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Lecture Notes in Mechanical Engineering
Mounir Ben Amar · Anas Bouguecha · Elhem Ghorbel · Aberrahim El Mahi · Fakher Chaari · Mohamed Haddar Editors
Advances in Materials, Mechanics and Manufacturing II Proceedings of the Third International Conference on Advanced Materials, Mechanics and Manufacturing (A3M’2021), March 25–27, 2021
Lecture Notes in Mechanical Engineering Series Editors Francisco CavasMartínez, Departamento de Estructuras, Universidad Politécnica de Cartagena, Cartagena, Murcia, Spain Fakher Chaari, National School of Engineers, University of Sfax, Sfax, Tunisia Francesca di Mare, Institute of Energy Technology, RuhrUniversität Bochum, Bochum, NordrheinWestfalen, Germany Francesco Gherardini, Dipartimento di Ingegneria, Università di Modena e Reggio Emilia, Modena, Italy Mohamed Haddar, National School of Engineers of Sfax (ENIS), Sfax, Tunisia Vitalii Ivanov, Department of Manufacturing Engineering, Machines and Tools, Sumy State University, Sumy, Ukraine 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
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 postproceedings represents the core of LNME. Volumes published in LNME embrace all aspects, subﬁelds and new challenges of mechanical engineering. Topics in the series include: • • • • • • • • • • • • • • • • •
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Mounir Ben Amar Anas Bouguecha Elhem Ghorbel Aberrahim El Mahi Fakher Chaari Mohamed Haddar •
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Editors
Advances in Materials, Mechanics and Manufacturing II Proceedings of the Third International Conference on Advanced Materials, Mechanics and Manufacturing (A3M’2021), March 25–27, 2021
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Editors Mounir Ben Amar Université Paris 13 Laboratoire LSPMCNRS VILLETANEUSE, France Elhem Ghorbel Voie Mail GayLussac Laboratoire L2MGC, CergyPontoise Univer Paris, France Fakher Chaari Department of Mechanical Engineering National School of Engineers of Sfax Sfax, Tunisia
Anas Bouguecha National Engineering School of Gafsa Gafsa, Tunisia Aberrahim El Mahi Acoustics Laboratory of Mans University le Mans cedex, France Mohamed Haddar National School of Engineers of Sfax Sfax, Tunisia
ISSN 21954356 ISSN 21954364 (electronic) Lecture Notes in Mechanical Engineering ISBN 9783030849573 ISBN 9783030849580 (eBook) https://doi.org/10.1007/9783030849580 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 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 Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
The International Conference on Advanced Materials Mechanics and Manufacturing, A3M, is a scientiﬁc event series organized by the Laboratory of Mechanics, Modeling and Manufacturing (LA2MP) within the National School of Engineers of Sfax (ENIS), University of Sfax (Tunisia). The main aim of this international conference is indeed to bring together academic and industrial researchers acting in the ﬁeld of mechanical engineering through the world to share their knowledge, to build new relationships and collaborations and also to offer new opportunities susceptible to create new innovative research projects. This event took place in its third edition, March 25 and 26, 2021, and ﬁrstly in digitalonline format, because of the difﬁcult current circumstances due to the COVID19 pandemic. The A3M brings out a large roundup of different topics in the ﬁeld of mechanical engineering, among others, such as: – – – – –
Material behavior: modeling and characterization Numerical Simulation Contact mechanics and tribology Metal forming technologies New Materials
The A3M offers a timely snapshot on the presented current research works that have seen a considerable evolution and brought a lot of new scientiﬁc knowledge in the last years. This book gathers 44 chapters that was presented during the conference which passed rigorous peerreviewed process. The organizers would like to express our gratitude to the researchers and scientists who take part in this international event as scientiﬁc committee members, keynote lecturers and oral session speakers, as well as to everybody who has
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contributed to the success of this conference with special mention to Springer for his continuous support.
March 2021
Mounir Ben Amar Anas Bouguecha Elhem Ghorbel Aberrahim El Mahi Fakher Chaari Mohamed Haddar
About the Conference
The Third International Conference on Acoustics and Vibration (ICAV’2020) was organized by the Tunisian Association of Industrial Acoustics and Vibration (ATAVI), March 15 and 16, 2021. This conference was initially scheduled in March 2020 and postponed to 2021 due COVID19 pandemic situation. After two successful editions in 2016 and 2018 with proceedings published under Applied Condition Monitoring (ACM) book series, ICAV conference series continue to promote highlevel contributions in the ﬁelds of acoustics and vibrations in order to promote communication and collaboration between international and local communities. Plenary sessions were presented by eminent scientists who kindly agreed to share their knowledge in the ﬁeld of acoustics and vibration. The organizers of the conference were honored by their presences with very interesting keynotes. Namely: – Prof. Weidong Zhu, Department of Mechanical Engineering, University of Maryland, USA. – Prof. Philippus Heyns, Mechanical and Aeronautical Engineering Department, University of Pretoria, South Africa. – Prof. PierreOlivier Mattei, Deputy Director of Mechanical and Acoustics Laboratory (LMA), CNRS,Marseille, France. – Prof. Abdelkhalek Elhami, Mechanical Engineering Department, National Institute of Applied Sciences in Rouen (INSA de Rouen), France. – Prof. Mabrouk Bentahar, Roberval Laboratory, University of Technology of Compiegne, France. – Professor Abderahim Elmahi, Laboratory of Acoustics, University of Lemans, France. – Prof. Jean Yves Choley, Research Director at Supmeca, Groupe ISAE, Paris, France. This book contains 31 chapters selected from the presented papers by eminent scientists which were rigorously peer reviewed. During the two days of the congress, about 80 attendees discussed several topics such as:
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About the Conference
Structural and machines dynamics and vibrations, Fault diagnosis and prognosis, Nonlinear dynamics, Vibration control of mechatronic systems, Fluidstructure interaction and computational vibroacoustics, Vibration ﬁeld measurements, Material behavior in dynamics.
A lot of thanks are addressed to the organizing committee, program committee and all participants from Tunisia, Algeria, Morocco, South Africa, France, China and Saudi Arabia. We would like to also thank Springer for continuous support of ICAV conference series.
March 2021
Nabih Feki Mohamed Slim Abbes Mohamed Taktak Mohamed Amine Ben Souf Fakher Chaari Mohamed Haddar
Contents
Prediction Efﬁciency of the Ultimate Load Capacity of Nut Thread with Insufﬁcient Engagement Length . . . . . . . . . . . . . . . . . . . . . . . . . . . Hela Soussi, Anis Swissi, and Abdelkader Krichen Cement Reduction and Strength Development of Conventional Mortars by Utilization of Dried Waste Marble Slurry . . . . . . . . . . . . . . Mohammad Raﬁ Raﬁ, Saﬁullah Omary, Elhem Ghorbel, and Amanullah Faqiri Experimental Analysis of the Crushing of Auxetic Structure Under Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Khawla Essassi, Jeanluc Rebiere, Abderrahim El Mahi, Mohamed Amine Ben Souf, Anas Bouguecha, and Mohamed Haddar System Level Speciﬁcation and Multiagent Simulation of Manufacturing Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Khalil Aloui, Amir Guizani, Moncef Hammadi, Thierry Soriano, and Mohamed Haddar On the ViscoHyperelasticity Relationship in Modeling Styrene Butadiene Rubber Under Uniaxial Cyclic Loadings: Experiments and Parameter Identiﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Amina Dinari, Hamza A. Ghulman, and Tarek BenAmeur Analysis of the Wells Turbine Structure of an Oscillating Water Column Wave Energy System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mohamed Ali Jemni, Hamdi Hentati, Sawsan Elmbarki, and Mohamed Salah Abid A TwoStage Approach to Solve Structural Damage Detection Problem in Plate Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kamel Belhadj, Najeh Ben Guedria, Ali Helali, and Chokri Bouraoui
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Experimental Analysis of the Dynamic Behavior of a Sandwich with a BioBased Auxetic Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Hamrouni, J. L. Rebiere, A. El Mahi, M. Beyaoui, and M. Haddar Numerical Analysis of Entropy Generation Inside the Diesel Injector . . Fraj Echouchene and Hafedh Belmabrouk Assessment of Surface Integrity and Dust While Drilling of GLARE® FMLs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Imed Boughdiri, Tarek Mabrouki, Redouane Zitoune, and Khaled Giasin
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An Adaptative Differential Evolution Algorithm for Vibration Level Reduction in Rotordynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Ibrahim Mlaouhi, Najeh Ben Guedria, and Chokri Bouraoui Nanoheat Transfer in GAAFET Transistor Using SinglePhaseLag Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Maissa Belkhiria, Fraj Echouchene, and Nejeh Jaba Hydrodynamics Flow in an Exocentric Input Dome TMixer (DTM) . . . 123 Fatma Ben Baha Spiridigliozzi, Slim Bouaziz, Mohamed Haddar, Mounir Ben Amar, and JeanPhilippe Passarello 3D Simulation of Two Stages Solar Tower . . . . . . . . . . . . . . . . . . . . . . . 131 Ons Ghriss, Abdallah Bouabidi, Zied Driss, and Mohamed Salah Abid A New Approach to Evaluate and Predict System Obsolescence: Mathematical Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Imen Trabelsi, Maher Barkallah, Marc Zolghadri, Besma Zeddini, and Mohamed Haddar Transient Response of Functionally Graded Porous Plate . . . . . . . . . . . 150 Souhir Zghal, Sourour Trabelsi, and Fakhreddine Dammak Water Aging Effect on the Vibration Behavior of the BioBased Flax/PLA Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 Zeineb Kesentini, Abderrahim El Mahi, Jean Luc Rebiere, Rachid El Guerjouma, Moez Beyaoui, and Mohamed Haddar An Anisotropic Model with Linear Perturbation Technique to Predict HCP Sheet Metal Ductility Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 Mohamed Yassine Jedidi, Mohamed Ben Bettaieb, Farid AbedMeraim, Mohamed Taouﬁk Khabou, Anas Bouguecha, and Mohamed Haddar Effect of AirGas Blend and Compression Ratio on Piston Behavior for HydrogenEnriched LPG Engine; Numerical Study . . . . . . . . . . . . . 177 Sahar Hadjkacem, Mohamed Ali Jemni, Hamdi Hentati, Zied Driss, and Mohamed Salah Abid
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Dynamic Modeling of Differential Bevel Gear with UncertainbutBounded Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Wassim Laﬁ, Fathi Djmal, Ali Akrout, Lassad Walha, and Mohamed Haddar Analysis of Geometrically Nonlinear Responses of Smart FG Cylindrical Shell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 H. Mallek, H. Mellouli, and F. Dammak Finite Rotation RPIM Formulation for Geometrically Nonlinear Analysis of FGCNTRC Shell Structure . . . . . . . . . . . . . . . . . . . . . . . . . 201 H. Mellouli, H. Mallek, M. Wali, and F. Dammak Numerical Investigation on Incremental Forming Process of an Elastoplastic Functionally Graded Material . . . . . . . . . . . . . . . . . 209 A. Bouhamed, J. Mars, H. Jrad, M. Wali, and F. Dammak Simulation of the Effects of Heat Introduced During Combustion on SI Engine Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Mohamed Brayek, Mohamed Ali Jemni, Amara Ibraim, Ali Damak, Zied Driss, and Mohamed Salah Abid Fracture Toughness Resistance and Mechanical Tensile Properties of Cold Rolled CuZn30 Brass Alloy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 Wafa Taktak and Raidh Elleuch Manufacturing of Sandwich Structure with Recycled Flax/Elium Skins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 Sami Allagui, Abderrahim El Mahi, Jeanluc Rebiere, Moez Beyaoui, Anas Bouguecha, and Mohamed Haddar Thermal Performance Comparison of Various Concentrating Solar Water Heating Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 Monia Chaabane, Hatem Mhiri, and Philippe Bournot The Prestrain Impact on Tensile Properties and Fracture Toughness of AA5754H111 Aluminum Alloy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 Wafa Taktak and Riadh Elleuch Disassembly Sequence Optimization for Proﬁt and Energy Consumption Using Petri Nets and Particle Swarm Optimization . . . . . 267 Syrine Bouazza, Hichem Hassine, Maher Barkallah, Saïd Amari, and Mohamed Haddar Numerical Model for Intake System in SI Engine . . . . . . . . . . . . . . . . . 277 Mohamed Brayek, Mohamed Ali Jemni, Ali Damak, Amara Ibraim, Zied Driss, and Mohamed Salah Abid
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Optimization of the Electrical Energy Consumed by a Machine Tool for a Coupled and Uncoupled Cutting System . . . . . . . . . . . . . . . . . . . . 288 Anoire Ben Jdidia, Taissir Hentati, Hichem Hassine, Mohamed Taouﬁk Khabou, and Mohamed Haddar Quasistatic Study of Gear Mesh Stiffness of a PolymerMetallic Spur Gear System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 Ala Eddin Chakroun, Chaima Hammami, Ahmed Hammami, Ana DeJuan, Fakher Chaari, Alfonso Fernandez, Fernando Viadero, and Mohamed Haddar Combined Approach for Modeling Progressive Damage in Unidirectional CFRP Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 B. Salem, A. Mkaddem, S. Rubaiee, A. S. Bin Mahfouz, A. AlZahrani, and A. Jarraya Impact of Venturi Shape on Performance of Solar Chimney Power Plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 Haythem Nasraoui, Abdallah Bouabidi, Zied Driss, and Hedi Kchaou Parametric Analysis of Steel Cutting Using Johnson and Cook Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 Nouha Kamoun, Nabih Feki, Hamdi Hentati, and Mohamed Haddar Experimental Study and Measurement of Vehicle Interior Vibration . . . 333 Hichem Hassine, Hadil Chaeib, Maher Barkallah, Jamel Louati, and Mohamed Haddar Design Discussion of a Mobile and Intelligent Infrared Detector for the Measurement of the Air Quality Index . . . . . . . . . . . . . . . . . . . . . . . . . . 342 Mohamed Abdessamia Chakchouk, Abdelkhalek El Hami, Wajih Gafsi, and Mohammed Haddar ElectroThermomechanical Modelling of a BGA Assembly Subjected to a Damaging Displacement and to Random Vibrations . . . . . . . . . . . . 353 Sinda Ghenam, Abdelkhalak Elhami, Ali Akrout, Wajih Gafsi, and Mohamed Haddar Predicting of Particle ExhaustEmissions from Urban Road Trafﬁc Using Artiﬁcial Neural Networks (ANNs) . . . . . . . . . . . . . . . . . . . . . . . . 365 Ines Belkacem, Ali Helali, Salah Khardi, and Khalifa Slimi Thermohydraulic Study of an Air/R22 Tubular Evaporator: Application of the Superposition Model . . . . . . . . . . . . . . . . . . . . . . . . . 374 Lazhar Ayed Aluminum Alloy Chips Regeneration by Sintering . . . . . . . . . . . . . . . . . 388 Ameny Ketata, Awatef Guidara, Anas Bouguecha, Jamel Bouaziz, and Mohamed Haddar
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Numerical Study of Elastic Properties of Porosity Controlled Flax/PP Nonwoven Composite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396 Hajer Hadiji, Wajdi Zouari, Mustapha Assarar, Bassem Zouari, Floran Pierre, Karim Behlouli, and Rezak Ayad Analysis of Geometrically Necessary Dislocations Density in the Vicinity of Grain Boundaries by Atomic Force Microscope Topography for 316L Austenetic Stainless Steel . . . . . . . . . . . . . . . . . . . 405 Ayda Majoul, Ghiath Monnet, and Charlie Kahloun Studies on Elastic Properties of Recycled Concrete by Micromechanical Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416 D. Fellah, S. Barboura, T. Tilmatine, J. Li, M. S. Kachi, and Y. Bouaﬁa Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435
Prediction Eﬃciency of the Ultimate Load Capacity of Nut Thread with Insuﬃcient Engagement Length Hela Soussi(B) , Anis Swissi, and Abdelkader Krichen Unit of Mechanical and Materials Production Engineering (UGPMM), UR17ES43, National Engineering School of Sfax, University of Sfax, B.P. 1173, 3038 Sfax, Tunisia
Abstract. The objective of this work is to present an evaluation of the ultimate load prediction of nut thread with insuﬃcient engagement length. It is focused on the case of nut with material’s stiﬀness and strength lower than that of the screw. Seven available predictions of ultimate load were considered from literature. A pullout test was carried out on a threaded connection between a nut thread and a steel screw grade 8.8. The A1050H14 aluminum alloy sheet with 2 mm thickness was chosen. During the test, the screw was animated with a progressive axial displacement until the complete destruction of the screwnut assembly. The pullout of the nut thread is generated by transverse shear stress without interfacial shear stress. The loaddisplacement relationship was investigated. The tapped hole morphology after the complete destruction of the screwnut assembly was also inspected. The available predictions and the average experimental value of the ultimate load capacity of threaded connection were compared. This comparison supported the need for theoretical development that must be speciﬁc to the studied assembly i.e. a screw that is fastened to a nut having lower stiﬀness and strength as well as an insuﬃcient engagement length. Keywords: Nut thread test
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· Ultimate load capacity · Rupture · Pullout
Introduction
The ultimate load capacity of threaded connections depends on the strength of the screw core, the screw thread and the nut thread. As a general design rule for threaded connections, it is required that the screw will fail before the nut. The respect of this design rule needs the check of the thread length which is engaged between the screw and the nut. It is often called thread engagement length and noted in this paper Le . In ordinary design, the recommended minimum value of Le is often proportional to the thread pitch. When both screw and nut are made from the same material, the minimum value of Le is recommended to be equal to 5 (Sacquepey and Spenl´e 1993) or 8 (Duan and Joshi 2011) times the thread pitch. Respecting c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 1–10, 2022. https://doi.org/10.1007/9783030849580_1
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this geometrical condition, the part with the internal thread is manufactured with suﬃcient Le and the rupture is so appeared in the screw. Therefore, this involves designed parts with relatively large thicknesses. However, nowadays the requirement of lightness is more rigorously imposed in the design practice. The wall of the part is getting thinner and thinner. This thinning trend makes difﬁcult the satisfaction of the geometrical condition of thread. Therefore, it is even impossible to satisfy both optimum lightness and recommended minimum value of Le . Consequently, it is accepted, in some industrial sectors, that parts could be designed with insuﬃcient thread engagement length, provided that the requested capacity is respected in complete safety. In the case of insuﬃcient Le and if both screw and nut are made from the same material, the rupture will occur in the screw thread. If the material’s strength of the nut is lower than that of the screw, such as some aluminum structures that are connected with highgrade steel screws, the rupture will particularly locate at the nut thread. Thus, it is needed a good control of loading on the nut thread. This later is often subjected to nonuniform combined loading. The heterogeneity of loading in the nut thread requires the consideration of an approach to evaluate the maximum value of stress. This allows localizing the most stressed point to determine the location of an eventual rupture at the nut thread. The most stressed point at the nut thread is characterized by the presence of a transverse shear stress, which is sometimes assumed predominantly pure and in some cases is considered as a consequence of thread bending and of a torsional stress generated by the thread friction torque. By considering various approaches, several relationships have been proposed to describe the capacity safely or the ultimate load capacity of nut thread. Some approaches are based on a detailed description of the stress states through the consideration of a volume element in the most stressed zone of the nut thread (Collins et al. 2009). Others approaches are based on simplifying assumptions. They frequently introduce a multiplicative correction coeﬃcient in the expressions used to evaluate the capacity safely and/or the ultimate load capacity of thread. Generally, the value of this coeﬃcient is empirically proposed as a constant or as a function of thread geometry. A review of some expressions is presented in the Sect. 2.3 for the case of nut thread. They were provided from the literature or also from technical documents. For example, the approach of Sacquepey and Spenl´e (1993) assumes a pure transverse shear while neglecting the eﬀects of both thread bending and interfacial shear stress generated at the thread ﬂanks. Either for this approach, or for others proposed for example by Oberg and Jones (1916) and Shigley (2011), the correction coeﬃcient is used to estimate an eﬀective area of thread supporting transverse shear stress. In some cases, this coeﬃcient is given depending on the classes of screw thread and nut thread (Barrett 1990). Its value depends on the quality of threads assembly, which can be perfectly mated or mismatched. In some approaches, this coeﬃcient is occasionally introduced to take into account the nonuniform distribution of load along the thread. This has been highlighted by the work of Yamamoto (1980). The author showed that the ﬁrst portion of the thread, starting from the interface of the assembled parts, alone supports of
Prediction Eﬃciency of the Ultimate Load Capacity of Nut Thread
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about 34% of the total axial load. Other researchers have proposed to incorporate some constants, which reﬂect the eﬀect of several parameters. These parameters are related to the thread surrounding and/or taken into account the degree of dissimilarity between the intrinsic properties of the assembled materials (Barron 1998). However, the evaluation of these constants is restricted to the cases of threaded connections speciﬁcally studied by the concerned investigations. From a practical point of view, the variety of expressions available in the literature can be considered as an enrichment for predicting the ultimate load capacity of nut thread. Nevertheless, a signiﬁcant diﬀerence is often noted in the estimation procedure. Unfortunately, there appears to be no documented information on the prediction of the ultimate load capacity of nut thread with insuﬃcient Le and dissimilar stiﬀness and strength of the nut and screw materials. This paper proposes then the investigation of the rupture behavior of nut thread with insuﬃcient engagement length and material’s stiﬀness and strength lower than that of the screw. The average experimental value of the ultimate load capacity of nut thread was determined from a pullout test performed on a threaded connection between A1050H14 aluminum alloy and a steel screw grade 8.8. Several predictions were considered from diﬀerent approaches available in the literature and were compared with the experimental result.
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Material and Techniques Material
The A1050H14 untreated aluminum alloy was chosen to carry out this study. It was delivered in the form of a 2 mm sheet. The stressstrain behavior of the aluminum alloy was characterized by uniaxial tensile test carried out on ﬁve specimens. By taking into account the weak anisotropy of the used material (Soussi et al. 2016), the tensile tests were limited to the rolling direction. The two extreme curves of the true stresstrue strain relationship are presented in Fig. 1a. Note that, the portion of the curve after necking is presented in indicative way. In order to characterize the shear behavior of the aluminum alloy, the shear test was performed by using a speciﬁc device directly connected to a tensile test machine. The shear direction is along the length of the specimen. The details of the shear test is particularly described in the work of Thuillier et al. (2009). A typical shear stressshear strain curve is illustrated in Fig. 1b. The ultimate shear strength τm was determined of about 68 MPa. All mechanical properties of the used material are summarized in Table 1.
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68 GPa
Poisson’s ratio (ν)
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Maximum strain at fracture f 0.105–0.144 0.2% proof stress (σy0.2 )
105 MPa
Ultimate tensile strength (σm ) 120–122 MPa Ultimate shear strength (τm )
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Experiments
Cut tapping process was performed on a washer with an external diameter of 20 mm. M8 tap with a pitch P of 1.25 mm was used to manufacture triangular ISO thread. The thread engagement length Le is then equal to 1.6 times the thread pitch P . The initial tap hole was utilized without chamfer. It was drilled by means of a drill bit with a diameter equal to 6.8 mm. The principle scheme of the thread manufacturing is illustrated in Fig. 2a. To conduct the pullout test, a steel screw grade 8.8 was mounted freely with the specimen. An axial displacement was then applied to the screw using a tensioncompression testing machine (Fig. 2b). The test was carried out until the complete destruction of the threaded connection. The preparation protocol of the specimens as well as the details of the experiments were accurately described in the works of Swissi et al. (2019). 2.3
Analytical Solutions
In order to predict the ultimate load capacity of the nut thread, the maximum th that the thread can support was determined from various expressions. load Fmax The used expressions are summarized in Table 2. Note that, Eq. 1 is used to allow mismatch between threads. Equation 2 is used when the threads were perfectly mated. Equation 3 is used in the case of dissimilarity between material properties
Prediction Eﬃciency of the Ultimate Load Capacity of Nut Thread (a)
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(b) Axial displacement
Tap Screw 8.8
Washer
Specimen
Fig. 2. Device principle scheme of (a) the thread manufacturing and (b) the pullout test by applying an axial displacement
of threads. In Eq. 6, C1 describes the thread surrounding and C3 relates the degree of materials dissimilarity. Equation 7 is developed with pure transverse shear assumption. It is also noted that these expressions are proposed to respect the general design rule that the screw will fail before the nut i.e. for the case of suﬃcient engagement length. Compared to our study case, Eqs. 1, 2, 3, 5 and 6 take into account the dissimilarity between the material properties of threads. Table 2. Theoretical expressions for the maximum load of nut thread References Barrett (1990) Barrett (1990) Strang (1970) Shigley (2011) Lee et al. (2011) Alexander (1977)
th Expression of Fmax
1 τm πd2 Le (1) 3 1 τm πd2 Le (2) 2 3 τm πd2 Le (3) 4 0.88τm πdLe (4) (d − D2 ) tan 30 1 + τm πdLe (5) 2 P (d − D2 ) tan 30 1 C1 C3 + τm πdLe 2 P
(6)
Sacquepey and Spenl´e (1993) 0.757τm πdLe (7) d: Basic major diameter, d2 and D2 : Pitch diameters of external and internal threads, respectively.
3 3.1
Results and Discussion Specimen After the PullOut Test
At the end of the pullout test, the screw was extracted intact after the assembly destruction. However, a portion of the nut thread was removed with the screw.
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Because of the dissimilarity between the ultimate strength of the screw and the ultimate strength of the specimen, the rupture was located in the nut thread. The removed portion took the form of a helical element. Typical examples of the specimen after the pullout test and the helical element are presented in Fig. 3. The same ﬁgure illustrates a radial section of the specimen after the pullout test. It was obtained by cutting operation, which was radially performed on the specimen by wirecut EDM (Electrical Discharge Machining).
A
A
A Helical element
AA
Radial section of the specimen
Fig. 3. Specimen after the pullout test
3.2
LoadDisplacement Relationship
The practice of the pullout test on a tensioncompression testing machine resulted to the evolution of the axial load versus the displacement. Typical curves acquired from two diﬀerent specimens are illustrated in Fig. 4. 2.5 II
I
III
Load (kN)
2 1.5 1
Specimen 1
Specimen 2
0.5
0 0
0.5
1 1.5 Displacement (mm)
2
2.5
Fig. 4. Typical examples of loaddisplacement curve
The comparison between both curves shows a good reproducibility. The analysis of the loaddisplacement relationship illustrates a shape that remains globally distinctive. Referring to Fransplass et al. (2013) and Grimsmo et al. (2016),
Prediction Eﬃciency of the Ultimate Load Capacity of Nut Thread
7
a similar shape was likewise observed when a rupture occurs at the screw thread. Recently, Swissi et al. (2019) also found the same shape when testing a steel nut thread by applying an axial displacement on the screw. These authors presented an intuitive reading of the kinematics during the test. They were distinguished three stages: the resistance stage (I), the destruction stage (II) and the extraction stage (III) of a helical element. These three stages are similarly observed for our case as shown in Fig. 4. The resistance stage concerns the nonlinear evolution, which is considered as an engagement between the screw thread and the nut thread. The destruction stage begins with the loss of linearity due to the plastic strain initiation of nut thread. It involves two peaks of load followed by two falls. The extraction stage of the helical element is characterized by an almost regular plateau. 3.3
Ultimate Load Capacity of Nut Thread
In order to analyze the ultimate load capacity of nut thread, the experimental exp resulted from the pullout test were considered. values of the maximum load Fmax The average value is presented in Fig. 5 in the form of a histogram. To verify the presence or not of bending phenomenon during the pullout test, the maximum displacement δmax of the specimen due to bending was determined based on the elasticity theory (Eq. 8) referring to Young (2002). It was evaluated equal to 0.0014 mm which is very low compared to the screw displacement. This shows that the test was performed without bending. exp Kr2 Fmax (8) Ee3 K: constant related to the specimen geometry (0.0242), r: radius of the initial tap hole, e: sheet thickness, E: Young’s modulus. The predicted values of the maximum load, which were determined from the expressions cited in Table 2 are also superimposed in Fig. 5. These predictions were evaluated based on the experimental value of the ultimate shear stress τm determined in the Sect. 2.1. C1 and C3 were evaluated equal to 1 and 0.897, respectively referring to Alexander (1977). The diameters values d, d2 and D2 were taken equal to 7.84, 7.188 and 7.188 mm, respectively. The comparison between the experimental and predicted results shows a signiﬁcant disagreement. For the majority of cases (Eq. 3–7), the theoretical predictions overestimate the maximum load and therefore the ultimate load capacity of the nut thread. In order to quantify this disagreement, the attention was paid on the percentage error E% between the experimental and predicted results. E% is expressed in absolute value and given as a percent. It is deﬁned as the diﬀerence between exp and its theoretical prediction the experimental value of the maximum load Fmax th Fmax divided to the experimental one (Eq. 9). The variation of E% is illustrated in the form of a histogram in Fig. 6. exp th Fmax − Fmax × 100 (9) E% = exp Fmax
δ=
8
H. Soussi et al. for the expressions: Eq. 4
3
Eq. 5 and Eq. 6 Eq. 7 Eq. 3
Maximum Load (kN)
2.5 2
Eq. 2 1.5 Eq. 1
1 0.5 0 1.5
Fig. 5. Average experimental value and theoretical predictions of maximum load 60
Percentage errort (E%)
50
40 30 20 10 0
Eq. 1
Eq. 2
Eq. 3
Eq. 4
Eq. 5
Eq. 6
Eq. 7
Fig. 6. Percentage error E% between the experimental and predicted results of maximum load
It is noted that the maximum value of the percentage error E% reaches 50% by using Eq. 1. If an indicative value of the maximum load is needed for estimation, Eq. 3 leads to the best prediction with an overestimation of about 12.5%. From a safely aspect, the use of Eq. 2 leads to the best predicted value of the ultimate load capacity with an underestimation of about 25%. It should be noted that in the corresponding reference (Barrett 1990), the correction coeﬃcient value is empirically related to the classes of threads or the dissimilarity of their material properties. 3.4
Tapped Hole Morphology After the Screw Extraction
In a attempt to perceive the tapped hole morphology after the screw extraction, the radial section of the specimen was visualized by means of optical macro photography implemented in 3D measuring machine. The result is illustrated in Fig. 7. It is observed that a portion of nut thread with partial section is ﬂanged without rupture. It is also observed that an unbroken portion of nut thread is slanted in the sense of the screw displacement. The observed slant proves that an excessive thread bending was occurred during the pullout test. This means
Prediction Eﬃciency of the Ultimate Load Capacity of Nut Thread
9
that a portion of thread material remains attached to the tapped hole after the test. This also indicates that the rupture was located in a zone relatively distant from the thread root. Therefore, the thread rupture was occurred with a reduced eﬀective area. In addition, the unbroken portion of the nut thread also exhibited a nonregular edge. This aspect can be attributed to a nonregular rupture which combines alternately the propagation of local rupture and crushing the sheared edge.
Displacement direcon Thread root
Slant of the unbrocken poron of thread
1mm
Flanging of poron of thread without rupture
Fig. 7. Tapped hole morphology after the thread destruction showing trace of thread bending
4
Conclusion
The main context of this work is the investigation of the rupture behavior of nut thread with insuﬃcient thread engagement length and material’s stiﬀness and strength lower than that of the screw. A pullout test was carried out on A1050H14 aluminum nut thread connected with a steel screw grade 8.8 by applying axial displacement to the screw. The analysis of the loaddisplacement relationship permits the identiﬁcation of three stages of thread rupture behavior: resistance, destruction and helical element extraction. The inspection of the tapped hole morphology after the assembly destruction exhibits that the thread rupture is located in a zone relatively distant from the thread root. This rupture combines alternately the propagation of local rupture and crushing the edge. Through the quantiﬁcation of the percentage error E% between the average experimental value and the theoretical predictions of the maximum load, it is noted that the use of Eq. 2 leads to the best predicted value of the ultimate load capacity below which no rupture occurs in the nut thread. In perspective, it would be better to further develop theoretical expressions or numerical models to describe the speciﬁc cases of threaded connections with dissimilar stiﬀness and strength and insuﬃcient engagement length of nut thread. Acknowledgement. This work is carried out thanks to the support and funding allocated to the Unit of Mechanical and Materials Production Engineering (UGPMM/UR17ES43) by the Tunisian Ministry of Higher Education and Scientiﬁc Research. The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.
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References Alexander, E.M.: Analysis and design of threaded assemblies. SAE Trans. 86, 1838– 1852 (1977) Barrett, R.T.: Fastener design manual, vol. 1228. NASA, Scientiﬁc and Technical Information Division (1990) Barron, J.: Computing the Strength of a Fastener. Marcel Dekker, New York (1998) Collins, J.A., Busby, H.R., Staab, G.H.: Mechanical Design of Machine Elements and Machines: A Failure Prevention Perspective. Wiley, New York (2009) Duan, W., Joshi, S.: Failure analysis of threaded connections in largescale steel tie rods. Eng. Fail. Anal. 18(8), 2008–2018 (2011). https://doi.org/10.1016/j.engfailanal. 2011.06.002 Fransplass, H., Langseth, M., Hopperstad, O.: Numerical study of the tensile behaviour of threaded steel fasteners at elevated rates of strain. Int. J. Impact Eng. 54, 19–30 (2013). https://doi.org/10.1016/j.ijimpeng.2012.10.009 Grimsmo, E.L., Aalberg, A., Langseth, M., Clausen, A.H.: Failure modes of bolt and nut assemblies under tensile loading. J. Constr. Steel Res. 126, 15–25 (2016). https:// doi.org/10.1016/j.jcsr.2016.06.023 Lee, Y.L., Barkey, M.E., Kang, H.T.: Metal Fatigue Analysis Handbook: Practical ProblemSolving Techniques for ComputerAided Engineering. Elsevier, Amsterdam (2011) Oberg, E., Jones, F.D.: Machinery’s Handbook, vol. 1916. Industrial Press, New York (1916) Sacquepey, D., Spenl´e, D.: Pr´ecis de construction m´ecanique: 3. Calculs, technologie et normalisation. Nathan (1993) Shigley, J.E.: Shigley’s Mechanical Engineering Design. Tata McGrawHill Education, New York (2011) Soussi, H., Masmoudi, N., Krichen, A.: Analysis of geometrical parameters and occurrence of defects in the holeﬂanging process on thin sheet metal. J. Mater. Process. Technol. 234, 228–242 (2016). https://doi.org/10.1016/j.jmatprotec.2016.03.027 Strang, A.G.: Handbook H28 1969 screw standards for federal services. PT. 1 Uniﬁed UNJ Uniﬁed Miniature Screw Threads. U.S. Government Printing Oﬃce (1970) Swissi, A., Soussi, H., Abid, M., Krichen, A.: Internal and interface shear behaviors of cut and form tapping thread. Int. J. Adv. Manuf. Technol. 105, 3463–3475 (2019). https://doi.org/10.1007/s0017001904519y Thuillier, S., Manach, P.Y.: Comparison of the workhardening of metallic sheets using tensile and shear strain paths. Int. J. Plast. 25(5), 733–751 (2009). https://doi.org/ 10.1016/j.ijplas.2008.07.002 Yamamoto, A.: The Theory and Computation of Threads Connection, pp. 39–54. Youkendo, Tokyo (1980) Young, W.C., Budynas, R.G., Sadegh, A.M.: Roark’s Formulas for Stress and Strain, vol. 7. McGrawHill, New York (2002)
Cement Reduction and Strength Development of Conventional Mortars by Utilization of Dried Waste Marble Slurry Mohammad Rafi Rafi1,3(B) , Safiullah Omary2 , Elhem Ghorbel1 , and Amanullah Faqiri3 1 Department of Civil Engineering, University de CergyPontoise, L2MGC,
95000 CergyPontoise, France [email protected], [email protected] 2 ICube, Department of Civil Engineering, INSA Strasbourg, University of Strasbourg, 67000 Strasbourg, France [email protected] 3 Department of Civil and Industrial Construction, Kabul Polytechnic University, Kabul, Afghanistan [email protected]
Abstract. Industrial waste, especially the mining sector’s waste, has been negatively treating human life and the ecosystem. This experimental work aims to keep the environment safe out of waste, produce high  strength mortars and support the national economy by utilizing dried waste marble slurry (DWMS) collected from the marble shaping industry in Kabul Afghanistan. Marble slurry was dried and grind to very fine powder shape with 90% partials passing through 0,063mm sieve. Mortars were prepared as a reference and partially cement replacement by DWMS with (5%, 10%, 15%, 20%, and 25%) by cement weight. The specific surface area of DWMS was 3957 cm2 /gr with a density of 3.12 gr/cm2 , while the mentioned parameters for Afghan ordinary Portland cement named (Ghori) was 3051 cm2 /gr and 2.997 gr/cm2 , respectively. Mortars’ mixes were tested against workability, porosity and water absorption, compressive and flexure strengths. The obtained results indicate that with the use of 15% DWMS dosage instead of cement, the compressive strength gets increased up to 15.5% compared to reference mortars. Also, porosity of the mortars’ specimens gradually decreased. The reduction in the amount of cement for the mortars’ production derive to support the national economy and protect the environment from waste. Keywords: Marble slurry · Mortar · Consistency · Compressive strength · Flexure strength
1 Introduction Afghanistan’s mountainous country is located in an area with different geological zones that consist of various precious rocks. Afghanistan has 60 marble mining of 40 different colors and 30 spices. According to the USA survey and geology department, the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 11–21, 2022. https://doi.org/10.1007/9783030849580_2
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worth of Afghanistan’s marble sources is estimated at around 2 billion dollars Ministry of Commerce and Industry of Afghanistan (2018). The marble mining is running unprofessionally by unskilled laborers. Beyond that, the lack of advanced machinery and unprofessional extraction is very regrettable. As a result of producing marble quarries, a tremendous amount of marble waste generates which is not comparable to international mining practices. Nearly 70 % of marble stone resource gets wasted due to mining and polishing processing, Ministry of Micro, Small & Medium Enterprises (2008). Leaving the waste storages to the surroundings or landfills of marble waste due to its highly alkaline property imposes a high risk of human health and ecosystem challenges Hamza et al. (2011). Recently many researches have been conducted worldwide on the utilization of waste marble in the mortars and concrete industry to reduce the overall cost of cementitious structures and manage the waste in scientific manners. Hence the overall quantity of C2S and C3S, the two crucial components to construct binder in the marble cement, is 56.23% Khan et al. (2020); therefore, it can be used as the binder. Due to high fineness, marble powder can prove sufficient cohesiveness in mortar and concrete Guneyisi et al. (2009). The effect of partially cement replacement by marble waste powder with different dosages (from 0% to 20%) by cement weight on various properties of concrete was studied by Hafiz et al. (2019), the optimum percentage for replacement of marble powder with cement, that can increase the concrete strength and play sufficient rule in concrete was pointed 10% . Similarly, waste marble was utilized as cement replacement in cement mortars by Vardhan et al. (2015) to explore the mechanical properties and microstructural analysis of cement mortar; the results indicate that up to 10% of marble powder can be used as cement replacement with no negative impact on the mechanical behaviors. Therefore, this study targeted to improve mortars’ strengths by replacing cement with marble waste partially, to support Afghanistan’s national economy and contribute to a lovely and safe environment.
2 Materials 2.1 Cement Afghan ordinary Portland cement with strength of 250 kg/cm2 is used for all mortar’s specimens. The particle size distribution by laser granulometry method is illustrated in Fig. 1 as well as the physical properties and chemical compositions are given in Table 1 and Table 2. 2.2 Marble Powder Marble industry zone, waste marble slurry (WMS) was collected with 53% water content and then dried in the oven for 24 h in 100 ± 10 C0 and then grained as a very fine powder. See Table 1 for the physical properties and Table 2 for chemical compositions.
Cement Reduction and Strength Development of Conventional Mortars
13
2.3 Sand Standard sand 0/2 mm according to the standard NF EN 1961 (2016), siliceous sand consisting of rounded particles and has a silica content of at least 98% with relative density of 2.55 gr/cm3 is used for the mortars’ mixes. Ghori Cement
Passing (%)
100 90 80 70 60 50 40 30 20 10 0 0.01
Waste Marble
0.1
1
10 100 Partial Size (μm)
1000
10000
Fig. 1. Particle size distribution of Ghori cement and waste marble Table 1. Physical properties of cements and marble
Table 2. The chemical composition Components
Properties
Ghori cement Marble waste
Specific gravity
2.984
3.12
Specific surface Area (cm2 /gr)
3051
3957
Chemical composition (%) Ghori cement
SiO2
17.63
Marble waste 2.18
Consistency (%) 24.3

Al2 O3
4.892
0.53
Initial and final sitting time

Fe2 O3
2.016
0.04
90.5
CaO
97 min 180 min
Particle’s size 55 (%) < 0.063 mm
MgO
1.327 63.44
3.394 51.21
Na2 O
1.374
0.536
SO3
4.215
0.054
3 Experimental Methodology Specimens of (40 × 40 × 160) mm with prismatic shape were prepared and caste in standard molds in line with ASTM C348 and European standard NF P18427. DWMS
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as cement replacement by weight with the dosage of (0%, 5%, 10%, 15%, 20%, and 25%) also a ratio of cement to sand 1:3 was prepared, W/B ratio was kept 0.5 for all specimens. Conforming to the reference mortar used worldwide in the cement industry EN 1971, a conventional mortar is formulated as a reference and incorporating DWMS. The mortars’ composition proportion is reported in Table 3. Furthermore, a robust device automatic programmable mortar mixer as shown in Fig. 2 was used to prepare cement paste and mortars. Table 3. Mortars’ proportion Constituents
Cement (g)
DWMS (g)
Sand (g)
Water (g)
W/B
0% DWMS
450
0
1350
225
0.5
5% DWMS
427.5
22.5
1350
225
0.5
10% DWMS
405
45
1350
225
0.5
15% DWMS
382.5
67.5
1350
225
0.5
20% DWMS
360
90
1350
225
0.5
25% DWMS
337.5
112.5
1350
225
0.5
Fig. 2. Robust device automatic mixer 65L0512 model
4 Results and Discussions To evaluate the effects of DWMP on mortar specimens, various type of tests were performed on both fresh and hardened state of samples. Setting times, flow table tests were carried out on fresh state of paste and mortars. Moreover, mechanical tests such as compressive and flexure strength also, water absorption, porosity tests were conducted on all mortar specimen in the hardened state.
Cement Reduction and Strength Development of Conventional Mortars
15
4.1 Fresh State 4.1.1 Setting Times According to the chemistry of cement and concrete Hewlett (2004) the process in which a ‘fresh’ cement paste of freely flowing or plastic consistency is surrounded into a set material by losing its unlimited deformation and fall under the reaction of enough considerable external force. It is accompanied by the ‘hardening’ of the paste in which the hardness, strength and modulus of elasticity improve until an ultimate value of these parameters is attained. Initial and final setting times were determined according to NF EN 1963 (2009) both initial and final setting get increased as much as the DWMS dosage increased. This was due to the lack of Si2 O3 in marble waste that plays an essential role in cement paste hardening. Furthermore, the reason for increment in setting time was to draw attention as the partial engagement of waste marble that influences the hydration process Vardhan et al. (2015). The hydration process slows down with increasing content of WMP leading to increased setting time. With 5% DWMP the setting time did not change remarkably but as much the dosage goes up the setting times increased rapidly; for instance, the amount of 25% DWMS instead of cement increase both initial setting time 84.6% and final setting time 65% see Fig. 3. Similar trend was obtained by Munir et al. (2017) in setting times when cement was replaced with dried waste marble slurry as 10, 20, 30, and 40% by cement weight.
Fig. 3. Dried waste marble powder effects on setting times
4.1.2 Flow Table The flow test of mortars containing different marble waste dosages to modify fresh mortar consistency, was conducted according to NF EN 10513 (1999) standard. Automatic mortar flow table with 300 mm diameter and conical brass mold with dimensions: top ø 70 mm × base ø 100 mm × height 60 mm was used and each test was repeated three
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times and the average of three tests were taken as the flow diameter after 15 table drops for each test. Based on the results, it can be set out that with the increase of DWMS content, the mortar flow decreased as seen in Fig. 4 the flow diameter gradually changes up to 15%, but after 15% replacement dosage the flow promptly reduced as the maximum reduction was noticed for 25% DWMS about 14%. This reduction tendency in flow diameter was stated in research by Ergün (2011) due to the high specific surface area of waste marble powder. Similarly, the reduction in flow diameter was observed by Seghir et al. (2019), Munir et al. (2017).
Fig. 4. Fresh mortar’s flow
4.2 Hardened State 4.2.1 Water Absorption and Porosity Water absorption and porosity tests were carried out based on NF P 18459 (2010) for all mortars’ specimens at 24 h of curing and graphically illustrated in Fig. 5, incorporating waste marble as a function of porosity represents a linear relation. Porosity and water absorption have decreased gradually with the increase in marble waste incorporation. For instance, with 25% DWMS the porosity reduced by 39.8%; this performance will be led to increase packing efficiency that eventually resulted in changing the large form of pores to a smaller number Silva et al. (2014). Furthermore, due to the smaller particle of marble powder filler effect stated by Demirel (2010), the porosity decreased effectively; this positive trend will develop the mortars’ strength and reduce drying shrinkage. 4.2.2 Compressive Strength The compressive strength of designed mortars was measured through the automatic 3R (Recherches Realisations Remy) machine. Compressive strength of mortars prepared with and without (DWMS) was studied at curing ages of 3, 7, 14, and 28 days. Obtained results are reported in Fig. 6. It was observed that usage of (DWMS) as cement replacement could be used up to 20%, which in this dosage, the compressive strength shows
Cement Reduction and Strength Development of Conventional Mortars
17
Fig. 5. Effects of dried waste marble slurry on mortars’ porosity
the same value demonstrated by the reference. The maximum strength was observed at 15% which the strength increased by 15.5% at 28 days; meanwhile this amount can be achieved as 12% from Fig. 7 which shows the relation porosity as a function of compressive strength. Due to disturbance in hydration process in late ages indicated by Munir et al. (2017), the compressive strength has a sudden drop off at 20% dosage of marble powder. The variation of compressive strength as seen in Fig. 6; due to the differences in the chemical composition of both cement and marble waste; there are not remarkable changes in early ages of 3, 7 and 14 days but the only variation can be notice in age of 28 days. In comparison, Vardhan et al. (2015) studied mechanical properties and microstructural analysis of cement mortar incorporating marble powder as partial replacement of cement. They observed that 10% of waste marble instead of cement can maintain both good workability and compressive strength, exceeding 10% replacement; the marble powder can only act as a micro filler which contributes to forming a denser structure by filling the voids. 4.2.3 Flexural Strength The flexure test was carried out at 3, 7, 14, and 28 days. The maximum strength was achieved at 10% DWMS dosage as cement replacement, with an increment of 10.1% compared to reference mortars. This increase is due to the reduction in porosity compare to the reference specimen. The optimal dosage of marble waste that indicates the same strength as the reference mortars was determined as 15% dosage. Beyond 15% dosage the flexural strength increases gradually. The amount of 25% (WMS) as cement replacement can reduce the flexure strength by 29.8% at 28 days. Considering the results in Fig. 9, achieving the flexural strength of the mortars for the age of 3, 7, and 14 days are almost in the same manner and this trend is very slow. The gradual strength development was due to the lower amount of C3 A and C2 S (required for hydration process) Singh et al. (2017). After replacing more than 15% cement with WMP, which requires plenty of time to complete the hydration process. Since the porosity is an essential parameter for maintaining concrete’s strength and durability, Fig. 10 the flexural strength as a function of porosity finally demonstrates that;
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Fig. 6. The compressive strength of mortars
Fig. 7. Compressive strength as function of porosity
the optimal dosage of waste marble as cement replacement to maintain all parameters in acceptable manner is indicated as 12.6% by cement weight.
5 Environmental and Economic Aspects Due to the fact, the cement industry is in charge of a remarkable amount of global carbon dioxide emissions. To control this phenomenon, civil engineers are trying to reduce the amount of cement in cementitious structures. Considering Fig. 8 the optimal amount of
Cement Reduction and Strength Development of Conventional Mortars
19
Fig. 8. Porosity as function of marble waste
Fig. 9. The flexure strength of mortars
12.6% waste marble as cement replacement in this study, addition to the development of mortars strength, it can keep surrounding free of waste and reduce the amount of carbon dioxide emissions. Furthermore, in each ten bags of cement one bag can be saved that would be a significant achievement to support the national economy.
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Fig. 10. Flexure strength as function of waste marble
6 Conclusion Dried waste marble powder could be utilized as a partial alternative binder in cementbased mortars. The optimal percentage of DWMS as cement replacement was obtained 12.6%, which can develop compressive strength, stabilized the flexure strength, maintain good workability, and produce cheaper mortars. Moreover, the investigation discloses that using (DWMS) as cement replacement for better utilization depends on two influential indicators; the particle size of the waste and the chemical composition. As much as the particles are smaller and marble’s chemical composition is closer to cement; the higher replacement dosage could be utilized substitution of cement.
References Demirel, B.: The effect of the using waste marble dust as fine sand on the mechanical properties of the concrete. Int. J. Phys. Sci. 5(9), 1372–1380 (2010). https://doi.org/10.1016/j.envint.2006. 11.003 Ergün, A.: Effects of the usage of diatomite and waste marble powder as partial replacement of cement on the mechanical properties of concrete. Constr. Build. Mater. 25(2), 806–812 (2011). https://doi.org/10.1016/j.conbuildmat.2010.07.002 Guneyisi, E., Gesoglu, M., Ozbay, E.: Effects of marble powder and slag on the properties of self compacting mortars. Mater. Struct. 42, 813–826 (2009). https://doi.org/10.1617/s1152700894262 Hafiz, S.S., Malhotra, S., Singh, T.: Experimental analysis of addition of marble waste dust powder partially replacing cement. Int. Res. J. Eng. Technol. (IRJET) 06(10 Oct), 487–491 (2019) Hamza, R.A., Elhaggar, S., Khedr, S.: Marble and granite waste : characterization and utilization in concrete bricks. Int. J. Biosci. Biochem. Bioinform. 1(4 Nov), 286–291 (2011). https://doi. org/10.7763/IJBBB.2011.V1.54. Hewlett, P.C. (ed.): Lea’s Chemistry of Cement and Concrete, 4 edn. Elsevier Ltd., Amsterdam (2004)
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Khan, M.A., Khan, B., Shahzada, K., Khan, S.W., Wahab, N., Ahmad, M.I.: Conversion of Waste Marble Powder into a Binding Material. Civil Engineering Journal 6(3), 431–445 (2020) Ministry of Commerce and Industry of Afghanistan. National Strategy of Afghanistan Exports: Marble and Granite Section (2018). http://www.intracen.org/uploadedFiles/intracenorg/Con tent/Redesign/Projects/AAT/AFG_MainNES_Dari.pdf. Ministry of Micro, Small & Medium Enterprises, Jaipur. Status Report on Commercial Utilization of Marble Slurry in Rajasthan (2008) Munir, M.J., Kazmi, S.M.S., YuFei, W.: Efficiency of waste marble powder in controlling alkali – silica reaction of concrete : a sustainable approach. Constr. Build. Mater. 154, 590–599 (2017). https://doi.org/10.1016/j.conbuildmat.2017.08.002 NF EN 10153. Determination of Consistence of Fresh Mortar (by Flow Table). AFNOR (1999) NF EN 1961. Méthodes d’essais Des CimentsPartie1: Détermination Des Résistances. AFNOR (2016) NF EN 1963. Méthodes d’essais Des Ciments  Partie 3 : Détermination Du Temps de Prise et de La Stabilité. AFNOR (2009) NF P 18459. Concrete — Testing Hardened Concrete — Testing Porosity and Density. CedexFrance: AFNOR (2010) Seghir, N.T., Mellas, M., Sadowski, Ł, Krolicka, A., Zak, A.: The utilization of waste marble dust as a cement replacement in aircured mortar. Sustainability 11(2215), 1–14 (2019) Silva, D., Gameiro, F., De Brito, J.: Mechanical properties of structural concrete containing fine aggregates from waste generated by the marble quarrying industry. J. Mater. Civ. Eng. 26, 1–8 (2014). https://doi.org/10.1061/(ASCE)MT Singh, M., Srivastava, A., Bhunia, D.: An investigation on effect of partial replacement of cement by waste marble slurry. Constr. Build. Mater. 134, 471–488 (2017). https://doi.org/10.1016/j. conbuildmat.2016.12.155 Vardhan, K., Goyal, S., Siddique, R., Singh, M.: Mechanical properties and microstructural analysis of cement mortar incorporating marble powder as partial replacement of cement. Constr. Build. Mater. 96, 615–621 (2015). https://doi.org/10.1016/j.conbuildmat.2015.08.071
Experimental Analysis of the Crushing of Auxetic Structure Under Compression Khawla Essassi1,2(B) , Jeanluc Rebiere1 , Abderrahim El Mahi1 , Mohamed Amine Ben Souf2 , Anas Bouguecha2 , and Mohamed Haddar2 1 Acoustics Laboratory of Mans University (LAUM), UMR CNRS 6613, Mans University, Av.
O. Messiaen, 72085 Le Mans Cedex 9, France {Khawla.Essassi.Etu,JeanLuc.Rebiere, abderrahim.elmahi}@univlemans.fr 2 Laboratory of Mechanics Modeling and Production (LA2MP), National School of Engineers of Sfax, University of Sfax, BP N° 1173, 3038 Sfax, Tunisia [email protected]
Abstract. Auxetic structures are increasingly used in all industrial fields due to their high mechanical properties. They possess a negative Poisson’s ratio. They contract laterally when they are subjected to compressive loads and extend when they are subjected to tensile loads. In this research contribution, an experimental study of the compression behavior of a reentrant honeycomb structure is developed. The material used for the construction of the specimens is a polylactic acid reinforced with flax fibers. It is a biodegradable material and made from renewable resources. The specimens were manufactured using 3D printing technique. The influence of the number of cells and specimen’s height were measured and discussed. The results present their effect on the compression behavior and the energy absorption capacity. During compression tests, the cells deform elastically and collapse under high stress. Then, the cells crush gradually, forming folds on the cell walls. The densification phase begins when the folds consume the full height of the structure. The results showed that the number of the cells as well as specimen’s height play a major role on the mechanical behavior. The compression modulus and the energy absorption are found to be higher for auxetic structure with the high number of cells and height. Keywords: Auxetic structure · Compression behavior · Energy absorption · 3Dprinting · Biobased material
1 Introduction Auxetic structures are applied in a wide range of fields, including automotive, marine and aerospace. These structures present high stiffnesstoweight ratios and high ability to dissipate energy under compression loading (Ganilova and Low 2018; Mertani et al. 2019). The reentrant honeycomb structure enhances the compressive properties when compared to their conventional counterpart. Hou et al. (2014) studied the flatwise compression tests of the conventional and auxetic honeycomb sandwich structures. The © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 22–29, 2022. https://doi.org/10.1007/9783030849580_3
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results show that the compressive modulus, the global and the peak compressive stresses for the auxetic core are 27%, 19% and 16% higher than that with conventional ones, respectively. Under a uniaxial compression stress, the honeycomb structure response has a large and flat constant phase. The energy absorption is high during this stage (Ivanez et al. 2017). Lu et al. (2005) studied the critical compression load of honeycomb structure analytically using the deflection theory. The equation of compression densification strain has also been evaluated adopting the relative density of the structure (Wang and Wang 2009). The absorbed energy property of honeycomb structure is determined using the energy absorption diagram (Wang et al. 2018). Also, finite element methods are largely used to study the deformation characteristics using computer simulations (Liang et al. 2015; Kadir et al. 2017). Honeycombs with negative Poisson’s ratio (auxetic) can be made adopting different technique. The most commonly used is the 3D printing process (Essassi et al. 2020). Due to the environmental problems, the use of biobased materials has become the center of attention of many studies (Cheng et al. 2013). Biocomposites have proven their ability to meet certain engineering challenges. They are biodegradable, recyclable and have low cost. Natural fibers are widely used as reinforcement in composite materials (Faruk et al. 2012). Flax fibers are the most used because of their ability to improve the strength and stiffness of composite materials (Essassi et al. 2020). In this context, an auxetic honeycomb has been manufactured using 3D printing technique. The material is a tape of filament made with polylactic acid reinforced with flax fibers (PFF). The compression properties have been investigated. The effect of the number of auxetic cells as well as the specimen’s height were tested. The influence of these parameters on the mechanical behavior and energy absorption capacity is discussed.
2 Materials and Method 2.1 Materials and Manufacturing Auxetic structures are manufactured using a spool of filament of biobased material. It is a polylactic acid reinforced with flax fibers (PFF). It is a biodegradable material devoted to 3D printing technique. The diameter of the filament is 1.75 mm and the volume fraction of the fiber reinforcement is less than 20%. The density and the Poisson’s ratio of the material are equal to 1000 kg.m−3 and 0.3, respectively. Figure 1 presents the design of the unit cell of the auxetic structures. θ is the angle between the inclined walls of the unit cell and the X direction, equal to −20°. t is the thickness of the unit cell wall, equal to 0.6 mm. The specimens have a dimension of 50 mm × 25 mm × e. The effect of the height of the auxetic structure under compression test were measured (e equal to 5, 10 and 15 mm). The width is divided to obtain different cell numbers in width: 1, 2, 3 and 4 cells. Therefore, the lengths of the inclined cell walls l are 13.3, 6.6, 4.4 and 3.3 mm, respectively. And, the lengths of the vertical cell walls h are 17, 8.5, 5.7 and 4.3 mm, respectively. The PFF properties are measured using a uniaxial tensile test performed on 3D printed dogbone following the ASTM D638 standard. The Young Modulus of PFF is equal to 2000 MPa. The cell geometry was created using CAD software. Afterward, 3D printing technique is used to manufacture the auxetic structures. A parametric study was elaborated
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Fig. 1. Design of the unit cell of the auxetic structure
to select printing parameters that allow the stability of the specimens. The temperature of the extrusion head and building platform is of 210 °C and 55 °C, respectively. The movement speed of the XY motion mechanism was about 100 mm.s−1 . All specimens are printed using the same direction to avoid the influence of the layer orientation on the mechanical properties of the material. 2.2 Experimental Setup Compression tests of the reentrant honeycomb structure were performed using a standard INSTRON 8801 hydraulic machine, with a load cell of 100 kN. Figure 2 shows the experimental setup. The compression tests were carried out according to ASTM C365 under displacementcontrol mode. The bottom plate is fixed and the top plate is moved downwards at a constant velocity of 1 mm.min−1 . The displacement of the auxetic structure in the compression tests is that given by the machine. For each configuration, three specimens were tested in order to take into account the variability of the experimental results.
Fig. 2. Setup of the compression test
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3 Results and Discussion 3.1 Mechanical Responses Compression tests were accomplished on different shapes of auxetic structure configurations. Figure 3 introduces a typical stress/strain curve of the auxetic behavior under compression loading. There are three zones which can be distinguished from the presented results. Initially, a linear elastic domain is noticed. The stress evolves linearly according to the applied strain, which makes it possible to measure the compression modulus. A threshold stress is observed at the end of this phase. It corresponds to the initial stress at break followed by a short phase of load reduction. Later, a second zone is observed. A constant stress plateau is defined during a significant applied strain interval. Finally, a third zone at the end of the test is defined. It corresponds to the total crushing of the structure. The stress increases rapidly in this area, allowing the definition of the phase of densification.
Fig. 3. Compression behavior of a 5 mm height structure with 1 cell in width
According to the stress/strain curves, the compression modulus can be determined. The result is shown in Fig. 4. For each configuration, three specimens were tested in order to take into account the variability of the experimental results. The standard deviation varies between 2 and 30 MPa. The influence of the number of cells is well noted. The increase of the number of cells implies the increase of the density of these structures, hence the improvement of the compression modulus. The increase in the number of cells affects not only the compression modulus, but also the entire compression response. Figure 5 shows the effect of the number of cells on the behavior of the auxetic structure. The fracture stress, plateau stress and stiffness increase with the number of cells. The effect of the auxetic structure height was also determined and shown in Fig. 6. It is noticeable that the increase of the structure height increases the stress plate which is expected. The stress at fracture decreases when the structure height increases. This can be explained by the ways in which the structures are damaged by compression. By increasing the length of the cell walls (increasing the height), the intracellular vacuum increases, which induce a low load to ‘collapse’ the material.
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Fig. 4. Compression modulus for different auxetic structure configurations
Fig. 5. Compression behavior of a 5 mm height structure with different number of cells in width
Fig. 6. Compression behavior of a structure with 1 cell in width and different height
3.2 Dissipated Energy The energy absorption capacity of the materials is an important feature for their applications. From the point of view of energy absorption, the number of cells is an important parameter. Experimental compression tests make it possible to calculate the quantity
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of the dissipated energy by the auxetic configurations (several number of cells as well as heights). The results are presented in Fig. 7. It is clearly seen that the dissipated energy increases with the number of cells and with the height of the structure. Indeed, the increase in the number of cells includes the increase in the rigidity of the structure. This improves its ability to support the crushing effort and thus improves its energy dissipation. Also, increasing the height of the structure serves to increase the stress plateau, which gives the structure more time before collapsing. Therefore, the choice of the number of cells as well as the height of the structure must be studied according to the desired results.
Fig. 7. Evolution of the dissipated energy for different auxetic configurations
3.3 Discussion In order to discuss the performance of the auxetic structures made with PFF, the experimental results of the maximum applied load are determined and presented in Fig. 8. It is noticeable that the core with a large number of cells and low height is the one who has the maximum load. Indeed, for the same height, the increase in the number of printed cells leads to a decrease in the intracellular voids of the structure. During the compression test, the cells will be crushed. For the structures containing more voids, the crushed cell walls will find more space to deform. On the other hand, the cells of the other structures will collapse, which requires more load. Also, the increase of the structure height implies a decrease in the applied load. This result can be explained by tracking damage in these structures. Figure 9 shows the damage process of the auxetic structure with 2 cells in width for different height. Initially, an elastic buckling of the cell walls is observed until a maximum stress from which the deformation of the walls becomes plastic. Subsequently, the cells are gradually crushed by forming folds, this is the phase where the stress becomes constant. In this phase, the crushed cell walls will be distributed in intracellular voids. The material deforms without increasing the stress until the voids disappear. When the height of the auxetic structure (length of the cell walls) is small, the intracellular voids are also small. Here, the stress plateau will be low, and the third phase will appear when
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Fig. 8. Evolution of the maximum load according to the number of cells for different height
the entire height of the cell walls is consumed by the folds. It is the densification phase. Consequently, auxetic structures are largely able to deform which favors the dissipation of the mechanical energy.
Fig. 9. Damage process of auxetic structures with different height: a) 5 mm; b) 10 mm and c) 15 mm
4 Conclusion The compression properties of a biobased auxetic structure are studied experimentally. Structures were made using 3D printing technique. Four different number of cells and three heights out of PFF were tested under quasistatic compression tests. The mechanical behavior and the dissipated energy capacity were calculated. It is found that the number of cells of the auxetic structure has a significant effect on the mechanical properties. Structures with the high number of cells and the high height dissipates more energy. Intercellular voids as well as the shape of auxetic cells are responsible for this result.
