is higher than that in the stiffer soil. The types of foundation soils have a considerable influences on the vibration attenuation, especially for the far track zone. The peak ground vibration acceleration decreases with increasing pile diameter and the decreasing pile spacing. Moreover, the pile diameter exters a greater impact on ground vibrations than the pile spacing, especially for the near track zone. Keywords High-speed railway · Ground vibrations · Pile-net composite subgrade · 3D FEM

1 Introduction Ground vibrations generated by high-speed trains exhibit different propagation characteristics compared to those generated by the traditional trains. The resulting vibrations can travel large distances from the track, thereby causing discomfort to residents, misalignment of sensitive instruments and possibly even building damage G. Gao (B) · J. Geng · Y. You Department of Geotechnical Engineering & Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, 1239 Siping Rd, Shanghai, China e-mail: [email protected] J. Bi Institute of Geotechnical and Underground Engineering, Guangzhou Design Institute Group Co., Ltd., Guangzhou 510620, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_60

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[1]. Consequently, there is growing concern about ground vibrations induced by high-speed trains. Over the past years, several scholars have carried out a series of numerical simulations to investigate the ground vibrations caused by railway transportation. To explore the effects of foundation conditions on the propagation of ground vibrations induced by external loads, Kouroussis et al. [2] developed a complete vehicle/track model, which demonstrated the critical role of soil stratification in ground vibrations. Yao et al. [3] investigated the high-speed train-induced ground vibrations using a semi-analytical vehicle-track-ground coupling model and identified several factors that significantly influence ground vibrations, including vehicle speed, observation location, rail irregularity, subgrade-bed stiffness, and vehicle type. However, the above researches have not considered any foundation reinforcements. In practice, the pile-net composite subgrade is widely used in the high-speed railway construction due to its attractive advantages, including convenient construction, low settlement and high embankment stability. Feng et al. [4] developed a 3D FEM model and examined the effects of subgrade treatments on vibration isolation. Fu et al. [5] established a 3D dynamic FEM model of tracks-embankment-pilesoil composite foundation and simulated the dynamic behavior of embankment and composite foundation. Gao et al. [6] established 3D FEM models to investigate the ground vibrations of a composite foundation under moving loads induced by highspeed trains, and demonstrated that the pile-reinforcement could significantly reduce ground vibrations. Though the ground vibrations generated by the pile-net composite subgrade under the same conditions have been studied, the knowledge of the influences of soil types and pile-net composite subgrade design parameters on ground vibrations induced by high-speed trains is still limited in literatures. Therefore, a 3D FEM model of composite subgrade involving the track, embankment, geogrid, plie caps and piles was developed. On this basis, the influences of soil types, pile diameter and pile spacing on ground vibrations are discussed in detail.

2 Modelling Approach and Validation 2.1 Model Development Zhai et al. [7] conducted an analysis of the train-induced ground vibrations through in-situ measurement on the east side of Suzhou Railway Station of the BeijingShanghai high-speed railway, and train passed through the test section at a speed of 350 km/h. This paper adopts the same parameters of the train as the Ref. [7], and soil and pile-net composite subgrade are presented in Table 1. Yang et al. [8] suggested that the ground vibrations induced by a high-speed train consisting of four carriages are almost identical to those with ten carriages. To reduce the calculation efforts, the train consisting of four carriages was used for the

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Table 1 Dynamic properties of the calculation model Name

Thickness (m)

Surface layer of subgrade

0.40

Bottom layer of subgrade

Elastic modulus (MPa)

Poisson’s ratio

Damping ratio

Density (g/ m3 )

Shear wave velocity (m/s)

150

0.30

0.038

1.90

174.3

2.30

110

0.35

0.034

1.95

144.5

The rest part under subgrade

0.60

50

0.32

0.030

1.90

99.8

Clay

2.86

20

0.29

0.030

1898

63.9

Saturated 0.97 silt and silty sand

65

0.33

0.030

1900

113.4

Clay

3.86

68

0.32

0.026

1902

116.4

Saturated silt

5.68

69

0.30

0.033

1899

118.2

Saturated clay and silty clay

4.58

70

0.34

0.029

1905

117.1

Saturated 4.78 silt and silty sand

71

0.35

0.034

1903

117.6

Clay, silty clay

2.16

72

0.34

0.04

1896

119.0

Saturated 5.54 siltand silty sand

75

0.31

0.038

1895

122.9

10,000

0.20

0.060

2.50

–

CFG pile

–

numerical analysis. Taking advantage of symmetry, only one half of the FEM model was established. Based on the ABAQUS software, a train-track-ground dynamic analysis model with dimensions of 120 m (length) × 70 m (width) × 40 m (depth) was developed, as illustrated in Fig. 1. The embankment, pile and soil were modelled by 8-nodes solid cubic elements, and the rail was modelled using Euler beam elements. The unit’s dimensions of the embankment and soil were controlled in the range between 0.250 and 0.500 m to balance the accuracy and efficiency of the dynamic analysis model, while the rail elements were set to be 0.025 m. Fasteners were substituted by spring dampers, and the elastic modulus and damping coefficient of which are 2.50 × 107 N/m and 7.50 × 104 N s/m, respectively.

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Pile Cap

Pile

(a) Piles and geogrid model

(b) FEM model of the track-ground

Fig. 1 Detail of 3D FEM model

In order to facilitate model management and grid division, the model has been divided into several parts, involving the embankment, geogrid, pile caps, piles and soil. All the parts are connected by binding constraints. The symmetric boundary was used on the symmetry plane of the model. The bottom adopts fixed boundary, and the other surfaces adopt viscoelastic artificial boundary [9]. A damping ratio of 0.05 was employed and realized with the Rayleigh damping approach [10].

2.2 Train Loading Artificial excitation combined by a series of periodic loads is applied to simulate the train loading. The train loading formula considers the coincident effect of adjacent wheel sets and dispersed effect of sleepers, and the vibration excitation caused by geometric track irregularities and other relevant factors as well. The mathematical description of train loading can be expressed as follows [11]: F(t) = k1 k2 ( P 0 + P 1 sin ω1 t + P 2 sin ω2 t + P 3 sin ω3 t)

(1)

ωi = 2πν/L i , i = 1, 2, 3

(2)

P i = M 0 ai ωi2 , i = 1, 2, 3

(3)

where P 0 denotes the static load of a train carriage; the constant k1 represents the superposition coefficient of adjacent wheel sets; the constant k2 is the dispersion coefficient of sleepers; P 1 , P 2 and P 3 are the typical values of the dynamic loads corresponding to ω1 , ω2 and ω3 which represent the low frequency, medium frequency and high frequency, respectively; v is train speed; ai and Li are the rise and wave

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length of the track geometric unevenness; M 0 represents unsprung mass of a train carriage [11]. According to parameters of high-speed trains [7], the movement process of the train loadings is programmed through the DLOAD subroutine in ABAQUS, and applied to the track surface of the 3D FEM model.

2.3 Validation The proposed 3D FEM model according Sect. 2.1 under train loading of 350 km/h was validated by comparing the predictions to the field measurements in Ref. [7]. Firstly, Fig. 2 presents the experimental results and numerical predictions of time histories curve of vertical accelerations at 1.7 m from track center with train speed of 350.0 km/h. The cluster of vibration peak values induced by each bogie of the train can be observed in numerical predictions, and the distributions and magnitudes agree well with experimental results. As shown in Fig. 3, with the increasing distance from the track center, the numerical calculation results agree well with the measurements. It indicates that the numerical model could well simulate the ground vibrations at both near and far offsets from the track center.

3 Influences of Soil Parameters and Pile-Net Composite Subgrade on Ground Vibrations

Vertical Acceleration/m*s-2

To investigate the influences of soil parameters, pile diameter and pile spacing of pile-net composite subgrade on ground vibrations induced by high-speed trains, the FEM model involving the track, embankment, gravel cushion, geogrid, pile caps and piles was established with the dimensions of 120.0 m (length) × 70.0 m (width) × 53.3 m (depth), as illustrated in Fig. 4. 3

Experimental results [7]

2

Numerical predictions

1 0 -1 -2 -3 0.0

0.5

1.0

1.5

2.0 2.5 Time/s

3.0

3.5

4.0

4.5

Fig. 2 Time-history curve of vertical vibration acceleration at 1.7 m from the track center

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Fig. 3 Comparison of peak vibration acceleration at different distances from the track center

Peak vertical acceleration(m/s2)

638 1.00

Numerical calculation results Measured results[7]

0.10

0.01 10

20 30 40 Distance from the track center (m)

50

High speed train loading

Bottom of embankment 2.3m high Rest part beneath embankment 0.6m high Cushion Layer 1 Pile cap Pile

Layer 2

Layer 3

Layer 4

Viscoelastic artificial boundary

53.3m (depth) Symmetrical boundary

Geogrid

Surface of embankment 0.4m high

Fixed boundary 70.0m(width)

Fig. 4 3D FEM model

In the computing model, the calculation parameters of piles are as follows: the length is 18.0 m, the spacing between pile’s center is 1.8 m, the diameter is 0.5 m, the dynamic elastic modulus is 10 GPa, the Poisson’s ratio is 0.20, the density is 2500 kg/ m3 , and the damping ratio is 0.03. The CFG piles are arranged in a rectangular pattern. The diameter and thickness of the pile cap are 1.0 and 0.4 m. The gravel cushion is set beneath the embankment. The calculation parameters of gravel cushion are as follows: the thickness is 0.6 m, the dynamic elastic modulus is 120 MPa, the Poisson’s ratio is 0.30, the density is 1500 kg/m3 , and the damping ratio is 0.05. Two layers of geogrid are laid in the gravel cushion. The calculation parameters of geogrid are as follows: the dynamic elastic modulus is 40 GPa, Poisson’s ratio is 0.20, the density is 1500 kg/m3 , and the axial tensile strength is 500 kN/m. The embankment model parameters are taken from Ref. [7]. Additionally, the rest of model parameters are the same as in Sect. 2. In order to analyze the influences of the soil types of pile-net composite subgrade on ground vibrations, four soil types neglecting the variation of soil thickness passed

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Table 2 Calculation parameters of four types of soils [12] Type

Name

Soil 1 Clay

Thickness (m)

Elastic modulus (MPa)

Poisson’s ratio

Density (kg*m−3 )

Shear wave velocity (m*s−1 )

Longitudinal velocity (m*s−1 )

6

25

0.31

1900

114.7

208.3

Mucky clay

12

15

0.30

1800

91.3

159.8

Clay, silt

15

30

0.30

1980

123.1

215.4

Residual soil

17

70

0.32

2020

186.2

351.6

Soil 2 Clay

6

40

0.31

1890

145.5

264.2

Mucky clay

12

25

0.30

1750

119.5

209.2

silty clay

15

40

0.30

1820

148.2

259.4

Fine sand 17

80

0.32

2010

199.5

376.8

6

50

0.31

1990

158.5

287.8

12

40

0.30

1840

147.4

258.0

Silty clay 15

50

0.30

1950

160.1

280.2

Clay, silt

17

90

0.32

2020

211.1

398.7

Soil 3 Clay Mucky clay

Soil 4 Clay

6

60

0.31

2020

172.3

312.9

12

15

0.30

1850

90.0

157.6

Silty clay 15

70

0.30

1890

192.5

336.8

Clay, silt

90

0.32

1990

212.7

401.7

Mucky clay

17

by the Shanghai-Nanjing Intercity Railway were selected [12], and the calculation parameters of which are presented in Table 2. Among these four types of representative soils, the shear wave velocities of Soil 1 is smaller than other types, which can be defined as the softer soil. Soil 3 has the largest shear wave velocities, which is defined as the stiffer soil. The shear wave speeds of Soil 2 is between Soil 1 and Soil 3, which can be defined as medium-stiff soil. The second layer of the Soil 4 is soft soil sandwiched between the stiff soil layers, which can be defined as the foundation with weak interlayer.

3.1 Influence of the Soil Types on Ground Vibrations Considering the train speed of 300 km/h, Fig. 5 shows the attenuation curves of peak ground vibration accelerations with the increasing distance from the track for four different soil types. Within 30 m from the track center, the ground vibration

Fig. 5 Peak vibration acceleration under different soil types

G. Gao et al. Peak vertical acceleration (m/s2)

640

Soil1 Soil2 Soil3 Soil4

0.5

0.05 8

16

24

32

40

48

56

64

Distance from the track center (m)

attenuates fast, and the curves of which for different soil types are approximately parallel. However, beyond 30 m from the track center, the attenuation trends for four types of foundation are different from each other, especially for the case of Soil 4 that is influenced by the soft interlayer. According to Ref. [1], the material damping and geometric damping contribute together to the attenuation of far field vibrations whereas the geometric damping is a primary contributor to the decay of near vibration source. This indicates that the soil types have obvious effects on ground vibrations in the far track zone. Additionally, as shown in Fig. 5, the decay rate of ground vibrations for Soil 1 is greater than that of Soil 3. It means that the ground vibrations attenuate higher in the softer soil. It should be note that, for the case of Soil 2, the ground peak acceleration near the track center is greater than other cases. As highlighted in Ref. [6], strong ground vibrations occur when the train speed (300.0 km/h, 83.3 m/s) is close to the Rayleigh wave velocity of the top layer (83.0 m/s), which could result in the phenomenon of resonance.

3.2 Influence of Pile Diameters and Pile Spacings on Ground Vibration Figure 6 shows attenuation curves of the peak ground vibration accelerations at the train speed of 350 km/h for different pile diameters of 0.4, 0.5 and 0.6 m. The Soil 4 in Table 2 was used in model, and pile spacing was set to 1.8 m. It can be seen that the ground vibration decreases with increasing pile diameter. It is because that the stiffness of the subgrade increases with increasing pile diameter, the vibration energy induced by trains is dissipated faster in the pile-net composite subgrade. Figure 7 shows that the attenuation curves of the peak ground vibration accelerations at the train speed of 350 km/h for varying pile spacings of 1.5, 1.8 and 2.1 m. The Soil 4 in Table 2 was used in calculation model, and pile spacing was set to 0.5 m. It can be seen that the ground vibration decreases with increasing pile spacing.

Fig. 6 Peak vibration acceleration under different pile diameters

Peak vertical acceleration(m/s2)

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641

a=0.4m a=0.5m a=0.6m

0.1

0.0 8

1.0 Peak vertical acceleration(m/s2)

Fig. 7 Peak vibration acceleration under different pile spacings

16 24 32 40 48 56 64 Distance from the track center (m)

s=2.1m s=1.8m s=1.5m

0.1

0.0 8

16 24 32 40 48 56 64 Distance from the track center (m)

From Figs. 6 and 7, both the pile diameter and pile spacing have great influences on the peak ground accelerations within 30 m from the track center, beyond which this influence of pile parameters on ground vibrations weakens gradually. In addition, the effects of pile diameter on ground vibrations are more remarkable than pile spacing, especially within 30 m from the track.

4 Conclusion Based on ABAQUS, 3D FEM models of pile-net composite subgrade were established in this paper, and the influence of pile-net composite subgrade design parameters and soil types on the ground vibrations induced by high-speed trains were studied. The main conclusions are as follows:

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(1) The ground vibration responses exhibit a downward tendency with the increasing distance from the track center under different soil types, and the attenuation rate of ground vibrations in softer soil is higher than that in the stiffer soil. The types of foundation soils play have great influences on the vibration attenuation, especially for the far track zoon. (2) The peak ground acceleration decreases with the increasing pile diameter, or the decreasing pile spacing. Comparing with the pile spacing, the pile diameter has greater effects on ground vibrations, especially for the near track zoon. Acknowledgements The work described in this paper was supported by the National Science Foundation of China (Grant no. 51978510).

References 1. Gao GY, Bi JW, Chen J (2021) Vibration mitigation performance of embankments and cuttings in transversely isotropic ground under high-speed train loading. Soil Dyn Earthq Eng 141:106478 2. Kouroussis G, Conti C, Verlinden O (2013) Investigating the influence of soil properties on railway traffic vibration using a numerical model. Veh Syst Dyn 51(3):421–442 3. Yao HL, Hu Z, Lu Z, Zhan Y, Liu J (2016) Prediction of ground vibration from high speed trains using a vehicle–track-ground coupling model. Int J Struct Stab Dyn 16(8):1550051 4. Feng SJ, Zhang XL, Zheng QT, Wang L (2017) Simulation and mitigation analysis of ground vibrations induced by high-speed train with three dimensional FEM. Soil Dyn Earthq Eng 94:204–214 5. Fu Q, Song JL, Ding XM, Jiang ZK (2017) Study on dynamic response characteristic of PCC pile-soil composite foundation under high-speed railway train load. J Railway Sci Eng 94:204–214 6. Gao GY, Bi JW, Chen QS, Chen RM (2020) Analysis of ground vibrations induced by highspeed train moving on pile-supported subgrade using three-dimensional FEM. J Central South Univ 27(08):2455–2464 7. Zhai WM, Wei K, Song XL, Shao MH (2015) Experimental investigation into ground vibrations induced by very high speed trains on a non-ballasted track. Soil Dyn Earthq Eng 72:24–36 8. Yang YB, Hung HH (2009) Wave propagation for train-induced vibrations: a finite/infinite element approach. World Scientific, Singapore 9. Gao GY, Yao SF, Yang J, Chen J (2019) Investigating ground vibration induced by moving train loads on unsaturated ground using 2.5D FEM. Soil Dyn Earthq Eng 124:72–85 10. Saikia A (2014) Numerical study on screening of surface waves using a pair of softer backfilled trenches. Soil Dyn Earthq Eng 65:206–213 11. Liang B, Luo H, Sun CX (2006) Simulated study on vibration load of high speed railway. J China Railway Soc 28(4):89–94 12. Ma LH, Liang QH, Gu AJ, Jiang H (2015) Research on impact of Shanghai-Nanjing intercity high-speed railway induced vibration on ambient environment and foundation settlement of adjacent Beijing-Shanghai railway. J China Railway Soc 37(02):98–105

Transferability of Railway Vibration Emission from One Site to Another M. Villot, C. Guigou-Carter, and P. Jean

Abstract This paper suggests a new method for characterizing and predicting railway vibration emission, which ensures transferability from one site to another. The method is based on a source-receiver mobility approach, where the vehicle-track system (including ballast) is the source, the ground the receiver and the contact forces between them represented by a line of uncorrelated forces. The method is numerically validated using a home-developed railway source model. It is shown that a railway source can be a “force” source, a “velocity” source or neither, depending on frequency and the mobility conditions with ground. The contact force can be estimated in any situation from the so-called blocked force, knowing the (complex) mobilities of the railway source and the ground. The blocked force can be measured in situ using a procedure similar to the US DOT FRA procedure. Procedures for measuring the ground mobility exist. Finding field measurement configurations and procedures to get the railway source mobility is the main future challenge to demonstrate the practicality of this novel idea. Keywords Railway vibration sources · Vibration source characterization · Mobility approach

1 Introduction Ground borne vibration generated by railway lines, and particularly vibration emission, is an ongoing issue, which shows a need for vibration emission characterization and prediction, where the approach used should ensure transferability from one site to another. How much vibration is transmitted to ground must be known to evaluate the source and the quantity quantifying well the transmission is the vibration power, M. Villot (B) Expert Consulting, 38100 Grenoble, France e-mail: [email protected] C. Guigou-Carter · P. Jean CSTB, Health and Comfort Department, 38400 Saint Martin d’Hères, France © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_61

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Fig. 1 Line transfer mobility measurement configuration

in the same way that sound power quantifies sound emission. This quantity, new in railway vibration, has been the subject of a presentation at IWRN 13 [1], which shows that the vibration power transmitted to ground can be approximated by the product of the forces (rms value squared) applied to ground and generated by the train passing on the track system, and the real part of the ground point mobility (velocity response to a unit force applied to ground). Both force and ground mobility can be measured or estimated by models, as shown in this paper. Railway vibration sources are commonly represented by a line of (non-moving) uncorrelated forces with the same magnitude applied to ground (see Fig. 1), which has led to the following measuring method called line transfer mobility procedure as defined in a US Department of Transportation Federal Railroad Administration (US DOT FRA) document [2], derived from another and similar Federal Transit Administration document (US DOT FTA). The force density level L F,train applied to ground and generated by the train passing on the track system is obtained in two steps: in a first step, the ground vertical meansquare velocity responses vi 2 at one location away from the tracks, to the vertical mean-square forces F i 2 applied to ground (usually produced by an instrumented impact hammer) are measured and the transfer mobility TM line calculated as: T Mline = 10lg



vi2 /Fi2

(1)

i

with a line of impact positions at 10- or 20-foot intervals according to [2]. In a second step, the ground velocity response level L v,train is measured during train passages at the same location and the force density level L F,train estimated as: L F = L v,train − T Mline

(2)

Is the measured force a characteristic of the railway source (the vehicle-track system), which can be used at any site? If not, how can railway vibration emission be transferred to another site? The answer is found in the source-receiver mechanical system theory, which is based on a mobility approach. This physical approach is new in railway vibration and involves quantities often used in broad frequency bands

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(1/3 octave bands), which should simplify the transfer calculations from one site to another, compared to using heavier and more detailed models, such as numerical models performed in narrow frequency bands. In this paper, the source-receiver theory applied to railway sources (vehicle-track systems) connected to the ground (the receiver) is first presented, leading to the definition of the source characteristics (Sect. 2). Then, the source characteristics required for transferring the source to another site are estimated using a home developed vehicle- track-ground model (Sect. 3). Finally, the method is applied to IC trains running on common ballasted tracks laid on the surface of typified half-space homogeneous soils of different stiffnesses (Sects. 4 and 5).

2 Source-Receiver Theory Applied to Railway Sources 2.1 Mobility Conditions The theory shows [3], that the measured force characterizes the source only if the source input mobility magnitude is much greater than the receiver input mobility magnitude. The source is then called “force source” and the contact force “blocked force” (the much stiffer receiver “blocks” the source). In our case, the railway source input mobility must therefore be estimated and compared to the ground input mobility. However, the railway source is a multi-contact line source and effective mobilities Y Σ [4] (particular input mobilities defined as velocity response at one contact to a line of uncorrelated forces applied at contacts) must be used and the condition written as: Σ Σ Y Sour ce  Y Receiver

(3)

The receiver (ground) effective mobility is very similar to the transfer mobility introduced in Sect. 1; however, the location chosen for measuring the receiver response is on the line contact between source and receiver (Fig. 2 right), and not away from it as in Fig. 1. Indeed, effective mobilities are multi-contact input mobilities. Fig. 2 Effective mobility measurement configuration (in 2D); (left) source; (right) receiver

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2.2 Source Effective Mobility Estimation The source effective mobility, characteristic of the source, can be indirectly estimated from two other source characteristics [3]: the source blocked force F bl , already mentioned above and the source free velocity vf , which, in our case, is the ground velocity response obtained if the railway source is connected to an extremely soft ground, much softer than the source (the source is “free”); the ground effective mobility magnitude is then much greater than the source effective mobility magnitude. The theory shows [3], that these three frequency dependent source characteristics are related to each other as:  = v˜ f / F˜bl Y˜S,i

(4a)

   ˜ Σ 2 2 Y S,i  = v 2f,r ms /Fbl,r ms

(4b)

where the symbol ~ indicates a complex quantity in the frequency domain. Equations (4) allow an indirect estimation of the source effective mobility. This indirect method is used in this paper, the input quantities (free velocity and blocked force) being numerically estimated, using the railway source model briefly described in the next section.

3 Source Mobility Calculation 3.1 Railway Source Model The railway source model used has been developed at CSTB; it is a 2D model taking into account vertical forces only and based on the wave approach [5]. The rail is an infinite beam on a continuous multi-layered support representing rail pads, sleepers and ballast or other track components. The coupling to ground (Fig. 3) is made by connecting the ballast lower interface to the ground input line mobility (ground surface velocity response to propagating stress waves of different wavelengths along a line, calculated for each frequency component in the wave number domain). This mobility is numerically obtained using a home-developed BEM ground model (MEFFISTO software, [6]) applied in our case to typified half space homogeneous grounds. Each train axle is modelled as a set of springs and lumped masses representing the car body, bogie, wheel (unsprung mass) and connecting suspensions. For a given combined wheel-rail unevenness, the model calculates the velocity at the interface ballast-ground, from which the force transmitted to ground is deduced, knowing the ground input mobility. It is important to note, that the excitation of the track by the train is also represented in the model by a line of uncorrelated forces generated by each train axle, regularly distributed every 5 m (4 axles per car of 20 m

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Fig. 3 Railway source model coupled to ground using the ground line mobility

length). Indeed, the neighbouring axles have an influence on the output quantities calculated (forces transmitted to ground).

3.2 Source Mobility Calculation The railway source is first connected to an extremely stiff ground and the (blocked) force at the interface ballast-ground calculated using the model. Then the source is connected to an extremely soft ground and the (free) velocity at the interface ballastground calculated using the model. The railway source effective mobility magnitude is then calculated using Eq. (4), with a spacing of 5 m between forces transmitted to ground (the same as the average axle spacing; see paragraph above).

4 Application to IC Trains on Ballasted Tracks 4.1 Source Description The source consists of Intercity (IC) trains rolling on common ballasted tracks as defined in the RIVAS project [7], deliverable D5.2 (properties not recalled here for the sake of brevity). The ballast has the dynamic characteristics given in Table 1. Three half-space homogeneous grounds (stiff, medium and soft), having the properties indicated in Table 2, have been considered. Table 1 Track components characteristics (from RIVAS) Component

Mass, kg/m

Dynamic stiffness, (MN/m)/m

Viscous damping, (MNs/m)/m

Ballast

520

1390

0.441

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Table 2 Ground properties Young modulus (MPa)

Loss factor (%)

Density (kg/ m3 )

Poisson ratio (−)

Shear wave speed (m/s)

50

10

1400

0.25

120

Ground (medium)

200

10

1600

0.25

224

Ground (stiff)

800

10

1800

0.25

422

Ground (soft)

Fig. 4 1/3 octave band spectrum of the average combined rail-wheel unevenness (from RIVAS)

The combined rail-wheel unevenness used corresponds to the average curve suggested in RIVAS D5.2 in the case of relatively smooth wheel and rail (Fig. 4).

4.2 Source Effective Mobility Magnitude Calculation The source effective mobility magnitude is calculated from Eq. (4b) using the method described in Sect. 3.2. All the input quantities are real and can be expressed in 1/3 octave bands by summing the velocity or force narrow band components calculated by the model within each broad band [8]. The railway source effective mobility magnitude obtained is shown in Fig. 5, as well as the three ground effective mobility magnitudes numerically calculated using MEFFISTO and approximated by the point mobility magnitudes (see Sect. 5). Figure 5 clearly shows that:

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Fig. 5 Calculated source effective mobility magnitude of the system IC trains/ballasted tracks (in 1/3 octave bands); comparison with ground effective mobility magnitudes

(i) the railway source acts as a “force source” only at low frequencies (source effective mobility much higher than the receiver effective mobility), if the ground is not too soft; (ii) it acts as a “velocity source” (source effective mobility much lower than the receiver effective mobility) at high frequencies; the ground (free) velocity characterizes then the source and is the quantity to be measured; (iii) otherwise (at mid frequencies), railway source and ground effective mobilities are of the same order of magnitude; in this case, the contact force, different from the blocked force, must and can be estimated, as shown in Sect. 5 below.

4.3 Interpreting the US DOT FRA Procedure Differently Railway source and ground effective mobilities being of the same order of magnitude, the ground line transfer mobility used for estimating the contact force in situ (US FRA procedure [2]) cannot be measured from ground excitations on the track line, where tracks and ground interact. However, according to standard ISO 20270 [9], the force estimated using line transfer mobility measurements from excitations at the contacts source/receiver with the source present but not operating (i.e. performed from the track line with the train on top, but not moving), is the blocked force. The US DOT FRA procedure applied from excitations on the track line with the train on top is indeed the proper way of getting the blocked force.

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5 Estimation of the Contact Force 5.1 Methodology When source and receiver effective mobilities are of the same order of magnitude, the source-receiver theory shows that the contact force can be determined from the source blocked force as [3]:

2 Fc,r ms

   ˜ Σ 2 2 Y S,i  .Fbl,r ms =  2  ˜Σ   Y S,i + Y˜ R,i 

(5)

where determining the denominator requires the knowledge of the complex source and receiver effective mobilities. It should be noted, that the complex mobilities in Eq. (5) can still be approximated in terms of 1/3 octave band quantities, by averaging their real and imaginary narrow 2 band components within each broad band [8] and Fc,r ms calculated in 1/3 octave bands.

5.2 Application to IC Trains on Ballasted Tracks The contact force levels obtained using Eq. (5) are shown in Fig. 6 and compared to the contact forces directly calculated in the wave number domain for each narrow frequency bands using the railway source model of Sect. 3.1 and expressed in 1/ 3 octave bands. The maxima correspond to mass-spring resonances between track system and ground, and to the crossing between source and ground mobility curves in Fig. 6. The mobility method gives the right force spectral shapes but amplifies much the resonance phenomena compared to the model (maybe due to the broad band approximation used); however, the stiffer the ground the better the estimation.

6 Concluding Remarks The above numerical study has led to the following useful results: • Railway vibration sources, (i) act as a “force source” only at low frequencies, (ii) act as “velocity source” at high frequencies, where the ground (contact) velocity is the quantity to be measured, (iii) railway source and ground effective mobilities are of the same order of magnitude at mid frequencies, where the contact force can be approximated in 1/3 octave bands from the blocked force rms values and the source and ground complex mobilities.

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Fig. 6 Contact force levels; comparison between mobility method and railway source model

• The US DOT FRA procedure applied from ground excitations on the track line with the train (not moving) on top is the way of getting the blocked force, The next step will consist in (i) defining relevant field measurements to support the theory and demonstrate the practicality of this novel idea and (ii) developing a mobility-based model, which separates the vehicle, acting as a primary source, from the tracks, acting as a vibration transfer system between vehicle and ground, thus making possible the transfer to situations, where vehicles (or their speed) or tracks systems are different.

References 1. Villot M, Guigou-Carter C, Jean P, Müller R (2020) Evaluation of the vibration power transmitted to ground due to rolling stock on straight tracks. In: Proceedings of the 13th international workshop on railway noise, vol 150 of Notes on numerical fluid mechanics and multidisciplinary design. Springer, Berlin, pp 394–402 2. US Department of Transportation (2012) Federal railroad administration: high-speed ground transportation noise and vibration impact assessment 3. Gibbs B, Villot M (2020) Structure-borne sound in buildings: advances in measurement and prediction methods. Noise Control Eng J 68(1) 4. Petersson B, Plunt J (1982) On effective mobilities in the prediction of structure-borne sound transmission between a source and a receiving structure, Parts 1&2. J Sound Vib 82(4) 5. Guigou-Carter C, Villot M, Guillerme B, Petit C (2006) Analytical and experimental study of sleeper SAT S 312 in slab track SATEBA system. J Sound Vib 293(3–5):878–887 6. Jean P, Guigou-Carter C, Villot M (2004) A 2D ½ BEM model for ground structure interaction. Build Acoust 11(3):157–163

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7. RIVAS Project. FP7 European project under grant agreement 265754, Nov 2013. Deliverables available from https://uic.org/projects/article/rivas 8. EN 15657:2017. Acoustic properties of building elements and of buildings—laboratory measurement of structure-borne sound from building service equipment for all installation conditions 9. Standard ISO 20270:2020. Acoustics, characterization of sources of structure-borne sound and vibration—indirect measurement of blocked forces

Ground Vibration Reduction Analysis of Pile-Supported Subgrade for High-Speed Railway Using 2.5D FEM Guang-yun Gao , Ji-yan Zhang , and Bi Jun-wei

Abstract A 2.5-dimensional finite element model (2.5D FEM) for predicting ground vibrations of the coupled track-pile-supported subgrade system was proposed. In the model, the equivalent pile wall approach was used to simulate the piles and surrounding soils. Reliability of the established model was verified with field measurements. Two types of high-speed railway subgrade, with or without piles, were chosen to be analyzed. The obtained results were compared to investigate the performance of subgrade improvement with piles in reducing ground vibration induced by high-speed train loads. Following that, the effects of pile parameters on ground vibration were studied. The study shows that subgrade improvement with piles significantly reduces the ground vibrations both for low-frequency and highfrequency components, and the vibration reduction performance gets better away from the track than close to it. Increasing pile diameter, increasing pile stiffness, or decreasing pile spacing could effectively reduce ground vibrations. However, there are critical values for these pile parameters in vibration reduction, beyond which the vibration reduction performance would no longer be improved. Keywords Pile-supported subgrade · Ground vibration reduction · High-speed railway · 2.5D FEM

G. Gao · J. Zhang Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, China G. Gao · J. Zhang · J. Bi (B) Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China e-mail: [email protected] J. Bi School of Civil Engineering & Transportation, South China University of Technology, Guangzhou 510641, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_62

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1 Introduction Pile-supported subgrade has been widely used in high-speed railway construction to deal with the issues of stability and settlement in soft grounds. In addition, the subgrade improvement using piles turns out to be effective in controlling the traininduced ground vibrations [1]. Some studies have been conducted both experimentally and numerically on vibration behaviors of pile-supported subgrade. Zhai et al. [2] and Wang et al. [3] performed field measurements of ground vibrations on Beijing-Shanghai high-speed railway in China, which provides data support for numerical and theoretical studies. So far, the numerical studies generally are performed by three-dimensional (3D FE) models. Feng et al. [4] simplified the piled subgrade as a mixed equivalent soil layer, and studied the influences of depth and extent of pile reinforcement on ground vibration. Considering the nonlinearity of materials through an equivalent linear approach, Thach et al. [5] indicates that pile reinforcement could significantly reduce the vibration responses. Similar conclusions are reached in [6–10] for single-phase elastic ground and in [11] for saturated ground. But there are ambiguities in terms of critical speed. Tang et al. [8] found that the existence of concrete piles has no impact on the critical speed of the track-ground system. However, contrary results were obtained in [9, 10], i.e., the ground improvement using piles would increase the critical speed. In addition, studies on the effects of certain pile parameters are addressed in [7, 8, 10]. Apparently, relevant studies are limited. The vibration reduction performance and pile parameter influences are not well known and still need further study. Therefore, to investigate the performance of pile reinforcements in reducing ground vibrations, an efficient 2.5D FEM for the coupled track-pile-supported subgrade system is developed based on the 2.5D FE theory [12], where the equivalent pile wall approach is employed in the train moving direction to model the character of piles and surrounding soils. Correctness of the proposed model has been well verified by comparing with field measurements. The vibration reduction performance and pile parameters influences are discussed in detail, through comparing the ground vibration in the unimproved ground and that of improved piles.