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References ASTM Standard C36503: standard test method for flatwise compressive properties of sandwich cores. Annual Book of ASTM Standards (2003) Cheng, H.N., Smith, P.B., Gross, R.A.: Green polymer chemistry: a brief review. Greens Polym. Chem.: Biocatal. Mater. II 112 (2013) Essassi, K., Rebiere, J.L., El Mahi, A., Ben Souf, M.A., Bouguecha, A., Haddar, M.: Experimental and analytical investigation of the bending behaviour of 3Dprinted biobased sandwich structures composites with auxetic core under cyclic fatigue tests. Compos. Part A: Appl. Sci. Manuf. 131, 105775 (2020) Essassi, K., Rebiere, J.L., El Mahi, A., Ben Souf, M.A., Bouguecha, A., Haddar, M.: Investigation of the static behavior and failure mechanisms of a 3D printed biobased sandwich with auxetic core. Int. J. Appl. Mech. 12(05), 2050051 (2020) Faruk, O., Bledzki, A.K., Fink, H.P., Sain, M.: Biocomposites reinforced with natural fibers: 2000–2010. Prog. Polym. Sci. 37(11), 1552–1596 (2012) Ganilova, O.A., Low, J.J.: Application of smart honeycomb structures for automotive passive safety. Proc. Inst. Mech. Eng. Part D: J. Automob. Eng. 232(6), 797–811 (2018) Hou, Y., Neville, R., Scarpa, F., Remillat, C., Gu, B., Ruzzene, M.: Graded conventionalauxetic Kirigami sandwich structures: Flatwise compression and edgewise loading. Compos. B Eng. 59, 33–42 (2014) Ivanez, I., FernandezCañadas, L.M., SanchezSaez, S.: Compressive deformation and energyabsorption capability of aluminium honeycomb core. Compos. Struct. 174, 123–133 (2017) Kadir, N.A., Aminanda, Y., Dawood, M.S.I.S., Mohktar, H.: Numerical analysis of kraft paper honeycomb subjected to uniform compression loading. J. Phy.: Conf. Ser. 914, 012004 (2017) Liang, X., Wang, Y.L., Ding, H.: Finite element analysis of static compression performance of honeycomb papercore. Packag. Eng. 36(19), 59–63 (2015) Lu, L.X., Sun, Y.P., Wang, Z.W.: Critical buckling load of paper honeycomb under outofplane pressure. Packag. Technol. Sci.: Int. J. 18(3), 141–150 (2005) Mertani, B.M.B., Keskes, B., Tarfaoui, M.: Experimental analysis of the crushing of honeycomb cores under compression. J. Mater. Eng. Perform. 28(3), 1628–1638 (2019). https://doi.org/10. 1007/s1166501838522 Wang, D., Bai, Z., Liao, Q.: 3D energy absorption diagram construction of paper honeycomb sandwich panel. Shock. Vib. 2018, 4067062 (2018) Wang, D.M., Wang, Z.W.: Evaluation of compressive densification strain of paper honeycombs. J. Mech. Eng. 45(5), 285–289 (2009)
System Level Specification and Multiagent Simulation of Manufacturing Systems Khalil Aloui1,2(B) , Amir Guizani2 , Moncef Hammadi1 , Thierry Soriano1 , and Mohamed Haddar2 1 QUARTZ Lab EA7393  SUPMECA  3 rue Fernand Hainaut, 93400 SaintOuen, France
{moncef.hammadi,thierry.soriano}@supmeca.fr 2 LA2MP, University of Sfax, Ecole National d’Ingénieurs, 3038 Sfax, Tunisia
[email protected]
Abstract. Lately, multiagent systems (MAS) are being exploited to solve emerging challenges in manufacturing processes that require adaptation, flexibility, and reconfigurability, which are important advantages over traditional centralized systems. The understanding, design and testing of such complex systems manufacturing processes based on distributed agents, and especially those with personal properties, is generally a difficult task. Multiagent systems offer an alternative way to design and improve manufacturing processes and control systems due to their inherent abilities to adapt autonomously to emergence. Multiagent simulation assumes a crucial role to analyze and improve the manufacturing process during the design phase. Indeed, it is well suited to simulate manufacturing processes that present complex phenomena like emergent behaviour and selforganization. This paper discusses the modeling and simulation of the steel converter process. The Systems Modeling Language (SysML) is used to illustrate the benefits of such tools in the manufacturing world on the specification of a steel converter process. Requirements diagrams are used to present the main requirements of the system. In addition, state machine diagrams are used to describe the activities of different steel converting process machines. Finally, block definition diagrams are also used to define the components of this process. A model of this process has been developed using SysML diagrams; and the simulation results are used to validate this model. Keywords: Manufacturing systems · Multiagent simulation · Systems Modeling Language (SysML) · Simulation tool (Anylogic)
1 Introduction Thanks to multiagent systems (MAS), the design and manufacturing of control solutions have become more flexible, adaptive, and reconfigurable compared to traditional systems (Wooldridge 2009). These systems are used to solve emerging challenges in the design and manufacture of industrial systems in terms of adaptation, flexibility and reconfigurability (Barbosa and Leitão 2011). © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 30–40, 2022. https://doi.org/10.1007/9783030849580_4
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(Marik and McFarlane 2005) have shown that MAS are characterized by the decentralization of the control of its distributed structures which provide robustness, modularity, and autonomy of the processes and solve at least 25% of manufacturing problems. For example, (Guizani et al. 2014a) have developed a new approach based on multiagent technologies for the optimal design of mechatronic systems. The proposed approach is further improved by the development of a coordination and negotiation process allowing agents to facilitate the collaborative design of distributed systems (Guizani et al. 2014b). They subsequently validated this work through a test case to optimize the preliminary design of an electric vehicle (Guizani et al. 2017). The multiagent swarm framework can adequately represent characteristics of supply chains, such as multiple levels of abstraction and separation of concerns. Through this multiagent model, individual agents are integrated with trust mechanisms to identify trusted partners to fulfill customer orders (Lin et al. 2005). In addition, the study of swarm robotic systems has been considered as a study of multiagent systems. Developers of swarm robot systems use realistic simulators to test and accelerate the development of new design methods (Aloui et al. 2020). They use simulators to model the interactions between robots and the interactions of robots with their environment (Schin et al. 2008). The software required to develop agents is simpler and shorter than the software required by centralized approaches (O’Hare and Jennings 1996). However, analyzing, testing, and validating the behavior of multiagent systems is generally difficult and timeconsuming. It is necessary to use tools that support the correction of errors during the design phase before its deployment in the real operation; These are the tools of multiagent simulation that simplify the representation, the testing, and therefore the understanding of the behavior of the system. In manufacturing, developers reduce the time and cost of developing control systems by using simulation which allows for the detection of errors, mistakes, and misunderstandings during the design phase and before moving on to implementation (De Vin and Jagstam 2001). In this article, we study the steel converter process with the aim of developing a model that focuses on the crane management algorithm to minimize discontinuities in the operation of continuous casting machines. In the first part, we model this process using Systems Modeling Language (Mhenni et al. 2014). In fact, several SysML diagrams are used such as requirements diagram to specify system requirements, sequence diagram and state machine diagram to model system behavior, and block definition diagrams to identify structural architecture. In the second part, we use a multiagent tool called “Anylogic” to simulate the modeled version and check the performances through the results obtained.
2 Steel Converter Process Today, we use steel to fabricate everything from sewing needles to oil tankers. It is the most used material for building industries and the world’s infrastructure (Lukša et al. 2020), (Tossavainen et al. 2007). In addition, all the tools required to build and manufacture are made of steel. The process of converting steel is very complicated (Kovalev et al. 2016). It can be simplified as follows: at first, the hot metal was treated in a converter where all secondary metallurgical work is done. Secondly, the hot metal
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is poured into a large refractorylined container called a ladle and transported to the cranes. Then the filled ladles loaded through cranes and carried to the continuous casting machines (CCM). These machines are used to pour hot metal into molds. (Nutting et al. 2019). In this paper, to develop a model of the steel converter process, the work mainly focused on the crane management algorithm to minimize discontinuities in the operation of continuous casting machines (CCM). 2.1 System Requirements To minimize discontinuities in the operation of continuous casting machines (CCMs), there are several constraints that cause difficulties. The requirements diagram shown in Fig. 1 presents the main system requirements.
Fig. 1. System requirements
The critical timing is imposed by the CCMs and additional constrains come from the steel converters and the ladle transportation vehicles. For a good productivity, the number of cranes should correspond to the number of other elements in the system. In addition, the model should be highly scalable: it can work with any number of converters, cranes, CCMs, etc. and any timing, distance and capacity parameters. 2.2 Behavior Modeling Modeling behavior requires the identification of the main components of the system. As mentioned, the steel conversion process consists of converters where all secondary metallurgical work is done, ladles to transfer hot metal, cranes and continuous casting machines (CCM). Figure 2 represents the sequence diagram which describes the chronological order of the functional scenario of the system.
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Fig. 2. Sequence diagram
At the beginning of the process, the empty ladles move to the converters for filling. The converters pour the hot metal into the ladles. The filled ladles are then moved to the cranes for loading onto the continuous casting machine (CCM). If the ladles connect to the continuous casting machines (CCM), these machines pour the hot metal into the molds and the process is repeated each time. Figure 3 shows the state machine diagram of the hot metal transport activity throughout the process. The ladle waits to be full at the converter. If the filling is carried out, the ladle moves to the crane for loading. Then, the empty ladle returns to the converter for refilling.
Fig. 3. State machine diagram of transportation activity
The state machine diagram shown in Fig. 4 describes the crane activity. The crane awaits the arrival of the ladle; it moves towards target 1 where it checks whether there is a ladle or not. If there is a ladle, the crane loads it and moves towards target 2 to unload, otherwise, it returns to the wait step.
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Fig. 4. State machine diagram of crane activity
The continuous casting of liquid steel into the mold is a very important step in the steel conversion process. This step is performed by a continuous casting machine (CCM). This machine is constituted by two right and left ladle holders. Its operating algorithm is illustrated in Fig. 5. At first, the machine waits for the arrival of a ladle. The crane checks whether one of the two CCM ladle holders is filled or not. If the right ladle holder is empty, the crane loads the ladle into this ladle holder; otherwise, the CCM rotates 180° so that the crane loads the ladle into the left ladle holder.
Fig. 5. State machine diagram of CCM activity
The simulation of the steel converter process requires the identification of the structural architecture of the system. That’s why the next section discusses structural modeling of the system using block definition diagrams. 2.3 Structural Modeling In this section, the structural architecture of the process has been studied. Figure 6 represents the activity diagram which describes the general structure of the steel converter process. This process generally consists of four subsystems; two subsystems for pouring activity at converter and CCM level, and two subsystems for loading activity at converter and crane level.
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Fig. 6. The steel converter process
The block definition diagram shown in Fig. 7 describes the components of the pouring system at the converter level. This subsystem consists of three converters, ten steel ladles and five rails. In fact, each component is characterized by a set of values that ensure the functioning of the system.
Fig. 7. Pouring system (Converter level)
Likewise, the block definition diagram illustrated in Fig. 8 describes the pouring system at the CCM level. This subsystem is made up of three CCM’s and two ladles.
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Fig. 8. Pouring system (CCM level)
The loading system at the converter level is shown in Fig. 9. This subsystem consists of two ladles and five rails.
Fig. 9. Loading system (converter level)
Finally, the block definition diagram illustrated in Fig. 10 defines the loading system at the crane level. This subsystem consists of rails, cranes, and ladles.
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Fig. 10. Loading system (crane level)
To ensure the continuity and consistency of the modeling approach, we use the allocation matrix and the traceability diagram. In fact, the allocation matrix illustrated in Fig. 12 links the functions with its system components; and the traceability diagram illustrated in Fig. 11 represents the links and the interactions between the different levels of the system.
Fig. 11. Traceability diagram
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Fig. 12. Allocation matrix
2.4 Multiagent Simulation In this section, we use a multiagent simulation tool called “AnyLogic”. This simulation tool has a graphical modeling language and also makes it easy to extend the simulation model with Java code (Borshchev et al. 2002). Generally, the model of steel converter process focuses on crane management algorithm that should minimize discontinuities in the continuous casting machines (CCM) operation. Figure 13 represents the simulated model of the steel converter process.
Fig. 13. Simulated model of the steel converter process
With the model developed in the previous sections, defining the simulation becomes easier. You just need to create the necessary components through the library found in the software (cranes, converters, CCM’s, and ladles). The aim of this work is to minimize discontinuities in the operation of continuous casting machines (CCM) to avoid solidification of the metal. Figure 14 represents the simulation results before and after the modification of the crane management algorithm. Before the intervention, the crane management algorithm is insufficient; which causes discontinuities in the operation of continuous casting machines and solidification of the metal. That’s why the model focuses on the crane management algorithm and
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Fig. 14. Simulation results
modify it to minimize these discontinuities. Finally, the discontinuities in the operation of continuous casting machines are minimized.
3 Conclusion In the field of manufacturing, the use of multiagent systems facilitates the design of processes and the improvement of their performances. In fact, a multiagent simulation is a tool for analyzing, understanding, and optimizing manufacturing processes such as the steel converter process. This paper discusses the use of SysML language in modeling and the multiagent tool in the simulation of agentbased manufacturing systems. Aiming to illustrate the applicability and benefits of using these tools in the modeling and simulation of agentbased systems, a steel converter process study was considered. For this purpose, the Anylogic tool was used as a simulation platform to focus on the crane management algorithm which should minimize discontinuities in the operation of continuous casting machines (CCM). As a future work, the developed model will continue to be used to finalize the specification of the steel converter process. Also, and due to some Anylogic limitations, the logical step is to move into a more powerful software.
References Aloui, K., Hammadi, M., Soriano, T., Guizani, A., Haddar, M.: On the continuity of the swarm robot design using MBSE method and simulation. In: 13th International Conference on Modelling, Optimization and Simulation (MOSIM 2020) (2020) Barbosa, J., Leitão, P.: Simulation of multiagent manufacturing systems using agentbased modelling platforms. In: 2011 9th IEEE International Conference on Industrial Informatics, pp. 477–482 (2011) Borshchev, A., Karpov, Y., Kharitonov, V.: Distributed simulation of hybrid systems with AnyLogic and HLA. Futur. Gener. Comput. Syst. 18, 829–839 (2002)
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De Vin, L.J., Jagstam, M.: Why we need to offer a modeling and simulation engineering curriculum. In: Proceeding of the 2001 Winter Simulation Conference (Cat. No. 01CH37304), 2, pp. 1599– 1604 (2001) Guizani, A., Hammadi, M., Choley, J.Y., Soriano, T., Abbes, M.S., Haddar, M.: Agentbased approach for the optimal design of mechatronic systems. In: Haddar, M., et al. (eds.) Multiphysics Modelling and Simulation for Systems Design and Monitoring. ACM, vol. 2, pp. 189–198. Springer, Cham (2014a). https://doi.org/10.1007/9783319145327_20 Guizani, A., Hammadi, M., Choley, J.Y., Soriano, T., Abbes, M. S., Haddar, M.: Agentbased approach for collaborative distributed mechatronic design. In: 2014 10th FranceJapan/8th EuropeAsia Congress on Mecatronics (MECATRONICS2014Tokyo), pp. 156–161 (2014b) Guizani, A., Hammadi, M., Choley, J.Y., Soriano, T., Abbes, M.S., Haddar, M.: Multiagent approach based on a design process for the optimization of mechatronic systems. Mech. Ind. 18, 507 (2017) Ives, D., et al.: Everyday Brave: Media Nomads: Thaiday BrothersEp 5 Of 6 (2019) Kovalev, P.V., et al.: Improving production technology of tube steel grades in converter process. Metalurgija 55, 715–718 (2016) Lin, F.R., Sung, Y.W., Lo, Y.P.: Effects of trust mechanisms on supplychain performance: a multiagent simulation study. Int. J. Electron. Commer. 9, 9–112 (2005) Luke, S., CioffiRevilla, C., Panait, L., Sullivan, K., Balan, G.: Mason: a multiagent simulation environment. Simulation 81, 517–527 (2005) Lukša, F., Domazet, Ž., Bugarin, M., Krstulovi´cOpara, L.: Comparison of knife fabricated from tool steel by heat treatment and knife fabricated from structural . steel by hard surface welding. In: Chaari, F. (eds.) Advances in Materials, Mechanics and Manufacturing. Lecture Notes in Mechanical Engineering, pp. 61–70. Springer, Cham (2020). https://doi.org/10.1007/9783030242473_8 Marik, V., McFarlane, D.: Industrial adoption of agentbased technologies. IEEE Intell. Syst. 20, 27–35 (2005) Mhenni, F., Choley, J.Y., Penas, O., Plateaux, R., Hammadi, M.: A SysMLbased methodology for mechatronic systems architectural design. Adv. Eng. Inform. 28, 218–231 (2014) O’Hare, G.M., Jennings, N.R.: Foundations of Distributed Artificial Intelligence, vol. 9. Wiley, Hoboken (1996) Sahin, ¸ E., Girgin, S., Bayindir, L., Turgut, A.E.: Swarm robotics. In: Blum, C., Merkle, D. (eds.) Swarm Intelligence. Natural Computing Series, pp. 87–100. Springer, Berlin, Heidelberg (2008). https://doi.org/10.1007/9783540740896_3 Tossavainen, M., Engstrom, F., Yang, Q., Menad, N., Larsson, M.L., Bjorkman, B.: Characteristics of steel slag under different cooling conditions. Waste Manage. 27, 1335–1344 (2007) Vrba, P., Marcík, V.: Simulation in agentbased control systems: MAST case study. IFAC Proc. Vol. 38(1), 145–152 (2005) Wooldridge, M.: An Introduction to Multiagent Systems. Wiley, Hoboken (2009)
On the ViscoHyperelasticity Relationship in Modeling Styrene Butadiene Rubber Under Uniaxial Cyclic Loadings: Experiments and Parameter Identification Amina Dinari1(B) , Hamza A. Ghulman2 , and Tarek BenAmeur1,2 1 Mechanical Engineering Lab, LR99ES32 ENIM, University of Monastir,
5000 Monastir, Tunisia [email protected] 2 Mechanical Engineering Department, Umm Al Qura University, CEAI, 21955 Makkah Mukarama, Kingdom of Saudi Arabia
Abstract. The mechanical response of Styrene Butadiene Rubber (SBRs) reinforced by carbon black particles is investigated under cyclic tension. An experimental characterization carried out in Diabolo specimens submitted to cyclic loading at constant strain rate 10−3 s−1 for different stretch level. Some of the key observations from the experiments is the strong influence of hard particles on the deviation from the nonlinear viscoelastic virgin network mechanical behavior in cyclic loadings. Indeed, semilogarithmic plots of normalized stress vs loading cycles elucidated the appearance of two stress softening fatigue behaviors as function of the loading conditions: a linear pattern for low stretch ratio and CB amount, and the second behavior (a deviation from the linear pattern) is seen at higher value of stretch amplitude, loading cycles and CB particles amount. In order to describe the stress softening of the SBRs materials, a modified viscohyperelastic model is developed to incorporate the irreversible changes of the microstructure. Using a nonlinear optimization methods, an identification process from the experimental data was employed to determine the parameters of the constitutive function. The predictive capability of the developed model showed a good accordance between the experimental and the predicted results. ANOVA tests were carried out to analyze the main effect of both carbon black filler and imposed maximum displacement factors the model constants. It is found that the CB filler play an important role on the viscoelastic behavior and stress softening phenomena almost 60% of increase in the constitutive function parameters. Keywords: Viscohyperelasticity · Elastomers · Cyclic uniaxialloadings · Network alteration
1 Introduction Elastomeric materials are well known by their ability to withstand very large strains and to regain their initial geometry without fracture. For this reason, they are employed in © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 41–52, 2022. https://doi.org/10.1007/9783030849580_5
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wide industrial employment including tires, shock absorbers etc. Further more, they are destined to specific applications such as isolation bearings which expose them to severe timevarying loading in service conditions. Therefore, longterm robustness is a demanding objective. In fact, these materials are characterized by a timedependent behavior under large deformation, material softening in addition to hysteresis phenomena after cyclic loading (Rohman et al. 2020; Dinari et al. 2019). These sights are indications of materials deterioration. Indeed, many researchers were extremely interested on fatigue characterisation. Dinari et al. (2020) focused on the relationship of the inelastic features and microstructure changes through a multiscale characterization. Under a large and repeated force, (Kim and Jeong 2005) showed that microcracks nucleation could take place due to the decohesion of filler from the rubber matrix or to others sources such as surface flaws and the coalescence of voids. In their work, (Mars and Fatemi 2011) have distinguished two stage in rubber fatigue life depending on the microstructure evolution: The first stage is the nucleation of crack and the second one is the duration of the crack growth until the failure of the material. Moreover, they examined the influence of both rubber composition and environmental conditions on the fatigue life. Most of the studies mainly focus the prediction of fatigue life via experimental or numerical modeling (Cho et al. 2000; Yan et al. 2012; Belkhiria et al. 2020; Luo et al. 2020; Tobajas et al. 2020). Nevertheless, a specific interest was targeted to modeling the mechanical behavior at the macro scale terms of inelastic features (hysteris loop/mullin effect) (Mokhireva et al. 2020; Rangarajan et al. 2019). In fact, the history dependent cyclic features are mainly observed in filled rubber, it was explained in the literature by slipping mechanism between the fibers chain and the filler surface, disentanglement, and the breakdownrebound mechanism of chains and filler aggregates (Guo et al. 2018; Chagnon et al. 2006; Ayoub et al. 2011; Lorenz and Kluppel 2012; Wan et al. 2019). Due to the complex behavior of elastomer in cyclic loading (Stanton and Roeder 1982), an extensive research was conducted in order to propose the most suitable model for time history analysis of elastomeric materials. These models can be classified as phenomological or micromechanical. (Marckmann and Verron 2006) presented a comparative study of 20 hyperelastic constitute models. Others like (Twizel and Ogden 1983; Saleeb et al. 1992) were interested in the identification of parameters in these hyperelastic models. In this paper, we present an experimental characterization of the mechanical behavior under cyclic loading of the selected elastomeric materials. Then, the phenomological model of (Bhuiyan et al. 2009) is modified. The number of settings employed by Bhuiyan and his collaborators is reduced, and the model is modified to describe the softening behavior of rubber. The capability of the proposed model is validated with cyclic loading tests. In Sect. 3, a statistical investigation of the model’s parameters combination is conducted.
2 Exprimental Details 2.1 Material and Method In this work we used vulcanized styrenebutadiene rubber (SBR) by sulfur and reinforced with three amount of carbon black (15, 25 and 43 phr). The carbonblack volumic fraction of the supplied samples by Trelleborg Group, are determined with the phr value, the densities of both the carbonblack fillers (ρf = 1.8 × 103 kg m−3 ) (Abe et al. 2003)
On the ViscoHyperelasticity Relationship in Modeling SBR
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and SBR matrix (ρm = 1.21 × 103 kg m−3 ) (Wood et al. 1943). The appropriate carbon black volume fraction formulation is provided by the following equation: −1 phr 100 phr νf = + ρf ρm ρf
(1)
The material formulation is detailed by Table 1 and the geometric feature of the specimens is given by the Fig. 1. Cyclic tension tests were conducted on universal testing machine Instron8874 equipped with a cell of 25 kN. The cyclic tests which have been carried out with AE42 correspond to a displacementcontrolled loading. The tested SBR specimens ramped to a maximum displacement Umax [6 mm, 10 mm, 14 mm, and 18 mm] at a true strain rate of 1 s−1 and returned to a zero displacement. Table 1. Composition of the SBRs. (in phr, weight %). Ingredients
SBR15 SBR25 SBR43
SBR
100
100
100
Sulfur
3
3
3
Processing oil 37.5
37.5
37.5
Carbon Black 15
25
43
Oxide zinc
5.5
5.5
5.5
Stearic acid
3
3
3
Antioxidant
5.5
5.5
5.5
Accelerators
4
4
4
Fig. 1. Geometry of Diabolo sample AE42
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2.2 Results and Discussion The maximal stress evolution issued from the uniaxial cyclic tests is presented in Fig. 2 for the three filled SBR materials. The stress softening is accentuated with the filler content and the imposed stretch level. In fact, the material softening could be explained by two timedependent. Network rearrangement within the reinforced rubber: the unrecoverable and recoverable damage mechanisms (Guo et al. 2018). The recoverable network is attributed to the movement of free fiber chains, while the unrecoverables rearrangement inducing damage are associated to the chains scissions/fillermatrix decohesion (Chagnon et al. 2006). There for, the observed stress softening is a network rearrangement under imposed displacement, in which junctions between fiber chains (entanglements), or between fibers chains and added fillers (carbone black/Zinc oxide) are destroyed (Mullins 1969).
Fig. 2. Normalized maximum stress as function of cycles number for SBR15, SBR25 and SBR43
The use of the Semilogarithmic scale shows more details about the evolution of the stress softening over loading conditions. In fact, Semi logarithmic plots of the normalized stress (σ/σmax) evolution as function of cycles number for imposed maximum displacement ranging from 6 mm to 18 mm at constant frequency 2 Hz and strain rate 1 s−1 , is shown in Fig. 3. It is clearly elucidated the appearance of two stress softening behaviors depending on the imposed stretch value. The first stress softening behavior is characterized by a linear pattern. Whereas, the second stress softening behavior is characterized by a deviation ‘D’ from the linear pattern, after a given number of cycles (Table 2). The first stress softening behavior is characterized by a linear pattern. Whereas, the second stress softening behavior is characterized by a deviation ‘D’ from the linear pattern, after a given number of cycles (Table 2). The linear patterns indicate that the damage is directly proportional to the normalized stress range. Besides, there is indirect evidence that the deviation from the linear curve upon increasing loading cycles, CB content, stretching ratios or frequency might therefore be associated with a tendency towards disparity from continuous Mullins softening. Since the early work of (Blanchard and Parkinson 1952), this damage is attributed to the rupture of the weaker bonds (physical bonds) at the elastomeric rubberfiller interface, and further prestrain breaks the stronger bonds (chemical crosslinks). Over the time, more competing analyses are developed to explain the origin of the Mullins effect by involving the filler: chain “slipping” over the filler surface, breakage of short chains between twofiller aggregates, rupture of filler aggregates and chain disentanglement (Marckmann et al. 2002).
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Table 2. Deviation from linear pattern for different imposed displacement Umax SBR15 SBR25 SBR43 2 Hz, 1 s−1 D, at number of cycles 6 mm 10 mm 14 mm
744 374 161 111
301 243 100 65
57 55 45 40
18 mm
Based on the rheology model proposed by Bhuiyan and his coworkers to describe the mechanical behavior of filled SBR as detailed in reference (Bhuiyan et al. 2009). The authors proposed an elastoviscoplastic rheology model of HDRBs. In the current model, the stress is globally composed of three parts:
σee
σ = σep + σee + σve
(2)
σep = α1 εa
(3)
⎧ ⎨ +1 when ε > 0 χ = α2 ε sgn(ε); where sgn(ε) = 0 when ε = 0 ⎩ −1 when ε < 0
(4)
(5) σep and σee represent the rateindependent elastoplastic behavior, while σve introduces the ratedependent behavior. αi (i = 1 to 3), B1 , Bu , χ and p are coefficients of the model to be identified from experimental results. In our case, the mechanical behavior of SBR can be described by bringing together the elastic and viscous elements: σ = σee + σve
(6)
In agreement with by Bhuiyan et al. (2009) (Shangguan et al. 2014), the stress can be given by: σ = α2 εχ + Bl e(p+) tanh(ga3 +)
(7)
For nonlinear evolution of strain depending on cycle fatigue number, the strain can be expressed according a simple nonlinear low given by the following equation: ε = ε = ρ[N]b
(8)
Where constants ρ and b, can be evaluated experimentally from Wöhler curve. The stress softening is given by: (9)
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σ σmax
= Cl e(−C2 [N]) tanh(C3 [N]) + C5 [N]−C4
(10)
In which σmax correspond to maximum stress evaluated from the first cycle loading stage, Kl = C1 , βρb = −C2 , γα3 ρb = C3 , b$ = −C4 and α2 ρ = C5 , are model parameters. A standard optimization method using excel solver tool is used to identify the physical parameters (C1/C2/C4/C5) and to fit the experience data. In the Eq. 10, C3 is the smoothing parameter in loading and unloading cycle. The coefficients of correlation R2 , determination are in the order of 0.999, and the sum of squared error SSE is better than 5 10−2 , as detailed in Table 3.
Fig. 3. Semilogarithmic plots of normalized stress vs cycle’s numbers for the SBRs materials continued lines: experience result, discontinuous red lines: Eq. (10)
3 Interaction of the Parameters Combination The purpose of this section is to emphasize the effects of interaction between two factors used in this study namely, the CB fraction and the imposed maximum displacement, and their influence on the model parameters. ANOVA tests were conducted via the commercial software Minitab17.These tests are used to test the surface response fitness of the approximation model. The main effects of factors were represented in Fig. 4 to compare their impacts on the model constants. Then, it is immediately possible to detect how the factors affect in their higher and lower levels the response evolution in a more adequate way. C4 and C5 characterize the power law fatigue expression. They influence the response of the material by modifying the level of stress. Generally, the power law function describe the material fatiguelife related to the damage parameter (Shangguan et al. 2014). Additionally, C1 and C2 balances elastic stresses (including softening) and viscous effects. The main effects graphs underline directly the most influencing factors. As illustrated in Figs. 4 and 5, a variation of carbon black fraction from 0.09 to 0.22 leads to an amplification of the two constants C2 ( the viscosity parameter) and C4 (the rate independent parameter). In the other hand, the variation of maximum imposed displacement leads to an increase in the rate independent parameter and a decrease in the viscosity parameter. According to graphs of Fig. 4 carbon black fraction is the
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Table 3. Identified stress softening model parameters Material Umax C1 [MPa/s] C2 frequency (2 Hz) SBR 15
SBR 25
SBR 43
C3 [MPa] C4
C5 [MPa] SSE
R2
6
0.157
7.939E−5 8.802
2.441 0.858 E−2
1.879 0.999 E−3
10
0.163
1.881 E−4
8.802
2.550 0.844 E−2
2.082 0.999 E−3
14
0.104
1.696 E−3
8.802
2.243 0.897 E−2
8.843 0.999 E−4
18
0.114
2. 266 E−3
8.802
2.441 0.827 E2
3.224 0.999 E−3
6
0.168
1.335 E−4
8. 767
3.318 0.792 E−2
4.396 0.999 E−3
10
0.174
4.224 E−4
8. 767
3.434 0.850 E−2
1.936 0.998 E−2
14
0.120
2.299 E−3
8. 767
3.196 0.900 E−2
4.155 0.999 E−3
18
0.143
3.196 E−3
8,763
2.963 0.788 E−2
2.992 0.999 E−3
6
0.122
4.591 E−4
8.766
3.633 0.903 E−2
4.889 0.999 E−3
10
0.110
2.102 E−3
8. 766
3.363 0.905 E−2
3.036 0.999 E−3
14
0.145
3.413 E−3
8. 766
4.149 0.893 E−2
8.894 0.999 E−3
18
0.177
4.653 E−3
8,774
3.327 0.754 E−2
1.806 0.999 E−3
most influencing factor. Indeed, as it seen in Fig. 4, the carbon black affect noticeably the stresssoftening phenomena (Clément et al. 2001; Rocha and Batista 2019). This behavior is accentuated in the composite with higher amounts of filler aggregates due to the breakdown of the fillerfiller network (Bahl et al. 2014). For the sake of simplicity, usually, the functions used in the approximations are polynomials. y = φ0 +
l m=1
φj xj +
l m=1
φjj xj2 +
l l−1 n=1 m=i+1
φj xi xj
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Fig. 4. Main effects graphs of CB fraction and Umax on model parameters
Where φ are referred to the polynomial coefficients, l describe the number of design variables and x represent the independent variables and. The regression equations defining our model parameters as function of carbon black fraction and maximum imposed displacement are as follows: C1 = 0, 2899 − 0, 904 CB fraction − 0, 01260 Umax + 0, 0768 CB fraction ∗ Umax
(11)
C2 = −0, 00144 − 0, 00077 CB fraction − 0, 000103 Umax + 0, 001113 CB fraction ∗ Umax
(12)
C3 = 8, 8234 − 0, 304 CB fraction − 0, 00067 Umax + 0, 0051 CB fraction ∗ Umax
(13)
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Fig. 5. Interaction effect of CB fraction and Umax for model parameters
C4 = 0, 01610 + 0, 1180 CB fraction + 0, 000138 Umax − 0, 00266 CB fraction ∗ Umax
(14)
C5 = 0, 729 + 1, 111 CB fraction + 0, 00917 Umax − 0, 0860 CB fraction ∗ Umax
(15)
SSE = 0, 0029 + 0, 0256 CB fraction − 0, 00005 Umax − 0, 00078 CB fraction ∗ Umax
(16)
These equations reproduce the response surface prediction of the parameters model with high precision, and relate accurately the objective function (the model parameters) and different factors via a mathematical relationship. Based on the preceding results, the polynomial regression equations can be employed to design the global approximation of the responses for various sampled points of analyzed space. Figure 6 shows the 2D surface response of the model parameters evolution given in form of contour plots. As it seen in the Fig. 6. C2 and C4, which control the softening behavior, are the most influenced constants by the conjoined effect of Umax and carbon black volume fraction. Indeed, the observable decrease in stress as shown in Fig. 7 is due to the viscoelastic mechanisms, and to the irreparable damage mechanisms. At the high level of both factors, the increase in C2 (Fig. 6b) can be related to the effective role of particles though the viscous movement between particles and particlesfiber of SBR chains. In fact, it is associated to the physical degradation mechanism either on the surface of the filler particles or within the glassy layer during its softening under cyclic uniaxialloadings (Dinari et al. 2020). The evolution of fatigue powerlaw constant C4 (Fig. 6c) may be associated to the unrecoverable mechanisms, breakdown of the network junctions, chain and CB clusters.
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Fig. 6. 2D Surface responses of model coefficients: (a) C1, (b) C2(c), C4 and (d) C5
Fig.7. Normalized stress softening vs. number of cycles for the three SBR materials at different imposed maximum displacement
4 Conclusion The mechanical behavior of the three rubberfilled materials under uniaxial cyclic loading was analyzed on the macroscale in terms of normalized stress as a function of cycle number. We observe a noticeable decrease in stress during the first 10 cycles, then the stress softening tend to be more stabilized. Semilogarithmic plots of normalized stress vs loading cycles elucidate the appearance of two stress softening fatigue behaviors as function of the loading conditions. The first stress softening fatigue is characterized by a linear pattern, while the second behavior is seen at given number of cycles. The deviation from the linear pattern is more pronounced at higher value of stretch amplitude
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and CB particles amount indicating a significant network alteration in SBR composites. A modified viscoelastic model is employed to represent the inelastic feature under uniaxial cyclic conditions. The model can adequately reproduce the material behavior. The constants of the constitutive function are determined from the uniaxial cyclic tests by an optimization method using excel solver tool. These letters were analyzed via ANOVA tests, it proved that the CB filler has significant effects on the parameters which control the viscoelastic behavior and stress softening phenomena.
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Analysis of the Wells Turbine Structure of an Oscillating Water Column Wave Energy System Mohamed Ali Jemni1(B) , Hamdi Hentati2 , Sawsan Elmbarki1 , and Mohamed Salah Abid1 1 Laboratory of Electro Mechanic Systems (LASEM), National School of Engineers of Sfax
(ENIS), University of Sfax, B.P. 1173, km 3.5, Soukra, 3038 Sfax, Tunisia [email protected], [email protected] 2 LA2MP Laboratory, National School of Engineers of Sfax, University of Sfax, Sfax, Tunisia
Abstract. Sea and ocean waves have the capability to produce a sustainable resource of energy that is transformed into electrical power by converters. The production of electricity is then dependent on the oscillatory movements of the water waves. A wellknown technique in this type of renewable energy is the oscillating water column (OWC), which is based on the pneumatic drive of air turbines. The choice of materials for aerofoil blades components is critical to an oscillating water column wave converter system. Supporting the imposed load and transmitting it to the rotor, the blade construction needs to be able to resist to centrifugal load and large aerodynamic cyclic. In this paper, Cambridge Engineering Selector (CES) method is used in order to select reliable material for Wells air turbine blades considering several criteria related to the density, cost and energy of production of the material. This method stated that the choice of the Aluminum 1060 family has optimal characteristics. A numerical analysis of the structure of the Wells turbine is performed to test the chosen material resistant via air drag solicitation and centrifugal loads. The numerical study is based on static finite element analysis and fatigue investigation on a NACA 0015 model of the wells turbine blades. Keywords: OWC · Wells turbine · Ocean energy conversion · Blade material · Simulation
1 Introduction As is known on a global scale, the main problem associated to the use of fossil fuels is the large amount of pollution. Causing an enormous quantity of carbon dioxide emission into the atmosphere, fossil fuels contribute in part to global warming. Fossil fuels are mainly used in the transport sector and in power generation plants. Research to minimize toxic emissions in the transport industry is oriented towards the use of alternative gaseous fuels (Jemni et al. 2018, 2020; HadjKacem et al. 2020).On the other hand, pollution reduction techniques in the power generation sector are focused on the use of renewable © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 53–62, 2022. https://doi.org/10.1007/9783030849580_6
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energies such as solar, wind and recently ocean wave energy (Ghoushchi et al. 2021; Ma et al. 2021; Scialò et al. 2021). World efforts to generate electric power from waves had already begun in Japan around the fifties of the twentieth century. Studies are accelerated in the last years of this century for several types of ocean wave energy converters such as the oscillating water column (Bruschi et al. 2019). An OWC power plant consists of a hollow structure fixed to the sea (onshore) or floating (offshore). The periodic oscillation of the quantity of water in the inner chamber alternately decompresses the trapped air and drives a turbine, or a set of turbines, coupled to an electric generator. Air flows from the oscillation chamber to the atmosphere and vice versa. The rotation direction of the turbines must remain unchanged regardless of the direction of attack of the air flow. The most common airfoil turbine in this type of power plant is the Wells turbine, a version of an axial/flow turbine. The blades of this turbine are nontwisted with a symmetrical crosssection. It typically belongs to the NACA symmetrical series, see Figs. 1 and 2. A standard wells turbine is composed of a rotor with about eight blades fitted to the hub with their chord lines located in the plane of rotation. With the aim of stabilizing the operation of these types of turbine, the researchers are still seeking to optimize its various functional parameters. The material making up the structure of the turbine blades is one of the most important factors influencing these operating parameters. Many recent research works focus on the choice and characterization of materials of different mechanical systems (Hentati et al. 2015; Moakhar et al. 2019; Mehmood et al. 2018). In this paper, a study of the choice of materials is completed using Cambridge Engineering Selector (CES) method and the numerical finite element analysis approach.
Air turbine Oscillating chamber
Water
Fig. 1. Oscillating water column devise
Fig. 2. Wells air turbine
2 Problem Statement and Turbine Model The primary requirement for a well air turbine is to develop a high torque at its output at a welldefined speed. The major purpose of this type of air turbine is to convert the pneumatic power generated by the bidirectional air attack flow into mechanical power for unidirectional rotation on the shaft. For this reason, the structure of the blades needs to resist the imposed cyclic load. The blades are therefore subject to considerable cyclic and centrifugal aerodynamic stress. The aim in selecting the wells turbine material is therefore to minimize its weight during operation, which is the goal of most rotating chains, while supporting a high
Analysis of the Wells Turbine Structure
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cyclic and centrifugal aerodynamic force without failure and sustaining it in a seaside setting. A great strengthtoweight balance is needed due to the large aerodynamic and centrifugal stresses acting on the blade and the requirement to have the lowest achievable weight in order to minimize the training load. The fatigue behavior of the blade under cyclic loading is particularly important and should be recognized. Material selection using the Cambridge material selector is considered in this study because of its performance (Granta 1995; Brechet et al. 2001; Shercliff and Ashby 2016).
3 Performance Parameters of the Wells Turbine The most important characteristic of the turbine well is that the oscillating air flow generates a oneway rotation of the rotor. The turbine blade profile is generally defined by a specific profile called NACA profiles (Saptono 2004; Shehata et al. 2016). Based on the conventional airfoil theory, a blade placed at inclination α in a fluid flow direction produces the lift force noted “L”, normal to the free flow and the drag force noted “D” in the direction of the air flow, Fig. 3. “α” is the angle of air attack that lies between the profile line and the axial direction of the air.
Fig. 3. Turbine aerodynamic forces
To verify the resistance of the turbine blades, the forces exerted on the blades must be identified. The resultant force FR caused by the forces of lift and drag is defined as follows: FR = L2 + D2 (1) This force is divided into axial and tangential forces FA and Ft in regard to lift and drag constituents such as: FA = L cos(α) + D sin(α) (2) Ft = L sin(α) − D cos(α)
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These forces are directly related to the air flow velocity, the mean turbine radius Rm and the rotor angular velocity ω. ρV 2 A C FA = r 2 A (3) ρV 2 A C Ft = r2 t Where ρ is the density (kg/m3 ), A is the total blade area (m2 ), CA is the axial flow coefficient, Ct is the tangential flow coefficient and Vr is the resultant air velocity (m/s). This velocity is given by: 1/2 Vr = VA2 + ω2 R2m
(4)
Where VA is the axial velocity component (m/s) and Rm is mean rotor radius (m) which is given by: Rm =
1 (Rt + Rh ) 2
(5)
Rt and Rh are the rotor radius at tip and the rotor radius at hub (m) respectively.
4 Turbine Material Selection The selection of materials for wells turbine component is among the major concerns in the optimal design of this turbine, and subsequently, in the conception of the OWC wave energy conversion system. Based on Cambridge engineering selector (CES) method, as previously stated, the selection of materials is achieved in this study. The CES selection method is based on the distribution diagrams of the large families of materials known as Ashby diagrams. It is used in an analytical approach. The criteria to be searched for in the turbine material are combined between the resistance of the rotor structure against the force applied by the fluid and the minimized weight. Figure 4 illustrates the elastic limit of the different families of materials as a function of density. As observed, the Fiber Reinforced Composites (CFRP class, epoxy matrix), Titanium Alloys, which are two families widely used in the manufacture of well turbines (Shehata 2016), show significant elasticity limit values when compared with the other families. Considering the density criterion, the Composites have lighter masses. The family of aluminum alloys also offers an acceptable tradeoff between limit and density. Figure 5 illustrates the elastic limit of the different families of materials as a function of price. Looking at the elaboration price of the materials we can notice that the composites family shows high manufacturing price values compared to the case of aluminum alloys family.
Analysis of the Wells Turbine Structure Titanium alloys
Alumina
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Stainless steel
100
CFRP, epoxy matrix (isotropic) Magnesium alloys
Tungsten carbides Cast iron, grey
10
Elastic Limit (ksi)
Wood, typical along grain
Aluminium alloys Silica glass
Polyvinylchloride (tpPVC) Rigid Polymer Foam (HD)
1
Copper alloys Stone
Rigid Polymer Foam (LD)
Concrete
Wood, typical across grain
0.1
Silicone elastomers
0.01
1
10
100
1000
Density (lb/ft^3)
Fig. 4. Ashby diagram, elastic limit vs density
Low alloy steel
100
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Alumina
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Aluminium nitride
Cast iron, grey Aluminium alloys
10
Aluminium alloys
Elastic Limit (ksi)
CFRP, epoxy matrix (isotropic) Stone 1
Concrete
Wood, typical across grain 0.1
0.01
0.1
1
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Fig. 5. Ashby diagram, elastic limit vs price
Aluminum alloys family also has an interest in the amount of energy released for the elaboration and preparation of the material by comparing them with the Titanium Alloys family as justified in Fig. 6. For the above reasons, we will propose the use of Aluminum alloys material in the manufacturing of the wells turbine especially by aiming at the advantages of the different aluminum alloys through the occurrence and the recycling (Bhouri et al. 2020). Then, a numerical study will be developed in the following part to compare the resistance of the structure using the two materials types.
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Magnesium alloys
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10000
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GFRP, epoxy matrix (isotropic)
Lead alloys
Cast iron, ductile (nodular)
Cork
1000
Concrete Brick 100
0.1
1
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Fig. 6. Ashby diagram, production energy vs price
5 Numerical Turbine Structure Analysis A finite element analysis was carried out using SolidWorks Simulation on a NACA 0015 model of the wells turbine blades to find Von Mises stresses under fluid load conditions. This blade profile is chosen because of its advantages through aerodynamic performance (Thakker and Abdulhadi 2008). We are interested, firstly, in the static study of the blades. The axial and centrifugal loads conditions modeled the bending stresses arising from an airflow velocity on the blades equal to 7.5 m/s and a maximum turbine rotor speed equal to 4000 rpm. The material of the wells turbine is the Aluminum alloy 1060, see Fig. 7. The characteristics of the studied turbine are the external and rotor diameter as well as the thickness. These characteristics are taken into consideration of the turbine used in the LIMPET project (Land Installed Marine Powered Energy Transformer) installed in the Great Brittan (Folley et al. 2006). A sizing reduction scale to the order of 1/10 is used. Turbine features are listed in Table 1. Table 1. Turbine features Parameters
Value
Turbine diameter
0.26 m
Nominal operating speed 1050 rpm Blade form
NACA0015
Number of blades
8
Hub to Tip ratio
0.62
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Figure 8 shows the results of the static numerical finite element analysis in terms of stress and displacement field. We remind that the two sources of loads applied to the blades are the air force and the centrifugal force due to the rotation of the rotor. It is noted that the stress concentration is localized at the level of the blade root. The load generated a tensile stress on one edge of the blade root; on the other hand a compressive stress is applied on the other side. As showing in Fig. 8 a, it is noted that the maximum stresses magnitude is far from the yield strength of this material. The maximum displacement, which is a few micrometers, also indicates that the stricture is well resisted to the applied loads, see Fig. 8 b.
Centrifugal load
Axial air force load
Fig. 7. Turbine condition loads for simulation
In order to estimate the fatigue life behavior, a fatigue analysis of wells blade is achieved with numbers of cycle of 106 , and fully reversed configuration basing on the SN curve modeling. To construct an SN curve model, considering the limitation of experiment test data of used alloy, a relationship may be assumed between multiples points based on the current empirical data in the simulation software. To predict the life of the turbine blades, the history of the pressure and the attack air velocity is taken into account in the loading on the blades. It can be seen from Fig. 9 that the low number of cycles to failure is located at the level of the blade roots. The strength of the structure is limited at this location. In conclusion, it has been noted that the Aluminum alloy family presents an adequate material for the realization of Wells turbines because of its advantages via the minimized weight, the reasonable costs and the acceptable strength.
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a
Stress field distribution
b
Displacement field
Fig. 8. Turbine static simulation results
Fig. 9. Total life cycles for fatigue simulation
6 Conclusion The environmental and mechanical behavior of materials is essential in the selection of materials used in manufacturing the air turbine operated in OWC plants. In this work, parametric engineering design techniques have been developed, using Cambridge Engineering Selector (CES) software for reliable material choice of Wells turbines used in OWC ocean energy conversion systems. The Aluminum alloy 1060 family showed appropriate results via the weight, the costs and the strength. Simulations are developed to study the endurance and fatigue behavior of the blades.
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Acknowledgements. This work is partially supported by the National School of Engineers of Sfax and the Laboratory of the Electromechanical Systems. The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved this paper.
References Bhouri, M., Mzali, F.: Study of Al 2017 Alloy prepared by recycling method via powder metallurgy route. In: Chaari, F., et al. (eds.) Advances in Materials, Mechanics and Manufacturing. LNME, pp. 9–16. Springer, Cham (2020). https://doi.org/10.1007/9783030242473_2 Brechet, Y., Bassetti, D., Landru, D., Salvo, L.: Challenges in materials and process selection. Prog. Mater Sci. 46, 407–428 (2001). https://doi.org/10.1016/S00796425(00)000190 Bruschi, D.L., Fernandes, J.C.S., Falcão, A.F.O., Bergmann, C.P.: Analysis of the degradation in the Wells turbine blades of the Pico oscillatingwatercolumn wave energy plant. Renew. Sustain. Energy Rev 115, 109368 (2019). https://doi.org/10.1016/j.rser.2019.109368 Ghoushchi, S.J., Manjili, S., Mardani, A., Saraj, M.K.: An extended new approach for forecasting shortterm wind power using modified fuzzy wavelet neural network: a case study in wind power plant. Energy 223, 120052 (2021). https://doi.org/10.1016/j.energy.2021.120052 Folley, M., Curran, R., Whittaker, T.: Comparison of LIMPET contrarotating wells turbine with theoretical and model test predictions. Ocean Eng. 33, 1056–1069 (2006). https://doi.org/10. 1016/j.oceaneng.2005.08.001 Hadjkacem, S., Jemni, M.A., Driss, Z., Abid, M.S.: Effect of engine compression ratio on thermodynamic behavior using alternative hydrogenLPG fuel. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects (2020). https://doi.org/10.1080/15567036.2020.183 9146 Hentati, H., Naceur, I.B., Bouzid, W., Maalej, A.: Numerical analysis of damage thermomechanical models. Adv. Appl. Math. Mech. 7(2), 1–19 (2015). https://doi.org/10.4208/aamm. 2014.m517 Jemni, M.A., HadjKacem, S., Driss, Z., Abid, M.S.: Effects of hydrogen enrichment and injection location on incylinder flow characteristics, performance and emissions of gaseous LPG engine. Energy 150, 92–108 (2018). https://doi.org/10.1016/j.energy.2018.02.120 Jemni, M.A., HadjKacem, S., Ammar, M., Saaidia, R., Brayek, M., Abid, M.S.: Variable intake manifold geometry influence on volumetric efficiency enhancement at gaseous engine starting speeds. Proc. IMechE Part E: J. Process Mech. Eng. (2020). https://doi.org/10.1177/095440 8920973129 Granta Design Ltd.: Cambridge Selection Software: CMS, Cambridge (1995) Ma, Z., Li, M.J., Zhang, K.M., Yuan, F.: Novel designs of hybrid thermal energy storage system and operation strategies for concentrated solar power plant. Energy 216, 119281 (2021). https:// doi.org/10.1016/j.energy.2020.119281 Mehmood, Z., Haneef, I., Udrea, F.: Material selection for microelectromechanicalsystems (MEMS) using Ashby’s approach. Mater. Des. 157, 412–430 (2018) Moakhar, S., Hentati, H., Barkallah, M., Louati, J., Haddar, M.: Influence of geometry on stress state in bulk characterization tests. C.R. Mec. 347, 930–943 (2019). https://doi.org/10.1016/j. crme.2019.10.003 Saptono, R.: Selection of materials for the aerofoil blades of a Wells turbine operated in an oscillating water column (OWC) wave power station. In: The 7th International Conference Quality in Research (QIR) (2004) Scialò, A., Henriques, J.C.C., Malara, G., Falcão, A.F.O., Gato, L.M.C., Arena, F.: Power takeoff selection for a fixed UOWC wave power plant in the Mediterranean Sea: the case of RoccellaJonica. Energy 215, 119085 (2021). https://doi.org/10.1016/j.energy.2020.119085
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Shehata, A.S., Xiao, Q., Saqr, K.M., Alexander, D.: Wells turbine for wave energy conversion: a review. Int. J. Energy Res. 41, 6–38 (2016). https://doi.org/10.1002/er.3583 Shercliff, H.R., Ashby, M.F.: Elastic structures in design. In: Reference Module in Materials Science and Materials Engineering. Elsevier, Amsterdam (2016) Thakker, A., Abdulhadi, R.: The performance of Wells turbine under bidirectional airflow. Renew. Energy 33, 2467–2474 (2008). https://doi.org/10.1016/j.renene.2008.02.013
A TwoStage Approach to Solve Structural Damage Detection Problem in Plate Structures Kamel Belhadj1(B) , Najeh Ben Guedria1,2 , Ali Helali1,2 , and Chokri Bouraoui1 1 Laboratory of Mechanics of Sousse (LMS), National Engineering
School of Sousse, Sousse, Tunisia [email protected] 2 Higher Institute of Transportation and Logistics of Sousse, University of Sousse, Sousse, Tunisia
Abstract. A twostage optimization approach, based on modal strain energy and an Efficient Accelerated Particle Swarm Optimization algorithm (EAPSO), for localization and quantification of damage in platelike structures is proposed. First, to localize damage sites, a new damage index is developed using modal strain energy and the statistical hypothesis analysis technique. Then, the proposed EAPSO algorithm is used to estimate the extent of damaged elements located in the first stage. The objective function to be minimized is established via flexibility Matrix changes of the structure. The EAPSO operates with a new updating model, created on random distribution of particles from the search space, which supports discovering and preserving interesting regions of the research space. Control parameters are finetuned to properly balance exploration/exploitation while accelerating convergence of EAPSO. In addition, a microsearch operator, which remove small damages from solutions, is embedded in the algorithm to decrease dimension of the search space and saves computational effort. To examine the effectiveness of the suggested approach, a numerical example for isotropic plate is carried out. The simulation results are compared with those of some recent algorithms, indicating the superiority of the proposed approach in terms of reliability, robustness to noise and rapidity of convergence. Keywords: Damage detection · Plate structure · Modal Strain Energy (MSE) · Particle Swarm Optimization (PSO) · Flexibility matrix
1 Introduction Isotropic plates are widely exploited in many types of modern engineering applications, including aircraft and spacecraft, civil construction and mechanical engineering structures (Saggar et al. 2020). Nevertheless, these structures are exposed to damage due to fatigue and effects of harsh environmental conditions, which can lead to failure and even hazardous accidents. Therefore, early identification of damage is essential to ensure their integrity as well as their safety. The problem of identifying damaged structural elements is usually formulated as a nonlinear inverse problem and, hence, requires suitable mathematical methods to solve © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 63–72, 2022. https://doi.org/10.1007/9783030849580_7
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it accurately. A useful two stages approach, used by many researchers, is to detect firstly damaged elements and then solving a reduced optimization problem to determine the magnitude of flawed elements. (Guo and Li 2009) conducted a twostep method for identifying the sites and extent of structural damage by utilizing the evidence theory and microsearch genetic algorithm, by applying an information fusion technique to locate sites of damaged elements in the first stage, then, used a Micro Search Genetic Algorithm (MSGA) to evaluate the damage extent. (Seyedpoor 2012) proposed a twostep method to identify location and extent of flawed elements by using, in the first step, a Modal Strain EnergyBased Index (MSEBI) to locate the damage elements on the structure. In the second step, the extent of the damaged elements, found during the first step, is determined employing a Particle Swarm Optimization (PSO) algorithm. (Xiang and Liang 2012) applied a twostage approach for detecting multiple damage in platelike structures. Firstly, they employ the 2D wavelet transform to the modal shape to expose peculiarities and damage locations. Secondly, a PSO algorithm is used to identify the extent of the located damaged elements. (Ben Guedria 2020) developed a new algorithm with new operators to detect damaged elements in platelike structures called an Accelerated Differential Evolution algorithm (ADE), including three techniques into the Differential Evolution (DE) algorithm. The first one is a population initialization technique used to accelerate the convergence of the algorithm. Secondly, a new difference vector formed based on the dispersion of individuals in the search space, utilized to confirm the balance between global and local searching ability, and Finally, a new Exchange Operator (EO) is applied to prevent early convergence to local optima. Furthermore, a MicroSearch operator (MS) is used to transform the lowdamage elements into healthy ones. In this study, a twostage approach to localize damaged structural elements and assessing damage extend for isotropic plates is proposed. In the first step, a damage index (MSEDI), based on modal strain energy, is developed and used to find damaged elements. Then, an Efficient Accelerated Particle Swarm Optimization algorithm (EAPSO) is created and employed to assess the extent of damaged elements, located in the first step, through solving a reduced optimization problem. In addition, a micro search operator (DinhCong et al. 2017) is embedded in the algorithm to remove law damage variables from solutions which decreases the search space and computation cost. The performance of the proposed approach is investigated using an isotropic plate as a numerical example.
2 Structures Damage Localization The dynamic characteristic equation of Ndof degree of freedom undamped structure, can be defined as follows. Kϕi = ωi2 Mϕi i = 1, . . . , Ndof
(1)
Where M and K are respectively the masses and stiffness matrices of the undamaged structural. ωi and ϕi are respectively the natural frequency and the normalized mode shape vector for the ith mode. The steps of the proposed approach for damage localization are expressed as follows.
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Step 1: calculate the MSE of the jth element in the ith mode j
j T
j
(MSE i )∗ = (ϕ i )∗ Kj (ϕ i )∗
i = 1, . . . , Ndof , j = 1, . . . , Nel,
(2) j
Where K j is the elemental stiffness matrix of element j and the components of vector ϕi are its nodal displacements in mode i. The subscripts (*) denotes the state of the element (h: healthy, d: damaged). (.)T denotes the vector transpose. Step 2: calculate the modal strain energy ratio j MSEi j d , i = 1, . . . , Ndof , j = 1, . . . , Nel (3) MSERi = j MSEi h
Step 3: normalized the MSE ratio j
j
NMSERi =
MSERi MSERmax i
Step 4: calculate the damage indices DI for each element j j DI j = Max NMSERi , i = 1, . . . , Nm i
(4)
(5)
Once the damage indices DI j , j = 1,…,Nel, are computed for each element of the structure, the goal is then to categorize structural elements into damaged and undamaged ones. Step 5: calculate the damage index Z j . The damage indices are standardized as follows. Zj =
DI j − μDI , σDI
(6)
Where μDI and σDI are respectively the mean and the standard deviation of the damage indices DI, We assume that the standardized damage index Z is normally distributed which lets us to employ its probability density function to classify damaged elements as follows. – Hypothesis H0 is retained if, Z j < C, i.e. the jth element is intact. – Hypothesis H1 is retained if, Z j ≥ C, i.e. the jth element is damaged. Where C is a threshold value. The commonly used values of C, for the localization of damage, are 1.28, 2 and 3 for levels of confidence of 90%, 95% and 99% for the occurrence of damage. (Bayissa et al. 2008). Step 6: Located the damaged elements 0 if Z j < C, (i.e. healthy elements) , j = 1, . . . , Nel (7) MSEDI j = Z j if Z j ≥ C, (i.e. damaged elements)
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3 Optimization Problem Once the potentially damaged elements are located, in the first step, the one is to evaluate their damage extents. In this study, damage is modelled as a reduction of the stiffness properties of the structure through an elemental stiffness reduction ratio (δi ). Therefore, the overall stiffness matrix for the damaged structure, denoted [K]d , and can be written as follows. [K]d =
Nel 1 − δj Kj
(8)
j=1
Nel represents the total number of elements in the structure Kj is the jth element stiffness matrix. The stiffness reduction ratio δi , (j = 1, …, Nel), ranges from 0 to 1, where δj = 0 signifies that the jth element is no damaged and δj = 1 indicates its rupture. The assessment of damage magnitude of suspected flawed elements is achieved through solving a reduced optimization problem formulated as follows. Find: δ T = {δ1 δ2 . . . δND }, Minimize: f (δ) Subject to: δL ≤ δ ≤ δU
(9)
Where δ is the vector of design variables representing the extents of the suspected damaged elements ND identified in the first step. δ L and δ U are, respectively, the lower and upper bounds of the design vector, and f (δ) is the objective function to be minimized. 3.1 Objective Function The objective function is expressed as the discrepancy between flexibility matrices of damaged and healthy structure. The flexibility matrix is employed due to its high sensitivity to damage and, moreover, can be estimated accurately by using only a few lower modes (Ben Guedria and Hassine 2019; Park et al. 1998). Therefore, the objective function of the optimization problem, Eq. (9), is formulated as follows: f (δ) =
FE − FC (δ)2Fro FE 2Fro
(10)
With FE representing, the modal flexibility matrix obtained from experimental results, FC (δ) the modal flexibility matrix computed through the numerical model using the stiffness reduction ratio vector. δ. 2Fro denotes the Frobenius norm on the residual matrix. 3.2 Proposed Optimization Algorithm: EAPSO To solve the reduced optimization problem an efficient adaptive PSO algorithm is developed. In EAPSO diversity is simulated using bests particle dispersion on the searching
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space (Ben Guedria, 2016). Thus, for the jth particle Xjt , a trial vector Yjt is generated using the following equation: (11) yjt = xjt + α ptg − xjt + β εtj Where ε tj is the jth row of a normally distributed (N × d) random matrix E = [ε1 , ε 2 , ..., ε N ]T , computed at each iteration t (Ben Guedria 2016). The particle’s positions are updated utilizing the following equation. t yi if f yit ≤ f xit (12) xit+1 = otherwise xit The pseudo code for the proposed EAPSO algorithm is shown in Fig. 1.
Fig. 1. Pseudo code for EAPSO algorithm
3.3 Micro Search Operator (MS) In the present work, a MS operator is e integrated in the EAPSO algorithm to reduce the search space and saves computation efforts. This helpful operator sets to zero design variables of particles with low damage values, i.e., considered as healthy elements, and consequently will be eliminated from design variables. The operator is applied to the whole of the swarm, during optimization process, repetitively after each T iterations (e.g. T = 3). Each component of a particle with value lower than a threshold value m (e.g. m = 0.02) is assumed a healthy element and subsequently fixed to zero to be eliminated from design variables.
4 Numerical Simulation The FE model of an isotropic plate, using various damage scenarios, was used to demonstrate the efficiency and fastness of the suggested twostep approach to accurately locate
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Fig. 2. The discretized square isotropic plate with two damage scenarios.
and quantify the structural damage. Moreover, the influence of noise on the accuracy of the proposed method are investigated, considering a noise level on frequencies ηf = 1% and on mode shapes ηm = 5%. This is simulated as follows finoise = 1 + ηf (2.rand [0, 1] − 1) fi (13) ϕijnoise = (1 + ηm (2.rand [0, 1] − 1))ϕij
(14)
where finoise is the ith eigenfrequency and ϕijnoise is the jth component of the ith eigenvector, both are contaminated by noise. The damaged elements localization is performed using the approach described in the Sect. 2. For noisefree cases, the level of significance is taken equal to 99% (i.e. the threshold value C = 3) and for cases with measurement noise it is set to 95% (i.e. C = 2). For the second step, the results of the damage assessment for each case are executed 5 times independently on the average and then compared to the recent results obtained by using a MultiStep method based on a Modified Differential Evolution (MSMDE) algorithm (DinhCong et al. 2017), and the standard PSO algorithm. The parameters used for PSO are as follows: The weight of inertia w is linearly reduced from 0.9 to 0.4 respect to the iteration counter. The maximum and minimum velocities Vmax and Vmin are fixed at half the value of the upper and lower limits, respectively. The acceleration constants c1 and c2 are both 2.0. The population size NP of those is 25 and the number of generations employed as stopping criterion is tmax = 50. 4.1 A Rectangular Isotropic Thick Plate A square plate made of an isotropic material, previously analyzed by (DinhCong et al. 2017) is considered as a numerical example. Material and geometrical parameters are given by Lx = Ly = 1 m, the thickness t = 0.1 m, Young’s modulus E = 2.0 × 1011 N/m2 , Poisson’s ratio ν = 0.3 and the mass density ρ = 8000 kg/m3 . The plate is clamped at its four edges and discretized using 4node quadratic finite elements with mesh 10 × 10, as depicted by Fig. 2. Two damage scenarios are studied, as shows Table 1.