2 Establishment and Verification of the 2.5D FEM 2.1 Mathematical Formulations for the 2.5D FEM A typical single-lane high-speed railway is schematically shown in Fig. 1. The highspeed train runs over a slab track resting on a pile-supported subgrade in the xdirection at speed c. As the dynamic strain of the ground caused by rail traffic is generally 10-5 or less [13], the embankment, ground soil, cushion, and piles are treated as viscoelastic media. The constitutive relationship and motion equation are as follows:

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Fig. 1 Diagram of a single-lane railway

σi j = 2μd εi j + λd δi j e

(1)

μd u i, j j + (λd + μd )u j, ji = ρ u¨ i

(2)

  where σi j is the stress tensor component; εi j = u i, j + u j,i /2 and e = u i,i are the strain and dilatation of the medium, which u i is the displacement; λd and μd denote the Lamé constants with material damping defined by λd = λ(1 + 2βi), μd = μ(1 + 2βi), in which λ = Eμ/(1 + v)/(1 − 2v), E, v, and μ are the Young’s modulus, poisson’s ratio and shear modulus respectively, β represents damping ratio and equals one half of the loss factor; ρ is the material density; δi j is the Kronecker delta; the subscript i, j denote the spatial coordinates x, y, z; the subscript ‘(), i’ and a superimposed dot ‘.’ each denote the spatial and time derivations. Applying the Fourier transformations for time t and horizontal coordinate x [14] on Eq. (2), and discretizing the calculation area with the 4-node isoparametric element, the governing equation in matrix form in the frequency and wavenumber domain is: 

  − ω2 M  K U = F

(3)

 and M are stiffness matrix and mass matrix;  where K U is displacement vector;  F is equivalent nodal load vector. The equivalent pile wall approach shown in Fig. 2 is used to model the piles and surrounding soils, thus the basic assumption of 2.5D FEM that the geometry and material properties remain invariant in the x-direction could be satisfied. By the volume-weighted average method, the equivalent Young’s modulus E eq is defined as:

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Fig. 2 Equivalent pile wall principle

E eq = π d E p /4s + (1 − π d/4s)E s

(4)

where E p and E s represent the Young’s modulus of the pile and soil; d and s are pile diameter and pile spacing. Based on the fact that the relative slip between the pile and surrounding soil could be negligible [9], the pile and the surrounding soil are coupled through the co-node approach. The whole track system is treated as a Euler beam with only vertical movement, and the train loads are modelled as successive axle loads [14].

2.2 Verification Through Comparison with Field Measurements The correctness of the proposed model is verified with the aid of an in-situ experiment, which was carried out by Zhai et al. [2] alongside the Beijing-Shanghai high-speed railway line in China. Noting that the test section is a double-lane railway and the type of high-speed train is CRH380AL. For validation, a full model was built, in which the profile and parameters of the pile-supported subgrade and track structures are consistent with Ref. [2]. Figure 3 compares the peak values of vertical ground vibration accelerations from the 2.5D FEM and field measurements. Results show that the proposed 2.5D FEM reproduces the peak vibration accelerations at all measurement points, which validates the reliability of the equivalent pile wall approach and 2.5D FEM for the coupled track-pile-supported subgrade system.

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Fig. 3 Comparison of ground acceleration

3 Vibration Reduction of Pile-Supported Subgrade A typical single-lane high-speed railway is adopted herewith, and the cross-section and scale for 2.5D FEM are shown in Fig. 1. The total height of the embankment is 3.0 m, beneath the embankment is the ground improved using piles, which has two soft layers overlying the bedrock. Table 1 shows the dynamic parameters of the pile supported subgrade. The Chinese CRTSII non-ballasted slab track is laid on the embankment, and the dynamic parameters of which are given in Table 2 referring to Ref. [2]. Six carriages of the CRH380AL train are adopted in simulation, the average axle load of which is 15 t, and the characteristic lengths of wheelbase, distance between bogies in one car, and car body are respectively 2.5 m, 17.5 m and 25.0 m. The viscoelastic boundary is imposed on the truncated boundary of the model to absorb the spurious reflected waves. A fixed boundary is applied at the bottom of the model to simulate the rigid bedrock. The scenario of the high-speed train running at a speed of 350 km/h is investigated. Vibration reduction performance of the pile-supported subgrade is investigated by comparing the vertical ground vibration accelerations of pile-supported and unimproved ground. For the pile-supported subgrade, the diameter, spacing and length of piles are fixed as 0.5 m, 2.0 m and 15.0 m, respectively. Figure 4 depicts the comparison results of ground accelerations at distances of 3.0, 8.8, and 20.0 m from the Table 1 Parameters of pile-supported subgrade Components

Thickness/m

Young’s modulus/ MPa

Poission’s ratio/v

Damping ratio/β

Density/ (kg/m3 )

Rayleigh wave speed cR /(km/h)

Embankment

3.0

200

0.30

0.05

2100

638.1

Cushion

0.6

12

0.30

0.05

1900

519.7

Silty clay

14.0

72

0.39

0.05

1870

398.3

Silty sand

6.0

90

0.32

0.05

1990

437.2

Pile

15.0

10,000

0.20

0.03

2500

–

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Table 2 Parameters of CRTSII non-ballasted slab Parameter

Rail

Concrete slab

Concrete base

Bending stiffness (N m2 )

6.63 × 106

5.87 × 107

2.28 × 108

Mass (kg/m)

60.64

1233.0

2232.0

track centerline (left for time-histories, right for frequency spectra). It can be seen from time-history curves that the ground vibration of the pile-supported subgrade is considerably smaller than that of unimproved subgrade. The vertical ground acceleration is reduced about 11% at 3.0 m to the track centerline, while at distances of 8.8 m and 20.0 m, the reduction reaches 38% and 67%. The vibration reduction performance of the piled subgrade is excellent, and is better away from track than close to it. Two acts caused by piles are responsible for the ground vibration reduction, one of which is that the pile-supported subgrade improves the ground stiffness, and thus improves the vibration resistance. The other side is that the existence of piles accelerates the attenuation of ground vibration waves. Near the track centerline, only the first act affects the ground vibration. For the ground vibrations away from the track centerline the second act also plays an important role. It is found from the distribution of the frequency spectra of ground accelerations in Fig. 4 (right) that, the significant frequency components of the pilesupported subgrade are consistent with those of unimproved subgrade. The significant frequency corresponds to multiples of base frequency which is defined as f b = c/L (L is the length of car body 25.0 m). The dominant frequency is the same for each distance from the track centerline, and similar conclusions have been drawn in Ref. [2]. It is noteworthy that piled subgrade will significantly reduce both the low-frequency contents and high-frequency contents.

4 Effect of Pile Parameters The influences of pile diameter, spacing and stiffness on ground vibrations and vibration reduction performance under c = 350 km/h are shown in Fig. 5. Pictures numbered (a), (c) and (e) are the comparisons in peak acceleration, while pictures (b), (d) and (f) depict the vibration reduction which is defined as the ratio of peak acceleration of pile improved ground to that of unimproved ground. The initial values of pile diameter d, spacing s, stiffness E p and length h are 0.5 m, 2.0 m, 10.0 GPa and 15.0 m, respectively. Three kinds of pile diameters are chosen, d = 0.3 m, 0.5 m, 0.8 m. Figure 5a– b illustrates the influence of pile diameter. The ground vibration decreases monotonously with distance to the track centerline for piled and unimproved subgrade cases. With the increase of pile diameter, the ground vibration decreases markedly, especially at a further distance from the track, with reductions reaching 40–70%.

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Fig. 4 Time histories (left) and frequency spectra (right) of vertical ground acceleration at a 3.0 m, b 8.8 m, c 20.0 m from the track centerline

From the trend of vibration reduction with pile diameter, the rate of vibration reduction decreases with the increase in pile diameter. This indicates that there is a critical value for pile diameter, beyond which it is hard to further reduce the ground vibrations by increasing the pile diameter. Figure 5c–d depicts the influence of pile spacing on ground vibrations. Pile Spacing with 1.5, 2.0, and 2.5 m are chosen for analysis. The pile spacing also has significant impact on ground vibrations. With the increase of pile spacing, the

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Fig. 5 Peak vertical acceleration and vibration reduction against distance from track centerline for different a–b pile diameter d, c–d pile spacing s, e–f pile stiffness E p

ground acceleration increases greatly. From the trend of vibration reduction varying with pile spacing, it can be inferred that there is also a critical value for pile spacing, beyond which further decreases in pile spacing would have no improvement in ground vibration reduction.

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Figure 5e–f shows the comparison curves of ground accelerations with various pile stiffness, i.e., 1.0, 5.0, 10.0, and 15.0 GPa. The increasing pile stiffness significantly contributes to the decrease in ground acceleration no matter located close to or away from the track. However, the rate of vibration reduction also decreases with the increase of pile stiffness, which indicates that a critical value of pile stiffness exists in ground vibration reduction improvement.

5 Conclusions Based on 2.5D FE theory and equivalent pile wall approach, a 2.5D FEM was proposed for predicting ground vibrations of the coupled track-pile-supported subgrade subjected to high-speed train loads. Compared to the ground vibrations of the unimproved subgrade, the ground vibration reduction performance of pilesupported subgrade together with the influences of pile parameters were investigated. The major conclusions are summarized as follows. Pile-supported subgrade has excellent ground vibration reduction performance, which is better away from track than close to it. The vibration reduction is significant for both low-frequency and high-frequency vibrations. Pile diameter, pile spacing and pile stiffness have significant effects on ground accelerations. Increasing pile diameter, increasing pile stiffness or decreasing pile spacing could effectively reduce the ground accelerations. Meanwhile, there are critical values for these pile parameters, beyond these values further improvement in pile parameters would no longer improve the vibration reduction effectiveness. Acknowledgements The study is supported by National Natural Science Foundation of China (no. 51978510).

References 1. Thach PN, Liu HL, Kong GQ (2013) Vibration analysis of pile-supported embankments under high-speed train passage. Soil Dyn Earthq Eng 55:92–99 2. Zhai WM, Wei K, Song XL et al (2015) Experimental investigation into ground vibrations induced by very high speed trains on a non-ballasted track. Soil Dyn Earthq Eng 72:24–36 3. Wang L, Wang P, Wei K et al (2022) Ground vibration induced by high speed trains on an embankment with pile-board foundation: modelling and validation with in situ tests. Transp Geotech 34:100734 4. Feng SJ, Zhang XL, Zheng QT et al (2017) Simulation and mitigation analysis of ground vibrations induced by high-speed train with three dimensional FEM. Soil Dyn Earthq Eng 94:204–214 5. Thach PN, Liu HL, Kong GQ (2013) Evaluation of PCC pile method in mitigating embankment vibrations from a high-speed train. J Geotech Geoenviron Eng 132(12):2225–2228

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6. Fu Q, Liu HL, Ding XM et al (2015) Numerical investigation of piled raft foundation in mitigating embankment vibrations induced by high-speed trains. J Cent South Univ 22(11):4434–4444 7. Gao GY, Bi JW, Chen QS et al (2020) Analysis of ground vibrations induced by high-speed train moving on pile-supported subgrade using three-dimensional FEM. J Central South Univ 27:2455–2464 8. Tang YQ, Xiao SQ, Yang Q (2019) Numerical study of dynamic stress developed in the high speed rail foundation under train loads. Soil Dyn Earthq Eng 123:36–47 9. Li T, Su Q, Kaewunruen S (2020) Influences of piles on the ground vibration considering the train-track-soil dynamic interactions. Comput Geotech 120:103455 10. Esmaeili M, Sabbaghi M, Kharaghani M (2022) Three-dimensional numerical simulation of the geometrical dimension pile group effects on the critical speed of high-speed railway track (case study: Tehran–Isfahan high speed railway track). Soil Dyn Earthq Eng 156:107217 11. Li T, Su Q, Kaewunruen S (2019) Saturated ground vibration analysis based on a threedimensional coupled train-track-soil interaction model. Appl Sci Basel 9(23):4991 12. Yang YB, Hung HH (2001) A 2.5D finite/infinite element approach for modelling visco-elastic bodies subjected to moving loads. Int J Numer Methods Eng 51(11):1317–1336 13. Zia H, Cao YM, De Roeck G (2010) Theoretical modeling and characteristic analysis of moving-train induced ground vibrations. J Sound Vib 329:819–832 14. Gao GY, Zhang JY, Chen J et al (2022) Investigation of saturation effects on vibrations of nearly saturated ground due to moving train loads using 2.5D FEM. Soil Dyn Earthq Eng 158:107288

Noise and Vibration Measurement and Analysis at a Metro Depot and Above Transit-Oriented-Development Hongdong Huang, Jian Wang, Xiaohan Phrain Gu, Anbin Wang, Longhua Ju, Xinwei Luo, and Qingming Tu

Abstract To meet a fast-growing demand of the Transit Oriented Development (TOD) in China, this study aims at a better understanding of noise and vibration characteristics due to activities at a train depot of the metro system, as well as the transmission from the depot to above TOD. Noise and vibration field measurements at the Luogang depot are presented. Noise and vibration source at the depot, transmitting through structural elements to the depot roof plate, and finally to housing properties above the depot were evaluated. Wheel-rail induced noise and vibration from the throat zone featuring rail switches, from the test track at higher train speeds, and as trains entering the inspection and maintenance yard were investigated. The influence of using different track-forms for vibration mitigation was examined. Keywords Depot track · Noise and vibration propagation · Vibration attenuation

1 Introduction Transit Oriented Development (TOD), in densely-populated cities in China, typically refers to a community comprising mainly residential properties, and necessary facilities such as schools and shops etc., designed and built above metro depots and/ or stations. A representative example of the TOD above the train depot at Luogang for the Guangzhou metro line 6 is shown in Fig. 1. H. Huang · J. Wang Guangzhou Metro Group Co. Ltd., 18th Floor, Wansheng Plaza Tower A, 1238 East Xingang Road, Guangzhou, People’s Republic of China X. P. Gu (B) · A. Wang · L. Ju School of Urban Railway Transportation, Shanghai University of Engineering Science, 333 Longteng Road, Shanghai 201620, People’s Republic of China e-mail: [email protected] X. Luo · Q. Tu Guangzhou Metro Design & Research Institute Co. Ltd., 204 West Huanshi Road, Guangzhou, People’s Republic of China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_63

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Fig. 1 TOD above the Luogang depot

Comparing to noise and vibration emitted from the mainline of metro, noise and vibration sources from depot are more complex, featuring a wider range of train speeds, track geometries and conditions (with more curves, and rail joints at switches and crossings), fixed plant noise etc.; vibration propagation from the track to buildings above could be with and without the attenuation effects of soils, depending on the foundation design and construction techniques; yet the noise and vibration limitation at the receiver end remains the same as that of receivers along the mainline, if not more stringent. Limited studies have been carried out due to the fast growing trend for TOD in China. Zou et al. looked into the relationship between vibration isolation efficiency and geometrical properties of open trenches via computer simulation [1]. Tao et al. investigated vibration transmission through structural elements in low-rise buildings and in high-rise buildings, and found that the Federal Transit Administration guidelines significantly overpredict the vibration transmission loss from the platform to the top of each building compared to the measured change in each level [2]. This on-going joint research project provides an opportunity for a large amount of field data, at source, through key structural elements along the propagation path, and at receivers, to be collected, for the analysis and understanding of the propagation pattern of various types of noise and vibration sources, covering a wide range of track-forms and building structures. Together with numerical simulation, the output of the project is expected to give design guidance for noise and vibration mitigation for TODs. This paper presents a small amount of field noise and vibration measurements and corresponding propagation patterns, from the throat zone, the test track and entering the stabling yard of the depot.

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Legend Ballast track with mat S&C Ballast track with mat

665

N&V source N&V receivers X-section for N&V test on depot roof plate

Test track at the depot

Train-running tracks during N&V tests

P1

S2, P2

P3 Inspection lines etc.

S3

S1, R1

R3 Existing Stabling yard

S0

Planned Stabling yard

Fig. 2 Depot plan with noise and vibration measurement locations

2 Test Plan and Set-Up Noise and Vibration (N&V) from three different types of sources, namely from ➀ the throat zone1 feathering Switches and Crossings (S&C), ➁ the test track where train speed is relatively high comparing to other activities at the depot, and ➂ the stabling yard when trains cruising at low speeds, were recorded and analysed. For each type of the above three N&V source, corresponding train operation is specifically arranged for during non-working hours (typically at nights except for trains running on the test track), to exclude other N&V sources such as construction noise from the TOD; and the train speed is the same as that in standard operation. For each type of source, a vertical cross section is defined, covering noise and vibration source location at the depot (denoted as ‘Sx’), ground noise and vibration on the depot roof plate (denoted as ‘Px’), and noise and vibration receiver at the property above its relevant source location (denoted as ‘Rx’). Detailed measurement locations are shown in Fig. 2 and in Table 1. Measurement device set-up on the track, along the transmission path and at the receiver location are shown in Figs. 3, 4 and 5.

1

The throat zone is loosely defined, amongst the metro line operators and relevant parties in China, as the area where tracks merge through switches at the metro depots.

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Table 1 Noise and vibration measurement locations Area

Location ID

Location description

Location category

No. of device channels

Throat zone

S0

Switch 34 (ballast track with ballast mat)

N&V source

19

S1

Switch 32 (ballast track without mat)

P1

Depot roof plate (above S1)

Path

R1

House No. 37 (above S1)

N&V receiver

S2

Interface between N&V source the tunnel and open space

14

P2

Depot roof plate (above S2)

12

Test track

Existing stabling yard

19

Path

12 3

R2

House No. 47

N&V receiver

3

S3

Track No. 13

N&V source

14

P3

Depot roof plate (above S3)

Path

12

R3A

3rd floor of building 9

N&V receiver

R3B

15th floor of building 9

3

R3C

Top floor of building 9

3

3

Fig. 3 Accelerometer set-up on rails and sleeper (mid-span between two sets of rail fasteners)

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Fig. 4 Noise and vibration measurement set-up at source and on the depot roof plate

Fig. 5 Noise and vibration measurement set-up at the receiver. Note A16, A17 and M4 also denote corresponding accelerometers and microphone in the bedroom close to the rail track on the ground floor of houses, i.e. house no. 37 and house no. 47

3 Results and Analyses 3.1 Vibration Isolation Performance with Ballast Mat at the Throat Zone Noise and vibration acceleration levels at different locations at the depot near the source area for standard ballast track (S1) and for standard ballast track with under ballast mat (S0) were examined, according to ISO2631-1:1997 [3]. Total noise and vibration levels, as well as corresponding 1/3 octave spectrum is given in Fig. 6. The mean recorded train speed during this comparison test was 12.0 km/h. It can be seen that the ballast mat can achieve a vibration insertion loss of 3–4 dB. The frequency corresponding to peak vibration magnitudes of ballast track without ballast

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Fig. 6 Comparison of vibration at ballast track and ballast track with mat

mat between 40 and 63 Hz were shifted down to between 25 and 40 Hz with ballast mat, respectively, with lower vibration peak values using ballast mat. In addition, transverse vibration measured at the structural column transmitting vibration from the depot to the plate and properties above is significantly greater than the vertical vibration at the same measurement location, indicating that mitigation of transverse vibration could be crucial to vibration reduction at the receiver end.

3.2 Noise and Vibration of the Throat Zone Cross-Section (S1, P1, R1) The transmission of noise and vibration from train-track interaction, through structural elements to the development property above the depot were measured with the train passing the source at 11.2 km/h. 1/3 octave vibration spectra are shown in Fig. 7. Total noise levels are shown in Fig. 8. Vertical vibration attenuation from the rail, through ballast, to the nearest structural column is 40.3 dBz; transverse vibration attenuation from rail to column is 28.8 dBz. Transverse vibration at the structural column is 6.8 dBz higher than the vertical vibration at the same point. Vibration reduction from the rail to the same position on the depot roof plate is 46.3 dBz. Total vibration reduces on the depot roof plate with an increase distance away from the track centre-line as expected. Vibration attenuation from the rail to the floor in the bedroom at house no. 37 is 47.6 dBz. Similarly, noise attenuation from source to the depot roof plate is 47.4 dBA, and the attenuation from source to bedroom at house no. 37 is 44.3 dBA.

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Fig. 7 Vibration level from the source to the receiver (throat zone)

Fig. 8 Total vibration level and noise level from the source to the receiver (throat zone)

3.3 Noise and Vibration Propagation at the Test Track (S2, P2) With train running on the test track at an average of 39 and 57 km/h, vibration levels at the source and the depot roof plate were recorded simultaneously, as shown in Fig. 9. Vibration attenuation from source to the depot roof plate is on average 70.5 dBz. It is found that the train speed has an influence on the vibration level at the vibration source, but as vibration propagates to the roof plate, less influence of the train speed on vibration reduction.

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Fig. 9 Vibration levels with the train running on the test track

3.4 Noise and Vibration at the Stabling Yard (S3, P3, R3) Noise and vibration transmission from source to three representative floors in the high-rise building, namely building no. 9 above the depot, were examined, results are plotted in Figs. 10 and 11. Vibration attenuation from the rail to the floor of the building is in minimum 56.7 dBz. In general, as floor level goes up, vibration on the floor reduces. For a 30 stories building, approximately 5 dBz of vibration reduction can be achieved for going up half of the building. Vertical vibration on the floor of a building room is significantly higher that on the wall of the same room; however the difference in vibration between the two locations decreases as floor level goes up. There is no clear trend as to the structural-borne noise level as trains passing by, and all structural-borne noise level meet the national design criteria.

4 Conclusions The following conclusions are drawn from this analysis: 1. The trend of vibration propagation at source, along transmission path vertically up to the depot roof plate and to the development properties is as expected: (i) vertical vibration attenuation from the rail, through ballast, to the nearest structural column is around 50 dBz. (ii) Train-induced vibration level on the floor of high-rise buildings reduces as floor level goes up; approximately a 5 dBz vibration reduction can be achieved going up half the building for a 30 stories building. (iii) Vertical vibration on the floor of a building room is significantly higher that on the wall of the same room. 2. Transverse vibration on structural columns are greater than vertical vibration measured at the same location, indicating that the horizontal component plays a crucial role in vibration transmission.

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Fig. 10 Vibration level from the source to the receiver (stabling yard)

Fig. 11 Total vibration level and noise level from the source to the receiver (stabling yard)

3. In general, at noise and vibration source, including on the ground and on structural columns at the depot, the higher the train speed, the higher noise and vibration level is, but the increment reduces at higher train speeds. 4. Under ballast mat used onsite provides an average of 3.5 dB vibration isolation.

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References 1. Zou C, Wang Y, Zhang X, Tao Z (2020) Vibration isolation of over-track buildings in a metro depot by using trackside wave barriers. J Build Eng 30:1–14 2. Tao Z, Wang Y, Sanayei M, Moore JA, Zou C (2019) Experimental study of train-induced vibration in over-track buildings in a metro depot. Eng Struct 198:1–16 3. Mechanical vibration and shock—evaluation of human exposure to whole-body vibration. Part 1: General requirements. ISO 2631-1 (1997)

Optimizing Components in the Rail Support System for Dynamic Vibration Absorption and Pass-By Noise Reduction Jannik Theyssen , Astrid Pieringer , and Wolfgang Kropp

Abstract The rail pad stiffness is central in the conflict of interest between reducing airborne noise or track loads. Slab tracks typically have a low rail pad stiffness. This study explores two-stage elastic rail supports for slab tracks as a means to reduce noise while not increasing the track loads and hence ground vibrations. In a timedomain simulation, track forces and noise radiation are compared for several setups with parametrized rail support components. The results show that (I) the rail pad stiffness is the major lever for adjusting the radiated sound power, (II) the lower stiffness is important for adjusting the rolling contact forces and load on the track components, and (III) that optimizing for a lower sound power generally produces higher rolling contact forces. Keywords Two-stage elastic support · Waveguide FE · Wavenumber BE · Discrete coupling · Moving Green’s functions · Slab track · 2.5D

1 Introduction Due to decreased acoustic absorption and softer rail pads, railway operations on slab tracks have been shown to increase the levels of rolling noise [1]. Increasing the rail pad stiffness is known to reduce airborne noise; however, this comes at the cost of increased rolling contact forces and increased loads on the track components. Further, ground-borne vibrations and noise are likely increased with higher forces in the contact. The stiffness of the rail pad is thus a key factor in a conflict of interest regarding where vibrational energy should be dissipated. This conflict of interest may be addressed by considering that ground-borne vibration and air-borne noise are problems that occur in different frequency ranges: While ground-borne noise is generally considered significant up to about 250 Hz, rail radiation is dominating between 500 Hz and 4 kHz [2]. The rail support, consisting of a serial combination of masses and elastic elements, produces a frequency-dependent J. Theyssen (B) · A. Pieringer · W. Kropp Chalmers University of Technology, Applied Acoustics, 412 96 Gothenburg, Sweden e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_64

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stiffness, which can be tuned by adjusting the properties of the dynamic components. On tracks with individually booted sleepers, this is exploited by using sleeper weights of roughly 100 kg, combined with a soft elasticity underneath, which efficiently reduces vibration transfer into the ground. With a load distribution steel plate between the rail pad and a highly elastic intermediate plate, rail support systems for slab tracks also feature this serial combination. Here, the mass is only in the order of about 8 kg. This work explores this filtering effect, ignoring the constructional constraints of differently-sized sleepers or elastic pads. A method for modelling the dynamics of a two-stage elastic support discretely coupled to two Waveguide Finite Element models is developed for the slab and the rail. A parametric study is conducted comparing the effect of such dynamic systems on (a) the sound radiation from rail, sleepers, and slab, (b) the contact forces, and (c) the forces acting in the elastic components.

2 Methodology Three components are needed to calculate the dynamic and acoustic properties of each track in time domain. These include, firstly, models of the dynamic response of track and wheel, secondly an interaction model for calculating the rolling contact forces in time-domain, and thirdly a model for the acoustic radiation from the track. The wheel radiation is neglected here.

2.1 Dynamic Model of the Track The dynamic response of the track is modelled based on two Waveguide Finite Element (WFE) models representing the free rail and the supporting concrete layers, which are coupled in the positions of the rail seats with a two-stage elastic support. Here, the modelling approach from [3] is extended to a two-stage elastic support. As presented in Fig. 1, the motion of the rail is a superposition of the free rail response and the reaction forces at the rail seats, ∑ .u r,i = αr,ie Fe − αr,i j Fa, j (1) j

with .αr,ie Fe describing the displacement response of the free rail at rail seat .i given the excitation force . Fe , the suspension force above the mass . Fa, j at rail seat . j, and the corresponding receptance in the free rail .αr,i j . The response at the connection point on the slab surface is a consequence of suspension forces, u f,i =

∑

.

α f,i j Fb, j

(2)

j

with the acting suspension forces . Fb, j below the mass and the corresponding receptances of the slab structure.α f,i j . The suspension forces act on the central mass, where

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Fig. 1 Forces, displacements and receptances at two rail seats in the two-stage support

the force equilibrium reads .m u¨ s,i = Fa,i − Fb,i with the mass .m and its acceleration u¨ . Assuming harmonic motion at angular frequency .ω,

. s,i

=

u

. s,i

1 Fa,i − Fb,i = αs,i (Fa,i − Fb,i ), with αs,i = 2 −ω m −ω2 m

(3)

The relative displacements between rail and mass, and mass and slab follow from Eqs. 1 to 3 and are also functions of the respective acting forces and receptances, u

. r,i

− u s,i = −

∑

αr,i j Fa, j − αs,i (Fa,i − Fb,i ) + αr,ie Fe = αa,i Fa,i

(4)

α f,i j Fb, j + αs,i (Fa,i − Fb,i ) = αb,i Fb,i

(5)

j

u

. s,i

− u f,i = −

∑ j

Equations 4 and 5 form two equations with only the unknown forces . Fa, j and. Fb, j . As each connection introduces two equations and two unknowns, so the problem can be formulated as a system of .2n equations, where .n is the number of connection points. The receptances .αr and .α f can be assembled into symmetric matrices of size .n · n. Since the mass and springs are only locally reacting, i.e., .αs,i j = 0 for i / = j, assembling these into matrices of the same shape produces diagonal matrices. The assembled system of equations can be written as [ .

αr + α a + α s −α s −α s α f + αb + αs

and solved for the unknown vector .[Fa Fb ]' .

] ] [ Fa α F = r,e e Fb 0

][

(6)

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The receptances of the rail and the foundation .αr and .α f are determined using the WFE models described in [4]. For the calculation of the radiation from the rail and the slab surface, it is beneficial to express the surface displacements in wavenumber domain [5], ∑ ˜ 0 (κ) = .U An U˜ n R Cn F˜0 (7) n

for an excitation at .x = 0, with j U˜ n L

, where D(κn ) = −2κn K 2 − j K 1 , and U˜ n L D(κn )U˜ n R Cn = − (s(κn ) − j (κ + k(κn )))−1 − (s(κn ) + j (κ − k(κn )))−1 .

An =

where .κn are the eigenvalue solutions to the homogenous equation of motion, .U˜ n L and .U˜ n R are the corresponding eigenvectors, . F˜0 is the excitation force distribution in wavenumber domain centred at.x = 0, and. K 1 and. K 2 are stiffness matrices related to the FE formulation. In this case, the discrete support introduces the forces . Fa and . Fb at each rail seat into the rail and the slab, respectively. Their individual contributions need to be included in addition to the excitation force, U˜ (κ) = U˜ 0 (κ) +

( L ∑ ∑

.

l=1

) An U˜ n R Cn F˜l e

jκ xl

(8)

n

with the forces . Fl acting at . L locations defined by their respective position .xl . The excitation force can similarly be positioned arbitrarily along the track. In this study, the two elasticities and the mass are varied to investigate the effect of each parameter on the slab vibration and sound radiation. The study parameters are as follows: The vertical stiffness above the mass .ka takes values of [25, 50, 100, 200, 400, 800] kN/mm, the mass .m is one of [8, 16, 32, 64, 128] kg, and the vertical stiffness below the mass .kb is either 20 kN/mm or 40 kN/mm. The geometry and material properties of the rail (UIC60) and the slab (CRTSIII) are identical in all calculations. Likewise constant are the sleeper spacing of 0.6 m, the total number of 99 sleepers, the complex loss factor .η in the elastic components (.ηa,v = 0.25, .ηa,l = 0.1, .ηb,v = 0.5, .ηa,l = 0.25) and ratio between the vertical and the lateral stiffness (.kv = 10kl ). For each parameter set, the model is used to calculate the transfer functions for a unit force input to the slab, sleeper and rail surface vibration, and the reaction forces in all rail seats. These transfer functions are calculated for eight evenly spaced positions in the central sleeper bay up to about 7 kHz with 5 Hz frequency resolution. Excitation positions in between these eight positions are interpolated. Impulse responses are generated by inverse Fourier transform, which act as moving Green’s functions in the following steps.

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Fig. 2 Geometry in the wavenumber boundary element method, including a rail and an approximation of a track superstructure on which normal velocities can be specified. An acoustically hard surface is included by half-space Green’s functions

2.2 Dynamic Wheel Response and Wheel-Track Interaction The wheel of type BA093 and the model for the dynamic model response are presented in more detail in [6]. The non-linear interaction between the wheel and the track is calculated in the time domain using the in-house software WERAN [7], which uses a Green’s functions approach. Below, a wheel preload of 55 kN and a vehicle speed of 100 km/h is used. Only vertical wheel-rail forces are considered. 1.8 s of the dynamic interaction are simulated with a spatial resolution of 1 mm per time step. This corresponds to 51 m of track and a sampling frequency of 27 kHz. The wheel and rail roughness data are based on measurements [6, 8]. As all simulations are dependent on these roughness spectra, the results presented in the following can be compared to each other, but they should not be generalized. The focus here is solely to develop a method to combine noise mitigation with vibration isolation.

2.3 Radiation of the Track The acoustic radiation from the track is computed using the Wavenumber Boundary Element Method as described in [5]. The geometry of the included surfaces is shown in Fig. 2. As an input to the calculation, the surface vibrations of one rail and the slab top surface are expressed in wavenumber domain as described above. The radiation from the sleepers is included by expressing their velocity profile along the track in a wavenumber spectrum. This wavenumber spectrum serves as the input to the WBE calculation at the cross-sectional nodes on the slab surface corresponding to the positions of the sleepers. The sound power is evaluated by integrating the intensity on an infinite half-cylinder with radius 5 m around the track. For computational efficiency, the acoustic transfer functions between each BE-element on the track surface to each point on the cylinder were precalculated. This allowed a sufficiently high resolution of the frequency- and wavenumber-spectrum to simulate the sound pressure variation during the pass-by of a force on the rail in time-domain. Assuming that each sleeper’s surface area is dependent on its weight, their widths .wm and depths .dm were roughly adjusted by linear interpolation between the dimension (.wm × dm ) .15 cm × 10 cm to .70 cm × 30 cm.

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Fig. 3 Typical result of the loads in the rail seat and the sound pressure over time

3 Results For each combination of the three varied parameters, a time-domain calculation of the contact forces was carried out. Figure 3 shows a typical example of such a calculation, in which the load on an individual rail seat reaches about half the static pre-load of the vehicle, and sound pressure peaks at 0.7 Pa (about 90 dB). The moving force passes by the sleeper and the stationary microphone at about 1.2 s. The microphone is positioned 7.5 m from the track centre, 1.2 m above the rail. The increased sound pressure right before and after this point is related to the angle of radiation from the bending waves in the rail. The rail support has a large influence on the rolling contact forces. The first column in Fig. 4 shows the highest measured vertical rolling contact force for all combinations of the researched parameters. The contact force expectedly increases with increasing stiffnesses .ka and .kb . This increase is not linear but, at least for .ka , the curves flatten towards higher stiffnesses. The sleeper’s mass is more influential at high .ka , due to its stronger coupling to the rail. No significant differences are observed for the three lighter masses and either combination of the stiffnesses. For the 128 kg mass, the contact forces are similar for both .kb and .k a ≥ 100 kN/mm. The forces acting on the track components during pass-by are an indicator for ground-borne vibrations. The peak forces . Fa and . Fb are compared in the second and third column of Fig. 4. As for . Fc , the mass becomes more influential with a stiffer .ka . Further, a stiffer .kb leads to a stronger dependency on .ka , i.e., the flattening of the curves above 200 kN/mm is more distinct for .kb = 20 kN/mm. Notably, the peak force above and below the mass are similar in all cases, except for the two heaviest masses. The sound radiation from the track is directly related to these forces. Figure 5 compares the A-weighted, total radiated sound power . L W for three selected .ka . The slab, radiating mostly below 100 Hz does not contribute significantly to the A-weighted sound power. The rail dominates even at high .ka , even though the contribution of the sleepers increases and the rail contribution decreases. The increased surface area and increasing sleeper mass seem to balance each other somewhat, so the sleeper contributes within a .± 3 dB range for each .ka . Figure 6 combines the presented data. From left to right, the peak forces . Fˆc , . Fˆa and . Fˆb are plotted with the respective A-weighted . L W in each calculation on the y-axis. For . Fˆc , the diagonal trend from the top left to bottom right underpins the

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Fig. 4 Influence of the support parameters on the peak forces . Fˆc , . Fˆa , and . Fˆb . For orientation, the area between the lightest and the heaviest mass is coloured in blue. Top: .kb = 20 kN/mm, bottom: .kb = 40 kN/mm

Fig. 5 Normalised sound power radiated from the different components for three cases of .ka indicated in the top left corner. These are results for .kb = 40 kN/mm

trade-off between noise reduction and contact forces. It is observed that often, . L W is similar for both .kb = 20 kN/mm and .kb = 40 kN/mm, while the peak contact force is typically higher with a stiffer .kb . This means, . L W depends mostly on the .ka , whereas the contact force depends on a combination of the considered parameters. The central figure shows this diagonal trend again, indicating that . L W can only be reduced when simultaneously increasing the load on the sleepers. Vertical sections indicate a potential for optimization. For the given excitation, reduction in . L W up to 5 dB seem possible without significantly affecting . Fˆa . This relation is even more pronounced for . Fb , where in the case of the soft support stiffness . L W can be adjusted by about 10 dB without significantly changing . Fb . It can be concluded that for a two-stage support, a soft stiffness below the central mass has the potential to achieve both vibration isolation while reducing . L W . The ideal rail seat receptance for this is however dependent on the combined roughness of wheel and rail and should not be generalized from these results.

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Fig. 6 Comparison of the maximum forces in the rolling contact . Fˆc (left), the rail seat . Fˆa (centre), and into the slab. Fˆb (right) to the emitted A-weighted sound power level from the track. The symbols’ for 8 kg, 16 kg, 32 kg, 64 kg and 128 kg, respectively), colours indicate the mass ( and their shapes represent different rail pad stiffnesses .ka ( 800 kN/mm, respectively). The line color indicates the stiffness .kb (

for 25 kN/mm to for 20 kN/mm and

40 kN/mm, respectively).

4 Conclusion Time-domain simulations of rolling contact forces, track forces and radiated track noise for several two-stage rail support configurations showed a potential noise reduction without negatively affecting the track forces. A high rail pad stiffness and a low support stiffness, separated by an appropriate mass, can lead to noise reduction with minor influence on track loads. Acknowledgements The current study is part of the ongoing activities in CHARMEC—Chalmers Railway Mechanics. Parts of the study have been funded from the European Union’s Horizon 2020 research and innovation programme in the In2Track3 project under grant agreements No. 101012456.

References 1. Poisson F (2015) Railway noise generated by high-speed trains. In: Nielsen JCO et al (eds) Noise and vibration mitigation for rail transportation systems, NNFM, vol 148. Springer, Berlin, pp 457–480 2. Thompson DJ (2009) Railway noise and vibration. ISBN 9780080451473 3. Theyssen JS, Pieringer A, Kropp W (2021) The influence of track parameters on the sound radiation from slab tracks. In: Degrande G et al (eds) Noise and vibration mitigation for rail transportation systems, NNFM, vol 150. Springer, Heidelberg, pp 90–97 4. Theyssen JS et al (2021) Calibration and validation of the dynamic response of two slab track models using data from a full-scale test rig. Eng Struct 234:111980

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5. Nilsson CM, Jones CJC, Thompson DJ, Ryue J (2009) A waveguide finite element and boundary element approach to calculating the sound radiated by railway and tram rails. J Sound Vib 321:813–836 6. Pieringer A, Kropp W (2022) Model-based estimation of rail roughness from axle box acceleration. Appl Acoust 193:108760 7. Pieringer A, Kropp W, Thompson DJ (2011) Investigation of the dynamic contact filter effect in vertical wheel/rail interaction using a 2D and a 3D non-Hertzian contact model. Wear 271:328– 338 8. Thompson DJ et al (2018) Assessment of measurement-based methods for separating wheel and track contributions to railway rolling noise. Appl Acoust 140:48–62

A Hybrid Prediction Tool for Railway Induced Vibration Pascal Bouvet, Brice Nélain, David Thompson, Evangelos Ntotsios, Andreas Nuber, Bernd Fröhling, Pieter Reumers, Fakhraddin Seyfaddini, Geertrui Herremans, Geert Lombaert, and Geert Degrande

Abstract One of the main objectives of the SILVARSTAR project is to develop a user-friendly frequency-based hybrid prediction tool to assess the environmental impact of railway induced vibration. This model is integrated in the noise mapping software IMMI. Following modern vibration standards and guidelines, the vibration velocity level in the building in each frequency band is expressed as the sum of a force density (source), line source transfer mobility (propagation) and building correction factor (receiver). This results in a framework that is ideally suited for a hybrid approach that combines experimental data with numerical predictions, providing increased flexibility and applicability. We also discuss the validation of the prototype vibration prediction tool. Keywords Railway induced vibration · Hybrid vibration prediction model

1 Introduction Although rail is a sustainable and climate-friendly mode of transport, noise and vibration remain particular environmental concerns. People living near railways are becoming increasingly sensitive to high levels of noise and vibration, while the operation of sensitive equipment is hampered by high vibration levels. SILVARSTAR [1] is a two-year collaborative project under the Shift2Rail Joint Undertaking that aims to develop validated software tools and methodologies to assess the noise and vibraP. Bouvet · B. Nélain Vibratec, 28 Chemin du petit bois, Ecully 69131, France D. Thompson · E. Ntotsios University of Southampton, ISVR, Highfield, Southampton SO17 1BJ, UK A. Nuber · B. Fröhling Wölfel Engineering, Max-Planck Strasse 15, Höchberg 97204, Germany P. Reumers · F. Seyfaddini · G. Herremans · G. Lombaert · G. Degrande (B) Department of Civil Engineering, KU Leuven, Kasteelpark Arenberg 40, Leuven 3001, Belgium e-mail: [email protected] URL: https://silvarstar.eu © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_65

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Fig. 1 a Source and receiver points for the FRA procedure and b excitation and receiver locations for line source transfer mobility measurements

tion environmental impact of railway traffic. One of the objectives is to provide the railway community with a commonly accepted, practical and validated methodology and a user-friendly vibration prediction tool, that will be used for environmental impact assessment of new or upgraded railways on a system level.

2 Methodology 2.1 Fully Empirical Prediction Scheme The empirical procedure for Detailed Vibration Assessment proposed by the FRA and FTA [2, 7] conforms to the general framework of ISO 14837-1:2005 [3] and is used as a basis for the development of a hybrid vibration prediction tool. The vibration velocity level .Lv (xb ) at a receiver .xb in the building (Fig. 1a) is defined as the root mean square value of the velocity during the stationary part of a train passage; it is expressed in decibels (.dB ref 5 × 10−8 m/s) in one-third octave bands as a sum of source, propagation and receiver terms: Lv (xb ) = LF (X, x1 ) + TML (X, x1 ) + Cb (x1 , xb )

.

(1)

√ LF (X, x1 ) is the equivalent force density .(dB ref 1N/ m) and a measure for the power per unit length radiated by the source. The vector .X collects all source points on the track, while the receivers .x1 are located on the ground surface. √ ) is The line source transfer mobility (LSTM) .TML (X, x1 ) .(dB ref 5 × 10−8 N/m/s m a measure for the vibration energy transmitted through the soil relative to the power per unit length radiated by the source. It is derived from the superposition of point source transfer mobilities .TMP (Xk , x1 ) for a series of .n equidistant source points .Xk with spacing .h (Fig. 1b):

.

[ TML (X, x1 ) = 10 log10 h

n ∑

.

k=1

] 10

TMP (Xk ,x1 ) 10

(2)

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Fig. 2 a 10-DOF vehicle, b ballasted track, and c floating slab track models

The force density.LF (X, x1 ) is determined indirectly from the vibration velocity level Lv (x1 ) and the LSTM .TML (X, x1 ) by rearranging Eq. (1) and omitting the building correction factor:

.

LF (X, x1 ) = Lv (x1 ) − TML (X, x1 )

.

(3)

The receiver term or building correction factor .Cb (x1 , xb ) can be quantified as a difference in vibration velocity level .Lv (xb ) at a point .xb in the building, and .Lv (x1 ) at a point .x1 on the ground surface with the building present (Fig. 1a): Cb (x1 , xb ) = Lv (xb ) − Lv (x1 )

.

(4)

The vibration velocity levels can either be determined by measurements during a train passage, or be calculated with a train-track-soil-building model. They can also be computed as a combination of adjustment factors to account for soil-structure interaction and attenuation or amplification within the building; in SILVARSTAR, adjustment factors from the RIVAS project [10] are used.

2.2 Fully Numerical Prediction Scheme Using a Modular Approach A semi-analytical train-track-soil interaction model (based on GroundVIB [5]) is integrated in the vibration prediction tool to compute dynamic axle loads and forces transmitted to the ground. The vehicle is represented by a multi-body model (e.g. a 10-DOF model, Fig. 2a). The ballasted or slab track (Fig. 2b) is modelled by EulerBernoulli beams for the rail (and slab) with resilient layers for rail pads, under-sleeper pads, ballast, and slab mat. The track is coupled to the soil over a finite width (Fig. 2c). The soil is represented by impedances in the frequency-wavenumber domain that are pre-computed for a range of track widths and soil properties using MOTIV [6] and TRAFFIC [4]. The train-track-soil interaction problem is solved in the frequency domain, considering rail and wheel unevenness. The ground response is calculated in the wavenumberfrequency domain using the force transmitted to the subgrade and pre-computed transfer functions. The building response is estimated by means of building correction factors [10].

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2.3 Hybrid Prediction Schemes Hybrid prediction schemes, in which numerical and empirical data are combined following Eq. (1), are also included, providing more flexibity and applicability than purely experimental or numerical models. Hybrid model 1 combines a numerical source model with an empirical propagation term. The force density .LFNUM (X) can be computed directly: LvHYB (x1 ) = LFNUM (X) + TMEXP L (X, x1 )

.

(5)

Alternatively, the force density .LFNUM (X, x1 ) is computed indirectly as the difference between a predicted vibration velocity and LSTM: LvHYB (x1 ) = LvNUM (x1 )−TMNUM (X, x1 ) + TMEXP L L (X, x1 )

.

(6)

The underlined term is a correction on the predicted vibration velocity level, accounting for the difference between the measured and predicted LSTM. Equations (5) and (6) are useful to assess new rolling stock or a new railway line. Hybrid model 2 combines a measured force density with a predicted LSTM: LvHYB (x1 ) = LFEXP (X, x1 ) + TMNUM (X, x1 ) L EXP EXP . = Lv (x1 )−TML (X, x1 ) + TMNUM (X, x1 ) L

.

(7) (8)

which is useful to assess mitigation measures in the transmission path. In all previous expressions, the building correction factor .Cb (x1 , xb ) was omitted for brevity. When assessing vibration in a new building close to an existing railway, for example, the following hybrid approach can be employed: NUM LvHYB (xb ) = LFEXP (X, x1 ) + TMEXP (x1 , xb ) L (X, x1 ) + Cb

.

(9)

while in case of an existing building next to a new-built railway, an empirical building correction factor .CEXP b (x1 , xb ) can be added to Eqs. (5) or (6).

2.4 Implementation of the Vibration Prediction Model The prediction model is integrated into the noise mapping software IMMI, developed by Wölfel, and linked to a Geographical Information System (GIS), providing a software platform with Graphical User Interfaces (GUIs) that allows engineers to perform noise and vibration environmental impact studies within the same integrated environment. The use of pre-computed soil impedance and transfer functions for selected track widths and soil properties [9] considerably speeds up calculations and allows the user to assess in real-time the effect of changes in train, track, and

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soil parameters on axle loads and vibration. An experimental database [9] of force densities, LSTMs, free field vibration and input parameters from well-documented measurement campaigns is also integrated in the hybrid vibration prediction tool. The user can import data from project databases dedicated to railway line development. Geographical and geotechnical data will be made importable through an interface with a GIS.

3 Validation of the Prototype Vibration Prediction Model 3.1 Modelling Assumptions A prototype vibration prediction model was developed based on the GroundVIB model, provided with a GUI. Three modelling simplifications are made to reduce computation times: (1) computation of the track compliance in a stationary instead of a moving frame of reference; (2) application of the dynamic axle loads at fixed positions (low-speed approximation neglecting the Doppler effect); and (3) assumption of incoherent instead of coherent axle loads. The influence of these modelling assumptions is assessed by means of a difference in vibration velocity level approx approx .ΔLv (x1 ) = Lv (x1 ) − Lvref (x1 ), where.Lv (x1 ) is the level predicted by the tool and .Lvref (x1 ) is a reference level computed with TRAFFIC. The assessment is made for a nominal InterCity (IC) train with 4 cars running at 50, 150, and 300 km/h on a ballast track (unevenness FRA6) supported by soft, medium, and stiff soil. Train, track, and soil parameters are detailed in [8]. When computing the dynamic axle loads, the track compliance can, in very good approximation, be assessed in a stationary frame of reference. The vibration level difference .ΔLv (x1 ) on the free field response for a train running at 300 km/h on a ballast track supported by soft soil is less than 1 dB [8], and even smaller for lower train speeds and stiffer soils. The low-speed approximation predicts the stationary part of the response by assuming fixed axle positions. At 16 m from the track, the vibration level difference .ΔLv (x1 ) increases with increasing train speed (Fig. 3) and is larger than 10 dB in individual frequency bands at high speed. The differences mainly correspond to a redistribution of energy into different bands, while the overall vibration level summed over all frequency bands is affected much less, with differences ranging from 2 to 3 dB [8]. Furthermore, the free field response is calculated assuming that the non-moving dynamic axle loads are incoherent, whereas in the full model the wheels are assumed to be excited by the same unevenness apart from a time lag. At 16 m from the track, largest differences at 50 km/h occur below 4 Hz (Fig. 4a); above 4 Hz, differences are less than 5 dB. At higher speeds of 150 and 300 km/h (Figs. 4b, c), there is good agreement above 10 Hz and 20 Hz, respectively.

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Fig. 3 Vibration velocity level difference .ΔLv (x1 ) between the low-speed approximation and the moving train response at 16 m from the ballast track for the IC train running at a 50, b 150, and c 300 km/h; soft, medium and stiff soil (light to dark)

Fig. 4 Vibration velocity level difference.ΔLv (x1 ) between the incoherent load approximation and the coherent load case at 16 m from the ballast track for the IC train running at a 50, b 150, and c 300 km/h; soft, medium and stiff soil (light to dark)

Fig. 5 Vibration velocity level .Lv (x1 ) at 16 m from the ballast track for the IC train running at 150 km/h; a soft, b medium, and c stiff soil. Results of TRAFFIC for a moving train (black) and the prediction tool with approximations (grey)

The combined effect of all three approximations at 16 m from the track is shown in Fig. 5 for the speed of 150 km/h; although there are significant differences in individual frequency bands, the spectrum shape is closely followed, while the overall vibration level summed over all frequency bands on average is 2–3 dB higher for the approximate model.

3.2 Numerical Validation Results obtained with the prototype vibration prediction tool and TRAFFIC are compared for a ballast track supported by homogeneous soil of varying stiffness. Identical modelling assumptions are made in both models; the only difference is

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Fig. 6 LSTM .TML (X, x1 ) at a 8 m, b 16 m, and c 32 m from the ballast track on soft, medium and stiff soil (light to dark). Results of TRAFFIC (grey) and the prediction tool (blue)

Fig. 7 Vibration velocity level .Lv (x1 ) at 16 m from the ballast track on soft, medium and stiff soil (light to dark) for the IC train running at a 50, b 150, and c 300 km/h. Results of TRAFFIC (grey) and the prediction tool (blue)

that we use pre-computed soil impedance and transfer functions for a 3.0 m wide track-soil interface, while the actual width of 3.6 m is used in the reference model. Figure 6 shows the LSTM .TML (X, x1 ) at 8, 16 and 32 m from the track. At low frequencies, the LSTM is highest for the soft soil; the peak shifts to lower frequencies for increasing distance. At higher frequencies, the LSTM decreases due to material damping in the soil. For the medium and stiff soil, maximum response is observed at higher frequencies, while the effect of material damping is less pronounced. The results computed with the prediction tool and TRAFFIC are in excellent agreement up to 10 Hz. At higher frequencies, slightly higher values (1–3 dB) are obtained with the prediction tool due to the lower track width, with higher discrepancy at larger distance. Figure 7 shows the vibration velocity level .Lv (x1 ) at 16 m from the track during the passage of the IC train. At 50 km/h, the velocity level is highest for the soft soil up to 30 Hz. For the medium and stiff soil, a maximum value is reached at the P2 resonance close to 80 Hz, where the velocity level is lower for the soft soil due to material damping. At higher speeds, the velocity level increases between 30 and 125 Hz by approximately 16 dB to 24 dB when increasing the speed to 150 and 300 km/h, respectively, independent of the soil stiffness. Below 30 Hz, the velocity level predicted with TRAFFIC is 1–2 dB higher than with the prototype tool. At high frequencies, the tool predicts a slightly higher velocity level. Figure 8 shows the force density .LF (X, x1 ) based on the vibration velocity level and LSTM at 16 m from the track during the passage of the IC train at 50, 150 and 300 km/h. As the influence of soil stiffness on dynamic axle loads is limited below

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Fig. 8 Force density .LF (X, x1 ) at 16 m from the ballast track on soft, medium and stiff soil (light to dark) for the IC train running at a 50, b 150, and c 300 km/h. Results of TRAFFIC (grey) and the prediction tool (blue)

50 Hz, the force density is almost identical for the three soils. At high frequencies, the force density is higher for the soft soil and increases with train speed, as the velocity level (Fig. 7). The force densities computed with the prediction tool and TRAFFIC are in very good agreement with a discrepancy lower than 3 dB in each frequency band, due to the different track width in both models.

3.3 Experimental Validation The case history of the high speed track in Lincent (Belgium) was used as a benchmark. Transfer functions between the track and the free field and vibration during train passages were processed (LSTMs and vibration velocity levels) to ensure compatibility with the hybrid vibration prediction model. Overall good correspondance between measured and predicted results is reported [8].

4 Conclusion The proposed modular approach provides full modelling flexibility at each stage of the design process. Embedding it in existing software simplifies the modelling process, as fewer interfaces are needed. Extensive validation and approval testing increases confidence levels. The tool enables the assessment of vibration levels for both large-scale studies and more detailed investigations for new and upgraded railway lines.

Acknowledgements This paper is the result of the project SILVARSTAR funded from the Shift2Rail Joint Undertaking under the European Union’s Horizon 2020 Research and Innovation Programme under Grant Agreement 101015442. This financial support is gratefully acknowledged. Disclaimer The information in this document is provided “as is”, and no guarantee or warranty is given that the information is fit for any particular purpose. The content of this document reflects only the authors’ view - the Shift2Rail Joint Undertaking is not responsible for any use that may be made of the information it contains. The users use the information at their sole risk and liability.

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References 1. Degrande G, Lombaert G, Ntotsios E, Thompson DJ, Nélain B, Bouvet P, Grabau S, Blaul J, Nuber A (2021) State-of-the-art and concept of the vibration prediction tool. SILVARSTAR project GA 101015442, deliverable D1.1, report to the EC, May 2021 2. Hanson CE, Ross JC, Towers DA (2012) High-speed ground transportation noise and vibration impact assessment. Technical Report DOT/FRA/ORD-12/15, U.S. Department of Transportation, Federal Railroad Administration, Office of Railroad Policy and Development, Sept 2012 3. International Organization for Standardization (2005) ISO 14837-1:2005 mechanical vibration—ground-borne noise and vibration arising from rail systems—part 1: general guidance 4. Lombaert G, François S, Degrande G (2012) TRAFFIC Matlab toolbox for traffic induced vibrations. Report BWM-2012-10, Department of Civil Engineering, KU Leuven, Nov 2012. User’s Guide Traffic 5.2 5. Nélain B, Vincent N, Reynaud E (2019) Towards hybrid models for the prediction of railway induced vibration: numerical verification of two methodologies. In: Degrande G, Lombaert G (eds) Proceedings of the 13th international workshop on railway noise, IWRN13, Ghent, Belgium, Sept 2019, pp 1–8 6. Ntotsios E, Thompson DJ, Hussein MFM (2019) A comparison of ground vibration due to ballasted and slab tracks. Transp Geotech 21:100256 7. Quagliata A, Ahearn M, Boeker E, Roof C, Meister L, Singleton H (2018) Transit noise and vibration impact assessment manual. FTA 0123, U.S. Department of Transportation, Federal Transit Administration, John A. Volpe National Transportation Systems Center, Sept 2018 8. Reumers P, Degrande G, Lombaert G, Seyfaddini F, Herremans G, Ntotsios E, Thompson DJ, Nélain B, Bouvet P, Fröhling B, Nuber A (2022) Validation of the prototype vibration prediction tool against documented cases. SILVARSTAR project GA 101015442, deliverable D1.3, report to the EC, June 2022 9. Thompson DJ, Ntotsios E, Degrande G, Lombaert G, Herremans G, Alexiou T, Nélain B, Barcet S, Bouvet P, Fröhling B, Nuber A (2023) Database for vibration emission, ground transmission and building transfer functions. SILVARSTAR project GA 101015442, deliverable D2.1, report to the EC, Feb 2023 10. Villot M, Guigou C, Jean P, Picard N (2012) Procedures to predict exposure in buildings and estimate annoyance. RIVAS project SCP0-GA-2010-265754, deliverable D1.6, report to the EC

Response of Periodic Railway Bridges Under Moving Loads Accounting for Dynamic Soil-Structure Interaction Pieter Reumers, Geert Lombaert, and Geert Degrande

Abstract This paper studies the effect of dynamic soil-structure interaction (SSI) on the response of long, periodic box girder bridges on piled foundations subjected to moving loads. To reduce the computational effort, the bridge is infinitely long and periodic structure theory is used. A case study illustrates that incorporating dynamic SSI leads to: (1) a shift in the natural frequencies of the bridge, (2) increased midspan deflection, and (3) lower peak mid-span acceleration compared to a bridge with fixed footings. The influence of foundation-soil-foundation interaction on the bridge response is also studied and shown to be negligible. Keywords Railway bridges · Soil-structure interaction · Periodic structure theory · Moving loads

1 Introduction This paper investigates the effect of dynamic SSI on the response of bridges consisting of identical spans repeated over a long distance. More particularly, we focus on continuous box girder bridges founded on piled foundations. For relatively short bridges, the influence of dynamic SSI on the response of railway bridges has been studied by many authors for various bridge types, e.g. single-span, simply supported bridges [1, 2], portal frame bridges [3], and multispan, simply supported bridges [4, 5]. A clear influence on the modal characteristics is observed: lower natural frequencies and higher modal damping ratios are found when SSI is accounted for. The bridge deck acceleration, however, can be positively or negatively affected by incorporating flexible bridge supports, depending on the bridge type, the foundation and the soil stiffness. In the aforementioned studies, the bridge length is relatively short (one or several spans) and 3D element-based models can be used. For longer bridges, however, the computational effort increases significantly; we therefore assume that the bridge is P. Reumers (B) · G. Lombaert · G. Degrande Department of Civil Engineering, KU Leuven, Kasteelpark Arenberg 40, 3001 Leuven, Belgium e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_66

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infinitely long and use periodic structure theory (Floquet theory). The methodology presented in this paper also takes into account foundation-soil-foundation interaction. A similar approach is used by Lu et al. [6] to predict the response of infinitely long multi-span, simply supported railway bridges. The paper is outlined as follows. Section 2 describes the periodic FE-BE methodology used in this paper. Section 3 introduces a numerical case history and shows the influence of dynamic SSI on the mid-span receptance and bridge response during a train passage. Both the train speed and the soil stiffness are varied in the analysis. The paper is concluded in Sect. 4.

2 Methodology The following steps are used to compute the bridge response using periodic structure theory. In a first step, the stiffness of a single piled foundation is computed with a 3D finite element-boundary element (FE-BE) model. A row of piled foundations with spacing . L is also considered, and the foundation stiffness is computed in the frequency-wavenumber domain using a periodic 3D FE-BE model taking into account foundation-soil-foundation interaction. Subsequently, a 3D periodic FE model of the bridge is constructed and the precomputed foundation stiffness is incorporated as spring-dashpot connections at the bridge footings. The bridge response is computed in the frequency-wavenumber domain and subsequently transformed to the frequency-spatial domain by means of the inverse Floquet transform.

2.1 The Floquet Transform Consider an infinitely long bridge consisting of identical cells (spans) extending in the . y-direction: the coordinate .x of a point along the bridge is expressed in terms of the span length . L, the cell number .n y , and the coordinate .x˜ of the corresponding point in a reference cell of the bridge (for which .n y = 0): x = x˜ + n y Le y

.

(1)

Using a periodic FE or FE-BE model, the computational domain is restricted to the ˜ x, κ y , ω) is computed in the wavenumber reference cell and the bridge response .u(˜ domain .κ y ∈ [−π/L , +π/L] for each frequency .ω. By application of the inverse Floquet transform, the response in any cell .n y , and hence any point .x, is recovered as: L ˆ x + n y Le y , ω) = .u(˜ 2π

+π/L ∫

˜ x, κ y , ω) exp(−in y Lκ y )dκ y u(˜ −π/L

(2)

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2.2 The Periodic FE Model A reference cell of the bridge is modeled with finite elements, yielding the stiffness matrix .K and mass matrix .M. The nodal displacement vector is denoted by ˜ x, κ y , ω), and is represented as a linear combination of modes .ψ˜ j (˜x, κ y ) [7]: .u(˜ ˜ x, κ y , ω) = u(˜

n ∑

.

ψ˜ j (˜x, κ y )α j (κ y , ω)

(3)

j=1 0 where .ψ˜ j (˜x, κ y ) is constructed from an eigenmode .ψ˜ j (˜x) of the reference cell: 0 ψ˜ j (˜x, κ y ) = ψ˜ j (˜x) exp(−iκ y e y · x˜ )

.

(4)

0 0 The eigenmodes .ψ˜ j (˜x) should be periodic of the first kind (i.e. .ψ˜ j (˜x + Le y ) = 0 ψ˜ j (˜x)), which can be ensured by the use of constraint equations. Subsequently, the FE system of equations becomes:

.

[ ] ˜ y ) − ω2 M(κ ˜ y ) α(κ y , ω) = F(κ ˜ y , ω) K(κ

(5)

] [ ˜ y ) = Ψ˜ H MΨ˜ , .Ψ˜ = ψ˜ , ψ˜ , . . . , ψ˜ , and .(·)H ˜ y ) = Ψ˜ H KΨ˜ and .M(κ where .K(κ 1 2 n denotes the conjugate transpose.

2.3 The Periodic FE-BE Model The structure-soil interface of the piled foundation is meshed with boundary elements ˜ y , ω) and.T(κ ˜ y , ω) are assembled from the discretized and the BE system matrices.U(κ boundary integral equations using periodic Green-Floquet functions [6, 8]. From the ˜ s (κ y , ω) is obtained. The coupled BE system matrices, the soil stiffness matrix .K FE-BE system of equations becomes: .

[ ] ˜ y , ω) ˜ s (κ y , ω) u(κ ˜ y , ω) = F(κ K − ω2 M + K

(6)

where .K and .M are the FE system matrices of the piles. This equation is valid if there is no direct coupling between the FE models of neighbouring cells, which is the case for a row of piled foundations: they are only coupled through the soil, which ˜ s (κ y , ω). is taken into account by .K

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3 Numerical Case Study 3.1 Case Description A concrete box girder bridge with span length . L = 24 m is supported by 6 m tall piers with a rectangular cross section of 5 m by 1 m (Fig. 1a). The piers are founded on a piled foundation consisting of 8 piles with diameter 0.4 m and length 10 m. The geometry of the bridge deck and the piled foundation is specified in Figs. 1b and 2, respectively. Constraint equations are used to represent the bridge bearings between the bridge deck and the piers, and to model the rigid pile cap with thickness 1 m. The entire bridge is made of concrete with a Young’s modulus . E = 30 GPa, a Poisson’s ratio .ν = 0.25, and a density .ρ = 2500 kg/m.3 . Rate-independent hysteretic material damping in the frequency domain is modeled by introducing a complex Young’s modulus . E ∗ = E(1 + 2iβ), assuming a material damping ratio .β of 0.02. The bridge deck and piers are modeled with 8-node quadratic shell elements based on Reissner-Mindlin plate theory; the maximum element size equals 1 m. An eccentric, vertical point load is applied to the bridge deck above one of the webs (Fig. 1a). To account for the load distribution by a track structure, the load is applied to an area with a width of 2 m and a depth of 1 m, as indicated on Fig. 1a. The track structure itself, however, is not included in the model. The piled foundation is embedded in a layered soil and is modeled with 10node quadratic tetrahedral elements (minimum 4 elements per shear wavelength).

Fig. 1 a Single bridge span and b cross section of the bridge deck

Fig. 2 a Piled foundation embedded in a horizontally layered halfspace and b geometry of the piled foundation indicating the position of the piles and the pier relative to the pile cap

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Table 1 Dynamic soil characteristics: shear wave velocity.Cs , dilatational wave velocity.Cp , density and material damping ratio’s .βs and .βp in shear and dilatational deformation

.ρ

Soil type

.C s

(m/s)

Soft soil Medium soil Stiff soil

100 200 400

.C p

(m/s)

200 400 800

.ρ

(kg/m.3 )

1800 1800 1800

.βs

(–)

0.02 0.02 0.02

.βp

(–)

0.02 0.02 0.02

The foundation-soil interface is meshed with 6-node quadratic triangular boundary elements. The soil layering consists of a 9 m thick layer of soft, medium or stiff soil on top of a stiff halfspace (Fig. 2a and Table 1).

3.2 Foundation Stiffness The foundation stiffness is defined as the force or moment required to impose a unit translation or rotation of the rigid (massless) pile cap. Results are computed for a single piled foundation embedded in soft, medium and stiff soil, and for a row of piled foundations with spacing . L = 24 m accounting for foundation-soil-foundation interaction. Fig. 3 shows the real and imaginary part of the vertical and rotational stiffness (about the .x- and . y-axis). The real part governs the actual stiffness, while the imaginary part represents the damping due to the radiation of waves into the soil. For the vertical stiffness .k zz , peaks are observed around 22 Hz for the soft soil and 45 Hz for the medium soil due to pile-soil-pile interaction. When foundation-soil-foundation interaction is accounted for, the stiffness functions oscillate around those computed for a single foundation. The separation of these oscillations is directly proportional to the soil stiffness. The rotational stiffness.kφx φx about the.x-axis is much lower compared to.kφ y φ y due to the lay-out of the piles. For .kφ y φ y , peaks are again observed because of pile-soilpile interaction. The effect of foundation-soil-foundation interaction on the rotational stiffness is very limited, and much less pronounced when compared to the vertical stiffness.

3.3 Bridge Receptance The foundation stiffness is added as spring-dashpot connections to the bridge piers. The mass of the rigid pile cap is also included. The mid-span receptance is computed by solving the FE system of Eq. (5) in the frequency-wavenumber domain and performing the inverse Floquet transform (2).

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Fig. 3 Real (top) and imaginary (bottom) part of a the vertical stiffness .k zz , b the rotational stiffness .kφx φx and c the rotational stiffness .kφ y φ y of the piled foundation embedded in stiff (black line), medium (dark grey line) and soft (light grey line) soil. Results are shown with (dotted line) and without (solid line) foundation-soil-foundation interaction

Fig. 4 Mid-span receptance for the bridge on a stiff soil, b medium soil, and c soft soil with (dotted grey line) and without (solid grey line) foundation-soil-foundation interaction. Results without SSI (black line) are shown as a reference

Figure 4 shows the vertical mid-span receptance for the bridge on stiff, medium and soft soil; the receptance for the bridge with fixed supports is shown as a reference. The first peak in the receptance functions corresponds to the first torsional mode of the bridge, for which the motion of neighboring spans is in-phase. It is situated close to 5 Hz for the bridge with fixed supports, but shifts towards lower frequencies for flexible supports (around 2.5 Hz for the bridge on soft soil). The second peak around 9 Hz is due to the first vertical bending mode (opposite-phase motion of neighboring spans); as this mode is mainly governed by the stiffness of the box girder, the peak occurs at nearly the same frequency for the bridge on flexible supports. The amplitude, however, changes significantly. The third peak around 12 Hz corresponds to the bending mode for which the motion in neighboring spans is in-phase. The peak shifts to 7.3 Hz for the case of soft soil. The effect of foundation-soil-foundation interaction on the bridge receptance is almost negligible for the stiff soil, and very limited for the medium and soft soil.

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Table 2 Characteristics of the InterCity train: total carriage length . L v , bogie spacing . L b , axle distance . L a , and total axle mass . Mt Axles . L v (m) . L b (m) . L a (m) . Mt (tons) Locomotive HLE13 Central coach HVI11 A End coach HVI11 BDx

4

19.11

10.40

3.00

22.50

4

26.40

18.40

2.56

11.61

4

26.40

18.40

2.56

11.83

Fig. 5 Vertical mid-span deflection for the bridge supported by a stiff soil, b medium soil, and c soft soil during a train passage at 200 km/h with (dotted grey line) and without (solid grey line) foundation-soil-foundation interaction. Results without SSI (black line) are shown as a reference

3.4 Bridge Response During a Train Passage The vertical bridge response .u z (x, t) at a point .x due to moving loads is computed as the time domain convolution of the (quasi-static) axle loads .gk and the transfer function .h zz (xk (τ ), x, t): u (x, t) =

na ∫ t ∑

. z

gk h zz (xk (τ ), x, t − τ )dτ

(7)

k=1 −∞

where .xk (t) = xk0 + vte y is the position of axle .k moving at speed .v, and .xk0 is the initial axle position. The transfer function .h zz (xk (τ ), x, t) is obtained by application of the inverse Fourier transform from the frequency domain to the time domain. We consider the passage of an InterCity train consisting of a locomotive, seven central coaches and one end coach. The train characteristics are taken from Lombaert and Degrande [9] and summarized in Table 2. Figure 5 shows the mid-span deflection during a train passage at 200 km/h. The response is mainly governed by the static stiffness, which decreases with decreasing soil stiffness. Hence, the bridge deflection is largest for the bridge supported by soft soil. Furthermore, if foundation-soil-foundation interaction is taken into account, the bridge deflection is slightly larger compared to the case where it is disregarded.

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Fig. 6 Peak acceleration at mid-span for the bridge supported by fixed piers (black line), and by taking into account SSI for the case of stiff, medium and soft soil (dark to light grey lines). Results are shown a with and b without foundation-soil-foundation interaction

Subsequently, the mid-span acceleration is computed. Figure 6 shows the peak acceleration for train speeds between 100 and 300 km/h. For train speeds below 200 km/h, there is almost no effect of SSI on the peak acceleration. At higher train speeds, the peak acceleration is generally lower when the bridge is supported by soft soil. It is also clear that, when comparing Fig. 6a and b, the effect of foundation-soilfoundation interaction on the peak acceleration is negligible.

4 Conclusions This paper investigated the effect of dynamic SSI on the response of long, periodic box girder bridges on piled foundations subjected to moving loads. The influence of foundation-soil-foundation interaction was also studied. Dynamic SSI affects the modal characteristics of the bridge, resulting in a shift of the resonance peaks to lower frequencies, particularly for the torsional modes. Furthermore, the mid-span deflection increases when the soil stiffness decreases. The peak acceleration, however, decreases with decreasing soil stiffness at high train speeds; at low train speeds, the influence of SSI is very limited. The effect of foundation-soil-foundation interaction on the mid-span deflection and acceleration can be disregarded, which significantly reduces the computational effort.