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4.2 Location of Damaged Elements During the first stage of damage location, the modal strain energy of the 100 elements of the plate for both the healthy and damaged structures are computed first, and then, the indices of suspected damaged elements are determined via the Eq. (8). For locating the damage, for both scenarios without noise, only the first frequency and its associated mode shape are employed, whereas for the cases with measurement noise, the first five frequencies with their corresponding eigenmodes are considered. Figure 3a–d shows values of the elements damage index MSEDI versus element number for all considered damage cases. As depicted in Fig. 3a–b, for damage scenarios 1 and 2 without noise, the 47th and 56th elements and the 27th, 43th and 56th elements, respectively, are identified as damaged elements which relate precisely to those truly damaged. This shows the efficiency of proposed damage index to locate accurately damage. For scenarios 1 and 2, considering a noise level ηf = 1% on frequencies and ηm = 5% on mode shapes, the real damaged elements are also located, however, some other elements are incorrectly identified as damaged elements. For example, using the first five frequencies with their corresponding mode shapes gives three false alarm elements for damage scenario 1, (10th, 11th and 63th elements) and similarly three ones (10th, 11th and 26th elements) for scenario 2, as shows Fig. 3c–d. Although the numerical simulation shows that an increase in the number of used modes leads to a decrease in the number of false alarms, however, in this study we reasonably use the first five modes.
Fig. 3. Isotropic plate damage index: (a) scenario 1, FreeNoise; (b) scenario 2, FreeNoise; (c) scenario 1, WithNoise; (d) scenario 2, WithNoise.
4.3 Quantification of Damage Extent Using EAPSO As suspected damaged elements are located for the two damage scenarios with and without noise measurement, the purpose in this section is to assess the extent of their
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damage using the proposed EAPSO algorithm. To achieve this goal, a reduced damage identification problem, for each case, is formulated as an optimization problem, following Eq. (9). The objective function, Eq. (10), is expressed using the first five natural frequencies and their associated mode shapes. The design parameters (δ1 δ2 …, δk ) are the extent of the k suspect damaged elements, located during the first stage. 4.3.1 Free Noise Cases For damage scenarios 1 and 2, without noise, two optimization problems are formulated. For the first scenario, there are only two design variables, which are (δ47 , δ56 ), and for the second scenario there are three design variables, (δ27 , δ43 , δ57 ). For both cases, design variables correspond to the actual damaged elements. The optimization results using EAPSO for the two scenarios are depicted in Tables 2 and 3, respectively. As can be noted, damage extents of the 47th and 56th elements and those of the 27th, 43th and 57th elements are exactly as the real damage ratios. This mean that the EAPSO has converged to the optimal solution for both scenarios. The EAPSO optimization results are contrasted with those of PSO and MSMDE methods. As can be notice from Tables 2 and 3, the three algorithms are converged to optimal solutions, however, EAPSO is the fastest algorithm compared to its rivals the standard PSO and the MSMDE. Table 2. Numerical results of the evaluation of the extent of damage in an isotropic plate for scenario 1 in the case without noise.
Table 3. Numerical results of the evaluation of the extent of damage in an isotropic plate for scenario 2 in the cases without noise.
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4.3.2 Cases with Noise In the same way, for scenarios 1 and 2 with noise measurement, two additional optimization problems are formulated. For the first damage scenario, five design variables, which are (δ10 , δ11 , δ47 , δ56 , δ63 ), must be determined. Similarly, for the second damage scenario there are six design variables to be determined which are (δ10 , δ11 , δ26 , δ 27 , δ43 , δ57 ). Optimization results using the proposed EAPSO algorithm, for scenarios 1 and 2 with measurement noise, are depicted in Tables 4 and 5, respectively. As can be noticed, damage extents of the 47th and 56th elements, for the first scenario, and those of the 27th, 43th and 57th elements, for the second scenario, are obtained with satisfactory accuracy. Moreover, false alarm elements are identified as healthy elements with damage severities equal to zero. In contrast, as can be observed, PSO algorithm fails to provide the actual solution since false alarm elements remain after convergence, i.e., their damage extents are nonzero. Furthermore, the EAPSO is more rapid than the PSO algorithm to converge to the optimal solution. The average number of structural analyses for scenario 1 and 2, by EAPSO and PSO, are displayed in the last rows of Tables 4 and 5. Table 4. Numerical results of the evaluation of the extent of damage in an isotropic plate for scenario 1 in the cases with noise.
Table 5. Numerical results of the evaluation of the extent of damage in an isotropic plate for scenario 2 in the cases with noise.
5 Conclusion This paper presents a twostep approach for identifying the location and extent of multiple damage in platelike structures. The proposed technique is based on modal strain energy
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and an Efficient Accelerated Particle Swarm Optimization (EAPSO) algorithm. For the first step, a damage index, using the modal strain energy and the statistical hypothesis testing technique concept, is developed to locate the flawed elements of a damaged plate. During the second step, a reduced optimization problem is formulated and solved using the newly developed EAPSO algorithm. The goal is to assess the extent of the damaged elements located in the first step. The EAPSO operates with a new updating model, using random dispersion of particles over the search space leading to accelerate convergence speed and to prevent premature convergence. Furthermore, a microsearch operator is employed to remove law damage variables from the solutions and to reduce the computational cost. The numerical results show that the proposed EAPSO is more efficient and effective than the standard PSO and MSMDE, for both noise and nonnoise scenarios, due to the effectiveness of the EAPSO in balancing well between exploration and exploitation of the search space.
References Bayissa, W.L., Haritos, N., Thelandersson, S.: Vibrationbased structural damage identification using wavelet transform. Mech. Syst. Signal Process. 22, 1194–1215 (2008). https://doi.org/ 10.1016/j.ymssp.2007.11.001 Ben Guedria, N.: An accelerated differential evolution algorithm with new operators for multidamage detection in platelike structures. Appl. Math. Model. 80, 366–383 (2020). https://doi. org/10.1016/j.apm.2019.11.023 Ben Guedria, N.: Improved accelerated PSO algorithm for mechanical engineering optimization problems. Appl. Soft Comput. 40, 455–467 (2016). https://doi.org/10.1016/j.asoc.2015.10.048 Guedria, N.B., Hassine, H.: Efficient cultural algorithm for structural damage detection problem based on modal data. In: Fakhfakh, T., Karra, C., Bouaziz, S., Chaari, F., Haddar, M. (eds.) ICAV 2018. ACM, vol. 13, pp. 204–217. Springer, Cham (2019). https://doi.org/10.1007/9783319946160_21 DinhCong, D., VoDuy, T., HoHuu, V., DangTrung, H., NguyenThoi, T.: An efficient multistage optimization approach for damage detection in plate structures. Adv. Eng. Softw. 112, 76–87 (2017). https://doi.org/10.1016/j.advengsoft.2017.06.015 Guo, H.Y., Li, Z.L.: A twostage method to identify structural damage sites and extents by using evidence theory and microsearch genetic algorithm. Mech. Syst. Signal Process. 23, 769–782 (2009). https://doi.org/10.1016/j.ymssp.2008.07.008 Park, K.C., Reich, G.W., Alvin, K.F.: Structural damage detection using localized flexibilities. J. Intell. Mater. Syst. Struct. 9, 911–919 (1998). https://doi.org/10.1177/1045389X9800901107 Saggar, M., Nasr, A., Bouraoui, C.: Initiation life prediction method for defective materials. In: Chaari, F., et al. (eds.) Advances in Materials, Mechanics and Manufacturing. LNME, pp. 17–25. Springer, Cham (2020). https://doi.org/10.1007/9783030242473_3 Seyedpoor, S.M.: A two stage method for structural damage detection using a modal strain energy based index and particle swarm optimization. Int. J. NonLinear Mech. 47, 1–8 (2012). https:// doi.org/10.1016/j.ijnonlinmec.2011.07.011 Xiang, J., Liang, M.: A twostep approach to multidamage detection for plate structures. Eng. Fract. Mech. 91, 73–86 (2012). https://doi.org/10.1016/j.engfracmech.2012.04.028
Experimental Analysis of the Dynamic Behavior of a Sandwich with a BioBased Auxetic Core A. Hamrouni1,2(B) , J. L. Rebiere1 , A. El Mahi1 , M. Beyaoui2 , and M. Haddar2 1 Acoustics Laboratory of Le Mans University (LAUM) UMR CNRS
6613, Le Mans University, Av. O. Messiaen, Le Mans, France {jeanluc.rebiere,abderrahim.elmahi}@Univlemans.fr 2 Laboratory of Mechanics Modeling and Production (LA2MP), National School of Engineers of Sfax, University of Sfax, Sfax, Tunisia [email protected]
Abstract. The auxetic materials that exhibit a negative Poisson’s ratio are shown to have better damping factors as well as impact shielding capability. This paper displays experimental results for the flexural vibration of a sandwich with a biobased auxetic core. Material design concept and the coupled geometry are enabled by the additive manufacturing technique. The core and skins printed from polylactic acid fortified by flax fibers (PFF) compose these sandwich structures. A clampedfree arrangement is used for the vibration tests. Experimental tests on the auxetic structure, the skins and the sandwich beams, were executed for the evaluation of their dynamic properties. These tests were realized on three core densities for auxetic structures, to investigate the influence over damping factors in addition to the dynamic stiffness. The results show that the loss factor increases with frequency on the contrary to the stiffness which decreases as a function of frequency. In addition, a decrease in the density of the auxetic core generates an improvement in the loss factor and a decrease in the dynamic stiffness of the sandwich beam. Keywords: Sandwich · Auxetic · 3D printing · Antitrichiral · Composite · Dynamic analysis · Biobased
1 Introduction Architectural structures use has increased in recent years because of unique characteristics. Higher rigidity, durability and high energy absorption capacities for instance (Scarpa et al. 2003) along with significantly lower weight in comparison with conventional materials (Zhang et al. 2015). With having such attractive features, it is usual to notice these structures used in many different areas, including sports, spacecraft, the automotive industry and many other applications. Core density variation has pros and cons that need to be investigated according to the application. The sandwich gains a high shear stiffness and energy absorption capability, as a result of skins being separated by an auxetic core. Honeycombs that have a negative Poisson’s ratio are studied as well (Essassi et al. 2019a). Various approaches are used to make these complex architectures © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 73–82, 2022. https://doi.org/10.1007/9783030849580_8
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(Qin and Yang 2019). The most efficient and effective process is additive manufacturing, also referred to as 3D printing, which ensures the structure’s shape durability as good as possible, regardless of geometry. The auxetic designs became the focus for plenty of researchers interested in their special properties (Subramani et al. 2016; Jin et al. 2016). These architectures display a synclastic curvature when submitted to bending out of the plane (Evans and Alderson 2000; Alderson et al. 2010). This behavior heartens the use of auxetic structures in complex offplane geometries. Later, Essassi et al. (2019b) investigated the dynamic behavior of a sandwich structure with reentrant honeycomb cores. In their study 3D printing technology was used to manufacture these complex architectures. Their results showed that reentrant honeycomb cores have significantly improved the stiffness and flexural strength (for the sandwich) along with energy absorption capability. It is known that biobased composites are very interesting materials to meet the current challenges of engineering. Many university research laboratories and industries have used biobased materials (Essassi et al. 2019b) for their multiple advantages, such as the biodegradability, low cost and most importantly damping properties. Most natural fibers that have been researched in recent years are flax fibers (Daoud et al. 2017, 2018). Various researches have shown that a biobased materials mix used for manufacturing architectural composites and auxetic cores, especially biocomposite (PLA) strengthen by flax fibers, most likely allow high dynamic properties within a material. In the present work, the focus is to highlight the dissipative characteristics for auxetic materials along with damping characteristics for flax fibers, with the implementation of three different densities for the antitrichiral structures. These damping characteristics were determined by vibration experiments according to the Frequency Response Function method. A comparative study of dynamic stiffness properties and damping is conducted for antitrichiral honeycomb structures with three different densities of auxetic core and the skins’ influence on the sandwich beams.
2 Experimental Analysis 2.1 Material and Method Polylactic acid strengthened by flax fibers (PFF) is used as the material for this study. Manufactured by NANOVIA in Louargat France and with a diameter of Ø 1.75 mm ± 50 μm, the mechanical characteristics are described in Table 1. Table 1. Mechanical properties of PFF [Nanovia DATA]. Material E (GPa) ρ (kg.m−3 ) ν PFF
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Table 4. Coefficients to calculate the equivalent stiffness. nth mode
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3 Discussion To study the sandwich dynamic characteristics. Vibration experiments were realized on the cores, the sandwich along with the skin, with lengths of structures defined as 140, 170 and 200 mm. Loss factor variation and normalized stiffness for the skin in function of frequency are represented in Fig. 5. The outcome indicates that skin damping characteristics vary inversely proportional to the normalized stiffness. Many hypotheses can be suggested to explain the frequencydependent dynamic behavior. The thermoplastic resin composing Polylactic acid is a polymer whose viscoelastic behavior is a significant contributor to the global reaction for the skin. It represents 80% of the total volume fraction. In addition, there are the effects created by flax fibers that need to be taken into account. These reinforcements are made of natural polymers which contain several viscoelastic components. Figure 6 represents the loss factor’s evolution in regards to the frequency. Three relative core densities are utilized: 13.31%, 23.35% and 39.93%. The damping factor rises with frequency, as shown by the results. At low frequencies, a close similarity can be noticed for different density results of damping. This similarity continues only for the cores with 2 and 3 cells, up to the frequency of 1600 Hz, however, the core with 1 cell shows an increase of 40% for this frequency. Over this frequency, the loss factor rises by 8% in regards to the 2cell core, compared to the 3cell one. This shows the consequence of density on an auxetic core’s dynamic behavior. On the other hand, the evolution curve of the loss factor changes in function of the density as represented with a linear curve for a 1 and 2 cells cores and with a parabolic curve for 3 cells core. This behavior can be explained by the saturation of the loss factor in function of frequency for the cores with a high density. The core, skin and sandwich dynamic behaviors are illustrated in Fig. 7. A particular density chosen for the core is equal to 13.31%. The results display the difference between a solid structure (skin with 7 mm thickness), a core and a sandwich. The loss factor of a sandwich is optimized by 27% for a frequency of 4000 Hz, compared to the skin.
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The variation of the loss factor in function of frequency in regards to the skin and sandwich beams with different densities of core is represented in Fig. 8. The results display that sandwich beams damping proprieties are slightly dependent on density value for the core. However, their equivalent stiffness largely depends on the core density and the frequency, as displayed in Fig. 9. This behavior can be explained by the percentage of the core density, when this density increases, the dynamic stiffness increases also.
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4 Conclusion In this research skin, sandwich, along with auxetic core structures were studied. A biobased material was used for the manufacturing of the specimens. This material is a polylactic acid reinforced by flax fibers. The RAISE3D Pro2 Plus printer was used for the manufacturing of the components. Three core densities were studied. Free vibration experiments were performed for the determination of sandwich damping factors utilizing the Half Power Bandwidth method (HPB). Also, dynamic properties for the skins along with the different densities that compose the core were investigated. The results obtained show that the interposition of the core between the two skins optimizes the damping characteristics of PFF. Furthermore, a comparison between the loss factors and the equivalent stiffness of the sandwich beams studied demonstrates that both these properties depend on frequency and core density. To conclude, several explanations can be provided for the behavior of the equivalent stiffness in function of sandwich damping. First, the material dissipates the vibration energy. This dissipation is explained by the fact that Flax fibers are used for reinforcements. These are natural polymers with viscoelastic properties. Secondly, unit cell geometry along with its periodicity contributes to this energy dissipation. Finally, core density plays a big factor in energy dissipation, along with rigidity.
References Scarpa, F., Burriesci, G., Smith, F., Chambers, B.: Mechanical and eletromagnetic behaviour of auxetic honeycomb structures. Aeronaut. J. 107(1079), 175 (2003) Zhang, Q.C., Yang, X.H., Li, P., et al.: Bioinspired engineering of honeycomb structure – using nature to inspire human innovation. Progr. Mater. Sci. 74, 332–400 (2015) Essassi, K, Rebiere, J.L., El Mahi, A., Ben Souf, M.A., Bouguecha, A., Haddar, M.: Experimental and numerical analysis of the dynamic behavior of a biobased sandwich with an auxetic core. J. Sandw. Struct. Mater. 1–20 (2019a). https://doi.org/10.1177/1099636219851547 Qin, H., Yang, D.: Vibration reduction design method of metamaterials with negative Poisson’s ratio. J. Mater. Sci. 54(22), 14038–14054 (2019). https://doi.org/10.1007/s1085301903903z Subramani, P., Rana, S., Ghiassi, B., et al.: Development and characterization of novel auxetic structures based on reentrant hexagon design produced from braided composites. Compos. B Eng. 93, 132–142 (2016) Jin, X., Wang, Z., Ning, J., et al.: Dynamic response of sandwich structures with graded auxetic honeycomb cores under blast loading. Compos. B Eng. 106, 206–217 (2016) Evans, K.E., Alderson, A.: Auxetic materials: functional materials and structures from lateral thinking! Adv. Mater. 12, 617–628 (2000) Alderson, A., Alderson, K.L., Chirima, G., et al.: The inplane linear elastic constants and outofplane bending of 3coordinated ligament and cylinderligament honeycombs. Compos. Sci. Technol. 70, 1034–1041 (2010) Essassi, K., Rebiere, J.L., El Mahi, A., Ben Souf, M.A., Bouguecha, A., Haddar, M.: Dynamic characterization of a biobased sandwich with auxetic core: experimental and numerical study. Int. J. Appl. Mech. (2019b). https://doi.org/10.1142/S1758825119500169 Daoud, H., El Mahi, A., Rebiere, J.L., Taktak, M., Haddar, M.: Characterization of the vibrational behaviour of flax fibre reinforced composites with an interleaved natural viscoelastic layer. Appl. Acoust. 128, 23–31 (2017)
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Daoud, H., El Mahi, A., Rebiere, J.L., Taktak, M., Haddar, M.: Experimental analysis of the linear and nonlinear vibration behavior of flax fibre reinforced composites with an interleaved natural viscoelastic layer. Compos. B Eng. 151, 201–214 (2018) Xu, X., Koomson, C., Doddamani, M., et al.: Extracting elastic modulus at different strain rates and temperatures from dynamic mechanical analysis data: a study on nanocomposites. Compos. B Eng. 159, 346–354 (2019) Monti, A., El Mahi, A., Jendli, Z., Guillaumat, L.: Experimental and finite elements analysis of the vibration behaviour of a biobased composite sandwich beam. Compos. B Eng. 110, 466–475 (2017) Daoud, H., et al.: Numerical and experimental characterization of the dynamic properties of flax fiber reinforced composites. Int. J. Appl. Mech. 8, 1650068 (2016) Gay, D.: Composite Materials: Design and Applications, 3rd edn. CRC Press, Boca Raton (2014) Lamanna, E., Gupta, N., Cappa, P., et al.: Evaluation of the dynamic properties of an aluminum syntactic foam core sandwich. J. Alloy Compd. 695, 2987–2994 (2017)
Numerical Analysis of Entropy Generation Inside the Diesel Injector Fraj Echouchene(B) and Hafedh Belmabrouk Faculty of Science of Monastir, Monastir, Tunisia [email protected]
Abstract. The development of cavitation will cause local hydraulic losses in the injection system. To calculate this loss, the theory of entropy production is very efficient. In this work, we study the entropy generation in the cavitating flow inside the Diesel injector. In order to simulate the cavitating flow, the homogenous mixture model coupled with the kε turbulence model are used. The rate of entropy production of the mixture is calculated assuming that the slip velocity between the two phases is negligible and the diffusion of species through the interface is ignored. The effect of wall roughness is presented in the steady case. The entropy production as a function of cavitation number is studied. The spacetime evolution of the vapor fraction is analyzed. The results prove that the wall roughness has an effect on velocity profile for high pressure. On the other hand, the local analysis shows that the entropy is important at the entrance of the orifice where cavitation is developed and an increase of total entropy generation when the cavitation number K tends towards unity. Keywords: Cavitation · Diesel injector · Entropy generation · Mixture model · Numerical simulation
1 Introduction The fuel flow through injector nozzles affects the spray formation, the atomization phenomenon of the liquid fuel and, therefore, the efficiency of the combustion process and pollutant emission. The high injection pressure (>2000 bar) (Jia et al. 2017; Yu et al. 2017; Yu 2019; Zhao et al. 2020; Zhai et al. 2021) and the abrupt change of the orifice section of the injector allows to have a pressure drop below the saturated vapor pressure and consequently the development of cavitation which has a great effect on both the fuel injection process and the performance of an engine. Cavitation generated at the entrance of the orifice affects the fluid flow and the atomization of the injected liquid jet (Arcoumanis et al. 2001; Payri et al. 2004; Habchi et al. 2008). The study investigation of cavitation phenomenon in the injection orifice is useful even important to control and optimize the atomization process. The high injection pressure, the high speed flow (Yuan and Schnerr 2003) and the small dimensions of the injection nozzle make the experimental studies complicated. In © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 83–92, 2022. https://doi.org/10.1007/9783030849580_9
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addition, experiments were performed on largescale and transparent injector configurations to visualize the phenomenon of cavitation (Suh et al. 2008; Payri et al. 2009; Zhang et al. 2018a). Confronted with experimental difficulties, several theoretical and numerical studies have been developed to study this cavitation problem in a real diesel injector (Echouchene et al. 2011; Xue et al. 2017; Li et al. 2018; Zhang et al. 2018b; Cristofaro et al. 2020; He et al. 2020; Santos et al. 2020). In a previous study (Echouchene et al. 2011), a numerical study was carried out, using the mixing model, the effect of the wall roughness of the orifice injection on the cavitation phenomenon. In another work (Echouchene and Belmabrouk 2010), the effect of inlet corner radius of orifice injection on the flow characteristic and the development of cavitation have been analyzed. A reduction in the intensity of cavitation when corner radius increases is achieved. The relative risk of erosion of the inner wall of the diesel injector orifice due to cavitation has been studied by Cristofaro et al. (2020) and Zhang et al. (2018b). Xue et al. (2017) studied the effect of cavitation in a multihole injector on the transient flow characteristic in a 3D asymmetric configuration using a twophase (liquidvapor) model (Xue et al. 2017). The effect of the needle lift was analyzed by these authors. They showed a difference in velocity profile and cavitation within the holes. Torelli et al. (2017) performed a 3D simulation in a fivehole diesel miniinjector to model the internal flow of the nozzle using three types of fuel (fullrange naphtha, light naphtha and nDodecane). They have shown that the cavitation is strongly related to the saturating vapor pressure of different fuels. In this paper, we aim to investigate the cavitating flow inside a Diesel injector using the mixture model and taking into account the turbulence. The effect of the orifice wall roughness is studied. The entropy production as a function of cavitation number is studied. Furthermore, the flow is simulated in the steady state as well as in the unsteady state.
2 Physical Model 2.1 Mixture Cavitation Model In this mixture model, the fluid (fuel) is composed of three phases: liquid, vapor and noncondensable gases (CO) which the mixture density is given by (1) ρm = αv ρv + αg ρg + 1 − αv − αg ρl where ρ is the density and α is the volume fraction. The indices l, v and g denote the liquid, vapor and gas phases, respectively. The transport equations describing the cavitating flow inside the diesel injector are: • Navier Stokes equations for the mixture; − ∂ρm → + ∇. ρm U m = 0 ∂t
(2)
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− → ∂ ρm U m ∂t
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− − − → − → → T → + ∇. ρm U m ⊗ U m = −∇p + ∇. (μt + μm ) ∇. U m + ∇. U m (3)
• kε turbulence model; − → ∂ ρm k U m μt − → ∇k + P − ρm ε (4) + ∇. ρm k U m = −∇p + ∇. μm + ∂t σk − → ∂ ρm ε U m ε ε2 μt − → ∇ε + C1ε P − C2ε + ∇. ρm ε U m = −∇p + ∇. μm + ∂t σε k k (5) • Transport equation of vapor fraction (Dular et al. 2005; Echouchene et al. 2011). ∂(ρm fv ) − → + ∇. ρm fv Uv = Re − Rc ∂t
(6)
where U m present the mixture velocity, μm is the laminar viscosity of the mixture, μt = ρ m C μ k 2 /ε is the turbulent viscosity, k is turbulent kinetic energy, ε is the dissipation − → − → − → rate P = μt [∇. U m +(∇. U m )T ]∇. U m and is the production term of turbulent kinetic energy, f v = α v ρ v /ρ m is the vapor mass fraction. The standard values of the constants are: C μ = 0.09, σ k = 1.0, σ ε = 1.3, C 1ε = 1.44 and C 2ε = 1.92 (Echouchene et al. 2011). Re and Rc denote the evaporation and condensation rates, respectively, given by (Singhal et al. 2002): √ 2 pv − p 1/2 k ρl ρv Re = Ce 1 − fv − fg if p < pv (7) σ 3 ρl √ 2 p − pv 1/2 k ρl ρv Rc = Cc fv if p < pv (8) σ 3 ρl where C e = 0.02 and C c = 0.01 are calibration constants, f v and f g are vapor mass fraction and noncondensable gas mass fraction, pv = psat + pt /2 is the vapor pressure, psat is the vapor saturation pressure and pt = 0.39ρ m k is the turbulence pressure (Echouchene et al. 2011). 2.2 Entropy Production Taking into account the following assumptions: • The slip velocity between the two phases is negligible; • The diffusion of species through the interface is ignored
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The entropy production rate for the mixture is then written: 1 μm + tm + Dm P˙ sm = T
(9)
where μm is the average entropy production for the mixture, tm is the entropy generation due to turbulent shear stress and Dm is the entropy production due to the turbulent dissipation term. The mean of the entropy production and the entropy production due to the turbulent shear stress can be written as follows:
− → t − → − → effm = μm + tm = μeffm ∇. U m + ∇. U m : ∇. U m (10) where μeffm = μm + μtm is the effective viscosity of the mixture. In a twodimensional flow in an injection orifice, the entropy production in cylindrical coordinates (2D) is then written: 2 2 2 2 μeffm ∂u ∂v s u ∂v ρ ∂u m m m m m m m + + + + + P˙ sm = 2 T ∂r r ∂z ∂z ∂r T (11)
3 Numerical Method and Nozzle Geometry To simulate the cavitating flow, the numerical code Fluent based on finite volume scheme was used. The SIMPLE algorithm (Ferziger et al. 2002) is used for the pressurevelocity coupling. Grid generation process for performing finite volume simulations were carried out using GAMBIT (v2.3.16) program available with the commercial code Fluent. Figure 1 illustrates the nozzle geometry of diesel injector in 2D axisymmetric. The geometric parameters of the nozzle are R1 = 0.3 mm, R2 = 0.1 mm and L1 = 0.5 mm. The transition radius between inlet pipe and orifice is rc .
Fig. 1. 2Daxisymmetric configuration of the Diesel injector with boundary conditions
In this study, a stationary single phase fluid containing a very small fraction of noncondensable gas (e.g., 15 ppm) is assumed as initial conditions. Uniform inlet and outlet static pressure were adopted as boundary conditions. A value of k0 and ε0 are imposed at the inlet.
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4 Results and Discussions Figure 2 presents the effect of wall roughness of orifice for three cavitation number values, K = 3.23, 1.45 and 1, respectively. The number of cavitation, corresponding to the injection pressure, is K = 3.23. The latter indicates that the injection pressure is too low and subsequently a noncavitating regime appears. This implies the existence of only one phase: continuous phase. 1.0
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The roughness affects the velocity profile slightly and especially in the region near the sharp entrance to the orifice (Fig. 2 (a)). Near the wall, we do not notice the influence of the roughness of the wall. For K = 1.45, the flow is cavitating since, according to the studies by Payri et al. (2009), the cavitation triggering regime requires a value of K = 1.45. A slight change in the speed profile under the effect of the roughness of the wall is noted from Fig. 2 (b) and especially when the flow is undeveloped. For K = 1, the cavitation is strongly developed and the roughness changes the speed profile, especially in the central region (Fig. 2 (c)). The entropy generation is a measure of the degree of irreversibility. It is a method for optimizing thermal and fluidic systems. It could be agreed to specific applications. To analyze entropy generation within the injector, we have studied the effect of the injection pressure. In this case, simulations were carried out for inlet pressure varying between
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1.9 bar and 1000 bar and for a fixed downstream pressure of 0.95 bar. Figure 3 illustrates the vapor fraction and local entropy distributions inside the injector for various values of cavitation number K. We notice from Fig. 3 (left) that the state of the fluid changes as it enters the orifice and as the injection pressure is increased. The change in the fluid state is due to the cavitation phenomenon that is created for significant local depression. The 2D results for the vapor fraction show that cavitation is triggered when K ≈ 1.45 confirms the previous results.
Fig. 3. Distribution of vapor fraction (left) and entropy (right) for various cavitation number values
In the center of the orifice, the fluid is formed by a dense core of fluid (liquid) and a dispersed phase (vapor), which is analogous to the experimental results of Yan and Thorpe (Yan and Thorpe 1990). For high injection pressures, the cavitation zone extends to the outlet leading to the formation of the hydraulic flip. According to the results of Fig. 3 (right) show the local entropy distribution for different K values. It is clear that the entropy generation takes place near the orifice edge with very high intensity. These results can be explained by the effect that near the wall, the radial component is important. Thus, the low pressure zone essentially gives rise to the formation of bubbles and the recirculation zone is very limited. The velocity gradient in the recirculation zone is very important causing viscous effects. This trend indicates that the maximum entropy
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produced near the edge of the orifice is mainly due to the irreversibility of fluid friction contributed by the velocity gradient due to the abrupt change of injector section. According to Fig. 3, for K = 1.96, cavitation has not yet started and the zone of constriction at the entrance of the orifice is composed of a mixture (vapor, liquid and noncondensable gas). In the vicinity of the wall just at the orifice inlet, the average velocity gradient has a maximum value. The entropy production is high due to strong fluid disturbance near the wall. Indeed, for K = 1.45 which corresponds to the development of cavitation, the narrowing zone close to the wall is formed only of steam, which tends to reduce the rate of entropy generation. In the liquiddominant zone where less cavitation occurs, the average dissipation of the mixture is dominated by the velocity gradient of the mixture. For z ≥ D1 , the flow is strongly developed. The turbulent velocity components promote the transfer of momentum between adjacent layers of the fluid and tend to reduce the average velocity gradient and subsequently a decrease in the degree of irreversibility. Total entropy refers to the integral of the local entropy over the total volume, given by the following expression: SdV (12) Stot = Figure 4 shows the evolution of total entropy as a function of the number of cavitation K. The results are presented on a logarithmic decimal scale.
Fig. 4. Total entropy production in decimal logarithm as a function of cavitation number K.
These results prove that the degree of irreversibility is proportional to the injection pressure. For high injection pressures, entropy production is important. By making a rational interpolation of the results, we obtain the following model: log10 (St ) =
p1 K 2 + p2 K + p3 K + q1
(13)
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where the p1 = −0.4171, p2 = −2.285, p3 = 2.702 and p4 = −0.9835 are the fitting parameters. Figure 5 represents the evolution of vapor volume fraction at different times for L2 /d2 = 5. The inlet corner radius rc is equal to zero. The injection pressure pin = 1000 bar and the exit pressure pout = 50 bar.
Fig. 5. Transient evolution of vapor volume fraction
The cavitation appears in the vicinity of the sharp edge for a time of the order of 0.6 μs. Then, the cavitation pocket elongates progressively through the orifice and reaches the nozzle exit at t = 3 μs. This result agrees well with the numerical simulation obtained by Dumont et al. (2001) in a similar injector and by experimental visualization and measurements Ohrn et al. (1991).
5 Conclusion A numerical simulation of cavitating flow inside a diesel injector nozzle using a turbulent mixture model was presented. The study is carried out in two regimes, namely stationary and transient. The effect of the orifice wall roughness on the cavitation phenomenon inside the nozzle has been studied. The study of the roughness of the wall shows that it affects the flow regime when cavitation is strongly developed in the orifice (K = 1). Unsteady simulations have also been carried out. The spacetime evolution of the vapor fraction is analyzed. It appears that the spray leaving the orifice and entering into the combustion chamber contains liquid and vapor. Hence, the cavitation is expected to have an effect on the atomization and the combustion processes.
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In the other hand, the local entropy production inside the diesel injector is analyzed. Consequently, the effect of cavitation number on the total entropy production is studied. The numerical results show the increase of total entropy generation by increasing the injection pressure.
References Arcoumanis, C., et al.: Visualisation of cavitation in diesel engine injectors. Mécanique Industr. 2(5), 375–381 (2001) Cristofaro, M., et al.: A numerical study on the effect of cavitation erosion in a diesel injector. Appl. Math. Model. 78, 200–216 (2020) Dular, M., et al.: Experimental evaluation of numerical simulation of cavitating flow around hydrofoil. Eur. J. Mech. B/Fluids 24(4), 522–538 (2005) Dumont, N., et al.: Numerical simulation of cavitating flows in diesel injectors by a homogeneous equilibrium modeling approach (2001). http://resolver.caltech.edu/cav2001:sessionB6.005 Echouchene, F., Belmabrouk, H.: Computation of cavitating flows in a diesel injector. In: IOP Conference Series: Materials Science and Engineering. IOP Publishing (2010) Echouchene, F., et al.: Numerical simulation of wall roughness effects in cavitating flow. Int. J. Heat Fluid Flow 32(5), 1068–1075 (2011) Ferziger, J.H., et al.: Computational Methods for Fluid Dynamics. Springer, Heidelberg (2002). https://doi.org/10.1007/9783642560262 Habchi, C., et al.: Multidimensional simulation of cavitating flows in diesel injectors by a homogeneous mixture modeling approach. Atomiz. Sprays 18(2) (2008) He, Z., et al.: Effects of nozzle geometries and needle lift on steadier string cavitation and larger spray angle in common rail diesel injector. Int. J. Engine Res. (2020). https://doi.org/10.1177/ 1468087420936490 Jia, T.M., et al.: Experimental investigation of effects of super high injection pressure on diesel spray and induced shock waves characteristics. Exp. Thermal Fluid Sci. 85, 399–408 (2017) Li, D., et al.: Numerical investigation on transient internal cavitating flow and spray characteristics in a singlehole diesel injector nozzle: a 3D method for cavitationinduced primary breakup. Fuel 233, 778–795 (2018) Ohrn, T., et al.: Geometrical effects on discharge coefficients for plainorifice atomizers. Atomiz. Sprays 1(2) (1991) Payri, F., et al.: The influence of cavitation on the internal flow and the spray characteristics in diesel injection nozzles. Fuel 83(4–5), 419–431 (2004) Payri, R., et al.: Study of cavitation phenomena based on a technique for visualizing bubbles in a liquid pressurized chamber. Int. J. Heat Fluid Flow 30(4), 768–777 (2009) Santos, E.G., et al.: Investigation of cavitation and air entrainment during pilot injection in realsize multihole diesel nozzles. Fuel 263, 116746 (2020) Singhal, A.K., et al.: Mathematical basis and validation of the full cavitation model. J. Fluids Eng. 124(3), 617–624 (2002) Suh, H., et al.: Experimental investigation of nozzle cavitating flow characteristics for diesel and biodiesel fuels. Int. J. Automot. Technol. 9(2), 217–224 (2008) Torelli, R., et al.: Influence of fuel properties on internal nozzle flow development in a multihole diesel injector. Fuel 204, 171–184 (2017) Xue, F., et al.: Numerical analyses of transient flow characteristics within each nozzle hole of an asymmetric diesel injector. Int. J. Heat Mass. Transf. 104, 18–27 (2017) Yan, Y., Thorpe, R.: Flow regime transitions due to cavitation in the flow through an orifice. Int. J. Multiph. Flow 16(6), 1023–1045 (1990)
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Yu, S., et al.: Numerical research on micro diesel spray characteristics under ultrahigh injection pressure by Large Eddy Simulation (LES). Int. J. Heat Fluid Flow 64, 129–136 (2017) Yu, Y.: Experimental study on effects of ethanoldiesel fuel blended on spray characteristics under ultrahigh injection pressure up to 350 MPa. Energy 186, 115768 (2019) Yuan, W., Schnerr, G.N.H.: Numerical simulation of twophase flow in injection nozzles: Interaction of cavitation and external jet formation. J. Fluids Eng. 125(6), 963–969 (2003) Zhai, C., et al.: Diesel spray and combustion of multihole injectors with microhole under ultrahigh injection pressure–nonevaporating spray characteristics. Fuel 283, 119322 (2021) Zhang, L., et al.: Simulations on the cavitating flow and corresponding risk of erosion in diesel injector nozzles with double array holes. Int. J. Heat Mass. Transf. 124, 900–911 (2018a) Zhang, X., et al.: Effect of fuel temperature on cavitation flow inside vertical multihole nozzles and spray characteristics with different nozzle geometries. Exp. Thermal Fluid Sci. 91, 374–387 (2018b) Zhao, J., et al.: Specific features of diesel fuel supply under ultrahigh pressure. Appl. Thermal Eng. 179, 115699 (2020)
Assessment of Surface Integrity and Dust While Drilling of GLARE® FMLs Imed Boughdiri1(B) , Tarek Mabrouki1 , Redouane Zitoune2 , and Khaled Giasin3 1 Applied Mechanics and Engineering Laboratory (LR11ES19), University of Tunis El Manar,
ENIT, BP 37, Le Belvédère, 1002 Tunis, Tunisia {imed.boughdiri,tarek.mabrouki}@enit.utm.tn 2 Clément Ader Institute, UMR CNRS 5312, University of Toulouse, Toulouse, France [email protected] 3 School of Mechanical and Design Engineering, University of Portsmouth, Portsmouth, UK [email protected]
Abstract. Fibermetal laminates represent a promising type of hybrid material, resulting from the combination of a metal, usually an aluminum alloy, and a fiberreinforced composite, such as a glassfiber reinforced epoxy. Currently, GLARE (a fiberglass/aluminum composite) is used by many aerospace manufacturers for primary aircraft components. Few researchers have investigated this type of hybrid material in terms of cutting effort and hole quality, but none have studied the impact of machining on operator health. The present work aims to investigate the effects of input cutting parameters and the tool coating when drilling multimaterial type GLARE® on finish roughness and generation of aerosol dust particles. The drilling tests were carried out using uncoated tools and coated ones with a thin film of diamondlike carbon (DLC) and Cristal. After drilling operations, obtained results reveal that DLC coated tools induced less roughness when compared to uncoated ones or Cristal coated drill. In addition, dust particle number generated while tests conducting, is affected by input cutting parameters. A lower speed of spindle promotes the diminution of the quantity of particles in the workplace compared to that recorded at higher speed of the spindle. Keywords: Drilling · GLARE® · Coated tools · Hole quality · Dust
1 Introduction Novel issues arise during the drilling of hybrid and composite structures especially for Glass Aluminum Reinforced Epoxy (GLARE® ), since a great number of holes are needed with high quality requirements. In addition, the low quality of drilled hole induces 60% rejection of achieved pieces (Giasin et al. 2015). Therefore, optimization of cutting parameters when drilling FMLs with its different components will ensure good surface quality. Regardless, hole with geometric defects can induce severe strains on the fasteners, yielding important damage to structure (Ashrafi et al. 2013). In literature, few researchers have proposed understanding to explain these weaknesses and their investigations were mainly based on hole surface quality. (Giasin et al. 2019) have underlined © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 93–102, 2022. https://doi.org/10.1007/9783030849580_10
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that roughness parameters (Ra and Rz) were higher when drilling GLARE® laminates using tools coated with TiAlN than those coated with TiN and AlTiN/TiAlN. They have noted that those criteria are higher with spindle speed increase, although their variations. When drilling composite/metal material, (Zitoune et al. 2010) have found that the higher is the feed rate, the higher is the Ra, whereas the speed spindle has a less impact on surface finish roughness. When drilling GLARE® 3 4/3–0.4 using cemented carbide tools, (Park et al. 2017) have reported that a combination of low spindle speed rotation (600 rpm) and high feed rate (0.2 mm/rev) induces the highest surface roughness. Many works have been conducted on cryogenic cooling (Giasin et al. 2021) and minimum quantity lubrication (MQL) (Giasin 2018) when drilling GLARE® type multimaterials. Indeed, authors mentioned that the use of minimum quantity lubrication and liquid nitrogen cryogenic coolant can reduce the surface roughness of drilled holes. Nevertheless, only few research works are dealing with the investigation of the health hazards induced by dust particle generation during cutting operations (Haddad et al. 2014). During trimming achievements, NguyenDinh et al. (NguyenDinh et al. 2020) emphasized that harmful dust amount evolves in the same direction as that of the feed rate and inversely decreases with spindle speed.. Other authors (Djebara et al. 2013) indicated that the higher the spindle speed and feed rate, the lower the emission of dust during machining. (Haddad et al. 2014) found that fine airborne dust particles released when cutting carbon fiber reinforced plastic materials at conventional speeds. Moreover, these authors have remarked that high trimming speeds affect operator health, significantly. The size of these harmful particles depends on the geometries of milling tools. In this framework, we intend to assess the effect of feed rate, spindle speed and coating tools on surface roughness evolution and dust generation while drilling composite GLARE® 2B 11/10–0.4 using an uncoated and coated tungsten carbide (K20) tool. The investigation will guide researchers to use optimized drilling conditions that induced the better surface finish and minimize harmful particles releasing.
2 Experimental Setups The drilling tests were performed by using a HSM machine tool which is referenced DMU 85 mono BLOCK CNC center with a maximum spindle rotation speed of 18000 rpm. The experimental procedure, as schematically illustrated in Fig. 1(b), consisted in using a forcetorque dynamometer (piezoelectric Kistler 9272 dynamometer, model 5019) in which the GLARE sample is mounted, and a GRIMM aerosol spectrometer is exploited to detect ejected particles. In order to facilitate the mounting of the GLARE specimens on the dynamometer, the GLARE specimen was cut into test samples by water jet technology using the MACHINE FLOW MACH4C abrasive water jet machine. Prior to the drilling trials, the drill must be firmly fastened to the tool holder by means of a thermal shrinkage process using an Easyshrink® 15 shrinkage bench. All trials performed in this investigation were performed in dry condition and were repeated three times to confirm the repeatability. Each ten holes set were drilled with new tool to avoid any effect on tool wear and aluminum alloy built up at drill edges.
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Table 1. Characteristics of the two materials (S2/FM94&Al2024T3) Mechanical property
Symbol
UD S2/FM94 epoxy prepeg
Al2024T3
Young modulus (GPa)
E 11
54–55
72.2
E 22 , E 33
9.4–9.5
–
Ultimate tensile strength (MPa)
σ ult
2640
455
Ultimate strain (%)
εult
4.7
19
Shear modulus (GPa)
G12
5.55
27.6
G23
3
–
G13
5.55
V 12
0.33
V 23
0.0575
V 13
0.33
Poisson’s ration
Density (kg/m3 )
ρ
1980
Thickness
(mm)
0.266
0.33
0.4064
Drilling trials of GLARE® 2B 11/10–0.4 samples were established using coated and uncoated cemented carbide twist drills (grade K20) with a fixed diameter of 6 mm. The tool coatings are DiamondLike Carbon (DLC) and Cristal. In this work, tools are coded by T1, T2 and T3 as shown in Fig. 1. The measuring of surface roughness was done by a Mitutoyo SJ500/P surface instrument (Fig. 2(b)). The quantity of particles released in the air during experimental tests of GLARE® drilling was calculated with GRIMM aerosol spectrometer (Fig. 2(a)) (Table 1). Different feed rates and spindle speeds were used for all experiments as shown in Table 2. There is no real specific cutting parameter range for drilling a multimaterial composed of two or three different types of materials in a single machining operation as shown in Fig. 3 (Jallageas et al. 2016). To overcome this problem, the experimental approach ToolMaterial Couple (TMW) was adopted for establishing the set range of cutting parameters defining the proper operation of the tool in the considered material. Add to this, feed rate and spindle speed are extended to 0.25 mm/rev and 18000 rpm, respectively, to study other parameters such delamination. Table 2. Cutting parameters Feed (mm/rev)
From 0.02 mm/tr to 0.25 mm/tr
Spindle speed (rpm) From 2000 rpm to 18000 rpm
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Fig. 1. (a) Drilling tools (b) experimental set up
Fig. 2. (a) Mitutoyo surface roughness instrument (b) GRIMM aerosol spectrometer
Fig. 3. Setting range of cutting parameters based on the material (Jallageas et al. 2016)
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3 Obtained Results and Discussion 3.1 Surface Finish in Drilling of GLARE® It is important to assess the geometric finish of drilled holes, that would result from the kinematic motions of the chisel, using standard measurement methods especially surface roughness. The values of roughness presented in this work correspond to the measure of generated surface when drilling both aluminum sheets and S2 fiberglass layers.
Fig. 4. Typical profile of average surface roughness for S2/FM94&Al2024T3
Figure 4 shows that average Ra of S2/FM94 are higher than those corresponding to S2/FM94 profile. Overall, a variation between the surface finish measured in the composite layers and those measured in the aluminum sheets, within the same hole, was found. When the profilometer stylus moves across sheets of aluminum, less variations are drawn. Whereas, when it moves across layers of S2/FM94 geometrics, the stylus records more important irregularities a less regular texture. For example, fibers that are reoriented, due to the tool movement into the workpiece, often seem to lift up after the chisel has passed through. This creates irregular and rougher surface finish ((Boughdiri et al. 2021). In addition, in other study (Zitoune et al. 2005) authors reported that the surface finish of the final specimen (depending on fiber orientation) indicated a significant increase whenever fiber direction formed an angle greater than 45° with drilling direction. This is due to the shear mode of failure of the laminate with those angle orientations. Moreover, it can also be stated that composite material orientation affects the microstructure of the machined surface (Boughdiri et al. 2021). This can be explained by the heterogeneity of composite material constituents (glass fiber layers and aluminum sheets) and the influence of their orientation with respect to the cutting line direction. Figure 5 presents the variations of the average value of Ra and the Rt at range of feed rates between 0.02 mm/rev and 0.25 mm/rev) and when spindle speeds vary from [4000 to 12000] rpm. It can be noted that when feeds rise from [0.02 to 0.25 mm/rev] the values of both Ra and Rt are higher. This result corroborates with those in of (Giasin et al. 2015). In fact, the authors observed that surface roughness values increase as feed rate and spindle speed increase during drilling of GLARE® 2B with two configurations (11/10 or 8/7). The values of Ra do not exceed 3 µm in the majority of the drilled holes, for all tool types. For uncoated and coated tools, Rt is higher as the spindle speed changes from [4000 to 12000] rpm during drilling of GLARE® 2B 11/10 feed rate of
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0.055 mm/rev. It has been noticed maximal and minimal values of Rt as a function of spindle speed for the cristalcoated tool and the DiamondLike Carbon tool, respectively.
Fig. 5. Mean values of (a) Ra and (b) Rt for used tools under different cutting parameters.
As conclusion, it can be also highlighted that the DLCcoated tool gives a better surface roughness in the drilled hole compared to the cristalcoated tools and uncoated ones. Moreover, surface roughness limits are 1.05 and 20.71 µm and these measurements are all within the range of values found in the study of (Giasin et al. 2016). For GLARE® machining/drilling, there is no data available helping to give the required surface roughness for the aerospace industry. Manufacturers (Coromant 2010) reports that Ra of the hole do not exceed 3.2 µm for CFRP and 1.6 µm for metal alloys. Some manufacturers and cutting tool specialists have mentioned that manufacturing requirements for the most structure aerospace in term of surface roughness are less than 3.2 µm for made of carbon fiber and 1.6 µm for workpieces made of Aluminum alloys or Titanium ones. 3.2 Dust Generation During the machining of GLARE or others multimaterials, two types of chips are formed from the two material components: aluminum chips and laminate chips. The latter, which are composed of fibers and matrix material, break down into very fine particles during machining, due to the high brittleness of the different components. These particles, suspended in the air near the machining area, represent a real danger for the environment and the health of the operators, due to their carcinogenic properties and the nonrespect of the industrial application standards. Indeed, if an operator inhales these particles, he risks encountering several respiratory problems, because these particles can become permanently lodged in the pulmonary alveoli. However, researchers have not studied this aspect and very few publications are available in the literature. This section focuses on the study of the effect of machining parameters on the number of harmful particles in such a production area contaminated with composite dust. This allows to establish the necessary procedures, depending on the parameters used, to avoid the harmful effects of these particles on the operator’s health.
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Figure 6 illustrates particles number of calculated sizes in one liter of air for different drilling parameters. It is pointed out that the majority of particles captured in the air have sizes of 0.25 µm and 1 µm. In further investigations, most of released particles have sizes from [0.5 to 1.5] µm during drilling operation of hybrid material made of biocomposite (Li et al. 2014) and from [0.25 to 0.70] when trimming CFRP (NguyenDinh et al. 2020). Another range less pronounced is between 1 µm and 2 µm, where the number of particles is fewer than in the first region. The other ranges present lower particle numbers. For all tools, the particle number in the size range [0.25 to 1.00] represents approximately 96% of measured aerosol dust. When drilling with the three drills it can be noticed (Fig. 5(a)–(c)), that for different particles ranges of size the increase in particles number is recorded with the higher spindle speed and lower feed rate. Figure 7 shows total number of particles measured at different (a) feed rates per reverse and (b) spindle speeds. It appears that the value of highest particles number per liter of air is produced at a spindle speed of 18,000 rpm and a feed of 0.055 mm/rev. For most holes, a reduction in feed rate from 0.25 mm/rev to 0.02 mm/rev and a rise in spindle speed variation from [2000 to 18000] rpm resulted in an increase in the total number of particles released when drilling tests of GLARE® 2B using tools T1, T2 and T3. This is due to the fact that theoretical chip thickness and feed rate – in contrast to spindle speed are directly proportional. This results automatically in a diminution in the number of airborne dust particles. The finer the chips have become, the more the dust is produced as a result of their defragmentation (because of its very low weight). Similarly, above certain sizes, these aerosols fall due to their weight (Haddad 2014). The results achieved with all types of tools do not give a meaningful comparison between uncoated and coated tools concerning the number of the released particles. Hence, coated tools make several effects on number and size of particles generated in the workplace as compared to uncoated ones. These observations differ from those in (Haddad et al. 2014) during trimming tests carried out during the machining of CFRP samples. It looks that DLC coated tool T2 records a lower generation of particles than uncoated drill T1 and Cristal coated drill T3. In addition, the T1 tool also releases less dust than the T3 coated tool. The Cristal coating is characterized by a microcrystalline morphology resulting in a rough reaction and increasing the release of dust particles.
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Fig. 6. Measurements of particles number with (a) fixed spindle speed and (b) fixed feed for different tool types
Fig. 7. Evolution of the number of particles measured at differents (a) feeds and (b) different spindle speeds (Boughdiri et al. 2021)
4 Conclusion In this work, an experimental investigation in samples of multimaterial type GLARE® 2B (with 11 sheets of aluminum and 10 layers of S2/FM94 composite) drilled with
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uncoated and coated tools, was realized at different cutting conditions. The effect of machining factors (feed rate per reverse and spindle speed) on the surface finish assessment and dust generation was analyzed. Results showed that surface roughness values are proportional to feed and speed of the spindle during drilling tests. The study of the surface roughness of the holes (Ra and Rt) in terms of feed rate and spindle speed shows that less surface defects are obtained when drilling GLARE® 2B 11/10 0.4 samples with spindle speeds lower than 8000 rpm and feed rates of 0.055 mm/rev. Also, DLC coating ensures better hole surface roughness than Cristal coated tool and uncoated tool. In addition, material type and cutting parameters have the most important impact on the generation of airborne dust. Two parameters affecting the number of aerosol dust which are the cutting parameters and coating types. The increase in feed and decrease in spindle speed reduces the number of particles released in the workplace. In the meantime, the present work will be extended to qualify the interaction between drill and this type of GLARE® based on cutting force measurements. A drilling numerical model is also going to be built to make more physical comprehension of the precited drill workpiece interaction. Acknowledgements. This research project was a result of collaboration between Applied Mechanics and Engineering Laboratory (University of Tunis El Manar, ENIT, Tunis, Tunisia) and Clément Ader Institute (Paul Sabatier University of Toulouse 3). The first author would like to thank Clément Ader Institute members for their technical support. GLARE® samples are provided by the Fiber Metal Laminate Center in the Netherlands, and tools were supplied by Guhring® company. So, special thanks for Prof.Jos Sinke from FMLC and Mr. Ian Goffey from Guhring® company.
References Giasin, K., AyvarSoberanis, S., Hodzic, A.: An experimental study on drilling of unidirectional GLARE fibre metal laminates. Compos. Struct. 133, 794–808 (2015). https://doi.org/10.1016/ j.compstruct.2015.08.007 Ashrafi, S., Sharif, S., Farid, A., Yahya, M.: Performance evaluation of carbide tools in drilling CFRPAl stacks. J. Compos. Mater. 48, 2071–2084 (2013). https://doi.org/10.1177/002199831 3494429 Giasin, K., Gorey, G., Byrne, C., et al.: Effect of machining parameters and cutting tool coating on hole quality in dry drilling of fibre metal laminates. Compos. Struct. 212, 159–174 (2019). https://doi.org/10.1016/j.compstruct.2019.01.023 Zitoune, R., Krishnaraj, V., Collombet, F.: Study of drilling of composite material and aluminium stack. Compos. Struct. 92, 1246–1255 (2010). https://doi.org/10.1016/j.compstruct. 2009.10.010 Giasin, K.: The effect of drilling parameters, cooling technology, and fiber orientation on hole perpendicularity error in fiber metal laminates. Int. J. Adv. Manuf. Technol. 97, 4081–4099 (2018) Giasin, K., et al.: The effects of through tool cryogenic machining on the hole quality in GLARE® fibre metal laminates. J. Manuf. Process. 64(April), 996–1012 (2021). https://doi.org/10.1016/ j.jmapro.2021.02.010 Park, S.Y., Choi, W.J., Choi, C.H., Choi, H.S.: Effect of drilling parameters on hole quality and delamination of hybrid GLARE laminate. Compos. Struct. 185(1), 684–698 (2017). https://doi. org/10.1016/j.compstruct.2017.11.073
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Haddad, M., Zitoune, R., Eyma, F., Castanie, B.: Study of the surface defects and dust generated during trimming of CFRP: Influence of tool geometry, machining parameters and cutting speed range. Compos. Part A Appl. Sci. Manuf. 66, 142–154 (2014). https://doi.org/10.1016/j.com positesa.2014.07.005 NguyenDinh, N., Hejjaji, A., Zitoune, R., Bouvet, C., Salem, M.: New tool for reduction of harmful particulate dispersion and to improve machining quality when trimming carbon/epoxy composites. Compos. Part A Appl. Sci. Manuf. 131, 105806 (2020). https://doi.org/10.1016/j. compositesa.2020.105806 Djebara, A., Jomaa, W., Bahloul, A., et al. : Dust emission during dry machining of Aeronautic Aluminum Alloys. In: Proceedings of the 1st International Conference on Aeronautical Science, pp. 1–8 (2013) Jallageas, J., Matthieu, A., Mehdi, C., Jean, Y.K., Olivier, C.: Selfadjusting cutting parameter technique for drilling multistacked material. SAE Int. J. Materials Manuf. 9(1), 2018–22 (2016). https://doi.org/10.4271/2015012502 Boughdiri, I., Giasin, K, Mabrouki, T., Zitoune, R.: Effect of cutting parameters on thrust force, torque, hole quality and dust generation during drilling of GLARE 2B laminates, Composstruct. 261, 113562 (2021). https://doi.org/10.1016/j.compstruct.2021.113562 Zitoune, R., Collombet, F., Lachaud, F., et al.: Experimentcalculation comparison of the cutting conditions representative of the long fiber composite drilling phase. Compos. Sci. Technol. 65, 455–466 (2005). https://doi.org/10.1016/j.compscitech.2004.09.028 Coromant, S.: Machining carbon fibre materials. In Sandvik Coromant User’s Guide  Composite Solutions (2010) Li, M.J., Soo, S.L., Aspinwall, D.K., Pearson, D., Leahy, W.: Influence of layup configuration and feed rate on surface integrity when drilling carbon fibre reinforced plastic (CFRP) composites. Procedia CIRP 13, 399–404 (2014). https://doi.org/10.1016/j.procir.2014.04.068 Khaled, G., Sabino, A.S.: An Investigation of burrs, chip formation, hole size, circularity and delamination during drilling operation of GLARE using ANOVA. Compos. Struct. 159, 745–760 (2017). https://doi.org/10.1016/j.compstruct.2016.10.015
An Adaptative Differential Evolution Algorithm for Vibration Level Reduction in Rotordynamics Ibrahim Mlaouhi1,4(B) , Najeh Ben Guedria2,4 , and Chokri Bouraoui3,4 1 Higher Institute of Technologic Studies of Sousse, University of Sousse, Sousse, Tunisia
[email protected] 2 Higher Institute of Transport and Logistics, University of Sousse, Sousse, Tunisia
[email protected] 3 National School of Engineers of Sousse (ENISO), University of Sousse, Sousse, Tunisia
[email protected] 4 Laboratory of Mechanic of Sousse (LMS), Sousse, Tunisia
Abstract. A New Adaptive Differential Evolution (ADE) algorithm focused on the parameter optimization of rotorbearings system is presented in this paper. In this subject field, the vibration level attenuation problem in rotordynamics it was expressed as an improvement optimization problem. The discrepancy between the displacements in the bearings and those of the target ones established according to the known initial model, is assumed as an objective function, and therefore the purpose is to decrease the vibration amplitude at critical speeds. The constraint function is built based on stability performance of the rotorbearing system. Considered design variables are dynamic characteristic parameters of the bearings such as the stiffness and damping coefficients. The proposed ADE algorithm is given by the suggestion of a new adaptive mutation operator controlled by two monotonous functions versus the iteration counter improving the movement of the individual and employed to escape quick merging to neighboring optima. A rotor finite element model of a lowpressure gas turbine supported by three balls bearings is considered as a numerical example to exam the efficiency of the intended ADE algorithm. The results confirm the performances of the suggested algorithm, in terms of solution accuracy and convergence rate compared to the standard DE. Keywords: Vibration level · Inverse problem · ADE algorithm · Dynamic characteristics · Stability
1 Introduction Excessive vibration of rotative systems such as turbines, wind turbine, compressors, electric motors, …etc., it is a persistent source of interest for engineers. In fact, vibration of mechanical compounds of rotating systems causes noise, material fatigue and untimely failure of system parts. Rotorbearings system is one of foremost vibration critical source of rotating machinery. Therefore, finding characteristics of the optimal values of its parts, to decrease vibration levels, is of enormous importance because it greatly influences the entire system performing. Improving the rotor dynamic behavior leads generally to solve © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 103–113, 2022. https://doi.org/10.1007/9783030849580_11
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a design parameter optimization problem. The goal is to reduce rotor vibration levels through altering geometric and/or dynamic characteristics values of system compounds (i.e., shaft, discs, and bearings) and satisfying some constraints such as dynamic stability. However, it is commonly known that dynamic characteristics of bearings have a large influence on vibration behavior of rotors. Hence, to solve the design problem of an operational rotorbearings system it is advantageous and also inexpensive to modify only bearings parameters and stay unchanged initial shaft and discs geometric ones. A wide variety of metaheuristic optimization techniques have already been applied to solve the rotorbearings design problem. For instance, a multiisland genetic algorithm (MIGA) was used in (Huang et al. 2019) to achieve the optimal position of the disc on the shaft which minimizes the vibration amplitudes at the critical speed. (Cho et al. 2012 presented an optimization methodology based on GA, to extend performance behavior of a centrifugal compressor. The Bezier curve control points, which strongly affect the impeller blade shape, were chosen as design variables. The objective function has been considered both in terms of efficiency and pressure ratio and the restriction of mechanical stress has been defined as a constraint function. (Mutra and Srinivas 2019) used a modified PSO algorithm (MPSO) to determine the bearing dynamics coefficients such as damping and cross stiffness based on the vibration reduction. The objective is to minimize the difference between lateral displacements of theoretical model in the bearings and measured ones. (Han et al. 2017) proposed a combination procedure based on the hybrid GA with Differential Evolution (DE) algorithms for the rotorbearings dynamic parameter identification and the mass unbalance magnitude of the disc. The objective function is considered as the variation between the response values obtained by the identification parameters during the new generation and those obtained from the last generation. In this study, stiffness and damping parameters of rotor bearings are considered as design variables. The objective function to be minimized is expressed as the discrepancy between the target and the current vibration levels while ensuring dynamic stability of the rotor system. To solve this design optimization problem a new Adaptive Differential Evolution (ADE) algorithm with new mutation schemes is proposed. The remainder of this article is organized as follows. Section 2 details the formulation of rotor design optimization problem. In Sect. 3, the standard DE algorithm is briefly presented in the first subsection. The proposed ADE algorithm is well detailed in the second subsection. The performance of the ADE is demonstrated through the design optimization of a rotor of a lowpressure gas turbine in Sect. 4. Section 5 provides a conclusion.
2 Rotor Design Optimization Problem A rotor of a lowpressure gas turbine is considered here as an example (taken from reference (Xu et al. 2020)), as shown in Fig. 1. The system consists of a flexible shaft maintained by three ball bearings and it has ninestage compressors and a singlestage turbine modeled as rigid discs fixed to the shaft at two distinct locations. The outer and inner diameters of the rotor shaft are respectively 0.17 m and 0.16 m. The rotor shaft has a length of 2.4 m. The finite element method (FEM) is used to discretize the rotorbearings system. The shaft is modeled with 20 shaft finite elements using Timoshenko beam model, in which
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Fig. 1. Finite element model of the rotor system (Xu et al. 2020).