References 1. Östlund JL, Ülker-Kaustell M, Andersson A, Battini J-M (2017) Considering dynamic soilstructure interaction in design of high-speed railway bridges. Procedia Eng 199:2384–2389. X International conference on structural dynamics, EURODYN 2017 2. Romero A, Solís M, Domínguez J, Galvín P (2013) Soil-structure interaction in resonant railway bridges. Soil Dyn Earthq Eng 47:108–116 3. Ülker-Kaustell M, Karoumi R, Pacoste C (2010) Simplified analysis of the dynamic soil-structure interaction of a portal frame railway bridge. Eng Struct 32:3692–3698

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4. Bhure H, Sidh G, Gharad A (2018) Dynamic analysis of metro rail bridge subjected to moving loads considering soil-structure interaction. Int J Adv Struct Eng 10:285–294. https://doi.org/ 10.1007/s40091-018-0198-9 5. Ju SH (2007) Finite element analysis of structure-borne vibration from high-speed train. Soil Dyn Earthq Eng 27:259–273 6. Lu JF, Mei H, Whong L (2015) Dynamic response of a periodic viaduct to a moving loading with consideration of the pile-soil-structure interaction. Acta Mech 226:2013–2034 7. Gupta S, Hussein MFM, Degrande G, Hunt HEM, Clouteau D (2007) A comparison of two numerical models for the prediction of vibrations from underground railway traffic. Soil Dyn Earthq Eng 27:608–624 8. Clouteau D, Elhabre ML, Aubry D (2000) Periodic BEM and FEM-BEM coupling: application to seismic behaviour of very long structures. Comp Mech 25:567–577 9. Lombaert G, Degrande G (2009) Ground-borne vibration due to static and dynamic axle loads of InterCity and high speed trains. J Sound Vib 319:1036–1066

Investigation of Differences in Wayside Ground Vibration Associated with Train Type Briony Croft, Radoslaw Kochanowski, David Hanson, and David Anderson

Abstract A dataset containing over a year of vibration information was collected adjacent to the rail corridor in Sydney. Vibration from one train type (Tangara trains) travelling on the track nearest to the vibration monitor was observed to be 5 dB higher on average than the vibration produced by newer generation Waratah trains. This observation is only partially explained by the 10% difference in unsprung mass. This paper describes the outcomes of investigations to understand the root cause of the higher Tangara train vibration levels. It is evident that these trains experience a much higher incidence of wheel flats than newer generation train types operating on the system. Keywords Rail · Ground-borne vibration · Vibration

1 Introduction An extended period of vibration monitoring commenced adjacent to Sydney Trains tracks during August of 2020. The primary purpose of the monitoring was to understand the effect on rail vibration of various changes in track configuration in the area. The dataset collected was reviewed to identify trends in vibration level, and differences in vibration level between tracks and train types over a year, as reported in [1]. At the monitoring location, the most common rolling stock types are Tangara and Waratah Trains. These train types are two different generations of suburban double-decker electric multiple units, operating predominately as 8 car trains. The Tangara trains (T-Sets) entered service between 1988 and 1995, with a total fleet of 447 cars. The Waratah trains (A-Sets, Series 1) were introduced in 2011, with B. Croft · D. Hanson · D. Anderson (B) Acoustic Studio, Unit 27 43-53 Bridge Road, Stanmore, NSW 2048, Australia e-mail: [email protected] R. Kochanowski Transport for NSW, 7 Harvest Street, Macquarie Park, NSW 2113, Australia © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_67

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sets added progressively over the following years up to 626 cars. A second series of Waratahs (B-Sets) were introduced starting in 2018 with 240 cars bringing the total number of Waratah cars to 866 [2]. The Waratahs are the newest rolling stock type operating on the Sydney Trains network. A relatively small number of other train types on intercity routes also operate past the monitoring location. An unexpected outcome of the vibration monitoring study was that Tangara trains were observed to generate significantly higher vibration levels than Waratah trains. Tangara trains made up approximately 16% of the total traffic but were responsible for over 70% of events above the overall population 95th percentile vibration level. The difference between train types was most notable on the UP track (trains travelling towards Sydney Central) nearest the monitor, with Tangara trains producing vertical and lateral vibration levels at least 5 dB higher on average than Waratahs, as shown in Fig. 1. This paper describes additional investigations to understand the root cause of the higher Tangara train vibration levels.

2 Vibration Measurement Overview The monitoring location was approximately 8 m horizontally from the nearest (UP) track centreline. The transducer (a Convergence Instruments VSEW mk2 vibration logger) was mounted on a noise barrier constructed at the top of a retaining wall, with the railway tracks below grade in a cutting. Vertical and lateral vibration from each passing train was recorded in triggered mode with a 1000 Hz sample rate. The raw vibration signals were uploaded to the cloud for analysis. Train identification information was obtained by cross-referencing run/trip references extracted from a live open data feed [3] with specific trainset identification from Sydney Trains’ Wayside Information Management System (WIMS). Train speeds have not been identified for specific events, but designated track speed is 75 km/h for trains travelling on the UP track. Approximately 250 trains a day in total travel past the monitoring location, typically with half of these on the UP track. Table 1 shows summary results for the various train types on the UP track forming the basis for this study, examining vibration data collected between October 2020 and November 2021. Noting the relatively small number of B-Set Waratah train events and mixed traffic “other” events (which includes some older rolling stock), for the purpose of this study analysis of the vibration measurement data is focused on passby events involving A-Set Waratah trains and Tangaras.

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Fig. 1 Vertical (top) and lateral (bottom) vibration mean and quartile distribution by train type travelling on UP track. Outlier results not shown Table 1 Vibration summary results for UP track by train type Train type

No. events

Vertical vibration Mean Lmax, S dBV re 1e-9 m/s

Lateral vibration Standard deviation

Mean Lmax, S dBV re 1e-9 m/s

Standard deviation

Waratah—A sets

26,469

96.5

2.4

103.3

3.7

Waratah—B sets

62

95.2

1.0

101.5

2.4

Tangara

5062

101.4

3.8

109.9

5.3

Other

931

97.6

3.4

105.9

5.2

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3 Discussion of Vibration Measurement Results 3.1 Preliminary Observations Lateral vibration levels measured perpendicular to the track at this location were typically greater than vertical vibration, as shown in Table 1. Although the fundamental excitation of the ground via the wheel/rail contact is in the vertical direction, the greatest energy transmission through the ground particularly extending over longer distances is usually due to Rayleigh wave propagation along the surface [4]. This involves a combination of shear and compressional wave effects resulting in a combination of vertical and horizontal motion. The geometry of the site, with the vibration logger mounted on the wall at the top of the cutting, is also likely to be a factor in the relatively high lateral vibration levels. As can be seen in both Fig. 1 and Table 1, vibration levels generated by Tangara (Tset) trains were typically higher than vibration levels due to Waratah (A-set) trains. On the UP track, Tangara vertical vibration was 5 dB higher on average than the Waratahs, and lateral vibration 6 dB higher. The standard deviation values for the UP track (Table 1) suggest greater vibration variability for Tangara trains, although it is noted that analysis of data from trains on two adjacent tracks [1] did not show a clear trend of higher Tangara standard deviation on all tracks. Higher standard deviation might be expected with more variability in wheel condition (i.e., a greater difference between the typical best and worst wheels). The observation of higher Tangara vibration levels relative to Waratah trains therefore could be due to fundamental design differences, or typically worse wheel condition for this train type, or a combination of these factors. Inherently higher vibration due to vehicle type could be due to design geometry/mass; material/metallurgical properties resulting in different wheel condition; or different maintenance practices linked to vehicle type, noting that the train types are maintained in different depots.

3.2 Rolling Stock Factors Contributing to Vibration The European Union research project Railway Induced Vibration Abatement Solutions (RIVAS) investigated rolling stock factors that contribute to vibration [5]. The project investigated design elements such as unsprung mass, suspension stiffness and axle spacing, and how these influence ground-borne vibration. The effects of wheel defects and out-of-round wheels were also quantified in relation to other vibration excitation mechanisms. The RIVAS vehicle studies [6] concluded that unsprung mass and wheel out-of-roundness (OOR) are the key vehicle parameters influencing vibration. In this context, wheel OOR includes both discrete surface defects such as wheel flats, and periodic irregularities around the wheel circumference such as eccentricity, ovality, and polygonisation. Primary suspension stiffness was also found to

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be important, however modification of suspension stiffness mostly caused a narrowband frequency shift rather than changes in vibration magnitude. Investigation of vibration spectra for this dataset has not indicated any frequency shifts between the Waratah and Tangara trains [1]. Reducing unsprung mass was found to have a broadband effect in reducing vibration in the RIVAS project [6]. A potential vibration reduction of 1–2 dB was identified for a 25% reduction in unsprung mass, a 2–4 dB reduction for a 35% unsprung mass reduction, and up to a 6 dB vibration reduction might be achieved if a 50% reduction in unsprung mass could feasibly be achieved. The unsprung mass is largely controlled by the geometry and mass of the wheelset. Reducing wheel OOR on passenger vehicles was found in the RIVAS project [6] to reduce vibration by up to 5 dB. The unsprung masses of the Waratah train are 4216 kg for the motor cars and 3100 kg for the trailer cars. Tangara wheels are about 50 kg heavier than the Waratah wheels, the motor axles are about 60 kg heavier and trailer axles are about 90 kg heavier [7]. Assuming similar motor and brake masses indicates that the unsprung mass of the Tangara trains is approximately 10% higher than the Waratah trains. With reference to the RIVAS project findings, the difference in unsprung mass may be a small factor explaining perhaps 1 dB of the observed 5–6 dB difference in vibration levels. Since unsprung mass is unlikely to fully explain the difference in vibration generation, systemic differences in wheel OOR or surface defects between vehicle types are likely. Further investigation of wheel condition differences has been undertaken by analysis of an additional dataset corresponding to the vibration measurement period from Wheel Impact Load Detector (WILD) systems on the Sydney Trains network.

4 Analysis of Wheel Impact Data Sydney Trains monitors rolling stock wheel defects via four TrackIQ Wheel Condition Monitor systems [8] distributed around the network. Alert levels to flag wheel defects and the resulting maintenance actions are described in [9]. Individual carriages are flagged (“set”) initially when impacts on any one axle rise above 100 kN indicating wheels are no longer “clean”. For disc-braked trains including Tangara and Waratah sets, this initial flag/set triggers a check of the Wheel Slide Protection (WSP) system. Wheel turning is subsequently triggered based on increasing severity of impact alert levels as follows: • • • •

Low alert (200–299 kN)—wheel turn within 3 months. Medium alert (300–399 kN)—wheel turn within 1 month. High alert (300–499 kN)—wheel turn, wheel set or bogie change within 5 days. Extreme alert (>500 kN)—Immediate speed reduction and removal from service.

WILD data in the form of daily step change reports covering the same time period as the vibration data were collated to understand the number of wheel defects

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generated by each train type, their initial and subsequent severity, and the average number of days from the initial “set” until the carriage is “cleared”, indicating impacts below 100 kN across all four axles. This dataset includes all rolling stock types operating on the Sydney Trains network, enabling comparison across all train types.

4.1 Number of Wheel Defects, Initial Severity and Days to Clear Table 2 shows a summary of the WILD data indicating the number of new wheel defects flagged, the initial severity and the average days for the carriage to be “cleared” from the active defect list. It is evident based on the number of WILD flags in Table 2 that Tangara cars had a considerably higher incidence of wheel defects in the time period of this study than other traincar types, and specifically the Waratah cars. Factoring in the total number of cars in service, Tangara cars generated approximately 15 times more flags in the WILD system than Waratah trains. The oldest trains operating on the network (Suburban/Intercity) also had relatively high numbers of wheel defects (note that these older sets use less sophisticated tread-braking systems whereas all trains from T-Sets onwards now have disc-braking). In general, newer train types appear to generate less wheel defects than older train types. Examining the initial severity of each defect indicates that there is no clear difference in initial severity of defects between Tangara and Waratah train sets. In general, very few defects were initially sufficiently severe to trigger a Low Alert level at the time the defect was first flagged by the WILD system. The exception to this is the older Suburban and Intercity trains, with 21% of flagged defects generating a Low Alert impact level. Table 2 Sydney trains WILD summary over one year commencing 29 October 2020 Train type

Total cars

New WILD flags (% of cars)

Initial severitya set/low alert

Cleared WILD flags

Average days to clear

Waratah (A + B sets)

866

60 (7%)

59/1

56

91

Tangara (T-sets)

447

476 (106%)

470/6

504

44

Oscars (H-sets) 220

41 (19%)

41/0

46

94

Suburban/ intercity (K + V Sets)

395

309 (78%)

243/66

298

40

Millennium (M-Sets)

141

5 (4%)

4/1

2

26

a No

carriages with initial severity greater than Low Alert level

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On the basis of the average number of days passing before a wheel defect is cleared from the WILD system, Tangara trains have defects rectified somewhat faster than the average across the whole rolling stock fleet (44 days vs 51 days for whole fleet). On average, wheel defects on Tangara trains are cleared twice as quickly as wheel defects on Waratah trains. Note the available data does not indicate with certainty that the cleared defect is always the result of a maintenance intervention—it is possible that some defects are flagged that are marginally above the 100 kN set level, followed by enough lower speed passes over WILD sites to clear the train. However, the available data suggests that a lack of maintenance intervention is unlikely to be the cause of higher Tangara vibration levels.

4.2 Defect Progression to Higher Severity Levels Additional analysis of the WILD data was undertaken to determine if any particular train type tends to exhibit more severe impact progression in the period between the defect being flagged and subsequently cleared. For each individual carriage flagged with a defect on a particular date, the subsequent maximum impact load on any individual axle prior to clearing the defect was identified. Then, the average of these maximum impact values was determined across the train types of interest, as shown in Table 3. This analysis indicates that on average, all train types with defects have similar maximum impact levels prior to clearing the wheel defect, below the Low Alert level of 200 kN. Tangara trains had slightly lower maximum impact levels on average than Waratah trains. This implies that although more wheel defects are generated on the Tangara wheels, these do not typically progress to become more severe than defects generated on the Waratah wheels. Table 3 Sydney trains WILD summary average maximum impact severity for wheel defects prior to clearing Train type

Average maximum impact level (kN)

Waratah (A + B sets)

172

Tangara (T-sets)

166

Oscars (H-sets)

182

Suburban/intercity (K + V sets)

183

Millennium (M-sets)

172

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5 Discussion The different traction control systems on Waratah and Tangara trains is a potential contributor to the higher incidences of wheel flats and hence to the observed higher vibration levels generated by Tangara trains. The Tangaras have DC traction systems whereas Waratah trains utilise more sophisticated and more modern AC traction systems. On Tangara trains, the dynamic braking fades out at lower speeds, with only friction braking applying down to stand-still. Waratahs (and other AC traction sets) can utilise more controlled dynamic-braking at all speeds down to standstill. In the absence of any identified metallurgical differences, differing maintenance practice/standards, and with a relatively small difference in unsprung mass, it is likely that fundamental design differences related to traction control, braking systems and WSP are a key factor in the higher incidence of wheel flats and hence higher vibration levels generated by Tangara trains, relative to the newer generation Waratah trains.

6 Conclusion Long term vibration monitoring of over a year of rail traffic at a site in Sydney identified that the vibration generated by one particular train type (Tangara trains) was 5 dB higher on average than the vibration produced by newer generation Waratah trains. Investigation of the root cause of the higher vibration levels required analysis of network-wide WILD data, establishing that Tangara trains produce approximately 15 times more wheel defects than Waratah trains. No differences in the severity of defects, maintenance practices or the rate of clearing these defects were identified. The different generations of vehicles do have fundamental design differences in traction control, braking systems and wheel slip protection systems. It is concluded that relative improvements in the design of these systems implemented on the newer generation trains differences are likely to be a key factor in minimising ground vibration impacts. Considering that vibration impact assessment, prediction and design of mitigation for new rail systems is often derived from measurement of existing rolling stock, it is clearly important to understand any differences in rolling stock design related to traction, braking and wheel slip protection, in addition to unsprung mass differences. It is possible that vibration impacts in Sydney will reduce over time as improvements in these systems continue to be implemented and older rolling stock is phased out. Acknowledgements Vibration monitoring was undertaken by Acoustic Studio under contract to Sydney Metro, supported by Jeff Parnell, Fil Cerone, Ben Armstrong, Stuart Hodgson and the Acoustics Working Group. Sydney Metro’s permission to utilise the data collected for the purpose of this paper is gratefully acknowledged. We appreciate the support of Jonathan Barnes and Eric Taylor in providing information on the differences between Tangara and Waratah trainsets, and Shane Doyle in supplying fleet maintenance data.

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References 1. Croft B, Hanson D, Anderson D (2022) Insights from long-term wayside monitoring of rail vibration. In: Proceedings of Australian acoustical society acoustics 2021 Wollongong: Making Waves 2. Transport for NSW. https://transportnsw.info/travel-info/ways-to-get-around/train/fleet-facili ties/sydney-intercity-train-fleet. Accessed 4 May 2022 3. NSW government open data portal https://data.nsw.gov.au/ 4. Thompson DJ (2009) Railway noise and vibration mechanisms modelling and means of control, 1st edn. Elsevier, Oxford 5. RIVAS Project (2013). https://cordis.europa.eu/project/id/265754/reporting. Accessed 5 Nov 2021 6. Nielsen J, Mirza A, Ruest P, Huber P, Cervello S, Müller R, Brice Nelain B (2013) Guideline for design of vehicles generating reduced ground vibration. RIVAS Project Deliverable D5.5 7. TfNSW. Personal communication 4 Nov 2021 8. TrackIQ. https://www.trackiq.net/WCM.html. Accessed 5 May 2022 9. Sydney Trains Procedure PR R 90310 RS—all rolling stock—wheels—wheel impact load detector (WILD) alert levels, version 2.0, 30 October 2018

Theoretical and Numerical Study on the Effect of TMD in Ground Borne Noise Control Ghazaleh Soltanieh, Yi-Qing Ni, Marco Ip, and Wilson Ho

Abstract The combined mass of wheelset and rail exhibits a simple harmonic motion on the resilient fastener. The natural resonance mode of this motion is called P2 resonance. P2 resonance typically happens at a frequency around 30–100 Hz proportional to the square root of the stiffness of the resilient fastener. Railway Groundborne noise (GBN) at the buildings near railway tunnels is associated with the vibration at the P2 resonance frequency of the rail. Tuned Mass Dampers (TMD) tuned to the P2 resonance frequency can significantly dissipate the ground-borne vibration energy. A TMD includes the mass-spring-damper system that counteracts the rail vibration and dissipates the energy at a resilient layer via amplified hysteresis motion of the oscillators. The theory and FEA simulation demonstrate the effect of the TMD on groundborne vibration reduction in this study. The results of the vibration reductions from FEA are compared with the laboratory test results. Keywords Groundborne noise · P2 resonance · Tuned mass damper

1 Introduction 1.1 The Potential Low-Frequency (Ground-Borne) Noise Issue and Existing Mitigation Methods The increase in axle load and train speed would cause intense wheel-rail interaction and potential vibration issues [1, 2]. The P2 resonance rail vibration will transmit to the ground in the frequency range of 30–100 Hz [3]. The current methods for G. Soltanieh (B) · Y.-Q. Ni · M. Ip Hong Kong Branch of National Rail Transit Electrification and Automation Engineering Technology Research Center, Hong Kong Polytechnic University, Hong Kong, SAR, China e-mail: [email protected] W. Ho Wilson Acoustic Limited, Hong Kong, SAR, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_68

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mitigation of ground-borne noise are applied in all three parts of the railway system, the vehicle, rail fasteners and slab track [4]. The mitigation methods in the vehicle include the reduction of the wheel out of roundness, unsprung mass, and vehicle speed. The reduction of the wheel out of roundness can be achieved with good maintenance. For example, re-profiling the wheel and rail will cause a noise reduction equal to 2–10 dB [4]. The reduction of unsprung mass is difficult to achieve due to rigidity requirement of the wheelset for safety concerns. The reduction of mass between 5–10% has only marginal effect on vibration reduction [5]. The reduction of vehicle speed by a factor of two can cause a vibration reduction up to 6 dB [6]. Because of the reduction of line capacity, this method is not viable for practical application. The mitigation methods in the track are the good track alignment, the resilient fastener and the sleeper enhancement, and using the technologies like floating slab track (FST). Good track alignment can cause up to a 10 dB reduction for GBN at the speed of 320 km/h [4]. The other high-cost methods like enhancing the resilient fasteners, using the elastomeric pads between the sleeper and ballast, and using softer ballast can reduce the vibration up to 13, 20, and 15 dB, respectively [8–10]. The track technologies like embedded rail, ballast with soft pads, resilient baseplate, and FST are typically used for GBN control when high reduction is required [11]. The vibration reductions were 10 dB with frequencies above 16 Hz or 25 dB by the frequency of 125 Hz [12]. FST is expensive because it requires a large tunnel (simultaneously designed with the tunnel). Rail dampers as the external passive vibration control devices can enhance the track as a retrofit solution. The rail dampers are less expensive than the other methods. These technologies are smart dampers (MR-dampers) [13, 14] or simple yet effective tuned mass dampers [15].

1.2 Using TMD for the Ground-Borne Noise Control TMD (Tuned Mass Damper) is a device mounted in structures to reduce the amplitude of vibrations. The previous generation of rail dampers causes the vibration reduction of rail up to 9 dB in high frequencies [7] but no reduction in low frequencies below 100 Hz [18]. A new generation of TMDs [15] with a rigid connection to the rail was developed and successfully tested in the laboratory for reduction of the low-frequency groundborne vibration up to 8.9 dB as shown in Fig. 1 [19].

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Fig. 1 Laboratory test results of rigid contact tuned mass rail damper

1.3 Calculation of TMD Parameters for the Ground-Borne Noise Control There is a spring connection between car and bogie (secondary suspension) and between bogie and wheel (primary suspension) for vibration isolation in trains. In such a case, only the wheel and rail will be combined as an un-sprung mass, and the vibration aroused by this mass is called P2 resonance. The P2 resonance frequency causes the ground-borne vibration. The TMD, including the mass and resilient layer, can reduce the vibration at P2 resonance. The floor mass, the half of the equivalent un-sprung mass (the track and wheelset mass), and TMD mass make a system of three degrees of freedom mass-spring-damper (Fig. 2).

Shaker

450kg half wheel 6m long rail

RCTMD

Fig. 2 Photos of the laboratory test of rigid contact tuned mass rail damper

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In this paper, a three-degree-of-freedom system of equations is solved regarding the TMD parameters of mass, resilient layer stiffness, and damping ratio [16]. The effect of each parameter in GB vibration is examined to find the best configuration for TMD. In the third section, the result of the parametric study on the TMD parameters from finite element analysis are presented and compared with the corresponding results from the theory and test.

2 Theory 2.1 Theory of P2 Resonance Frequency The P2 resonance frequency can be calculated according to the half of the stiffness of the track (KTr ) and the half of the total mass of the track and wheelset (MTr + Mw ) [17–19]. / f P2

1 = 2π

KTr (M T r + M w)

(1)

The stiffness and mass are calculated as below )1 ( K T r = 2 × 4 × E I z × k3f 4 kf = ( M T r = 3 × mt r ×

EIz KTr

(2)

k pv l0

) 13

(3) (

= 3×ρA×

EIz KTr

) 13 (4)

Notations and their respective values are introduced in Table 1. The rail is UIC60 from steel material with the track mass per unit length (Mtr ) equal to 60 kg/m. According to Table 1, the P2 resonance frequency (fP2 ) is obtained equal to 48.4 Hz. Table 1 Parameters of track system Symbol and unit

Parameters

Value

Bending stiffness of rail

6.24 × 106

Kf (N/m/m)

Fastener vertical stiffness per unit length

2.5 × 107

l0 (m)

Fastener spacing

0.6

MTr (kg)

Equivalent mass of half track

91

Mw (kg)

Equivalent mass of half wheelset

450

EIz

(Nm2 )

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2.2 Analytical Model for Three-DOF Mass-Spring-Damper Vibration System Under Harmonic Load The equation of motion for a three DOF mass-spring-damper system (Fig. 3), including the floor mass (M1 ), half of the equivalent unsprung mass (M2 ), and the TMD mass (M3 ) is written as ⎡

⎤⎡ ⎤ ⎡ ⎤⎡ ⎤ 0 M1 0 0 y¨1 C1 + C2 −C2 y˙1 ⎣ 0 M2 0 ⎦⎣ y¨2 ⎦ + ⎣ −C2 C2 + C3 −C3 ⎦⎣ y˙2 ⎦+ y¨3 0 −C3 C3 y˙3 0 0 M3 ⎤⎡ ⎤ ⎡ ⎡ ⎤ 0 0 y1 K 1 + K 2 −K 2 ⎣ ⎦ ⎣ ⎦ ⎣ −K 2 = K 2 + K 3 −K 3 y2 −F0 cos(Ωt)⎦ 0 −K 3 K3 y3 0

(5)

The load is considered to be a harmonic load (F0 cos(Ωt)) applied to the unsprung mass (M2). Initial force (F0) is equal to 100 kN and the frequency ( f ) is changed from 20 to 90 Hz (Ω = 2∏ f ). TMD is tuned to P2 resonance frequency measured from laboratory test (48 Hz) [19]. TMD switched on (3) and (3_off) off means allowing and not allowing to oscillate. To “switch off” the oscillators, rigid gap fillers will be inserted between oscillators and rail in practice and set the resilient layer to become rigid in the simulation. The notations and their values are shown in Table 2. The steady-state response of the system under harmonic load is shown in Eq. (6) y(t) = a cos(Ωt) + b sin(Ωt) Fig. 3 Mass-spring-damper system of the floor, rail and TMD

(6)

K3

K2

K1

C3

C2 C1

Table 2 Mass, stiffness, and damping ratio for 3DOF mass-spring-damper system Notation

Mass (kg)

Stiffness (N/m)

Viscous damping ratio (%)

1 (floor)

1.3e7

7.1e11

5

2 (unsprung)

541

1.7e8

10

3 (TMD)

34

0.31e6

10

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with ⎡

⎡ ⎤ ⎤ ⎡ ⎤ y1 (t) b1 a1 y(t)⎣ y2 (t) ⎦; a = ⎣ a2 ⎦; b = ⎣ b2 ⎦ y3 (t) a3 b3

(7)

The system of Eq. (5) is solved using Matlab software [20]. Velocity, V, is obtained by taking the derivative of y(t). The maximum velocity ratios of the floor (VTMD on / VTMD off ) in the frequency range of 20, 30, …, and 90 Hz are shown in Table 3. Table 3 shows the effectiveness of TMD depending on the frequency of the applied load. In the current study, the maximum velocity reduction is obtained for the applied load with the frequency of 80 Hz. The velocity of the floor under the harmonic load with the frequency of 80 Hz is shown in Fig. 4. The graph is presented for TMD on and off in FFT (dB scale) in 0.5Hz bandwidth. The velocity reduction at P2 resonance (48 Hz) is approximately equal to 3.4 dB. The parametric study is done to understand the effect of different parameters like Table 3 Maximum velocity ratios of floor Frequency of applied load

Maximum velocity ratio (VTMD on /VTMD off )

20

1.00

30

1.01

40

1.02

50

0.872

60

0.873

70

0.840

80

0.78

90

0.99

Fig. 4 The floor vibration (velocity) under harmonic cosine load with frequency of 80 Hz

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Table 4 Parametric study on TMD mass and viscous damping ratio of resilient material Total TMD oscillator mass (kg)

Viscous damping ratio (%)

Velocity reduction (dB) at P2 resonance

17 (1 set)

10

1.7

34 (2 sets)

10

3.36

51 (3 sets)

10

5

34 (2 sets)

5

3.4

34 (2 sets)

20

3.3

the TMD mass and damping ratio of the resilient material in vibration reduction of the floor at P2 resonance. The installed TMDs are assumed to be a single set, two sets, and three sets. The viscous damping ratios are 5, 10, and 20%, as summarised in Table 4. The maximum reduction at P2 resonance (48 Hz) is obtained for three sets of TMD equal to ~ 5 dB. The results show that the damping ratios for different resilient materials from 5 to 20% do not affect the results significantly. The vibration reduction from increasing the mass will decrease the vibration proportional to the mass ratio.

3 Finite Element Analysis A three-dimensional FEA is used to simulate the test setup [21] in the lab on the first floor of the six-story building using Strand 7 software [22]. The model consists of three main features: (1) the floor slab, (2) the rail-wheelset, and the TMD (3). The concrete sleepers and the floor slab are simulated using 3D Hexa8 elements. The rail and floor element sizes are according to the size of ten elements per wavelength of steel and concrete. 1D beam elements are used to simulate a 6 m long rail (UIC60). Rail is fastened with 20 rail pads and baseplates at 0.6 m intervals. The rail fastening system is modeled using 1D spring-damper elements and 2D plate/shell elements from the perspective of elasticity and vibration attenuation [23]. The rail baseplates are rigidly fixed to the sleepers, and the sleepers are fixed to floor slab (Fig. 3a). The wheelset mass is attached to the middle of the rail as a nodal mass. The white noise excitation load is applied to the rail-wheel mass. TMD is simulated using a nodal mass connected to the rail via 1D spring-damper element (resilient layer). The TMD sets tuned to 48 Hz have been installed below the wheelset. The FEA model has been shown in Fig. 5. The parametric study has been done on the number of TMD sets and the damping ratios of the resilient layers. The velocities at the rail with and without TMD and the floor are presented in the one-third-octave bandpass (see Fig. 5). The rail and floor velocities are taken at the middle of the rail, same as the laboratory test there. The baseline (TMD off) has shown a peak at P2 resonance (50 Hz). The FEA results show very near to the result from theory (Table 4). Comparing the FEA with the test results [24], the vibration

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Rail location

Fig. 5 3D-FEM: (left) floor, rail, and TMD (right) six-story building

Fig. 6 The floor velocity (1/3-octave band) from test and FEA under white noise load

reduction from the test at P2 resonance (7.5 dB(A)) is almost 1 dB(A) more than the FEA result. The results show that the damping ratios for different resilient materials from 5 to 20% do not affect the results significantly (Fig. 6).

4 Conclusion Typically, railway groundborne noise (GBN) is mitigated by floating slab track (FST) or other resilient trackform. But they are not retrofittable if GBN is discovered after construction phase. Retrofit mitigations by installation of low frequency TMD tuned to the P2-resonance of the rail may be further developed to resolve GBN problems economically and transform the EIA’s over-conservative approach using FST

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extensively. Laboratory test results show a 7.5 dB(A) peak-to-peak floor vibration reduction at P2 resonance using the new TMD. The FEA and theory illustrate the effectiveness of the new TMD with vibration reduction at low frequency (50 Hz). Further investigation is necessary for the more exact results. Acknowledgements The funding support from the Innovation and Technology Commission of the Hong Kong Special Administrative Region to the Hong Kong Branch of National Rail Transit Electrification and Automation Engineering Technology Research Center (K-BBY1).

References 1. Lombaert G, Degrande G, Vanhauwere B, Vandeborght B, François S (2006) The control of ground-borne vibrations from railway traffic by means of continuous floating slabs. J Sound Vib 297(3–5):946–961 2. Xu G, Su S, Wang A, Hu R (2021) Theoretical analysis and experimental research on multi-layer elastic damping track structure. Adv Mech Eng 13(2):1687814021994975 3. Connolly DP, Kouroussis G, Laghrouche O, Ho CL, Forde MC (2015) Benchmarking railway vibrations–track, vehicle, ground and building effects. Constr Build Mater 92:64–81 4. Ouakka S, Verlinden O, Kouroussis G (2022) Railway ground vibration and mitigation measures: benchmarking of best practices. Railway Eng Sci 30(1):1–22 5. RIVAS Railway Induced Vibration Abatement Solutions Collaborative project (2013) 6. Hanson CE, Towers DA, Meister LD (2006) Transit noise and vibration impact assessment. No. FTA-VA-90-1003-06 7. Benton D (2006) Engineering aspects of rail damper design and installation. Rail Noise 8. Bewes OG, Jakielaszek LJ, Richardson ML (2015) An assessment of the effectiveness of replacing slab track to control groundborne noise and vibration in buildings above an existing railway tunnel. In: Noise and vibration mitigation for rail transportation systems. Springer, Berlin, Heidelberg, pp 393–400 9. De Vos P (2017) Railway induced vibration: state of the art report. UIC International Union of Railways, Paris 10. Sol-Sánchez M, Moreno-Navarro F, Rubio-Gámez MC (2015) The use of elastic elements in railway tracks: a state of the art review. Constr Build Mater 75:293–305 11. Cui F, Chew CH (2000) The effectiveness of floating slab track system—Part I. Recept Meth Appl Acoustics 61(4):441–453 12. Hemsworth B (2000) Reducing groundborne vibrations: state-of-the-art study. J Sound Vib 231(3):703–709 13. Ying Z, Ni Y, Sajjadi M (2013) Nonlinear dynamic characteristics of magneto-rheological visco-elastomers. Sci China Technol Sci 56(4):878–883 14. Alehashem SS, Ni YQ, Liu XZ (2021) A full-scale experimental investigation on ride comfort and rolling motion of high-speed train equipped with MR dampers. IEEE Access 9:118113– 118123 15. Ho W, Soltanieh G, Wang W (2021) Noise reduction by rail damper tunable for individual rails in curve. In: INTER-NOISE and NOISE-CON congress and conference proceedings, vol 263, No 1. Institute of Noise Control Engineering, pp 5531–5537 16. Van Khang N, Loc TQ, Tuan NA (2013) Parameter optimization of tuned mass damper for three-degree-of-freedom vibration systems. Vietnam J Mech 35(3):215–224 17. Cai W, Chi M, Wu X, Sun J, Zhou Y, Wen Z, Liang S (2021) A long-term tracking test of high-speed train with wheel polygonal wear. Veh Syst Dyn 59(11):1735–1758

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18. Croft BE, Weber CM (2018) Vibration reduction with installation of rail dampers—a case study. In: Noise and vibration mitigation for rail transportation systems. Springer, Cham, pp 557–569 19. Ho W, Ip M, Soltanieh G, Wong W, Tse D (2021) Groundborne noise reduction by rail damper effect on P2 resonance, proceeding of the ICSV 27, July 2021 20. MATLAB and Statistics Toolbox Release 2020a, The MathWorks, Inc., Natick, Massachusetts, United States 21. Ho W, Soltanieh G, Wang W (2021) Noise reduction by Rail Damper Tunable for individual rails in curve. In: INTER-NOISE and NOISE-CON congress and conference proceedings, vol 263, no 1. Institute of Noise Control Engineering, USA, pp 5531–5537 22. Strand7 Pty Ltd. Strand7, Finite element analysis system. User Manual 2005, Sydney, Australia 23. Zhan Z, Sun H, Yu X, Yu J, Zhao Y, Sha X, Li WJ (2019) Wireless rail fastener looseness detection based on MEMS accelerometer and vibration entropy. IEEE Sens J 20(6):3226–3234 24. Ho W, Yiu M, Wong R, Soltanieh G, Ni YQ (2022) Railway ground borne noise (GBN) reduction by rail dampers. In: INTER-NOISE and NOISE-CON congress and conference proceedings. Institute of Noise Control Engineering, Glasgow

Finite Element Modelling of Tunnel Shielding in Vibration Measurements of Ground-Borne Noise Fatemeh Dashti, Patrik Höstmad, and Jens Forssén

Abstract Several factors can affect vibration levels during transmission from a tunnel to the ground surface. This study investigates the effect of a tunnel cavity in bedrock with force excitation at the tunnel floor. The tunnel geometry affects the wave propagation around the tunnel and the directivity pattern of waves propagating to the ground surface. For instance, there is no direct propagation path of ground waves from the excitation in the tunnel floor to positions on the tunnel walls. The waves reaching the walls have been diffracted at the tunnel corners. This tunnel shielding effect is here investigated regarding sensor position and direction and directivity of wave propagation up to 1 kHz using the finite element method. An underground tunnel is modelled in 2D and 3D for a bedrock ground typical for Swedish conditions. The results show that the velocity levels at the tunnel floor are higher than at the tunnel wall. It is also shown that the tunnel shielding effect causes decreased vibration levels at mid-frequencies above the tunnel and significant level fluctuations, especially at higher frequencies. The results from the 3D modeling support the 2D results. Keywords Ground-borne noise · Wave propagation · Finite element method · Railway tunnel · Tunnel shielding effect

1 Introduction The generation of ground-borne noise and vibration by trains and its effects on humans and the community have been a concern for researchers in recent years. Therefore, ground-borne noise and vibration prediction is vital before constructing a new railway in tunnels or on the ground surface close to residential areas. In recent decades, many different numerical [8, 9], theoretical [1, 4], and experimental [6, 7] approaches have been developed for the prediction of ground-borne F. Dashti (B) · P. Höstmad · J. Forssén Department of Architecture and Civil Engineering, Division of Applied Acoustics, Chalmers University of Technology, 412 96 Gothenburg, Sweden e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_69

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noise and vibration. To develop the experimental models, extensive measurement campaigns in the field are needed to reach a usable precision in the model. However, there are always some situations that are not feasible to investigate in field measurements. For such phenomena, numerical studies may be carried out. Hussein and Hunt [3] developed a numerical model to predict vibration from railway tunnels embedded in full space. This model was extended by Kuo et al. [5] to consider the effect of two parallel tunnels on ground vibrations. Heidari et al. [2] considered the soil layer’s effect on single and twin tunnels. A methodology and model are being developed for ground-borne noise prediction in Swedish bedrock conditions. The frequency range of interest is up to 1 kHz since firm Swedish bedrock without notable cracks may carry ground-borne noise at relatively high frequencies. In the ongoing project, measurements are needed as input for calibrating the model and finding vibration levels and transfer functions as a function of frequency. The train forces excite waves in the tunnel floor and vibration sensors are commonly placed at the easily accessible tunnel wall. When conducting vibration measurements in a tunnel, there are important factors to consider, such as the influence of sensor position and direction, which are investigated in this study. The tunnel geometry affects also the wave propagation and gives an interference pattern between body waves on the ground and surface waves at the surface [10]. There is no direct propagation path of ground waves from the excitation in the tunnel floor to positions on the tunnel walls. The waves reaching the walls have been diffracted around the tunnel corners. Thus, the tunnel geometry gives a shielding effect. Therefore, it is of interest to investigate how the tunnel shielding influences the sensor responses when measuring in different locations and directions in the tunnel. The remainder of this paper is structured as follows. In Sect. 2, the numerical modeling is described. In Sect. 3, the results are presented and discussed. In Sect. 4, the conclusions are presented.