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Fig. 2. Campbell diagram for the rotor (Xu et al. 2020).
gyroscopic and rotational inertia effects are included. Thus, the system has 21 nodes, each node has 4 degrees of freedom, the displacement, and the slope in both the XZ and YZ planes. And hence 84 degrees of freedom. In addition, the discs gyroscopic effect has also been introduced. The shaft is in uniform steel with a Young’s module E = 81.2 GPa, a mass density ρ = 7810 Kg/m3 and a Poisson’s ratio v = 0.3. The compressors and turbine are fixed respectively at nodes 2, 3, …, 10 and 20, as shows Fig. 1. The inside diameter of each disc is assumed to be equal to the associated shaft element outside diameter. The three ball bearings, which are attached at nodes 1, 11 and 21, are modeled using springs and dashpots. It is assumed that the bearings stiffness values are identical in the vertical and horizontal directions. All geometric, inertial characteristics of discs and dynamics coefficients of bearings are illustrated in Tables 1. The system is subject to three residual unbalance forces of 3 × 10− 4 (kg.m) acting respectively at nodes 2, 10 and 20 as shown in Fig. 1. Figure 2 show Campbell’s diagram of the rotorbearings system. We can notice from this diagram that the rotor has two forward (Nf1 = 3480, Nf2 = 9960 tr/min) and three backward (Nb1 = 3140, Nb2 = 6843 and Nb3 = 9643 tr/min) critical speeds in the range of 0–12000 (tr/min). The mode shapes of the 1st and 2nd forward critical speeds, the unbalance responses at the three bearings, and the frequency response functions are shown in Fig. 3. As can be noted from Fig. 3, the rotating system shows undesirable vibration behaviour due to large response amplitude at forwards critical speeds manly at the first bearing. In order to reduce its lateral vibration level, a design optimization problem is formulated. The design variables are chosen to be the bearings dynamics characteristics parameters expressed as (1) x = { kb1 , cb1 , kb2 , cb2 , kb3 , cb3 } where kb1 , kb2 , kb3 are the horizontal (kxx ) and vertical kyy stiffness coefficients and cb1 , cb2 , cb3 are the horizontal (cxx ) and vertical cyy damping coefficients, for the three bearings respectively. The objective function to be minimize is the discrepancy between the amplitude of unbalance responses aij(ωm (x)) and the target value a∗ij(ωm (x)) , computed at the jth mode (critical speed ωm ) for the ith bearing. The values of the desired amplitudes are established according to those of the initial responses, reducing them by 20%. This percentage value is set according to experience and standard requirement for
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Location Node
Compressors and turbine characteristics Inner Diameter (m)
Outer Diameter (m)
Polar inertia (m4 )
1
–
–
–
2
0.17
0.4
2.431276 × 10–3
3
0.17
0.4375
4
0.17
5
Nominal Bearings dynamics coefficients Mass (kg)
stiffness (N/m) kxx , kyy
damping (N.s/m) cxx , cyy
2 × 107
6 × 103
32.17
–
–
3.514766 × 10–3
37.38
–
–
0.475
4.915747 × 10–3
42.23
–
–
0.17
0.5125
6.690909 × 10–3
47.15
–
–
6
0.17
0.55
8.901601 × 10–3
50.35
–
–
7
0.17
0.5875
1.1613833 × 10–2
53.35
–
–
8
0.17
0.625
1.4898272 × 10–2
55.47
–
–
9
0.17
0.6625
1.8830247 × 10–2
56.59
–
–
10
0.17
0.7
2.3489746 × 10–2
56.57
–
–
11
–
–
–
1 × 109
1 × 103
20
0.17
0.7
2.3489746 × 10–2
–
–
21
–
–
–
1 × 109
1 × 103
–
– 56.57 
the design of turbines and compressors (Strauß et al. 2007). The constrain function g(x) is established through the growth rate δq(ωm (x)) in order to ensure dynamic stability of the rotorbearing system. Hence the mathematical formulation of the design optimization problem is expressed as follows. minimize f (x) =
m n ∗ aij(ωm (x)) − aij(ωm (x)) i=1 j=1
Subject to g(x) = δq(ωm (x)) ≤ 0 (q = 1, . . . , N ) and L ≤ x ≤ Ub
(2)
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Fig. 3. Unbalance response at 1st forward critical speed (left) and 2nd forward critical speed (right) of initial model. Small (left and right) figures show the mode shapes of 1st forward critical speed and 2nd forward critical speed, respectively. (Xu et al. 2020)
Where, f (x) is the objective function to be minimized. g(x) is the constrain function. The subindex m denotes the vibration mode. Lb and Ub are the lower and upper limits, respectively. And are set to −30% and +30% with respect to the corresponding values of the initial model. As can be noted the optimization problem, is nonlinear with a coplexe inequality constraints. An efficient and a global search algorithm must be used to solve it efficiently. The details of a developed ADE to solve this intercaed problem are presented in following section.
3 The Proposed Adaptative Differential Evolution (ADE) Algorithm 3.1 Standard DE Algorithm Differential Evolution (DE), introduced by Storn and Price in (Storn and Price 1997), is stochastic, populationbased optimization algorithm where individuals in the population progress and enhance their aptitude through probabilistic operators such as recombination and mutation. In this section, the fundamental four steps of the conventional G DE algorithm are briefly described. In each population, new individuals (vectors) xi i = 1, ..., Npop are produced by the combination of randomly chosen vectors. This operation can be referred as mutation The output vectors ViG are then mixed with a target vector and this operation can be called recombination (Crossover). This operation initiates the trial vector uiG . The selection operation accepts the trial vector for the subsequent generation only if it reduces the objective function value. A description of the four levels of operators mentioned above (for a generation G) is given below.
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DEAlgorithm Step 1. Initialization N pop : population size, F: mutation factor, CR: crossover probability, tMAX : maximum of iteration number Ub , Lb Upper and Lower limits 0
Xi
Lb
rand 0,1 Ub
Step 2. Mutation step:
G Vi
Lb
i 1,..., N p
= Mutation ( XGi )
Step 3. Crossover step uGi = Crossover ( ViG ) Step 4. Selection step:
G
Xi
uGi G
Xi
if
f uGi
f
G
Xi
otherwise
Generally, the mutation strategy is represented as “DE/a/b”, where DE, a and b denote the DE algorithm, the vector to be altered and the number of employed difference vectors, respectively. Six mutation schemes are frequently used in DE, as described in (Storn and Price 1997; Plagianakos et al. 2008; Ben Guedria 2020) (for more details). In this study we consider only the two standard mutation operators based on the best individual vector, described as: G G G G G + F × x (3) = x + F × x − x − x DE/currrent − to − best/1 : vG r1 r2 i i i best G G G G G DE/rand − to − best/1 : vG + F × x = x + F × x − x − x r1 r1 r1 r3 i best
(4)
Where the subscribed indices r 1, ...,3 ∈ {1, 2, ..., N pop }\ i are randomly selected, F is a positive scaling parameter ∈ [0, 2], used to control the difference vector, and xG best is the best person vector in generation G. 3.2 The Developed ADE Algorithm It’s well known that mutation strategy plays a key role in balancing exploitation and exploration capabilities of the search space, as well as in the convergence of the DE algorithm (Qin et al. 2009). From the literature related to DE, there are at least six mutation operators (Plagianakos et al. 2008; Qin et al. 2009; Ben Guedria 2020), with various effects on the DE convergence behavior. However, this effect will never be balanced between improved exploration and exploitation. Indeed, if we win the exploration of the research space, we lose it on the exploitation. In order to avoid such deficiencies, many researchers have made considerable efforts to develop a variety of useful mutation approaches and strategies to increase the DE performance, interested readers may refer to references (Ben Guedria 2020) for more details. In the present study we propose an adaptive mutation operator, controlled by two monotonically functions with respect to the iteration counter t, refining the individual’s movement, and making it progressive, improving the exploration and the exploitation of the search space, and avoiding the premature convergence of the algorithm towards a local
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optimum. Furthermore, a new vector εiG (Ben Guedria 2020) established as a function of the dispersion of individuals during search space, is used to automatically guarantee a balanced global and local search. The proposed mutation operator, is expressed as: G − xiG + β(t) × εiG (5) viG = xiG + α(t) × xbest Where, i = 1, ..., Np , t is the iteration number, the decreasing step function α(t) is used to control particles exploration of the search space and expression as follows: αmax − αmin t (6) α(t) = αmax − tmax where tmax , is the maximum of iteration number. as can be noted, during the iterative process α(t) decreases between the upper and lower limits αmax = 2 and αmin = 0.5, respectively. indeed, a large value of α(t) favor global exploration, while a small value tends to enable exploitation. During the optimization process, the function α(t) enables the individual’s diversity to be preserved and therefore avoiding the premature convergence. likewise, β(t) is further considered as an increasing function expressed as follows: π t (7) β(t) = βmin + (βmax − βmin ) sin 2 tmax Where βmax = 0.9 and βmin = 0.1 are respectively maximal and minimal values of β(t) at first and last iterations. during the optimization procedure, β(t) is involved to supervise balancing among exploration and exploitation.
4 Results and Discussion To get an idea of the modes that induce problems, the unbalance responses are computed in a speed range of [0∼12000 tr/mn]. This gives an overview about the vibration levels in the relevant operating speed range (cf. Fig. 3). The modes with a higher amplitude at the three bearings were chosen to be the targets of the optimization procedure, and their amplitudes should be reduced. To solve this nonlinear design optimization problem, the proposed ADE algorithm was applied, and the best results were compared to those of standard DE’s (Storn and Price 1997) using the following mutation operator: (DE/currenttobest/1) and (DE/randtobest/1). For both algorithms, the maximum number of generations tmax considered as a stop criterion was set at 100, the population size Npop used was picked to be 20 and the optimization task was performed using 10 independent execution times. Table 2 illustrates the statistical simulation results provided by ADE and DE algorithms, where it can be noted that ADE algorithm offered better results compared to those of DE, in terms of best, mean, and worst solutions. Moreover, ADE stably converge to the best solution reporting the smallest value of the standard deviation (Std) compared to DE algorithm. The best solution given by the proposed ADE algorithm is shown in Table 3, where the optimal values of all damping and stiffness coefficients, which minimize the lateral displacement of the gas turbine rotor are found.
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Algorithms
Best value
Mean
Worst value
Std
DE
DE/currenttobest/1
0.003758524
0.011617393
0.064155008
0.018791101
DE/randtobest/1
0.002963640
0.010648261
0.065176303
0.019223650
0.002156784
0.005299544
0.006986551
0.001572836
ADE
Table 3. Initial and optimized design variables. Bearing #1
Bearing #2
Bearing #3
Design variables
kxx , kyy [N/m]
cxx , cyy [Ns/m]
kxx , kyy [N/m]
cxx , cyy [Ns/m]
kxx , kyy [N/m]
cxx , cyy [Ns/m]
Initial values
2 × 107
1 × 109
1 × 109
6 × 103
1 × 103
1 × 103
Optimized values
1.9763 × 107
1.0150 × 109
1.1470 × 109
7.4960 × 103
0.7172 × 103
1.1175 × 103
Figure 4 depicts the convergence history, using ADE and DE algorithms, for the best and average objective function values versus the number of iterations, clearly, ADE algorithm has a convergence rate better than the DE, for the problem at hand. Thinks to its new mutation operator and to its balanced exploration and exploitation abilities.
Fig. 4. Convergence history for the lowpressure rotor of a gas turbine design optimization problem using DE and ADE algorithm.
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As can be noted from Table 4, results show that the amplitude of unbalance response of the optimal design, obtained using ADE algorithm, are less than those provided using the basic DE algorithm. Figures 5, 6, 7 and 8 depicts that the target to decrease vibration level and ensuring dynamic stability of the rotor system was accomplished. The amplitude is decreased to a desired level. The unbalance response is now 20% of the initial design unbalance response. The optimal and the initial values of unbalance response at each bearing of the lowpressure rotor of a gas turbine, provided using ADE algorithm, are shown in Fig. 5, Fig. 6 and Fig. 7, respectively. Table 4. Optimized unbalance responses given by DE and ADE. Unbalance responses [mm] × 10–2 Bearing # 1
Bearing # 2
Bearing # 3
a11
a12
a21
a22
a31
a32
Initial Values
2.079
3.079
0.06388
0.2369
0.012801
0.05339
DE
DE/currenttobest/1
1.6634
2.4636
0.04968
0.18859
0.009226
0.04270
DE/randtobest/1
1.6633
2.4637
0.05337
0.18966
0.009541
0.04271
1.6632
2.4637
0.04995
0.18952
0.009240
0.04271
ADE
Fig. 5. Unbalance response at bearing1
Fig. 6. Unbalance response at bearing2
The rotor speed is incremented from zero to 12.000 tr/min, and the roots of the characteristic turbocharger equation of motion are calculated and plotted at both critical speeds 3480 tr/min and 9960 tr/min, as shown in root locus diagram Fig. 8 which can illustrate the stability of the lowpressure rotor of a gas turbine at these two critical speeds.
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Fig. 7. Unbalance response at bearing3
Fig. 8. Stability analyses at critical speeds.
5 Conclusion In this paper, we show a complete design optimization approach for a lowpressure rotor of a gas turbine focusing on the vibration level reduction while ensuring dynamic stability of the rotor system. A specific rotorbearings design optimization problem has been formulated to come across these objectives. Results simulations show that a significant reduction of unbalance response for the considered lowpressure rotor of a gas turbine is achieved. The presented results lead to the desired requirements for the considered rotor. As algorithms to solve the design optimization problem, a DE and a new ADE algorithm with new mutation schemes is proposed, and their performance was compared. The optimization results show that the new ADE algorithm has much better potential in terms of solution accuracy in comparison with standard DE algorithm for the problem at hand. Moreover, statistical results clearly reveal the superiority of the ADE algorithm, in terms of mean and standard deviation, as well as a better convergence behavior compared to DE algorithm.
References Ben Guedria, N.: An accelerated differential evolution algorithm with new operators for multidamage detection in platelike structures. Appl. Math. Model. 80, 366–383 (2020). https://doi. org/10.1016/j.apm.2019.11.023 Cho, S.Y., Ahn, K.Y., Lee, Y.D., Kim, Y.C.: Optimal design of a centrifugal compressor impeller using evolutionary algorithms. Math. Probl. Eng. 2012, 1–22 (2012). https://doi.org/10.1155/ 2012/752931 Han, F., Mo, C., Gao, H.: An adaptive hybrid differential evolutionary algorithm for the parameter identification of rotating machinery. J. Vib. Control 107754631774389,(2017). https://doi.org/ 10.1177/1077546317743890 Huang, J., Zheng, L., Mechefske, C.K., Han, B.: Optimization design and experimental study of a twodisk rotor system based on multiisland genetic algorithm. Int. J. Turbo JetEngines 36, 1–8 (2019). https://doi.org/10.1515/tjj20170010 Mutra, R.R., Srinivas, J.: An optimized bearing parameter identification approach from vibrtion response spectra. J. Vibro. 21, 1519–1532 (2019). https://doi.org/10.21595/jve.2018.20005
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Plagianakos, V.P., Tasoulis, D.K., Vrahatis, M.N.: A review of major application areas of differential evolution. In: Chakraborty, U.K. (ed.) Advances in Differential Evolution, pp. 197–238. Springer, Berlin Heidelberg, Berlin, Heidelberg (2008) Qin, A.K., Huang, V.L., Suganthan, P.N.: Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans. Evol. Comput. 13, 398–417 (2009). https://doi. org/10.1109/TEVC.2008.927706 Storn, R., Price, K.: Differential evolutiona simple and efficient heuristic for global optimization over continuous spaces. J.Glob. Optim. 11, 341–359 (1997). https://doi.org/https://doi.org/10. 1023/A:1008202821328 Strauß, F., Inagaki, M., Starke, J.: Reduction of vibration level in rotordynamics by design optimization. Struct. Multidiscip. Optim. 34, 139–149 (2007). https://doi.org/10.1007/s0015800600653 Xu, B., Zang, C., Zhang, G.: Intelligent approach to robust design optimization of a rotor system due to its support stiffness uncertainty. Shock Vib. 2020, 1–11 (2020). https://doi.org/10.1155/ 2020/2564679
Nanoheat Transfer in GAAFET Transistor Using SinglePhaseLag Model Maissa Belkhiria(B) , Fraj Echouchene, and Nejeh Jaba Laboratory of Electronic and Microelectronic, Faculty of Science of Monastir, Monastir, Tunisia
Abstract. Due to the progress of devices miniaturization combined with the increase in packing density in integrated circuits, modern transistors, such as Gate All Around Field Effect Transistors (GAAFETs), suffer from excessive thermal confinement. This causes in device a selfheating problem which can increases leakage and destroy device performance. In this context, we propose in this paper to investigate the selfheating effect (SHE) in the TripleMaterialSurroundingGateFieldEffectTransistor (TMSGFET) using an electrothermal model. Numerical simulation is based on solving the semiconductor equations (Poisson and continuities equations) coupled with the heat transfer equation. The SinglePhaseLag (SPL) nonlinear heat conduction model has been used to describe the nanoheat. The numerical solutions have been developed based on the finite element method. The results are also compared to the classical FourierKirchhoff Law. The electrical and thermal properties of the TMSG transistor have been analyzed. The obtained results predict an appropriate electrical behavior of the simulated structure. However, the TMSG device suffers more from a selfheating problem illustrated with a significant local temperature. This result proves the poor thermal management of this nanowire structure. On the other hand, the wave properties in the temperature response are observed using the SPL model, which makes it more suitable for estimating the selfheating effect in the device. Keywords: Finite element method · GAAFET transistor · Nanoheat transfer · SPL model
1 Introduction Following the miniaturization of electronic devices, adverse problems such as short channel effect (SCE) and tunnel effect are faced and have reduced the control of the gate over the drain current. Consequently, it results in an increase in gate leakage current and selfheating [1]. This has become an issue of great importance recently due to its impact in device performance. Thereby, this phenomenon have been investigated extensively to enhance the thermal stability of the device [2]. In our previous work [3], we have investigated the effect of selfheating in PiFET structures and we have suggested that the insertion of highk dielectric layers above the dioxide can be a solution to mitigate the selfheating in the device. A 3D numerical simulation of selfheating have been investigated in a stacked threelayer GAA nanosheet transistors by Cai et al. [4]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 114–122, 2022. https://doi.org/10.1007/9783030849580_12
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The anisotropic thermal conductivity of nanosheets have been taken into consideration to evaluate thermal behavior. As a conclusion, they showed that the optimizations of layout design are given to suppress the thermal effects, including selfheating. Furthermore, to estimate temperature distribution in electronic structure, several models have been developed such as the parabolic heat conduction Fourier [5], ballisticdiffusive (BDE) model [6], the Boltzmann transport equation (BTE) [7], the SinglephaseLag heat conduction model [8] and the DualPhaseLag heat conduction model [9–11]. Many research have investigated the heat conduction based on the Fourier, model in which the heat flux is directly proportional to the temperature gradient [12, 13]. However, recent researches show that results of the Fourier model does not agree with experimental observations in microtemporal and special scale. In fact, the finding results of differential equation turns out to predict unrealistic infinite thermal speed. Consequently, a time relaxation τq in the Fourier law has been included to predict the phonons transport by attributing finite speed to the heat transfer [14, 15]. This model eliminates the paradox of infinite speed of heat waves and assume that the heat flux vector occurs later than the temperature gradient [8, 16]. Based on this model, we have earlier investigated the selfheating effect in GAAFET transistor [17] and compared the simulated results with the Fourier Law. In the present work, we investigate numerically the electrothermal analysis of TMSG FET structure base on the nonlinear heat conduction SPL model. Firstly, we focuses on the electric analysis in Triple Material Surrounding Gate (TMSG) device. Then, we analysis the selfheating effect in this structure.
2 Physical Model The SPL heat conduction model used in this simulation is defined as follow. More details are found in our previous work [17]. ∂T ∂ 2T (1) + τ 2 = kT + H ρcp ∂t ∂t Here T ρ, cp , τ and k are the temperature, density, specific heat capacity, time relaxation and thermal conductivity of materials, respectively. The heat source H is given by [17, 18] + R × Eg + 3kB T (2) H = J .E , and the current = −∇V The electric field E, derived from the electric potential V E density inside this structure are obtained from solving the semiconductor equations [19] q Cp − Cn + ND − NA (3) ∇.(−∇V ) = ε0 εr ∇. Dn,p ∇Cn,p − Cn,p μn,p ∇V = ±R (4) Here Cn,p , μn,p and Dn,p are the concentration, mobility and diffusion coefficient of carriers, respectively. N D and N A are the donor and acceptor concentration. The ShockleyReadHall recombination R is adopted in this simulation [3, 17].
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The nonlinear heat conduction model (Eq. 1) coupled with the semiconductor equations (Eq. 3 and Eq. 4) have been discretized based on the finite element method [20–22] using linear and quadratic interpolations between the nodes. Whereas, the temporal discretization of ordinary differential equations is carried out by a timecentered schemes. The resolution of the obtained systems of nonlinear algebraic equations is carried out using the NewtonRaphson method. An unstructured triangular mesh is used in this work. The mesh is refined at the Si/SiO2 interface, at the contact level (drain, gate and source) and in doped region.
3 Simulation Result
Fig. 1. 2D axisymmetric view of TMSG device.
A 2Daxisymetric configuration of the TMSG device adopted in this work is illustrated in Fig. 1. The gate materials Mi=1,2,3 having different work functions ϕM ,i=1,2,3 and different lengths Li=1,2,3 , respectively are used in this simulation. Physical and geometric parameters are summarized in Table 1. The accordance of comparison of the output characteristic of 3D and 2D GAAFET transistor is illustrated in Fig. (2a). (a) 70
(b) 2D 3D
60
700 600
50
L=180 nm R=2.5 nm tox=1 nm VG=0.6 V
ID(µA/µm)
ID (µA)
500 40 30
400
model simulation exprimental data [23]
300
20
200 10
100
0 0.0
0.2
0.4
0.6
VD (V)
0.8
1.0
0 0.0
0.2
0.4
0.6
0.8
1.0
VD(V)
Fig. 2. The output characteristics of 2Daxisymmetric and 3D structure’s results (a) and experimental data (b).
The drain current ID versus the drain voltage VD of the simulated structure, in Fig. (2b), agree with the experimental data [23] with 180 nm channel length and 5 nm cylindrical diameter of GAAFET.
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Table 1. Parameter used for the simulation Symbol
Description
Value
L
Channel length
20 nm
R
Radius
5 nm
tox
Oxide thickness
1 nm
φM ,i=1,2,3
Gate work function
4.8 eV, 4.6 eV, 4.4 eV [24]
Figure 3 exhibits the axial profile of the surface potential along the channel. The axis is oriented from the drain towards the source. The relevant results concern the TMSG MOSFET with L1 = L2 = L3 = 6 nm, VG = 0.1 V, and for VD = 1 V for two values of radius, namely R = 5 nm and R = 10 nm. It appears clearly that the TMSG MOSFET shows two steps up a profile, which reduces the short channel effects and when the radius R is decreased, the position corresponding to the minimum surface potential shifts towards the source side. This reveals better gate controllability and better bandbending. The impact of the drain induced barrier lowering (DIBL) and SCEs are therefore reduced.
Variation of surface Potential (V)
3.9
TMSG MOSFET 4.0 4.1 4.2 4.3
R=10 nm 4.4 4.5
R=5 nm
4.6 0
2
4
6
8
10
12
14
16
18
20
Position along the channel (nm)
Fig. 3. Variation of surface potential as a function of the position along the channel for TMSG MOSFET for radius R = 10 nm and R = 20 nm
The material having the higher work function φM 1 = 4.8 eV, is kept near the source region to function as the control gate [25], in order to increase the electric field along the channel and increase the threshold voltage. The lower is kept at the drain side functioning as screen gate. We can deduct from this figure the behavior of the electric field.
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Lateral Electric Field Ez in [106 V/cm]
Figure 4 depicts the lateral electric field along the channel for a constant VD = 1 V and VG = 0.1 V. As indicated in Fig. 4, the electrical field created in the middle of the channel is larger in the one or twostep potential. This enhances the carrier drift velocity and the driving aptitude of the device. Such findings are also reported with [24, 26]. Figure 4 proves also that the electric field along the channel peaked at the twogate material interface. The variation of electric field near the drain is almost negligible. VD=1V and V G=0.1V
3 2 1 0 1 2 3 4 5 6 0
5
10
15
20
Postion along the channel in [nm]
Fig. 4. Axial profile of the lateral electric field component versus the position for TMSG structure.
Figure 5(a, b) shows the steady state temperature distribution in TMSG structures for VG = 0.8 V and VD = 0.8V and 1V. The results are based on the SPL heat conduction model. It’s clear from this figure that the SHE is accumulated near the drain region, which is confirmed with the literature results [27]. The peak temperatures illustrated are 509 K and 605 K for VD = 0.8 and 1 V, respectively. The heat dissipation is carried out along the z axis, this is explained by the low radial temperature gradient and the significant axial.
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Fig. 5. Surface temperature in TMSG device for gate voltage of 0.8 V and for two drain voltage 0.8 and 1 V 750
TMSG MOSFET
Fourier SPL
700
Temperature (K)
650 600 550 500 450 400 350 300 0
100
200
300
400
500
Time (ps)
Fig. 6. Comparison of the transient temperature inside TMSG structure using the SPL model and Fourier law.
The temporal temperature evolution in the TMSG FETs is shown in Fig. 6. The temperature response using the SPL model is compared to the Fourier law, for VD = 1 V and VG = 0.8 V at the position r = 0 and z = 30 nm. From this figure we can noted that:
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• The steady state is achieved earlier using the Fourier law. • The wave properties are observed using the SPL model. • The temperature increases linearly until reaching a maximum exceeding 700 K at t = 100 ps. The heat flux along the zaxis of the simulated device is presented in Fig. 7 for VG = 0.8 V and VD = 1 V, at t = 200 ps. This result is carried out the oxide/semiconductor interface. Based on the SPL model the results are also compared to the Fourier Law. As it is observed from figure, the same trend and profile are illustrated with the two models along the z direction, while, a decrease in peak heat flux is achieved using the Fourier model near the drain region. In fact, for z = 30 nm, the heat flux is qmax = 3,84 × 1012 W/m2 using the Fourier model and qmax = 4.24 × 1012 W/m2 using the SPL model. x10 12 4.5
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Fig. 7. Comparison of the heat flux profile along zaxis in TMSG device using the SPL and FourierKirchhoff model.
4 Conclusion In this chapter, the nanoheat transfer is investigate numerically using the singlephaselag (SPL) model coupled with semiconductor equations in Triple Material Surrounding Gate (TMSG) FET devices. The nonlinear electrothermal model is solved using the finite element method. The selfheating effect inside the simulated device obtained with the SPL model was compared to the FourierKirchhoff model. The SPL heat conduction model reveals the wave properties in the temperature response and large rising time than the Fourier law. As a conclusion, unless, the multigate structure offer an excellent electrical behavior which is in agreement with the study of shora et al. [28], it shows an important lattice
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temperature and a significant temperature generation in the channel closed to the drain side.
References 1. Koh, M., et al.: Limit of gate oxide thickness scaling in MOSFETs due to apparent threshold voltage fluctuation induced by tunnel leakage current. IEEE Trans. Electron Devices 48(2), 259–264 (2001) 2. Reuveny, A., et al.: Thermal stability of organic transistors with short channel length on ultrathin foils. Org. Electron. 26, 279–284 (2015) 3. Belkhiria, M., et al.: Impact of highk gate dielectric on selfheating effects in PiFETs structure. IEEE Trans. Electron Devices 67(9), 3522–3529 (2020) 4. Cai, L., et al.: Layout design correlated with selfheating effect in stacked nanosheet transistors. IEEE Trans. Electron Devices 65(6), 2647–2653 (2018) 5. Garegnani, G., et al.: Wafer level measurements and numerical analysis of selfheating phenomena in nanoscale SOI MOSFETs. Microelectron. Reliab. 63, 90–96 (2016) 6. Belmabrouk, H., Rezgui, H., Nasri, F., Aissa, M.F.B., Guizani, A.A.: Interfacial heat transport across multilayer nanofilms in ballistic–diffusive regime. Eur. Phys. J. Plus 135(1), 1–17 (2020). https://doi.org/10.1140/epjp/s13360020001807 7. Rezgui, H., et al.: Investigation of heat transport across Ge/Si interface using an enhanced ballisticdiffusive model. Superlattices Microstruct. 124, 218–230 (2018) 8. Chen, J., Zhang, X.: NonFourier effects on the temperature timedependence of a silicon igniter. IEEE Electron Device Lett. 40(6), 854–857 (2019) 9. Belkhiria, M., Echouchene, F., Mejri, H.: Nanoscale heat transfer in MOSFET transistor with highk dielectrics using a non linear DPL heat conduction model. In: 2018 9th International Renewable Energy Congress (IREC). IEEE (2018) 10. Echouchene, F., Mabrouk, H.B.: Non equilibrium entropy generation in nano scale MOSFET transistor based a nonlinear DPL heat conduction model. In: 2018 9th International Renewable Energy Congress (IREC). IEEE (2018) 11. Echouchene, F., Belmabrouk, H.: Effect of temperature jump on nonequilibrium entropy generation in a MOSFET transistor using dualphaselagging model. J. Heat Transfer 139(12) (2017). https://doi.org/10.1115/1.4037061 12. Ahn, W., et al.: Integrated modeling of selfheating of confined geometry (FinFET, NWFET, and NSHFET) transistors and its implications for the reliability of sub20 nm modern integrated circuits. Microelectron. Reliab. 81, 262–273 (2018) 13. O’Neill, A., et al.: Reduced selfheating by strained silicon substrate engineering. Appl. Surf. Sci. 254(19), 6182–6185 (2008) 14. Cattaneo, C.: A form of heatconduction equations which eliminates the paradox of instantaneous propagation. Comptes. Rendus. 247, 431 (1958) 15. Vernotte, P.: Les paradoxes de la theorie continue de l’equation de la chaleur. Compt. Rendu. 246, 3154–3155 (1958) 16. Sellitto, A., Carlomagno, I., Jou, D.: Twodimensional phonon hydrodynamics in narrow strips. Proc. Royal Soc. A: Math. Phys. Eng. Sci. 471(2182), 20150376 (2015) 17. Belkhiria, M., et al.: 2DNonlinear electrothermal model for investigating the selfheating effect in GAAFET transistors. IEEE Trans. Electron Devices 68, 954–961 (2021). https://doi. org/10.1109/TED.2020.3048919 18. Yi, M., Yin, W.Y.: Electrothermomechanical analysis of partially insulated fieldeffect transistors using hybrid nonlinear finite element method. Microelectron. Reliab. 51(5), 895–903 (2011)
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19. Nasri, F., Aissa, M.F.B., Belmabrouk, H.: Nonlinear electrothermal model for investigation of heat transfer process in a 22nm FDSOI MOSFET. IEEE Trans. Electron Devices 64(4), 1461–1466 (2017) 20. Echouchene, F., Jemii, E.: Analysis of the transient Joule heating effect in a conductivebridge randomaccess memory (CBRAM) using a singlephaselag (SPL) model. J. Comput. Electron. 20(3), 1422–1429 (2021). https://doi.org/10.1007/s1082502101681z 21. Xu, B., Li, B.: Finite element solution of nonFourier thermal wave problems. Num. Heat Transfer: Part B: Fundamentals 44(1), 45–60 (2003) 22. Ben Belgacem, I., Khochtali, H., Cheikh, L., Barhoumi, E.M., Ben Salem, W.: Comparison between two numerical methods SPH/FEM and CEL by numerical simulation of an impacting water jet. In: Chaari, F., et al. (eds.) Advances in Materials, Mechanics and Manufacturing. LNME, pp. 50–60. Springer, Cham (2020). https://doi.org/10.1007/9783030242473_7 23. Singh, N., et al.: Highperformance fully depleted silicon nanowire (diameter/spl les/5 nm) gateallaround CMOS devices. IEEE Electron Device Lett. 27(5), 383–386 (2006) 24. Dhanaselvam, P.S., Balamurugan, N.: Analytical approach of a nanoscale triplematerial surrounding gate (TMSG) MOSFETs for reduced shortchannel effects. Microelectron. J. 44(5), 400–404 (2013) 25. Pal, A., Sarkar, A.: Analytical study of dual material surrounding gate MOSFET to suppress shortchannel effects (SCEs). Eng. Sci. Technol. Int. J. 17(4), 205–212 (2014) 26. Pratap, Y., et al.: An analytical subthreshold current modeling of cylindrical gate all around (CGAA) MOSFET incorporating the influence of device design engineering. Microelectron. J. 45(4), 408–415 (2014) 27. Park, J.Y., et al.: Investigation of selfheating effects in gateallaround MOSFETs with vertically stacked multiple silicon nanowire channels. IEEE Trans. Electron Devices 64(11), 4393–4399 (2017) 28. Shora, A.T., Khanday, F.A.: Analytical modelling and performance analysis of gateand channelengineered trapezoidal trigate MOSFET. IET Circuits Devices Syst. 13(8), 1107–1116 (2019)
Hydrodynamics Flow in an Exocentric Input Dome TMixer (DTM) Fatma Ben Baha Spiridigliozzi1 , Slim Bouaziz2(B) , Mohamed Haddar2 , Mounir Ben Amar1 , and JeanPhilippe Passarello1 1 Laboratory of Science of Processes and Materials (LSPM), CNRS, University Sorbonne Paris
Nord (USPN), 93430 Villetaneuse, France [email protected] 2 Mechanics, Modeling and Production Laboratory (LA2MP), National School of Engineers of Sfax, University of Sfax, BP.1173, 3038 Sfax, Tunisia
Abstract. The mixing step of fluids at microscale is one of the most important operations in the development of microfluid systems in chemical reactors for applications in chemical and biochemical engineering, biomedical systems. The apparition of the cavitation phenomenon, in chemical precipitation reactors with rapid micromixing, can significantly affect the elaboration process. The bubbles appear in the reactive fluid flow when the local hydrostatic pressure decreases down to the liquid vapor pressure, which also corresponds to the maximum energy input producing the micromixing. In this article we report on a new Tmixer geometry with exocentric input of two reacting fluids for the preparation of homogeneous monodisperses nanoparticles. The inputs are in a perpendicular plane on the main output tube. The new Tmixer geometry (DTM) has a dome at the intersection of the two inputs. The dome affects the flow parameters: speed and pressure. We describe fluid dynamic calculations of water injection into a (DTM) at high Reynolds numbers up to 1.2 × 104 . The fluid velocity profile shows an instantaneous formation of a vortex in the contact area at the fluids injection. The simulations are performed with the CFD software “Ansys Fluent”. Numerical calculations support the assignment to cavitation and show its critical relation to the (DTM) geometry. Keywords: Tmixer · Nanoparticles · DTM · Cavitation · CFD
1 Introduction The design of the micro mixer in general and of the Tmixers in particular, is a tradeoff between several parameters, such as: pressure drop, mixing time, reactor volume, velocity field, stream lines and integration with chemical detection devices. Some biochemical analyses require the two reagents to be completely mixed before the reaction has proceeded considerably. A critical step, in the most chemical engineering processes, is mixing; Bałdyga et al. (1995). Oualha et al. (2017) studied hydrodynamics of water flow through exocentric Tmixer in the regime of high Reynolds numbers 0 < Re < 1.2·104. Schwarzer, W. Peukert (2004) investigated nanoparticle precipitation and turbulent flow © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 123–130, 2022. https://doi.org/10.1007/9783030849580_13
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hydrodynamics in the Hartridge and Roughton static Tblender. Engler et al. (2003) carried out numerical studies of mixing in the T and Yshape geometries. Nanoparticle precipitation process has been considered in studies of Marchisio et al. (2006) and Gradl et al. (2006). More studies of the micromixing in Tmixer were carried out. Rivallin (2003) studied the kinetics of nucleationgrowth of solid nanoparticles during the solgel process. This device makes it possible to have a rapid micromixing of the reagents in a controlled atmosphere and temperature and the production of monodisperse nanoparticles. Livage et al. (1988) consider solgel synthesis in order to prepare glasses and ceramics. A study of the nanoparticles size evolution as a function of the hydrolysis rate was carried out by Azouani et al. (2010). They studied the nucleationgrowth kinetics of TTIP/H2 O particles in the Tmixer by means of light scattering. This study allowed the optimization of the nanoparticles radius according to the hydrolysis rate. Cheng et al. (2017) studied the nucleationgrowth of oxoalkoxy titanium nanoparticles (TOA) for different solvents: npropanol and isopropanol. The nucleus size, which appears for H < 1.7, was 1.6 nm in both cases. However, the initial nanoparticles size during the induction period was 1.9 nm in npropanol and 2.6 nm in isopropanol: the growth kinetics in isopropanol was significantly faster. Jia et al. (2012–2013) have developed Ag/TiO2 nanostructured composite materials for the depollution of gaseous effluents through the plasmacatalysis process. The development process consists in depositing TiO2 nanoparticles on plates or glass beads as nanostructured monolayers (TiO2 bed) using the dipcoting technique. The Tmixer has been also successfully used by Azouani et al. (2007) and Labidi et al. (2015) to obtain respectively selected TiO2 and ZrO2 nanoparticles size in the solgel process. In this paper, we investigate the DTM effect on the flow parameters: velocity and pressure. The aim of this work is to optimize the geometry of micromixers to improve the new mixing devices in chemical reactors.
2 Design and Setup 2.1 Geometry The Tmixer shown in the Fig. 1a includes two cylindrical inlet channels of d = 1 mm diameter and = 2 cm length, connected to the main outlet channel of D = 2 mm diameter and L = 20 cm length. The Reynolds number of the fluids is conserved in this geometry. The two input channels of the Tmixer are in the (x, y) plane and the output leg is carried by the z axis. The DTM, having the same dimensions, is given in the Fig. 1b.
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Fig. 1. Schema of the Tmixer: (1a) and dome Tmixer (DTM): (1b)
2.2 Meshing Optimized mesh model of the DTM is depicted in the Fig. 2. The accuracy of the numerical simulations was checked by considering progressive meshing with a total node number varying between 2.5 × 105 and 3 × 106 .
Fig. 2. View of the finite element model of the DTM
2.3 Theory The numerical fluid dynamics calculations were carried out with Fluent V19.2 software package based on kε turbulence model and treated the multiphase and homogeneous fluid behavior with respectively Eulerian/Lagrangian, Cerutti et al. (2000) or Eulerian/Eulerian approaches, Singhal et al. (2002). The flow of an incompressible Newtonian liquid in microchannels can generally be described by the averaged Navier–Stokes equation and continuity equation. Each instantaneous quantity can be split into timeaveraged and fluctuating components and
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the resulting equation timeaveraged to yield, Livage et al. (1988): ⎧ ⎨ ∂ui ∂ uj ui ∂ uj ui ∂ 2 ui = − ρ1 ∂p ∂t + ∂xj + ∂xj ∂xi + υ ∂xj ∂xj ⎩ ∂ui = 0
(1)
∂xi
The closure used on the Reynolds stress is based on the viscosity. It is to express the fact that the Reynolds stress behaves with all viscous stresses:
∂ui ∂ uj 2 ui uj = −υt + (2) + δij k ∂xj ∂xi 3 υt is the fluid viscosity and k is the instant turbulent kinetic energy, it can be written as: k=
1 2 u 2 i
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and ε=υ
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It remains to determine k and ε with the two respective transport equations: ∂u ∂k ∂k ∂ ∂k j + uj = − ui uj −ε+ (υ + σk υt ) ∂t ∂xj ∂xj ∂xj ∂xj ε ∂ ∂ε ∂ε ε2 ∂ε + uj = −Cε1 ui uj Sij − Cε2 + (υ + σε υt ) ∂t ∂xj k k ∂xj ∂xj Where the mean rate of the strain tensor is:
1 ∂ui ∂ uj Sij = + 2 ∂xj ∂xi
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(6) (7)
(8)
Constants C μ , C ε1 , C ε2 , σ k , σ ε are adjusted ones. They are determined through experiments on fundamental flows (turbulence grids, sheared flow…) and summarized in Table 1.
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Table 1. Constants of kε model Cμ
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In our simulation the adequate boundaries conditions imposed are given in Fig. 3. The pressure at the input arms following the yaxis is Pinp = 7 bar and the outlet pressure in the exit leg following the zaxis is equal to atmospheric pressure; Pout = Patm = 1 bar.
ℓ P =7 bar
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Fig. 3. Boundaries conditions
3 Simulated Results and Discussions First, the velocity streamlines, Fig. 4, and the velocity fields, Fig. 5, were calculated for the DTM described in the Fig. 1b. After simulation and to highlight the cavitation, we will focus on the speed evolution along one of the two entry channels and then on the pressure evolution in the DTM. Along the entry arm in the yaxis, the velocity remains constant until the point of contact between the jets coming from the two arms where it increases sharply to 38 m/s (Fig. 6a). Following the xaxis, the velocity decreases towards the center (Fig. 6b). Indeed, along the xaxis, the speed decreases as it approaches the output axis of the leg to reach the minimum value of 5 m/s. The evolution of the pressure from the input channel of the DTM, following the yaxis, then along the exit leg, following the zaxis is shown in Fig. 7a.
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Fig. 4. Velocity streamlines on (x, y) plane in the DTM
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According to the Bernoulli law, the highest velocity zones of a liquid correspond to the lowest hydraulic pressure (Pliq ). The lowest hydraulic pressure may decrease below the vapor pressure (Pvap ), estimated by Clapeyron, resulting to cavitation: Pliq ≤ Pvap . Compared to Oualha (2017) results, the calculated distribution of local hydraulic pressure in the yz plane, under the same conditions (Pinp = 7 Bar), is greater in the DTM then in Tmixer, (Fig. 7b).
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Fig. 7. Calculated axial static pressure along y and z axis of the input and output tubes of DTM (a). The cavitation threshold is attained at y = 0 and 0 ≤ Z ≤ 20 mm (a)
4 Conclusion In this article, we studied hydrodynamics of the water flow through the exocentric Tmixer with a dome, DTM, in the regime of high Reynolds numbers 0 < Re < 1.2 × 104 . The numerical fluid dynamics calculations were carried out with Computational Fluid Dynamics (CFD) modeling using Fluent V19.2 software package. The velocity of water flow increases at the point of contact of the two arms to a maximum of 38 m/s. According to the Bernoulli principle, this increase causes an instantaneous decrease in the pressure thus creating the cavitation phenomenon. The appearance of cavitation, in the DTM, means the transition of the common twophase “liquid/gas” regime. The new geometry of DTM affects this phenomenon. Biphasic flow (liquid/gas), can flow up to 20 mm Zbiphasic height. This value does not exceed 4 mm in the case of a Tmixer. Cavitation phenomenon should be taken into account in properly designing the new generations of chemical reactors. Experimental validation of the model is underway on a transparent material DTM (glass) to allow optical measurements of fluid flow.
References Azouani, R., et al.: Elaboration of pure and doped TiO2 nanoparticles in sol–gel reactor with turbulent micromixing: Application to nanocoatings and photocatalysis. Chem. Eng. Res. Des. 88(9), 1123–1130 (2010) Azouani, R., Soloviev, A., Chhor, K., Bocquet, J.F., Kanaev, A.: Stability and growth of titaniumoxoalcoxy TixOy(OiPr)z clusters. J. Phys. Chem. C 111(44), 16243–16248 (2007) Bałdyga, J., Pohorecki, R.: Turbulent micromixing in chemical reactors  a review. Chem. Eng. J. 58, 183–195 (1995) Cheng, K., Chhor K., Kanaev A.: Solvent effect on nucleationgrowth of titaniumoxoalkoxy nanoparticles. Chem. Phys. Lett. 672, 119–123 (2017) Cerutti, S., Omar, M.K., Katz, J.: Numerical study of cavitation inception in the near field of an axisymmetric jet at high Reynolds number. Phys. Fluids 12(10), 2444–2460 (2000)
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Engler, M., Föll, C., Kockmann, N., Woias, P.: Investigations of liquid mixing in static micro mixers Proceed. In: 11th European Conference on Mixing, pp. 277–284 (2003) Gradl, J., Schwarzer, H.C., Schwertfirm, F., Manhart, M., Peukert, W.: Precipitation of nanoparticles in a Tmixer: Coupling the particle population dynamics with hydrodynamics through direct numerical simulation. Chem. Eng. Process. 45, 908–916 (2006) Jia, Z., et al.: Growth of silver nanoclusters on monolayer nanoparticulate titaniumoxoalkoxy coatings. J. Phys. Chem. C 116, 17239–17247 (2012) Jia, Z., et al.: Acetaldehyde removal using a diphasic process coupling a silverbased nanostructured catalyst and a plasma at atmospheric pressure. Catal. Today 208, 82–89 (2013) Labidi, S., Jia, Z., Ben, A.M., Chhor, K., Kanaev, A.: Nucleation and growth kinetics of zirconiumoxoalkoxy nanopparticles. Phys. Chem. 17, 2651–2659 (2015) Livage, J., Henry, M., Sanchez, C.: Solgel chemistry of transition metal oxides. Prog. Solid State Chem. 18(4), 259–341 (1988) Marchisio, D.L., Rivautella, L., Barresi, A.A.: Design and ScaleUp of Chemical Reactors for Nanoparticle Precipitation. AIChE. J. 52, 1877–1887 (2006) Oualha, K., Ben, A.M., Michau, A., Kanaev, A.: Cavitation phenomenon in Tmixer with exocentric inputs. Chem. Eng. Trans. 57, 1231–1236 (2017) Rivallin, M.,: Evolution de sols nanométriques d’oxyde de titane durant l’induction d’une précipitation de type solgel en réacteur à mélangeur rapide: mesures granulométriques insitu et modélisation, Phd university Paris 13 (2003) Schwarzer, H.C., Peukert, W.: Combined experimental/numerical study on the precipitation of nanoparticles. AIChE. J. 50(12), 3234–3247 (2004) Singhal, A.K., Athavale, M.M., Huiying, L., Jiang, L.: Mathematical bases and validation of the full cavitation model, J. Fluids Eng. 124 (3) 617–624 (2002)
3D Simulation of Two Stages Solar Tower Ons Ghriss1(B) , Abdallah Bouabidi2,3 , Zied Driss3 , and Mohamed Salah Abid3 1 National Engineering School of Gabes (ENIG), Research Laboratory “Processes, Energetics
Environment and Electrical Systems”, Gabes University, Omar Ibn Kattab ZRIG, 6029 Gabes, Tunisia 2 National Engineering School of Gafsa (ENGA), University of Gafsa, Sidi Ahmed Zarroug University Campus, 2112 Gafsa, Tunisia [email protected] 3 Laboratory of ElectroMechanic Systems (LASEM), National Engineering School of Sfax (ENIS), University of Sfax (US), B.P. 1173, km 3.5 Soukra, 3038 Sfax, Tunisia {zied.driss,Mohamedsalah.abid}@enis.tn
Abstract. Solar updraft systems are used to convert sun energy to electric energy. The optimization of these systems is a key parameter in order to enhance the electric energy production from sun energy. In this paper, a new solar updraft system was proposed in order to enhance the efficiency of the solar updraft systems. The new design consists on a multistage system composed from two successive divergent chimneys. A 3D model was developed to investigate the flow behavior solar updraft system. The commercial software “Ansys Fluent” was used. The mathematical model was presented. The turbulence model and the boundaries conditions were specified. The two stages system was compared to the simple system with divergent chimney. The air flow characteristics within the system were presented and discussed. The velocity and the static pressure distributions were analyzed. The numerical results showed that the new system presents a very high performance comparing to the conventional one. Two zones of high velocity appear for the two stage system instead of one. The velocity in the two zones reached important value similar to them for the conventional system. The use of two stages system gives the advantage of double generation of electric energy in the two zones of high velocity. Keywords: Solar updraft · Chimney design · CFD · Numerical analysis
1 Introduction The sun energy represents one of the most important renewable sources of clean energy. This type of energy is exploited using various methods for numerous applications (El Ouederni et al. 2019). The solar updraft systems are developed as efficient system to convert sun’s energy into electricity. The solar updraft efficiency is directly related on its geometrical parameters and the ambient conditions. These two parameters are investigated experimentally and numerically in several works. For example, Sangi et al. (2011) carried out a series of Computational fluid Dynamics (CFD) simulations to predict the behavior of the air flow in the solar updraft tower. CFD code FLUENT was used in their © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 131–140, 2022. https://doi.org/10.1007/9783030849580_14
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simulations. Ayadi et al. (2018a) performed several simulations to study the turbulence model effect on the numerical results. They compared the numerical results with their experimental data. They found that the standard kε turbulence model is the most adequate model. Nia and Ghazikhani (2015) analyzed the air flow and the heat transfer with the consideration of three passive flow control devices. They showed that both of the heat transfer and the air flow velocity increase with consideration of flow control devices. Gholamalizadeh and Kim (2014) developed a series of numerical simulations to investigate the effect of the greenhouse phenomena on the solar updraft system. They showed that the numerical results depend significantly on the consideration of the greenhouse. Cao et al. (2013) investigated the solar tower performance with various weather conditions. Their results revealed that the performance of the solar tower systems is directly related to the solar radiation intensity and the ambient temperature value. Tingzhen et al. (2008) studied the solar updraft with a turbine installed in the chimney. They compared the simulation results with the experimental data. Guo et al. (2015) carried out a series of numerical simulations to predict the flow behavior inside the solar tower equipped with turbine installed in the chimney. Ayadi et al. (2018b) investigated the performance of the solar tower equipped with turbine installed in the chimney. They analyzed the effect of the turbine diameter on the generated power. Their results showed that the system performance depends on the turbine diameter. The geometrical configuration of the collector influences significantly the solar tower performance. Bouabidi et al. (2019a) conducted a series of CFD simulation with different cases of divergent collector. They compared the standard system with three configurations of divergent collector. Their results confirmed that the collector inclination influences the air flow characteristics of the solar tower. Ayadi et al. (2018c) studied the collector inlet influence on the air flow characteristics of the fluid flow and the heat transfer. Their simulations revealed that collector input dimension influences the air flow behavior inside the solar tower. Ayadi et al. (2017a) studied the solar tower system for different inclination of the collector. They studied the performance with positive and negative inclination angle collector. They found that the system negative inclination angle of the collector is the efficient one. Nasraoui et al. (2019) carried out series of numerical simulations and experiments to study the solar tower with collector concavity. They studied four geometries. They found that the collector concavity enhances the performance of the solar tower system. Ayadi et al. (2017b) performed numerous CFD simulations to investigate the effect of the chimney height on the solar tower performance. They showed that the chimney height has a significant influence on the flow behavior inside the tower system. It was found that the maximum velocity increases with the increase of the chimney height. Bouabidi et al. (2019b) analyzed the effect of the chimney diameter. They found that the change of the chimney diameter has a significant effect on the air flow characteristics inside the system. Zhou et al. (2009) investigated the influence of the chimney design on the solar tower efficiency. They showed that the chimney design presents a key parameter to enhance the solar tower efficiency. Ming et al. (2013) carried out several simulations to study the chimney configuration effect on the solar tower efficiency. Their results confirmed that the solar tower efficiency depends on the chimney configurations. Bouabidi et al. (2018) investigated the turbulent flow behavior inside the solar tower system with
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different chimney configurations. They showed that the system with divergent configuration presents the most efficient one. Also, the use of the convergent configuration changes the location of the maximum velocity from the base of the chimney to the top. In this chapter, a new proposed multistage solar updraft system is studied. The distribution of velocity, static pressure and temperature are presented and discussed for all the studied cases. The performance of the new proposed design is compared with the simple convergent design.
2 Geometries Configurations The new proposed design of the solar tower consists on the development of two stage solar tower system as depicted in Fig. 1. The new proposed system is composed of two successive stage divergent chimneys. The collector diameter is equal to 3 m. The chimney diameter and the chimney height are respectively equals to 3 m and 0.2 m.
Second stage
Divergent angle 1.50
First stage Divergent angle 10
Fig. 1. New proposed design
3 Numerical Method The simulations are performed with the CFD software “Ansys Fluent 16.2”. The Navier Stokes and the energy equations are presented: 1 ∂ ∂ ∂ ρ+ (rρu) + (ρw) = 0 ∂t r ∂r ∂z
(1)
∂ 1 ∂ ∂ dP 1 ∂ ∂ ∂ ∂ u (ρu) + (rρuu) + (ρuw) = − + (μr (u)) + (μ (u)) − 2μ 2 ∂t r ∂r ∂z dr r ∂r ∂r ∂z ∂z r (2)
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∂ 1 ∂ ∂ dP 1 ∂ ∂ (ρt) + (rρuw) + (ρVw) = − + (μr (w)) ∂t r ∂r ∂z dy r ∂r ∂r ∂ ∂ + (μ (w)) − (ρ0 − ρ)g ∂z ∂z
(3)
The energy equation is written as follow: ∂ 1 ∂ ∂ 1 ∂ λ ∂ ∂ λ ∂ (ρT) + (rρuT) + (ρwT) = (r (T)) + ( (T)) ∂t r ∂r ∂y r ∂r cp ∂r ∂y cp ∂y
(4)
The standard kε turbulence model is used in our simulations. This model is defined by the turbulent kinetic energy k and its dissipation rate ε (Bouabidi et al. 2018): μt ∂k ∂ ∂ ∂ μ+ + Gk − rε rk + ∂kui = (5) ∂t Xi ∂xj σk ∂Xj μt ∂ε ∂ ε ∂ ε2 ∂ μ+ + C1ε Gk − C2ε ρ ρε + (6) ρεui = ∂t ∂xi ∂xj σε ∂Xj k k The turbulent viscosity μt (Pa.s) is given by: μt = ρ C μ
k2 ε
(7)
Table 1 presents the constants C1ε , C2ε , Cμ , σk and σε . Table 1. Constants values of kε model(Bouabidi et al. 2018) C1ε
C2ε
Cμ
σk
σε
1.44
1.92
0.09
1.0
1.3
It is essential for each simulation to impose adequate boundaries conditions. In this work, a pressure inlet condition is specified in the collector inlet to ensure the natural flow (Fig. 2). A pressure outlet condition is imposed in the chimney outlet. The boundary condition is semitransparent wall for the collector.
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Pressure outlet
Chimney
Collector
Pressure inlet Absorber
Fig. 2. Boundaries conditions
4 Results and Discussions In this section, the velocity, static pressure and temperature distribution are presented and discussed in the center plane of the solar updraft system as shown in Fig. 3.
Fig. 3. Geometrical configurations
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4.1 Velocity Distribution Figure 4 displays the velocity distribution inside the solar tower system for the different considered configurations; Standard, divergent and two stages. From these results, it is clear that the velocity distribution depends on the solar tower geometry. For the standard solar tower system, the velocity appears with significant value along the chimney and very weak inside the collector. In the chimney inlet, the velocity reaches its maximum value. The same observation can be dawn for the solar tower with divergent chimney. However, the maximum value located in the chimney inlet increases from 2.029 m/s to 2.616 m/s for the divergent chimney. For these two cases, the velocity value appears with an important value in just one location in the chimney inlet. For the new proposed design, the numerical results show that the velocity appears with important value in two zones. The first important value appears in the inlet of the first stage, whereas the second one appears in the inlet of the second stage. These results confirm that the use of two stage system with the new chimney design enhances the solar tower system. The operation mode of solar towers is based on the rotation of a turbine. This turbine is installed in the chimney, especially in the zone of high velocity. Consequently, the solar tower efficiency is directly related on the value of the maximum velocity in the chimney. Thus, we take advantage of double points of high velocity value with the use of the new chimney configuration and consequently we take advantage of the double generation of electric energy using this new multistage system. For the first and the second configuration, a single location of high velocity value appears. 4.2 Static Pressure Distribution Figure 5 displays the static pressure distribution inside the solar tower system for the different considered configurations; Standard, divergent and two stages. Such results showed that the static pressure distribution changes from one configuration to another. Generally, one depression area appears for the systems with the simple stage. However, two depression areas occur in the case of the systems with two stages. For the one stage solar tower, the pressure reaches a very weak value only in the bottom of the chimney. Then, it increases until reached its maximum in the outlet of the system. For the two stages system, the pressure appears with very weak value in two zones. The first one corresponds to the inlet of the first stage. The second zone appears in the inlet of the second stage. The pressure zone in the chimney bottom of the first stage is similar to the depression area of the system with simple stage. However, the depression area in the inlet of the second stage is due to the reduction of chimney section. In fact, the section reduction causes the decrease of the static pressure value and the increase of the velocity according to Bernoulli’s principle.
3D Simulation of Two Stages Solar Tower
(a) Standard
(b) Divergent one stage
(c) Two stage θ=1.5° Fig. 4. Effect of the divergence angle
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(a) Standard
(b) Divergent one stage
(c) Two stage θ=1.5° Fig. 5. Static pressure distribution
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5 Conclusion In this paper, a new multistage solar tower was proposed in order to enhance the performance of the conventional system. The impact of two stages chimney was examined using CFD simulation. The velocity and the static pressure distribution were presented for the standard configuration and the new proposed designs. It was found that the use of the two stage chimney provides the performance equivalent to two solar tower systems. With the new design, two zones of high velocity appeared instead one zone for the conventional system. The static pressure was observed with two depression areas in the bottom of each stage. In the future, we propose to develop a series of solar multistage system and examine multistage system upper than two stages.
References El Ouederni, A.R., Wahabi, A., Dhahri, H.: Design and Simulation of a Low Cost Mini Solar Concentrator, Advances in Materials, Mechanics and Manufacturing, pp 94–102(2019) Sangi, R., Amidpour, M., Hosseinizadeh, B.: Modeling and numerical simulation of solar chimney power plants. Sol. Energy 85, 829–838 (2011) Ayadi, A., Nasraoui, H., Bouabidi, A., Driss, Z., Bsisa, M., Abid, M.S.: a) Effect of the turbulence model on the simulation of the air flow in a solar chimney. Int. J. Therm. Sci. 130, 423–434 (2018) Nia, E.S., Ghazikhani, M.: Numerical investigation on heat transfer characteristics amelioration of a solar chimney power plant through passive flow control approach. Energy Convers. Manag. 105, 588–595 (2015) Gholamalizadeh, E., Kim, M.: Threedimensional CFD analysis for simulating the greenhouse effect in solar chimney power plants using a twoband radiation model. Renew. Energy 63, 498–506 (2014) Cao, F., Li, H., Zhao, L., Bao, T., Guo, L.: Design and simulation of the solar chimney power plants with TRNSYS. Sol. Energy 98, 23–33 (2013) Tingzhen, M., Wei, L., Guoling, X., Yanbin, X., Xuhu, G., Yuan, P.: Numerical simulation of the solar chimney power plant systems coupled with turbine. Renew. Energy 33, 897–905 (2008) Guo, P., Li, J., Wang, Y., Wang, Y.: Numerical study on the performance of a solar chimney power plant. Energy Convers. Manag. 105, 197–205 (2015) Ayadi, A., Driss, Z., Bouabidi, A., Abid, M.S.: b) Effect of the number of turbine blades on the air flow within a solar chimney power plant. Proc. Inst. Mech. Eng. Part A: J. Power Energy 232, 425–436 (2018) Bouabidi, A., Nasraoui, H., Ayadi, A., Driss, Z., Abid, M.S.: a) Numerical and experimental study of the solar chimney with divergent collector. Heat Trans. Res. 50, 1–15 (2019) Ayadi, A., Bouabidi, A., Driss, Z., Abid, M.S.: c) Experimental and numerical analysis of the collector roof height effect on the solar chimney performance. Renew. Energy 115, 649–662 (2018) Ayadi, A., Driss, Z., Bouabidi, A., Abid, M.S.: a) Experimental and numerical study of the impact of the collector roof inclination on the performance of a solar chimney power plant. Energy Build. 139, 263–276 (2017) Nasraoui, H., Ayadi, A., Bouabidi, A., Driss, Z., Kchaou, H.: Influence of the collector concavity on the airflow behavoir within solar chimney power plant. Int. J. Green Energy 16, 1562–1570 (2019)
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Ayadi, A., Driss, Z., Bouabidi, A., Abid, M.S.: b) A computational and an experimental study on the effect of the chimney height on the thermal characteristics of a solar chimney power plant. Proc. Inst. Mech. Eng.Part E: J. Process Mech. Eng. 232, 503–516 (2017) Bouabidi, A., Nasraoui, H., Ayadi, A., Driss, Z., Abid, M.S.: b) Numerical analysis of chimney diameter effect on the fluid flow and the heat transfer characteristics within the solar tower. Energy Sources Part A Recovery Utilization Environ. Effects 41, 2494–2506 (2019) Zhou, X.P., Yang, J.K., Xiao, B., Hou, G., Xing, F.: Analysis of chimney height for solar chimney power plant. Appl. Therm. Eng. 29, 178–185 (2009) Ming, T., Richter, R.K., Meng, F., Pan, Y., Liu, W.: Chimney shape numerical study for solar chimney power generating systems. Int. J. Energ. Res. 37, 310–322 (2013) Bouabidi, A., Ayadi, A., Nasraoui, H., Driss, Z., Abid, M.S.: Study of solar chimney in Tunisia: Effect of the chimney configurations on the local flow characteristics. Energy Build. 169, 27–38 (2018)
A New Approach to Evaluate and Predict System Obsolescence: Mathematical Formulation Imen Trabelsi1,2(B) , Maher Barkallah1 , Marc Zolghadri2 , Besma Zeddini3 , and Mohamed Haddar1 1 LA2MP Laboratory, National School of Engineers of Sfax, University of Sfax, Sfax, Tunisia
[email protected], {maher.barkallah, mohamed.haddar}@enis.tn 2 QUARTZ Laboratory, SUPMECAParis, SaintOuen, France [email protected] 3 SATIE Laboratory CNRS  UMR 8029, CYTeh ENS ParisSaclay, Cergy, France
Abstract. In recent years, obsolescence has become one of the most critical issues that can affect a system’s useful life in different domains. To better manage system obsolescence, it is crucial to deal first with the obsolescence of its components and determine the factors that affect it. The prediction of component obsolescence is considered an important challenge in the life cycle management of systems to improve their sustainability. The objective of this study is to propose a strategic approach to evaluate and predict the obsolescence of the system in time according to the obsolescence of its components. In fact, the different obsolescence factors have been identified. The obsolescence process is due to six main factors, which are technological, functional, logistical, economic, aesthetic, and legal. Then, a mathematical model for predicting component obsolescence was developed while addressing the several factors that affect it. Based on this model, a mathematical formulation of system obsolescence is presented. This approach is evaluated using a numerical example on a rotary machine. Using a Monte Carlo simulation, the system obsolescence degree is determined by studying the obsolescence of its main components over a thirtyyear horizon. Results are presented and discussed while clarifying the scientific issues that should be tackled in future works. Keywords: Obsolescence modeling · Obsolescence prediction · Rotary machine
1 Introduction Now, obsolescence is a very common concept in our society, where everything is constantly changing. Indeed, anyone anywhere in the world can be confronted with the various problems induced by obsolescence. A statistical study has shown that on average one person throws away about nine electrical and electronic appliances each year. Obsolescence is defined as “the state of being which occurs when an object, service or practice is no longer wanted even though it may still be in good working order” (Edition 1995). Obsolescence is a complex term that can be defined in different ways. According to Standard IEC 62402: 2019, obsolescence is defined as “the transition of an item from © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 141–149, 2022. https://doi.org/10.1007/9783030849580_15
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available to unavailable from the manufacturer in accordance with the original specification”. In (Sandborn 2007a and b), authors define it such as “the loss or imminent loss of original manufacturers of items or suppliers of items or raw materials”. Some of the reasons that make products obsolete include technology advances, depletion of natural resources, loss of suppliers, geopolitical conflicts and regulations, etc. Indeed, obsolescence is inevitable but anticipation and careful planning can minimize its impact and potentially high cost. The aim of obsolescence management is to ensure that obsolescence is managed as an integral part of design, development, production and maintenance in order to minimize costs and negative impact throughout the product life cycle. Thus, the purpose of obsolescence management is to determine the optimal dates and quantity of last time to buy (LTB), the optimal date for redesign, the components that should be considered for redesign or that should be replaced (Meng et al. 2014). Sandborn has defined three terms for obsolescence management as follows (Sandborn 2013): • Reactive management consists in taking actions when the obsolescence has already occurred. • Proactive management is implemented for critical components that have a risk of going obsolete. • Strategic management is done in addition to proactive and reactive management and involves the determination of the optimum mix of mitigation approaches and design refreshes. The most common type of management used is reactive management because it is easier to implement. It is advisable to use it only if the cost associated with the obsolescence of a component is low (Pingle 2015). However, if the probability of obsolescence and associated costs are high, it is recommended to apply proactive management strategies to minimize the risk of obsolescence and associated costs (Rojo et al. 2010). The objective of obsolescence management is to ensure that obsolescence is controlled during the entire useful life of a product. The existing works were done to deal with obsolescence as a static way. This paper presents a novel approach to predict and evaluate obsolescence regarding the several factors that affect it. The remainder of this paper is organized as follows: Sect. 2 presents a novel obsolescence modeling at component and system level. Section 3 describes the application of the modeling obsolescence for rotary machines. We illustrate our approach in Sect. 4 by a numerical example. Finally, conclusion and future work are given in Sect. 5.