2 Numerical Modelling The finite element method has been used to model wave propagation and resulting vibration amplitudes in a lightly damped elastic medium when excited by forces up to 1 kHz. An underground tunnel is modeled in 2D in half and full space. The advantage of a 2D model compared with a 3D model is that analysis at higher frequencies is computationally feasible. The disadvantage is that a modeled point force in 2D corresponds to a coherent line force in 3D, while the real train case is rather an incoherent line force or moving point forces. A corresponding 3D finite element model is used to confirm the relevance of the 2D simulations. The ground type studied is bedrock typical for Swedish ground conditions. In our simulation, the bedrock has Young’s modulus of 50 GPa, a density of 2400 kg/ m3 , a Poisson ratio of 0.3, and a damping ratio of 0.008. The elastic medium is homogeneous and isotropic, i.e., no effects of cracks are included. The Structural

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Mechanics Module of COMSOL Multiphysics software and its Solid Mechanics interface in the frequency domain is used to calculate the velocity response due to a unit force. Low reflection boundary conditions are used to simulate infinite domain extension. condition is an impedance matching strategy using  The boundary  an impedance of c p + cs /2, where c p is the speed of P-waves and cs is the speed of S-waves. The performance of this boundary condition has been validated. The mesh size is chosen to cover frequencies up to 1 kHz, i.e., at least six nodes per wavelength. Four simulations are carried out to assess the directivity of the wave propagation (Fig. 1a). First, a full space without tunnel or ground surface is modeled as a reference case. Second, a full space including a tunnel in the center of the ground is modeled to investigate how the directivity changes around the excitation point. Third, a half space without tunnel is simulated to evaluate how the ground surface affects the vibration levels. Finally, a tunnel in a half-space is modeled to analyze the complete shielding effect of the tunnel. In the cases with a tunnel, a downward point force was applied close to where a track is likely to be present in real conditions. The directivity is evaluated on a circle with a radius of 28.5 m around the point force (red dotted circle in Fig. 1a). The tunnel has a width of 13 m, a height of 8.5 m and is located 20 m below the ground surface (Fig. 2b). The tunnel shielding is expected to affect the velocity level at the ground surface. As indicated in Fig. 2a (red dotted line), receiver positions are placed on the ground surface along a line of 120 m centered above the tunnel, using a spatial resolution of 1 m. The vibration amplitudes perpendicular to the ground surface are evaluated. The simulation is carried out with and without the tunnel in the half-space. The tunnel wall partly shields the waves generated by force excitation in the tunnel floor due to the tunnel geometry. The velocity amplitude in both x- and y-directions are evaluated at the receiver positions on the tunnel wall and tunnel floor. As shown in Fig. 2b, three receiver positions are placed each 1 m starting from the force position

Fig. 1 Geometrical layouts of the study: a 2D model where the dashed line indicates the free surface in the half-space case, b 3D model

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Fig. 2 Receiver positions a on the ground surface, b in the tunnel

on the tunnel floor. Four receiver positions are on the tunnel wall up to 4 m above the floor with a 1 m separation. To model the real case and to validate the results of the 2D model, 3D models of a half-space with and without the tunnel were set up. The tunnel geometry, boundary condition and material data are the same as in the 2D modeling, see Fig. 1b. However, the dimensions of the domain were reduced to get reasonable computation times. As shown in Fig. 1b, the distance from the tunnel floor to the boundary below the tunnel is lower than 20 m. Therefore, some angles are not evaluated in the directivity results.

3 Results Figure 3 shows the directivity of the vibration magnitude level in the radial direction for the 2D calculations. The results are presented for six different 1/3-octave bands to show typical results at low frequencies (10 and 20 Hz), medium frequencies (80, 160 and 250 Hz) and high frequencies (1 kHz). For the full space cases, we can conclude that the tunnel causes the vibration levels to increase below the tunnel and generally to decrease above the tunnel at low frequencies whereas the patterns at higher frequencies break up. The full and half-space results are very similar for the directions below the tunnel but differ clearly above the tunnel where the 2D evaluation positions reach the ground surface, where coupling between wave types occurs and also R-waves are present. For the half-space and 1 kHz case, the directivity is violently fluctuating depending on the direction and there is no clear reduction above the tunnel as the tunnel is added. However, the levels above the tunnel are generally lower than below, indicating that most energy is propagated downward. For the response at the ground surface, the vibration levels in the y-direction are considered and typical results with and without tunnel from low to high frequencies are presented in Fig. 4. In the 10 Hz band, the distance attenuation is clearly visible. At high frequencies, interference effects between the wave types cause fluctuations. The effect is stronger in the mid-frequency range where the wavelength of S-waves is on the order of the tunnel width. These fluctuations increase when the wavelength

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Fig. 3 Directivity: a f = 10 Hz, b f = 20 Hz, c f = 80 Hz, d f = 160 Hz, e f = 250 Hz, f f = 1 KHz

of P-waves is smaller than the tunnel width. In general, the levels with the tunnel are significantly lower than without the tunnel, demonstrating that tunnel shielding reduces the velocities at the surface. The effect is smaller at low frequencies. At higher frequencies, the results start to fluctuate as a function of position and in general, the levels are approximately 4–10 dB lower for the shielded case. Additionally, the asymmetric directivity pattern due to the asymmetric position of the force is clear.

Fig. 4 Velocity level perpendicular to the ground surface: a half-space without tunnel, b half-space with tunnel. The legend shows the 1/3 octave center frequency in Hz

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Fig. 5 Velocity level in 1/3 octave bands in the tunnel: a velocity level at floor in y-direction and at tunnel wall in x and y-direction, b normalized velocity level at floor in y-direction and at tunnel wall in x and y-direction

Figure 5 shows results for receiver positions located along the tunnel’s floor and wall. The vibration levels in y-direction are considered in the tunnel floor and both x and y-directions are considered for the tunnel wall (see Fig. 2b). Figure 5a shows the vibration level in x and y-directions on the tunnel wall, and Fig. 5b presents the same results normalized to the velocity in y-direction at the tunnel floor 1 m from the excitation point. As expected, the velocity level is decreased on the tunnel floor by increasing the distance from the excitation point. The level in the y-direction at the tunnel wall decreases by increasing the height of the receiver position. In comparison, the velocity level in the x-direction is mainly insensitive to height, except at mid-frequencies (about 50–200 Hz). As shown in Fig. 6, the 3D results follow the same trends as the 2D results. The reduction in velocity level when adding the tunnel is slightly larger when modelling in 3D compared with 2D, most clearly seen at the lower frequencies. Also, for the velocity level on the ground surface, the 2D and 3D results show similar trends (Fig. 6).

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Fig. 6 Comparing the directivity in 2D with 3D: a f = 20 Hz, b f = 80 Hz, c f = 160 Hz, d f = 250 Hz

4 Conclusion In this study, numerical analyses were conducted to evaluate how a tunnel affects vibration levels at tunnel boundary and ground surface, and directivity patterns. To consider how the vibration levels change with position in the tunnel, receiver positions are located along a part of the tunnel floor and tunnel wall. It can be concluded that, when going from the tunnel floor to the tunnel wall, there is a clear reduction in vertical velocity for frequencies above 20 Hz, and the horizontal velocity at the tunnel wall is even lower. This phenomenon can be called tunnel shielding effect. This can be used to estimate correction terms when converting from one direction to another. Concerning the directivity, four simulations were carried out using half and full-space models with and without tunnel. In general, the levels above the tunnel are lower than below the tunnel. This means that most energy is propagated downward. Also, increasing level fluctuations are generated at higher frequencies

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above the tunnel. The tunnel shielding effect on the velocity level at the ground surface is noticeable at frequencies above 20 Hz. The interference between different wave types creates fluctuations, especially in the mid-frequency range where the wavelength of P-waves is shorter than the width of the tunnel. Finally, by comparing 3D with 2D results, it is concluded that they follow the same pattern.

References 1. Forrest JA, Hunt HEM (2006) A three-dimensional tunnel model for calculation of traininduced ground vibration. J Sound Vib 294:678–705.https://doi.org/10.1016/j.jsv.2005.12.032 2. Heidary R, Esmaeili M, Nik MG (2021) Evaluation of the soil layering and soil lens effect on the ground-borne vibrations induced by twin metro tunnels. Eur J Environ Civ Eng 1–20. https://doi.org/10.1080/19648189.2021 3. Hussein MFM, Hunt HEM (2007) A numerical model for calculating vibration from a railway tunnel embedded in a full-space. J Sound Vib 305:401–431.https://doi.org/10.1016/j.jsv.2007. 03.068 4. Jones CJC, Block JR (1996) ZIB prediction of ground vibration from freight trains. J Sound Vib 193:205–213. https://doi.org/10.1006/jsvi.1996.0260 5. Kuo KA, Hunt HEM, Hussein MFM (2011) The effect of a twin tunnel on the propagation of ground-borne vibration from an underground railway. J Sound Vib 330:6203–6222. https:// doi.org/10.1016/j.jsv.2011.07.035 6. Kurzweil LG (1979) Ground-borne noise and vibration from underground rail systems. J Sound Vib 66:363–370. https://doi.org/10.1016/0022-460X(79)90853-8 7. Madshus C, Bessason B, Hårvik L (1996) Prediction model for low frequency vibration from high speed railways on soft ground. J Sound Vib 193:195–203. https://doi.org/10.1006/jsvi. 1996.0259 8. Yang J, Li P, Lu Z (2018) Numerical simulation and in-situ measurement of ground-borne vibration due to subway system. Sustainability 10(7):2439. https://doi.org/10.3390/su1007 2439 9. Fiala P, Degrande G, Augusztinovicz F (2007) Numerical modelling of ground-borne noise and vibration in buildings due to surface rail traffic. J Sound Vib 301:718–738. https://doi.org/ 10.1016/j.jsv.2006.10.019 10. Bohlen T, Giese R, Müller C, Landerer F (2003) Modeling of seismic waves around a tunnel with irregular wall. In: 65th EAGE conference exhibition. EAGE Publications BV

Assessment of Building Performance Against Train Induced Vibrations by a Hybrid Experimental-Numerical Methodology Hamid Masoumi, Behshad Noori, Joan Cardona, and Patrick Carels

Abstract This paper describes the experimental assessment of the acoustic performance of a two-story building constructed adjacent to a train station in Barcelona (ES). The building has been isolated at the top of the foundation footings at the ground level. The acoustic performance of the isolation system has been investigated by means of an in-situ measurement campaign at different construction phases. The results of the measurement campaign have been used to validate the Building Base Isolation indicator implemented within the frame of the BIOVIB project. Keywords Building base isolation (BBI) · Train induced vibration · Building performance

1 Introduction Buildings, especially those near railway or subway networks, can be subjected to ground-borne vibrations resulting in an unacceptable level of structure-borne noise and vibration for the occupants of the building. In order to protect a building from the consequential structure-borne noise and vibration, it is necessary to decouple the building from the surrounding sources at the foundation level or at the columns or walls in an upper level by introducing a building base (vibration) isolation solution. The assessment of real insertion gain requires a comparison between the noise/vibration inside the building with and without the isolation system. However, in practice, when a building is isolated, a non-isolated building does not exist, and the real insertion gain is not measurable. Today, the required vibration attenuation and the performance of a Building Base Isolation (BBI) system is defined only in terms of the resonance frequency of a Single-Degree-Of-Freedom (SDOF) mass-spring system whereas the dynamic mass is taken as the building self-weight including a H. Masoumi (B) · P. Carels CDM Stravitec, Overijse 3090, Belgium URL: https://www.cdm-stravitec.com B. Noori · J. Cardona AV Enginyers, St Cugat del Vallès 08174, Spain © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_70

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portion of the equipment/furnishes defined by acousticians as the Acoustic Design Loads, and the spring stiffness is defined equivalent to the dynamic stiffness of the isolation bearings provided by the bearings manufacturers. However, in reality, this simple SDOF model cannot fully represent the real dynamic behavior of an isolated building with its flexible elements nor the vibration transmission mechanism from the substructure (non-isolated part) towards the superstructure (the isolated part). In the frame of BIOVIB project, “Building Insulation against Outdoor Vibrations”, considering the aforementioned effects, a new isolation performance indicator has been introduced [1, 2]. Furthermore, it has been shown that the real insertion gain would be influenced not only by the dynamic characteristics of the isolation bearings but also by the dynamic characteristics of the soil-foundation system as well as the vibration modes of the building’s floors [3, 4].

2 Building Isolation Performance Based on Power Flow Insertion Gain (PFIG), the acoustic performance of a BBI system can be defined as the ratio between the total power flow of the coming waves entering the superstructure in an isolated and that of a non-isolated building [3], as follows: ( ) ∏s,iso .PFIG (dB) = 10 log10 (1) ∏s,non-iso where .∏s = 21 Re{FsT · Vs } is the total power flow obtained by means of the vector of contact forces .(Fs) and the vector of velocities at bearing locations (Fig. 1). The vector of velocities and the forces are related to each other by the mobility of the building .(Ys): .Vs = Ys .· Fs. In the frequency range from 1 to 250 Hz, Villot et al. [4] have shown that Eq. (1) can be simplified and be presented in terms of the vibration Transmission Loss (TL) through the isolator as well as the building and foundation mobilities, as follows: ) ( [Yf ] + [Ys ] .BBI indicator (dB) = TL + 20 log10 (2) . [Ys ] The first term in Eq. (2), the Transmission Loss, can be either obtained by measuring the vibration level above (.Vs,iso ) and below (.Vf,iso ) the isolator: ( TL (dB) = 10 log10

.

2 Vs,iso

)

2 Vf,iso

or, can be calculated based on the mobility of the isolator and the building as:

(3)

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Fig. 1 A general model of the building base (vibration) isolation

( TL (dB) = 20 log10

.

[Ys ] [Ys ] + [YI ]

) (4)

where .Ys , .Yf and .YI are the mobility of the foundation, the building (the superstructure above the vibration cut) and the isolator, respectively. The mobility of a massless isolator depends only on the dynamic stiffness of the bearings: .YI = |iω/K∗iso |. The complex dynamic stiffness of the isolation bearing ∗ .Kiso = Kiso (1 + iη) can be obtained by means of the dynamic test of the isolation bearing where .η refers to the loss factor. The mobility of the building, however, depends on the participating mass of the building as well as on the resonance frequency of the building sub-elements such as the beams and the floors. The building mobility can only be obtained numerically using FEA (Finite Element Analysis) in the frequency domain. The second term in Eq. (2) acts as a correction factor and it considers the effect of the dynamic soil-foundation interaction. The mobility of the foundation can be determined by different methods: 1. Experimentally measured in-situ by hammer-impact test; 2. Numerically calculated using Finite Element modelling of the soil and the foundation [5]; 3. Analytically calculated using the foundation impedance given in the literature for different types of foundation and soil [6]. In practice, assuming the isolated building as a simplified SDOF (mass-spring) system, Eq. (4) can be formulated as a function of the resonance frequency, .fres , of the SDOF system:

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⎛√

⎞ 2 )2 + η 2 (1 − β ⎠ .TL (SDOF) (dB) = −20 log10 ⎝ 1 + η2

(5)

√ where .β = ffexc is the excitation frequency ratio and .fres = 1/2π Kiso /Ms is the res resonance frequency of the isolation system. .Ms denotes to a part of the superstructure mass that participates at the main vibration mode which would not be practically equal to the building mass. In the design phase, to predict the performance of the future building, the Transmission Loss in Eq. (2) can be replaced by a simplified formula given for a SDOF system in Eq. (5). In the following, a hybrid experimental-numerical methodology is proposed to assess the BBI indicator. To examine the proposed hybrid approach, a two-story building constructed adjacent to a train station, was selected whereas the building has been seated on top of the steel reinforced rubber bearings installed between concrete grade beams and the footings, as shown in Fig. 2.

Fig. 2 The scheme of the two-story building isolated on top of the footings

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3 Hybrid Experimental-Numerical Methodology The proposed methodology has three parts: 1. Part 1: The mobility of the building (super-structure) calculated numerically by means of FEA (Finite Element Analysis) in frequency domain; 2. Part 2: The foundation mobility, .Yf = |Vf /Ff |, measured by in-situ hammer impact test in the absence of the building; 3. Part 3: (a) In the absence of the building, the foundation response is obtained by measuring train pass-bys on the foundation. (b) After the completion of the building, the transmission loss (TL) is obtained by measuring the vibration level below and above the isolation bearings due to the train passages.

3.1 Part 1: Mobility of the Building (Super-Structure) To determine the mobility of the building, a plane strain 2D-Finite Element model of the building has been made, with three supports, as shown in Fig. 3. The concrete frame including the floors, beams and columns has been modeled with the plain strain 2D shell elements. The mobility of the building is defined as the frequency response of the building (super-structure) at different bearing locations due to a unit vertical force applied at the bearing location .Ys,ij = Vs,ij /Ps,i . Therefore, for a 2D model of the building with three supports, the mobility is presented as a.3 × 3 matrix: .Ys = [Ys,ij ]3×3 , where .Ys,ij refers to the vertical response of the building at point . j due to the vertical load applied at point .i.

Fig. 3 2D—finite element modeling of the building

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Fig. 4 The mobility of the building calculated by FEA

Figure 4 shows the diagonal entries of the building mobility matrix. Disregarding the cross-spectrum mobilities, in the following, the building ∑3 mobility can be given Ys,ii . as an average of the auto-spectrums mobilities: .Ys = 13 i=1 It can be seen that the building mobility which is mostly dominated by the mass effect .Ys ≈ |1/ωMs |, has been locally affected by the bending modes of the building.

3.2 Part 2: Mobility of the Foundation (Sub-structure) In the second step, an in-situ measurement campaign was carried out to obtain the foundation mobility using an instrumented hammer. Because of similarities of the footings, the mobility has been measured only at one of the footings. Figure 5 shows the correction factor obtained by means of the measured foundation mobility and the calculated building mobility. The correction factor becomes more pronounced and increases by 2–5 dB at frequencies above 30 Hz where the mobility of the foundation shows a higher value in comparison to the mobility of the building.

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Fig. 5 (left) The mobility of the foundation (the blue line) compared with the building mobility (the red line). (right) The correction factor based on the building and foundation mobilities

3.3 Part 3: The Building and Foundation Responses The train pass-bys have been measured on top of the foundation and inside the building on the floors at different construction phases: 1. After the construction of the foundation and prior to the building construction 2. After the building construction. At the first phase, the train pass-bys are measured on top of the foundation. The vibration level at free foundation can be used for a better understanding of the groundborne vibration characteristics and, eventually, for applying the final adjustment on the isolation design before the installation. The floor vibration has been measured once at the end of the concrete structure construction while only self-weight of the structure has been applied on the bearings and again, after the completion and furnishing of the building when the bearings have been received the total permanent load as well as a part of service loads. Figure 6 displays the spectrum of the train pass-bys vibrations measured on the building floors (above the vibration cut) and those measured on top of the foundation (below the vibration cut). It’s worth mentioning that the peak at 10 Hz corresponds to the resonance frequency of the isolation system. When comparing floor vibrations during various construction stages, a clear enhancement in transmission loss (resulting in reduced floor vibrations) of around 5 dB was achieved. This improvement was observed when measurements were taken after the installation of final floor coverings, partitions, walls, and the facade. This progress can be attributed to two key factors. Firstly, the bearing loads are better aligned with the acoustic design load due to the inclusion of these final elements. Secondly, the floor vibration benefits from increased damping as a result of the addition of final coverings and partitions. Finally, the building performance has been calculated using the performance indicator in Eq. (2) where an average of about 12 dB in the frequency range of interest

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Fig. 6 The average train pass-by vibrations measured on top of the foundation (grey line), on top of the floor after completion of the concrete structure (gray dashed line) and after completion and furnishing of the building (black line)

Fig. 7 The BBI indicator (black line) and the transmission loss (grey line) measured after the completion and furnishing of the building

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(31.5–63 Hz) has been obtained (Fig. 7). In addition, a comparison has been made between the BBI indicator and the measured transmission loss (TL) to show the effect of the mobility modification factor.

4 Conclusions The application of the BBI indicator has been examined by means of a hybrid experimental-numerical approach. It has been shown how the performance of the building can be affected by the mobility correction factor of about 2–5 dB at frequencies above 31.5 Hz which falls within the primary frequency range of train-induced vibrations. This impact can be even more pronounced when the foundation is seating on a relatively soft soil (exhibiting higher foundation mobility). In addition, the building performance demonstrates an improvement of about 5 dB when the measurement were taken after furnishing the building, compared to those obtained in the construction stage when only the self-weight of the concrete structure (the permanent load) contributed to the dynamic system. Acknowledgements The results presented in this paper have been obtained within the frame of the BIOVIB project (in collaboration with ACOUPHEN) funded by VLAIO and EUROSTARS. Their financial support is gratefully acknowledged.

References 1. Masoumi H, Veelhaver B, Papadopoulos M, Augusztinovicz F, Carels P (2021) Evaluation of BBI performance indicator in a full-scale test bench. In: Degrande G, Lombaert G, Anderson D, de Vos P, Gautier P-E, Iida M, Nelson J, Nielsen JCO, Thompson DJ, Tielke T, Towers DA (eds) Proceedings of the 11th international workshop on railway noise. Notes on numerical fluid mechanics and multidisciplinary design, vol 150. Springer, Cham, Switzerland, pp 267–274 2. BIOVib project: “Building Isolation against Outdoor Vibration” Project Reports, CDM and ACOUPHEN, EUROSTARS-VLAIO projects. Sept 2017–March 2019 3. Talbot JP, Hunt HEH (2000) On the performance of base-isolated buildings. Build Acoust 7(3):163–178 4. Villot M, Trévisan B, Grau L, Jean P (2019) Indirect method for evaluating the in-situ performance of building base isolation. Acta Acust 105:630–637 5. Jean Ph, Villot M (2015) A comparison of 2D, 2.5D and 3D BEM models for the study of railway induced vibrations. In: Proceeding of Euronoise conference, Maastricht, The Netherlands 6. Sieffert JG, Cevaer F (1992) Handbook of impedance functions: surface foundations. Ouest Editions, Nantes

Resilient Track Forms

Resilient Track Components Modelling Options for Time Domain Train-Track Interaction Simulation Qianqian Li, Egidio Di Gialleonardo, Roberto Corradi, and Andrea Collina

Abstract Resilient components are widely used in railway tracks. For time domain train-track interaction simulation, the components are usually considered as linear Kelvin-Voigt models. However, the dynamic properties of the resilient components are often dependent on frequency and static preload, and this requires alternative methods to be adopted. The current study aims at comparing four different rheological models for the viscoelastic behaviour of the resilient components: a linear KelvinVoigt model, a linear three-element parameter model, a linear five-element parameter model and a non-linear three element model. Except for the linear Kelvin-Voigt, the other three models are able to reproduce the dependence on frequency, and the nonlinear three-element model can also reproduce the dependence on static preload. The rheological models are used as the foundation of the rail in vertical direction to study the effect of the different options on train-track dynamic interaction. To that aim, their effects on track dynamics are first studied in frequency domain with unitlength track models comparing the dynamic characteristics of the proposed models. Then the investigation is extended to time domain train-track interaction simulation analysing the force transmitted to the ground. Remarkable differences of the results are observed in the frequency ranges associated with the wheelset-track coupled vibration and the resonance of the track. Keywords Train-track dynamic interaction · Track nonlinearity · Resilient track component

Q. Li (B) · E. Di Gialleonardo · R. Corradi · A. Collina Politecnico di Milano, 20156 Milan, MI, Italy e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_71

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1 Introduction Resilient track components are widely used in different types of tracks in various forms, such as the rail pads, the under sleeper pads, the continuous support of Embedded Rail Systems, with the main objective to tune the track stiffness and therefore to optimise the train-track interaction performance. For the study of train-track dynamic interaction in time domain, in most cases the resilient track components are represented by Kelvin-Voigt models whose parameters are constant. However, it is also well acknowledged that the dynamic properties of the resilient track components, which can be comprehended as the equivalent stiffness and damping (considering the resilient track component as a Kelvin-Voigt model), are usually dependent on different parameters, mainly frequency, static preload and dynamic strain amplitude [1, 2]. Due to the strong influence on the overall track stiffness, for a precise prediction of the track response, the dependence of the dynamic properties of the resilient track components on different parameters should be properly modelled and considered in the numerical modelling of train-track interaction. The current work aims at comparing four rheological models as the modelling options of the resilient track components, one of which is non-linear, for the frequency- and preload-dependent dynamic properties. In Sect. 2, the equivalent dynamic properties of the modelling options are studied and compared in frequency domain. Then, the effect on the track dynamic characteristics is assessed with unitlength track models in Sect. 3. After that, time domain wheelset-track simulation is performed to investigate the influence on the force transmitted to the ground induced by the moving wheelset and rail roughness excitation in Sect. 4.

2 Rheological Models for Resilient Track Components The proposed rheological models are presented in Fig. 1, which includes a linear Kelvin-Voigt model, a linear three-element model, a linear five-element model, and a non-linear three-element model [3]. The element parameters of the last model are dependent on static preload. The three-element model is composed of a spring with stiffness k 1 in parallel with a Maxwell model with stiffness k 2 and damping c2 . The equivalent stiffness and damping of the linear three-element model can be computed as (c2 ω/k2 )2 , 1 + (c2 ω/k2 )2 1 , ceq = c2 1 + (c2 ω/k2 )2

keq = k1 + k2

(1)

where ω is the angular frequency of deformation. Equation (1) implies that the equivalent stiffness of the model k eq is mainly contributed by k 1 for low frequency and

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Fig. 1 Rheological models for resilient track component modelling: a linear Kelvin-Voigt model; b linear three-element model; c linear five-element model; d non-linear three-element model (the element parameters are dependent on static preload)

approaches (k 1 + k 2 ) with increasing frequency. The approaching rate is determined by the ratio of c2 to k 2 . For the equivalent damping ceq , its value decreases from c2 to zero with increasing frequency. Similar to the composition of the model, the dynamic properties of the model can be seen as the sum of the dynamic property of the single spring and the ones of the Maxwell model in parallel. Indeed, the terms related to k 2 and c2 in Eq. (1) are respectively the equivalent stiffness and damping of a Maxwell model. For the same reason, the equivalent stiffness and damping of the linear five-element model can be computed as the sum of the single spring and two Maxwell models in parallel. Compared to the three-element model, the equivalent dynamic properties of the five-element model can have two asymptotes if the ratios of c2 to k 2 and c3 to k 3 are different, which allows the modelling of more complex dynamic behaviour. For the non-linear three-element model, the equivalent dynamic properties can be computed in the same form presented in Eq. (1), but the element parameters are now dependent on the static preload applied to the model. Taking the single spring as an example, its stiffness is computed as k1∗ (Fs ) = k1,0 (1 + Fs /F0 )β ,

(2)

where F s is the static preload applied on the model; k 1,0 is the reference stiffness of the single spring; F 0 is the reference value of the static preload; and β is a dimensionless parameter. The other two parameters k2∗ and c2∗ are computed in the same form of Eq. (2). Compared to other models, the non-linear three-element model can reproduce the dependence of the dynamic properties of the resilient track components on both frequency and static preload. For the present work, the parameters reported in Table 1 are used. They are based on the commonly adopted values for the frequency domain modelling of a rail viscoelastic foundation in vertical direction [4], which is composed of a linear elastic foundation (stiffness per unit length equal to 100 × 106 N/m2 ) with a constant loss factor (0.1). The reference static preload of the non-linear three-element model is set to 40 kN/ m because it corresponds to the value of a static distributed load on the track (rail on Winkler foundation) that leads to a uniform rail deflection which is equal to the one of the rail section under a single axle load, considering that the stiffness is equal to 100 × 106 N/m2 .

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Table 1 Parameters of the rheological models Rheological models Linear Kelvin-Voigt model

k 100 ×

Linear three-element model Linear five-element model Non-linear three-element model

c 106

7.4 × 103

k1

k2

c2

60 × 106

40 × 106

0.19 × 106

k1

k2

c2

60 × 106

30 × 106

1.28 × 106 30 × 106 1.62 × 106

k3 β

c3

k 1,0

k 2,0

c2,0

60 × 106

10 × 106

0.05 × 106 0.505

F0

N/m2

Damping parameters c*

N s/m2

Static preload reference value F 0

N/m

40 × 103

Units of parameters Stiffness parameters k *

Static preload dependence factor β /

The equivalent dynamic properties of the rheological models are computed from 0 to 250 Hz and are presented in Fig. 2. The results of the linear models are reported in part (a) while the ones of the non-linear model with different static preloads are presented in part (b). Regarding the equivalent stiffness shown in part (a), the values of the three- and five-element models increase with frequency as implied by Eqs. (1) and (2). For the five-element model, the trend is almost bilinear with a rapid increase below 20 Hz and a slow one for higher frequency. With the employed data, all the models have similar equivalent stiffness around 200 Hz. Concerning the equivalent damping reported in

Fig. 2 Equivalent stiffness, damping of the rheologic models: a linear models; b linear and nonlinear three-element models. – – Linear elastic spring with constant loss factor; blue line indicates linear Kelvin-Voigt model; red line indicates linear three-element model; yellow line indicates linear five-element model; violet line indicates non-linear three-element model with no static preload; green line indicates non-linear three-element model with static preload (40 kN/m)

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part (a), the values of all models but the linear Kelvin Voigt model decrease with frequency. For the non-linear three-element model, the results are computed for two cases (static preload equal to 0 and 40 kN/m) and are compared to the ones of the linear three-element model. The results of the equivalent stiffness are strongly dependent on the static preload while the dependence of the equivalent damping is less remarkable. The difference of the equivalent stiffness between the non-linear (40 kN/m static preload) and linear model is negligible around 200 Hz.

3 Unit-Length Track Models To study the impact of the different rheological models on track dynamics, a unitlength track model configuration is used. The unit-length track model consists of a unit-length rail on a foundation represented by the various rheological models and is essentially a single degree-of-freedom system. Although the unit-length track model does not take into consideration the deformability of the rail, it can still lead to a couple of important comments on the dynamic characteristics of the track. The track Frequency Response Functions (FRFs) are presented in Fig. 3 in terms of rail receptance. The results of the linear models are reported in part (a) while the ones of the non-linear model with different static preloads are presented in part (b). For all the linear track models, the FRFs suggest that the resonance is located around 205 Hz. The values are similar because the equivalent stiffness represented by the various models are comparable around 200 Hz. The natural frequency of the sectional rail model is named as the “cut-on frequency” of the rail supported by an

Fig. 3 Frequency Response Functions of the unit-length track models (rail receptance): a linear models; b linear and non-linear three-element models. – – Linear elastic spring with constant loss factor; blue line indicates linear Kelvin-Voigt model; red line indicates linear three-element model; yellow line indicates linear five-element model; violet line indicates non-linear three-element model with no static preload; green line indicates non-linear three-element model with static preload (40 kN/m)

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elastic foundation [4]. The rail vibration is an evanescent wave below such frequency and corresponds to a propagating wave above it. Consequently, the dynamic characteristic of the track is dominated by the foundation stiffness below the cut-on frequency, the foundation damping around the cut-on frequency, and the rail properties above the cut-on frequency. Thus, the frequency range under discussion is limited to 250 Hz since the rail deformability is not taken into account in the sectional model. The difference between the moduli is mainly observed in the resonance zone. The magnitude relationship coincides with the one of the equivalent damping presented in Fig. 2. Regarding the non-linear three-element model, the reasoning is similar for the case where a 40 kN/m static preload is applied. However, when the static preload is low, the resonance of the sectional track model decreases significantly to around 170 Hz. The decrease of the cut-on frequency varies the properties of the waves with the frequency between 170 and 205 Hz, which are evanescent with the linear track models but are propagating with the non-linear three-element model.

4 Time Domain Wheelset-Track Interaction Simulation To better investigate the effect of the various foundations, time domain wheelsettrack interaction simulation is performed. The scheme of the simulation model is presented in Fig. 4. The simulation model consists of a Finite Element (FE) track model with rail roughness, a moving wheelset, and linear Hertzian contact springs between the rails and wheels. The wheelset moves from the left end towards the right one with constant speed v (200 km/h). A flexible wheelset model is used which describes the wheelset

Fig. 4 Scheme of the time domain wheelset-track interaction simulation model

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motion adopting the mode superposition technique [5]. Three bending modes (at 69, 132 and 268 Hz) are included. The wheelset mass is approximately 1700 kg. The static load on each wheel F s equals 55 kN. The wheel-rail contact force is described by a non-linear Hertzian contact relationship,  3/2 FH = G H y − z r,0 ej2π/λr x − w ,

(3)

where GH is the Hertzian coefficient and is equal to 0.69 × 1011 N m2/3 . The track model is composed by the FE rails (60E1) on the foundation made up of a set of rheological models connecting the FE nodes and the ground. The model length L is 160 m, and the mesh size l is 0.08 m so that the finite-element-passing frequency is higher than the frequency range under discussion (0–250 Hz). The structural damping of the rail is taken into account through the Rayleigh damping parameters α and β which are set to 0 and 2e−5. The spectrum of the rail roughness amplitude (zr,0 ) is presented in Fig. 5. The amplitude is defined according to ISO 3095 [6] for components whose wavelengths are shorter than 0.7 m and according to ORE B176 [7] for components with longer wavelengths. The defect level is between the small and large levels defined by the ORE B176 to guarantee the continuity of the roughness amplitude at 0.7 m. The excitation frequencies f d of the roughness components are converted from the wavelength λr to the frequency f d with the wheelset moving speed ( f d = v/λr ). The simulation is completed by performing numerical integration with Newmark method (the integration step equals 2 × 10–5 s). No static preload is assigned to the non-linear rheological models and the instantaneous load applied to them is used to compute the parameter values at each integration step. Therefore, the static preload on a single non-linear rheological model varies according to the position of the wheelset and results in a variation of the equivalent dynamic properties of the rheological model itself. To investigate the possible effects of the different foundation models on ground vibration, the one-third octave band spectra of the transmitted force in the middle of the track section are computed (based on a 1 s time window centred

Fig. 5 Spectrum of the rail irregularity/roughness components used for time domain wheelset-track interaction simulation. The wavelength is converted to excitation frequency considering a constant wheelset speed of 200 km/h

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Fig. 6 One-third octave band spectra of the transmitted force in the middle of the 160 m long track section induced by the wheelset passage at 200 km/h (the axle load is 110 kN) and the rail roughness excitation. The transmitted force is converted to force per unit length of the track models. Blue line indicates linear Kelvin-Voigt model; red line indicates linear three-element model; yellow line indicates linear five-element model; violet line indicates non-linear three-element model

at the time instant of the wheelset passage, i.e., 1.44 s) and presented in Fig. 6. It should be noted that the transmitted force at a single FE node depends on the mesh size. Thus, the results are converted to unit length of the track model. The spectra obtained with linear track foundations have similar trends, which are quite different to that with the non-linear foundation. Nonetheless, the differences between the transmitted force levels computed with the linear foundations are not negligible for some bands. For instance, the levels computed with the linear three-/ five-element model foundation are about 3.5 dB higher than the one with the linear Kelvin-Voigt foundation at the bands centred at 80 Hz. Similar comments can be raised regarding the bands centred at 62.5, 200 and 250 Hz. The levels of the transmitted force obtained with the non-linear foundation are significantly higher than those of linear foundations for the bands centred at 50, 62.5, 80 and 200 Hz. The higher levels of the bands below the cut-on frequency are associated with the higher amplitudes of the wheelset-track coupled vibration. Concerning the 200 Hz band, the evanescent waves for the linear foundations become propagating for the non-linear foundation and therefore the level becomes much higher (6–10 dB).