2 Obsolescence Modeling This section proposes a new modeling for the obsolescence problem. To do, the main obsolescence factors are identified and formalized in a component level and system level obsolescence models.
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2.1 Obsolescence Factors Obsolescence is a complex term due to its different forms and factors. In the scientific literature {Bartels et al. (2012); Sandborn (2007a and b); AmankwahAmoah (2017); Mellal (2020); (Trabelsi et al. 2021)}, several obsolescence typologies have been identified, including the following: i. ii. iii. iv. v. vi.
Technological obsolescence: it occurs when a new technology can replace an older technology (higher camera resolution for example). Functional obsolescence: it refers to the reduction of the usefulness, reliability or performance of a product due to a change in its specific requirements. Logistical obsolescence: It means that the product can no longer be purchased due to reduced manufacturing sources and material shortages. Economic obsolescence: It relates to the rejection of a product due to its high cost of use, maintenance and/or repair. Aesthetic obsolescence: It occurs when consumers replace a product before it wears out because a styling or other change make it less desirable. Legal Obsolescence: It is caused by government directives, rules and other laws, such as the Restriction of Hazardous Substances (RoHS) Directive (Brewin 2005), or the ban on the use of Freon because of its ozonedepleting characteristics.
The automotive, military, aeronautics, etc. sectors are the most exposed to obsolescence problems by building long field life systems (Trabelsi et al. 2020). As a result, the life cycle of each component cannot be guaranteed during the system useful life (Solomon et al. 2000), which requires parts obsolescence management to avoid this problem. 2.2 Obsolescence Modeling: Component Level As mentioned on the Sect. 2.1, obsolescence process is due to six main factors, which are technological, functional, logistical, economic, aesthetic and legal. Existing works consider obsolescence as a final stage of the product life cycle. Whereas in our work, we consider obsolescence as an action that takes time to move from the state of availability to the state of unavailability due to several factors. During the component useful life, obsolescence is considered as a function of time. However, each factor influences the component obsolescence with a specific degree or weight. The obsolescence model of the component is then given by the Eq. 1: n αij fij (t) (1) ODi (t) = j=1
where, ODi is the obsolescence degree of the component i, n is the number of obsolescence factors, α ij is the weight for the factor j, and f ij (t) is the obsolescence modeling function according to the factor j. Each evolution function can be considered as cumulative distribution function which ranges from 0 to 1 (Trabelsi et al. 2020). For legal obsolescence, the function is 0 when the law is not yet announced. Once the law is imposed, the obsolescence degree becomes 1.
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2.3 Obsolescence Modeling: System Level The aim of our work is to model the system obsolescence according to the obsolescence of its components. Regardless the interaction between the system’s components, the obsolescence degree function of the whole system is estimated as the function of the component that has a high obsolescence. m OD(t) = maxi=1 [ODi (t)]
(2)
where m is the system’s components number, and ODi (t) refers to the obsolescence model of the component i (Eq. 1). In reality, the system’s components are dependent to each other. Thus, component obsolescence is affected by the obsolescence of other components that interact with it. The authors in (Trabelsi et al. 2020) study the impact of component interaction on system obsolescence and propose to model this dependence by a Weibull distribution. However, the proposed modeling is limited by the unidirectional character of the obsolescence (obsolescence propagates from one component to another without an adverse effect). In a general way and taking into account the interaction between the components, the system obsolescence is calculated as: OD(t) = g[ODi (t)]
(3)
where g is a function that calculates the interdependence between the system’s components.
3 Obsolescence for Rotary Machines Rotary machines have been widely used in the manufacturing industry. In this section, we propose to formalize the obsolescence of this type of machines based on the previous detailed obsolescence modeling. 3.1 Generalities on Rotary Machines A rotary machine is a machine tool, typically for the manufacture of metal parts, allowing a wide range of operations. These operations include turning, milling, drilling, etc. As shown in Fig. 1, this kind of machine includes three main components: engine, gearbox and tool. Unlike tools, engines and gearboxes are highly susceptible to obsolescence due to their sensitivity to the previously detailed obsolescence causes. Thus, we propose in this study to model rotary machines obsolescence according to the obsolescence state of these two components. 3.2 Engine Obsolescence To determine the factors that influence the obsolescence of rotary machine engines, we propose to conduct a qualitative research. Based on a literature review, the engine’s obsolescence process is driven by technological evolution, a decrease in its function or
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Fig. 1. A brief chart of a rotary machine.
performance, logistical, economic and legal problems. The aesthetic factor in this case is negligible. The engine obsolescence is then determined by studying the evolution of these five factors, according to the Eq. (4): ODe (t) = α1 ftech (t) + α2 ffun (t) + α3 flog (t) + α4 feco (t) + α5 fleg (t)
(4)
where α 1 , α 2 , α 3 , α 4 , and α 5 are positive number ≤1. 3.3 GearBox Obsolescence To study the gearbox obsolescence, it is essential to determine the various factors that affect it. In fact, legal and aesthetic obsolescence are not considered. Therefore, only factors related to technological evolution, function, logistics and economics were considered in the study of gearbox obsolescence. In the same way, the obsolescence degree of the gearbox is determined by the formula (5): ODg (t) = α1 ftech (t) + α2 ffun (t) + α3 flog (t) + α4 feco (t)
(5)
where α1 , α2 , α3 , and α4 are positive number ≤1.
4 Numerical Example and Results To illustrate our approach, we suppose to study the system’s obsolescence over a 30year horizon. To this end, the obsolescence degree of each component, taking into account the different factors that affect it, is determined by following the formulas (4) and (5).
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4.1 Simulation SetUp Based on the advice of a group of experts, the distribution function for each factor and its parameters are determined, as shown in the Table 1. To respect law enforcement, the experts propose that the weight related to the legal factor should be equal to one; in other words, the law imposition that prohibits the use of a component renders it 100% obsolete. In this case study, the probability of introducing a new law is set at 1%. Table 1. Illustration of the simulation configuration. Component
Factors
Weight
Distribution function
Parameters estimation
Engine
Technological
0.3
Gamma
1 ± 0.5
Functional
0.4
Beta
0.5 ± 0.1
0.5 ± 0.1
Logistical
0.25
Weibull
1 ± 0.5
2 ± 0.2
Economic
0.05
Beta
6 ± 0.3
1 ± 0.1
Legal
1
Heaviside
Probability 1%
Technological
0.35
Gamma
0.5 ± 0.2
Functional
0.45
Weibull
6 ± 0.5
1 ± 0.2
Logistical
0.15
Weibull
2 ± 0.1
5 ± 0.5
Economic
0.05
Beta
5 ± 0.5
1 ± 0.1
Gearbox
A MonteCarlo simulation is established to evaluate the obsolescence evolution of each component. 4.2 Component Level Results By varying randomly the parameters of the functions according to the experts’ uncertainty interval, the results on 100 simulations are presented in the Fig. 2. The results show that the obsolescence degree can be modeled according to the evolution of the different factors. By averaging the values of these simulations, the obsolescence degree of both the engine and the gearbox are determined over time, as shown in Fig. 3. As shown in this figure, the OD can evolve over time and varies between 0 (at the beginning of the observation) and 1 (at the end of the observation). 4.3 System Level Results As detailed in the Sect. 2.3, the system obsolescence degree can be determined using two solutions: as the component function that has a high obsolescence or by studying the dependence between components. By considering the system obsolescence degree as the maximum between the OD of the engine and the gearbox, the system OD is given by the Fig. 4. In fact, for 29 years,
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Fig. 2. MonteCarlo simulation for the engine and gearbox obsolescence.
Fig. 3. Obsolescence degree evolution of the engine and gearbox.
the engine OD was greater than the gearbox. Whereas in the last year of observation, the OD of the gearbox is higher. Therefore: ODengine for t < 30 years ODsystem = (6) ODgearbox for t = 30 years Taking into account the interaction between the components, it appears that the identification of the interdependence in term of obsolescence is difficult to solve it. In fact, there is no clear methodology to formalize this interaction. For that, we propose to fill this research gap in future works.
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Fig. 4. System obsolescence degree evolution.
5 Conclusion and Future Work Obsolescence is an inevitable problem that affects all sectors such as mechanics, electronics, and computers. For longlife systems, the life cycle of each component cannot be guaranteed during the useful life of the system, which requires parts obsolescence management to avoid this problem. This paper presents a mathematical formulation to evaluate and predict the system obsolescence based on the obsolescence evolution of its main components. The first step requires identifying the most critical components and the factors that affect their obsolescence. Several factors can affect obsolescence, namely technological, functional, logistical, economic, aesthetic, and legal, and each one affects it with a specific weighting. Based on experts’ advice, the obsolescence evolution of rotary machines is studied. As future work, the authors suggest to further study the components interdependence and their impact on the system obsolescence. In this context, mathematical models and artificial intelligence techniques can be jointly used to best exploit the large amounts of information collected from heterogeneous sources on the one hand and the strength of mathematical theories on the other.
References AmankwahAmoah, J.: Integrated vs. addon: a multidimensional conceptualisation of technology obsolescence. Technol. Forecast. Soc. Change 116, 299–307 (2017) Bartels, B., Ermel, U., Sandborn, P., Pecht, M.G.: Strategies to the Prediction, Mitigation and Management of Product Obsolescence, vol. 87. Wiley, Hoboken (2012) Brewin, A.: The Pbfree minefield: a guide to mitigating risk during the transition to RoHS compliance (2005) Edition, N.: The concise Oxford dictionary (1995) Mellal, M.A.: Obsolescence–a review of the literature. Technol. Soc. 63, 101347 (2020) Meng, X., Thörnberg, B., Olsson, L.: Strategic proactive obsolescence management model. IEEE Trans. Compon. Packag. Manuf. Technol. 4(6), 1099–1108 (2014) Pingle, P.: Selection of obsolescence resolution strategy based on a multi criteria decision model (2015) Rojo, F.J.R., Roy, R., Shehab, E.: Obsolescence management for longlife contracts: state of the art and future trends. Int. J. Adv. Manuf. Technol. 49(9–12), 1235–1250 (2010)
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Sandborn, P.: Designing for technology obsolescence management. In: Proceedings of the IIE Annual Conference, p. 1684. Institute of Industrial and Systems Engineers (IISE) (2007) Sandborn, P.: Software obsolescencecomplicating the part and technology obsolescence management problem. IEEE Trans. Compon. Packag. Technol. 30(4), 886–888 (2007) Sandborn, P.: Design for obsolescence risk management. Proc. CIRP 11, 15–22 (2013) Solomon, R., Sandborn, P.A., Pecht, M.G.: Electronic part life cycle concepts and obsolescence forecasting. IEEE Trans. Compon. Packag. Technol. 23(4), 707–717 (2000) Trabelsi, I., Zolghadri, M., Zeddini, B., Barkallah, M., Haddar, M.: FMECAbased risk assessment approach for proactive obsolescence management. In: Nyffenegger, F., Ríos, J., Rivest, L., Bouras, A. (eds.) Product Lifecycle Management Enabling Smart X: 17th IFIP WG 5.1 International Conference, PLM 2020, Rapperswil, Switzerland, July 5–8, 2020, Revised Selected Papers, pp. 215–226. Springer, Cham (2020). https://doi.org/10.1007/9783030628079_18 Trabelsi, I., Zeddini, B., Zolghadri, M., Barkallah, M., Haddar, M.: Obsolescence prediction based on joint feature selection and machine learning techniques. In: 13th International Conference on Agents and Artificial Intelligence, pp. 787–794. SCITEPRESSScience and Technology Publications (2021)
Transient Response of Functionally Graded Porous Plate Souhir Zghal(B) , Sourour Trabelsi, and Fakhreddine Dammak Laboratory of Electromechanical Systems (LASEM), National Engineering School of Sfax, University of Sfax, B.P W3038, Sfax, Tunisia [email protected], [email protected]
Abstract. This paper presents transient response of a functionally graded porous plate. The plate is made of metal and ceramic portions in its bottom and top surfaces. From these two extreme surfaces, the porosity is functionally graded distributed through the thickness direction of the plate with two forms, namely even and uneven porosity distributions. The former reflects a uniformly distribution of the pores into the structure, while the latter indicates a randomly distributed pores along the thickness direction. The material properties of porous FGM plates are determined by a modified power law distribution, for which the porosity volume fraction is described by the porosity coefficient, noted alpha. The equations of motion are elaborated using the KirchoffLove kinematic assumptions, for which the effect of transverse shear deformations is neglected, and the discretization of the displacement and strain fields is carried out using the finite element method. Then, the temporal responses are computed using the Newmark’s integration scheme. The influence of the volume rate of porosity and the way of its distribution is examined for frequency and temporal responses of the FGM plates. Results show that the porosity has a significant effect on temporal responses of FGM plates which must be considered in the control of the vibrations of such strucutres. Keywords: Transient · Functionally graded · Porous · Finite element
1 Introduction Functionally graded materials are a new advanced materials discovered by a material scientist group in Japan (Koizumi 1997) during an aerospace thermal project and they are recognized by their high tenacity for high temperature fields. Another advantage of these materials, is the smoothly and continuous variation of its material properties from one surface to another. Typically, the functionally graded strucutre is made by a mixture of metal and ceramic portions and it is called perfect FGM strucutre. However, porosity can be found in these material as a defect caused by fabrication procedure leading hence to a novel FGM, called, porous FGM which is also attracted the attention of many researchers. Regarding FGM materials, several works are elaborated, in the last years, concerning static, bending and vibrational analysis (Wattanasakulpong and Ungbhakorn 2014; © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 150–155, 2022. https://doi.org/10.1007/9783030849580_16
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Chen et al. 2016; Zenkour 2018; Trabelsi et al. 2020; Zghal et al. 2020; Zghal and Dammak 2020; Zghal et al. 2021). Nevertheless, the most of these works focus on perfect FGM strucutres and less works are found for imperfect porous plates and shells. Therefore, the investigation of the mechanical behavior of FGM porous plate appears interesting. Hence, in this paper transient response of FGM porous plate with even and uneven porosity distributions is preformed. The equations of motion are derived using the KirchhoffLove assumptions and the discretization is carried out by the finite element method. The material properties of the FGM porous plate are described by a power law distribution and the influence of porosity the volume fraction is explored via a frequency and temporal analysis. The results show that the porosity parameter should be considered in the phase of vibration control.
2 Equations of Motion The equations of motion are elaborated based on the KirchhoffLove assumptions. Accordingly, the position vector of only point (q) can be written as: Xq (ξ1 , ξ2 , z) = Xp (ξ1 , ξ2 ) + zD(ξ1 , ξ2 ),
xq = xp + zd
(1)
Where: z ∈ [−h/2, h/2] is the thickness variable and d is the shell director vector. The components of the strain field are expressed by: ⎧ ⎫ ⎧ ⎫ ⎨ e11 ⎬ ⎨ χ11 ⎬ γ (2) e = e22 , χ = χ22 , γ = 1 ⎩ ⎭ ⎩ ⎭ γ2 2e12 2χ12 With: e,χ and γ are the membrane, the bending and the shear components. According the KirchhoffLove assumptions, the transverse shear strains are neglected γ = 0. The material behavior law can be written as:
h/2 N e H11 H12 1, z, z2 Hdz (3) = , (H11 , H12 , H22 ) = M H12 H22 χ −h/2 H defines the in plane linear elastic matrix: ⎡ ⎤ 1 ν(z) 0 E(z) ⎣ ⎦ H= ν(z) 1 0 1 − ν2 (z) 0 0 (1 − ν(z))/2
(4)
The Young’s modulus E(z) can be expressed in terms of thickness variable z and porosity coefficient α as: p (Em − Ec ) 21 + hz + Ec − α2 (Em + Ec ) (Even porosity) 1 z p E(z) = 2z α (Em − Ec ) 2 + h + Ec − 2 (Em + Ec ) 1 − h (Uneven porosity) (5) Em and Ec are the Young’s modulus of metal and ceramic portions and α is the porosity coefficient (0 ≤ α ≺ 1). The subscript p is the gradient index.
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Using the total Lagrangian formulation, the weak form of equilibrium equations is derived. Then, the finite element method is used for the discretization of the equations of motion. The Newmark’s integration scheme is then, used to resolve the following discrete equation of motion: ¨ n + KUn = F MU
(6)
Where Un the nodal vector and (M, K) are the global mass and stiffness matrices, and F is the external load vector.
3 Numerical Analysis Transient response of a FGM porous plate is preformed. The geometry of the plate with evenly and unevenly pores distributions is presented in Fig. 1. The material characteristics of metal and ceramic constituents reads as: Al (Em = 70 GPa; density ρ m = 2702 kg/m3 ; Poisson’s ratio υ m = 0.3) and Alumina (Al2 O3 : with Young’s modulus Ec = 380 GPa; density ρ c = 3960 kg/m3 ; Poisson’s ratio υ c = 0.3).
Fig. 1. Functionally graded plate with two types of porosity distributions.
The analysis are carried out for a moderately thick plate with a lengthtothickness ratio (a/h = 20). Continuously, the FGM plate is subjected to a harmonic load of the form: F(t) = F0 cos(t) where F0 = 40 N and = 1500 rad/s is the eigenpulsation near the first mode of vibration. Before the temporal analysis, a quick check out of the consistence of the formulation towards frequency response of the FGM √ plate is presented in Table 1. The adimensional frequency is evaluated as: ω = ωh ρm /Em . As can be remarked a good agreement between the results is reveled. The relative error between results which can reaches 5% in some cases is related to the neglect of shear strains in the present formulation. Otherwise, an acceptable concordance is shown and the current
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Table 1. Natural frequencies of a simply supported (SSSS) porous FGM plate (p = 1) Porosity coefficient Present α Even
(FSDT, Rezaei et al. (2017)) Uneven Even
Uneven
0
0.02350 0.02350 0.02224 0.02224
0.2
0.02265 0.02390 0.02104 0.02247
0.4
0.02107 0.02440 0.01817 0.02269
W(t)[m]
model is simple and efficient for the determination of natural frequencies of porous FGM plates. The temporal response of the FGM plate (SSSS, a/h = 20) with different porosity coefficients (α = 0, 0.2, 0.4) is plotted in Fig. 2. As can be seen, the increase of the porosity coefficient induces an increase in the amplitude of the temporal response. This phenomenon may be explained by the low rigidity of the structure with the rise of porosity volume fraction and the plate becomes more flexible and bends easy. Therefore, the porosity parameter should be taken into account in the control phase of vibrations.
Fig. 2. Transient response of FGM even porous plate (SSSS, a/h = 20, p = 1) subjected to harmonic excitation load
The impact of the way of porosity distributions is also examined in Fig. 3, where transient response of FGM porous simply supported (SSSS, a/h = 20) plate are plotted and presented. As can be remarked, when the pores are evenly distributed, the deflection of the plate is pronounced compared to uneven type of distribution. Moreover, the period of the transient response is affected in the time range [0.25–0.5] s which highlight that the way of pores distributions in the whole of the strucutres can significantly influences the dynamic response of FGM plates.
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Fig.3. Temporal response of FGM porous plate with evenly and unevenly porosity distributions
4 Conclusion In the current work, temporal analysis of functionally graded porous plate is presented. The equations of motion are established using the Kirchhoff Love assumptions and the finite element method is used for the discretization of the displacement and strains field. The material characteristics of the FGM plate are graded in the thickness direction and porosity dependent with two types of distributions, namely even and uneven forms. The effect of the variation of porosity coefficient on frequency and transient response of FGM plate is examined. A deep investigation on the effects of porosity parameters and others geometrical parameters will be presented in future works.
References Koizumi, M.: FGM activities in Japan. Compos. Part B 28, 1–4 (1997) Wattanasakulpong, N., Ungbhakorn, V.: Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities. Aerosp. Sci. Technol. 36, 111–120 (2014) Chen, D., Yang, J., Kitipornchai, S.: Free and forced vibrations of shear deformable functionally graded porous beams. Int. J. Mech. Sci. 108–109, 14–22 (2016) Zenkour, A.M.: A quasi3d refined theory for functionally graded singlelayered and sandwich plates with porosities. Compos. Struct. 201, 38–48 (2018) Rezaei, A.S., Saidi, A.R., Abrishamdari, M., Pour Mohammadi, M.H.: Natural frequencies of functionally graded plates with porosities via a simple four variable plate theory: an analytical approach. ThinWalled Struct. 120, 366–377 (2017) Trabelsi, S., Zghal, S., Dammak, F.: Thermoelastic buckling and postbuckling analysis of functionally graded thin plate and shell structures. J. Braz. Soc. Mech. Sci. Eng. 42(5), 1–22 (2020). https://doi.org/10.1007/s40430020023145 Zghal, S., Ataoui, D., Dammak, F.: Static bending analysis of beams made of functionally graded porous materials. Mech. Based Des. Struct. Mach. (2020). https://doi.org/10.1080/15397734. 2020.1748053
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Zghal, S., Dammak, F.: Vibrational behavior of beams made of functionally graded materials by using a mixed formulation. Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 234(18), 3650–3666 (2020) Zghal, S., Trabelsi, S., Frikha, A., Dammak, F.: Thermal free vibration analysis of functionally graded plates and panels with an improved finite shell element. J. Therm. Stresses 44(3), 315–341 (2021)
Water Aging Effect on the Vibration Behavior of the BioBased Flax/PLA Composites Zeineb Kesentini1,2(B) , Abderrahim El Mahi1 , Jean Luc Rebiere1 , Rachid El Guerjouma1 , Moez Beyaoui2 , and Mohamed Haddar2 1 Laboratoire d’Acoustique de l’Université du Mans (LAUM) UMR CNRS 6613, Avenue O.
Messiaen, 2085 Le Mans cedex 9, France 2 Laboratoire de Modélisation et Production Mécanique (LA2MP), Ecole Nationale
d’Ingénieurs de Sfax, Université de Sfax, BP N ° 11733038 Sfax, Tunisie
Abstract. Because of the many advantages that biobased composites have, their use has increased significantly in recent years. Many experiments have emphasized the good properties of these materials. The objective of this paper is to study the influence of water aging of biobased flax/PLA composite on their vibration behavior. The material used in this analysis is a polylactic acid (PLA) tape reinforced with flax fiber filament. It’s made of a biobased, biodegradable, and recyclable fiber. The composites that were studied, were produced by 3D printer and immersed in tap water at ambient temperature. First, the water absorption is tested by immersing five samples and checking the mass gain at each period. Secondly, for different percentages of absorption, the vibration behavior of aged materials was investigated using a free vibration test. Next, it was compared with the nonaged composite behavior, which is considered as the reference. When measured in terms of aging period, water absorption causes a decrease in Young’s modulus and an increase in loss factors. Results show that biobased composite is very sensitive to humidity, that is why, the stiffness is weakened but the loss factor is improved. Keywords: Biobased composite flax/PLA · Water aging · Absorption · Vibration · 3D printing
1 Introduction Reinforcement of composite materials with synthetic fibers raises a number of environmental problems in term of their recyclability. These environmental concerns inspired researchers to study other elements of more environmentally sustainable composite fabrics, like plant fibers [1–5].
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 156–163, 2022. https://doi.org/10.1007/9783030849580_17
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The difficulty of testing these performances in a humid atmosphere remains an obstacle, and their usage is likely to be substantially impeded, which is a big barrier that also slows down their production. Their biochemical structure and composition can explain the water sensitivity [6, 7]. The secondary cell wall, which is responsible for the bulk of the mechanical performance of the fabric, is the primary structural layer. Several researchers have recently conducted various studies to explore the water aging effect on dynamic behavior of biobased composite materials. They demonstrated that as water spills into the material, exposing a plant fiber composite to a humid atmosphere results in a decline in mechanical properties. This degradation of characteristics caused by the aging was found on various plant fiber composites, such as composites of bamboo [8], jute [9], sisal [10] or flax fibers [11, 12]. Chilali et al. [13] used cyclic and monotonic loadunload experiments to study the water aging effect on the loadunload cyclic behavior of thermoplastic composites reinforced by flax fiber. The results show that water ageing degrades the mechanical characteristics of these materials significantly. The vulnerability of the fiber/matrix interface and the damage caused by fiber deterioration are the main reasons for this difference. Loadunload experiments also shown an improvement in load testing. Loadunload experiments have indicated an increase in stiffness loss by aging due to the plasticizing phenomenon caused by water absorption. The combination of plant fibers may be a unique selling point in light of the commercial appeal of these fully biobased composites. Essassi et al. are investigating the biocomposite flax/PLA in this sense. Significant properties are found in this composite, according to the results. However, in the manufacture of biocomposites for such uses, certain hurdles, such as humidity, must be considered. Le Duigou et al. [15] studied the effects of seawater aging at various temperatures on characteristics of a flax fiber reinforced biopolymer (PLA). They discovered that the interface fiber/matrix of the biopolymer composite, which is affected by water leakage, is the main cause of this deficiency. The effect of humidity on the vibration activity of flax/PLA is studied in this report. 3D printing technologies 1are used to create specimens. Free vibration tests are used to determine the Young’s modulus and the loss factor coefficient.
2 Materials and Methods The material utilized in this analysis is a 1.75 mm diameter polylactic acid (PLA) tape reinforced with flax fiber filament provided by NANOVIA. It’s made of a biobased, biodegradable, and recyclable fiber. It’s all about using additive manufacturing techniques.The MakerBot Replicator2 Desktop was used for the 3D printing. By following parameters proposed by the company, the extrusion temperature is set to be equal to 210 °C and the building platform temperature is equal to 55 °C. The specimens were designed with solidworks and then translated into instructions compatible with the software MakerBot Replicator2 Desktop to be printed. The samples were immersed in tap water at room temperature as part of the aging procedure. The percentage of water absorption of flax/PLA was determined by immersing five samples of a 25 × 25 × 5 mm measurement in water. This suggests studying the progression of the samples’ mass over time. The samples were weighted with an
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accurate SARTORIUS balance of 10−4 g precision. To be measured and characterized, samples were routinely taken. The materials’ damping properties were determined by subjecting beams to flexural vibrations in accordance with ASTM E756 [16]. Figure 1 depicts the devices used. Specimens measuring 230, 25 and 5 mm in length, width, and thickness, respectively, was supported horizontally and measured in a clampfree configuration. The clamping length has been set to 40 mm. To attain different frequencies, the specimens are excited with a PCB084A14 impact hammer over three free lengths (230, 200, and 170 mm). The excitation of the beam’s flexural movements is induced with an impulse hammer, and the beam response is measured with a laser vibrometer. The excitation and reaction signals are then digitalized and analysed by a signal dynamic analyzer. This analyzer, which is connected to a PC computer, acquires signals, monitors the acquisition conditions, and then analyzes the signals obtained (Fourier transform, frequency response, mode shapes, etc…). Furthermore, a minimum of 5 beams were checked for each duration to account for the theoretically dispersed properties of these natural materials. The data was then used to produce the beam frequency response function (FRF) using MATLAB software [17–19]. To detect resonance peaks, an automated procedure was added to each FRF. Each mode’s resonance frequency fi and modal loss factor I were measured using a half power bandwidth (HPB) system and a Matlab software optimization package, as seen in Fig. 2.
Fig. 1. Experimental equipment for clampedfree vibration tests: (a) experimental set up and (b) embedded specimen
The modal damping factor is calculated using equation Eq. (1). The damping factor ηi is the ratio between the bandwidth frequencies where fi the amplitude resonance decreases by 3 db, split up by the resonance frequency fi . ηi =
fi f2 − f1 = fi fi
(1)
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The Young’s modulus E of composite for every mode is calculated by equation Eq. (2) E=
12ρl 4 fn2 e2 Cn2
(2)
Where ρ is the density of the composite material, l is the free length of the specimen, fn is the resonance frequency of the nth flexural mode, e is the thickness of the specimen in the vibration direction and Cn is a coefficient for the nth mode of a clampedfree specimen, with: C1 = 0.55959, C2 = 3.5069, C3 = 9.8194 Cn = (π/2).(n − 0.5)2 for n3 [16].
Fig. 2. Half power bandwidth method [20]
These tests were applied to a dry specimen and for other aged specimens for absorption percentage in order to identify the humidity effect on the vibration behavior. Five specimens are tested to take into account the variability of results due to experimental conditions for each absorption percentage.
3 Aging Effect on the Vibration Behavior Eleven percentages of water uptakes have been picked to research the aging effect on the composite. For each immersion period, five experiments are undertaken. The evolution with the frequency of vibration characteristics for 3 different percentages of water uptakes is presented in Fig. 3. Results indicate that as the frequency as well as immersion time increase, the Young’s modulus decreases. Intrusion of molecules of water into the composition of the biocomposite, breaking down the hydrogen bonds between the polar groups of neighboring macromolecular chains that bind to a water molecule, describes the loss of mechanical properties. At high frequency and a high absorption of water, the stiffness of specimens becomes lower. The chemical fiber composition and the multilayer arrangement of the primary and secondary cell wall can explain a substantial rise in weight. Extremely hygroscopic lignin
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and hemicelluloses [21–25] in matrix which is amorphous, biofibers are themselves hybrid fabrics fortified with cellulose fibers. The plant fibers’ hydrophilic behavior is primarily due to hydroxyl groups OH, which trap water. Water molecules found on cellulose crystallites surface in amorphous cellulose regions or at the level of hemicelluloses are picked up by hydroxyl classes.
2.4 0%
Young's modulus [GPa]
2.3
0.60%
1.20%
2.2 2.1 2 1.9 1.8 1.7 0
1000
2000 3000 4000 Frequency [Hz]
5000
Fig. 3. Evolution of flax/PLA Young’s modulus with frequency for three percentages of absorption
In relation to the Young’s modulus, Fig. 4 presents that in relation to the frequency, the damping factor increases. The morphology of flax fibers, which promotes energy dissipation by friction between cellulose and hemicellulose and by friction between cell walls, may be responsible for the significant damping properties of composite flax fibers [26]. Generally, the failure factor of nonaged materials is low since they have few defects and the fiber/matrix interfaces are not yet impaired. However, as function of the absorption percentage as seen in Fig. 4, it don’t provide a clear outcome where the four periods are regrouped due to the dispersion. To clarify that, the evolution of the absorption percentage and loss factor of three percentages was plotted for three selected frequencies, 250, 500 and 2000 Hz respectively (Fig. 5). It is noted that in relation with the frequency and also the absorption percentage, the loss factor increases. Thus, with increasing absorption percentage, the Young’s modulus and the loss factor have a conflicting tendency.
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4 0%
Loss factor [%]
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3
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1.5 0
1000
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Frequency [Hz] Fig. 4. Evolution of flax/PLA loss factor with frequency for three percentages of absorption
3.5 250 Hz 500 Hz
Loss factor [%]
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2000 Hz 2.5
2
1.5
0
0.2
0.4
0.6 0.8 1 Absorption [%]
1.2
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Fig. 5. Comparison of flax/PLA’s loss factor with absorption percentage for three frequencies
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4 Conclusion The effect of water aging on vibration behavior of the composite produced using 3D printing technology was investigated. First of all, absorption was studied. Secondly, the mechanical behavior of nonaged composite which is the reference was studied. After that, to understand the water aging effect, vibration tests were effectuated out for different water uptake percentage. Water absorption plasticizes specimens. In consequence, due to this phenomenon, the mechanical characteristics will be deteriorated with increasing absorption percentage. The vibration test showed a decrease in the Young’s modulus unlike the loss factor which increased with the increasing of absorption percentage. To conclude, the biobased composite is very sensitive to humidity, that is why, the mechanical properties are weakened. Due to the strong basic mechanical properties of the plant fibers, similar to those of glass fibers but with a much higher damping capacity, surface treatment for protection against humidity would be helpful in future work.
References 1. Monti, A., El Mahi, A., Jendli, Z., Guillaumat, L.: Experimental and finite elements analysis of the vibration behaviour of a biobased composite sandwich beam. Compos. B Eng. 110, 466–475 (2017) 2. Daoud, H., El Mahi, A., Rebiere, J.L., Mechri, C., Taktak, M., Haddar, M.: Experimental analysis of the linear and nonlinear vibration behavior of flax fibre reinforced composites with an interleaved natural viscoelastic layer. Compos. B Eng. 151, 201–214 (2018) 3. Malloum, A., El Mahi, A., Idriss, M.: The effects of water ageing on the tensile static and fatigue behaviors of greenpoxy–flax fiber composites. J. Compos. Mater. 53(21), 2927–2939 (2019) 4. Allagui, S., El Mahi, A., Rebiere, J.L., Beyaoui, M., Bouguecha, A., Haddar, M.: Effect of recycling cycles on the mechanical and damping properties of flax fibre reinforced elium composite: experimental and numerical studies. J. Renew. Mater. 9(4), 695–721 (2021) 5. Bayart, M., Gauvin, F., Foruzanmehr, M.R., et al.: Mechanical and moisture absorption characterization of PLA composites reinforced with nanocoated flax fibers. Fibers Polym. 18(7), 1288–1295 (2017). https://doi.org/10.1007/s122210177123x 6. Hill, C.A., Norton, A., Newman, G.: The water vapor sorption behavior of natural fibers. J. Appl. Polym. Sci. 112(3), 1524–1537 (2009) 7. Azwa, Z.N., Yousif, B.F., Manalo, A.C., Karunasena, W.A.: Review on the degradability of polymeric composites based on natural fibres. Mater. Des. 47, 424–442 (2013) 8. Chen, H., Miao, M., Ding, X.: Influence of moisture absorption on the interfacial strength of bamboo/vinyl ester composites. Compos. A Appl. Sci. Manuf. 40(12), 2013–2019 (2009) 9. Akil, H.M., Cheng, L.W., Ishak, Z.M., Bakar, A.A., Abd Rahman, M.A.: Water absorption study on pultruded jute fibre reinforced unsaturated polyester composites. Compos. Sci. Technol. 69(11–12), 1942–1948 (2009) 10. Chow, C.P.L., Xing, X.S., Li, R.K.Y.: Moisture absorption studies of sisal fibre reinforced polypropylene composites. Compos. Sci. Technol. 67(2), 306–313 (2007) 11. Alix, S., Lebrun, L., Morvan, C., Marais, S.: Study of water behaviour of chemically treated flax fibresbased composites: a way to approach the hydric interface. Compos. Sci. Technol. 71(6), 893–899 (2011)
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12. Le Duigou, A., Davies, P., Baley, C.: Seawater ageing of flax/poly (lactic acid) biocomposites. Polym. Degrad. Stab. 94(7), 1151–1162 (2009) 13. Chilali, A., Zouari, W., Assarar, M., Kebir, H., Ayad, R.: Effect of water ageing on the loadunload cyclic behaviour of flax fibrereinforced thermoplastic and thermosetting composites. Compos. Struct. 183, 309–319 (2018) 14. Essassi, K., Rebiere, J.L., El Mahi, A., Souf, M.A.B., Bouguecha, A., Haddar, M.: Experimental and analytical investigation of the bending behaviour of 3Dprinted biobased sandwich structures composites with auxetic core under cyclic fatigue tests. Compos. Part A: Appl. Sci. Manuf. 131, 105775 (2020) 15. Baley, C., Le Duigou, A., Bourmaud, A., Davies, P.: Influence of drying on the mechanical behaviour of flax fibres and their unidirectional composites. Compos. A Appl. Sci. Manuf. 43(8), 1226–1233 (2012) 16. Standard test method for measuring vibrationdamping properties of materials. ASTM International. American Society For Testing and Materials (2010) 17. El Mahi, A., Assarar, M., Sefrani, Y., Berthelot, J.M.: Damping analysis of orthotropic composite materials and laminates. Compos. B Eng. 39(7–8), 1069–1076 (2008) 18. Daoud, H., El Mahi, A., Rebiere, J.L., Taktak, M., Haddar, M.: Characterization of the vibrational behaviour of flax fibre reinforced composites with an interleaved natural viscoelastic layer. Appl. Acoust. 128, 23–31 (2017) 19. Daoud, H., et al.: Numerical and experimental characterization of the dynamic properties of flax fiber reinforced composites. Int. J. Appl. Mech. 8(05), 1650068 (2016) 20. Essassi, K., Rebiere, J.L., El Mahi, A., Ben, S.M., A., Bouguecha A., Haddar M. : Dynamic characterization of a biobased sandwich with auxetic core: experimental and numerical study. Int. J. Appl. Mech. 11(02), 1950016 (2019) 21. Khalil, A., Rozman, H.D., Ahamd, N.N., Ismail, H.: Acetylated plantfibrereinforced polyester composites: a study of mechanical, hydrothermal and ageing characteristics. Polym. Plast. Technol. Eng. 39(4), 757–781 (2000) 22. Tröger, F., Wegener, G., Seemann, C.: Miscanthus and flax as raw material for reinforced particleboards. Ind. Crops Prod. 8(2), 113–121 (1998) 23. Dittenber, D.B., GangaRao, H.V.: Critical review of recent publications on use of natural composites in infrastructure. Compos. A Appl. Sci. Manuf. 43(8), 1419–1429 (2012) 24. Charlet, K., Baley, C., Morvan, C., Jernot, J.P., Gomina, M., Breard, J.: Characteristics of Hermès flax fibres as a function of their location in the stem and properties of the derived unidirectional composites. Compos. A 38(8), 1912–1921 (2007) 25. Baley, C.: Analysis of the flax fibres tensile behaviour and analysis of the tensile stiffness increase. Compos. A 33(7), 939–948 (2002) 26. Duc, F., Bourban, P.E., Manson, J.A.: The role of twist and crimp on the vibration behaviour of flax fibre composites. Compos. Sci. Technol. 102, 94–99 (2014)
An Anisotropic Model with Linear Perturbation Technique to Predict HCP Sheet Metal Ductility Limit Mohamed Yassine Jedidi1,2(B) , Mohamed Ben Bettaieb2,3 , Farid AbedMeraim2,3 , Mohamed Taoufik Khabou1 , Anas Bouguecha1 , and Mohamed Haddar1 1 Laboratoire de Mécanique, Modélisation et de Production (LA2MP), École Nationale
d’Ingénieurs de Sfax (ENIS), Route Soukra Km 3.5, Sfax, Tunisia [email protected], [email protected], [email protected] 2 Arts et Métiers ParisTech, Université de Lorraine, CNRS, LEM3, 57000 Nancy, France {mohamed.benbettaieb,farid.abedmeraim}@ensam.eu 3 DAMAS, Laboratory of Excellence on Design of Alloy Metals for lowmAss Structures, Université de Lorraine, Nancy, France
Abstract. In this paper, hexagonal closed packed (HCP) sheet metal ductility for a viscoplastic material is analyzed by using a linear perturbation technique. It can be used for the analysis of localized necking. This technique is used to perturbate the material behavior in a rate dependent formulation by superimposing a perturbation to the basic flow. Its stability or instability is characterized by the increasing or decreasing of the perturbation. Hardening and initial anisotropic parameters are fitted by experimental results from the literature. In this investigation, Cazacu yield function is used to predict the forming limit diagrams (FLD) of HCP sheet metals. The coupling between analytic perturbation method and the behavior modelling is provided by an efficient implicit algorithm to solve the constitutive equations. After verifications and validations of the numerical simulations from the literature, the ductility limit of a particular HCP magnesium alloy is numerically predicted. A parametric study is presented to analyze the effect of instability and mechanical parameters, viscosity and distortion on the FLD. Moreover, a comparative study between Marciniak and Kuckzynski ductility approach and linear perturbation technique is done in this contribution. Keywords: Necking criteria · Plastic instabilities · Forming limit diagrams · Hexagonal closed packed material · Behavior modelling · Linear perturbation technique
1 Introduction Formability in sheet metal forming process is required in many engineering applications (aircraft, aerospace, automotive, etc.) to predict its ductility limit. Furthermore, several theoretical works were developed to predict the wellknown forming limit diagrams © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 164–176, 2022. https://doi.org/10.1007/9783030849580_18
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(FLD). This concept will be carried out using a coupling between instability necking criterion and one or more than one phenomenological model. In fact, several instability criteria are developed to predict the occurrence of plastic instability in thin sheet metals. The wellused approach has been investigated by Marciniak and Kuckzynski (Marciniak and Kuczy´nski 1967) which is called in the rest of the current paper by MK. They have been introduced an initial geometric imperfection in order to obtain a theoretical complete FLD based on heterogeneous continuum model. This necking criterion is based on the comparison of the strain rate in only expansion domain. Several studies (Molinari 1985; Dudzinski and Molinari 1991; Boudeau and Gelin 1992, etc.) have been used a homogeneous continuum model where the necking is perturbed to be an instability of the mechanical equilibrium state. This alternative approach is called the linear perturbation analysis. It is used to predict the FLD by imposing a geometrical defect which generates to an imperfection on main strain rates. This technique leads to a linear perturbation at certain stage of deformation process of the thin sheet metals which are assumed to be initially homogeneous. Several contributions are investigated in last decades based on linear perturbation technique. Fressengeas and Molinari (1987) have been used the classical perturbation technique (Molinari 1985) taking into account the heat conduction to evolve the instability and localization effects of the plastic flow in shear at high strain rates. Perturbation analysis is used analytically to predict FLD for quite general material behavior based on their viscoplastic instabilities in biaxial loading (Dudzinski and Molinari 1991). The ductility limit has been predicted by Toth et al. 1996 using stress potential function for viscoplastic material. A computational prediction of the localized necking has been executed by Boudeau et al. (1998) based on microstructural material aspects using perturbation analysis. Boudeau et al. (2002) have been extended the linear stability analysis to three dimensions (3D) stress states to allow the detection of defects during hydroforming process. Recently, Zaera et al. (2015) have been investigated the spacing between necking bands in sheet thermoviscoplastic metals based on linear perturbation technique within a 2D framework. All previous investigations are dedicated especially for body centered cubic materials (BCC) and face centered materials (FCC). Hexagonal closed packed materials (HCP) have been used recently by several researchers due to their mechanical characteristics (lightweight, high specific strength, high fatigue resistance, etc.). In last decades, several researchers have been predicted the ductility limit of HCP materials (Wu et al. 2015; Kondori et al. 2018…) at room temperature. However, ductility limit predictions for HCP materials at room temperature are presented in limited works from the literature (Wu et al. 2015; Kondori et al. 2018…). Despite the limitation of ductility for HCP materials, many researchers have succeeded to model its mechanical behavior (Cazacu et al. 2006; Plunkett et al. 2006…) in order to predict its ductility limit (Jedidi et al. 2020a; Jedidi et al. 2020b…), at room temperature. The onset of localized necking of HCP materials is predicted numerically in the literature generally by MK analysis and bifurcation. In the current paper, the onset of localized necking of HCP sheet metals is predicted for the first time using the linear perturbation technique of Dudzinski and Molinari (1991) to assess and validate our
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numerical simulations. The constitutive model of Cazacu et al. 2006 is used at room temperature to model the mechanical behavior of HCP materials. A brief outline of this paper is presented by 5 sections. We have dedicated the Sect. 2 of this paper to the constitutive framework to model the mechanical behavior of HCP materials as well as the main equations which leads to define the linear perturbation technique. Whereas Sect. 3 outlines the numerical implementation of the MK instability criterion and constitutive equations of Sect. 2. The Sect. 4 provides the validation of the developed model and the numerical investigation. Then, it presents a comparative study to analyze viscosity and distortion effects, and to show the difference between linear perturbation technique and the MK approach in terms of FLD. Finally, Sect. 5 closes the present contribution by some conclusions and perspectives.
2 Theoretical Framework 2.1 Constitutive Model Due to the twinning mechanism which leads to tensioncompression asymmetry of the stress rate for HCP materials, the behavior modelling is estimated in this paper, by the yield locus of Cazacu et al. (2006) and briefly called CPB06. This model is expressed by the equivalent plastic stress: a a a 1/ a σ =B −k + −k + −k ,
1
1
2
2
3
(1)
3
where B is a material parameter, k describes the asymmetry of the deformation behavior, 1 , 2 and 3 are the eigenvalues of the linear transformation equals to L : T : σ such as L is the fourthorder transformation tensor and T is the passage matrix: ⎞ ⎛ ⎞ ⎛ 2 −1 −1 0 0 0 L11 L12 L13 0 0 0 ⎜ −1 2 −1 0 0 0 ⎟ ⎜L L L 0 0 0 ⎟ ⎟ ⎜ ⎟ ⎜ 12 22 23 ⎟ ⎟ ⎜ 1⎜ ⎜ −1 −1 2 0 0 0 ⎟ ⎜ L13 L23 L33 0 0 0 ⎟ (2) L =⎜ ⎟, T = ⎜ ⎟. ⎜ 0 0 0 L44 0 0 ⎟ 3⎜0 0 0 3 0 0⎟ ⎟ ⎜ ⎟ ⎜ ⎝0 0 0 0 3 0⎠ ⎝ 0 0 0 0 L55 0 ⎠ 0 0 0 003 0 0 0 0 0 L66 In this investigation, the hardening law is supposed isotropic, isochoric and obeys to the normality law. Moreover, the assumption of a rigid viscoplastic material is done. The used Swift hardening law in this work is presented by:
m ˙ n σy = σ˜ = K ε0 + ε ε , (3) ˙ where ε is the equivalent strain and ε the equivalent strain rate, K the hardening parameter, n the hardening exponent and m is the rate sensitivity exponent.
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The constitutive relation between the strain rate and its equivalent is expressed in this contribution by the associated flow rule using the normal vector on the yield locus ∂ σ /∂ σ:
˙ ∂σ P ε =ε , ∂σ
(4)
2.2 Linear Perturbation Technique The principle of the perturbation technique is described as shown in Fig. 1. Note that x 1 x 2 is a plane coordinate system, which is referred for wavy line. The second coordinates system xy refers the sheet metal. Two parameters characterize geometrically the instability mode; the angle orientation ψ of x 1 x 2 and the wave number ξ . Thus, the perturbation δP0 is described as below: δP =δP0 exp(η(t − t0 ) exp(i ξ.x1 )),
(5)
where (t − t0 ) is the time of the perturbation, δP0 is the initial perturbation and η is
the rate of the growth of the perturbation knowing that if Re η˙ < 0 ⇒ stability and ε η if Re ˙ > 0 ⇒ instability. The perturbation described in Eq. (5) leads to obtain the ε
homogeneous solution in the rotated frame. However, this solution requires equilibrium equations, compatibility and incompressibility conditions.
Fig. 1. Linear perturbation in thin sheet metal.
In case of long wave perturbation and plane stress condition (Fig. 1) the equilibrium equation are: ⎧ ∂(hσ11 ) ∂(hσ12 ) ⎪ ⎪ + =0 ⎨ ∂x1 ∂x2 div(hσ) = 0 ⇔ , (6) ∂(hσ12 ) ∂(hσ22 ) ⎪ ⎪ ⎩ + =0 ∂x1 ∂x2 where h equals to h0 exp(ε33 ) is the current thickness of the thin sheet metal, h0 is the initial thickness and ε33 is related to ε11 and ε22 within incompressibility condition.
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Aside the equilibrium equation to the homogeneous solution, the compatibility condition can be expressed as: ∂ 2 ε˙ 11 ∂ 2 ε˙ 12 ∂ 2 ε˙ 11 + = 2 , ∂x1 ∂x2 ∂x22 ∂x12
(7)
and the incompressibility condition in the rotated reference system is expressed as: ε˙ 11 + ε˙ 22 + ε˙ 33 = 0
(8)
Based on the investigation of Dudzinski and Molinari (1991) and Toth et al. (1996), strain rates ε˙ 11 , ε˙ 22 and ε˙ 33 can be expressed in the fixed coordinate system x 1 x 2 by:
˙ ∂σ ˙ = εTxx , ε˙ xx = ε ∂σxx ε˙ yy
˙ ∂σ ˙ =ε = εTyy , ∂σyy
(9)
˙ ∂σ ˙ ε˙ xy = ε = εTxy . ∂σxy However, the flow law in the rotated reference system has to be expressed by:
˙ ˙ ε˙ 11 = εT11 = ε Txx cos2 (ψ) + Tyy sin2 (ψ) + Txy sin(2ψ) ,
˙ ˙ (10) ε˙ 11 = εT22 = ε Txx sin2 (ψ) + Tyy cos2 (ψ) − Txy sin(2ψ) , ˙ ˙ ε˙ 12 = εT12 = ε Txy − Txx sin(ψ) cos(ψ) + Txy cos(2ψ) , Cauchy stress are also described in the rotated frame by: σ11 = σxx cos2 (ψ) + σyy sin2 (ψ) + σxy sin(2ψ), σ22 = σxx sin2 (ψ) + σyy cos2 (ψ) − σxy sin(2ψ), σ12 = σyy − σxx sin(ψ) cos(ψ) + σxy cos(2ψ).
(11)
Using all previous equations, the homogeneous solution in the rotated frame at time t 0 is a vector which contains 10 initial values. Thus, this vector is given by: ˙0 0 0 0 0 0 0 0 0 0 0 0 P = ε˙ 11 , ε˙ 22 , ε˙ 33 , ε˙ 12 , ε˙ 11 , ε˙ 22 , ε˙ 12 , σ12 , σ , ε , h (12) Due to this relation: h = h0 exp(ε33 ), the thickness h can be eliminated. Thus, for each value of the angle orientation ψ, the unknown vector P contains 9 initial values without considering the thickness h. At t = t0 , the homogeneous solution is tested by superposing small perturbations δP. Therefore, components of the perturbed solution P equals to P0 + δP0 exp(η(t − t0 )exp(iξ.x1 )) are: 0 0 0 0 + δ˙ε11 ,˙ε22 = ε˙ 22 + δ˙ε22 ,˙ε33 = ε˙ 33 + δ˙ε33 ,˙ε12 = ε˙ 12 + δ˙ε12 , ε˙ 11 = ε˙ 11 0 0 0 + δσ11 ,σ22 = σ22 + δσ22 ,σ12 = σ12 + δσ12 . σ11 = σ11
(13)
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δP 0
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˙0 0 0 0 0 0 0 0 0 0 = δ˙ε11 , δ˙ε22 , δ˙ε33 , δ˙ε12 , δσ11 , δσ22 , δσ12 , δσ , δ ε , δh is the polar
ization vector. Due to linearization of the previous equations, the vector polarization is supposed as solution of the nine equations already calculated and presented by Toth et al. (1996). Based on their investigation, a nonlinear operator called O is a function of the perturbed vector. This nonlinear system is linearized by neglecting the exponential part of the perturbation. This is due to the small perturbation at the initial stage compared by the regular solution. Thus, the nonlinear function O is described by:
O(P) = O P0 + δP0 exp(η(t − t0 )exp(iξ.x1 )) = O P0 + δP0 . (14) This leads to the following linear system:
M P0 ,ηc ,ψ .δP0 = 0. where ηc =
(15)
η
and M is a matrix made up based on nine equations in the work of Toth et al. (1996). A, the regular solution is obtained when det M P0 ,ηc ,ψ .δP0 = 0, to give finally the polynomial equation which is a function of ψ and ηc : ηc a(ψ)ηe2 + b(ψ)ηe + c(ψ) = 0, (16) ˙ ε
where components of a(ψ), b(ψ) and c(ψ) are described with details in the contribution of (Toth et al. 1996). For each angle orientation ψ, three values of ηc are obtained. The ηc = 0 is a possible solution. However, it is neglected because it does not occur a growing instability. Moreover, two other solutions of ηc are generally complex. To pass from stability to instability, one of the three roots has a positive real part; Re(ηc ) ≥ e where e is the effective instability parameter (Dudzinski and Molinari 1991). Note that if e = 0, the absolute instability is observed. Based on the work of Dudzinski and Molinari (1991), several values of e (0 < e < 25) leads to an instability. For each angle orientation, we obtain the strain value which the material can be deformed. To characterize the critical strain value εc and the optimal orientation of the band ψ c , we minimize the strain value by the absolute value εa : εa (e, ρ) = min εa (e, ρ, ψ) = εa e, ρ, ψ c (17) It is very important to note that Dudzinski and Molinari (1991) has been shown that general bifurcation is obtained when the effective parameter e → ∞ and the rate sensitivity exponent equal zero. After the definition of perturbation technique theoretically, numerical implementation is clearly presented in Sect. 3.
3 Implicit Incremental Algorithm The prediction of the ductility limit for viscoplastic material using the linear perturbation analysis is clearly described as below:
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Step 1: calculate ∂σ∂σ to obtain Eq. 18. This step is based on the derivative formulation ij ∂σkl described in the appendix of the contribution of (Jedidi et al. 2020b). Step 2: solve the following four equations from the integration code to calculate Cauchy stress components and the equivalent plastic strain: 2
ε = ε
∂σ → σ11 =?; σ22 =?; σ12 =?. ∂σ
σ = ε = ε.σ → ε =?.
(18) (19)
˙ In this step, we obtain P = ε˙ 11 , ε˙ 22 , ε˙ 33 , ε˙ 12 , σ11 , σ22 , σ12 , σ , ε . Step 3: consider the previous solutions as initial solution in perturbed equations. Thus, the initial solution P0 to begin the perturbation is equal to P. Moreover, the resolution of the new solution P is based these contributions (Toth et al. 1996; Jedidi et al. 2020.b), and the previous equations from 1 to 16. Step 4: solve the polynomial equation for each increment and each angle orientation. This step describes the resolution of the polynomial equation (Eq. 18) for ψ from 0° to 90°. Step 5: if the instability condition is observed for an iteration and a strain path, iterative calculation is stopped. Thus, for each ψ, if ηc > e and nε˙ < 1 → calculation is stopped. The prediction of FLD is ensured by means a two nested loops of an efficient algorithm implemented in the multiparadigm, numerical computing environment Mathematica, as shown as below: • For the strain path ratio ρ = −1/2 to ρ = 1 with ρ = 0.1. • For t = t0 to t = tn+1 with t =n+1 tn + t and t is the time increment tn , t =n+1 . – Apply the implicit incremental algorithm described in the previous section. If ηˆ > e and nε˙ < 1 → the implicit algorithm is stopped. c = min{ε } and ε c = ρε c where ε c and ε c are – Over all possible initial angles, ε11 11 22 11 11 22 the major and minor localization limit strains.
4 Results and Discussions To predict the FLD of HCP materials, Cazacu yield criterion is chosen in this investigation (CPB06) as the constitutive model. This yield criterion is extremely dependent to anisotropic parameters of the material. MagnesiumLithium alloy (MgLi (4% Li)) is used in our contribution to predict FLD. However, before using this alloy, we should validate our work. Dudzinski and Molinari (1991) have been used an isotropic material which its isotropic parameters are K = 120 MPa, n = 0.25 and ε0 = 0. Figure 2 presents a comparison between the FLD predicted numerically by our simulation and the FLD predicted by Dudzinski and Molinari (1991). It is very clear
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that the ductility limit for anisotropic material is in good agreement with the work of Dudzinski and Molinari (1991) for uniaxial tensile test. For plane strain and biaxial loading, a small difference between FLD is clearly shown in Fig. 2a which can be due to the method of the implementation of the linear perturbation technique in our numerical simulations. Figure 2b presents for a viscous isotropic material, the evolution of the positive real part of the root solved from Eq. 18. This evolution is represented versus the strain ε11 for plane strain (ρ = 0). A good correlation is shown in this figure (Fig. 2b) between the work of Dudzinski and Molinari (1991) and our numerical predictions. Thus, our numerical simulations are assessed and validated with the work of Dudzinski and Molinari (1991). 60 1 1
our simulation
our simulation
Dudzynski and Molinari, 1991
Dudzynski and Molinari, 1991
0.35
50
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40 0.25
c
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0
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0.3
1 1
2 2
(a): Forming limit diagrams (m=0)
(b): Evolution of the rate
ηc (m=105)
Fig. 2. Comparison between numerical simulations and the work of Dudzinski and Molinari 1991
After validation of our numerical model, we predict in this contribution the ductility limit for MgLi 4% which is soft and ductile. The choose of HCP material in this work is dependent on experimental results to predict anisotropic parameters of CPB06. A fitting method is used in a numerical implementation to predict anisotropic parameters from an experimental yield locus. Thus, our investigation is based on experimental results of Cazacu et al. (2006) for the MgLi (4% Li) as shown in Fig. 3. This figure (Fig. 3) presents a good correlation between our fitted yield surface and experimental points. Table 1. Material parameters for the MgLi (4% Li) magnesium alloy (stresslike parameters are expressed in MPa). Hardening K
n
405.26 0.166 Anisotropy LC 11
LC 22
ε0 0.0015 LC 33
LC 12
LC 23
LC 13
1
0.9783 0.1648 0.6114 0.2479 0.7819
LC 44
LC 55
LC 66
a
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1
1
1
2
0.2126
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This good agreement signifies that our fitted anisotropic parameters are validated for the MgLi 4%. Numerical predictions of fitting based on experimental results gives the anisotropic and swift hardening parameters based on CPB06 as shown in Table 1. We note that hardening parameters are fitted in this contribution based on the experimental hardening curve of Bochniak et al. (2018).
Fig. 3. Experimental (points) and fitted (lines) yield locus of MgLi (4% Li)
Fig. 4. Effect of instability parameter e on FLD
Validation of our numerical simulations and fitting of anisotropic parameters based on experimental results allow to predict the ductility limit of the magnesium alloy MgLi 4%. Forming limit diagrams predicted by the coupling between CPB06 yield criterion and linear perturbation method are strongly dependent on the effective instability parameter e. This parameter can be varied between 1 and 25, thus, we can obtain an infinity of FLD as presented in Fig. 4. The onset of instability corresponds to e = 0. However, the instability is effective only for a significantly large value of e. The linearized analysis presented here is completely justified for a large enough values of e. In this paper, a reasonable value (e = 20) is fixed for the rest of this paper.
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In order to enhance the behavior modelling of the magnesium alloy MgLi 4% in nonproportional loading, a modification of the classical CPB06 model including distortion of the yield surface is proposed. Thus, yield surface distortions depends on new material parameters at a variety of strains scales. Consequently, it is very important to identify distortion effects on FLD. A preliminary study is done to identify anisotropic parameters at a variety of strain scales (1%, 5% and 10% in our contribution). This study is based on fitting using experimental results. Fitted anisotropic parameters presented in Table. 2 allow to predict three yield surfaces at 1%, 5% and 10% of strain. In this paper, linear interpolation technique employed in Plunkett et al. (2006) is used to predict anisotropic parameters for each value of strain to predict FLD using these three fitted yield surface. Table 2. Material parameters for the MgLi (4% Li) magnesium alloy at a variety of strain scales (stresslike parameters are expressed in MPa). Anisotropy: 1% of deformation
C LC LC LC LC LC 11 L22 33 12 23 13 1 0.9783 0.1648 0.6114 0.2479 0.7819 C LC 44 L55 1 1
Anisotropy: 5% of deformation
Anisotropy: 10% of deformation
LC 66
a
k
1
2
0.2126
C LC LC LC LC LC 11 L22 33 12 23 13 1 0.9783 0.2017 0.5492 0.4077 0.6056 C LC 44 L55 1 1
LC 66
a
k
1
2
0.2249
C LC 11 L22
LC 33
LC 12
LC 23
1
LC 13
0.9783 0.6622 0.7590 0.8985 0.9305
C LC 44 L55 1 1
LC 66
a
k
1
2
0.0472
Figure 5a presents two forming limit diagrams with and without taking into account distortion of yield surface. Distortion has no effect on FLD in uniaxial tensile test and plane strain. However, the level and the shape of the FLD is sensitive to distortion in biaxial stretching, especially for the strain path ratio ρ equals more than 0.3. This sensitivity to distortion allows the increasing of the ductility limit on the positive part of FLD. Nevertheless, distortion has almost no effect on the band orientation for all strain path ratio as shown in Fig. 5b. Actually we intend to predict the onset of the localized necking in a MgLi 4% magnesium sheet alloy using the MK ductility approach. Our goal is to compare our FLD predicted by MK approach with FLD predicted by linear perturbation technique. For MK ductility approach, the used initial imperfection factor in this work equals to 0.995. Figure 6a shows a comparison between FLD predicted by linear perturbation technique and MK ductility approach, respectively. A higher ductility of the MgLi 4%
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(a): Forming limit diagram
(b): Band orientation
Fig. 5. Effect of distortion (m = 0)
magnesium alloy is obtained by the perturbation technique for all strain path ratio except the equibiaxial stretching. This is due to the initial imperfection factor proposed by MK which increases the values of major strains, especially in biaxial stretching. Numerical simulations of the initial imperfection model take a huge calculation time to predict an FLD compared with the perturbation technique.
(a): Comparison between perturbation technique and MK ductility (FLD).
(b): Linear perturbation method
(c): MK ductility approach
Fig. 6. (a): Comparison between 2 necking criteria; (b) and (c): Effect of viscosity on FLD
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Effect of viscosity on FLD is an important thing for scientific researchers. For this reason, we predict in this work the ductility limit for plastic material and viscoplastic material using two different necking criteria (MK ductility approach and linear perturbation technique). Figure 6b presents two FLD predicted by perturbation techniques which have the same shape, but not the same level. It is clear that viscosity allow to increase the ductility limit of the material. This increase is due to the rate sensitivity exponent m of the equivalent strain rate. Thus, we obtain a highest hardening curve. The sensitivity of m on hardening allows to obtain highest values of major strain. Consequently, we obtain highest level of FLD. Same conclusions describe the effect of viscosity on FLD predicted by MK ductility approach as shown in Fig. 6c.
5 Conclusions In this paper, the problem of plastic instabilities in biaxial sheet deformation is solved by using the linear perturbation technique. This technique was coupled with the phenomenological model presented in Cazacu et al. (2006) to predict the forming limit for the MgLi 4% magnesium alloy. Based on constitutive equations presented in this contribution, a robust numerical procedure is implemented to describe the linear perturbation technique. This numerical procedure is used in conjunction with two plastic instability criteria (the linear perturbation technique and the initial imperfection approach), to predict the onset of necking in HCP materials. From results of the numerical predictions, our simulations are assessed and validated with Dudzinski and Molinari (1991) for anisotropic material. After validation of our numerical results, a sensitivity study is conducted to analyze the effect of the instability parameter on the necking limit after fitting anisotropic parameters of the MgLi 4% magnesium alloy based on experimental results of Cazacu et al. (2006). Bifurcation analysis for rate independent formulation appears clearly when this effective instability parameter e→∞. A linear interpolation is used to take into account of the distortion of the yield surface. The shape and the level of the predicted forming limit diagrams are strongly sensitive to the effective instability parameter, distortion and viscosity, especially in biaxial stretching. The level of limit strains predicted by the initial imperfection approach is inferior to limit strain predicted by the perturbation method. Consequently, with the linear perturbation, ductility limit of MgLi 4% increases. The implementation of the proposed implicit integration algorithm into a finite element code using damage model and nonassociated model will be the subject of the future investigations.
References Boudeau, N., Gelin, J.C.: Finite element simulation of the ductile fracture in 3D sheet metal forming process. J. Mater. Process. Technol. 32(1–2), 521–530 (1992) Boudeau, N., Gelin, J.C., Salhi, S.: Computational prediction of the localized necking in sheet forming based on microstructural material aspects. Comput. Mater. Sci. 11(1), 45–64 (1998) Boudeau, N., Lejeune, A., Gelin, J.C.: Influence of material and process parameters on the development of necking and bursting in flange and tube hydroforming. J. Mater. Process. Technol. 125, 849–855 (2002)
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Bochniak, W., Korbel, A., Ostachowski, P., Łagoda, M.: Plastic flow of metals under cyclic change of deformation path conditions. Arch. Civil Mech. Eng. 18(3), 679–686 (2018). https://doi.org/ 10.1016/j.acme.2017.11.004 Cazacu, O., Plunkett, B., Barlat, F.: Orthotropic yield criterion for hexagonal closed packed metals. Int. J. Plast. 22(7), 1171–1194 (2006) Dudzinski, D., Molinari, A.: Perturbation analysis of thermoviscoplastic instabilities in biaxial loading. Int. J. Solids Struct. 27(5), 601–628 (1991) Fressengeas, C., Molinari, A.: Instability and localization of plastic flow in shear at high strain rates. J. Mech. Phys. Solids 35(2), 185–211 (1987) Jedidi, M.Y., Bettaieb, M.B., Bouguecha, A., AbedMeraim, F., Khabou, M.T., Haddar, M.: Prediction of the ductility limit of magnesium AZ31B alloy. In: Chaari, F., et al. (eds.) Advances in Materials, Mechanics and Manufacturing. LNME, pp. 182–193. Springer, Cham (2020). https://doi.org/10.1007/9783030242473_21 Jedidi, M.Y., Bettaieb, M.B., AbedMeraim, F., Khabou, M.T., Bouguecha, A., Haddar, M.: Prediction of necking in HCP sheet metals using a twosurface plasticity model. Int. J. Plast. 128, 102641 (2020) Kondori, B., Madi, Y., Besson, J., Benzerga, A.A.: Evolution of the 3D plastic anisotropy of HCP metals: experiments and modeling. Int. J. Plast. (2018).https://doi.org/10.1016/j.ijplas.2017. 12.002 Marciniak, Z., Kuczy´nski, K.: Limit strains in the processes of stretchforming sheet metal. Int. J. Mech. Sci. 9(9), 609IN1613–612IN2620 (1967) Molinari, A.: Instabilité thermoviscoplastique en cisaillement simple. J. de mécanique théorique et appliquée 4(5), 659–684 (1985) Plunkett, B., Lebensohn, R.A., Cazacu, O., Barlat, F.: Anisotropic yield function of hexagonal materials taking into account texture development and anisotropic hardening. Acta Mater. 54(16), 4159–4169 (2006) Toth, L.S., Hirsch, J., Van Houtte, P.: On the role of texture development in the forming limits of sheet metals. Int. J. Mech. Sci. 38(10), 1117–1126 (1996) Wu, S.H., Song, N.N., Pires, F.M.A., Santos, A.D.: Prediction of forming limit diagrams for materials with HCP structure. Acta Metall. Sin. 28(12), 1442–1514 (2015). https://doi.org/10. 1007/s4019501503443 Zaera, R., RodríguezMartínez, J.A., Vadillo, G., FernándezSáez, J., Molinari, A.: Collective behaviour and spacing of necks in ductile plates subjected to dynamic biaxial loading. J. Mech. Phys. Solids 85, 245–269 (2015)
Effect of AirGas Blend and Compression Ratio on Piston Behavior for HydrogenEnriched LPG Engine; Numerical Study Sahar Hadjkacem1(B) , Mohamed Ali Jemni1 , Hamdi Hentati2 , Zied Driss1 , and Mohamed Salah Abid1 1 National School Engineers of Sfax, Laboratory of the Electromechanical Systems, University
of Sfax, BP 1173, Road of Soukra, 3038 Sfax, Tunisia 2 LA2MP Laboratory, National School of Engineers of Sfax, University of Sfax, Sfax, Tunisia
Abstract. The adoption of alternative fuel engines has been considered as one of the most important strategies to solve the problems of energy dependence and air quality. The use of LPGHydrogen blends in internal combustion engines is an effective alternative to pure fossil fuels because of its high efficiency and its superior properties. Small percentage of hydrogen addition can improve LPG engine performance. In this study, the effects of Hydrogen enrichment and compression ratio on engine piston are numerically evaluated on a gaseous engine. Piston made of Aluminum alloy, is a primordial part and behaves as heart of the internal combustion engine. Furthermore, the stress distribution is evaluated on the piston of engine fueled with LPGH2 blend by using finite element analysis technique. In the present study, the piston model is developed using Solidworks software. The analysis part was carried out using SolidworksSimulation for static analysis. The mechanical stresses distribution is calculated. AlpaxAluminum alloy is used as piston material. The results showed that increasing Hydrogen volumetric fraction and compression ratio have similar effects on the engine incylinder pressure. The stress analysis results also showed that the piston resistance of the converted engine is verified. A comparison with literature work is performed to validate the numerical work. Keywords: LPG engine · Hydrogen · Compression ratio · Incylinder pressure · Piston material
1 Introduction Numerous scientists have been forced by ecological problems and exhaustion of oil potentials to perform in the area of using alternative fuels in SI engines which must be renewable and clear. Typical alternative fuels consist of liquefied petroleum gas (LPG), compressed natural gas (CNG), biodiesel, and hydrogen. Among them, LPG produces lower carbon emissions and gives better fuel efficiency than the most common fuels such as gasoline and diesel (Woo et al. 2020; Jemni et al. 2020). Moreover, the use of © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 177–184, 2022. https://doi.org/10.1007/9783030849580_19
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Hydrogen in combination with petroleumderived fuels in internal combustion engines can reduce toxic exhaust emissions from fossil fuels (Hadj Kacem et al. 2016). The study of the effect of the use of alternative fuels in engines is generally carried out using either the experimental process or the numerical and analytical modeling process. Two usually types of computational modeling strategies are thermodynamic modeling and computational fluid dynamics (CFD) are used. The first uses the laws of thermodynamics to determine parameters such as the incylinder pressure and temperature, whereas the second solves the incylinder processes as a fluid flow using defined boundary conditions. The advantage of using thermodynamic analysis compared to CFD is run time. Indeed, the thermodynamic models are usually adopted to provide the engine combustion performances (Selmane et al. 2020). Because it’s a clarified approach to the various incylinder phenomena concerned in the combustion stroke, the thermodynamic zerodimensional model is generally used to calculate the incylinder combustion procedure (Ricardo et al. 2020). Several scientists were developed thermodynamics models for the combustion procedure simulation of Hydrogen blends engines (Hadjkacem et al. 2020; Khodamrezaee and Keshavarz 2020). On the other hand, thermodynamic analyses are developed by many researchers to study the impact of Hydrogen enrichment on parameters of gaseous engine (Ayad et al. 2020; Djermouni and Ouadha 2021). A careful examination of the above literature review indicates that the compression ratio (CR) has an effect on the performances of a Hydrogen blends engine (Sanli and Yilmaz 2020). With the conversion of the gasoline engine to H2 enriched LPG, the pressure in the combustion chamber is modified, i.e. the force applied to the engine’s pistons is also modified. A piston is the mobile element, it is contained by a cylinder and their rings made gastight. As an important element in an engine, piston supports the inertial forces at work and the cyclic gas pressure. This condition of work can cause the piston fatigue damage, like piston head cracks, piston side wear and so on (Kumar 2016). The main objective is to investigate and analyze the mechanical stress distribution of engine piston at the real operating conditions. The piston model was designed in Solidworks then imported into solidworkssimulation for static analysis. The parameters of simulation used in this study were piston material and combustion pressure. This numerical study is carried out in order to validate the compression ratio found in thermodynamic study of LPG20H2 engine.
2 Presentation of Problematic This section describes the theoretical background used as basis for evaluating the structure of the piston of LPGH2 engine when using different percentage of Hydrogen. The engine test bench is illustrated in Fig. 1. To analyze the effects of various operating parameters on the engine piston structure, the thermodynamic models can be used. They are more flexible and cheaper than experimental studies and CFD models. Modeling is carried out based on the zero zone model. For the static study of the piston, it has been considered that the charge applied on the piston is treated as a uniformly distributed charge on the free surface of the piston and that the centrifugal forces linked to the piston motion are neglected compared to the force resulting from the combustion.
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All the necessary equations for the thermodynamic study are given in a previous work (Hadjkacem et al. 2020; Heywood 1988). Basing on the equations describing the kinematics of the connecting rodcrank mechanism, we can define the thermodynamic parameters acting on the compression ratio. The ideal gas equation is written as follows: P V (θ ) = N R T
(1)
By integrating Laplace’s law, the equation becomes: pV (θ )γ = cst
(2)
where: γ: Isentropic coefficient.
Fig. 1. Engine test bench
3 Results and Discussions This section develops a comprehensive study of incylinder pressure for different Hydrogen percentage and compression ratios. Also, a static study of engine piston using 20%H2 is developed. 3.1 Effect of the Compression Ratio on the InCylinder Pressure Incylinder pressure analysis is a key tool for engine research, it is a significant thermodynamic parameter directly related to the volumetric efficiency of engine. In fact, Figs. 2, 3, 4 and 5 exhibit the incylinder pressure curves against crank angle for LPG0% H2 , LPG30% H2 , LPG40% H2 and LPG50% H2 respectively. Results have been obtained for different values of engine compression ratio (CR = 9, 9.7 and 11). According to the
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graphs, the incylinder pressure peak rises remarkably with the rise of the engine compression ratio. Moreover, it can be noticed that the peak of incylinder pressure plotted in Fig. 5 is the higher compared to that in the other figures. The rapid pressure rates rise along using LPG50% H2 blend operation (see Fig. 5), hence reducing NOx emissions and the engine knock possibility. When we have CR = 9.7 and LPG50% H2, a higher pressure peak position with a value of 1.12% higher compared to pure LPG is observed. This phenomenon is linked to the higher hydrogen burning velocity (Hariharan et al. 2019). As a result, using CE = 9.7 (the original engine compression ratio) gives acceptable results for all Hydrogen mixtures.
Incylinder pressure (bar)
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30 25 20 15 10 5 0 50
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Fig. 2. Incylinder pressure versus compression ratio using LPG 0%H2
3.2 Comparison with the Literature Work Figure 6 shows a comparison of the thermodynamic model with the results found in the literature study of incylinder pressure. The present comparison is performed for an LPG15H2 blend and an CR = 10.5. A similarity in the all curves appearance is observed with the existence of a negligible difference between them. This observation confirms the reliability of used thermodynamic model. The error average value between the two curves is equal to 7.1%, which represents a minor value. 3.3 Verification of Piston Resistance Versus InCylinder Pressure Structural analysis is carried out on the piston using Alluminium alloy (alpax) as material using finite element analysis. Also a pressure on the piston head for different engine
Effect of AirGas Blend and Compression Ratio on Piston Behavior
Incylinder pressure (bar)
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40 35 30 25 20 15 10 5 0 50
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Fig. 3. Incylinder pressure versus compression ratio using LPG 30%H2
Incylinder pressure (bar)
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40 35 30 25 20 15 10 5 0 50
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Fig. 4. Incylinder pressure versus compression ratio using LPG 40%H2
compression ratio. This part is carried out for a fuel blend of LPG20H2 . In this case, the maximum pressure is equal to 32.24 bar. It is observed by the following figure that the stress for all used compression ratio is within the allowable limits of the respective material.
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40 35 30 25 20 15 10 5 0 50
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Fig. 5. Incylinder pressure versus compression ratio using LPG 50%H2
Fig. 6. Incylinder pressure comparison with literature work
By comparing the results, it can be easily concluded that the piston holds up well using the compression ratio 9.7, this is the engine’s original compression ratio (Fig. 7).
Effect of AirGas Blend and Compression Ratio on Piston Behavior
a.
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Fig. 7. Distribution of Von Mises stress
4 Conclusion In this work, finite element analysis of the engine piston with different compression ratio was performed at the real operating conditions. This numerical study is carried out in order to validate the compression ratio found in thermodynamic study of LPG20H2 engine. From the results it is concluded that: • Incylinder pressure increase using CR = 9.7 and LPG50% H2 compared to pure LPG of 1.12%. • Structural Static Analysis of Piston shows that the piston holds up well using the engine’s original compression ratio (CR = 9.7). • There is a satisfactory agreement between the numerical simulation, the experimental and literature studies.
Acknowledgements. The authors express their gratitude to National School of Engineers of Sfax (ENIS) and Laboratory of the Electromechanical Systems (LASEM) for supporting this research and supplying us with valuable numerical data.
References Ayad, S.M.M.E., Belchior, C.R.P., Silva, G.L.R., Lucena, R.S., Carreira, E.S., Miranda, P.E.V.: Analysis of performance parameters of an ethanol fueled spark ignition engine operating with hydrogen enrichment. Int. J. Hydrogen Energy 45(8), 5588–5606 (2020). https://doi.org/10. 1016/j.ijhydene.2019.05.151 Djermouni, M., Ouadha, A.: Hydrogen versus alternative fuels in an HCCI engine: a thermodynamic study. In: Khellaf, A. (ed.) Advances in Renewable Hydrogen and Other Sustainable Energy Carriers. SPE, pp. 211–220. Springer, Singapore (2021). https://doi.org/10.1007/9789811565953_28 Hadj Kacem, S., Jemni, M.A., Driss, Z., Abid, M.S.: The effect of H2 enrichment on incylinder flow behavior, engine performances and exhaust emissions: case of LPGhydrogen engine. Appl. Energy 179, 961–971 (2016). https://doi.org/10.1016/j.apenergy.2016.07.075 Hadjkacem, S., Jemni, M.A., Driss, Z., Abid, M.S.: Effect of engine compression ratio on thermodynamic behavior using alternative hydrogenLPG fuel. Energy Sources Part A: Recov. Util. Environ. Effects (2020). https://doi.org/10.1080/15567036.2020.1839146
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Hariharan, N., Senthil, V., Karthic, S.V., Krishnamoorthi, M.: Influence of hydrogen enrichment on the combustion, efficiency and emissions of dual fuel engine. Energy Sources Part A: Recov. Util. Environ. Effects (2019). https://doi.org/10.1080/15567036.2019.1675816 Heywood, J.: Internal Combustion Engine Fundamentals. Automotive Technology Series. McGrawHill, New York (1988). ISBN 9780071004992 Jemni, M.A., HadjKacem, S., Ammar, M., Saaidia, R., Brayek, M., Abid, M.S.: Variable intake manifold geometry influence on volumetric efficiency enhancement at gaseous engine starting speeds. Proc. IMechE Part E: J. Process. Mech. Eng. (2020). https://doi.org/10.1177/095440 8920973129 Khodamrezaee, F., Keshavarz, A.: Thermodynamic and experimental analysis of hydrogen addition to CNG in a spark ignition engine for emission reduction. Energy Sources Part A: Recov. Util. Environ. Effects (2020). https://doi.org/10.1080/15567036.2020.1743388 Kumar, K.S.: Design and analysis of I.C. engine piston and pistonring on composite material using Creo and Ansys software. J. Eng. Sci. 01(01) (2016) Gutiérrez, R.H.R., Monteiro, U.A., Vaz, L.A.: Predictive thermodynamic model of the performance of a stationary sparkignition engine running on natural gas. J. Braz. Soc. Mech. Sci. Eng. 42(8), 1–16 (2020). https://doi.org/10.1007/s4043002002496y Ravi, K., Bhasker, J.P., Porpatham, E.: Effect of compression ratio and hydrogen addition on part throttle performance of a LPG fuelled lean burn spark ignition engine. Fuel 205, 71–79 (2017). https://doi.org/10.1016/j.fuel.2017.05.062 Sanli, A., Yilmaz, I.T., Gumus, M.: Assessment of combustion and exhaust emissions in a commonrail diesel engine fueled with methane and hydrogen/methane mixtures under different compression ratio. Int. J. Hydrogen Energy 45(4), 3263–3283 (2020). https://doi.org/10.1016/j.ijh ydene.2019.11.222 Selmane, F., Djermouni, M., Ouadha, A.: Thermodynamic modeling of a turbocharged diesel– hydrogen dualfuel marine engine. J. Inst. Eng. (India) Ser. C 102(1), 221–234 (2020). https:// doi.org/10.1007/s4003202000633z Woo, S., Baek, S., Lee, K.: Onboard LPG reforming system for an LPG.hydrogen mixed combustion engine. Int. J. Hydrogen Energy 45, 12203–12215 (2020). https://doi.org/10.1016/j.ijh ydene.2020.02.139
Dynamic Modeling of Diﬀerential Bevel Gear with UncertainbutBounded Parameters Wassim Laﬁ1(B) , Fathi Djmal1 , Ali Akrout1,2 , Lassad Walha1 , and Mohamed Haddar1 1
2
Mechanics, Modeling and Production Laboratory (LA2MP), National Engineering School of Sfax, University of Sfax, Sfax, Tunisia [email protected], [email protected] National Engineering school of Tunis, University of Tunis El Manar, Tunis, Tunisia
Abstract. The existence of the diﬀerential mechanism is imperative in all vehicles. Its importance stems from allowing the side wheels to have diﬀerent angular velocities. However, its dynamic response remains mysterious due to a unique arrangement of the bevel gears making up the system and uncertainties in its physical parameters that cannot be determined statistically. In this paper, a 3D automotive diﬀerential system has been proposed in the hope of scrutinizing it dynamically. Dynamic equations have been derived utilizing NewtonEuler formulation. Besides uncertainties in masses of the components and bearing stiﬀnesses, mesh stiﬀness functions tackling the variation of the number of pairs of teeth in contact are considered to be timevarying uncertain parameters. The Chebyshev interval process has been used for analyzing the system with interval parameters. The dynamic displacement bounds have been determined by using newmark resolution methods along with the interval process model. The results have been compared with those determined by the scanning method. The results showed the accuracy of the proposed method is very high. The algorithm presented in this paper can handle uncertain system with multiple interval variables. This study can be regarded as an important threshold to analyze the limitedslip diﬀerential dynamically in much detail. Keywords: Automotive diﬀerential · Interval analysis gear · Chebyshev interval process · Mesh stiﬀness
1
· Straight bevel
Introduction
A diﬀerential bevel gear is an essential mechanical component in most vehicles. Without it, a car can not take a curve properly. Using this mechanism can not only allow the car to take a curve, but it can also avoid posing the axle under excessive strain. In order to achieve the latter aim, the diﬀerential system has a unique conﬁguration that makes it elusive to be analyzed dynamically. c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 185–194, 2022. https://doi.org/10.1007/9783030849580_20
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The complexity stems mainly from the type of gear used in the mechanism and the way bevel gears are arranged. But it is imperative to understand how to analyze the system dynamically to observe the vibration level in the diﬀerential mechanism and to pave the way for amelioration and intervention in case of noticing any of the faults in it. In contrasts to the parallelshafts gear system[1], a few studies have been devoted to analyzing diﬀerential mechanisms consisting of a set of bevel gears. Some of them are: Morselli et al. [2] proposed the reduced and detailed dynamic models to simulate four types of diﬀerential. The detailed model aims to simulate and scrutinize the internal phenomena that can signiﬁcantly modify the diﬀerential dynamics. On the other hand, the purpose of the reduced model is tailored only to highlight the essential features of the diﬀerential. The author used the reduced model to compare the four diﬀerentials dynamically. Such approaches, however, have failed to address the eﬀects of the ﬂexibility of bearings and the timevarying aspect of the mesh stiﬀness on the dynamic behavior of the diﬀerential mechanism. Laﬁ et al. [3] have embarked on analyzing the diﬀerential mechanism which is composed of a set of straight bevel gears. In the latter study, the mesh phasing relations have been revealed, and the mesh stiﬀness for the straight bevel gear has been computed using the potential energy method. The eﬀects of the ﬂoating gear have been revealed by comparing the system with the dynamic response of twostage straight bevel gear. The inﬂuences of the assembly error of the planet have been highlighted. The drawback of this study is that the conﬁguration of the diﬀerential system is relatively simple, and many parts of the diﬀerential system have been ignored. The aim of this paper is threefold. The ﬁrst aim is to determine the dynamic equations of the system using NewtonEuler formulation to scrutinize the dynamic properties of the automotive diﬀerential. The second one is to propose a numerical computational method for scrutinizing the dynamic behavior of the diﬀerential mechanism when some physical parameters of the system are regarded as uncertain parameters that can be represented by interval analysis. The ﬁnal aim is to scrutinize the dynamic performances of the diﬀerential system with interval parameters. The paper has been organized in the following way. The ﬁrst section will examine the dynamic model of the automotive diﬀerential. The second section is concerned with the dynamic equations for each subsystem. After that, the dynamic equations of the diﬀerential system will be written in matrix form. The fourth section is devoted to analyzing the interval analysis process. The last section presents uncertain responses of the diﬀerential system.
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Dynamic Model of the Diﬀerential Mechanism
Fig. 1. Diﬀerential bevel gear set
The diﬀerential bevel gear model is composed of four central members (the diﬀerential pinion, the crown wheel, the two side gears) and two diﬀerential planets. The diﬀerential pinion and the side gears are linked to driver and two side wheels respectively, so that each element is considered as a single body. The previous combined gearshaftwheel bodies are each supported by a bearing located at arbitrary axial locations. Besides, the crown wheel and the carrier are rigidly linked so that they are considered as a single body. However, the crowncarrier is mounted on up to two bearings located at speciﬁc axial locations. Two diﬀerential planets are attached to the carrier by dint of two bearings. The diﬀerential system studied in this paper consists of a set of straight bevel gears as shown in Fig. 1. The indexing conventions b = dp, c, rs, ls, p1, p2 for the diﬀerential pinionshaftdriver, the crown wheelcarrier, left side body, the right side body and two planets are maintained throughout this paper. The lumped parameter of the system is represented in Fig. 2. The system varies in function of its degrees of the freedom, which are around 39. The several bearings used to support various bodies in the system. They are modeled by the three springs placed along three directions. The alternation between the number of teeth in contact is represented by a elastic spring acting normal to the active surface of gear tooth. The mesh stiﬀness for the straight bevel in this chapter has been derived by dint of the potential energy method along with slice theory. The proportional damping method is adopted in this chapter. Thus, we have obscured the damping symbol in Fig. 2. All the detailed methodology used to derive the dynamic equations of the system are found in [4].
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Fig. 2. Lumped parameter of the diﬀerential model
2.1
Dynamic Equations of the System
The NewtonEuler formulation has been utilized to determine the dynamic equations governing the motion of the diﬀerential mechanism. The dynamic equation in matrix from is written as follows: Mq + Cq + (K (t) + Ks ) q = Fext
(1)
Where: q gathers the generalized coordinates of the system and it can be written: q = [qdp , qc , qp1 , qp2 , qls , qrs ]
(2)
qj symbolizes the generalized coordinates gathering the degrees of the freedom for block (j). M reﬂects the mass matrix that lists all masses of the components making up the diﬀerential system. The timevarying mesh matrix is represented by K (t) while the static matrix, Ks , collects the bearing stiﬀnesses and the torsional stiﬀnesses of the shafts. The proportional damping is adopted in this chapter, which is written as:
Where:
˜ C = ηM + ν K
(3)
˜ = Ks + Kmoy K
(4)
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Kmoy stands for the mean value of timevarying mesh matrix K (t) and it can be calculated as follows: L L L L Kmoy = k1,mean Kdp mesh,c + kp1,mean Kmesh,p1 + kp2,mean Kmesh,p2 R R R + kp1,mean KR mesh,p1 + kp2,mean Kmesh,p2
(5)
L L R R Where: k1,mean , kp1,mean , kp2,mean , kp1,mean , kp2,mean are the mean values of the L L R R timevarying mesh stiﬀnesses of k1 (t) , kp1 (t) , kp2 (t) , kp1 (t) and kp2 (t) respecdp L L R R tively. Kmesh,c , Kmesh,p1 , Kmesh,p2 , Kmesh,p1 , Kmesh,p2 collect the mesh coefﬁcients of the ﬁve gear meshes existed in the system, and they are deﬁned in [4].
3
Interval Analysis of the Diﬀerential System
In some cases, it is impossible to predict the exact values of the physical parameters on account of measurement errors, assembly error, and other external factors. On top of that, the statistical information about those parameters is limited. Interval arithmetic is used for representing each value of the uncertain parameter as a range of possibilities. Thus, the range of an uncertain parameter can be written as: e1 (6) xI = xm + Δx Where: xI stands for the interval of an uncertain parameter x, and xm is the mean value of the uncertain parameter, which can be expressed as: xm =
x+x 2
(7)
Where: x and x denote the lower and higher bounds of the uncertain parameter x, and eˆ1 is the aﬃne arithmetic variable. Where: Δx stands for the center of the uncertain parameter, which can be expressed as: x−x (8) Δx = 2 It is important to mention that the uncertain variable can be timedepending variable, so for each time step tj , the uncertain parameter x (tj ) varies in an unique interval as shown in Fig. 3.
Fig. 3. Timevarying uncertain parameter
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The uncertainty in the system stemming from the uncertain parameters is propagated to the diﬀerential responses through the dynamic equations governing the motion of the system. Thus, the general equations take the form of [5]: (9) M xI (t) q (t) + C xI (t) q (t) + K xI (t) q (t) = Fext y I (t) Where: K xI (t) , C xI (t) and M xI (t) stand for the timevarying stiﬀness matrix, timevarying damping matrix and timevarying mass matrix respectively. The timevarying external load is denoted as: Fext y I (t) . xI (t) and y I (t) stand for the interval process vector pertained to the system parameters and external loads. The newmark resolution method is used to determine the bounds of the diﬀerential response in this case. The updated displacement vector qt+1 can be determined by the following expression [5]. qt+1 = (Kef f )
−1
Ref f
(10)
Where: Kef f =
2 m 4 I I C xt + Δxt sIt + K xm M xm t + Δxt st + t + Δxt st (11) Δt2 Δt
4 2 m I m I m I Ref f = F yt + Δyt ut + M xt + Δxt st + C xt + Δxt st qt Δt2 Δt 4 I m I I + M xm qt + M xm t + Δxt st + C xt + Δxt st t + Δxt st qt (12) Δt
Where: sIt and uIt denote as the aﬃne arithmetic variables. The displacement vector can be approximated by the Chebyshev series expansion as: s 1 fj1 ,.....,jm Cj1 ,....,jm ([β]) (13) qt+1 ≈ 2 0≤j1 +.....+jm ≤h
The number of zero(s) in the subscripts j1 , ....., jm is denoted by s. Cj1 ,....,jm ([β]) stands for the mdimensional chebyshev. Its general expression is written as: Cp1 ,p2 ,.....,pn (y1 , y2 , ......, yn ) = Cp1 (y1 ) Cp2 (y2 ) Cp3 (y3 ) .....Cpn (yn ) = cos (p1 θ1 ) cos (p2 θ2 ) cos (p3 θ3 ) ...... cos (pn θn )
(14)
Where: θi = arccos (yi ). For more than a onedimensional problem, the total interpolation points can be calculated by the tensor multiplication of each dimensional interpolam tion points. Thus, the number of interpolation points is equal to (h + 1) . The number of coeﬃcients fj1 ,......,jm accounts to the total number of interpolation points. For the case of vast dimensional problems, the computational dynamic
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analysis will be timeconsuming due to a large number of interpolation points. As result, the Chebyshev series expansion can be rewritten as: qt+1 ≈
0≤j1 +.....+jm ≤h
s k−1 1 fj1 ,.....,jm Cj1 ,....,jm ([β]) ≈ ϕi ψi ([β]) 2 i=0
ϕi and ψi can be computed by the following expression: ⎧ s ⎪ ϕ0 = 12 f0,....,0 ψ0 ([β]) = C0,.....,0 ([β]) ⎪ ⎪ ⎪ ⎨ ϕ1 = 1 s−1 f1,....,0 ψ1 ([β]) = C1,.....,0 ([β]) 2 .. .. ⎪ ⎪ . . ⎪ ⎪ s−1 ⎩ f0,....,h ψk−1 ([β]) = C0,.....,h ([β]) ϕk−1 = 12
(15)
(16)
It is important to mention that the terms greater than order h are neglected. Thus, the number of the other terms amounts to k = (h+m)! m!h! . In order to determine the coeﬃcient of ϕi , the least square method will be used. Thus, the coefﬁcient ϕ can be determined by the following expression: ⎤ ⎡ ψ0 (β1 ) · · · ψk−1 (β1 )
−1 ⎥ ⎢ T T .. .. .. ϕ = Y(β) Y (β) Y(β) f where Y (β) = ⎣ ⎦ (17) . . . ψ0 (βM ) · · · ψk−1 (βM ) T
Where: M reﬂects the number of the interpolation points, f = [f (β1 ) ....f (βM )] stands for the system output vector at the interpolation points βi . The coeﬃcient vector of the Chebyshev polynomials is represented by ϕ = T −1 . Thus, at each instance t, the bounds of the interval [ϕ0 , ϕ1 , ϕ2 , ....., ϕk−1 ] displacement vector can be computed by: qt+1 ([β]) =
k−1
ϕi ψi ([β])
(18)
i=0
In order to avoid the overestimation created by the wrapping eﬀect, the particle swarm optimization method should be used to compute the bounds.
4
Numerical Results
The mean values of the primary parameters of the automotive diﬀerential are listed in Table 1.
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Parameters
Diﬀerential pinion body
Crown body Planet(i)
Side bodies
Rotational stiﬀness of the shaft (j) 3 kθ N m rad−1 × 105
–
–
3
Axial stiﬀness of bearing (j) kjp N m−1 × 108 p ∈ {x, y, z}
8
–
–
8
Number of the teeth of gear
Zdp =42
Zc =52
Zpi =22
Zls =22
Tooth width (m) × 10−3
W = 40
W = 40
W = 20
W = 20
Mass of the block (j) (kg)
mdp = 21
mc = 40
mp1 = 3
m3 = 15
Rotational inertia of block (j) kgm2
Idp = 0.08
Ic = 0.17
Ip1 = 0.01 Ils = 0.07
External Torque (N m)
Td = 100
–
–
Tlw =124
Uncertainty amounts
5%
10%
15%
25%
106
0
Chebyshev Polynomial Expansion Scanning Method
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6 0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
Fig. 4. Transmission error δ1 in the ﬁrst stage of the automotive diﬀerential.
The dynamic displacement of the diﬀerential system can be depicted as a range of possibilities. The ﬁrst set of questions aimed to be answered in this study is what the eﬀect of uncertain timeinvariant parameters on the dynamic features of the diﬀerential system is. Thus, in this section, the dynamic response of the system with uncertain timeinvariant parameters will be tackled. The masses of diﬀerent diﬀerential components and the bearing stiﬀnesses can be written as interval parameters: mIs = ms + Δms sIs ksI = ks + Δks aIs
(19)
s is the subscript indicating the index of the block of the diﬀerential bevel gear. Where ms and ks are the mean of the interval parameters while Δks and Δms
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1.5
Chebyshev Polynomial Expansion Scanning Method
1
0.5
0 0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
R Fig. 5. Transmission error δp2 in the ﬁrst stage of the automotive diﬀerential.
are the center bearing stiﬀness and the center mass respectively. In this case, the bounds of the system response can be easily determined. The scanning method is used here as a reference method. Figure 4 compares the bounds of the dynamic transmission error in the ﬁrst stage, δ1 , (diﬀerential pinioncrown gear pair) of the automotive diﬀerential computed by two methods (the Cheybeshev polynomial expansion and the scanning method). It is apparent from the latter ﬁgure that there is an almost perfect match between the results derived by two methods. The same interpretation is veriﬁed in Fig. 5, where the bounds of dynamic R are depicted. transmission error between the planet (2) and the right side gear,δp2 These results further support the idea that the uncertain parameters can alter the dynamic features of the automotive diﬀerential. Closer inspection of the ﬁgures shows the amplitude of vibration of the automotive system doesn’t exceed 3 × 10−6 . It is safe to conclude that the vibration level doesn’t exceed the safe level despite the fact that there is a modiﬁcation of the system response.
5
Conclusion
The main goal of the current study was to determine the dynamic equations of the diﬀerential system and to propose a method for scrutinizing the dynamic performances of the diﬀerential whose physical parameters are uncertain. In this paper, the threedimensional diﬀerential method was proposed. All possible degrees of freedom of the system have been taken into account. The NewtonEuler formulation has been used for determining the dynamic equations governing the motion of the system. The Chebyshev interval method using the least square method has been used for analyzing the dynamic behavior of the system when both static and timedependent parameters of the system have been assumed as uncertain parameters. Concerning the bounds of the transmission errors in various stages of the system, it has been shown that there is a good agreement between the proposed method and the scanning method. On top of
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that, the proposed method can provide a result in a short time. This study could help the engineers to understand the dynamic features of the diﬀerential system and could facilitate to scrutinize such a system when its physical parameters are considered as uncertain.
References 1. Yousﬁ, N., Akrout, A., Zghal, B., Walha, L., Haddar, M.: Rayleigh damping coefﬁcients identiﬁcation using the wavelet transform on two stage gear system. In: Advances in Materials, Mechanics and Manufacturing. Springer (2020) 2. Morselli, R., Zanasi, R., Sandoni, G.: Detailed and reduced dynamic models of passive and active limitedslip car diﬀerentials. Math. Comput. Model. Dyn. Syst. 4, 347–362 (2006) 3. Laﬁ, W., Djemal, F., Tounsi, D., Akrout, A., Walha, L., Haddar, M.: Dynamic modelling of diﬀerential bevel gear system in the presence of a defect. Mech. Mach. Theory 139, 81–108 (2019) 4. Wassim, L.: Robustness and modal analysis of the diﬀerential system with uncertainties. Dissertation, National Engineering School of Tunis (2020) 5. Laﬁ, W., Djemal, F., Tounsi, D., Akrout, A., Walha, L., Haddar, M.: Nonprobabilistic interval process method for analyzing twostage straight bevel gear system with uncertain timevarying parameters. Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 1–17 (2020)
Analysis of Geometrically Nonlinear Responses of Smart FG Cylindrical Shell H. Mallek(B) , H. Mellouli, and F. Dammak Laboratory of Electromechanical Systems (LASEM), National Engineering School of Sfax, University of Sfax, Route de Soukra km 4, 3038 Sfax, Tunisia {hanen.mallek,hana.mellouli,fakhreddine.dammak}@enis.tn
Abstract. This paper deals with geometrically nonlinear analysis (GNLA) of semicylindrical structure made of functionally graded material (FGM) with surfacebondedpiezoelectric layers (SBPL). The governing equations are developed via a double directors shell theory (DDST), which reflects a high distribution of the displacement. Moreover this theory takes into account the effect of transverse shear deformations (TSD). The material properties of the FGM structures are assumed to vary continuously across the shell thickness obeying a powerlaw function. The effectiveness of the present method is showed by validating the obtained results against those of other studies. Numerical results reveal the effect of power law index and geometric parameter on the nonlinear (NL) responses of smart FGM structures. Keywords: Geometrically nonlinear theory · SBPL · FGM · DDST
1 Introduction The investigation of GNLA of shell structures has attracted a considerable attention especially for engineering since structures can tolerate large deformations. A several researches have been achieved to anticipate the nonlinear (NL) behavior of structures under mechanical loading (Mars et al. 2017; Mellouli et al. 2020). However, NL shell with SBPL were notably less studied in the literature. Using FSDT theory, NL behavior of intelligent shells were elaborated by (Marinkovic and Rama 2017; Rama et al. 2018; Rama 2017). Another approach on the basis of an FSDT theory, which is improved, was used for GNLA of intelligent structures (Mallek et al. 2019b, 2021). Recently, FGM have got intensive consideration because its properties modify continuously in the direction of the thickness. Recently, piezomaterials are combined with FG materials in order to obtain a system of intelligent materials. (Mallek et al. 2019c, 2020) investigated linear behavior of intelligent FGM structures using DDST.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 195–200, 2022. https://doi.org/10.1007/9783030849580_21
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In the literature, no work was found investigating the geometrically non linear analysis (GNLA) of thin FG shell structures with integrated piezolayers, although these structures undergo moderate deformation because of their flexible nature, and hence geometrical nonlinearity has to be accounted for the behavior analysis (Kulkarni and Bajoria 2007; Lee 2005; Lentzen et al. 2007; Schulz and Klinkel 2008). This work makes a first attempt to conduct a GNLA of FG structure with SBPL based on DDST. The large deflection of FG structure with SBPL is investigated so as to delineate the validness of the developed model.
2 Formulation of a DDST The DDST is used in this research to predict geometrically non linear (GNL) response of a FGM shell with SBPL. In the deformed configuration and using the curvilinear coordinates ξ = (ξ, η, z), the position vector of point q that is positioned at the distance z from its normal projection on the mid surface, the point p, can be defined as: xq (ξ, η, z) = xp (ξ, η) + f1 (z)d 1 (ξ, η) + f2 (z)d 2 (ξ, η) f1 (z) = z −
h h 4z 3 4z 3 , ; f , z ∈ − = (z) 2 3h2 3h2 2 2
(1) (2)
In which, d 1 and d 2 represent the DDS vectors in the deformed configuration. The Lagrangian strain components are determined from the membrane eαβ , the k and the shear γ k strains as follows: bending χαβ α 1 2 εαβ = eαβ + f1 (z)χαβ + f2 (z)χαβ ; α, β = 1, 2
(3)
2εα3 = f1 (z)γα1 +f2 (z)γα2
(4)
These components are in the following form: δe = Bm .δx ; δχ k = Bbmk δx + Bbbk δd k
(5)
δγ k = Bsmk δx + Bsbk δd k ; k = 1, 2
(6)
In an attempt to prove the condition of zero TSD at top surface and bottom once, δγ 2 should be cancelled in the variational formulation with discrete configuration (Mallek et al. 2019a). The distribution of the electric field E is calculated as (Mallek et al. 2019c): E = −Be .ϕ
(7)
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3 Variational Formulation The weak form WF is obtained by: 2 k 1 G= M k δχ + T 1 δγ + qδE dA − Gext = 0 Nδe + A
(8)
k=1
where N,T 1 and M k symbolize respectively the membrane, the shear and the bending stress resultants. q is the electric displacement resultant. Utilizing Newton procedure, the NL problem is unraveled using the WF directional derivatives in the direction of through to the increment. The tangent operator is separated toward geometric and material particles, indicated by DG G.Φ and DM G.Φ respectively: D G.Φ = DG G.Φ + DM G.Φ DM G. Φ =
δΣ T RdA ; DG G. Φ = A
ΔδΣ T . R dA
(9) (10)
A
where the generalized resultant of stress R and strain Σ are designative as: T T
R = N M 1 M 2 T 1 q 14×1 ; Σ = e χ 1 χ 2 γ 1 −E 14×1
(11)
ΔΦ = (Δu, Δd 1 , Δd 2 , Δϕ) represents the increment of the generalized displacement. After developing the weak form of equilibrium, the interpolation of the displacement, stain and electric fields is deposited inside a 4nodes FE. For more details, see (Mallek et al. 2019a).
4 Functionally Graded Materials The powerlaw function is used to report the continuous variability of the composition of the characteristics a long with the thickness. Subsequently, the young modulus YFGM is determined by the mixture rule:
1 n z + YFGM (z) = YAl + (YTi − YAl )V (z); V (z) = (12) h 2 where YAl = 349.55 GPa and YTi = 122.56 GPa are the Young modulus of the Aluminum oxide and Ti6Al4V, respectively and n is the powerlaw parameter. The Poisson’s ratio for both materials is supposed to be constant (νTi = 0.2884 and νAl = 0.26).
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5 Numerical Results A clamped cylindrical arch with two piezoelectric PZT layers joined on the top surface and bottom once (Fig. 1) is analyzed in this section intending to estimate the efficiency of the proposed model. The dimensions of curved structure are displayed in Fig. 1. Material and piezocharacteristics of PZT are Y1 = Y2 = 63 GPa, ν12 = 0.3, e31 = e32 = 16.11 C/m2 and k33 = 1.65 × 10–8 F/m. Each pizo–layer has a thickness equal to 0.254 mm. The material of the middle layer is considered firstly as a steel metal, (Y1 = 68.95 GPa and ν12 = 0.3). The structure is exposed to a force F = 100 N at point A. A 16 × 16 mesh is obtained to design the structure. The analysis considers large rotations. Figure 2 depicts load vs deflection at point A of the structure. Numerical results using the DDS model prove a good agreement with those reported in (Marinkovic and Rama 2017).
Fig. 1. Cylindrical arch with two piezo–layers
Fig. 2. Load vs deflection of the isotropic shell with SBPL at point A.
Extending the preceding analysis to FGM, the GNLA is cared for a smart–FGM shell. Figure 3 illustrates the loop deflection of the structure with joined actuators under
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different n. It is found that the increase in the power low index n leads to a decrease in the deflection of the structure. This is expected since for higher values of power low index n, the structure loses stiffness due to the increasing of the percentage of aluminum phase. The sensitivity of the GNL response to the structure’s curvature is considered in this part. Figure 4 shows the hoop deflection of the FGM cylindrical shell at the tip point, considering n = 1, for different (R/h) values. It should be mentioned that, the rise of the ratio R/h leads to a cylindrical shell with flat form since the radius of curvature is broaden. Moreover, with the increase of the ratio R/h, the tip hoop displacement spreads up and higher stiffness is provided to the piezolaminated shell, thanks to the presence of its geometrical initial curvatures, with comparison to the piezolaminated plate.
Fig. 3. Deflection of the FGM structure with SBPL at point A
Fig. 4. Load–deflection curves of the FGM shell with SBPL at point A
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6 Conclusion In this paper, the GNLA of FG arch with joined piezo–layers is presented using a FE procedure. The results juxtaposed with those accessible in the literature result in performing the efficacy of proposed model. Further, this formulation is extended for its application to FGM intelligent structures. A parametric study, which includes the variation of the power index and geometrical parameter, is executed. It is found that each parameter has a significant effect on the nonlinear behavior of the active structure, which should be carefully considered for the structure design.
References Kulkarni, S.A., Bajoria, K.M.: Large deformation analysis of piezolaminated smart structures using higherorder shear deformation theory. Smart Mater. Struct. 16, 1506–1516 (2007) Lee, H.J.: Layerwise laminate analysis of functionally graded piezoelectric bimorph beams. J. Intell. Mater. Syst. Struct. 16(4), 365–371 (2005) Lentzen, S., Klosowski, P., Schmidt, R.: Geometrically nonlinear finite element simulation of smart piezolaminated plates and shells. Smart Mater. Struct. 16, 2265–2274 (2007) Mallek, H., Jrad, H., Algahtani, A., Wali, M., Dammak, F.: Geometrically nonlinear analysis of FGCNTRC shell structures with surfacebonded piezoelectric layers. Comput. Methods Appl. Mech. Eng. 347, 679–699 (2019a) Mallek, H., Jrad, H., Wali, M., Dammak, F.: Geometrically nonlinear finite element simulation of smart laminated shells using a modified firstorder shear deformation theory. J. Intell. Mater. Syst. Struct. 30(4), 517–535 (2019b) Mallek, H., Jrad, H., Wali, M., Dammak, F.: Nonlinear dynamic analysis of piezoelectricbonded FGCNTR composite structures using an improved FSDT theory. Eng. Comput. 37(2), 1389– 1407 (2021). https://doi.org/10.1007/s00366019008911 Mallek, H., Jrad, H., Wali, M., Dammak, F.: Piezoelastic response of smart functionally graded structure with integrated piezoelectric layers using discrete double directors shell element. Compos. Struct. 210, 354–366 (2019c) Mallek, H., Jrad, H., Wali, M., Kessentini, A., Gamaoun, F., Dammak, F.: J. Vib. Control 26(13–14), 1157–1172 (2020) Marinkovic, D., Rama, G.: Corotational shell element for numerical analysis of laminated piezoelectric composite structures. Compos. B 125, 144–156 (2017) Mars, J., Koubaa, S., Wali, M., Dammak, F.: Numerical analysis of geometrically nonlinear behavior of functionally graded shells. Latin Am. J. Solids Struct. 14, 1952–1978 (2017) Mellouli, H., Jrad, H., Wali, M., Dammak, F.: Free vibration analysis of FGCNTRC shell structures using the meshfree radial point interpolation method. Comput. Math. Appl. 79(11), 3160–3178 (2020) Rama, G., Marinkovic, D., Zehn, M.: Efficient threenode finite shell element for linear and geometrically nonlinear analyses of piezoelectric laminated structures. J. Intell. Mater. Syst. Struct. 29, 345–357 (2018) Rama, G.: A 3node piezoelectric shell element for linear and geometrically nonlinear dynamic analysis of smart structures. Facta Universitatis Ser. Mech. Eng. 15(1), 31–44 (2017) Schulz, K., Klinkel, S.: A geometrically nonlinear mixed finite element formulation for the simulation of piezoelectric shell structures. Sens. Smart Struct. Technol. Civil Mech. Aerosp. Syst. 6932, 69320G (2008)
Finite Rotation RPIM Formulation for Geometrically Nonlinear Analysis of FGCNTRC Shell Structure H. Mellouli(B) , H. Mallek, M. Wali, and F. Dammak Laboratory of Electromechanical Systems (LASEM), National Engineering School of Sfax, University of Sfax, Route de Soukra km 4, 3038 Sfax, Tunisia {hana.mellouli,hanen.mallek,Fakhreddine.dammak}@enis.tn, [email protected]
Abstract. This work considers the geometrically nonlinear analysis of functionally graded carbon nanotubesreinforced composite (FGCNTRC) hemispherical shell with finite rotations using the radial point interpolation method (RPIM). This study does not exist yet in literature. The proposed model, based on the double directors theory (DDT), consists in considering the shear stress’ parabolic distribution. The present meshfree method is based on the radial point interpolation method which is employed for the construction of shape functions for a set of nodes distributed in a problem domain. The RPIM shape functions are constructed using only nodes within overlapping domains named as support domains. The NewtonRaphson procedure is used to solve the discrete system of geometrically nonlinear equilibrium equations, incorporated into the weak form. Four types of carbon nanotubes (CNTs) distribution along the shell thickness’s directions, such that uniformly (UD) and three functionally graded distributions (FGO, FGV and FGX), are considered in order to outline the improvement that brings the CNTs to the structure with its different profiles. Deflections on loading points of the studied shell structure with geometrical nonlinearities are computed and depicted for different profiles of CNTs and various radius/thickness ratios of the hemispherical shell with 18° hole. Keywords: Geometrically nonlinear · Finite rotations · Shell structure · FGCNTRC · RPIM · Double directors theory
1 Introduction Nonlinear analysis of shells is carried out for large deformations problems. Numerical methods, such as the finite element method (FEM) are extensively used for analyzing large deformation behavior of plates and shells (Mallek et al. 2019). With the meshfree methods, (Zhao et al. 2008) studied the plates and cylindrical shells’ analysis with geometric nonlinearities using the FSDT. Moreover, a coupling isogeometricmeshfree approach for the nonlinear simulation of thinshells is considered by (Li et al. 2018). Lately, (Mellouli et al. 2019) studied the geometrically nonlinear behavior of isotropic © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 201–208, 2022. https://doi.org/10.1007/9783030849580_22
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and orthotropic plates and shells using the radial point interpolation method (RPIM) and the double directors theory (DDT). Recently, the carbon nanotubes (CNTs) have been accepted as an excellent developed material with appealing properties. Distributions of the CNTs, in a polymeric matrix, can be uniformly aligned or functionally graded (FG). Limited works have been undergoing through the use of the functionally graded carbon nanotubesreinforced composite (FGCNTRC) for the geometrically nonlinear modeling of shells. (Zhang et al. 2014) examined the geometrical nonlinearities of FGCNTRC cylindrical panels using the kpRitz method. The RPIM used as a meshfree method to examine the geometrically nonlinear analysis of FGCNTRC shell does not yet exist in the literature. In this work, we aim to study for the first time in the literature, the geometrically nonlinear analysis of FGCNTRC hemispherical shell with 18° hole using the RPIM in order to outline the accuracy and performance of the present method.
2 Kinematics of FGCNTRC Shells Using the DDT 2.1 Displacement and Strain Fields In this section, the nonlinear formulation of shells based on the DDT is developed. Vectors tensors are denoted by bold format. Using the curvilinear coordinates ξ = 1 2 and ξ , ξ , ξ 3 = z and in the deformed state, the position vector of a point (l), is expressed, using its normal projection on midsurface’s point (j) and the double director vectors d 1 and d 2 of the DDT, as: xl ξ 1 , ξ 2 , z = xj ξ 1 , ξ 2 + f1 (z)d 1 ξ 1 , ξ 2 + f2 (z)d 2 ξ 1 , ξ 2 (1) h h 4z 3 f1 (z) = z − f2 (z) , f2 (z) = 2 , z ∈ − , 3h 2 2 The Lagrangian strain E is given by: 1 + f (z)χ 2 Eαβ = eαβ + f1 (z)χαβ 2 αβ , (α, β) = {1, 2} 2Eα3 = f1 (z)γα1 + f2 (z)γα2
(2)
k and γ k (k = 1, 2) designate respectively the membrane, the first Where eαβ , χαβ α (respectively the second) bending and shear strains. These particles are expressed in matrix form as (more details about the procedure in (Mellouli et al. 2019)):
δe = Bm .δx, δχ k = Bkm δx + Bkb δd k , , δγ k = Bksm δx + Bksb δd k , k = 1, 2
(3)
2.2 The Radial Point Interpolation Method (RPIM) The approximation of a point of interest X = (x, y)’s displacement vector, using the RPIM interpolator method is given by: U(X ) =
N I=1
RI (X )aI +
M J=1
P J (X )bJ = RT (X )a + P T (X )b
(4)
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RJ (X ) = (XJ − X 2 + c2 )q represents the Multiquadratic radial basis funcT tion, P J (X ) is the polynomial basis function with the matrix form P (X ) =
2 2 1, x, y, x , xy, y whereas aI and bJ denote respectively the nonconstants coefficients of RI (X ) and P J (X ). ‘N’ enumerates the nodes’ number grouping in a support domain and ‘M’ defines the monomial terms’ number. XJ − X designates the Euclidean norm delimiting the distance between the point of interest X and a definingpoint XJ . The parameter ‘c’ assigns the average spacing for the totality of nodes in a support domain whereas the optimal parameter ‘q’ is taken equal to q = 1.03(Liu et al. 2005) achieving good results. 2.3 The Weak Form Numerical solutions of equilibrium equations with the present method are obtained using the weak form given as: 2 k k M k .δχ + T k .δγ (5) G= N.δe + dA − Gext = 0 A
k=1
where N, M k and T k (k = 1, 2) represent respectively the membrane, the first and second bending and shear stress resultants whereas δe,δχ k and δγ k (k = 1, 2) denote the shell strains mentioned in Eq. (3). Equation (5), with the variation of the generalized displacement vector Φ = (U, d 1 , d 2 ), can be reformulated using the generalized resultants of T T stress R = N M 1 M 2 T 1 T 2 13×1 and strain Σ = e χ 1 χ 2 γ 1 γ 2 13×1 as: δΣ T .RdA − Gext (Φ, δΦ) = 0
G(Φ, δΦ) =
(6)
A
The nonlinear problem is solved by the Newton iterative procedure using the weak form directional derivatives, which is expressed with the linearized form as: G + DG.Φ = 0
(7)
Then, the tangent operator D G.Φ is divided into geometric and material constituents, defined by DG G.Φ and DM G.Φ respectively: D G.Φ = DG G.Φ + DM G.Φ
(8)
DG G.Φ = A ΔδΣ T .RdA DM G.Φ = A δΣ T .R dA
(9)
2.4 The Functionally Graded Carbon NanotubesReinforced Composite (FGCNTRC) The FGCNTRC is a composite that mixes a polymeric matrix, having isotropic properties, with CNT fibers. The reinforcement of CNTs is considered uniaxially aligned in
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Fig. 1. Four profiles of CNTs’ distributions along the shell thickness
the matrix and also functionally graded in direction of the thickness bringing out four profiles designated by uniform (UD), FGO, FGV and FGX configurations (Fig. 1) (Mellouli et al. 2020). The FGCNTRC structure’s effective Young as well as shear moduli are defined, using the modified mixing rule in (Shen 2011; Mellouli et al. 2020; Mallek et al. 2020, 2021). CNT + V E , E11 = η1 VCNT E11 m m VCNT η2 Vm E22 = E CNT + Em , 22 VCNT η2 Vm G12 = G CNT + Gm 12
(10)
CNT , E CNT and G CNT represent the Young and shear moduli of CNTs respecwhere E11 22 12 tively whereas Em and Gm are the isotropic matrix’s material properties. η1 , η2 and η3 are referred to the CNT efficiency parameters to consider the sizedependent material properties. VCNT and Vm indicate the volume fractions of the CNTs and the isotropic matrix respectively verifying the following condition:
VCNT + Vm = 1
(11)
3 Numerical Shell Modeling The present model, used for the nonlinear analysis of isotropic and orthotropic plates and shells and compared with other formulations presented in the literature, has proved a good accuracy (Mellouli et al. 2019). Therefore, it is worthy to broaden the present formulation to the FGCNTRC material. In this section, the pinched hemispherical shell with 18° hole (Fig. 2) is considered with the FGCNTRC material in where its properties are mentioned in Tables 1 and 2. Geometrical parameters are: radius R = 10 mm and thickness h = 0.04 mm. For this test, the Multiquadratic function is adopted, with the consideration of the parameter c = 0.6 and a 13 × 13 total grid nodes are used as a background quadratures for the Gauss’s integration procedure.
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Table 1. Material characteristics of the FGCNTRC. The CNTs material properties
The matrix characteristics
CNT = 5.6466 TPa E11
Em = 2.1 GPa
CNT = 7.0800 TPa E22
ρ m = 1150 Kg/m3 υm = 0.34
CNT = 1.9445 TPa G12
ρ CNT = 1400 Kg/m3 CNT = 0.175 υ12
Table 2. The efficiency parameters for the volume fraction of the CNTs. ∗ VCNT η1
0.11
η2
η3
0.149 0.934 0.934
Fig. 2. Geometry of the pinched hemisphere with 18° hole
4 Results and Discussions In this section, the geometrically nonlinear analysis of the pinched hemispherical shell model is treated. Numerical results and discussions are introduced. Figure 3a and b illustrate results of deflections at the loading points A and B for the four configurations of the CNTs using the ratio R/h = 250. Figure 4 shows deflections for the FGX configuration of the CNTs using different ratios R/h. It can be seen from these figures that results of deflections associated to the FGO configuration are the highest ones while the lowest ones are associated to the FGX configuration. Hence, more the CNT reinforcements are close to the midsurface, less the FGCNTRC shell structure is stiff and this implies high values of deflection results.
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Fig. 3. Results of deflections for the four configurations of CNTs using the ratio R/h = 250. a) at the point A, b) at the point B
Therefore, the best configuration of the CNTs reinforcements is the FGX configuration since the top and bottom surface of the shell structure are CNT rich and this in turn increases the stiffness of the structure and entails its less deformation. In addition, it can be remarked that the variations of the ratio R/h affect the deflection solutions and high results are given to the ratio R/h = 300 since with the increase of this ratio, the structure becomes thinner and thus deforms easily.
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Fig. 4. Deflection solutions of the FGX configuration using different ratios R/h at the loading points A and B
5 Conclusion In this work, a meshfree RPIM method is developed to study the geometrically nonlinear analysis of FGCNTRC hemisphere using the Double Directors Theory. Four configurations of the CNTs are inspected in this study and its effects are investigated on deflection results at the loading points of the hemisphere with hole. The extension of the present model via the addition of CNTs to composite structures appears valuable compared to the isotropic and orthotropic ones (Mellouli et al. 2019).
References Li, W., NguyenThanh, N., Zhou, K.: Geometrically nonlinear analysis of thinshell structures based on an isogeometricmeshfree coupling approach. Comput. Methods Appl. Mech. Eng. 336, 111–134 (2018) Liu, X., Liu, G.R., Tai, K., Lam, K.Y.: Radial point interpolation collocation method (RPICM) for partial differential equations. Comput. Math. Appl. 50(8–9), 1425–1442 (2005) Mallek, H., Jrad, H., Algahtani, A., Wali, M., Dammak, F.: Geometrically nonlinear analysis of FGCNTRC shell structures with surfacebonded piezoelectric layers. Comput. Methods Appl. Mech. Eng. 347, 679–699 (2019) Mallek, H., Jrad, H., Wali, M., Dammak, F.: Nonlinear dynamic analysis of piezoelectricbonded FGCNTR composite structures using an improved FSDT theory. Eng. Comput. 37(2), 1389– 1407 (2021). https://doi.org/10.1007/s00366019008911 Mallek, H., Jrad, H., Wali, M., Kessentini, A., Gamaoun, F., Dammak, F.: Dynamic analysis of functionally graded carbon nanotube–reinforced shell structures with piezoelectric layers under dynamic loads. J. Vib. Control 26(13–14), 1157–1172 (2020) Mellouli, H., Jrad, H., Wali, M., Dammak, F.: Free vibration analysis of FGCNTRC shell structures using the meshfree radial point interpolation method. Comput. Math. Appl. 79, 3160–3178 (2020) Mellouli, H., Jrad, H., Wali, M., Dammak, F.: Geometrically nonlinear meshfree analysis of 3Dshell structures based on the double directors shell theory with finite rotations. Steel Compos. Struct. 31(4), 397–408 (2019)
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Shen, H.S.: Postbuckling of nanotubereinforced composite cylindrical shells in thermal environments, part I: axiallyloaded shells. Compos. Struct. 93, 2096–2108 (2011) Shen, H.S., Xiang, Y.: Nonlinear bending of nanotubereinforced composite cylindrical panels resting on elastic foundations in thermal environments. Eng. Struct. 80, 163–172 (2014) Zhang, L.W., Lei, Z.X., Liew, K.M., Yu, J.L.: Large deflection geometrically nonlinear analysis of carbon nanotubereinforced functionally graded cylindrical panels. Comput. Methods Appl. Mech. Eng. 273, 1–18 (2014) Zhao, X., Liu, G.R., Dai, K.Y., Zhong, Z.H., Li, G.Y., Han, X.: Geometric nonlinear analysis of plates and cylindrical shells via a linearly conforming radial point interpolation method. Comput. Mech. 42(1), 133–144 (2008)
Numerical Investigation on Incremental Forming Process of an Elastoplastic Functionally Graded Material A. Bouhamed(B) , J. Mars, H. Jrad, M. Wali, and F. Dammak Laboratory of Electromechanical Systems (LASEM), National Engineering School of Sfax, University of Sfax, Route de Soukra km 4, 3038 Sfax, Tunisia {abir.bouhamed,fakhreddine.dammak}@enis.tn
Abstract. Incremental forming process is an emerging processing technology that has attracted considerable attention just recently. This kind of flexible sheet metal forming process adopted to produce complex shapes without the need of expensive and specific tools. The movement of a hemispherical punch creates highly localized deformation on the sheet metal in order to obtain the desired shape. The current work presents a numerical investigation, which is made on the feasibility of using a Single Point Incremental Forming (SPIF) process to deform an elastoplastic Functionally Graded Material (FGM) sheet. Comparative study is developed in the presented research to show the effect of the FGM sheet’s constituent phases arrangement on the mechanical response of a part deformed by the SPIF process. The main contribution of this research is to predict the FGM sheet’s behavior when the hemispherical forming tool is moved during the simulation from a less rigid face (Aluminum) to a more rigid face (Titanium). The obtained results indicate the applications and practices of the SPIF manufacturing process with respect to FGM sheet. This numerical study illustrates a valuable guide for new products not already studied in the literature, to predict a thin FGM sheet’s mechanical behavior deformed by a SPIF process. Keywords: Functionally graded material (FGM) · Single point incremental forming (SPIF) · Elastoplastic behavior · Finite element simulation
1 Introduction Single point incremental forming (SPIF) presents one of the process with the most potential in human implants and aerospace development. It has acquired importance in sheet metal forming thanks to its ability to produce complex shapes. Nowadays, the SPIF becomes one of the appropriate process used for rapid prototyping and small batch components. It is a flexible manufacturing process, which do not require specified dies and punches as in conventional manufacturing process. This innovative process is based in local plastic deformation to deform the sheet metal using a hemispherical forming tool of small diameter. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 209–216, 2022. https://doi.org/10.1007/9783030849580_23
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Many researchers have been concerned on the SPIF process of sheet metal, post of which are interested with the experimental aspect, as reported on (Zhan et al. 2020), (wang et al. 2020) and (Guo et al. 2018). Finite element simulations of SPIF process for sheet metal have been carried out in some investigations, as mentioned in (Bouhamed et al. 2019a), (Ben Said et al. 2017) and (Gatea et al. 2016). The SPIF technology is an emerging operation that is being favored in many engineering applications especially in medical field. For instance, (Ambrogio et al. 2005) are manufactured ankle foot orthosis used the SPIF process. Further, (Duflou et al. 2008) made a cranial prosthesis with this technology. Recently, some papers have been proposed concerning the application of SPIF process to metal sheets made by Titanium alloys as (Palumbo et al. 2011) and (Fan et al. 2010), or aluminum alloys like (Bouhamed et al. 2019a) and (Malhotra et al. 2012) thanks to the mechanical and physical properties presented in these materials. Inspired from these works, (Bouhamed et al. 2019b) are offered the opportunity to combine these two materials: Aluminum and Titanium to make an elastoplastic spheresreinforced FGM composite. The authors are firstly made a numerical investigation on the applicability of using SPIF process to deform an elastoplastic functionally graded material (FGM). FGMs depict kind of advanced materials that have been made by mixing two different material phases. They are characterized throughout the gradation of their material properties depending on the volume fraction of the constituents along the sheet’s thickness. Many investigations have used ceramic/metal FGM composite, as illustrated in (Jrad et al. 2019) and (Mars et al. 2018), whereas (Bouhamed et al. 2019b) are concerned in Titanium grade 2/Al 6061 FGM composite. This composite is homogenized using two approaches: the first approach is based on the MoriTanaka model to estimate the effective elastic properties of the elastoplastic FGM. The second approach is a representative volume element (RVE), which is mentioned to determine the elastoplastic behavior of the FGM composite. From their work, they found a valuable guide to present the potential use of the elastoplastic Titanium grade 2/Al 6061 FGM composite for SPIF process and its feasibility. The current work presents an extension of the work of (Bouhamed et al. 2019b) to investigate the homogenized FGM mechanical response during SPIF operation when the FGM sheet is inverted. This means that the first contact between the punch and the sheet will be with Aluminum. Then, the punch is moved from a less rigid face to a more rigid face counter to the research of (Bouhamed et al. 2019b) where the first contact between the forming tool and the FGM sheet was with Titanium. Comparative study is developed in the presented research to depict the effect of FGM sheet’s constituent phases arrangement on the mechanical response of a part deformed by the SPIF process. The numerical simulation is used in ABAQUS/Explicit via two userdefined subroutines (VUSFLD) and (VUMAT), in which the homogenization equations and the calculation algorithms are detailed to represent accurately the homogenized FGM behavior.