5 Conclusion The current paper investigates the effect of different modelling options for resilient track components on train-track dynamic interaction. Three linear and one non-linear rheological models are used to simulate the rail foundation. The investigated results are the forces transmitted to the ground. The results show that the different modelling options lead to remarkable differences. Specifically, there are two frequency ranges that are affected the most. The first one is the range associated with the wheelsettrack coupled vibration and the second one is around the cut-on frequency of the track model (the resonance zone of the unit-length track model). For linear modelling options, the difference is originated by the equivalent stiffness and damping of the rheological models. Concerning the non-linear model, the difference is also related

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to the non-linear dynamic characteristics of the foundation due to the changing load induced by the wheelset passage and rail roughness excitation. In particular, the frequency domain analysis shows that the equivalent dynamic properties of the nonlinear option are comparable to those of linear ones when it is loaded by the wheelset but are significantly different when it is not loaded. Since for most of the time of a wheelset/vehicle passage the track is not loaded, the different modelling options result in considerably different track responses.

References 1. Thompson DJ, Verheij JW (1997) The dynamic behaviour of rail fasteners at high frequencies. Appl Acoust 52(1):1–17 2. Johansson A, Nielsen JCO, Bolmsvik R, Karlström A, Lundén R (2008) Under sleeper pads— influence on dynamic train–track interaction. Wear 265(9–10):1479–1487 3. Li Q, Corradi R, Di Gialleonardo E, Bionda S, Collina A (2021) Testing and modelling of elastomeric element for an embedded rail system. Materials (Basel) 14(22):6968 4. Thompson DJ (2009) Railway noise and vibration. Elsevier 5. Di Gialleonardo E, Braghin F, Bruni S (2012) The influence of track modelling options on the simulation of rail vehicle dynamics. J Sound Vib 331(19):4246–4258 6. Acoustics—Railway applications—Measurement of noise emitted by railbound vehicles (ISO 3095:2013). BSI Standards Limited, UK (2013) 7. ORE B176 (1989) Bogies with steered or steering wheelsets. ORE, Utrecht

An Analytical Model in Frequency Domain for Embedded Rail Systems Leonardo Faccini, Federico Castellini, Stefano Alfi, Egidio Di Gialleonardo, Andrea Collina, and Roberto Corradi

Abstract The dynamics of railway track plays a fundamental role on the generation of ground-borne vibrations and rolling noise, that are among the main sources of discomfort related to urban railway lines. For this reason, an accurate model to represent the dynamics of urban tracks is needed for the quantitative evaluation of the vibro-acoustical impact of new vehicles or railway infrastructures. Several analytical models for the dynamics of railway tracks exist, but they are not suitable to describe the dynamics of embedded rail track systems, usually adopted for tramways, since they neglect the dynamic coupling between vertical and lateral dynamics. An analytical model for embedded rail systems is proposed and the results are compared with experimental tests on a track section of the Milan tramway network. As a general comment, a good agreement between experimental and numerical results is observed. As far as the track receptance in vertical direction is concerned, differences are highlighted. In this regard non-linearities typical of elastomeric elements seems to affect the overall track dynamics. Keywords Embedded rail system · Track dynamics · Multiple beam model

1 Introduction The dynamics of railway track plays a fundamental role on the generation of groundborne vibrations and rolling noise, that are among the main sources of discomfort related to urban railway lines. For this reason, an accurate model to represent the dynamics of the track is needed for the quantitative evaluation of the vibro-acoustical impact of new vehicles or railway infrastructures. Dynamic models representing the behaviour of railway track can be divided into two main groups: finite element-based models and analytical models. The L. Faccini (B) · F. Castellini · S. Alfi · E. Di Gialleonardo · A. Collina · R. Corradi Department of Mechanical Engineering, Politecnico di Milano, Via Giuseppe La Masa 1, 20156 Milano, Italy e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_72

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models belonging to the first group (e.g., [1, 2]) account for the non-linearities and the deformability of the rail cross-section, but require a relatively high computational time. On the other hand, analytical models are based on simplifications and assumptions, but the computational time required is much lower. For this reason, an analytical model is an attractive solution for sensitivity analyses to the effect of rail and/or fastening system parameters on the evaluation of noise and vibration issues related to the dynamics of wheel/rail interaction, but also in the experimental identification of track parameters. In analytical models representing the vertical dynamics of railway track [3, 4], the rail is modelled as an infinite Timoshenko beam laying on either discrete or continuous support. However, the same models are not suitable for the study of lateral dynamics at high frequency, since the lateral motion of the rail is strongly coupled with its torsion and, moreover, the deformability of the cross-section cannot be neglected [5]. Wu and Thompson [6, 7] developed a multiple beam model for track lateral dynamics that is able to account for the deformability of the crosssection involving the flexibility of the rail web. Since these models focus on a single direction of motion, their usage imply the hypothesis that vertical and lateral motion are dynamically decoupled. This assumption is reasonable if wheel-rail contact forces are aligned with the principal axes of the rail cross section, as in the case of Vignole rails (EN 13674-1) when the vehicle runs on straight track. However, most tramways adopt grooved rails (EN 14811), where a coupling between vertical and lateral motion occurs since the contact forces are not aligned with the principal axes of the rail cross-section, as represented in Fig. 1. The dynamic coupling between vertical and lateral directions is considered in the 3D model developed by Kostovasilis [8], along with shear center eccentricity and

Fy

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restrained warping effect. However, no cross-section deformation is accounted for, except for the axial deformation due to warping. The purpose of this work is the development of an analytical model in frequency domain for the study of the high-frequency dynamics of tramways adopting an embedded rail system (ERS). To this aim, the multiple beam model for lateral dynamics presented in [6] is extended to three dimensions to account for the dynamic coupling between vertical and lateral motion and, at the same time, for the deformability of the rail cross-section.

2 Analytical Model for Embedded Rail Systems An analytical model for ERS equipped with grooved rails has been developed by following the approach introduced by Wu et al. [6] extended to three dimensions. Railhead and foot are modelled as infinite Timoshenko beams, while the web is represented as an array of Timoshenko beam finite elements with infinitesimal dimension along the rail axis. The elastic material in which the rail is embedded is modelled as a continuous viscoelastic foundation acting on railhead and foot.

2.1 Equation of Motion of the Free Rail The key points of the rail cross-section and the adopted reference system are represented in Fig. 2a. The centres of gravity (CoG) of the cross-section of railhead and foot are indicated as C G h and C G f , respectively. The coordinates of the other points are expressed with respect to the CoG of the infinite beam to which they belong. The points Si represent the shear centres of the cross-sections, while Wi are the connection points between the infinite beams and the rail web, i.e. the nodes of the finite beam element. Finally, C P is the rail excitation point. The equation of motion of the rail is derived by imposing the dynamic equilibrium on the infinitesimal beam elements representing railhead and foot. The 12 degrees

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Fig. 2 Rail cross-section (a) and forces acting on the free infinitesimal beam element (b)

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of freedom of the rail are displacements (u h/ f,i ) and rotations (θh/ f,i ) of C G h and C G f , which are functions of time and of the coordinate x along the rail axis. The degrees of freedom are collected in the column vector u(x, t):  T  T u(x, t) = u h (x, t)u f (x, t) = u h,x u h,y u h,z θh,x θh,y θh,z · · ·

(1)

The forces and moments acting on the generic free infinitesimal beam element are represented in Fig. 2b, where Fi and Mi represent the internal forces and moments per unit length of the rail. The dynamic coupling between the two infinite beam is W W accounted for by the reaction forces Fh/ f,i and moments Mh/ f,i that they exchange with the beam finite element representing the web. These reaction are considered applied in the points labelled as Wh and W f in Fig. 2a. Thus, the equilibrium equations relative to the railhead can be written as: ⎧ ⎫ ⎫ ⎧ ⎧ W ⎫ Fh,x ⎪ ⎪ ⎪ ⎪ 0 ⎪ ∂ Fh,x /∂ x ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ W ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ Fh,y 0 /∂ x ∂ F h,y ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎨ ⎬ ⎬ ⎬ ⎪ ⎨ W ⎪ Fh,z 0 ∂ Fh,z /∂ x − [Mh ]u¨ h (x, t) + =0 + (2) W ⎪ ⎪ ⎪ 0 ⎪ Mh,x ⎪ ∂ Mh,x /∂ x ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ −F ⎪ ⎪ ∂ M /∂ x ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ MW ⎪ ⎪ ⎪ h,y h,z ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ⎩ ⎭ ⎭ ⎭ ⎪ ⎩ h,y W Fh,y ∂ Mh,z /∂ x Mh,z where u¨ h is the double derivative of the railhead displacement vector with respect to time and [Mh ] is the mass matrix per unit length of the infinite beam representing the railhead. The equilibrium equations relative to the rail foot have the same form. The analytical expression of the internal forces and moments are derived from the constitutive relationships of a Timoshenko beam along with the stress–strain relationship. The detailed calculation procedure can be found in [8]. The effect of the shear center eccentricity is accounted for in the calculation of the internal forces, while restrained warping effect is neglected and homogeneous torsion only is considered. The structural damping of the rail is included through a loss factor equal to 0.02 [4]. By substituting the analytical expression of internal forces in the equilibrium equations, the equation of motion of the free rail can be written as: −[D]u  (x, t) − [G]u  (x, t) + [K ]u(x, t) + [M]u(x, ¨ t) + F W = 0

(3)

where u  indicates the derivative of the displacement vector with respect to the coordinate x along the rail axis, while F W contains the reaction forces that the web exchanges with railhead and foot, which need to be calculated.

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2.2 Reaction Forces As mentioned above, the dynamic coupling between railhead and foot occurs by means of the reaction forces and moments that railhead and foot exchanges with the web, as represented in Fig. 3. The reference system in the figure is relative to the web beam finite element. The reaction forces are derived from the equations of motion of the beam finite element representing the web, whose nodes are the connection points Wh and W f :

F Wf F hW



 

W u Wf u¨ f = [Mweb ] W + [K web ] W u¨ h uh

(4)

where u Wf / h are the displacements and rotations of W f / h , F Wf / h are the reaction forces and moments in W f / h and [Mweb ] and [K web ] are the mass and stiffness matrix of a 3D Timoshenko beam finite element, whose expression can be found in [9]. The properties of the beam finite element are calculated considering that it has length h W and a cross-section (2–3 plane) equal to bW d x. From Eq. (4) it is clear that the reaction forces at the nodes are expressed as a function of the node displacements u Wf and u hW . The displacements of the nodes are derived from the displacements of the infinite beams CoGs by assuming that their cross-section undergoes a rigid motion. Fig. 3 Reaction forces per unit length that web exchanges with railhead and foot

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Since the equation of motion of the infinite beams are referred to their CoGs, the force vector F W in Eq. (3) is obtained from F Wf and F hW by considering appropriate transport moments and has the form: ¨ F W = [MW ]u(x, t) + [K W ]u(x, t)

(5)

where the 12 × 12 matrices [MW ] and [K W ] represent the contribution of the web finite element which must be added to the mass and stiffness matrices of the infinite beams. Thus, the motion equations of the rail becomes:     − [D]u  (x, t) − [G]u  (x, t) + K˜ u(x, t) + M˜ u(x, ¨ t) = 0   M˜ = [M] + [Mw ]   K˜ = [K ] + [K w ]

(6)

2.3 Embedded Rail System Dynamics The material in which the rail is embedded is modelled as a continuous elastic foundation. Since the rail is completely embedded within the resilient material, both the railhead and the foot are considered continuously supported through springs and dampers connecting their CoG to the ground. Two contributions to the damping are used: viscous damping and hysteretic damping, through loss factors, to account for the hysteretic behavior of the rubber-like material. The stiffness of the elastic bed is distributed between the springs acting on the rail-head and rail foot on the basis of the corresponding supported surface. In the calculation of stiffness values, it is assumed that the elastic material works only in compression, while the effect of shear is neglected. The values of viscous damping and loss factors should be determined experimentally for the specific material constituting the embedding materials. Since the springs and dampers representing the embedding material are applied directly on the CoGs of the infinite beams, the effect of the support on the equation of motion can be added by diagonal damping and stiffness matrices:   [K s ] = diag kh,x kh,y kh,z kh,θx kh,θy kh,θz · · · [Cs ] = diag ch,x ch,y ch,z ch,θx ch,θy ch,θz · · ·

(7)

The external harmonic forces, indicated as Fext eit , are applied on the railhead in correspondence of the point labelled as CP in Fig. 2a, that represents the contact point between the wheel and the rail. The external forces are acting at a longitudinal coordinate corresponding to x = 0. Appropriate transport moments are used to refer

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the contact forces to the railhead CoG. By assuming an harmonic response of the rail in both space and time, the displacement vector can be written as: u(x, t) = U e−ikx eit

(8)

where U is the vector of the complex amplitudes, k are the wavenumbers and  is the circular frequency of excitation. Therefore, the equation of motion of the ERS can be reformulated as:       − k 2 [D] + ik[G] − 2 M˜ + i[Cs ] + K˜ + [K s ] U e−ikx = F ext δ(x) (9) where δ is the Kronecker’s delta. The displacements and rotations of the CoGs of railhead and foot are obtained by following the approach proposed by Wu et al. [6] based on Laplace Transform and contour integration. The complex amplitudes of the displacements of the excitation point, i.e., the receptances, can be derived from the railhead CoG displacement by assuming that railhead cross-section undergoes a rigid motion: ⎧ ⎫ ⎧ ⎫ ⎡ ⎫ ⎤⎧ 0 −h,z h,y ⎨ 0 ⎬ ⎨ UC P,x ⎬ ⎨ Uh,x ⎬ = U + ⎣ h,z U 0 −h,x ⎦ eCy P ⎩ CP ⎭ ⎩ C P,y ⎭ ⎩ h,y ⎭ UC P,z Uh,z −h,y h,x 0 ez

(10)

3 Results The proposed modelling approach is used to represent the dynamic behaviour of an ERS with grooved rails of type 62R1 (EN 14811). The rail geometry is imported into a CAD software to derive the geometrical parameters of railhead and foot crosssections. An impact test has been performed on a section of the Milan tramway network adopting the embedded rail system under analysis: the railhead has been excited along vertical (z) and lateral (y) directions with an impulse hammer and the induced vibration response in correspondence of the excitation points is measured by means of piezoelectric accelerometers. Numerical vertical, lateral and cross receptances have been compared to the experimental ones. A good agreement between analytical and experimental curves is observed along the lateral direction (Fig. 4b). Conversely, the track receptance in vertical direction (Fig. 4a) shows a slightly different trend, except for the frequency region close to the resonance peak at about 220 Hz related to the rail vibrating on the vertical stiffness of the elastic bed. This difference in the dynamic behaviour reflects also on the cross receptance (Fig. 4c). The discrepancy between experimental and numerical vertical receptance may be caused by modelling the embedding material as a single elastic layer foundation. The equivalent dynamic stiffness and damping of elastomeric elements of ERSs

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Fig. 4 Comparison between experimental and analytical receptances. Point vertical receptance (a), point lateral receptance (b) and vertical-lateral cross receptance (c)

are frequency dependent due to the non-linearities typical of rubber-like materials. In particular, their equivalent stiffness increases with frequency while the equivalent damping decreases [10, 11]. Probably this effect is more pronounced along the vertical direction with respect to the lateral one. For this reason, a rheological model that accounts for the non-linearities of the elastic bed should be employed to better reproduce the high frequency dynamics of the ERS. The rheological model must be built by performing experimental dynamic tests of the elastomeric material in which the rail is embedded.

4 Conclusions A three-dimensional analytical model in frequency domain has been developed to represent the dynamics of Embedded Track Systems (ERS), typically adopted for tramways. Railhead and foot are modelled as infinite Timoshenko beams, while the web is schematized as an array of Timoshenko beam finite elements. The model accounts for the dynamic coupling between vertical and lateral directions, neglected

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in the most of the analytical models for track dynamics, and for deformable modes of the rail cross-section that involves the flexibility of the web. The stiffness of the embedding material is represented through springs acting on the centres of gravity of railhead and foot. The model is used to study the dynamics of an ERS adopting 62R1 grooved rails and the obtained results are compared to the experimental receptances derived from an impact test. Analytical results have a good agreement in terms of receptance along the lateral direction, while a slightly different behaviour is observed in the vertical response. This discrepancy is related to the modelling of the elastic bed as an elastic foundation. A non-linear rheological model should be used to better reproduce the dynamics of an embedded track system. Future developments of this work are envisaged, as the introduction of a rheological model of the rail support and the adoption of the proposed track model for the study of vibro-acoustic problems related to the dynamics of wheel-rail interaction, e.g. ground-borne vibrations, curve squeal noise occurrence, etc.

References 1. Betgen B, Squicciarini G, Thompson DJ (2015) On the prediction of rail cross mobility and track decay rates using Finite Element Models. In: Proceedings of the 10th European congress and exposition on noise control engineering, Maastricht, pp 2019–2024 2. Zhang X, Thompson DJ, Li Q, Kostovasilis D, Toward MGR, Squicciarini G, Ryue J (2019) A model of a discretely supported railway track based on a 2.5D finite element approach. J Sound Vib 438:153–174 3. Grassie SL, Gregory RW, Harrison D, Johnson KL (1982) Dynamic response of railway track to high frequency vertical excitation. J Mech Eng Sci 24(2):97–102 4. Thompson DJ (2009) Railway noise and vibration: mechanisms, modelling and means of control. Elsevier Ltd., Oxford, UK 5. Grassie SL, Gregory RW, Johnson KL (1982) The dynamic response of railway track to high frequency lateral excitation. J Mech Eng Sci 24(2):91–95 6. Wu TX, Thompson DJ (1999) Analysis of lateral vibration behavior of railway track at high frequencies using a continuously supported multiple beam model. J Acoust Soc Am 106(3):1369–1376 7. Wu TX, Thompson DJ (2000) Application of a multiple-beam model for lateral vibration analysis of a discretely supported rail at high frequencies. J Acoust Soc Am 108(3):1341–1344 8. Kostovasilis D (2017) Analytical modelling of the vibration of railway track. PhD Thesis, University of Southampton 9. Palazzolo A (2016) Vibration theory and applications with finite elements and active vibration control. Wiley 10. Li Q, Corradi R, Di Gialleonardo E, Bionda S, Collina A (2021) Testing and modelling of elastomeric element for an embedded rail system. Materials 14(22):6968 11. Li Q, Dai B, Zhu Z, Thompson DJ (2021) Improved indirect measurement of the dynamic stiffness of a rail fastener and its dependence on load and frequency. Constr Build Mater 304:124588

Bridge Noise and Vibration

A Rapid Calculation of the Vibration of the Bridge with Constrained Layer Damping Based on the Wave and Finite Element Method Quanmin Liu, Yifei Sun, Peipei Xu, and Lizhong Song

Abstract As an important part of rail transit, the vibration and noise of bridges have been a hot issue in recent years. The vibration and noise problem of steel–concrete composite bridges is more serious than that of concrete bridges. The vibration characteristics of steel–concrete composite bridges with and without constrained layer damping are studied based on the wave and finite element method and superposition principle. Firstly, based on the wave finite element method, a calculation model of the vibration response of a steel–concrete composite bridge is established, and the calculation results using this method agree well with those obtained by the traditional FEM and the field measurement. The dominant frequency band of the bridge vibration is 63–100 Hz and 500–1000 Hz, and the peak appears at 80 Hz. Secondly, the segment model of the bridge with constrained layer damping is established. The dynamic equation is constructed using the stiffness and mass matrix from the model to solve its response under the wheel-rail force. The constrained layer damping can reduce the vibration acceleration level of steel components by 5–10 dB. The influence of material and thickness of constraining layer on the vibration reduction is analyzed. Keywords Composite bridge · Vibration · Mitigation · Constrained layer damping · Wave and finite element method

1 Introduction The noise caused by the train running of high-speed railway and urban rail transit is becoming more and more severe. As an important part of rail transit, the vibration and noise of bridges have been a hot issue in recent years. Q. Liu (B) · Y. Sun · P. Xu · L. Song MOE Engineering Research Center of Railway Environmental Vibration and Noise, East China Jiaotong University, Nanchang 330013, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_73

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Scholars have studied the vibration and noise of bridges, Ngai and Ng [1], Song et al. [2] and Zhang et al. [3] used the finite element method (FEM) and the boundary element method (BEM) to predict the vibration and noise of a concrete bridge. Based on the statistical energy analysis (SEA) method, Bewes et al. [4], Li et al. [5] and Liu et al. [6] established a rapid calculation model to predict noise and vibration from steel or composite bridges. Both FEM and BEM are able to take the complex geometry of bridges into account in the calculation of the structure-borne noise from railway bridges or viaducts. However, the computation is not efficient for high-frequency vibration of large scale structures. The SEA method is suitable for medium- and high-frequency vibration analysis and its applicable frequency is much wider than FEM, but the calculation accuracy of SEA method is dependent on the estimation of modal density, damping loss factor and coupling loss factor which are difficult to be obtained exactly. The wave and finite element method (WFEM) is proposed to calculate the wave characteristics and vibration response of waveguide structure in 1973. Started from the equation of motion of a repeated segment of structure, this method makes full use of the advantages of finite element analysis software, and is implemented to predict the dynamic response of the structure efficiently. Early applications of the WFEM mainly focused on one-dimensional waveguide structures such as pipes. Mace et al. [7] used WFEM to study the dispersion characteristics and modes of waves in waveguide structures such as uniform viscoelastic laminates. Waki et al. [8] investigated the difficulties that an improved WFEM might encounter in a numerical calculation and studied the vibration characteristics of tires using this method. In recent years, the application of the WFEM in railway tracks has also gradually expanded [9]. At present, the study of structure-borne noise of bridge is mainly focused on concrete bridges. The steel–concrete composite bridge is also one of the common bridge forms in rail transit because of its light weight and low cost. Moreover, compared with concrete bridges, the vibration and noise problem of steel–concrete composite bridges is more serious. Therefore, the vibration characteristics of steel– concrete composite bridges are studied through WFEM in this paper. Based on the contact-filtered roughness and the receptances of the wheel, track, and contact, the wheel-rail forces are computed in the frequency domain by moving roughness model. The accuracy of the WFE models is verified by comparing the computed results with the tested ones and the calculation efficiency of the WFE model is compared with the FE model. The vibration response of the bridge with constrained layer damping (CLD) is also calculated and the results before and after CLD treatment are compared. Finally, the influence of material and thicknesses of constraining layer on the vibration reduction is investigated.

A Rapid Calculation of the Vibration of the Bridge with Constrained …

767

2 Methodology of WFEM 2.1 Equation of Motion Based on WFEM The equation of motion of a cell can be written as [10] (K + jωC − ω2 M)q = f

(1)

where K, C, M represent the stiffness matrix, damping matrix, and mass matrix, respectively; q and f represent the vector of the nodal degrees of freedom, nodal force vector; ω is the angular frequency; j is the imaginary unit; D = K +jωC−ω2 M is defined as the dynamic stiffness matrix. Because the waveguide structure is homogeneous along the y-axis, the propagation coefficient of the motion of the structure along the y-axis can be defined as e−jky , where k is the wavenumber. The structure is divided into N segments, and Eq. (1) is written as a matrix form      DLL DLR qL f = L (2) DRL DRR qR fR where the subscripts L and R represent the left and right cross-sections of the cell, respectively. Because the structure along the y-axis is uniform and the dynamic stiffness matrix is symmetrical, so ⎧ T ⎨ DLL = DLL DT = DRL ⎩ TLR DRR = DRR

(3)

where the superscript T indicates the transpose. When two segments of the waveguide structure is taken into account, it can be shown in Fig. 1. If no external force affects internal nodes, dynamic equations can be expressed as ⎤⎡ ⎤ ⎡ ⎤ fL DLL DLI O qL ⎣ DIL DII DIR ⎦⎣ qI ⎦ = ⎣ 0 ⎦ O DRL DRR qR fR ⎡

where O is a zero matrix, subscript I represents the intermediate section

Fig. 1 Two segments of a waveguide structure

(4)

768

Q. Liu et al.

qI = −D−1 II (DLI qL + DIR qR )

(5)

Eliminate the degrees of freedom of the intermediate cross-section 

˜ LR ˜ LL D D ˜ ˜ DRL DRR



 qL f = L qR fR

(6)

Therefore, for cross-sections without external forces, the global stiffness, damping, and mass matrices of the waveguide structure can be obtained by eliminating the internal degrees of freedom. With the introduction of boundary conditions and external forces, the dynamic equation of the whole structure is established, and the vibration response can be obtained by solving the equation.

2.2 Response of Waveguide Structures In practice, the waves are reflected at the boundary of the structure. Assuming that the amplitude of the incident wave is a+ and the reflected wave is a− , then a − = Ra +

(7)

where R is the reflection coefficient matrix. The boundary conditions can be expressed as Af + Bq = 0

(8)

f and q represent the boundary node forces and degrees of freedom, respectively, while the elements in the matrices A and B are usually related to complex numbers and frequencies. Using the wave relation, the reflection coefficient matrix can be expressed as R = −(Aφf− + Bφq− )−1 (Aφf+ + Bφq+ )

(9)

Taking the waveguide structure with a length of L as an example in Fig. 2, it is subjected to a force f ext at y0 , and the amplitudes a+ and g− are the sum of the direct excitation waves e+ and e− and the incident waves g+ and a− , a + = e+ + g + , g − = e− + a − Introducing the wave propagation matrix Γ (y)

(10)

A Rapid Calculation of the Vibration of the Bridge with Constrained …

769

Fig. 2 Waves amplitudes in a finite waveguide structure

⎡

e− jk1 y 0 ⎢ 0 e− jk2 y ⎢ (y) = ⎢ . .. ⎣ .. . 0 0

··· ··· .. .

0 0 .. .

⎤ ⎥ ⎥ ⎥ ⎦

(11)

· · · e− jk N s y

The propagation and reflection relationship can be expressed as c+ = (L − y0 )a + , d − = (y0 )g −

(12)

If RL and RR are the reflection coefficient matrices of the left and right boundaries, waves c+ and d − are reflected at the left and right ends respectively and generate waves c− and d + c− = R R c+ , d + = R L d − , a − = (L − y0 )c− , g + = (y0 )d +

(13)

According to the above relationship, a+ and a− can be expressed as   a + = {I − (y0 )R L (L)R R (L − y0 )}−1 e+ + (y0 )R L (y0 )e− a − = (L − y0 )R R (L − y0 )a +

(14) (15)

By analogy, the amplitude b+ and b− at any position y can be written as b+ = (y − y0 )a + , b− = (L − y)R R (L − y)b+

(16)

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3 Case Study 3.1 Model of the Bridge Without CLD Study has shown that the noise from steel–concrete composite bridges is 5 ~ 20 dB higher than that from the plain track [11]. The secondary dead load of the bridge is 160 kN/m. In order to make the finite element model closer to the actual situation, the material density of the deck element is increased correspondingly. The parameters of bridge and track can be found in [12].

3.2 Model of the Bridge with CLD The noise of the web of the composited bridge is dominant in most frequency bands, so the most reduction of vibration can be achieved by laying the CLD on the web. Since the CLD laid on the steel beam serves in the normal environment temperature, the maximum loss factor of the selected viscoelastic material should occur at the normal temperature for the achievement of the highest damping of the bridge under working condition. When the vibration analysis of the bridge with CLD is conducted, the parameters of the constrained layer damping are listed in [13].

3.3 Model Validation Reference [14] uses the superposition principle to analyze the vibration response of track subject to multiple wheel-rail forces assuming that the whole system is linear. The superposition principle is employed to compute the dynamic response of the bridge under the action of multiple wheel-sets in this paper. Table 1 shows the calculation time of the two methods under the same device. The WFE model shows a significant advantage in memory space and computation efficiency over the traditional FE model. The acceleration level of the bottom flange is shown in Fig. 3a. Calculations of WFEM and FEM are consistent with each other and share the tread with the measured response in the frequency domain. The peak of acceleration level appears at 80 Hz Table 1 Comparisons of the calculation cost by FE and WFE models Model

Number of elements

Number of nodes

Model file (kB)

Result file (kB)

Computing time (min)

FE

15,702

15,953

101,632

40,121,472

83

370

390

42

126

9

WFE

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771

Test FE WFE

Acceleration level (dB,Ref=1×10 -6m/s 2)

120 110 100 90 80 70

25

40

Acceleration level (dB,Ref=1×10-6m/s2)

and the dominant frequency range is from 63 to 100 Hz, 500 to 1000 Hz respectively. The measured acceleration level after installing the CLD is shown in Fig. 3b. It can be found that the calculation results by the method in this paper are in agreement with the measured data within 500 Hz mostly. The possible reasons for the differences in the high-frequency band are as follows: (1) There are still some inevitable differences of the parameters between the simulation and the field measurement; (2) Essentially WFEM is still a kind of finite element method, and the accuracy of the high-frequency band depends on the mesh dimension. In order to compare the accuracy and efficiency of shell and solid elements, the response by solid element is also computed in this paper. It can be seen from Fig. 4a that the simulation results about bridge without CLD using two types of elements are close to each other. However, the computation cost of shell element is about a quarter of solid element, as shown in Table 2.

Test Computed

120

110

100

90

80

70

63 100 160 250 400 630 1000 1600

25

1/3 octave center frequency (Hz)

40

63

100

160

250

400

630 1000 1600

1/3 octave center frequency (Hz)

(a)

(b)

Fig. 3 Measured and computed acceleration level of bottom flange: a without CLD; b CLD 120 Test Solid Shell

120

110

100

90

80

70 25

40

63

100

160

250

400

630 1000 1600

1/3 octave center frequency (Hz)

(a)

Acceleration level (dB,Ref=1×10-6m/s2)

Acceleration level (dB,Ref=1×10-6m/s2)

130

Bare CLD

110

100

90

80

70

60

25

40

63

100

160

250

400

630 1000 1600

1/3 octave center frequency (Hz)

(b)

Fig. 4 a Acceleration level of the bottom flange using solid and shell elements; b acceleration level of the bottom flange: Bare and CLD

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Table 2 Comparisons of the calculation cost by shell and solid elements Element type

Number of elements

Number of nodes

Model file (kB)

Computing time (min)

Shell

370

390

42

9

Solid

546

2044

38,553

34

The acceleration level before and after webs of bridge are treated by CLD is shown in Fig. 4b. It can be found that the installed CLD can reduce the vibration of all frequency bands. The constrained layer damping can reduce the vibration acceleration level of steel components by 5–10 dB. The result indicates that CLD is quite effective to mitigate the vibration of composite bridges.

4 Conclusions Based on the WFE method, a framework to predict the vibration responses of bridges with CLD is presented and verified in this paper. The influence of properties of the constraining layer on the vibration reduction is investigated. The conclusions drawn from the study are as follows: (1) The treatment of CLD can significantly reduce the vibration in all frequency bands and is quite suitable for controlling the vibration of steel structures. (2) Compared with the traditional FEM, WFEM improves the calculation efficiency several times without the loss of accuracy. (3) The dominant frequency of vibration of the steel–concrete composite bridge induced by a moving train is 63–100 Hz and 500–1000 Hz, and the peak appears at about 80 Hz.

References 1. Ngai KW, Ng CF (2002) Structure-borne noise and vibration of concrete box structure and rail viaduct. J Sound Vib 255(2):281–297 2. Song XD, Wu DJ, Li Q, Botteldooren D (2016) Structure-borne low-frequency noise from multi-span bridges: a prediction method and spatial distribution. J Sound Vib 367:114–128 3. Zhang X, Li XZ, Hao H et al (2016) A case study of interior low-frequency noise from box-shaped bridge girders induced by running trains: Its mechanism, prediction and countermeasures. J Sound Vib 367:129–144 4. Bewes OG, Thompson DJ, Jones CJC, Wang A (2006) Calculation of noise from railway bridges and viaducts: Experimental validation of a rapid calculation model. J Sound Vib 293(3):933– 943 5. Li XZ, Liu QM, Pei SL et al (2015) Structure-borne noise of railway composite bridge: numerical simulation and experimental validation. J Sound Vib 353:378–394

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6. Liu QM, Liu LY, Chen HP et al (2020) Prediction of vibration and noise from steel/composite bridges based on receptance and statistical energy analysis. Steel Compos Struct 37(3):291–306 7. Mace BR, Duhamel D, Brennan MJ, Hinke L (2005) Finite element prediction of wave motion in structural waveguides. J Acoust Soc Am 117(5):2835–2843 8. Waki Y, Mace BR, Brennan MJ (2009) Free and forced vibrations of a tyre using a wave/finite element approach. J Sound Vib 323(3):737–756 9. Fabre F, Theyssen J, Pieringer A, Kropp W (2021) Sound radiation from railway wheels including ground reflections: a half-space formulation for the Fourier boundary element method. J Sound Vib 493:115822 10. Zhong WX, Williams FW (1995) On the direct solution of wave propagation for repetitive structures. J Sound Vib 181(3):485–501 11. Thompson DJ (2009) Railway noise and vibration: mechanisms, modeling and means of control. Elsevier, Oxford, pp 359–397 12. Liu QM, Li XZ, Zhang X et al (2020) Applying constrained layer damping to reduce vibration and noise from a steel-concrete composite bridge: an experimental and numerical investigation. J Sandwich Struct Mater 22(6):1743–1769 13. Liu QM, Li XZ, Xu PP et al (2020) Acoustic radiation and dynamic study of a steel beam damped with viscoelastic material. KSCE J Civ Eng 24(7):2132–2146 14. Wu TX, Thompson DJ (2001) Vibration analysis of railway track with multiple wheels on the rail. J Sound Vib 239(1):69–97

Study on Devices to Reduce Pass-by Noise Along Viaducts with Snow-Removing Openings Toshiki Kitagawa, Toki Uda, Kiyoshi Nagakura, Kaoru Murata, and Hiroki Aoyagi

Abstract In heavy snowfall areas in Japan, a new Shinkansen train network is scheduled to open in the near future. The construction of viaducts with snow-removing openings on the floor slab has been planned to effectively remove snow on railway tracks during the winter. However, the noise generated by Shinkansen vehicles is directly radiated from the openings. In this study, an attempt is made to understand the acoustical performances of devices to reduce the noise radiated from the openings using both laboratory measurements on scale models and field tests in full-scale with running Shinkansen vehicles. The effects of 14 types of devices on Shinkansen noise are investigated in the scale model studies and Shinkansen noise is effectively reduced by approximately 10 dB at locations below the viaduct and at 25 m to the side for devices with sound-absorbing materials. The effects of the devices on Shinkansen noise were almost equal in the field tests to those obtained in the laboratory measurements. Keywords High-speed railway · Wayside noise · Acoustic measurement · Viaduct

1 Introduction In heavy snowfall areas in Japan, a new Shinkansen train network is scheduled to open in the near future. The construction of viaducts with snow-removing openings (hereafter, “open-type viaduct”) has been planned to effectively remove snow on railway tracks (see Fig. 1a). There are openings on the floor slab along the tracks in the viaducts, through which snow on the track is removed to the ground by snowplow vehicles. However, the noise generated by the Shinkansen vehicles is directly radiated T. Kitagawa (B) · T. Uda · K. Nagakura · K. Murata Environmental Engineering Division, Railway Technical Research Institute, Noise Analysis, 2-8-38, Hikari-cho, Kokubunji-shi, Tokyo, Japan e-mail: [email protected] H. Aoyagi Japan Railway Construction, Transport and Technology Agency, Yokohama, Japan © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_74

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(a)

T. Kitagawa et al.

(b)

Anechoic room Vehicle

Open-type viaduct

Device Ground Fig. 1 a Overview of the viaduct with snow-removing openings, b laboratory measurements by using 1/25 scale models

from the openings, and pass-by noise along the viaduct can be greater than that along the viaduct without the openings (hereafter, “normal viaduct”). In this study, an attempt is made to understand the acoustical performances of the devices to reduce the noise radiated from the openings (hereafter, “opening noise”) using both laboratory measurements on scale models (see Fig. 1b) and the field tests at fullscale with running Shinkansen vehicles. The effects of various device shapes and sound-absorptive materials, which are installed on the inner walls of the devices, on Shinkansen noise are studied. The devices were installed in the openings of the viaducts in the field tests, and the effects of the devices on Shinkansen noise were investigated.