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2 An Elastoplastic FGM The current elastoplastic functionally graded material (FGM), including two constituents: Titanium grade 2 and Aluminum (Al6061), with A and T are referred, respectively, to aluminum and titanium constituents phases. The current nonhomogeneous FGM composite with continuously varying properties throughout the thickness direction is modeled as elastoplastic titanium spherical particles, which are reinforced in an elastoplastic aluminum matrix. The profile volume fractions of titanium and aluminum constituents are presumed to pursue, along the thickness of FGM sheet, the power law distribution as below: h 2z + h p −h ≤z≤ (1) , VT (z) = 1 − VA (z), VA (z) = 2h 2 2 In which, h presents the thickness of the FGM sheet and p denote the power law index that depicts the gradation profile along the thickness direction z. The proposed FGM composite is homogenized in the work of (Bouhamed et al. 2019b) as follows: The effective elastic properties (E, ν) is estimated using the MoriTanaka model. Further, a representative volume element (RVE) method that presents a numerical homogenization approach is used to provide the elastoplastic behavior for different volume fraction of FGM composite and to determine their elastoplastic properties. Based on the results obtained from this work, it can be obviously observed that the power law index p has a significant effect on the FGM sheet’s mechanical response using the SPIF process. The FGM used in (Bouhamed et al. 2019b) is constituted of a top surface that is Titaniumrich, whereas a bottom surface is Aluminumrich (Configuration A). For the present research, the FGM sheet is inverted, that means that the upper surface will be in Aluminum and the lower surface will be in Titanium (Configuration B). Thus, the first contact between the punch and the sheet metal during the SPIF process will be with the Aluminum. The power law index will be fixed to a value p = 1 throughout this study in order to highlight the effect of the FGM sheet’s constituent phases arrangement, as depicted in Fig. 1. The elastoplastic constitutive model describing the FGM sheet’s behavior is briefly developed in Table 1. In Table 1, σ is the Cauchy stress tensor, σY presents the yield strength, εp indicates the plastic strain tensor, K and n are the isotropic hardening parameters of Ludwik and γ˙ presents the plastic multiplier.
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Fig. 1. FGM sheets for both configurations.
3 FE Modeling In this section, the numerical model of the SPIF process is represented using ABAQUS/Explicit via two userdefined subroutines (VUSFLD) and (VUMAT), in which the homogenization equations determined in the work of (Bouhamed et al. 2019b) and the calculation algorithms are detailed. A squared sheet of 200 × 200 mm2 and 0.2 mm thickness is meshed by 3node triangular shell element with reduced integration (S3R). Nine Simpson integration points are illustrated through the thickness. The hemispherical forming tool is moved during the simulation to follow a cone tool path with a clearance
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angle of 45°. The punch is designed as discretized rigid body (R3D3). Further, the contact condition is verified between the sheet and the forming tool with surfacetosurface contact. The FGM sheet is presumed to be isotropic and elastoplastic. The friction coefficient between the blank and the punch is 0.1 to describe the contact condition, as shown in (Ben Said et al. 2017). Table 2 illustrates the homogenization equations determined in the work of (Bouhamed et al. 2019b). These equations are implemented in (VUSFLD) subroutine to indicate the elastoplastic parameters for each volume fraction of Titanium particles. The effective parameters presented in Table 2, are used, to simulate the SPIF process. In T, K and n indicate the isotropic hardening parameters of Ludwik law and σY presents the yield strength. Table 2. Homogenization equations (Bouhamed et al. 2019b).
4 Results and Discussions Numerical results of the elastoplastic FGM sheets behavior during the SPIF process have been depicted using the FE model for both configurations. Figure 2 and Fig. 3. describe the evolutions of Von Mises equivalent stress for the two configurations. After the FGM sheet’s reversal, it can be observed that the equivalent stress is important for the configuration (B). This can be explained by the fact that the forming tool is moving during the simulation from a less rigid face to a more rigid face, so the value of the stresses will be increased compared to configuration (A). Thus, the behavior of configuration (B) that has different material properties through the sheet thickness will be similar to the pure Titanium elastoplastic behavior. Figure 4 illustrates the plastic strain evolution for both configurations. From this figure, it should be mentioned that the reversal of the sheet has a significant effect on the FGM sheet’s plastic behavior. The plastic strain presents movements within the material. This is accompanied by friction, which produces heat. This heat causes a remarkable rise at sheet temperature. In other words, during SPIF operation, the use of a sheet in configuration (A) heats the manufactured part much more than the use of a sheet in configuration (B). This comparative study is carried out to show that the FGM sheet’s constituent phases arrangement has an important influence on the mechanical response of a part deformed by the SPIF process.
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Fig. 2. Von Mises equivalent stress distribution for configuration A.
Fig. 3. Von Mises equivalent stress distribution for configuration B.
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Fig. 4. Plastic strain evolution for both configurations.
5 Conclusion The presented research makes the opportunity to determine the behavior of an elastoplastic spheresreinforced FGM during the SPIF process. A comparative study is carried out to present the important influence of the FGM sheet’s constituent phases arrangement on the mechanical response of the manufactured part obtained by the SPIF process. The FGM sheet’s reversal makes an elastoplastic similar behavior to the Titanium pure. The use of a top face rich in Aluminum does not require a great effort to deform the FGM sheet and no lubrication is needed. On the other hand, if the top face is Titanium rich, it needs the lubrication that rusts the sheet. The obtained results indicate the application and practices of the SPIF manufacturing process with respect to FGM sheet. This numerical study illustrates a valuable guide for new products not already studied in the literature, to predict a thin FGM sheet’s mechanical behavior deformed by a SPIF process.
References Zhan, X., Wang, Z., Li, M., Hu, Q., Chen, J.: Investigations on failuretofracture mechanism and prediction of forming limit for aluminum alloy incremental forming process. J. Mater. Process. Technol. 282, 116687 (2020) Wang, H., Wu, T., Wang, J., Li, J., Jin, K.: Experimental study on the incremental forming limit of the aluminum alloy AA2024 sheet. Int. J. Adv. Manuf. Technol. 108(11–12), 3507–3515 (2020). https://doi.org/10.1007/s00170020056132 Guo, X., Gu, Y., Wang, H., Jin, K., Tao, J.: The Bauschinger effect and mechanical properties of AA5754 aluminum alloy in incremental forming process. Int. J. Adv. Manuf. Technol. 94(1–4), 1387–1396 (2017). https://doi.org/10.1007/s001700170965y
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Bouhamed, A., Jrad, H., Said, L.B., Wali, M., Dammak, F.: A nonassociated anisotropic plasticity model with mixed isotropic–kinematic hardening for finite element simulation of incremental sheet metal forming process. Int. J. Adv. Manuf. Technol. 100(1–4), 929–940 (2018). https:// doi.org/10.1007/s0017001827823 Ben Said, L., Mars, J., Wali, M., Dammak, F.: Numerical prediction of the ductile damage in single point incremental forming process. Int. J. Mech. Sci. 131, 546–558 (2017) Gatea, S., Ou, H., McCartney, G.: Review on the influence of process parameters in incremental sheet forming. Int. J. Adv. Manuf. Technol. 87(1–4), 479–499 (2016). https://doi.org/10.1007/ s0017001684266 Ambrogio, G., De Napoli, L., Filice, L., Gagliardi, F., Muzzupappa, M.: Application of Incremental Forming process for high customised medical product manufacturing. J. Mater. Process. Technol. 162, 156–162 (2005) Duflou, J.R., et al.: Process window enhancement for single point incremental forming through multistep toolpaths. CIRP Ann. 57(1), 253–256 (2008) Bouhamed, A., Jrad, H., Mars, J., Wali, M., Gamaoun, F., Dammak, F.: Homogenization of elastoplastic functionally graded material based on representative volume element: application to incremental forming process. Int. J. Mech. Sci. 160, 412–420 (2019) Malhotra, R., Xue, L., Belytschko, T., Cao, J.: Mechanics of fracture in single point incremental forming. J. Mater. Process. Technol. 212(7), 1573–1590 (2012) Palumbo, G., Brandizzi, M., Cervelli, G., Fracchiolla, M.: Investigations about the single point incremental forming of anisotropic Titanium alloy sheets. Adv. Mat. Res. 264, 188–193 (2011) Fan, G., Sun, F., Meng, X., Gao, L., Tong, G.: Electric hot incremental forming of Ti6Al4V titanium sheet. Int. J. Adv. Manuf. Technol. 49(9–12), 941–947 (2010) Jrad, H., Mars, J., Wali, M., Dammak, F.: Geometrically nonlinear analysis of elastoplastic behavior of functionally graded shells. Eng. Comput. 35(3), 833–847 (2018). https://doi.org/10.1007/ s0036601806333 Mars, J., Ben Said, L., Wali, M., Dammak, F.: Elastoplastic modeling of lowvelocity impact on functionally graded circular plates. Int. J. Appl. Mech. 10(04), 1850038 (2018)
Simulation of the Effects of Heat Introduced During Combustion on SI Engine Performance Mohamed Brayek1(B) , Mohamed Ali Jemni1 , Amara Ibraim2 , Ali Damak1 , Zied Driss1 , and Mohamed Salah Abid1 1 Laboratory of ElectroMechanic Systems (LASEM), National School of Engineers of Sfax
(ENIS), University of Sfax (US), B.P. 1173, Road Soukra km 3.5, 3038 Sfax, Tunisia 2 Higher Institute of Technological Studies ISET Nabeul, Nabeul, Tunisia
Abstract. A singlezone model using Matlab was prepared for a thermodynamic simulation of a spark ignited engine. The simulation model based on close cycle allowed the prediction of mass fraction burned, pressure, temperature, heat transfer coefficient, work and heat loss. The model could be used for several fuels based on Wiebe heat release function. Woschni’s model for convective heat losses was taken for modeling the engine cycle. The current work involves testing the effect of heat introduced on the performance of an SI engine Honda GX100 generally used to power SHX2000 Generator. Simulation was carried on a 98 cm3 SI engine at 3600 rpm (5.7 Nm). This paper investigates the effect of the heat release on the engine performance. Five different chosen values were tested from 200 to 250 J with a step of 10 J. Results shows an increase in pressure, temperature and heat transfer coefficient. As consequence the heat loss increases and follows the trend of the cumulative work. It can be stated that engine performance improves linearly with the increase of the heat release. It should be notice that the only limitation of the amount of heat introduced in the combustion chamber is the fuel characteristics and the mechanical limits of the engine component. Keywords: Combustion · Heat release model · Matlab · Performance characteristics · Simulation · Spark ignition engine
1 Introduction Internal combustion engines will continue to exist for the few next decades, therefore improving performance and reducing emission will continue to be an interesting research area. Researches on the purpose of improving engine performance are ongoing worldwide. Experimentally testing new injection systems such GDI (Gasoline Direct injection) and HCCI (Homogeneous Charge Compression Ignition) has led to more efficient combustion and produce lesser emissions (Ganesan 2007). However, it is time consuming and costly affair to experimentally test the influence of changing several parameters on engine performance. Also, it is significantly complicated to experimentally isolate one input parameter to define its effects on engine output. There are numerous examples where theoretical methods are preferred as they are based on mathematical and fundamental equations and because they require a limited set of experimental data. Therefore © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 217–230, 2022. https://doi.org/10.1007/9783030849580_24
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there is a need for an accurate, fast and simple model for the engine simulation. Analysis of different technologies could become easier, more economical and less time consuming using simulation in different environments like Simulink, CFD etc.… based on mathematical model. Various researchers have done rigorous work in the field to develop mathematical models and used them in Matlab Simulink for analytical analysis of engine performance characteristics (Chaudhari et al. 2014; Buttsworth 2002). These relations can be used to investigate the behavior of ethanol blending with gasoline in spark ignition engine. These simulations results could be applied to perform new technology in the engine. Shapiro and Gerpen (1989) used a twozone combustion model to settle a model to analyse the exergy of both diesel and gasoline engines. The present investigation is an attempt to develop a mathematical model of the combustion process of SI engine using Matlab environment. Matlab is one of the most popular software used to analyze experimental data and to solve theoretical equations. Given the relative simplicity of internal combustion (IC) engine routines presented by Ferguson (2015) it appeared reasonable to develop equivalent routines using Matlab. The fundamental routines of calculation are available in Matlab environment, it offers the capacity to adapt and extend rapidly the routines as required. Here, a simulation model of actual process occurring during thermodynamic cycle of a real spark ignition (98 cubic centimeter aircooled fourstroke SI engine) is developed. This singlezone SI engine model is based on the first law of thermodynamics and Waschni’s correlation for the heat transfer (Wu et al. 2006; Heywood 1988). This model offers the ability to predict combustion performance parameters. The present work aims to establishing the dynamics relation cause effect between the heat introduced in the combustion chamber and engine performance. The dynamic relations used in modeling are differential equations obtained from conservation of mass and energy laws. The challenge in engine modeling is to establish the relations between the engine input and output variables which describe better the model and predict the output variables in different working conditions of the engine. The output variables are the heat flux, heat loss, pressure, temperature and work. In the next section the Matlab routines will be described.
2 Mathematical Model Development The main aim for this work is to implement a thermodynamic model using the Matlab platform to predict engine performance. Treating the cylinder contents as a single fluid or zone is one of the most used approaches when modeling engines (Klein 2004). This model is based on assuming that the cylinder contain only an ideal gas characterized by a uniform homogenous temperature and pressure. The amount of flow in mass and burn characteristic is described by the Wiebe function. In this work, air will be considered as ideal gas. It is supposed that closing of the exhaust valve is instantaneous with the opening of the intake valve. During this simulation the heat transfer is assumed to occur uniformly in the cylinder. Compression and expansion are the two stroke presented during 360º crank angle (CA) of onethermodynamic cycle. Engine geometries, such as bore, stroke and compression ratio are used to determine the instantaneous physical information such as area and volume as function of crank
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angle. With another line of information about heat input, these information will be used to predict the cylinder pressure. It will be utilized to present temperature inside the combustion chamber and the heat transfer coefficient as consequence the heat transfer from gas to cylinder wall. The rate of heat loss will be fed back to the pressure prediction function. Results will be converted to indicate the mean effective pressure, and then work will be known finally. 2.1 Cylinder Volume and Surface The piston position and combustion chamber surface and volume as function of the crank angle can be defined using the crank slider model and the engine geometric parameters presented in Fig. 1. The engine geometry are: displacement Vd , compression ratio r, crankshaft angle r, bore b, stroke a and connecting rod l.
Fig. 1. Engine geometry
The piston position is deduced from fundamental trigonometric equations (Heywood 1988). The geometric surfaces and volume will be transformed into a geometric submodel then used in the combustion model to determine engine performance (the heat transfer, pressure and temperature during combustion). The volume and the surface of the combustion chamber can be expressed, respectively, by: ⎤ ⎡ 2 l Vd ⎣ l Vd + 1 − cos θ − + − sin2 θ ⎦ (1) V(θ ) = 2 a a (r − 1) ⎤ ⎡ 2 l s⎣l π 2 + 1 − cos θ − − sin2 θ ⎦ A(θ ) = b + π b 2 2 a a
(2)
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2.2 Fuel Burning Rate It is quite difficult to experimentally investigate the combustion process in the engine. The burn rate is defined as the rate of the fuel mass consumption during the combustion process in the cylinder. The mass fraction burned versus crank angle curve is frequently presented as functional form. (Rakopoulos and Kyritsis 2006; Yeliana et al. 2011). The burning rate starts at low rate after the spark discharge then it increase rapidly to reach the maximum at about halfway then decrease at the end of the burning process to about zero as the combustion ends. Therefore, the function describing the burning is characterized by its SShape. The following functional form (Wiebe function) is frequently used to characterize the curve of the mass fraction burned vs. the crank angle:
θ − θ0 m+1 (3) xb (θ ) = 1 − exp −a θ From this function the fuel mass burn rate can be presented in the following form:
a(m + 1) θ − θ0 m θ − θ0 m+1 dxb = exp −a (4) dθ θ θ θ where a: the completeness factor m: the form factor θ : the total combustion duration (from xb = 0 to xb = 1). θ : the crank angle θ0 : the crank angle corresponding to the start of combustion a and m are adaptable constants generally 5 and 2 are the selected values. These two parameters can be modified to accurate the profile to a specific application or engine. The completeness factor (a) is the combustion efficiency indicator. It depends on engine design, combustion duration and the intensity of charge motion (Heywood 1988) it is typically between 2 and 6. The form factor (m) influence the shape of mass burned profile. Although, the starting and the ending points of xb are independent of m, the shape of mass fraction burned changes with the variation of a and m. 2.3 Thermodynamic Model The first law of thermodynamics could be presented as follow: d Q dW dU = − dθ dθ dθ
(5)
where U : the change in internal energy within the system, Q: the total energy transferred into the system, W : the work transferred out of the system. A heat transfer occurs in the combustion chamber then the heat release could be defined as: dQch dQht dQ = − d" d" d"
(6)
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where Qch : the total heat release (chemical energy). Qht : the total transferred out of the system. The first law of thermodynamics applied to a closed volume of combustion chamber can be presented in the following equation. δQch dU d Qht δW = + + (7) dθ dθ dθ dθ The amount of internal energy change and the work transferred of the working fluid can be determined as function of P and V as follows: δQch = dU + δQht + δW ⇒
δW dV dT dU + = mcv +P dθ dθ dθ dθ where:m: the total mass of in system gases in kg cv : Specific heat of the combustion chamber gas in kJ/kg. K.
(8)
2.4 Heat Release During Combustion Combustion process is the release of the chemical heat in the fuel, it is the reason of the increase of temperature and as consequence the pressure which pushes the piston down instantaneously. Combustions reaction (the heat release) occurs following the burning rate. Therefore, the heat release rate (∂Q) with respect to the crank angle could be expressed as follow: ∂Q = Qch
dxb dθ
(9)
2.5 Heat Loss Where there are a difference in temperature there are a heat transfer phenomena. In the internal combustion engine the heat exchange occurs between the combustion gats, the cylinder walls and the coolants (oil and water). The Newtonian model that describe the convective heat loss thought cylinder wall is expressed as follow: Q = hA(Tw − T∞ )
(10)
where, Tw : the surface temperature T∞ : the outside temperature h: the coefficient of convection. A: the surface between the combustion chamber wall and the combustion gas Radiation influence is limited when compared to convection in SI engine, it is only about 5% of the heat transfer from cylinder gases to cylinder walls. Therefore, in the present work convection is the only heat transfer mechanism counted. The convective heat loss rate as function of the crank angle is described as follow: h(θ )A(θ )(T (θ ) − Tw ) d Qht = dθ 2π N where N : the engine speed.
(11)
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2.6 Heat Transfer Coefficient In order to calculate heat loss from the cylinder, the heat transfer coefficient is needed. Convection is the main heat release phenomena occurring during combustion. The most popular correlations used to define the convective heat transfer coefficient in the engine cylinder are that of Woschni, Annand, and Eichleberg (Chan et al. 2013). Woschni correlation assume that the heat transfer coefficient depends to the incylinder pressure, temperature and instantaneous cylinder volume which is more accurate than assuming that it is constant during combustion. The other two heat transfer correlations Annand (Heywood 1988; Wu et al. 2006) and Eichleberg (Zeng et al. 2004) are limited in use where they are used essentially in special applications. They are used for example in cases where the variation of heat transfer coefficient is supposed as uniform on all cylinder walls (Bayraktar and Durgun 2004). Woschni’s correlation for the convective heat transfer coefficient is expressed as follow (Woschni 1967). h = 3.26b−0.2 P 0.8 T −0.55 V 0.8
(12)
where P: the cylinder pressure (kPa), T is the cylinder temperature (K) and V is the cylinder volume (m3 ). 2.7 In Cylinder Pressure For an ideal gas with constant specific heat, the first law of thermodynamics in differential form is mcv
dQ dV dT = −P dθ dθ dθ cp =γ cv
(13) (14)
where cp : specific heat of the combustion chamber gas at constant pressure in kJ/kg. K γ : ratio of specific heats at constant volume and pressure. The incremental work done by the piston can be expressed by the incremental change of system volume and the mean cylinder pressure as follow: dW = PdV
(15)
Consequently the pressure evolution as function of the crank angle could be delivered as the following equation (Heywood 1988): dP γ − 1 ∂Qch h(θ )A(θ )(T (θ ) − Tw ) P dV = − −γ (16) dθ V dθ 2π N V dθ (θ ).
dV dθ
can be determined from Eq. 1 by taking derivative with respect to the crank angle
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2.8 In Cylinder Temperature The incylinder temperature evolution as function of the crank angle is expressed as follow dT 1 δQch h(θ )A(θ )(T (θ ) − Tw ) dV = − −P (17) dθ mcv d θ 2π N dθ
2.9 Thermal Efficiency Internal combustion engines convert heat (thermal energy Qin ) into mechanical energy (work) W . However, a fraction of the introduced thermal energy Qin is transferred into the environment (heat loss Qht ). The thermal efficiency of the internal combustion engine is defined as the ratio between the mechanical energy. W and the heat introduced in the combustion chamber Qin . η=
W Qht =1− Qin Qin
(18)
2.10 Indicated Mean Effective Pressure The Indicated Mean Effective Pressure imep is the ratio of the work delivered to the piston over the compression and expansion strokes, per cycle per unit displaced volume imep = where Vd =
ηQin Vd
(19)
π 2 4 b s.
3 Modeling Engine on Matlab The Matlab environment offers the ability to build a model using the previous mathematical formulation presented in appropriate logical manner. Matlab contain several differential equations solvers, in the present work the predefined ode23 solver was used to solve the pressure and temperature differential equations. The engine model has been constructed using Matlab. A graphical user interface GUI is created with a block of customizable parameters. It offers easier method to introduce different engine characteristics and to read and graphically present simulation results (Fig. 2). In the present work the Matlab routine was essentially following Ferguson (2015) investigation. This mathematical model allows the prediction of SI engine in cylinder variable as a function of crank angle. The present investigation focus on the effects of only the heat release introduced in the combustion chamber on engine performance (Table 1). The Matlab GUI contain editable boxes where the engine geometry and operating parameters could be introduced as simulation input. This interface allow a simple
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Fig. 2. GUI of the simulation program Table 1. Engine specifications Parameters
Value
Bore and stroke
56 × 40 mm
Displacement
98 cm3
Compression ratio 8.5:1 Maximum torque
5.7 Nm at 3600 rpm
Net power
2.1 kW (2.8 HP)/3600 rpm
interaction with different users where it allows to change engine geometry or operating condition if needed. Once the input cases are loaded, the GUI is fitted with a Start button that run the script and shows the results. The mass fraction burned go from xb = 0 to xb = 1, equations are then integrated for crank angles from −π to π. The heat release follow the fuel burned rate and then affects the incylinder environment. Results are presented in the convenient boxes and figures are presented graphically in their places.
4 Simulation Conditions The engine studied is a specific singlecylinder gasoline engine. The main engine specifications and operational conditions are given in Table 2. For these operational characteristics, the program uses a predicted total heat addition values from 200 to 250 J which is in good agreement with the experimental value of (Ferguson 2015; Ramachandran 2009). The good selection of this value provides a good approximation since it is used in the calculation of all parameters corresponding to the engine performance. For the simulation of combustion in the cylinder, the Matlab code
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Table 2. Simulation conditions Parameters
Value
Initial temperature
300 K
Initial pressure
1 atm
Cylinder wall temperature 400 K Heat transfer
Convection
Fuel consumption
0.67 kg/h
Combustion duration
60° CA
Wall temperature
400 K
Ignition advance
25° CA BTDC
divides the compression and expansion strokes into 360 steps of the crank angle in order to produce an accurate solution in the different piston positions.
5 Results and Discussion The heat release during combustion differs from one fuel to another and also varies depending on airfuel mixtures introduced into the cylinder. With the change of the fuel it is imperative to study the effect of varying the heat input on engine performance.
Fig. 3. Effect of the heat release on incylinder pressure evolution
To examine the effects of the heat change on engine a performance, a numerical analyzes was performed using the above equations and imposing the ignition engine configuration chosen. The values used are from 200 to 250 J with a step of 10 J as step. The simulation conditions are presented in Table 2. temperature distribution in
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the chamber walls and temperature, pressure, heat loss to the walls are studied for different heat release and under the same operating condition. This study can provide an investigation about the effect of the fuel type on the engine performance due to the difference of the heat release of fuels. Cylinder pressure calculations versus crank angle are done for different heat release. Results presented in Fig. 3, takes into consideration the heat transfer in the engine and the variable heats release, using a dual Wiebe function. The calculated maximum pressure increases linearly with the increase of the heat released. Where the maximum pressure passes from 47.06 to 55.25 bar with the increase of the heat release from 200 to 250 J respectively. Table 3. Summarise of the effects of heat release on engine performance Qin (J)
200
Pmax (bar)
47.06 48.71 50.35 51.98 53.62
θ at Pmax (deg) 16.0
210 16.0
220 16.0
230 16.0
240 16.0
250 55.25 16.0
Wnet (J)
83.03 86.95 90.85 94.72 98.58 102.41
heatLoss
25.11 27.03 29.01 31.05 33.14
35.30
Efficiency (η)
0.42
0.41
0.41
0.41
0.41
0.41
imep (bar)
8.47
8.87
9.27
9.67 10.06
10.45
Ce (Nm)
6.3
6.6
6.8
7.2
7.4
7.7
Pe (KW)
2.36
2.47
2.59
2.70
2.81
2.92
Figure 4 shows the variation of incylinder gas temperature profile versus crank angle during compression and power strokes, considering temperature dependence to specific heats. Incylinder gas temperature increase with the increase of the heat release, it reaches a maximum value of about 3000 K when the heat introduced is 250 J. The exhaust gas temperature corresponding to the crank angle 180° CA increased sharply with the increase of the heat release. It is also observed that the crank angles corresponding to the peaks of pressure and temperature, predicted with program, are constant for different heat input. This could be explained by the fact that the burning duration is fixed during these calculations. The effect of increasing the heat release on the heat transfer coefficient is presented in Fig. 5. It is observed that the effect on the heat transfer coefficient is similar to that on the pressure and temperature in the cylinder. The increases of temperature and heat transfer coefficient with the increase heat introduced are responsible for the heat loss intensification. Heat loss is very low during compression, indicating an almost isentropic compression process, then it increases rapidly during the heat release process. As seen in Fig. 6. Heat loss passes from 25 to 35 J with the increase in of the heat introduced to the combustion chamber from 200 to 250 J.
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Fig. 4. Effect of the heat release on incylinder temperature evolution
Fig. 5. Effect of the heat release on the heat transfert coeficient evolution
In order to study the effect the heat release on the heat loss, Figs. 6 and 7 are presented. It shows variation of work and the heat loss versus the crank angle using different heat release at engine speed of 3600 rpm. During compression the cumulative work is negative then with the increase of pressure during expansion it increase and becomes positive. During compression the heat loss is limited which indicates a nearly isentropic compression process then it rise dramatically through the heat release process. It is obvious that there is some difference when different heat releases are used. Although they have similar trends, the maximum work and heat loss are significantly increased with the increase of the heat release. The increase of the difference between the work and heat loss with the increase the heat release is accompanied by a decrease of this difference fraction (percentage).
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Fig. 6. Effect of heat release on the heat loss
Fig. 7. Effect of heat release on cumulative work
Table 3 presents results of the mathematical program of Matlab for five heat inputs. It can be notice that cumulative work (and power) increases linearly with the increase of the heat release. The engine efficiency was not affect by the variation of the heat release. As consequence it can be stated that there is two limitation of the amount of heat introduced in the combustion chamber first the fuel high heat value and the mechanical limits of the materials of constriction of the engine.
6 Conclusions SI engine model was implemented in Matlab/GUI environment to analyse the engine performance characteristics. The effect of heat release introduced to the combustion chamber on engine performance was investigated. Pressure, temperature and heat transfer
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coefficient increases as the heat release increases. As consequence to the increase of the exhaust gas temperature the heat loss increase and follows the trend of cumulative work. The engine efficiency was not affect by the variation of the heat release. It can be concluded that engine performance is improved linearly with the increase of heat release. Furthermore, through users’ needs the best compromise between the consumed heat, the power output and the heat losses could be made. It should be notice that the only limitation of the amount of heat introduced in the combustion chamber are the fuel characteristics and the mechanical limits of the engine component.
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Yeliana, Y., Cooney, C., Worm, J., Michalek, D.J., Naber, J.D.: Estimation of doubleWiebe function parameters using least square method for burn durations of ethanolgasoline blends in spark ignition engine over variable compression ratios and EGR levels. Appl. Therm. Eng. 31, 2213–2220 (2011). https://doi.org/10.1016/j.applthermaleng.2011.01.040 Zeng, P., Prucka, R.G., Filipi, Z.S., Assanis, D.N.: Reconstructing cylinder pressure of a sparkignition engine for heat transfer and heat release analyses, pp. 43–52 (2004). https://doi.org/ 10.1115/ICEF20040886
Fracture Toughness Resistance and Mechanical Tensile Properties of Cold Rolled CuZn30 Brass Alloy Wafa Taktak(B) and Raidh Elleuch Laboratoire des Systems ElectroMecaniques, National School of Engineering of Sfax, University of Sfax, Sfax, Tunisia [email protected]
Abstract. The present work studies the effect of cold rolling on the mechanical tensile, hardness and fracture toughness properties of alpha brass alloy (CuZn30). The material was cold rolled at room temperature to different percentage 25%, 50% and 75%. The mechanical tensile properties of the specimens with different cold rolling percentage were established by monotonic tensile test along three directions (L: rolling direction, T: transversal direction and D: diagonal direction). Therefore, the micro hardness of the as received and cold rolled alloy was determined by micro Vickers hardness test. Furthermore, the fracture toughness resistance of the cold rolled and as received alloy was evaluated by ductile tearing test using central cracked panels (CCP) samples in two directions (L and T). Experimental results found that mechanical tensile property, micro hardness and fracture toughness of brass alloy CuZn30 were considerably influenced by cold rolling. When the cold rolling increases, the strength and hardness increase rapidly however the ductility and the toughness fracture resistance lower. That is linked to the increase of density dislocation during the cold rolling. The highest strength and fracture toughness were shown in the longitudinal direction in the studies alloy. But the maximum ductility was noticed in the transversal direction. Keywords: CuZn30 brass alloy · Cold rolling; tensile test · Hardness · Ductile fracture
1 Introduction The alloys of copper with zinc (brass) have been successfully used in various domains of industry (armaments industry, aircraft industry, automobile industry, precision mechanics….) due to excellent combination of strength and ductility. Also it has a high workable and formability at ambient temperature (Darmawan et al. 2018; Rahman et al. 2018; Ozgowicz et al. 2010 and Chen et al. 2020). However, during the cold working process, the brass subjected to high plastic deformation. The mechanical properties and the fracture behavior can be notably changed by the plastic deformation presented in the material (Darmawan et al. 2013; Bai et al. 2018 and Darmawan et al. 2018). © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 231–239, 2022. https://doi.org/10.1007/9783030849580_25
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The strain harding leads to an important growth in strength dislocation barriers to block the dislocation movements. It explicated by the enhance in dislocation density witch happens when the material is cold deformed (Lan et al. 2017; Wang et al. 2017 and Eskandari and Szpunay 2016). The existence of dislocations stretches the atom lattice by softly displacing atoms from their equilibrium positions. This lattice stretch reacts to reduce the mobility of the dislocations. The decrease dislocation mobility interprets in to the growth in the stress desired to move the dislocation so consequently the enhance in the strength and the lowering in the ductility of the material (Callister 2007 and Bodude et al. 2016). The cold rolling effect on fracture toughness is less well understood. In the literature, most studies concentrate on the impact of cold rolling on fracture toughness of steels but not much information is accessible concerning brass alloys. These studies on a variety of different steels have shown that the cold rolling reduces the resistance to initiation of cracking and the resistance to ductile tearing (Tajally 2010 and Cosham 2001). Therefore, in this investigation, the effect of various cold rolled percent on the mechanical tensile proprieties and hardness of brass (CuZn30) was explored. Moreover, the cold rolling effect on the fracture toughness behavior of the brass alloy was studied.
2 Experimental Tests The CuZn30 brass alloy of nominal thickness 2,8 mm has been chosen for study. The chemical composition of CuZn30 sheet is given in the Table 1. The initial plates samples with the size of 600 mm (length) × 300 mm (width) × 2,8 mm (thickness) was cold rolled at room temperature using a laboratory rolling mill. The thickness of plates samples was reduced from 2.8 to 2.1, 1.4 and 0.7 mm and the percentage of cold rolling reductions are 25%, 50% and 75% respectively. The mechanical tensile proprieties of the different cold rolled samples was studied at ambient temperature along three different direction (L: corresponds to the rolling direction, T: the transverse direction and D: the diagonal direction) using tensile test samples. The dimensions and geometry of the used tensile sample were in accordance with standard NF EN 100021. Figure 1 presents the tensile samples used for this study. The tensile samples were machined in three directions in the rolled plates. The tensile tests were performed at room temperature using a 50kN LLOYD universal tensile machine with an extensometer of length 25 mm at a cross head speed of 10 mm/min for the as received and cold rolled alloy. For identification of the fracture toughness behavior of the brass alloy, central cracked panels (CCP) were used. The geometry of CCP sample used is presented in Fig. 2. The CCP samples were precrack in fatigue to obtain a normalized crack length ratio a/w equal to 0.36 (where W is the half width of sample and a is the half crack length). The ductile tearing tests were carried out in a universal testing machine under displacement control at a constant crosshead speed of 1 mm/min. Samples were tested for two directions. The load vs displacement curves were on record during the test. The micro hardness test of the as received and cold rolled samples was investigated using a micro hardness Vickers testing machine by applying a load of 50 g for 15 s. Five measurements were realized for each sample.
Fracture Toughness Resistance and Mechanical Tensile Properties Table 1. Chemical composition of CuZn30 (wt%). Element Composition (wt%) Zn
30
Ni
0.3
Pb
0.05
Fe
0.05
Sn
0.1
Al
0.02
Cu
Bal
Fig. 1. Geometry of the tensile specimen (in mm)
Fig. 2. CCP specimens Geometry (in mm).
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3 Resultants and Discussion 3.1 Cold Rolling Effect on Tensile Tests The true stressstrain curves of cold rolled CuZn30 brass alloy (CR25%, CR50% and CR75%) along three different directions (L, T and D) were represented in Fig. 3. It’s notable that the changes of anisotropy in tensile proprieties during cold rolling deformation. It can see from Fig. 3a that the tensile properties of CR25% samples along three directions are most the same, with the yield strength being about 350 MPa. With growing the percentage cold rolling to 50%, the mechanical tensile properties of the CR50% samples begin to present a difference along three directions, as indicated in Fig. 3b. The CR50% samples along transversal direction T have the highest elongation but the lowest yield strength, and CR50% samples along longitudinal direction presents the highest yield strength but the lowest elongation. The modification of the yield strength anisotropy is very low but the elongation anisotropy indicates an important difference during cold rolling deformation. The tensile proprieties of CR75% along three directions are shown in Fig. 3c. When the percentage of cold rolling increases to 75%, the elongation and yield strength anisotropy along three directions presents a significant difference. The CR75% samples along longitudinal direction have the highest yield strength of about 730 MPa, while the CR75% samples along transversal direction show the best elongation of about 4,36%. The increase in cold rolling deformation has an important effect on the mechanical tensile proprieties of CuZn30. Figure 4 shows the true stressstrain curves of the cold rolled CuZn30along three different directions. Figure 4a reveals the true stressstrain curves of CuZn30 brass alloy with different percentage of cold rolling for longitudinal direction. As marked in Fig. 4a, cold rolling shows a significant modification in tensile properties of the CuZn30 brass alloy. For as received CuZn30 alloy, the yield strength (YS), ultimate tensile strength (UTS) and elongation are 228 MPa, 458 MPa and 37% respectively. With growing cold rolling percentage, the YS and UTS increase progressively, whereas the elongation decreases greatly. UTS increases from 458 to 898 MPa and YS increases from 228 to 609 MPa. While the elongation reduces from 37% to 4.2%. For transversal direction, as percentage of cold rolling increases from 0% to 25%, 50% and 75%, the ultimate tensile strength (UTS) values grows from 448 to 471, 527 and 829 MPa and the yield strength (YS) values enhances from 219 to 308, 447 and 502 MPa. Whereas the elongation reduces from 38% to 27%, 9% and 4.4% (see Fig. 4b). The same results determined in both directions (L and T) are obtained in the diagonal direction. The strength increases rapidly while the ductility declines after cold rolling. Figure 4c shows that the ultimate tensile strength (UTS) rise from 456 to 847MPa and YS increases from 210 to 582 MPa, but the elongation reduces from 38.5% to 3.8% when the percentage cold rolling increases from 0% to 75%. The results show that the modification of the mechanical property along three directions presents similar fracture, with the strength growing and elongation is lowering with increasing the percentage cold rolling. The maximum values of UTS and YS and the minimum value of elongation are obtained in the longitudinal direction. During cold rolling process, the strength of the CuZn30 brass alloy has a noticeable increase and important decrease of plasticity in longitudinal direction. The results can be attributed
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to the following reasons. Firstly, during the cold rolling, grains are sorely elongated in the rolling direction. Therefore a fiber texture is formed along the rolling direction, which offers increase to the ameliorated tensile strength. Secondly, with increasing cold rolling percentage, the dislocations density increase which leads to rise tensile strength and drop elongation. 3.2 Cold Rolling Effect on Hardness The value of micro Vikers hardness of as received and cold rolled brass CuZn30 is given in the Table 2. It is found that the hardness has increased from 145 Hv0.05 to 180, 231 and 308 Hv0.05 with increasing the cold rolling percentage. Similar to the tensile tests results, hardness values increased with increasing the cold rolling percentage. Table 2. Hardness of CuZn30 with different cold rolling percentage. % CR
Hv0.05
0
145
CR25% 180 CR50% 231 CR75% 308
3.3 Cold Rolling Effect on Ductile Tearing Figure 5 shows the effect of cold rolling on CuZn30 brass alloy along two directions (longitudinal direction L and transversal direction T). The maximum loads for cold rolled samples are lower than those for without cold rolling. It shows that the longitudinal direction samples show higher maximum loads value than transverse samples, representing higher loaddisplacement curves. The energy needed for the tearing of a precracked specimens, determined from the area of loaddisplacement curves, decrease with increasing the percent of the cold rolling in the two directions (L and T). Note that ductile behavior is frequently related to high energy absorption at fracture. The samples in longitudinal direction show larger area ender curve than the samples in transversal direction. It is shown that the CuZn30 brass alloy is slightly tougher when tested in longitudinal direction compared to the transverse direction.
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4 Conclusion In this work, CuZn30 brass alloy subjected to cold rolling with different percent has been investigated for understanding it’s tensile and fracture behavior. The main conclusions presented in this work are as follows: • The yield strength (YS) and hardness increased with an increase in the coldrolling percentage. The increase in the density of dislocation by cold rolling leads to the strengthening of coldrolled CuZn30 brass alloy. • The elongation of coldrolled CuZn30 brass alloy decreased with a cold rolling percentage due to the decrease of the average distance between dislocations and start blocking the motion of each other. • The cold rolling has a profound effect on strength anisotropy that increase with cold rolling percentage.
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• The maximum strengths were obtained for a specimen in the rolling direction. • The results indicate that cold rolling has a significant effect on decreasing the fracture toughness of the alloy that increases the cold rolling percentage.
References Darmawan, A.S., Febriantoko, B.W., Anggono, A.D., Riyadi, T.W.B., Hamid, A.: Effect of thickness reduction on cold rolling process to microstructure and brass hardness. In: MATEC Web of Conferences, vol. 248, p. 01001. EDP Sciences (2018). https://doi.org/10.1051/matecconf/ 201824801001 Rahman, M.M., Sufian, M.A., Rehgir, A.L., Shahid, M.S., Ahmed, S.R.: Effect of hot and cold rolling on electromechanical properties of a commercial highconductive metallic material. In: The 11th International Conference on Marine Technology, MARTEC (2018) Ozgowicz, W., KalinowskaOzgowicz, E., Grzegorczyk, B.: The microstructure and mechanical properties of the alloy CuZn30 after recrystallizion annealing. J. Achiev. Mater. Manuf. Eng. 40(1), 15–24 (2010) Chen, K.J.: Novel application research on critical hightemperature deformation of lowlead brass alloy. Metals 10(6), 722 (2020). https://doi.org/10.3390/met10060722 Darmawan, A.S., Siswanto, W.A., Sujitno, T.: Adv. Mater. Res. 789, 347 (2013) Bai, Y., He, T., Liu, Y.: Effects of Sn microalloying on cold rolling and recrystallization textures and microstructure of a ferritic stainless steel. Mater. Charact. 137, 142–150 (2018). https:// doi.org/10.1016/j.matchar.2018.01.022 Lan, C., Wu, Y., Guo, L., Chen, F.: (2017) Effects of cold rolling on microstructure, texture evolution and mechanical properties of Ti32.5Nb6.8Zr2.7Sn0.3O alloy for biomedical applications. Mater. Sci. Eng. A, 690, 170–176 (2007). https://doi.org/10.1016/j.msea.2017. 02.045 Wang, S., et al.: The evolution of deformation microstructure in electron beam melted Ta2.5W alloy during cold rolling. Fusion Eng. Design, 125 510 (2017). https://doi.org/10.1016/j.fuseng des.2017.03.101 Eskandari, M., MohtadiBonab, M.A., Szpunar, J.A.: Evolution of the microstructure and texture of X70 pipeline steel during coldrolling and annealing treatments. Mater. Design 90, 618 (2016). https://doi.org/10.1016/j.matdes.2015.11.015 Callister, Jr., W.D.: Materials Science and Engineering: An Introduction, 7th edn. Wiley, New York (2007) Bodude, M.A., Momohjimo, I., Nnaji, R.N.: Mechanical and microstructural evaluation of plastically deformed brass. J. Med. Sci. Technol. 59–69 (2016) Cosham, A.: A model of prestrain effects on fracture toughness. J. Offshore Mech. Arct. Eng. 123(4), 182–190 (2001). https://doi.org/10.1115/1.1408613 Tajally, M., Huda, Z., Masjuki, H.H.: A comparative analysis of tensile and impacttoughness behavior of coldworked and annealed 7075 aluminum alloy. Int. J. Impact Eng. 37(4), 425–432 (2010). https://doi.org/10.1016/j.ijimpeng.2009.08.009
Manufacturing of Sandwich Structure with Recycled Flax/Elium Skins Sami Allagui1,2(B) , Abderrahim El Mahi1 , Jeanluc Rebiere1 , Moez Beyaoui2 , Anas Bouguecha2 , and Mohamed Haddar2 1 Le Mans University, Acoustics Laboratory of Le Mans University LAUM, UMR CNRS 6613,
Av. O. Messiaen, 72085 Le Mans Cedex 9, France {abderrahim.elmahi,jeanluc.rebiere}@univlemans.fr 2 Department of Mechanical Engineering, National School of Engineering of Sfax Laboratory of Mechanics, Modelling and Production, Route Soukra, 3038 Sfax, Tunisia [email protected], [email protected]
Abstract. This work presents the results of several experimental analyses realized on a biobased sandwich structures that are manufactured by recycled composite skins reinforced applied to a balsa core. The skins are made up by a thermocompression recycling process applied for the production waste of thermoplastic composite reinforced with flax fibers. This recycling process consists of reshaping the flax/Elium composite waste by the combined action of temperature and pressure. This is possible thanks to the thermoplastic Elium resin that make possible the manufacturing of recycled skins with good mechanical behavior. After the recycling process, a short fiber reinforced composite is produced in which direction of fibers is random. The recycled skins properties are then measured and compared to an unrecycled material. The unrecycled material has an identical composition of the recycled composite and it is made up by a liquid resin infusion process (LRI). The mechanical properties of unrecycled and recycled composites are studied using quasistatic characterization tensile tests. Then, quasistatic bending tests are carried out to study the sandwich structure bending behavior. Keywords: Recycling · Thermocompression · Biobased composite · Sandwich structure · Bending behavior
1 Introduction Compared to thermosetting materials, the production of thermoplastic composites is increasing quickly. Thermoplastics composites present great chemical and impact resistance, excellent stiffness, and provide high design flexibility at a relatively low price (Bahlouli et al. 2012). For example, the polyamide (PA), the polyurethane (TPU), the polyethyleneteraphthalate (PET), the polybutyleneteraphthalate (PBT) and the polycarbonate (PC) are thermoplastic resins frequently used in composite production (Van Rijswijk et al. 2007). This study concentrates on a novel thermoplastic polymer resin called Elium. It is made up of two propenoic acid, two methyl, methyl ester or methylmethacrylate monomer (MMA) and acrylic copolymers in which MMA polymerized © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 240–248, 2022. https://doi.org/10.1007/9783030849580_26
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to polymethylmethacrylate (PMMA) (Han et al. 2020). As a consequence of the low viscosity, Elium is appropriate for VARI and RTM implementation processes (Bhudolia et al. 2018; Bhuldolia et al. 2017). The viscosity is about 200 cP which allows the polymerization at a low temperature (25 °C). Cousins et al. (2019) have studied the recycling processes effects on glass/Elium composite. They have compared different recycling operations: mechanical grinding, pyrolysis, dissolution and thermoforming. Using pyrolysis process, the results show that the polymer decomposition needs approximately lower energy compared to other recycling methods. The authors demonstrate also that the fiber recovered from composites by dissolution, present a stiffness reduction of only 12% compared to unrecycled material. The best mechanical properties are showed against the initial material using the injection and grinding process. Besides, that study proves the possibility of recycling the glass/Elium composite into other components like skateboards using the thermoforming process. The main objective of our work is to study the recyclability of the liquid resin “Elium” reinforced with “flax fibers”. An advanced recycling method is developed in which a thermocompression process is used. The recycling method is applied to flax/Elium composites waste. For this, sandwich structures with recycled flax/Elium skin and balsa core are manufactured. Quasi static tensile tests are realized on the recycled skins to analyze the recycling process effect on the flax/Elium composite. Then quasistatic bending analyses are performed to explore the bending behavior of the manufactured sandwich.
2 Materials and Recycling Method 2.1 Unrecycled Flax/Elium Composite In the presented work, an unrecycled material having an identical composition of the recycled skins is carried out. This material is a short fiber composite in which direction of fibers is random (Allagui et al. 2021). A liquid resin infusion process (LRI) (Gholampour and Ozbakkaloglu 2020) is used for the manufacturing of this composite. Firstly, the process consists of drying flax fibers in an oven with a temperature of about 110 °C. This step permits the elimination of exciting water. After 1 h of drying, flax fiber layers are manually cut into bundles of fibers with a dimension of about 5 mm × 20 mm. Then, these short fibers are then disposed randomly on a waxed mold, between two peel plies that aim to ensure the disassembly of the produced composite. The ensemble is then coated by a micro perforated film. This tissue ensures parallel circulation of Elium resin during the LRI process. The shape is then closed with an impermeable plastic film. The sealing of the mould is ensured with an adhesive sealer. After all, two flexible pipes are inserted into two couplings to allow the entry and the exit of resin. The entry pipe is plunged in a recipient containing Elium resin and the exit pipe is connected to a vacuum pump. Before the infusion process, the vacuum pump is activated for about 1h to enable the degassing of the mould. The infusion is then done at 0.5 bar pressure in which Elium resin circulates through the preform and impregnates fibers. When fibers are well impregnated, the resin intake is closed and the infusion process is stopped. The disassembly of the composite plate is then carried out after 24 h. In the rest of this study, the notation CR0 is referred to the unrecycled composite specimen.
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2.2 Recycled Flax/Elium composites Thermocompression process is realized on flax/Elium waste to create the recycled skin (Fig. 1). Composite Waste
Step 1: Preparation of waste
A 40ton TCE press machine
Prepared composite Compression mold
Mechanical tests
Recycled specimens
Step 2: Manufacturing using thermocompression machine
Fig. 1. Recycling method applied to flax/Elium composite waste
Firstly, the recycling process consists of cutting waste into small rectangular pieces. Secondly, we put these tiny particles between two steel plates which create the compression mould. The ensemble is then placed in a thermocompression machine, commercialized by DK technologies, to obtain recycled plate. Once the cycle of fabrication is defined, the mobile plate rises towards the fixed plate to create the compression on the mould have been computed. For the sandwich material, the greenpoxy 56 is used to maintain the skins to the balsa core. Then the composite is cured at room temperature with pressure using a vacuum molding process. The tensile specimens and the sandwich composite were cut by a lasercutting machine marketed by Epilog Laser Company.
3 Experimental Setups 3.1 Tensile Test In the quasistatic tensile tests, the specimens are exposed to uniaxial loading accordingly the method ASTM D3039/D3039M. The experiments are carried out with a tensile machine of 10 kN load cell (Fig. 2). The tensile specimens are flat (180 × 20 × 2 mm3 ). Figure 2 illustrates the experimental setup. The Young’s modulus and failure properties (failure stress and strain) are determined. For statistical purposes, the tests were repeated five times at ambient temperature with a strain rate of 0.5 mm/min. An extensometer is utilized to control the strain measurement in the tensile direction.
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Fig. 2. Experimental dispositive of tensile tests
3.2 ThreePoints Bending Test Threepoints bending experiments are carried out according to the standard test methods ASTM C393 and ASTM D7249 to study the bending action of the sandwich made with recycled skins. The load is performed at a 5 mm/min displacement rate. As mentioned in Fig. 3, the tests are realized on a computer with a 10 kN load cell.
Load Cellule 10 KN Upper support Test specimen
Lower support
Antirotation device
Fig. 3. Experimental dispositive of three point bending test
Sandwich specimens with length, width and thickness respectively of 250, 30 and 20 are made (4 mm for the two recycled skins and 15,9 mm for the sandwich core). Beams with a span length of 220 mm are broken to analyze the sandwiches properties at failure. In addition, beams are evaluated in their linear domain in monotonic threepoints bending tests for various span lengths (220, 200, 180, 160, 140, 120, and 100) to determine the sandwiches’ bending and shear stiffness.
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4 Results and Discussion 4.1 Tensile Behavior Quasistatic tensile characterization tests are performed on the unrecyled composite (CR0 ) and the recycled composite (CR1 ) to determine the recycling effect on the mechanical properties. The results of these experiments are given in Fig. 4. It represents the stress/strain curves of CR0 and CR1 specimens. For CR0 materials, we can notice that the curve can be analyzed in two phases. The first part is a short linear response that corresponds to the elastic domain, and the second part is a quasilinear response that indicates a decrease in rigidity until a fragile failure. After the yield point, which occurs at a very low deformation level (about 0.18%) and corresponds to a stress level of about 10 MPa, the loss of stiffness occurs. Since the elastic part is too short, some authors suggest determining two Young’s modulus: one from the elastic zone and the other from the second part (Bensadoun et al. 2016). Only Young’s modulus defined by the first elastic part is of our interest. In this zone, we notice a good superposition, as shown in Fig. 4. However, it seems that the failure properties present a dispersion of about 15%. This variety can be explained by the fact that the direction of fibers is random. For the CR1 composite, we notice also a linear behavior until a strain of about 0.1 percent and a stress of about 5 MPa. This zone is followed by a decrease in the rigidity and corresponds to a quasilinear behavior. Tableau presents the mechanical properties of unrecyled and recycled composite (CR0 and CR1 ). Based on Fig. 4 and Table 1, we notice that CR1 specimens present lower mechanical characteristics compared to CR0 specimens. The difference in manufacturing methods may explain this result (liquid resin infusion LRI for CR0 and the thermocompression method for recycled composites). The degradation of mechanical properties can also relate to the manufacturing conditions in which high temperature and great pressure are necessary for the manufacturing of recycled composite. These conditions cause damages to the polymer and a deterioration of the fiber/matrix interface. Table 1. Mechanical properties of unrecyled and recycled composites CR0 and CR1 Materials
Unit
E ±S tan d .dev [GPa]
CR0
CR1
8.2±0.5
5.4±0.8
σR±S tan d .dev [MPa] 50±9.5 εR±S tan d .dev [%]
15.6±2.3
0.82±0.1 0.53±0.1
4.2 Bending Performance of the Manufactured Sandwich with Recycled Skins 4.2.1 Quasi Static Results Sandwich composites are usually based on bending loads. To evaluate the flexural behavior of a [recycled flax/Elium (skin)]/[Balsa (core)] sandwich beam, threepoint bending
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60 CR0
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tests with a span length of 220 mm are carried out. The load/displacement curve obtained is shown in Fig. 5. Up to a deflection of about 1 mm, the results show a linear elastic domain, followed by a quasilinear behavior before sandwich failure. 600 500
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4.2.2 Equivalents Stiffnesses Properties To evaluate the bending deflection, tensile and compressive modulus of recycled skins are calculated. The shear deflection is calculated by the balsa core shear modulus. The equation representing the correlation between load and deflection in threepoint bending tests is shown by Monti et al. (2019): d2 1 W = + Pd 48D 4N
(1)
where d is the span length, and D and N present the flexural and shear properties of the sandwich structure. Regarding a symmetrical sandwich cross section, we have: D=
Ef tf2 6
+
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E f and E c are respectively Young’s Modulus of the recycled skins and the balsa core, t f and t c present their thickness (h = t f + t c ), Df is the flexural recycled skins stiffness in the neutral axes, D0 is the recycled faces bending stiffness in the median axis and Dc is the flexural stiffness of balsa core. If we consider the thin face and weak balsa core approximations, which are defined by (2Df /D0 < 0.01) and (DC /D0 < 0.01) respectively, we can obtain the flexural rigidity D and shear rigidity N by this simplified equation: D=
Ef tf h2 Gc h2 and N = 6 tc
(3)
The bending stiffness D and shear stiffness N can be determined using Eqs. (1) and the linear equation W/Pd = f. (d 2 ). As a result, sandwich beams are put to the test in their elastic domain, with span lengths ranging from 100 to 220 mm. Then, in Fig. 6, the evolution of W/(Pd) as a function of d 2 (the square of the span length) is plotted and equipped with a linear equation. 16 14
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12 10 8 6 4 2 0 0
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The stiffness D is calculated like the fitting curve slope and the shear stiffness N is calculated as the interception point, as shown in Fig. 6. Equation (3) was used to determine recycled flax/Elium skins stiffness E f and shear modulus of the balsa core Gc . Results are summarized in Table 2. Table 2. Elastic and shear properties of the recycled skins and balsa core Properties E f [GPa] Gc [MPa] Value
5.2
120.6
The calculated Young’s modulus is very close to the Young’s modulus of recycled flax/Elium CR1 in tensile test. However, shear modulus of the balsa core is 30% lower than the modulus calculated by the manufacturer and measured according to ASTM C273 test method. The shear properties of recycled skins, and the existence of a small amount of resin trapped in the center, particularly in the gaps between adjacent balsa blocks, may explain this result.
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5 Conclusions The aim of this study is to show that the flax/Elium waste composite can be recoverable and reused as a skin for a sandwich structure. For that, a thermocompression process is applied on composite waste to produce recycled materials. In the first part of this chapter, the recycled skin is compared to an unrecycled flax/Elium composite using quasistatic tensile tests. The results of the experimental investigations show lower mechanical performances compared to that of virgin specimens. This deterioration is mainly related to processing conditions which causes damages to the polymer and a deterioration of the fiber/matrix interface. In the second part of this paper, threepoints bending tests are realized on a sandwich structure produced by a recycled skin and balsa core. Results show flexural properties comparable to short fiber composites (Gourier 2016). The recycled flax/Elium associated to balsa core is very promising materials for polymerbased Wood/Plastic Composite (WPC) applications. Finally, we point out that the recycling process allows the reusing of flax/Elium waste composite as a skin for a sandwich structure.
References Allagui, S., El Mahi, A., Rebiere, J.L., Beyaoui, M., Bouguecha, A., et al.: Effect of recycling cycles on the mechanical and damping properties of flax fibre reinforced elium composite: experimental and numerical studies. J. Renew. Mater. 9(4), 695 (2021) ASTM C393/C393M –16. Standard test method for core shear properties of sandwich constructions by beam flexure. ASTM, West Conshohocken (2016) ASTM C273/C273M –16. Standard test method for shear properties of sandwich core materials. ASTM, West Conshohocken (2016) ASTM D30309/D3039M14: Standard test method for tensile properties of polymer matrix composite ASTM D7249/D7249M –06. Standard test method for facing properties of sandwich constructions by long beam flexure. ASTM, West Conshohocken (2006) Bahlouli, N., Pessey, D., Raveyre, C., Guillet, J., et al.: Recycling effects on the rheological and thermomechanical properties of polypropylenebased composites. Mater. Des. 33, 451–458 (2012) Bensadoun, F., Vallons, K.A.M., Lessard, L.B., Verpoest, I., Van Vuure, A.W.: Fatigue behaviour assessment of flax–epoxy composites. Compos. A Appl. Sci. Manuf. 82, 253–266 (2016) Bhudolia, S.K., Perrotey, P., Joshi, S.C.: Optimizing polymer infusion process for thin ply textile composites with novel matrix system. Materials 10(3), 293 (2017) Bhudolia, S.K., Perrotey, P., Joshi, S.C.: Mode I fracture toughness and fractographic investigation of carbon fibre composites with liquid Methylmethacrylate thermoplastic matrix. Compos. B Eng. 134, 246–253 (2018) Cousins, D.S., Suzuki, Y., Murray, R.E., Samaniuk, J.R., Stebner, A.P.: Recycling glass fiber thermoplastic composites from wind turbine blades. J. Clean. Prod. 209, 1252–1263 (2019) Gholampour, A., Ozbakkaloglu, T.: A review of natural fiber composites: Properties, modification and processing techniques, characterization, applications. J. Mater. Sci. 55(3), 829–892 (2020). https://doi.org/10.1007/s1085301903990y Gourier, C.: Contribution à l’étude de matériaux biocomposites à matrice thermoplastique polyamide11 et renforcés par des fibres de lin, Doctoral dissertation, Université de Bretagne Sud (2016)
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Han, N., Baran, I., Zanjani, J.S.M., Yuksel, O., An, L., et al.: Experimental and computational analysis of the polymerization overheating in thick glass/Elium® acrylic thermoplastic resin composites. Compos. Part B: Eng, 202, 108430 (2020) Monti, A., El Mahi, A., Jendli, Z., Guillaumat, L.: Quasistatic and fatigue properties of a balsa cored sandwich structure with thermoplastic skins reinforced by flax fibres. J. Sandwich Struct. Mater. 21(7), 2358–2381 (2019) Van Rijswijk, K., Bersee, H.E.N.: Reactive processing of textile fiberreinforced thermoplastic composites – an overview. Compos. A Appl. Sci. Manuf. 38(3), 666–681 (2007)
Thermal Performance Comparison of Various Concentrating Solar Water Heating Systems Monia Chaabane1,2,3(B) , Hatem Mhiri1 , and Philippe Bournot2 1 Laboratoire de thermique et thermodynamique des procédés industriels, Ecole Nationale
d’Ingénieurs de Monastir, route de Ouardanine, 5000 Monastir, Tunisia [email protected] 2 Aix Marseille Univ, CNRS, IUSTI, Marseille, France 3 Ecole Nationale d’Ingénieurs de Gafsa, Gafsa, Tunisia
Abstract. In this paper, various designs of concentrating solar water heater systems are studied. Our reference system is an integrated collector storage (ICSSWH). The proposed changes concern the concentrating technology by considering a dish instead of a CPC reflector, and the design of the concentrating solar water heater (CSWH) by considering a vertical instead of the horizontal mounting of the cylindrical storage tank in addition to the removal of the glass covering the system. Numerical results of the water temperature evolution and distribution show that the solar system which consists of a dish with a vertical storage tank performs better than the other systems. Indeed, in this solar system, the water temperature achieves 365 K while that in the ICSSWH does not exceed 328 K. The optimum storage tank diameter for the hottest day of the year is also evaluated for the chosen concentrated solar water heater and its operating is simulated for a typical day of each season. Results show that a tank diameter of 0.14 m allows the best hot water production throughout all the year. So CFD results show a satisfactory performance of the dishbased system with a vertical storage tank of 0.14 m diameter and prove the suitability of this pointfocus solar collector for a solar water heater application through all the year. Keywords: Thermal performance · Computational Fluid Dynamics (CFD) · Integrated Collector Storage Solar Water Heater (ICSSWH) · Dish
1 Introduction Thermal energy production using the solar energy is one of the most attractive technologies to exploit this renewable source. Several researchers worked on concentrating systems, they proposed different designs of collectors and discussed the effect of some changes on their performance. (Behar et al. 2016) presented a review of studies on central
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 249–258, 2022. https://doi.org/10.1007/9783030849580_27
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receiver solar thermal plants. (Fareed et al. 2012) designed a solar dish concentrator for water heating application. They showed that their solar system allows a water temperature increase of 80 °C. (Gorjian et al. 2015) presented a theoretical investigation of pointfocus solar collector performance. They used an artificial neural network ANN. Similarly, (Beltran et al. 2012) considered a mathematical model of a solar dish collector with cavity receiver. Another numerical investigation was proposed by (Marif et al. 2014) who developed a calculation program based on one dimensional finite difference method. Other researchers were interested to the effect of some parameters on the performance of their solar systems. (Yadav et al. 2013) studied the reflector nature. (Hafez et al. 2016) used the numerical tool Matlab to carry out their parametric study. Similarly, (Affandi et al. 2015) used Matlab to perform their parametric study. (Shuai et al. 2008) were based on the MonteCarloray tracing method to study the performance of dish solar concentrator/cavity systems. In another numerical investigation, (Cheng et al. 2013) used this method to developed their numerical model for improving design of concentrating solar collector. Similarly, (Mao et al. 2014) used this method to investigate the impacts of incident radiation and aspect ratio on the radiation flux of the receiver of a solar dish system. (Tao et al. 2013) coupled this calculation method to the Finite Volume Method (FMV) to study the coupling heat transfer problem in a solar dish collector with phase change materials (PCM). Other researchers used this MCRT method (Fuqiang et al. 2017), combined it with the Fluent software (Fuqiang et al. 2014), carried out CFD simulations using the commercial code Fluent (Kumar and Reddy 2012) and experimental tests (Reddy et al. 2015) to study the effect of pours disc receiver configurations on the thermal performance of different designs of solar parabolic trough concentrators. (Wang and Siddiqui 2010) chose to develop, using the commercial software FEMAP, their threedimensional model of a parabolic dishreceiver system which is working with argon gaz. (Li et al. 2016) used both experimental and numerical methods to investigate the effect of absorber material on the thermal performance of a lowprofile concentrated solar thermal collector. (Zhu et al. 2015) proposed an experimental investigation of a coil type solar dish receiver under actual concentrated solar radiation conditions. The novelty of this study consists of the use of a parabolic dish for a solar water heating application. Indeed, this pointfocus solar collector which has high concentration ratio is generally used for thermodynamic applications. In this numerical investigation, different water storage capacities are studied and the optimum tank diameter, which allows keeping the water in the liquid state for the hottest day of the year, is evaluated.