2 Laboratory Measurements 2.1 Measurement Set-Up and Data-Processing In the laboratory measurements, the acoustical performances of 14 types of devices were investigated using a 1/25 scale model. Schematic examples of the devices in full-scale dimensions are shown in Fig. 2. The devices were set around the openings of the open-type viaducts. The devices are composed of tubes with a rectangular crosssection. The lengths of the device are 4 m (Devices 1-1 and 2-1), 6 m (Devices 1-2 and 2-2), 1 m (Device 3-1) and 3 m (Device 3-2). The sound-absorbing material could be installed on the inner walls of the devices, with sound absorption coefficients of approximately 0.8 above 800 Hz (corresponding to 20 kHz in the 1/25 scale model). The partition plates could be installed in the internal space of Devices 3-1 and 3-2 in order to increase the area of the installed sound-absorbing materials. A straight-type barrier with a height of 3.5 m is also installed. Shinkansen noise mainly consists of noise generated from the lower part of vehicles (hereafter, “lower part noise”), aerodynamic noise generated from the upper

3m

1m

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6m

4m

6m

4 m 3.5 m

Study on Devices to Reduce Pass-by Noise Along Viaducts …

(a) Device 1-1 (b) Device 1-2 (c) Device 2-1 (d) Device 2-2 (e) Device 3-1 (f) Device 3-2

Fig. 2 Devices to reduce the noise radiated from the openings of the open-type viaduct

part of the vehicles (hereafter, “aerodynamic noise”), and bridge noise. The contributions of the three sources using the Shinkansen noise prediction model [1] when the Shinkansen train runs at 260 km/h on the normal viaduct are shown in Table 1. This estimate was made at a distance of 25 m from the adjacent track and 8.8 m below rail level (hereafter, “PL 25”). The lower part noise has greater contribution to the total noise. The trends are similar to those seen in newly developed Shinkansen vehicles [2]. In the measurements, both the lower part and aerodynamic noise were modeled as a line source. For the lower part noise, a line source was located under a vehicle. The line source was also arranged on the top of the vehicle to simulate the aerodynamic noise. To estimate the representative sound power spectra for the two noise sources, it is assumed that the shapes of the spectra are the same as those shown in [1]. By using the Shinkansen noise prediction model [1], the OAs of the spectra are tuned to be equal to the contributions of the two noises at PL 25 shown in Table 1. The measured data were analyzed using a multichannel FFT analyzer. The following procedures were used to analyze the results; (1) apply a scale factor (n = 25) to both frequency and dimensions (distances and heights) according to the acoustic similarity law [3], (2) estimate the difference, ΔSPL ( f ), in noise level at each 1/3 octave band center frequency, f , between two measuring points, where one is positioned closest to the source and the other is positioned around the viaduct, (3) add the difference, ΔSPL ( f ), to the representative spectra, and (4) calculate the overall level as the sum of the estimated results in (3). The contributions of the bridge noise at the measuring points are predicted using the Shinkansen noise prediction model. Table 1 Contribution of the three noise sources using the Shinkansen noise prediction model Aerodynamic noise generated from the upper part of vehicles

Noise generated from the lower part of vehicles

Bridge noise

Total noise

60.2

68.5

61.0

69.7

Condition: viaduct [10 m in height (Rail level to ground level)], slab track, plain barrier (3.5 m in height), 10 cars, 260 km/h. The measuring point is located 25 m away from the adjacent track and 8.8 m below rail level. Unit: dBA

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2.2 Results of the Laboratory Experiments Table 2 shows the total noise levels at PL 25. For the normal viaduct, the total noise is below 70 dB at PL 25, while, for the open-type viaduct, the total noise is above 80 dB and the lower part noise has greater contribution to the total noise. This suggests that the opening noise mainly consists of the lower part noise. For the devices without the sound-absorbing materials set inside of the devices, the results are greater by approximately 5 dB than those for the normal viaduct. In these cases, the lower part noise would still be a significant source. This indicates that the lower part noise was screened by the device but propagated from the openings of the device to the wayside. The noise levels for most of the devices with sound-absorbing materials are below 70 dB at PL 25, which is almost equal to the result of the normal viaduct, and a greater noise reduction of approximately 10 dB can be observed. This suggests that the opening noise is effectively reduced by the synergy effect of the attenuation of the sound-absorbing materials in the device and the multiple sound reflections within the device. However, the results of the devices with sound-absorbing materials, such as Devices 1-1 and 2-1, are somewhat different. This could be due to the difference in sound fields in the devices or the difference in area between the sound-absorbing materials set inside of the devices. For the results of Device 3-1, the noise level is above 70 dB at PL 25. This could be because the lower part noise propagates from the openings without proper attenuation of the sound-absorbing materials. However, the noise levels are lower than 70 dB Table 2 Total noise levels. Shinkansen train runs at 260 km/h Device

Sound-absorbing materials

Partition plate

PL 25, adjacent track

PL 25, remote track

1-1

✓

None

69.5

68.3

1-1

None

None

77.1

76.4

1-2

✓

None

68.7

67.0

1-2

None

None

74.6

73.7

2-1

✓

None

69.1

67.4

2-1

None

None

76.3

75.0

2-2

✓

None

68.5

67.0

2-2

None

None

74.9

73.7

3-1

✓

None

71.6

70.8

3-1

✓

✓

70.7

70.2

3-2

✓

None

69.1

67.2

3-2

✓

✓

68.8

67.0

Normal viaduct

69.7

67.8

Open-type viaduct

80.6

78.8

✓, installed, Unit: dBA.

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779

for the results of Device 3-2. This indicates that the length of the device must be at least longer than 1 m to properly reduce the opening noise. The result of Device 3-2 (3 m) is almost equal to that of Device 2-2 (6 m). This means that better acoustic properties could be obtained by arranging the geometric shape of the devices. Figure 3 shows the separate contributions of the lower part and aerodynamic noise of Devices 3-1 and 3-2 at PL 25, respectively. The contribution of the lower part noise is greater by 5 to10 dB than that of the aerodynamic noise in the frequency range of 250–2500 Hz for the normal viaduct. This suggests that, even for the normal viaduct, the lower part noise is dominant. Furthermore, the lower part noise of the open-type viaduct is significantly greater than that of the normal viaduct over the entire frequency range. This indicates that, for the open-type viaduct, the lower part noise is dominant. Without partition plates, the lower part noise of Device 3-1 is greater than that of Device 3-2. This suggests that the length of Device 3-1 is so short that even partition plates do not effectively reduce the opening noise. The lower part noise of the results of Device 3-2 with partition plates is almost equal to that of the normal viaduct in most one-third octave bands. This means that the lower part noise is effectively reduced because of the sound-absorbing materials installed on the inside of the device. The noise reduction effect of the device is greater when partition plates are set inside the device. 90

A-weighted SPL (dB)

80

70

60

50 125

250

500

1k

2k

4k

OA

Frequency (Hz) Fig. 3 Separate contribution of the lower part noise and aerodynamic noise at PL 25. The vehicle is located at the track adjacent to the measuring point. The Shinkansen train runs at 260 km/h. Gray dotted line and gray square, aerodynamic noise; gray line and gray circle, lower part noise of normal viaduct; gray dashed line and gray triangle, lower part noise of open-type viaduct; black line and black circle, lower part noise of open-type viaduct with Device 3-1 with partition plates; black dashed line and black square, lower part noise of open-type viaduct with Device 3-2 with partition plates

(a)

Distance from adjacent track centre (m)

(b)

Distance from adjacent track centre (m)

Height above the ground (m)

T. Kitagawa et al. Height above the ground (m)

780

Distance from adjacent track centre (m)

(b)

Distance from adjacent track centre (m)

Height above the ground (m)

(a)

Height above the ground (m)

Fig. 4 Spatial distributions in overall A-weighted sound pressure level. a Normal viaduct, b opentype viaduct. Shinkansen train runs at 260 km/h

Fig. 5 Spatial distributions in overall A-weighted sound pressure level of the viaduct with Device 2-2. a Without sound-absorbing materials, b with sound-absorbing materials

Figure 4 shows the spatial distributions of the overall A-weighted sound pressure level in the normal and open-type viaducts. The overall levels for the normal viaduct are higher only at the measuring points above the barrier. However, for the opentype viaduct, the overall levels are higher at the measuring points both under the viaduct and above the barrier. This is because the opening noise has significantly greater contribution to the overall levels at the points under the viaduct. The spatial distributions for Device 3-2 are shown in Fig. 5. The overall levels for the results of Device 2-2 without the sound-absorbing materials remain higher at the points below the viaduct. This indicates that the lower part noise is still radiated from the openings of the devices. The result of Device 2-2 with the sound-absorbing materials is similar to that of the normal viaduct and Device 2-2 has a noise reduction effect of more than 10 dB at PL 25. This is because the lower part noise is effectively reduced by the synergy effect of the attenuation of the sound-absorbing materials and multiple sound reflections within the device.

3 Field Tests 3.1 Measurement Set-Up and Data-Processing The effects of the acoustic properties of the devices in full-scale on Shinkansen railway noise are investigated. Running measurements were performed for two sections of the Shinkansen railway line. The two sections have the same type of viaduct and track. One of the two sections is open-type viaducts (hereafter, “Section

Study on Devices to Reduce Pass-by Noise Along Viaducts … (a)

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(b)

Fig. 6 Photograph of the measurement section. a Section A, b Section B

A,” see Fig. 6a), whereas the other section consists of test devices with a total length of 50 m installed on the snow-removing openings of the same open-type viaducts, as Section A (hereafter, Section B, see Fig. 6b). The test device was a 2-m long rectangular cross-section tube. The sound-absorbing materials were installed inside the device. The tests were performed at various speeds ranging from 200 to 260 km/ h. Measurements were taken in both sections at the following positions during a train pass-by: • a microphone at 2 m laterally from the center of the track and 0.43 m above the railhead (the “P2” location), • a microphone at 25 m laterally from the center of the track (the “P25” location). Furthermore, microphone array measurements were carried out 25 m laterally from the center of the track (the “PA” location), which is located at the same location as P25. This is because the total length of the devices was so short that the properties of the devices could not be properly examined using the microphone at P25 only.

3.2 Overall Trends Figure 7 shows the overall noise in dB(A) plotted against train speed. In these figures, 0 dB denotes the maximum overall level at P2. For the measurements at P2, the results at the two sections have similar trends and increase at a rate of approximately 20log10 V, where V is the train speed. This indicates that the sound power of the lower part noise in Section A is almost equal to that in Section B and the rolling noise has greater contribution to the total lower part noise. At P25, the difference between the measurements of the two sections is approximately 6 dB, which is also due to the noise reduction effects of the devices. This is because the noise propagating to the measuring points at P25 in Section B is effectively reduced by the synergy effect of the attenuation of the sound-absorbing materials and the multiple reflections of sound within the device.

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Fig. 7 Overall noise in dB(A) plotted against train speed. a P2, b P25, c PA. Black line and black circle, Section A; gray line and gray circle, Section B. 0 dB denotes the maximum overall level at P2. V denotes train speed

For the results measured with the microphone array at PA, the noise reduction effect is up to 10 dB greater. This effect is significantly greater than that measured using the microphone at P25. This is because the noise radiated from the open-type viaducts adjacent to Section B affects the results measured with the microphone at P25. The results measured at both sections at PA increase at a rate of approximately 20log10 V. This suggests that the lower part noise also has greater contribution the total noise at the two sections.

3.3 Spectral Results Figure 8 shows the noise spectra at 260 km/h for the two sections. In the figure, 0 dB denotes the maximum overall level at P2. For the noise spectra at P2, the results in Section A are almost equal to that in Section B above 250 Hz. This again indicates that the sound power of the lower part noise in Section A is almost equal to that in Section B. The components with

Fig. 8 Spectra of the measured noise. Black circle, Section A; gray circle, Section B. a P2, b P25, c PA. 0 dB denotes the maximum overall level at P2

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frequencies ranging from 630 to 3150 Hz have greater contribution to the overall levels. The shape of the results measured at P25 in Section A is similar to those at P2 in the frequency range of 630 to 3150 Hz. This implies that in Section A, the lower part noise has greater contribution to the results measured at P25. The difference in level between the results of the two sections can be observed over the entire frequency range. This indicates that the device significantly reduced the dominant components generated from the openings of the open-type viaduct. For the measurements at PA, the results measured in Section B are approximately 10 dB lower than those measured in Section A over the entire frequency range. The components in this frequency range have greater contribution to the total noise in Section A. This suggests that the dominant frequency components of the lower part noise are effectively reduced by approximately 10 dB by the device. The results measured in the field tests agree well with those in the laboratory measurements. Therefore, when the devices are installed on the open-type viaducts all along the line, the noise levels at the wayside of the open-type viaduct are almost equal to those at the normal viaducts.

4 Conclusions The acoustical performances of the devices for reducing noise radiated from the openings were investigated using laboratory measurements on 1/25 scale models. Furthermore, the effect of the devices developed through the laboratory measurements was examined using full-scale field tests with running the Shinkansen vehicles. The following are the conclusions: (1) The result for the devices with the sound-absorbing materials is almost equal to that of the normal viaduct and a noise reduction effect of more than 10 dB at locations below the viaduct and at 25 m to the side can be seen. This is because the lower part noise is effectively reduced by the synergy effect of the attenuation of the sound-absorbing materials and multiple sound reflections within the device. (2) The results of the measurements with the microphone array in Section B (opentype viaducts with the device) are approximately10 dB lower than those in Section A (open-type viaducts without the device) over the entire frequency range. The results obtained in the field tests agree well with those obtained in the laboratory.

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References 1. Nagakura K, Zenda Y (2002) Prediction model of wayside noise level of Shinaknsen. Wave 2002:237–244 2. Sawamura Y, Uda T, Kitagawa T, Yokoyama H, Iida A (2021) Measurement and reduction of the aerodynamic bogie noise generated by high-speed trains in terms of wind tunnel testing, noise and vibration mitigation for rail transportation systems. Springer, Switzerland, pp 73–80 3. Ishi S, Tachibana H (1975) Scale model experiment on architectural acoustics and noise control. Television 29(11):942–950 (in Japanese)

Bridge Noise Reduction by Acoustic Short Circuit Yuanpeng He, Xinghuan Wang, Qing Zhou, Xiaozhen Sheng, and Yulong He

Abstract When a train passes through the bridge structure, the low-frequency structural noise radiated by the bridge often is an important noise source disturbing nearby residents. The noise affects the quality of life and even causes harms to the physical and mental health of nearby residents. Therefore, more and more scholars begin to study how to effectively reduce the structural noise of the bridge. Currently, the treatment principle of brige noise mainly focuses on vibration isolation, vibration absorption, and optimization of the dynamic characteristics of bridges, very few researches have taken advantage of ascoutic short circuit principle to control the bridge noise. This article firstly analyzes the noise contribution volume of various parts of a bridge, controlling the bridge noise by utilizing the ascoutic short circuit principle based on the contribution of various plates of the bridge structure. Keywords Acoustic short circuit · The structure acoustic finite element element method · Bridge noise

1 Introduction In order to save urban space and reduce construction cost, many railway lines are laid on viaduct bridges. However, when a train passes through the bridge structure, the low-frequency structural noise radiated by the bridge often is an important noise Y. He (B) · X. Wang · Q. Zhou State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, Sichuan, China e-mail: [email protected] X. Sheng School of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai 201620, China Y. He Faculty of Geosciences and Ground Engineering, Southwest Jiaotong University, Chengdu 610031, Sichuan, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_75

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source disturbing nearby residents. The noise affects the quality of life and even causes harms to the physical and mental health of nearby residents [1, 2]. Therefore, more and more scholars begin to study how to effectively reduce the structural noise of the bridge [2–5]. At current moment, the treatment principles of bridge noise mainly focus on vibration isolation [4, 6–8], vibration absorption [9, 10], optimization of bridge dynamic characteristics [11–14] and reduction of wheel-rail excitation sources [15] etc. Apart from that, Putra and Thompson [16, 17] utilized ascoutic short circuit principle to generate sound radiation efficiency calculation formular for rectangular opening plate. They have investigated the influences on sound radiation efficiency of plates by the hole numbers of opening plates, hole size, opening rate. The result showed that the opening of slabs would reduce sound radiation efficiency; when holesizes were uniform, higher the opening rate of plates, lower sound radiation efficiency would be; when opening rate for plates showed consistent, smaller hole size was, lower sound radiation efficiency would be. At present, there are few studies on bridge noise in this area. From research it is found that for the bridge structure which is mostly used in China, the main sound source of bridge noise is the top and wing slabs. If noise from the wing slab were removed, sound pressure level at the railway noise assessment point could be reduced by about 6–8 dB of bridge noise. Acoustic short-circuit principle is often used for reducing low-frequency noise from a slab [16, 17]. Due to the weak directivity of low-frequency sound, sound radiation directions on both sides of the slab are just opposite, that is, the phase difference is 180°. Because the wavelength of low-frequency sound wave is very long and its diffraction ability is very strong, it can be diffracted more easily by opening holes, so as to offset the sound pressure on both sides. Therefore, openings on a slab are conducive to reducing the low-frequency sound radiation. Bridge noise is low-frequency structural noise, therefore, the acoustic short-circuit principle may be used to reduce the radiation efficiency of the wing slab of the bridge structure, offering a solution to the problem of bridge noise.

2 Establishment of Vibration and Acoustic Radiation Model for Bridge 2.1 Model Establishment This section gives a description to the modelling approach. A flowchart of prediction is shown in Fig. 1. As pointed out above, it involves two parts, a vehicle-track-bridge interaction part, and acoustic radiation model.

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Fig. 1 A flowchart of prediction of noise radiation from concrete box girders

Vehicle model. Here prediction of vehicle dynamics is to calculate the vibration of vehicles due to a unit harmonic wheel/rail force, generating a receptance matrix for the vehicles at the wheel/rail contact points. The model of track-bridge system. In the past, most scholars used beam element or beam shell mixed element to do the modeling for the bridge [18]. However, when the frequency is high enough, the bridge vibration no longer satisfies the rigid crosssection assumption. When the frequency is high, the bridge is prone to local modal shapes, and because of the large chamfer between the wing slab and the web of the bridge structure, it is difficult to simulate the transition section of chamfer well by using the slab element. In order to better simulate the actual vibration of the bridge, the solid element (20 nodes high-order hexahedron element) is used to model the one line simply supported box girder. The track structure on the bridge is ordinary fastener plate ballastless track, the thickness of slab is 0.2 m, the thickness of self compacting concrete is 0.16 m, the rail type is CHN 60 rail, and the fastener type is WJ-8 fastener system. The bridge FEM with holes with a diameter of 0.75 and a spacing of 1.5 m on the wing plate. Wheel-rail interaction. Vehicle-track-bridge system interaction models developed in the past may be grouped into two categories: moving roughness models [1] and moving vehicle models [19, 20]. The main difference between moving roughness model and moving vehicle model lies in that the moving vehicle model has parameter excitation [19] (such as sleeper-passing, axle-passing, vehicle-passing etc.). But

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under the condition when the speed is lower than 200 km/h, the influence incurred by roughness excitation is greater than influence of parameter excitation. Although the sleeper-passing frequency falls into the frequency range analyzed in this paper, the corresponding excitement of sleeper-passing frequency is not significant. The moving roughness model has been adopted by a great number of literatures, and the measured result has verified that it has a pretty good characteristic of consistency [18, 21]. The studies from literatures and authors indicate that, when the speed falls into the studied speed range by the paper, the two models can be regarded as equivalent for their analysis of bridge vibration and noise. Therefore, the moving roughness model [1] is suitable in this paper. Acoustic radiation model. Acoustic FEM is used to establish the bridge structure radiation model. To achieve accurate calculations, the element size on the bridge surface is shorter than 0.28 m, which is approximately 1/6 of the shortest acoustic wavelength at 200 Hz with a sound speed of 340 m/s.

2.2 Model Validation In order to verify the model, this paper uses the measurement results of literature to verify the model. Figure 2 shows the 1/3 octave band diagram of the structural noise of measurement point under the bridge floor (Observation point S). The train runs at a speed of approximately 140 km/h, and there is no hole in the bridge. The joint wheel-rail roughness spectrum is consistent with the Ref [15]. In Fig. 2, the model has some uncertainty in the input parameters, resulting in some discrepancies between the measured and predicted results in the low frequency band (below about 40 Hz). Fortunately, the measured and predicted results are in good agreement in terms of trend and dominant frequency, proving that the prediction method for bridge structure noise in this paper is feasible. In order to explore the reason why the noise pressure level of the bridge structure has a peak at 63 Hz, the wheel rail force spectrum of the first wheelset vehicle is given according to the above method of calculating wheel-rail force, as shown in Fig. 2b. It can be seen from the figure that the peak value of the wheel rail resonance force (P2 resonance force) appears near 63 Hz. It can be seen that the wheel rail resonance force (P2 force) in this frequency range is an important reason for the increase of sound pressure level.

3 Results Figure 3 shows total contribution of sound pressure levels at different sites. As shown in Fig. 3, except for S site close to bottom slab, wing plate is the major radiation sound source for box girder structure. Hence, when optimizing the design of box girder structure, if one wants to reduce radiation sound pressure level for box girder

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(a) Diagram of tested point 1.0x104

100

P2 resonance force Magnitude of wheel-rail force (N)

Sound Pressure Level (dB)

Measured results Predicted results 90

80

70

60

20

25

31.5

40

50

63

80

100

125

160

8.0x103

6.0x103

4.0x103

2.0x103

200

50

Frequency (Hz)

(b) Validation

100

150

200

Frequency (Hz)

(c) Wheel-rail interaction force

Fig. 2 Comparison between measurement and prediction

structure close to N1, N2 and N3 sites, it is suggested to start from the wing plate of box girders. Figure 4 gives the nephogram of the total sound pressure level radiated by the site at the midspan cross section before and after the opening of the wing plate. After making wing plate opening, it will affect greatly on the sound pressure level in the area above the right side of box girder, while the influence on the bottom zone of box girder is really small. Noise amplifying phenomenon for box girder structure even occurs at the certain areas underneath the bridge. It might be due to that the sound radiation for rail slab has been transmitted to the area underneath box girder through the openings on wing plate. Similar to wing opening, when design the web opening, the article has refered to the relevant requirement of opening round holes on the concrete structure web and designed three web opening schemes, as shown in Table 1. To compare the reduction effect of box girder structural noise generated by adopting the three schemes mentioned above, Table 2 presents the overall sound pressure level of box girder structural noise at N1, N2, and N3 locations for three different web opening schemes, where there is no opening in the flange plate.

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Fig. 3 Total contribution of sound pressure levels at different sites

100

94.6

Sound pressure level/dB

92.7

87.6

86.2 81.0

78.8

80 72.3

Slab Wing plate Web Bottom plate

71.4

73.1

75.2

79.7 72.3 72.5

74.2

72.5 67.7

60

40

20

S

N1

Site

N2

N3

Fig. 4 Distribution of noise reduction Table 1 Scheme of opening round holes for box girder web

Opening scheme

1

2

3

Opening diameter (m)

0.2

0.4

0.2

Opening spacing (m)

1

2

2

Table 2 Overall sound pressure level (dB) of structural noise at various sites of different schemes Holes unopened

Scheme 1

Scheme 2

Scheme 3

N1

86.0

85.9

86.1

85.8

N2

87.0

86.9

87.2

86.7

N3

82.2

82.1

82.0

82.0

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It can be inferred from Table 2 that the above three web opening schemes have no obvious effect on reducing the total sound pressure level of box girder structure noise at three standard points, and there will be a small increase in the total sound pressure level at individual sites. It is analyzed that the reasons for their failure may be: 1. The sound pressure within the box girder cavity may be higher than that outside the cavity. After making openings, the sound pressure inside the cavity may leak to exterior of cavity and result in that the sound pressure level at standard point is not reduced but increased instead. 2. It can be known from the calculation made in Sect. 2 about the sound radiation contribution of various slabs of box girder, for three standard sites, sound radiation contribution of wing plate is far greater than that of web, hence the opening on web cannot effectively reduce the overall sound pressure level at various sites. 3. The hole size of the openings at both sides of web is pretty small, which does not generate obvious impacts for large scale box girder structure.

4 Conclusion The article starts from the box girder structure to explore the feasible scheme of reducing box girder structural noise. On the basis of acoustic short circuit principle, the author has carried out the opening design for wing plate and web of 24 m single line simply supported box girde. Finally, the following conclusions have been drawn: 1. when the wing plate opening diameter is 0.75 m, opening spacing is 1.5 m, the overall sound pressure level reduction at N1 is 6.1 dB, the overall sound pressure level reduction at N2 is 6.8 dB, the overall sound pressure reduction at N3 is 3.2 dB, which proves to have a good noise reduction effect. 2. The sound pressure within the box girder cavity may be higher than that outside the cavity. After making openings, the sound pressure inside the cavity may leak to exterior of cavity and result in that the sound pressure level at standard point is not reduced but increased instead. Acknowledgements This study was supported by the National Natural Science Foundation of China (52002340, 52078433 and U1934203).

References 1. Thompson DJ (2009) Railway noise and vibration: mechanisms, modelling and means of control (Elsevier Press, Amsterdam) 2. Li Q, Song XD, Wu DJ (2014) A 2.5-dimensional method for the prediction of structure-borne low-frequency noise from concrete rail transit bridges. J Acoust Soc Am 135(5):2718–2726

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3. Costley RD, Diaz-Alvarez H, Mckenna MH et al (2012) Vibration and acoustic analysis of a trussed railroad bridge under moving loads. J Vib Acoust 137(3):617–629 4. Li X, Liang L, Wang D (2018) Vibration and noise characteristics of an elevated box girder paved with different track structures. J Sound Vib 425:21–40 5. Zhang YF, Li L, Lei ZY et al (2021) Environmental noise beside an elevated box girder bridge for urban rail transit. J Zhejiang Univ Sci 22(1):53–69 6. Li Q, Thompson DJ (2018) Prediction of rail and bridge noise arising from concrete railway viaducts by using a multilayer rail fastener model and a wavenumber domain method. J Rail Rapid Transit 232(5):1326–1346 7. Liang L, Li XZ, Zheng J et al (2020) Structure-borne noise from long-span steel truss cablestayed bridge under damping pad floating slab: experimental and numerical analysis. Appl Acoust 157:106988 8. He W, Zou C, Pang Y et al (2021) Environmental noise and vibration characteristics of rubberspring floating slab track. Environ Sci Pollut Res 28(11):13671–13689 9. Hanel JJ, Seeger T (1978) Schallgedaempfte Stahlkonstruktionen Im Brueckenbau-Grundlagen Und Erste Anwendung. Veroeffentlichungen Des Instituts Fuer Statik Und Stahlbau Der Th Darmstadt (32):166 10. Pepler RD, Vallerie LL, Jacobson ID et al (1978) Development of techniques and data for evaluating ride quality. Volume 2: ride-quality research. John A Volpe National Transportation Systems Center (Washington, US) 11. Thompson D, Jones C (2011) Reply to comments on chapter 12 of railway noise and vibration: mechanisms, modelling and means of control, by Thompson D (with contributions from Jones C, Gautier P-E). Appl Acoust 72(10):787–788 (Elsevier, 2009) 12. Janssens MHA, Thompson DJ (1996) A calculation model for the noise from steel railway bridges. J Sound Vib 193(1):295–305 13. Augusztinovicz F, Márki F, Carels P et al (2003) Noise and vibration control of the South Railway bridge of Budapest. In: Barham R, Piper B (eds) CD-ROM proceeding of the 11th international congress on noise and vibration. Stockholm: tenth international congress on noise and vibration, pp 1713–1720 14. Li Q, Dai B, Zhu Z et al (2022) Comparison of vibration and noise characteristics of urban rail transit bridges with box-girder and U-shaped sections. Appl Acoust 186:108494 15. He Y, Wang X, Han J et al (2022) Study on the influence of resilient wheels on vibration and acoustic radiation characteristics of suburban railway concrete box girder bridges. Appl Acoust 187:108529 16. Putra A, Thompson DJ (2011) Radiation efficiency of unbaffled and perforated slabs near a rigid reflecting surface. J Sound Vib 330(22):5443–5459 17. Putra A, Thompson DJ (2010) Sound radiation from perforated slabs. J Sound Vib 329(20):4227–4250 18. Zhang X, Li X, Hao H et al (2016) A case study of interior low-frequency noise from box-shaped bridge girders induced by running trains: its mechanism, prediction and countermeasures. J Sound Vib 367:129–144 19. Sheng X, Li M, Jones C et al (2007) Using the Fourier-series approach to study interactions between moving wheels and a periodically supported rail. J Sound Vib 303(3–5):873–894 20. Zhai WM, Wang KY, Cai CB (2009) Fundamentals of vehicle-track coupled dynamics. Veh Syst Dyn 47(11):1349–1376 21. Li Q, Li WQ, Wu DJ et al (2016) A combined power flow and infinite element approach to the simulation of medium-frequency noise radiated from bridges and rails. J Sound Vib 365:134–156

Comparison of Vibration Characteristics of Floating Slab Track in Rail Transit Viaduct with Time-Domain and Frequency-Domain Models Qingyuan Song

and Qi Li

Abstract Floating slab tracks have been widely adopted in rail transit viaducts to reduce the bridge vibration and structure-borne noise. To calculate the vibration of the coupled track-bridge systems, both time-domain and frequency-domain methods can be applied although their relative performance is not very clear. This study aims to compare the two methods and then provide some guidelines in choosing the appropriate method in the vibration prediction. The principle and methodology of the two calculation methods are firstly introduced, and the models for the train, track and bridge are developed using the same parameters. Comparison is made of the vibration of bridge and floating slab obtained from the two methods with different train speeds. It is found that the results from the two methods show good consistency in the frequency region above 20 Hz. It is shown that the results from different loading cases should be averaged with care when the frequency domain method is adopted. When using irregularity measured on site, the simulated vibration of floating slab and bridge from the two methods match well with the experimental results. Keywords Floating slab track · Bridge · Vibration · Coupled track-bridge systems

1 Introduction With the development of urban rail transit in China, the vibration and noise problems are becoming one of the hot focus in the rail transit field. In recent years, the floating slab tracks, which can reduce the vibration transmitted to the subgrade and bridge, have been widely adopted in rail transit systems, especially in the sections which are sensitive to environmental vibration or noise. Many methods have been proposed to obtain the vibration of bridges paved with floating slab tracks. A train-track-bridge coupled model in the time-domain is often established to calculate the vibration of the system subjected to track irregularities. Q. Song · Q. Li (B) Department of Bridge Engineering, Tongji University, 1239 Siping Road, Shanghai, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_76

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However, the computational cost is usually high with such methods for large track lengths and high frequency vibration [1]. Xu et al. [2] used the mode superposition method to calculate dynamic responses of train-bridge and train-track coupled systems. Few studies use this method for the train-track-bridge coupled systems with floating slab tracks. Compared to the time-domain method, the frequency-domain method has higher computational efficiency with the moving roughness assumption. Li et al. [3] established a frequency-domain theoretical model, taking into account the effect of multiple wheels, for the floating slab track to obtain the vibration characteristics of vehicle-track coupled system. Li and Wu [4] proposed a power flow analysis method for the vehicle-track-bridge system based on the force method which has the ability to model the rail, track and bridge with different models and arbitrary spring connections. This study aims to compare the accuracy of the power flow method and a time-domain model for the prediction of vibration of the floating slab track and the bridge. The structure of the paper is organized as follows. Section 2 introduces the principle of the train-track-bridge vibration prediction methods in both the time domain and the frequency domain. Section 3 introduces the model and related parameters of the two models. Section 4 compares the vibration of the bridge and floating slab calculated by two different methods. Section 5 gives the conclusions and guidelines for the selection of the method for vibration prediction.

2 Methodology 2.1 Time-Domain Method The time-domain method for train-track-bridge dynamic interaction analysis has been developed by Li et al. [5] based on modal superposition method. To account for the interaction between wheelsets, a multi-rigid body model is adopted for the single vehicle including one car body, two bogies, four wheelsets and related suspension springs. The rail, floating slab and bridge are all represented by corresponding finite element models, and the nonlinear stiffness and viscous damping of the connections within the vehicle, rail, floating slab and bridge subsystems are expressed by virtual excitation loads. The dynamic equation of the coupled train-track-bridge system can be expressed as [5].

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⎧ ·· q +2ξ v ωv q˙ v + ω2v q v = Φ vT f v ⎪ ⎪ ⎪ v ⎪ ⎪ ·· ⎪ ⎪ ⎨ q +2ξ r ωr q˙ r + ωr2 q r = Φ tT f r r

·· ⎪ q +2ξ s ωs q˙ s + ω2s q s = Φ sT f s ⎪ ⎪ ⎪ s ⎪ ⎪ ·· ⎪ ⎩ q +2ξ b ωb q˙ b + ω2b q b = Φ bT f b

(1)

b

where subscripts v, r, s and b denote the vehicle, rail, floating slab and bridge subsystems; q, ξ , ω, Φ are the modal coordinate vector, modal damping matrix, modal circular frequency vector and modal displacement matrix of the subsystems; f is the load vector, including dynamic wheel-rail forces produced by the track irregularities and virtual excitation loads corresponding to nonlinear stiffness and viscous damping of the connections. It is noted that the nonlinear Hertz contact model is adopted in the wheel-rail interaction. The equations can be solved with a step-by-step numerical integration method in the time domain.

2.2 Frequency-Domain Method The frequency-domain model neglects the motion of the train on the bridge but adopts the moving roughness assumption [6]. From the compatibility condition of connections within the wheel-track-bridge system, the vertical wheel-rail contact forces F(ω) can be expressed as the unknowns in the following equation [6–8]. (Yr +Yc +Yw )F(ω) = jωr

(2)

Where j is the imaginary unit; r is the vector of wheel-rail combined roughness at each wheel; Yr is the matrix of driving point and transfer mobilities of the rail under all wheels; Yc denotes the mobility matrix of the linearized Hertzian contact spring; and Yw is the wheel mobility matrix. It is noted that the rail mobility Yr is computed from a unit force excited track-bridge coupling model consisting of an infinite Timoshenko beam model of the rail, a finite element model of the slab track and another finite element model of the bridge. After obtaining the wheel-rail dynamic forces, the dynamic response of the bridge and floating slab can be calculated by the same track-bridge coupled model used for the calculation of rail mobility Yr .

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3 Model and Parameters Figure 1 shows the train-track-bridge coupled model with floating-slab track. The floating slab and bridge models are established in finite element software ANSYS. The bridge is a box girder structure with a span of 24 m, meshed by solid elements. The floating slab track is composed of several slabs each with a length of 4.8 m and 8 steel springs located under the slab, meshed by shell elements. Figure 2 shows the finite element model of the floating slab and box girder bridge. The size of the model and the distribution of the steel springs of the floating track are consistent with the actual situation in a section of a viaduct line used for tests in Shanghai. The vibration modes with natural frequencies below 300 Hz are included in the dynamic analysis with the mode superposition method. Table 1 gives some parameters of the model. The train in the time-domain model comprises six vehicles. In the frequencydomain model, considering the position of the measuring points in the experiment and the vehicle organization, two typical wheel position cases named as I and II (Figs. 3 and 4) are considered in this study. In case I, two wheels at the two rails are loading above the measuring point, which will produce the maximum response at the measuring points. In case II, the position of the wheels is symmetrical with case I within the zone of the measured bridge span. Train speeds of 40 and 60 km/h are analyzed in the two models.

Fig. 1 The train-track-bridge coupled model with floating-slab track

Fig. 2 Three dimensional finite element models of floating slab and box girder

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Table 1 Parameters of the model Parameter

Value

Parameter

Value

Vertical stiffness of fastener

40 MN/m

Wheel mass

831.5 kg

Vertical damping of fastener

60 kNs/m

Wheel-rail contact stiffness

1400 MN/m

Vertical stiffness of steel spring

6.6 MN/m

Rail length

72 m

Vertical damping of steel spring

68.7 kNs/m

Fastener distance

0.6 m

Density of floating slab

2500 kg/m3

Length of floating slab

4.8 m

Elastic modulus of floating slab

3.45 × 1010 Pa

Width of floating slab

2.8 m (edge) 2.56 m (middle)

Density of bridge

2600 kg/m3

Thick of floating slab

0.26 m

Elastic modulus of bridge

3.45 × 1010 Pa

Bridge length

24 m

Fig. 3 Case I: two wheels at the two rails loading on the measuring point

Fig. 4 Case II: position of wheels symmetrical with Case I in the zone of measured bridge span

To obtain the track irregularity in numerical model, short-wave irregularity was measured on site by measuring device. Figure 5 shows the irregularity spectrum generated by the irregularity measured on site.

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Fig. 5 Irregularity spectrum generated by irregularity measured on spot

4 Comparison 4.1 Time-Domain and Frequency-Domain To compare the two methods in the vibration prediction, this section uses acceleration level in one-third octave bands to indicate the vibration characteristic of floating slab and bridge at different frequencies. The acceleration time history of the track-bridge system obtained from the timedomain model is converted into one-third octave spectrum based on the time of train passing-by. When using the frequency domain vibration model, all wheels on both sides of the track are calculated to obtain the acceleration of the bridge and slab by the energy summation principle. Both the result of Case I and the averaged result of Case I and Case II are exhibited to determine a more accurate simulation methods. Figures 6 and 7 show the acceleration levels of rail, slab and bridge for the two models with two different train speeds. The calculation results indicate that in the frequency region above 20 Hz, the timedomain model and frequency-domain model have a high consistency. It is also shown that, when using the frequency-domain model, the average result of two cases is more accurate than using only one certain case. However, in some frequency region, the result of Case I has better consistency than that of averaged one. The probable reason is that the average result uses simplified method, averaging the energy of just two typical cases, which may lead to differences. The average result of different cases in frequency-domain model is used to compare with the experiment result.

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Fig. 6 The acceleration level of the rail (left) and bridge (right) (60 km/h)

Fig. 7 The acceleration level of the floating slab (left) and bridge (right) (40 km/h)

4.2 Numerical Model and Experiment In this section, the acceleration level in one-third octave bands is used to compare the result between numerical model and experiment. Figures 8 and 9 show the vibration of rail, floating slab and bridge from numerical model and experiment with train speed of 40–60 km/h with track irregularity from the experiment. It is shown that the acceleration level of the rail, floating slab and bridge of numerical model match well with experiment. However, there is a small difference in acceleration levels between numerical model and experiment. There are several probable reasons leading to the difference: 1. The measuring device of short-wave irregularity includes measurement noise, especially for longer waves. 2. The rail irregularity is the only input in numerical simulation, neglecting the wheel irregularity. 3. The values of stiffness and damping of fastener and steel spring used in the simulation has differences with those in the experiment.

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Fig. 8 The acceleration level of rail (left) and bridge (right) in numerical model and experiment with train speed of 60 km/h

Fig. 9 The acceleration level of floating slab (left) and bridge (right) in numerical model and experiment with train speed of 40 km/h

4. The arrangement of the diaphragm and the dimension of variable section of the bridge model has differences with the bridge on site.

5 Conclusions This study adopts a time-domain model based on modal superposition methods and a frequency-domain model based on the moving roughness method to simulate the vibration of a rail transit viaduct with floating slab track, and compares the simulated results with measured ones. The calculation results show the time-domain model and frequency-domain model can both be applied to simulate the vibration of floating slab track-bridge system. It is suggested that the results from different loading positions should be averaged in the frequency-domain analysis. The vibration of floating slab from the two methods matches well with the experimental results. In the frequency region above 20 Hz, the time-domain model and frequency-domain model have

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high consistency. For the noise-oriented prediction, the frequency-domain model is recommended considering its accuracy and efficiency in obtaining the vibration level spectra.

References 1. Li Q, Song X, Wu D (2014) A 2.5-dimensional method for the prediction of structure-borne low-frequency noise from concrete rail transit bridges. J Acoust Soci Am 135(5):2718–2726 2. Xu YL, Li Q, Wu DJ et al (2010) Stress and acceleration analysis of coupled vehicle and long-span bridge systems using the mode superposition method. Eng Struct 32(5):1356–1368 3. Li XZ, Liang L, Wang DX (2018) Vibration and noise characteristics of an elevated box girder paved with different track structures. J Sound Vib 425:21–40 4. Li Q, Wu DJ (2013) Analysis of the dominant vibration frequencies of rail bridges for structureborne noise using a power flow method. J Sound Vib 332(18):4153–4163 5. Li Q, Xu Y L, Wu DJ et al (2010) Computer-aided nonlinear vehicle-bridge interaction analysis. J Vib Control 16(12) 6. Wu TX, Thompson DJ (2001) Vibration analysis of railway track with multiple wheels on the rail. J Sound Vib 239(1):69–97 7. Li Q, Li WQ, Wu DJ et al (2016) A combined power flow and infinite element approach to the simulation of medium-frequency noise radiated from bridges and rails. J Sound Vib 365:134–156 8. Li Q, Dai B, Zhu Z et al (2022) Comparison of vibration and noise characteristics of urban rail transit bridges with box-girder and U-shaped sections. Appl Acoust 186

Pantograph-Catenary System Vibration

A Preliminary Study Towards the Understanding of the Pantograph-Catenary Irregular Wear Problem in the Rigid Overhead Catenary System Xiaohan Phrain Gu, Anbin Wang, Qirui Wu, and Ziyan Ma

Abstract This paper presents some early-stage works and findings of the irregular wear problem found in pantograph-catenary interaction with rigid overhead catenary system of metro lines. Laboratory tests and computational simulation were conducted to examine the vibration characteristics of the coupled system. It was found that the wear pattern of pantograph strips resembles the mode shape of dominant natural frequencies in the high-frequency range, indicating that resonance happens at the carbon strip and contact wire sliding interface, leading to poor contact quality. Damping treatments were applied to standard pantograph strips, to improve the damping performance of pantograph strips to control high frequency vibration of pantograph strips. Laboratory tests and field tests were carried out to evaluate the damping performance and vibration characteristics of damping treated pantograph strips. It was found that applied damping treatment was able to achieve a maximum of 7 dB of vibration reduction. The worse the initial condition of the pantographcatenary system, the more prominent the damping effects on the control of high frequency vibration. Keywords Pantograph-catenary system · Irregular wear · Vibration characteristics · Damping performance · Pantograph strips

X. P. Gu (B) · A. Wang · Q. Wu · Z. Ma School of Urban Railway Transportation, Shanghai University of Engineering Science, 333 Longteng Road, 201620 Shanghai, People’s Republic of China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_77

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1 Introduction Wheel-rail interaction and pantograph-catenary interaction are two main coupled systems in railway engineering. While the wheel-rail coupled system introduces noise and vibration problems with regards to primarily environment issues, pantographcatenary interaction is more crucial to operational safety, power quality, as well as maintenance cost. Researchers have studied the interaction between pantograph and traditional suspension catenary system [1–3], focusing primarily on the catenary system, and in low frequency range, typically below 100 Hz. Compared to the traditional catenary system with suspension wires, the rigid Overhead Contact System (OCS), per Fig. 1, has advantages such as more capability of current carrying, better reliability, maintainability and availability, therefore overall lower life-cycle costs. Rigid OCS has been increasingly used in tunnel sections of metro system in China, South Korea, and Europe. That said, due to the lack of tension and the discontinuous layout of the aluminium frame, the contact quality of the system is largely compromised. In plan view, the layout of a rigid OCS is typically a ‘Z’ or sine wave in relation to the track centre-line. The contact wire runs back and forwards across the pantograph strip, to achieve an even wear across the pantograph strip. As the vehicle runs through the catenary, defects and discontinuities along the catenary introduce impact loads thus vibration, together with adhesive wear at the interface. Both mechanical wear and electrical wear contribute to the overall wear of the pantograph strip. Under normal loading condition, pantograph strips are in continuous contact with the contact wire. However, when external impact load comes into the system, large magnitude vibration occurs at high frequency. Pantograph strip could lose contact with the contact wire, intensifying electrical wear, even causing arc events. At this stage of the study, only mechanical wear is considered.

Supports Insulator Steady clamp Aluminium profile Contact wire

(a) Discontinuous layout of OCS Fig. 1 A rigid Overhead Contact System (OCS)

(b) The Cross-section of a rigid OCS

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1.1 The Irregular Wear Problem in the Rigid Pantograph-Catenary System Irregular wear of the pantograph-catenary system has been found in metro-lines with rigid OCS in cities in China. The design life of a standard current collector strip is approximately of 100,000 km in China. In the metro system, this corresponds to between 1 and 3 years of service life, depending on the operational condition of a specific metro-line, including the condition of the pantograph-category system. Irregular wear, however, is featured with uneven and excessively high wear depths taking place within a very short period of time, e.g. several days or weeks. Figure 2 shows the carbon strip wear rate of the Line 1 metro-line of S city. Comparing to the normal carbon strip wear rate of 0.9– 1.9 mm per 10,000 km, irregular wear increases the carbon strip wear rate to some 148.2 mm per 10,000 km. Representative pictures of worn conditions of pantograph strips after a few days from new are shown in Fig. 3. In the attempt of addressing the irregular wear problem, practitioners in the industry have tried using various technologies, such as using Artificial Intelligence camera, high precision scanning devices etc. for health monitoring of the OCS. Limited research works have also been conducted, for instance, to study the influence of the layout of rigid OCS [4]. But the cause of irregular wear is yet unknown. 160 Vehicle 2

Wear/10k Km (mm)

140

Vehicle 5

120 100 80 60 40 20 14-Dec

13-Dec

12-Dec

11-Dec

10-Dec

9-Dec

8-Dec

7-Dec

6-Dec

5-Dec

4-Dec

3-Dec

2-Dec

1-Dec

0

Vehicle 2

2.11

1.45

3.06

4.22

5.08

7.14

10.38

10.64

40.41

1011121314Dec Dec Dec Dec Dec 49.42 101.25 110.23 121.54 148.20

Vehicle 5

0.50

0.40

0.98

1.28

1.93

Date 2.56 2.76

4.98

14.61

29.73

1-Dec 2-Dec 3-Dec 4-Dec 5-Dec 6-Dec 7-Dec 8-Dec 9-Dec

75.41 105.01 117.22 127.67

Fig. 2 Carbon strip average daily wear rate (per 10,000 km)

(a) Two grooves wear Fig. 3 Pantograph strips with irregular wear

(b) Three grooves wear

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1.2 Research Project Background and Contents of This Paper This research project aims at the understanding of the mechanism of irregular wear of the pantograph catenary system, and solving the problem by optimising the dynamic characteristics of the pantograph strip at its design stage. Both numerical simulation and laboratory tests were performed to investigate multi-dimensional dynamic characteristics of pantograph and pantograph strips. Laboratory test results were used to validate computational simulation of pantographcatenary interaction. Parametric studies were undertaken using computational simulation, results of which assisted in the improvement of the damping property of pantograph strips. Damping treatments were applied to standard pantograph strips, and were tested in the laboratory and onsite, to verify the effectiveness of using damping treatment in the control of high frequency vibration. Computational simulation and laboratory tests using a 1:5 scaled full model of the OCS-train-track test platform are used to establish the relationship between vibration level and the wear rate of pantograph strips. Field data are to be collected when the trains’ under normal operation condition, using optical-fibre accelerometers, to investigate the correlation between mechanical wear and electrical wear. In this paper, vibration characteristics of pantograph strips through laboratory tests are presented. The effectiveness of using different damping treatment for the control of high frequency vibration of pantograph strips is evaluated both in the laboratory and onsite.

2 Vibration Characteristics of the Pantograph Strip Modal tests were carried out on pantograph strips, to investigate their vibration characteristics. As shown in Fig. 4, with pantograph strips in free and in mounted conditions, two accelerometers measuring vertical and transverse vibration are located at point 4–9 along the pantograph strip. A point load is applied at 13 excitation points along the pantograph strip. Mode shapes, with corresponding modal frequencies, of the first six vertical modes of pantograph strips are plotted in Fig. 5. The transfer function of the pantograph strip tested is plotted as the black dash line labelled ‘Original’ in Fig. 7. Peak vibration response happen at the 3rd and 5th vertical mode, with vibration magnitude of 139.6 dB and 148.5 dB respectively. It was further found that the wear pattern of pantograph strips with two grooves wear resembles closely the mode shape of the 3rd vertical mode of the pantograph strip, as shown in Fig. 6. Likewise, the three grooves wear pattern is similar to the 5th vertical mode of the pantograph strip. It was therefore deduced that irregular wear is due to pantograph strips vibration at the sliding interface in the high frequency range.

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Fig. 4 Pantograph strips modal tests set-up

(a) 1st vertical mode 119 Hz

(b) 2nd vertical mode 264 Hz

(c) 3rd vertical mode 334 Hz

(d) 4th vertical mode 547 Hz

(e) 5th vertical mode 659 Hz

(f) 6th vertical mode 932 Hz

Fig. 5 Modal frequencies and mode shapes of pantograph strips

3 Damping Treatment for Pantograph Strips 3.1 Laboratory Tests Improvement of the damping property is one of the most effective means for a system which undergoes resonance. A parametric study of the damping property of pantograph strips was undertaken using computational simulation. Based on the preliminary study, three types of damping treatment, namely Scheme A-C, were applied to standard pantograph strips, for the control of high frequency vibration at the sliding contact. Damping ratios ζ at the 3rd and 5th vertical mode of pantograph strips using different treatments are compared against those of the original pantograph

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(a) Irregular wear with two grooves

(b) Irregular wear with three grooves

(a) Mode shape of the 3rd vertical mode

(b) Mode shape of the 5th vertical mode

(a) Two grooves wear vs. 3 rd mode shape

(b) Three grooves wear vs. 5th mode shape

Fig. 6 Relationship between the wear pattern and the peak response mode shape of pantograph strips

Transfer function dB (Ref=1e6ms-2)

150

5th mode, 659 Hz

3rd mode, 334 Hz

140 130 120 110 100 90 80 Original

70 0

Scheme A

200

Scheme B

Scheme C

400 600 Frequency (Hz)

800

1000

Fig. 7 Transfer function of the pantograph strips under vertical excitation at point 9 in Fig. 4

strips, shown in Table 1. Transfer functions of the four pantograph strips are plotted in Fig. 7. Amongst the three damping options, scheme C shows the best damping performance, giving an increase in the damping ratio from 0.39 to 7.7% at the 5th vertical mode, which corresponds to three-groove irregular wear. The modal frequency of Table 1 Comparison of measured damping ratio of pantograph strips Vibration Mode

Original

Scheme A

Scheme B

Scheme C

F (Hz)

ζ (%)

F (Hz)

ζ (%)

F (Hz)

ζ (%)

F (Hz)

ζ (%)

3rd vertical mode

334

1.05

315

1.69

314

0.96

299

1.99

5th vertical mode

659

0.39

625

2.81

651

4.86

644

7.70

A Preliminary Study Towards the Understanding … Traditional OCS

811 Rigid OCS Stop X

Underground section

Viaduct section Stop L

Fig. 8 Illustration of the test route

the 5th vertical mode shifted from 659 down to 644 Hz, with a significant vibration reduction of 22 dB. Therefore, scheme C damping treatment of pantograph strips were further examined with trains running in the field.

3.2 Field Tests To further verify the effectiveness of damping treatment scheme C, field tests were carried out between two stops of Metro Line 1 of city X (Fig. 8). The test section contains both traditional suspension catenary and rigid OCS, so was chosen for the test. The distance between the two stops, stop L and stop X, is 1988 m, with 1044 m of rigid catenary underground and 944 m of traditional suspension wire catenary on the viaduct. Test route includes both straight and curved tracks. A new pantograph strip without damping treatment, named PS A, and one with damping treatment (scheme C), named PS B, were both installed on the pantograph of an engineering train. Accelerometers were set up per Fig. 9. Accelerometers 1, 2, 5 and 6 were at the middle of PS A and PS B respectively. Accelerometers 3, 4, 7, and 8 were at the quarter position of PS A and PS B respectively. Accelerometers 9 and 10 were at the base of the pantograph frame. Accelerometers 11 and 12 were fixed on the roof of the engineering train. Accelerometers 1, 3, 5, 7, and 9 measure vertical vibration. Accelerometers 2, 4, 6, 8, 10, and 12 measure transverse vibration. New pantograph strip PS A was first tested. Data were collected with the train running at 20 km/h both ways between the two stops; then at 48 km/h. Damping treated pantograph strip PS B was then tested under exactly the same conditions. All tests were conducted without the train being electrified, to examine only the mechanical aspects of irregular wear. All tests were carried out during planned possession time at nights. Test results in terms of vibration reduction comparing total acceleration from PS A and from PS B are shown in Table 2. Damping scheme C can achieve up to

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Plan View

Side View

Fig. 9 Field test set-up

some 7.0 dB of vibration reduction. In addition, vibration reduction in the rigid OCS section is generally higher than that found in the traditional OCS section, showing that the damping effect is more prominent in the rigid OCS. The higher the train speed, the more reduction in vibration level using damping treatment. In other words, the worse the initial condition of the pantograph-catenary system, the more prominent the damping effects on the control of high frequency vibration. Table 2 Summary of vibration reduction Train speed Accelerometer position Vibration reduction (dB) (km/h) Rigid OCS

Traditional suspension wire

Upline

Downline

Upline

Downline

A

B

A

B

A

B

A

B

6.6

2.8

2.8

2.4

5.7

2.2

1.4

3.1

20

Middle 1/4 position

3.8

2.2

5.4

1.9

1.1

2.0

2.4

1.9

48

Middle

5.9

7.0

5.5

1.5

1.9

2.0

1.0

2.6

1/4 position

4.9

5.0

1.9

1.8

2.1

2.0

2.1

0.7

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4 Conclusions Through the preliminary study of the vibration characteristics of pantograph strips, towards the understanding of the irregular wear problem found in the pantographcatenary system, especially of the rigid catenary system, the following can be concluded: 1. The irregular wear problem is characterised by the consistency between the wear pattern and the dominant vibration mode shape of pantograph strips. Furthermore, it is due to resonance in the high frequency range at the pantograph strip and copper wire sliding interface. 2. Improvement of the damping performance is an effective means to control high frequency vibration of pantograph strips. Damping treated pantograph strips can reduce vibration the level up to 7 dB. 3. By comparing damping performance between traditional suspension catenary and rigid OCS, and with varying train speeds, it was found that the worse the initial condition of the pantograph-catenary system, the more prominent the damping effects on the control of high frequency vibration in the irregular wear problem.

References 1. Jimenez-Octavio JR, Carnicero A, Sanchez-Rebollo C, Such M (2015) A moving mesh method to deal with cable structures subjected to moving loads and its application to the catenary– pantograph dynamic interaction. J Sound Vib 349:216–229 2. Sorrentino S, Anastasio D, Fasana A, Marchesiello S (2017) Distributed parameter and finite element models for wave propagation in railway contact lines. J Sound Vib 417:1–18 3. VoVan O, Massat J, Balmes E (2017) Waves, modes and properties with a major impact on dynamic pantograph-catenary interaction. J Sound Vib 402:51–69 4. Wei XK, Meng HF, He JH, Jia LM, Li ZG (2020) Wear analysis and prediction of rigid catenary contact wire and pantograph strip for railway system. Wear 442–443:1–15

Research of Influence of Pantograph-Catenary System Vibration on Irregular Wear of Carbon Contact Strip Qirui Wu, Xiaohan Phrain Gu, and Anbin Wang

Abstract In order to study the effect of carbon contact strip vibration on the irregular wear, a simplified pantograph-catenary coupled model is established to analyze its vibration response. It is found that the vibration of pantograph and rigid catenary mainly occur at low frequency and has little effect on irregular wear, whereas irregular wear of the carbon contact strip is from its the third vertical bending mode to its third lateral bending mode, which aggravate the mechanical wear in the middle of the carbon contact strip and the mechanical-electrical wear on both sides. Keywords Carbon contact strip · Pantograph-catenary vibration · Irregular wear

1 Introduction As one of the important parts of electrification for trains, carbon contact strips transmit electrical energy by sliding contact with the contact wire. The carbon contact strip vibrates at high frequency due to the inherent properties of the pantographcatenary system during high-speed motion, vibration causes irregular contact pressure between the carbon contact strip and the contact wire, contact pressure aggravates the wear of carbon contact strip, reducing the service life of carbon contact strip, and introducing safety hazards to running trains. Small contact pressure leads to poor contact between the carbon contact strip and the catenary, which affects the quality of power supply of the train. Electrical erosion causes the damage of catenary and affects the operation of the line, so the vibration and wear of the carbon contact strips plays an extremely important role in the safe operation of train vehicles. At present, scholars [1–3] have conducted in-depth research on the contact strip from the aspects of external temperature, current intensity and contact strip material, which have made great progress. However, there are few studies on the impact of Q. Wu (B) · X. P. Gu · A. Wang School of Urban Railway Transportation, Shanghai University of Engineering Science, 333 Longteng Road, 201620 Shanghai, People’s Republic of China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Sheng et al. (eds.), Noise and Vibration Mitigation for Rail Transportation Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-99-7852-6_78

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vibration on the irregular wear of carbon contact strips. There are cases of irregular wear of carbon contact strips found in metro-line operations. This paper obtains the relationship between the resonance of pantograph-catenary system and the irregular wear of carbon contact strips.

2 Numerical Model of the Pantograph-Catenary System In this paper, a numerical model of the pantograph and catenary system is established. The model is simplified with equivalent substitution of element structure and contact relationships. The basic characteristics including material properties and key structural properties are not changed while simplifying the model.

2.1 Numerical Model of the Rigid Catenary As shown in Fig. 1, the suspension mechanism of the rigid catenary composes of channel steel and anchor bolts. Anchor bolts simplified to the spring, and the channel steel is equivalent to the beam element, so the following relationship is obtained. δ=

b a δ1 + δ2 + δ3 l l

(1)

According to the static equilibrium conditions, it can be obtained: k 1 δ1 + k 2 δ2 = k 3 δ3 k 1 δ1 = k=

(2)

b k 3 δ3 l

(3)

E n An (n = 1, 2, 3) ln

(4)

p1 k1

p2 k2

Fig. 1 Mechanical model of rigid catenary

1 3

A

a

C

Q

2

b

B

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where l 1 , l 2 are the lengths of the bolts at the two ends. E 1 A1 , E 2 A2 represent the rigidity of the bolts of the ends. E is elastic modulus of the material. δ 1 , δ 2 and δ 3 are elongation of the springs and the beam. k 1 , k 2 are stiffness of the spring, k 3 is stiffness of the beam element. l is the length of the channel steel connected to the bolt. Combine the above formulas to get the result: ⎧ k1 k3 bl ⎪ δ1 = δ ⎪ ⎪ 2 + k k b2 + k k l 2 ⎪ k k a 1 3 2 3 1 2 ⎪ ⎪ ⎨ k1 k3 al δ2 = δ 2 k1 k3 a + k2 k3 b2 + k1 k2 l 2 ⎪ ⎪ ⎪ ⎪ ⎪ k1 k3 l 2 ⎪ ⎩ δ3 = δ k1 k3 a 2 + k2 k3 b2 + k1 k2 l 2

(5)

The elastic potential energy is: V =

1 2 1 2 1 2 1 k1 δ1 + k2 δ2 + k3 δ3 = keq δ 2 2 2 2 2

(6)

k1 k2 k3 l 2 k1 k3 a 2 + k2 k3 b2 + k1 k2 l 2

(7)

keq =

k eq is the equivalent stiffness of the suspension mechanism. A, B and C represent the contact point, Q is the static force. a/b defines the distance between points A/B and C, δ is the displacement of point C.

2.2 The Pantograph Numerical Model Because there are many types and complex structures of pantographs, which include many hinges, gaps and frictions, it is not easy to simulate the vibration characteristics of the pantograph according to the actual situation of the pantograph. Therefore, in the theoretical analysis of the pantograph, the method of imputed the quality is usually used in the simulation analysis. The pantograph is equivalent to a lumped mass block with mass, damping and spring characteristics. For the convenience of calculation and analysis, as shown in Fig. 2, most of the current researches use the pantograph as a three-mass model for analysis. The motion equation of the pantograph three-mass model is:

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m1

Fig. 2 Imputed model of pantograph

F0

Pan-head

k1 m2

c1

k2 m3

c2

k3

c3

upper arm lower arm

⎧ ⎪ ⎨ m 1 y¨1 + C1 y˙1 + C1 y˙2 + k1 y1 + k1 y2 = −F(t) m 2 y¨2 − C1 y˙1 + (C1 + C2 ) y˙2 − C2 y˙3 − k1 y1 + (k1 + k2 )y2 − k2 y3 = 0 ⎪ ⎩ m 3 y¨3 − C2 y˙2 + (C1 + C3 ) y˙3 + k2 y2 + (k1 y1 )y3 = F0

(8)

m1 is the pan-head mass. m2 /m3 is the equivalent mass of the upper/lower arm. k 1 , k 2 and k 3 are the equivalent stiffness between different mass elements. F(t) is the contact force of the pantograph. F 0 is the static lifting force.

2.3 The Pantograph-Catenary Contact Model As shown in Fig. 3, when the contact line is in elastic contact with the carbon strip, the contact area can be simplified as a rectangle based on the Hertz theory, which is: p(x) =

2F √ 2 a − x2 πa 2 L

(9)

L is the length, 2a is the width. p is the contact stress, distribution of the contact force, F is the external load. x is the distance from the contact point to the contact center. When x = 0, the contact stress at the center of the contact area is the largest, which is: √ F E∗ 2F = (10) p0 = πa L π RL E* is the equivalent elastic modulus, E* = E/(1-v)2 , E is the elastic modulus. V is the Poisson’s ratio, R is the radius of the cylinder of the contact wire.

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Contact line

F z

Carbon strip

R p L x

2a Fig. 3 Contact model of pantograph-catenary system

The normal stress and principal shear stress at the point on the z-axis of the central symmetry plane of the cylinder of the contact line are: ( ( p0 a 2 + 2z 2 − 2z √ a a2 + z2 p0 a σz = − √ a2 + z2 ( ) √ a2 + z2 z − σ y = v(σx + σz ) = 2vp0 a a ( ( z2 p0 z−√ τx y = a a2 − z2 σx = −

τ yz = τzx = 0

(11) (12)

(13)

(14) (15)

According to the relationship between the contact stress and the load, the contact half-width a can be obtained as: √ 2 p0 R 4F R = a= . (16) π E∗L E∗

2.4 Pantograph-catenary Coupling Model As shown in Fig. 4, a finite element model of the pantograph-catenary system is established to analyze its vibration response according to above simplified model. The pantograph-catenary system parameters are shown in Tables 1 and 2.

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Fig. 4 An illustration of the finite element model of the pantograph-catenary system

Suspension structure Rigid catenary Carbon contact strip 1 2 Pantograph

3

Table 1 Parameter of rigid catenary and carbon contact strip

Rigid catenary

Carbon contact strip

Components

Material

Elastic modulus /GPa

Density/(kg/ m3 )

Poisson’s ratio

Busbar

Aluminum alloy

72.0

2800

0.33

Contact line

Copper silver alloy

120

9183

0.3

Support

Aluminum alloy

72.0

2800

0.33

Carbon strip

Carbon

12.7

2000

0.35

Table 2 Parameter of pantograph

m/kg

k/(N/m)

c/(N s/m)

1

11

13,300

2

10

7540

0 0

3

12

3500

120

Mode responses of rigid catenary, carbon contact strip and pantograph are obtained.

3 Sensitivity Study of the Numerical Model The length of the catenary model has an influence on the validity of the model. In order to simplify the calculation, a unit harmonic load is applied vertically to the rigid catenary model at different positions along the length as shown in Fig. 5a. Vibration responses of catenary models at different positions are plotted in Fig. 5b, where the response represents the displacement due to a unit force.

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1

Vertical excitation 6m 18m ···

66m

Vertical excitation response/m

Fixed constraint

···

6m 42m

0.1

18m 54m

30m 66m

0.01 0.001 1E-4 1E-5 1E-6 1E-7 1E-8 1E-9

100

200

300

400

500

600

700

800

900

1000

Frequency/Hz

a) Loading case of the rigid catenary model of different lengths

b) Vibration response of the catenary model

Fig. 5 Rigid catenary of different lengths

As shown in Fig. 5b, the vertical excitation of the 6 m rigid catenary is different from others. Its resonance crests are significantly less than others near 400, 650– 940 Hz, many high frequency vibrational modes are not excited, but especially the vibration response of 940 Hz is much larger than others. The reason is that only part of the high-frequency vibration is reflected by the fixed constraints when the rigid catenary of other lengths is transmitted, and the other part continues to transmit to both ends, because the vibration has media to allow energy to dissipate further. The high-frequency vibration wave still has high energy after being reflected by the boundary because the distance is too short and the energy attenuation is too small during the transmission process. It can be found that the difference of vibration response with the model of 18 m length and above is small, so the 18 m rigid catenary model is accurate enough to be used in all subsequent simulations.

4 Vibration Response of the Pantograph-Catenary System The first few mode shapes of the rigid catenary and pantograph are shown in Tables 3 and 4 respectively. The modes of the rigid catenary and the pantograph mainly come from the low frequencies, and it has less influence on the irregular wear of the carbon contact strip in the high frequency range. When the pantograph-strip interact with the contact wire, the contact surface presents as a sine wave, but the width of the carbon contact strip is very short compared to the length of the contact wire, and their contact load is regarded as a linear load. The vertical dynamic pressure between the contact wire and the carbon contact strip is assumed as a unit force to obtain the frequency response functions, the lateral friction force is estimated as half of the vertical contact force (assuming a friction coefficient of 0.3). The threaded hole at the bottom of the carbon contact

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Table 3 Modal response of rigid catenary Frequency/Hz

Total deformation

2.1

First-order vertical bending

3.3

Second-order lateral bending

11.6

Third-order vertical bending

49.1

First-order twist

Table 4 Modal response of pantograph

Mode shape

Frequency/Hz

Total deformation

3.6

Upper frame lateral bending

5.0

Pantograph deflection

strip is regarded as a fixed constraint. Because the staggered value of the catenary doesn’t exceed 47.5 cm, the vibration response of vertical pressure and lateral friction for four positions in 10 cm apart on the carbon contact strip is analyzed to get the effect of different stagger values on the carbon contact strip as shown in Fig. 6. Combined with its mode shapes, which obtains the relationship between the change of the excitation surface of the carbon contact strip and the vibration response, the response of the carbon contact strips are given in Fig. 7. Here the response is shown as acceleration in order to com- pare the high frequency dynamic apparent force relative to the wear. As shown in Fig. 7, there are two resonance peaks in the vertical response of the carbon contact strip from 100 to 1000 Hz, namely the first vertical bending mode at 119 Hz and the third vertical bending mode at 600 Hz, The response magnitude at 600 Hz is significantly larger than that at 119 Hz. The vertical vibration at 600 Hz of the contact strip has more serious impact than others. The lateral resonance of the carbon contact strip includes the first lateral bending mode at 160 Hz, the second lateral bending mode at 580 Hz and the third lateral

Carbon contact strip

1 2 3 4

Contact Rigid catenary

Fixed constraint Fig. 6 Schematic diagram of the excitation point

Research of Influence of Pantograph-Catenary System Vibration … 104

spot 1 spot 2 spot 3 spot 4

600

600 Hz

Lateral vibration acceleration/(m/s2)

Vertical vibration acceleration/(m/s2)

800

400

200

823

119 Hz

0 100

200

300

400

500

600

700

800

900

1000

900 Hz

spot 1 spot 2 spot 3 spot 4

103

160 Hz

580 Hz

102

101

100 100

200

300

400

500

600

700

Frequency/Hz

Frequency/Hz

a) Vertical

b) Lateral

800

900

1000

Fig. 7 Vibration response of the carbon contact strip

bending mode at 900 Hz. The vibration magnitude at 900 Hz is much larger than others, which also contributes to excessive wear of carbon contact strips. For both the vertical and lateral vibration, the vibration magnitude at point 2 is much larger than others, which means that the high-frequency vibration of the pantograph-catenary system is the most serious when he stagger value is one-quarter length of the carbon contact strip. In general, irregular wear is most significant at the third bending mode of the carbon contact strip at 600 Hz in the vertical direction and at 900 Hz in the lateral direction. The carbon contact strip at the third vertical bending mode is likely to undergo the loss of contact with the contact wire, increasing possibility of arc melting. The contact pressure is greater at the crest of the response, increasing the frictional force. The deformation of the carbon contact strip at its third lateral bending mode is the largest at the crest and troughs, its lateral swing increases the wear with the contact wire, so the wear at the crest is mainly mechanical wear, and the wear at the troughs is mainly mechanical wear and electrical wear. The irregular wear of the carbon contact strip is formed as a W-shaped, which is the same as the mode shape of the third vertical bending mode, indicating that the wear at the troughs is greater than that at the crest as shown in Fig. 8.

Mechanical wear trough

Mechanical- electrical wear crest

Fig. 8 Irregular wear mode shapes of carbon contact strips

The third bending mode

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Q. Wu et al.

5 Conclusions By studying the effect of high-frequency vibration of pantograph-catenary system on irregular wear of carbon contact strips, the following conclusions are obtained: (a) The main resonance frequency of the rigid catenary and pantograph in the pantograph-catenary system is lower than 50 Hz, which has little effect on the irregular wear of the carbon contact strip. (b) When the stagger value is one-quarter length, the high-frequency vibration of the carbon contact strip is the most serious, so avoiding one-quarter length stagger value can effectively reduce vibration. (c) Irregular wear of the pantograph-catenary system is attributed by the natural frequencies of the carbon contact strip, which can be deducted from the vibration response of the carbon strips, i.e. resonance happens at the third vertical bending mode at 600 Hz and the third lateral bending mode at 900 Hz. The resonance triggers higher mechanical wear in the middle of the carbon contact strip and the mechanical-electrical wear on both sides.

References 1. Liu XL et al (2021) Research on the wear properties of carbon strips and contact wires at frigid temperatures. Wear 486–487 2. Yang H et al (2021) Study on the delamination wear and its influence on the conductivity of the carbon contact strip in pantograph-catenary system under high-speed current-carrying condition. Wear 477 3. Wang P et al (2021) Effect of pyrolytic carbon interface thickness on conductivity and tribological properties of copper foam/carbon composite. Appl Compos Mat 1–15