2 Numerical Modeling In this numerical investigation, a CFD model is developed and used to predict the thermal performance of different concentrating solar water heating systems. The reference system is an integrated collector storage solar water heater (ICSSWH). Different changes are then considered and the most appropriate system for the pointfocus solar collector is evaluated. These changes consist of using a dish as a concentration system, a vertical mounting of the storage tank and a nonglass covered system. Concerning the CFD model validation, the ICSSWH was modeled in previous work (Chaabane et al. 2012) and a good agreement between our CFD results and experimental data from literature
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was found. This CFD model is so used to discuss the effect of the different changes and to compare the thermal performance of the proposed systems to that of the ICSSWH. 2.1 Geometric Description and Meshing The basic design, noted CSWH1 and presented in Fig. 1a, is the ICSSWH experimentally studied by (Chaouachi and Gabsi 2006). It consists of a cylindrical storage tank of 95 l capacity, properly mounted inside the CPC reflector thought and covered with a 3.7 m2 glass surface. A grid independence test was carried out and the optimum mesh size was obtained with 604836 cells. The corresponding mesh, which consists of hexahedral cells, is presented for a cross section in Fig. 1b. In this numerical investigation, we propose at first to change the concentration system by considering a parabolic dish instead of a CPC reflector. In this design of solar water heater noted CSWH2 and presented in Fig. 2, the parabolic surface is chosen as equal to that of the reflector in the basic design. The outer glass is kept as well as the horizontal storage tank which is now placed at the focal length of the parabolic dish. In the following change defining the concentrating solar system noted CSWH3 and presented in Fig. 3a, we only considered a parabolic dish and horizontal storage tank, and removed thus the glass. The mesh corresponding to the CSWH2 and CSWH3, which consists of hexahedral cells and is presented for a cross section in Fig. 3b, is the same. Only the boundary condition is changed from wall in the first case to pressure outlet in the second one. The last change concerns the mounting of the storage tank and the corresponding solar system which is noted CSWH4, presented in Fig. 4a and meshed in Fig. 4b, consists of a parabolic dish in which a vertical storage tank is properly mounted at the focal position.
Fig. 1. Description of the CSWH1. b) Generated mesh for the CSWH1
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Fig. 3. a) CSWH3. b) Mesh of CSWH2 and CSWH3
Fig. 4. a) CSWH4 b) Generated mesh for CSWH4
2.2 Numerical Simulations The numerical simulations of all these concentrating solar water heaters designs is carried out using ANSYS. This software solves the Reynolds average NavierStockes equations using a finite volume method. For the closure of these equations, we chosen the standard Kε turbulence model. The turbulence kinetic energy and dissipation rate equations can be written as follows: ∂(ρk) ∂t + ∂(ρkui ∂xi = ∂ μ+ μt σk ∂k ∂xj ∂xj + Gk + Gb − ρε − YM + Sk ∂(ρε) ∂t + ∂(ρεui ∂xi = ∂ μ+ μt σε ∂ε ∂xi ∂Xi + C1ε (ε k) (Gk + C3ε · Gb ) − C2ε ρ ε2 k + Sε
Where Gk represents generation of turbulence kinetic energy due to the mean velocity gradients, Gb represents generation of turbulence kinetic energy due to buoyancy, YM is the contribution of fluctuating dilatation during compressible turbulence to the overall dissipation rate and SK and Sε are source terms.
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The surfacetosurface radiation model is used to introduce the radiative term. It is used to account for radiation exchange in graydiffuse surfaces. This exactly fits the solar system in the experimental study by (Chaouachi and Gabsi 2006) and allows one to write the equation that governs radiative transfer as follows: KJ = E. Where K is the N × N matrix; J is the radiosity vector and E is the emissive power vector. The different studied solar systems are considered as southeast facing and 36° inclined above the horizontal. Simulations are carried out for a spring day (14 May) in the Tunisian city Gabes and initialized at a temperature of 294K. For the boundary conditions, the CPC reflector and the parabolic dish are defined as adiabatic wall: heat flux = 0 W/m2 with a reflectivity coefficient ρ = 1. The storage tank is defined as coupled which allows the different heat transfer modes in this surface, and has an absorptivity coefficient α = 1. Concerning the covering external surface, it has a transmissivity coefficient τ = 0.8, it is defined as mixed for the CSWH 1 and 2, allowing so to consider both convective and radiation exchange, and as pressure outlet for the CSWH 3 and 4 where we considered an open design which is not covered with an external glass surface.
3 Numerical Results Results of the CFD model validation are presented in previous published papers (Chaabane et al. 2012). We propose in this paper to discuss the effect of the proposed changes on the SWH performance. This study allows to identify the role of all the components of any concentrating solar water heater and particularly the covering glass, the storage tank mounting and the concentrating system nature. It allows also to identify the most appropriate system for a pointfocus collector used in solar water heater application. Numerical simulations of the proposed concentrating solar water heating systems are carried out and results of the temporal evolution of the water temperature are presented in Fig. 5. The analysis of these results shows that for the CSWH2, the glass, by its greenhouse effect, generates a very significant rise in the temperature of the water which exceeds 100 °C, which makes this system more suitable for a thermodynamic application. Concerning non glasscovered systems CSWH 3 and 4, it is seen that the water temperature is higher than that noted in the ICSSWH, and it remains lower than 100 °C (87 °C and 92 °C as a maximum value respectively for the CSWH 3 and 4), which shows that the corresponding solar systems are suitable for a solar water heater application. Indeed, despite being a pointfocus system, the water volume in this concentration system is chosen, unlike in thermodynamic applications, quite high which allows satisfactory results for the water temperature in these solar systems. The water temperature is found relatively close for the noncovered systems CSWH 3 and 4 where the maximum temperature difference doesn’t exceed 5 °C. The choice must be made according to the global assembly of the whole system. Indeed, as the parabolic dish is a pointfocus concentration system, the temperature distribution depends on the storage tank mounting. The temperature contours are so presented in Fig. 6 for the CSWH 3 and 4 at the maximum solar radiation intensity. The temperature contours show that the vertical mounting of the storage tank allows a better temperature distribution as the flow is more stratified and the temperature is more homogeneous through the storage tank, the corresponding CSWH configuration can so be chosen as the most appropriate.
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These results clearly show the potential of the dish based concentrated system for solar hot water production. But results also show that the water temperature in this pointfocus collector achieves 92 °C for the chosen design hence the risk of the water evaporation for warmer climatic. Different tank diameters are so considered and simulations are carried out for the hottest day of the year. The basic tank diameter is of 0.116 m, the studied values are respectively 0.13 m, 0.14 m and 0.15 m and the temporal evolution of the water temperature is presented for these different tank storage capacities in Fig. 7. The analysis of this figure shows that for the tank diameter lower than 0.14 m, the water temperature maximum value is
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higher than 100 °C. This tank diameter can so be used for the chosen dishbased system in order to ensure a solar hot water production throughout all the year. After having chosen the design of the CSWH which consists of the solar dish and the vertical cylindrical tank of 0.14 m of diameter, this solar system’s operating is studied for a typical day of each season and the water temperature temporal evolution is presented in Fig. 8. Numerical results clearly show the satisfactory production of this concentrated solar water heater which ensures hot water production at high temperature throughout all the year despite its simple design which includes only the dish and the vertical balloon of 138 L volume. From these results, different concentration solar water heating systems are simulated, and the optimum design performance is evaluated. In fact, a vertical cylindrical storage tank of 0.14 m diameter and 2.232 m length properly mounted in the focal distance of a solar dish has shown its good production of solar hot water throughout the year and can be chosen as the most appropriate design for this solar application in the chosen site. Indeed, the useful heat is, even for the coldest day, higher than that for a spring day in the ICSSWH, and it is 3.4 times higher for the same spring day.
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4 Conclusion In this research paper, two concentration technologies are compared and the most appropriate design for a solar water heating application is identified. The thermal performance of different Pointfocus Solar Collector configurations is compared to that of a surfaceconcentration design based system which is the integrated collector storage solar water heater. Numerical results clearly show the advantage of the point concentration technology which allows an important water temperature and consequently high useful heat gain. To ensure the adequacy of the chosen devise with the solar water heater application, different diameters of the storage tank were studied and results showed that from a value of 0.14 m, we obtain an important solar hot water production throughout all the year without any risk of transition to the thermodynamic application. Therefore, it can be concluded that for the considered conditions, a cylindrical storage tank vertically mounted in the focal distance of a dish allows continuous and maximum production of hot water through the year. It can so be considered as the most appropriate design due to it better production and lower cost relatively to the ICSSWH.
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References Affandi, R., Ruddin, M., Ab, G., Ghan, C.K., Peng, L.G.: The impact of the solar irradiation, collector and the receiver to the receiver losses in parabolic dish system. Procedia Soc. Behav. Sci. 195, 2382–2390 (2015) Behar, O., Khellaf, A., Mohammedi, K.: A review of studies on central receiver solar thermal power plants. Renew. Sustain. Energy Rev. 23, 12–39 (2016) Beltran, R., Velazquez, N., Espericueta, A.C., Sauceda, D., Perez, G.: Mathematical model for the study and design of a solar dish collector with cavity receiver for its application in Stirling engines. J. Mech. Sci. Technol. 26(10), 3311–3332 (2012). https://doi.org/10.1007/s1220601208010 Chaabane, M., Mhiri, H., Bournot, P.: Thermal performance of an integrated collector storage solar water heater (ICSSWH) with a storage tank equipped with radial fins of rectangular profile. Heat Mass Transf. 49, 107–115 (2012). https://doi.org/10.1007/s002310121065z Chaouachi, B., Gabsi, S.: Experimental study of integrated collector storage solar water heater under real conditions. Renew. Energy Rev. 9(2), 75–82 (2006). (in French) Cheng, Z.D., He, Y.L., Cui, F.Q.: A new modelling method and unified code with MCRT for concentrating solar collectors and its applications. Appl. Energy 101, 686–698 (2013) Fareed, M.M., Jaseen, A.S., Yaseen, H.M., Ahmed, A.K.: Design and study of portable solar dish concentrator. Int. J. Recent Res. Rev. 3, 12–23 (2012) Fuqiang, W., Jianyu, T., Lanxin, M., Yong, S., Heping, T., Yu, L.: Thermal performance analysis of porous medium solar receiver with quartz window to minimize heat flux gradient. Sol. Energy 108, 348–359 (2017) Fuqiang, W., Jianyu, T., Yong, S., Heping, T., Shuangxia, C.: Thermal performance analyses of porous media solar receiver with different irradiative transfer models. Int. J. Heat Mass Transf. 78, 7–16 (2014) Gorjian, S., Hashjin, T.T., Ghobadian, B., Banakar, A.: A thermal performance evaluation of a mediumtemperature pointfocus solar collector using local weather data and artificial neural networks. Int. J. Green Energy 12, 493–505 (2015) Hafez, A.Z., Soliman, A., ElMetwally, K.A., Ismail, I.M.: Solar parabolic dish stirling engine system design, simulation and thermal analysis. Energy Convers. Manag. 126, 60–75 (2016) Kumar, K.R., Reddy, K.S.: Effect of porous disc receiver configurations on performance of solar parabolic trough concentrator. Heat Mass Transf. 48, 555–571 (2012). https://doi.org/10.1007/ s0023101109038 Li, Q., et al.: Experimental and numerical investigation of volumetric versus surface solar absorbers for a concentrated solar thermal collector. Sol. Energy 136, 349–364 (2016) Marif, Y.L., Benmoussa, H., Bouguettaia, H., Belhadj, M.M., Zerrouki, M.: Numerical simulation of solar parabolic trough collector performance in the Algeria Saharan region. Energy Convers. Manage. 85, 521–529 (2014) Mao, Q., Shuai, Y., Yuan, Y.: Study on radiation flux of the receiver with a parabolic solar concentrator system. Energy Convers. Manag. 84, 1–6 (2014) Reddy, K.S., Kumar, K.R., Ajay, C.S.: Experimental investigation of porous disc enhanced receiver for solar parabolic trough collector. Renew. Energy 77, 308–319 (2015) Shuai, Y., Xia, X.L., Tan, H.P.: Radiation performance of dish solar concentrator/cavity receiver systems. Sol. Energy 82, 13–21 (2008) Tao, Y.B., He, Y.L., Cui, F.Q., Lin, C.H.: Numerical study on coupling change heat transfer performance of solar dish collector. Sol. Energy 90, 84–93 (2013) Wang, M., Siddiqui, K.: The impact of geometrical parameters on the thermal performance of a solar receiver dishtype concentrated solar energy system. Renew. Energy 35, 2501–2513 (2010)
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Yadav, A., Kumar, M., Balram: Experimental study and analysis of parabolic trough collector with various reflectors. Int. J. Phys. Nat. Sci. Eng. 7(12), 71–81 (2013) Zhu, J., Wang, K., Wu, H., Wang, D., Du, J., Labi, A.G.: Experimental investigation on the energy and energy performance of a coiled tube solar receiver. Appl. Energy 156, 519–527 (2015)
The Prestrain Impact on Tensile Properties and Fracture Toughness of AA5754H111 Aluminum Alloy Wafa Taktak(B) and Riadh Elleuch Laboratoire des Systems ElectroMecaniques, National School of Engineering of Sfax, University of Sfax, Sfax, Tunisia [email protected]
Abstract. AA5754H111aluminum alloy is the current AA5xxx alloy used in the manufacturing automotive components due to the good combination of high strength with good formability. Cold forming process is the most manufacturing process for automotive panel components. During the cold forming operations, AA5754H111 aluminum alloy subjected to plastic predeformation (prestrain). However the prestrain can modifier the tensile properties and fracture toughness behavior of this alloy. For this reason, it’s very interesting to investigate the impact of prestrain on the fracture toughness behavior and tensile properties of AA5754H111 aluminum alloy. The prestrain level was evaluated for 3, 8 and 12%. The behavior of 5754H111 aluminum alloy is discussed before and after prestraining. It has been show that prestrain has a significant effect on increasing the tensile proprieties (yield strength YS and ultimate tensile strength UTS). Furthermore, a notable decrease of the ductility of AA5757H111aluminum alloy with increasing the prestrain level. Prestrain has also been found to give a considerable impact on decreasing the toughness parameters (the tenacity at crack initiation J 0.2 and the tearing modulus T (dJ/da)) of the alloy that elevate with the prestrain percentage, this loss in toughness parameters is due to the growth of density dislocation obtained during plastic strain. Keywords: AA5754H111 · Prestrain · Tensile properties · Fracture toughness
1 Introduction Nowadays, the employ of aluminum and it alloys in automotive industry applications shows a remarkable increase (Nekaterih DIKL 2002 and Zhang L et al. 2017). The aluminum alloys make a good and strong replacing for steel at automotive fabrication due to high density and considerable formability and high strength (Hirsch J et al. 2013 and Ghosh M et al. 2015). The further aluminum alloy series employed in the body parts and structural parts of the automotive is the nonheattreatable AlMg alloys because of its specific mechanical proprieties like large formability at room temperature, corrosion © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 259–266, 2022. https://doi.org/10.1007/9783030849580_28
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resistance, high strength, low density, ductility and toughness (Ubertalli G et al. 2020, Demir H et al. 2009, Sotirov N et al. 2015 and Dhara S et al. 2016). The fracture toughness behavior toughness and the mechanical proprieties of these alloys are influenced by the prestrain occurs during the cold forming process (Cosham A 2001, Chang L et al. 2017 and Madi Y et al. 2020). In general, the prestrain results by grow of the density dislocation which creates the blockage in the dislocation movements. Together with the growth of prestrain, the mechanical strength is rapid increased but the toughness and ductility are decreased (Sarkar JKTRG et al. 2001, Oh C K et al. 2007 and Wowk D et al. 2009). In this work, the non heattreatable AA5754H111 was chosen to discuss the prestrain effect on the fracture toughness and mechanical tensile properties.
2 Experimental Tests 2.1 Material The aluminum alloys used is AA5754H111 sheet with thickness of 3 mm and employed in the manufacture of the automotive body and interior structural. Table 1 shows the chemical composition of AA5754H111. The uniaxial prestrain was effectuated along the longitudinal direction under the constant elongation of 3%, 8% and 12% respectively. Different levers of prestrain were carried out at the selfsame cross head speed with the presence of the 25 mm extensometer control. Table 1. Chemical composition of AA5754H111 (wt%). Element Composition (wt%) Al
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2.2 Tensile Measurement Tests The uniaxial tensile test specimen, schematically present in Fig. 1 is used to evaluate the tensile proprieties (the ultimate tensile strength (UTS), the yield strength (YS) and
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elongation A %) of the virgin and prestrain materials. All tensile tests were machined in the longitudinal direction at room temperature using universal tensile testing machine with a capacity of 50KN LLOYD at a static cross head speed 10 mm/min. During tensile test, the axial strain was controlled by 25 mm extensometer. Three samples were tested for the virgin and prestrained aluminum alloy 5754H111.
Fig. 1. Geometry of the tensile specimen (in mm)
2.3 Ductile Tearing Tests The ductile tearing tests were affected in universal tensile testing machine 50KN LLOYD at a constant cross head speed 1 mm/min. The central cracked panels (CCP) specimen is tested in longitudinal direction. The CCP specimen dimensions are presented in Fig. 2. The CCP specimens are precracked to length a0 equal to 0, 36 W by fatigue test. For both virgin and prestrained AA5754 alloy, the Jcurves were estimated using the single samples technique. For each level of prestrain, three specimens were operated. The values of displacement and load were recorded in computer at the same time during the test, in order to calculate the J values by Schwalbe and Neale equation (Schwalbe KH et al. 1995). J =
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For a CCP specimen case, the stress intensity factor K is proposed by Eq. (2) (Lei Y et al. 1997): a 4 a 2 π(a/w) p K= √ + 0.06 1 − 0.025 (2) w w cos(τπ α/w) B 2W Where: E is the Young’s modulus, W is the width of sample, B is the specimen thickness and a0 is the initial crack length.
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Fig. 2. CCP specimens Geometry (in mm).
Fig. 3. Definition of U* for a CCP sample.
U* present the energy measured under the loaddisplacement curve record as shown in Fig. 3. The value of crack growth Δa can be calculated through images obtained by the high resolution video camera placed in the fact of the sample. The chosen sequence of high resolution video camera pictures representing the crack growth Δa in AA5754H111 specimen reveling a ductile tearing behavior are shown in Fig. 4. The starting loading present the time t = 0s.
Fig. 4. A sequence of images illustrating crack growth in AA 5754H111 (case of a received material).
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3 Results and Discussion 3.1 Impact of Prestrain on Tensile Properties In Fig. 5 presented the true strain stress curves of virgin and prestrained specimens. It can be noted that the true strain stress curve mounts after prestraining. A continual growth in tensile proprieties (yield strength (YS) and ultimate tensile strength (UTS)) and gradually decrease of the percentage elongation (A %) is observed with increase the prestrain level. The greatest YS and UTS and the lower percentage elongation are noted for the 12% prestrained AA5754H111. A growth in values of two tensile proprieties (YS and UTS) and a drop in percentage elongation could be explicated by the high density of dislocations and an accumulated energy created in AA5754H111 alloy during plastic strain (prestrain). This shows that the principal responsible for change of tensile proprieties is increase of the quantity of dislocation density in AA5754H111 during the prestraining. Also, it is noted that with growing dislocation density, ductility drop because of the reduction dislocation movement (Howeyz M et al. 2020). 350
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3.2 Impact of Prestrain on Fracture Toughness Jcurves for virgin and prestrain AA5754H111 are plotted in Fig. (6). The tenacity at crack initiation J 0.2 is obtained by the intersection of Jcurve and the 0.2 mm offset line according to ASTME 1820 (Frómeta D et al. 2020). It can be seen that, after prestrain, Jcurve descents. The prestrain generates a decrease of J 0.2 from 35.8 kJ/m2 to 26.5, 19.67 and 14.36 kJ/m2 respectively. Beside, the tearing modulus T (dJ/da) decreases with increase the level prestrain. The values of J 0.2 and T are given in the Table 2.
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The prestrain led to drop the fracture toughness resistance in the tested AA5457H111. It changes the fracture mechanism, from ductile to brittle with increasing the prestrain level. This change can be justified by the important lower of the tenacity at crack initiation J 0.2 of prestrained AA5754H111 as compared to the virgin AA5754H111. This less of J 0.2 for prestrain samples due to the increase of density dislocation and stock energy during the strain harding of AA5754H111.
J(KJ/m²)
Table 2. Values of tenacity at crack initiation J 0.2 and tearing modulus T for the virgin and prestrained AA5754H111 Prestrain level
J 0.2 (JK/m2 )
T (dJ/da)
0%
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26
3%
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60 55 50 45 40 35 30 25 20 15 10 5 0
0%
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0
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0,4
0,6
0,8
1
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1,4
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Fig. 6. JΔa curves with different prestrain level.
4 Conclusion In the present study, the impact of uniaxial prestrain with different levels on the tensile and toughness proprieties of AA5754H111 alloy was investigated. The following is the important conclusions obtain from this study:
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• The interesting increase in strength characteristics (yield strength and ultimate tensile strength) and the remarkable decrease in percentage elongation with increasing the prestrain levels. It was found that prestrain has a profound impact on mechanical tensile proprieties. • The modification effected in the tensile proprieties due to increase in the density dislocations occurs during the plastic deformation of AA5754. • The virgin AA5754H111 alloy shows a ductile toughness behavior. • A comparison of the toughness of the prestain alloy and with virgin specimens marked a drop in J 0,2 and T values. • The loss in fracture thoughness due to number of the dislocation created during the prestrain of AA5754H111.
References Nekaterih, D.I.K.L.: The ductility and corrosion properties of some aa5xxx auto body sheets. Mater. Tehnol. 36, 3–4 (2002) Zhang, L., et al.: Texture, microstructure and mechanical properties of 6111 aluminum alloy subject to rolling deformation. Mater. Res. 20(5), 1360–1368 (2017). https://doi.org/10.1590/ 19805373MR20170549 Hirsch, J., AlSamman, T.: Superior light metals by texture engineering: optimized aluminum and magnesium alloys for automotive applications. Acta Mater. 61(3), 818–843 (2013). https://doi. org/10.1016/j.actamat.2012.10.044 Ghosh, M., Miroux, A., Kestens, L.A.I.: Correlating rvalue and through thickness texture in AlMgSi alloy sheets. J. Alloy. Compd. 619, 585–591 (2015). https://doi.org/10.1016/j.jallcom. 2014.09.038 Ubertalli, G., et al.: High strain rate behavior of aluminum alloy for sheet metal forming processes. Metals 10(2), 242 (2020). https://doi.org/10.3390/met9101129 Demir, H., Gündüz, S.: The effects of aging on machinability of 6061 aluminium alloy. Mater. Des. 30, 1480–1483 (2009). https://doi.org/10.1016/j.matdes.2008.08.007 Sotirov, N., et al.: Improved formability of AA5182 aluminium alloy sheet at cryogenic temperatures. Mater. Today Proc. 2, S113–S118 (2015). https://doi.org/10.1016/j.matpr.2015. 05.027 Dhara, S., Basak, S., Panda, S.K., Hazra, S., Shollock, B., Dashwood, R.: Formability analysis of prestrained AA5754O sheet metal using Yld96 plasticity theory: role of amount and direction of uniaxial prestrain. J. Manuf. Process. 24, 270–282 (2016). https://doi.org/10.1016/j.jma pro.2016.09.014 Cosham, A.: A model of prestrain effects on fracture toughness. J. Offshore Mech. Arct. Eng. 123(4), 182–190 (2001). https://doi.org/10.1115/1.1408613 Chang, L., Zhou, C.Y., He, X.H.: The effects of prestrain and subsequent annealing on tensile properties of CPTi. Metals 7(3), 99 (2017). https://doi.org/10.3390/met7030099 Madi, Y., Shinohara, Y., Besson, J.: Effect of prestrain on ductility and toughness in a highstrength line pipe steel. Int. J. Fract. 224(1), 15–29 (2020). https://doi.org/10.1007/s10704020004426 Sarkar, J.K.T.R.G., Kutty, T.R.G., Conlon, K.T., Wilkinson, D.S., Embury, J.D., Lloyd, D.J.: Tensile and bending properties of AA5754 aluminum alloys. Mater. Sci. Eng. A 316(1–2), 52–59 (2001). https://doi.org/10.1016/S09215093(01)012266 Oh, C.K., Kim, Y.J., Baek, J.H., Kim, Y.P., Kim, W.: A phenomenological model of ductile fracture for API X65 steel. Int. J. Mech. Sci. 49(12), 1399–1412 (2007). https://doi.org/10.1016/j.ijm ecsci.2007.03.008
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Wowk, D., Pilkey, K.: Effect of prestrain with a path change on the strain rate sensitivity of AA5754 sheet. Mater. Sci. Eng. A 520(1–2), 174–178 (2009). https://doi.org/10.1016/j.msea. 2009.05.019 Schwalbe, K.H., Neale, B.: A procedure for determining the fracture behaviour of materials—the unied mechanics test method EFAM GTP 94. Fatigue Fract. Eng. Mater. Struct. 18, 413–424 (1995). https://doi.org/10.1111/j.14602695.1995.tb01185.x Lei, Y., Neale, B.K.: The fracture behaviour of a centre cracked tensile specimen. Fatigue Fract. Eng. Mater. Struct. 20, 201–216 (1997). https://doi.org/10.1111/j.14602695.1997.tb00278.x Howeyze, M., Eivani, A.R., Arabi, H., Jafarian, H.R., Park, N.: The effect of amount of prestrain using equal channel angular pressing on softening response of AA5052 alloy. J. Mater. Res. Technol. 9(3), 6682–6695 (2020).https://doi.org/10.1016/j.jmrt.2020.04.065 Frómeta, D., et al.: Identification of fracture toughness parameters to understand the fracture resistance of advanced high strength sheet steels. Eng. Fract. Mech. 229, 106949 (2020). https:// doi.org/10.1016/j.engfracmech.2020.106949
Disassembly Sequence Optimization for Profit and Energy Consumption Using Petri Nets and Particle Swarm Optimization Syrine Bouazza1,2(B) , Hichem Hassine1 , Maher Barkallah1 , Saïd Amari2 , and Mohamed Haddar1 1 Mechanics, Modelling and Production Research Laboratory (LA2MP), National Engineering
School of Sfax, Sfax, Tunisia [email protected], [email protected], [email protected] 2 LURPA, ENS ParisSaclay, University of Sorbonne Paris Nord, Villetaneuse, France [email protected]
Abstract. Environment, resources and energy have garnered global attention in several countries of major societal concern. Manufacturers must be mindful of the environmental impact by monitoring their products throughout their life cycle in order to manage the pollution problem. Nowadays, the disassembly operation plays a fundamental role in component remanufacturing considering their importance in product recovery by recover value and conserving energy from endoflife products. Reducing the energy consumption of disassembly sequences has been an important subject. This paper establishes a dualobjective disassembly sequencing problem that aims to maximize disassembly profit and minimize energy consumption. This approach is based on the adaptation of the Petri net (PNs) as modeling tool that allows representing all possible disassembly sequences using the extended process graph, the disassembly priority, and the incidence matrices. Then, the particle swarm optimization (PSO) algorithm is applied to determine the optimal disassembly sequence that ensure the least energy consumption and the maximum profit. To evaluate the efficient of the proposed approach, a case study of a radio set is proposed. Simulation results demonstrate the efficacy of the proposed methods to resolve this type of problem by determining the optimal or near optimal disassembly sequence. Keywords: Disassembly sequence · Energy consumption · PSO · Petri nets · Multiobjective optimization
1 Introduction Remanufacturing has become the fundamental notion to sustainable development (Gao et al. 2019). In fact, it aims to recover, reduce and recycle endoflife products and decrease their impact on environmental pollution and solve the problem of shortage of
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 267–276, 2022. https://doi.org/10.1007/9783030849580_29
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resources. Product recovery aims to obtain useful and valuable components from endoflife products to maximize their recycling/reuse value as well as lessen the quantity of waste and reduce raw substance extraction and energy consumption. The disassembly operation is the key step since it is the most efficient and economical operation. It is required to minimize the harm of endoflife components/products and their negative impact to the environment, and reduce disassembly cost, time and energy. Therefore, studies for disassembly can be classified according to three axes such as, disassembly sequence planning, disassembly evaluation and disassembly modeling. Disassembly sequence planning aim to break down a recyclable and reusable component, respecting the constrained relationship between components and parts. It is considered as a combinatorial optimization problem. Disassembly modeling approaches principally include AND/OR graphs (Lu et al. 2020) (Guo et al. 2018), PNs (Guo et al. 2015) (Guo et al. 2020b) (Zhao et al. 2015), undirected graphs, and directed graphs (Zhang et al. 2011). The PNs is a graphical modeling structure which it used to solve disassembly sequence optimization problem. Guo et al. (2015), used PNs and two scatter search to maximize disassembly profit with multiresource constraints. Zhao et al. (2014) combined fuzzy reasoning PNs with matrix operation to study disassembly sequence decision making. Different intelligent algorithms are proposed to solve this type of problem. Jeunet et al. (2019), has addressed this problem by developing Greedy algorithm and a metaheuristic. ElSayed (2012), developed an evolutionary algorithm for discarded products to determine an optimal selective disassembly sequence. Also, Genetic algorithm is adopted to solve the problem of optimization of disassembly sequence (Tseng et al. 2018). Luo et al. (2016) proposed an ant colony optimization to find the optimal or near optimal disassembly sequence. Other works proposed PSO (Ben Jdidia et al. 2020) (Pornsing and Watanasungsuit, 2014). Yeh (2012), used a selfadaptive simplified swarm algorithm. As well, Pornsing and Watanasungsuit, (2014), applied PSO to solve a combinatorial optimization problem. Work on the disassembly sequence varies depending on the objective functions being treated. Some authors proposed to solve a multiobjective optimization problem such as that by Guo et al. (2018). They aim to maximize disassembly profit and minimize disassembly time of an EOL product by adapting Scatter search algorithm for selective disassembly sequence problem subject to the multiresource constraints. Likewise, to solve a stochastic dualobjective disassembly sequencing problem, Fu et al. (2018) developed a sorting genetic algorithm II and multiobjective evolutionary algorithm founded on decomposition which purpose to maximize disassembly profit and minimize energy consumption. Tian et al. (2018) proposed a scatter search. Other work, such as that by Guo et al. (2020a), addressed a lexicographic multiobjective scatter search method to achieve three goals, minimizing disassembly time, minimizing energy consumption, and maximizing revenue. By analyzing the above discussion, the disassembly sequence optimization problem was treated more with a single objective, the minimization of time or cost, the quality uncertain of the product, or the maximization of profit. The resolution of this type of problem with multiobjectives have not been given enough concern. Therefore, reducing the
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energy consumption of disassembly sequences has been very important to develop sustainable modes of remanufacturing. This work establishes a dualobjective optimization subject to maximize disassembly profit and minimize disassembly energy consumption to solve optimal disassembly sequence. Therefore, to have the most optimal sequence and bee more efficient, we consider extra power/cost to perform an operation due to resource change and energy consumption/cost when performing operation. This paper presents a new mathematical modeling framework by coupling two objectives, cost, and energy as objective function with multi resource constraints based on the adaptation of the petri net (PN) as modeling tools to analyze the product and represent a physical basis of disassembly constraints. It defined a matrix of disassembly priority and the incidence matrices that presented all possible disassembly sequences. The PSO algorithm is used to solve the proposed model so as to represent to the optimal disassembly sequence. The remaining contents of this paper is organized as follows: Sect. 2 defines PNs disassembly process model. Section 3 describes the mathematical model and PSO algorithm. Section 4 presents the case study and the results. We summarize the main conclusion and we propose some perspectives of this study in Sect. 5.
2 Petri Nets Disassembly Process Model A PN is a graphic model structure, which is extensively used in modeling discrete event systems. PN disassembly of a product can be constructed based on geometric constraint relationship, operations, removal state, AND/OR logical relationship and disassembly resource component information database. A PN is a 10tuples and it is noted: PN = (P, T , F, S, k, t, C, R, w, M ) where: P = {p1 , p2 , . . . , pn } : A set of places. T = {t1 , t2 , . . . , tm } : A set of transitions with P ∩ T = ∅, F = P × T → Z + : a set of arcs directed from P to T. It presents an input function. S = {S(p1 ), S(p2 ), S(p3 ), . . .} : The constraint state of component, k = {k(t1 ), k(t2 ), k(t3 ), . . .}; The occurrence of the transition; T: The time needed to disassembly a product. C: T → R+ : A disassembly cost associated with a transition, R: P → R+ : A recycling/reuse value of the subassembly associated with a place. W: T → Z + , A weight functions. M: P → Z + , A marking. M 0 is the initial disassembly marking of PN. In a disassembly process, the precedence relationship between operation must be defined and satisfied. Therefore, a precedence matrix S = [s ] is proposed, where, jk column j and row k represent the disassembly operation indices. 1, if operation k is obtained after operation j sjk 0, Otherwise Subassembly can be obtained only by one disassembly operation. Then, the relation between the operations and the subsets is defined in a PN disassembly with a disassembly
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matrix D = [dij ], where column i and row j respectively represent a disassembly operation and a subassembly. ⎧ ⎨ 1, if subassembly i is obtained by execution operation j dij −1, if the subassembly i is obtained by execution operation j ⎩ 0 otherwise
3 Mathematical Modeling of DualObjective Disassembly Sequence Optimization Using the Particle Swarm Optimization Algorithm 3.1 Mathematical Modeling of DualObjective Disassembly Sequence Optimization This section presents a new mathematical modeling framework by coupling cost and energy consumption as objective function to solve disassembly sequences optimization problem. The notations used are summarized as following: i,
The index of a subassemblies, i = 1, 2,…, N where N is the number of subassemblies composing a product
j, k
The index of an operation: j, k = 0, 1, 2,…, J, where J is the number of operations
R
The index of a resource type needed to execute an operation, r = 1, 2,…, Q
Ri
Revenue of subassembly i
ej
Energy consumption when executing operation j
Pjk
Extra power to execute operation k due to resource change
Ejk
Energy consumption in a setup period of operation k if it is executed after j
cj
Cost of executing an operation j
Cjk
Extra cost to execute operationk due to the change of resources
Bjk
Disassembling cost in a setup period of an operation k
DTj
Disassembly operation time
bjk
Setup time of executing operation k
Tjk
Extra time to execute operation k after its preceding operationj due to the change of resource
Gri
The quantity of resource r needed to execute the preparation of the disassembly article i
grjk
The number of resources r needed to execute operation j after operation k
Qr
The maximum quantities of resource r
D
Disassembly matrix
S
Priority matrix;
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Decision variables • xj : x = 1 if operation j is executed, besides, xj =0 j • y : yjk = 1 if the operation k executed after the precedent adjacent operation j, jk otherwise y = 0, jk To ensure the maximum revenue (1) and minimum disassembly energy consumption (2), we propose a dualobjective disassembly sequence optimization model as follows: Max Z1 = J J
N J
−
J
j=1 cj xj
−
J
J
k=0 Cjk yjk − b B y j=1 K=1 jk jk jk Min Z2 = Jj=1 JK=1 Pjk Tjk yjk + Jj=1 JK=1 DTjk ej xj + J J j=1 K=1 Ejk bjk yjk j=1 dij Ri xj
i=1
j=1
(1)
(2)
By respecting the following constraints: J j=1
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yjk
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j=0
J k=0
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Dij xj ≥ 0
J=0
yjk
i = 1, 2, . . . , N
grj xj ≤ Qr r = 1, 2, . . . , Q
J
y k=0 kj
xj , ykj ∈ {0, 1}, M
r = 1, 2, . . . , Q
y m=1 jm
≤1
≤
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(3) (4) (5) (6) (7) (8)
j, k = 0, 1, . . . , J
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Constraint (3–9) presented respectively: the constraints of disassembly capacity; The relationship between the two decision variables; the priority relationship; the relation between the operations and subassemblies; the resource constraints to disassemble a product, the equilibrium relation between the upper degree Jk=0 ykm and the lower degree Jk=0 ymk of a subset, except degree m respectively, and the estimated values. Constraint (10) define that a disassembly operation can be performed only once. 3.2 The Particle Swarm Optimization Algorithm PSO is an evolutionary computation method included to the domain of Swarm Intelligence. It is introduced by Kennedy and Eberhard (1997). It is an optimization method that allows to determine the optimal solution in a reasonable time. PSO is a populationbased algorithm; the population is called swarm and its individuals are called the particles, S = {X1 , X2 . . . XN }. It is based on the sharing of information between particles. In the Ddimension search space, each particle i has a position that can be represented as X = x , x , . . . , x , . . . , x and velocity denotes i i,1 i,2 i,D i,d a personal historical best Vi = Vi1 , Vi,1 , . . . , Vi,d , . . . , Vi,D . Also, each particle has position, denoted by Pi = Pi,1 , Pi,2 , . . . , Pi,d , . . . , Pi,D representing the particle’s personal best (pbest) at time t. The global best position (gbest) which is the best position of all the in the whole population is represented by
personal historical best position Pg = Pg,1 , Pg,2, , . . . , Pg,j,..., Pg,D , . The algorithm of the standard PSO is presented in Fig. 1.
Fig. 1. Algorithm of the standard PSO
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4 Cases Study To evaluate the effectiveness of the investigated approach, an example of radio set (AdensoDíaz, GarcíaCarbajal, and Gupta 2008) is proposed. The product consists of 29 parts, numbered from P1 to P29 and 30 disassembly operations, numbered from t1 to t30 . The constraintbased PN model is shown in Fig. 2. Precedence matrix and disassembly matrix are presented as follow. Two types of resources, disassembly tools and operators, are considerate. The PSO parameters of our proposed model are presented as follows: swarm size is 50; the maximum number of iterations is 500. According to the Table 1, the most optimal path is 1–3–4–5–9–10–12–13–16–18– 19–20–21–24–27–28–29 seen that it presents the best compromise between cost and time. The objective function Z1 , that is, disassembly profit is 2786 RMB (Ren Min Bi, Chinese money unit), and energy consumption Z2 equal 595 J.The convergence graph is shown in Fig. 3.
Fig. 2. Disassembly PN of a radio set.
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Table 1. Optimization results of PSO Number Swarm Disassembly sequence of size iteration
Z1
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1–34–5–9–10–12–13–16–17–18–19–20–21–24–25–27–28–29 4103 1460 5563 1–34–5–9–10–12–13–16–18–19–20–21–24–27–28–29
2786 595
3381
Fig. 3. Evolution of fitness function
5 Conclusion This work proposes a new model to solve a disassembly sequence problem by considering dualobjectives, maximize disassembly profit and minimize energy consumption based on PN modeling and PSO algorithm. Using PN, disassembly, and precedence matrices are defined to present the structured relation/constraints between operations or/and components. Therefore, the PSO algorithm is applied to determine to the optimal disassembly sequence. A disassembly case of radio set is simulated to evaluate the effective and feasibility of the proposed methodology. For the future research, a novel model on the basis of this model will be proposed by considering either the overall profit, the cost of disposal, of the cost of preparation of EOL products. In addition, integrate the evaluation of quality uncertainty of endoflife products should be further discussed.
References Ben Jdidia, A., Hentati, T., Bellacicco, A., Khabou, M.T., Rivier, A., Haddar, M.: Optimizing cutting conditions in single pass face milling for minimum cutting energy, time, cost, and surface roughness. In: Chaari, F., Barkallah, M., Bouguecha, A., Zouari, B., Khabou, M.T.,
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Kchaou, M., Haddar, M. (eds.) Advances in Materials, Mechanics and Manufacturing. LNME, pp. 214–222. Springer, Cham (2020). https://doi.org/10.1007/9783030242473_24 ElSayed, A., Kongar, E., Gupta, S.M.: An evolutionary algorithm for selective disassembly of endoflife products. Int. J. Swarm Intell. Evol. Comput. 22(1), 1–7 (2012) Eberhart, R., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the 6th International Symposium on Micro Machine and Human Science, Nagoya, Japan, 39–43 (1995) Fu, Y., Zhou, M., Guo, X., Qi, L.: Stochastic disassembly sequence optimization for profit and energy consumption. IEEE Int. Conf. Syst. Man, Cybern. (SMC), Miyazaki, Japan, 1410–1415 (2018). https://doi.org/10.1109/SMC.2018.00246 Guo, X., Liu, S., Zhou, M., Tian, G.: Disassembly Sequence Optimization for LargeScale products with multiresource constraints using scatter search and petri nets. IEEE Trans. Cybern. 46(11), 2435–2446 (2015) Guo, X., Liu, S., Zhou, M., Tian, G.: Dual objective program and scatter search for the optimization of disassembly sequences subject to multiresource constraints. IEEE Trans. Autom. Sci. Eng. 1–13 (2018).https://doi.org/10.1109/TASE.2017.2731981 Gao, Y., et al.: An energysaving optimization method of dynamic scheduling for disassembly line. Energies 11(5), 1261–1279 (2018) Guo, X., Zhou, M., Liu, S., Qi, L.: Lexicographic multiobjective scatter search for the optimization of sequencedependent selective disassembly subject to multiresource constraints. IEEE Trans. Cybern. 50(7), 3307–3317 (2020). https://doi.org/10.1109/TCYB.2019.2901834 Guo, X., Zhou, M., Liu, S., Qi, L.: Multiresourceconstrained selective disassembly With maximal profit and minimal energy consumption. IEEE Trans. Autom. Sci. Eng. (2020). https://doi.org/ 10.1109/TASE.2020.2992220 Jeunet, J., Della, F., Fabio Salassa, C.F.: Heuristic Solution Methods for the Selective Disassembly Sequencing Problem under SequenceDependent Costs. IFACPapers Online 52(13), 1908–1913 (2019) Luo, Y., Peng, Q., Gu, P.: Integrated multilayer representation and ant colony search for product selective disassembly planning. Comput. Ind. 75, 13–26 (2016) Lu, Q., Ren, Y., Jin, H., Meng, L., Li, L., Zhang, C., Sutherland, J.W.: A hybrid metaheuristic algorithm for a profitoriented and energy efficient disassembly sequencing problem. Robot. Comput. Integr. Manufact. 61, 101828 (2020) Pornsing, C., Watanasungsuit, A.: Discrete particle swarm optimization for disassembly sequence planning, IEEE International Conference on Management of Innovation and Technology., Singapore, 480–485 (2014) Tang, Y., Zhou, M.C., Zussman, E., Caudill, R.J.: Disassembly modeling, planning and applications. J. Manuf. Syst. 21(2), 200–217 (2002) Tseng, H.E., Chang, C., Lee, S., Huang, Y.M.: A Blockbased genetic algorithm for disassembly sequence planning. Expert Syst. Appl. 96, 492–505 (2018) Yeh, w.: Optimization of the disassembly sequencing problem on the basis of selfadaptive simplified swarm optimization. IEEE Trans. Syst. Man, Cybern. A, Syst. Hum. 42, 250–261 (2012) Zhao, S., Li, Y., Fu, F., Yuan, W.: Fuzzy reasoning Petri nets and its application to disassembly sequence decisionmaking for the endof life product recycling and remanufacturing. Int. J. Comput. Integr. Manuf. 27(5), 415–421 (2014) Zhang, L., Liu, Z., Yang, M.: Disassembly sequence planning based on interpretative structural model. J. CAD Comput. Graph. 23(5), 667–675 (2011)
Numerical Model for Intake System in SI Engine Mohamed Brayek1(B) , Mohamed Ali Jemni1 , Ali Damak1 , Amara Ibraim2 , Zied Driss1 , and Mohamed Salah Abid1 1 Laboratory of ElectroMechanic Systems (LASEM), National School of Engineers of Sfax
(ENIS), University of Sfax (US), Road Soukra km 3.5, 1173, 3038 Sfax, Tunisia 2 Higher Institute of Technological Studies ISET Nabeul, Nabeul, Tunisia
Abstract. Exploiting acoustic phenomena of gas dynamics means to increase charge density. The acoustic phenomena in the intake system give a supercharging effect and influence the volumetric efficiency of the engine. Helmholtz resonance theory can be exploited to achieve the design of the intake manifold. Intake airflow pressure loss was minimized and tuned for peak airflow at the desired RPM corresponding to maximum torque. The current work involves testing various intake lengths on a SI engine Honda G×100 generally used to power SH×2000 Generator. Also, the effect of air temperature traveling the intake manifold was evaluated. Comparison with experimental results provide empirical verification of computer modeling and confirm the role of reflecting compression and expansion pressure waves as the primary mechanism of intake tuning. An acceptable agreement between numerical and existent experimental results was obtained, especially at low engine speed, which highlight the validity of the theoretical chosen model. This research identifies the optimal intake manifold geometry corresponding to the maximum torque, the optimum length is at 180 mm and the optimum A/L ratio is at 3.7 mm. Additionally, adding 20 °C the intake temperature will lead to an increase of the optimal engine speed with about 100 rpm. A three dimensional mesh give a satisfactorily understand of the relationship between optimal intake manifold geometry, intake temperature and engine speed. Keywords: Acoustic · Air temperature · Engine performance · Intake manifold length and diameter
1 Introduction Improving volumetric efficiency of spark ignition engine is essential to enhance engine performance. One of the most attractive solutions to achieve better engine performance without introducing several modifications on the main component is the optimization of the intake manifold length and diameter. This solution is based on the use the gas dynamics in intake system to increase the amount of air introduced to the combustion chamber during the intake stroke. In the present work the acoustical phenomenon will be used to identify the best inlet pipe geometry. Several research dealing with the intake system dimensioning shows the importance of optimizing this part of the engine. A number of theories were tested and several practical experiences where conducted. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 277–287, 2022. https://doi.org/10.1007/9783030849580_30
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In their study Sulaiman et al. (2010) finds that optimizing the intake air system geometry can lead to an improvement by up to 20% in the mass flow rate of air going to the combustion chamber. Mahmoud (2012) developed an analytical solution to predict the intake pipe diameter of naturally aspired internal combustion engines, a comparison of his results with commercial vehicles shows a good accuracy to define intake pipe diameter, especially for highspeed engines. Rubayi (1972) conducted an investigation on a multicylinder fourstroke gasoline engine. He found a supercharging effect is achieved using only the acoustical phenomenon and the length and diameter of the inlet pipe, this can improve the compression pressure. It was found that not only the combustion pressure is enhanced when optimizing the intake geometry but also the combustion emission. Ceviz (2007) results showed that it is possible to improve engine performance and reduce pollutant emissions with the optimization of the plenum volume. He also found that change in runner length had a considerable effect on the rpm at which peak value of torque was occurring. Philip (1995) designed and build a new intake manifold based on simple calculations based on Helmholtz theory the complete tuned intake system increased the torque by 28% over the simple leg manifold at the design speed. Figure 1 shows that the movements of the intake valve causes basically two different waves, the closing momentum of the intake valve suddenly halt the air flow and generate a compression wave. The low pressure wave is generated at the time of the suction stroke of the engine. It moves upstream through to airflow pipe and gets reflected from the open intake end as a high pressure wave. The low pressure wave amplitude is reflected in a positive pressure wave one half a resonance period later (Tabaczynski, 1982). This effect is usually brought up as acoustic supercharging or natural supercharging.
Fig.1. The wave’s propagation in the intake manifold.
The compression travels back and forth along the closed intake runner length. If this compression wave arrives at proper time (exactly at the time when the inlet valve opens) it will increase local density of inlet flow. The intake pipe length is decided by Englman (1952) theory. Both waves can useful to increase the volumetric efficiency and masse flow rate thus increasing the engine performance.
2 Mathematical Model Development The relationship between intake runner diameter and the engine speed expressed as (Mahmoud 2012): 5 1 lc D4 (SN )2 (1) d = 0, 06045 T
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Where N = the engine speed in rpm at which maximum effect is desired, T = the inlet temperature, D = the bore, S = the stroke, lc = leq + ls , leq esteemed 12 m, ls = 0, 75 Nc , and c = the velocity of sound in the intake pipe. Engelman (1953) adopt the concept of the Helmholtz resonator (shown in Fig. 2) of the resonant frequency to define the optimum intake pipe length. The resonant frequency is defined as: As cs (2) f = 2π LVc With cs = the velocity of sound in the intake pipe (ft / sec), L = the length of the neck (in), As = the crosssectional area of the neck (in2 ), V c = the static volume of the cavity (in3 ). The resonant cycle period has a major influence if it lasts approximately 180° of the crank angle. Maximum supercharging will occur when the natural Helmholtz resonant frequency is equal to twice the piston frequency. The inlet valve opens simultaneously with the resonance period. The maximum amount of air can be drowned in the combustion chamber. This is due to the inertia of charge entering to the cylinder. This is what could be defined as natural supercharging without a turbocharger or supercharger. The relationship between the resonant speed of the engine and the optimal pipe length is expressed as: A(RS − 1) (3) N = 77cs LV (R + 1) where N = the engine speed at which maximum effect is desired (rpm). As = the crosssectional area intake pipe (in2 ). L = length of intake pipe in inches (in). V = piston displacement of the cylinder (in3 ). R = the compression ratio of the cylinder. The constant, 77, provides for conversion of units. Assumptions used in this analysis are that: • The heat transfer and friction are neglected. • The gas in the inlet pipe is incompressible. • The gas in the inlet act as a linear spring. Thompson (1963) presented a similar approach which relates every engine speed with an optimal intake length. A(R − 1) 162 cs (4) N= k LV (R + 1)
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Fig. 2. Helmholtz resonator
Where k = the ratio of frequency and may varied from 2 to 2.5 depending largely on valve timing. The optimal inlet pipe depends on cross section area. The intake pipe diameter has several effects on inlet air flow. Tabaczynki (1982) and Rubayi (1972) focus on the effect of the intake pipe diameter on the volumetric efficiency of the engine. In many cases there are difficulties in manufacturing the optimal intake pipe length dedicated to a specific engine speed. As previously demonstrated resonant engine speed is directly proportional to the A/L ratio. Changing the intake pipe area directly affects the choice of optimal length. The nonconstant pipe areas require a method to count the effective L/A ratio. Analytical consideration leads to the equation bellow for inlet tube with different area and shape: L = A effective
L
dx = A
nemberofsection
0
i=1
Li Ai
(5)
For different intake pipe area, the calculation of the optimal A/L ratio corresponding to each engine speeds leads to the optimal length.
3 Comparison with Reference Results Table 1 represent the maximum supercharging effect experimentally achieved for different pipe length (Rubay et al. 1972). A comparison between analytical results based on Engelman (1973) theory and Rubayi (1972) experimental results shows a similar trend of the curve representing the optimal intake pipe length corresponding to specific engine speed. It is clear that with the increase of the engine speed the optimal intake pipe length decrease. It should be notice that this model is more accurate at low engine speed where experimental and analytical results are in good agreement. The difference between analytical and experimental results increase with the increase of engine speed and the decrease of intake pipe length. However, a trend similarity is observed at all speeds.
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Table 1. Optimal engine speed for different intake pipe length (Rubay et al. 1972). Pipe length (in) Engine frequency (rps) 40.5 52.5 64.5 76.5 88.5 100.5
16 15 14 13.2 12.5 11.5
OpƟmal intake pipe length (mm)
3000 2500 2000 1500
Experimental results TheoriƟcal results
1000 500 0 0
500
1000
1500
Engine speed (RPM)
Fig. 3. Comparison between analytical and experimental results
The releation between optimal intake and the engine speed is presented in Fig. 3. It is clear from Figs. 3 and 4 that the wave oscillations do not involve a sufficient mass of air for shorter pipes, whereas for long pipes the effect of the standing waves is very pronounced. The air quantity in the combustion chamber is involved thanks to the natural supercharging. The agreement between theory and experimental curve become superposed with increase of the optimal intake length. As shown in Fig. 4 the optimal A/L ratio increase with the engine speed, it can be noticed that the chosen theory is more related to the experimental results for low engine speed.
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OpƟmal A/L raƟo (mm)
0.2
0.15 Experimenal resuls
0.1
Theoriical results
0.05
0 0
500
1000
1500
Engine speed (RPM)
Fig.4. Comparaison between analylitical and experimental results
4 Results and Discussions 4.1 Geometrical Arrangement This work concentrate on the acoustical phenomenon in the intake manifold. Optimal inlet pipe length hence on the pressure of single cylinder fourstroke gasoline engine. The optimum length and diameter of intake pipe are chosen for the engine speed corresponding to the maximum torque (Table 2). Table 2. Engine specifications Bore and stroke
56 × 40 mm
Displacement
98 cm3
Compression ratio
8.5:1
Maximum torque
5.7 Nm at 3600 rpm
Dimension (L W H) 287 × 304 × 402 (mm) Ignition system
Transistorised
4.2 Intake Pipe with Constant Area Figure 5 is a plot of the variation of optimal intake pipe length to the RPM using the recommended k factor of 2, an intake pipe diameter 30 mm and the temperature is
opmal intake pipe length(mm)
Numerical Model for Intake System in SI Engine 1000 900 800 700 600 500 400 300 200 100 0 1000
3000
5000
7000
283
9000
engine speed (RPM)
Fig. 5. Variation of optimal intake pipe length with engine speed
estimated 25 °C. Figure 5 illustrates an exponential behavior of length as function of the engine speed. Figure 5 shows that the theoretical tuning length is approximately 189 mm from the intake valve to the end of the pipe for 3700 RPM corresponding to the maximum torque.
" opƟmal A/L raƟo (mm)
4.3 Intake Pipe with Nonconstant Area
20 18 16 14 12 10 8 6 4 2 0 1000
3000
5000
7000
9000
"engine speed (RPM)
Fig. 6. Variation of optimal A/L ratio with engine speed
Figure 6 represent the evolution of optimal A/L ratio as function of the engine speed. Figure 6 illustrates an linear behavior of A/L ratio as function of the engine speed. Theoretical tuning A/L ratio is approximately 3,75 mm for engine speed 3700 RPM.
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4.4 Effect of Intake Temperature The speed of sound depends on temperature. As consequence it affects the optimal length. Assumption used in this analyses are that: a) b) c) d)
the molar gas constant is independent of temperature. the intake manifold contained just a homogenize air. the mean molar mass of air is independent of temperature. the ideal diatomic gas value is independent of temperature. Using the ideal gas law the equation becomes: RT p cideal = γ = γ ρ M
where. cideal : = the speed of sound in an ideal gas. R = the molar gas constant. γ = the adiabatic index. At 0 °C, it is experimentally defined between 1.3991 and 1.403. T = the absolute temperature in kelvin. M = the mass of a single molecule in kilograms. 4.4.1 Effect of Temperature for Constant Intake Pipe Area Figure 7 shows optimal inlet temperature corresponding to the engine speed for three different inlet length: 200mm, 250mm and 300 mm. Figure 7 illustrates a linear behavior of intake temperature as function of the engine speed. Figure 7 shows the effect of intake temperature for 3 different intake pipe length 200, 250 and 300 mm. it can be seen that increasing intake temperature will lead to the increase of the optimal engine speed. For example for an intake pipe length 250 mm the increase of intake temperature from 10 to 30 °C will lead to an increase of the optimal engine speed with about 100 rpm (from 3116 to 3224 rpm). 4.4.2 Effect of Temperature for Nonconstant Intake Pipe Area Figure 8 represent the effect of intake temperature on optimal engine speed for 3 different A/L ratio 2.5, 3 and 3.5 mm. it can be seen that for a fixed geometry increasing intake tempreaure means that the optimal engine speed increase, for instance for A/L ratio of 3 the optimal engine speed increase from 3200 to 3300 rpm with the increase of intake tempreaturefrom 10 to 30.
5 The Optimal Combination Between Inlet Air Temperature; the Intake Manifold Characteristic and the Engine Speed It has been shown that optimal intake length depends on two parameters; the engine speed and the temperature such. A three dimensional presentation could give a satisfactorily understand of the relationship between these parameters.
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OpƟmal intake temperature (°C)
50 40 30 L= 300mm
20
L=250 mm 10 0 2700 10
L=200 mm 2900
20
3100
3300
3500
3700
Engine speed (RPM)
Fig. 7. Variation of optimal temperature with engine speed for different intake pipe length.
50
OpƟmal intake temperature (°C)
40 30 20
A/L = 3,5mm A/L = 3mm
10
A/L = 2,5 mm 0 2700
2900
3100
3300
3500
3700
10 20
Engine speed (RPM)
Fig. 8. Variation of optimal temperature with engine speed for different ratio A/L
Figure 9 represent the optimal intake pipe length as function of the engine speed and the inlet temperature. It is remarkable that it decrease sharply with the low engine speed. It becomes more unruffled with the increase of the engine speed. The curve of the optimal intake length represents a vertical look for low speed and horizontal look at high speed. As function of the temperature, Fig. 8 shows that the decrease slope of the
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optimum length is quasi constant depending on the temperature, it varies only for high engine speed. It was observed optimal intake temperature depends on the A/L ratio. The output characteristics varied significantly with the change in engine speed and intake air temperature. For a desired engine speed the increase of inlet temperature requires the decrease of A/L ratio to acquire the acoustical phnenomenan and the natural supercharging. As shown in Fig. 6, at low enginespeed, combination between intake air temperature with the optimal A/L ratio produce an horizontal shape plan.
Fig. 9. Optimal intake pipe length versus engine speed and intake air temperature
6 Conclusion The intake manifold geometry of a four strok engine is designed using the Helmholtz resonator model then it was performed. Therefore it can be seen that by appropriate change of the intake pipes (length and diameter) and captivating benefits of the work of the pumping loop, a supercharging effect can be reached. This process has more advantages over the conventional supercharging methods. Also has been shown that optimal intake length and optimal A/L ratio depend on two parameter; the engine speed and the temperature. In addition, this method is economically viable as these pipes do not require extra mechanisms or moving parts. A three dimensional mesh give a satisfactorily understand of the relationship between these
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parameters. Comparison between computed and reference results shows a reasonable agreement. Future work will focus on fluid flow in the optimal intake manifold geometry.
References Sulaiman, S.A., Murad, S.H.M., Ibrahim, I., Abdul, K.Z., A. : Study of flow in airintake system for a singlecylinder gokart engine. Int. J. Autom. Mech. Eng. (IJAME) 1, 91–104 (2010). https://doi.org/10.15282/ijame.1.2010.8.0008 Mahmoud, A.M.: Analytical investigation to predict the Intake pipe diameter in naturally aspirated internal combustion engine. J. Appl. Sci. 12(2), 161–167 (2012). https://doi.org/10.3929/jas. 2012.161.167 Rubayi, N.A.: Acoustic vibrations in intake manifold system and the supercharging of engines. Appl. Acoust. 5(1), 39–53 (1972). https://doi.org/10.1016/0003682X(72)900059 Ceviz, M.A.: Intake plenum volume and its influence on the engine performance, cyclic variability and emissions. Energy Convers. Manage. 48, 961–966 (2007). https://doi.org/10.1016/j.enc onman.2006.08.006 Philip, R.G.: Intake tuning, ethanol conversion, and emissions analysis of a 620 cc four stroke vtwim engine. Thesis, University of Dlinois at UrbanaChampaign Urbana, Dlinois; 61801 (1995). www.ideals.illinois.edu/bitstream/handle/2142/34929/6559202_opt.pdf? sequence=2&isAllowed=y Tabaczynski, R.: Effects of Inlet and Exhaust System Design on Engine Performance, SAE Technical Paper 821577 (1982). https://doi.org/10.4271/821577 Engelman, H.W.: Surge phenomena in engine scavenging. Ph.D Thesis, University of Wisconsin (1953). http://digital.library.wisc.edu/1793/396 Thompson, M.P.: Non mechanical supercharging of four stroke diesel engine, thesis. Ohio State University (1968). http://rave.ohiolink.edu/etdc/view?acc_num=osu1116357818 Engelman, H.W.: Design of a Tuned Intake Manifold, ASME paper 73WA/DGP2) (1973)
Optimization of the Electrical Energy Consumed by a Machine Tool for a Coupled and Uncoupled Cutting System Anoire Ben Jdidia(B) , Taissir Hentati, Hichem Hassine, Mohamed Taoufik Khabou, and Mohamed Haddar Laboratory Mechanics, Modeling and Production, National Engineering School of Sfax (ENIS), BP 1173, 3038 Sfax, Tunisia [email protected]
Abstract. Machine tool utilization has various significant environmental negative impacts caused by the energy consumption such as the global warming and greenhouse emission. Thus, manufacturing parts with sustainable methods is needed to decrease the ratio of environmental negative impacts. This conducts to using models to predict energy during the cutting operation. The objective of this study is to calculate the quantity of the variable energy consumed by the cutting system using two methods: coupled and uncoupled system. This work takes into account the cutting force dynamic behavior. Furthermore, in this work a comparison of consumed energy by two systems for two types of machining (face milling and peripheral) and rotational speed. Results prove that there is no difference between the coupled and uncoupled systems. In addition, the peripheral operation consumes more energy than the face milling. In a second time, this paper presents a formulation to optimize the consumed power during a single pass of face milling operation. Based on the Particle Swarm Optimization (PSO) algorithm, the optimum values of cutting parameters (rotational speed , feed per tooth f z and axial depth of cut ap ) is determined which leads to a minimal consumption of electrical energy during the removing material process. Keywords: Manufacturing · Machine tool · Cutting system · Energy consumption · Sustainable manufacturing
1 Introduction In manufacturing, a high portion of total electrical energy provided is consumed by the cutting phase (Ben Jdidia et al. 2020) which conducts to various negatives impacts on environment such as the global warming and greenhouse emission (Peng and Xu 2017). Thus, it is urgent to reduce the quantity of consumed energy during machining (Jin et al. 2015). That’s why the formulation of the energy is needed during the removing material phase to analyze the impact of various parameters on energy consumption and then to decrease the required energy for machining (Bhushan 2013; Jia et al. 2014). Several © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 288–300, 2022. https://doi.org/10.1007/9783030849580_31
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works aim to model the electrical energy demanded by different machine tool components. The cutting system formed by the table and the spindle system is the movable parts in manufacturing and the exploration of this motion system is very important. To estimate the quantity of the energy consumed by the cutting system during a face milling operation, two models to determine the consumed energy by the axis feed and the spindle system are elaborated by (Avram and Xirouchakis 2011). Authors used a constant value of cutting force components to calculate the energy needed to remove the material. The dynamic nature of the cutting forces is neglected. Similarly, for milling operation (Edem and Mativenga 2017) includes the impacts of the weights of the table in the axis feed model. Besides, the total power consumed by the spindle is composed of a power needed to spindle acceleration and a power needed to remove the material. This latter is obtained by multiplying the specific pressure of cut by the rate of the removal material. Also, in his study the variation of the cutting force with time which impacts the cutting power prediction accuracy is neglected. (Borgia et al. 2016) have established two models to determine the power consumed by the cutting system by considering the effect of the material shear and the friction contact area between the tool flank face and workpiece surface. However, the cutting force model neglects its dynamic behavior. To estimate the cutting force (Lv et al. 2016; Deng et al. 2017; Li et al. 2017; Hu et al. 2017) are based on a generic exponential formulation of the cutting parameters. The model coefficients are identified thanks to a regression analysis which needs several cost experiments. In these works, the cutting force is modeled without considering its dynamic nature during the milling operation. By consequence, the energy needed to rotate the spindle to cut the material is constant while the spindle system is described by (Rief et al. 2017) as a dynamic consumer of energy. In fact, in his investigation, the cutting power is modeled as a fraction between the material removal rate and the specific material removal rate. The cutting section variation over time is not considered. The cutting section variation over time intervenes in the chip thickness formation. Thus, this static behavior, which neglects the temporal parameter, is satisfactory only for turning process where the cutting section is constant. The background of models presented above is used to calculate the energy supplied to the machine tool to produce parts. However, the milling force dynamic nature is totally absent which conducts to inaccurate energy estimation. Until now, there are no works that model the coupling between the axis feed and the spindle system. That’s why; the objective of this study is to look after a better prediction of the demanded cutting system power for a face milling operation. The investigation presents a consideration of the dynamic behavior of the cutting force in order to ameliorate the evaluation of the cutting system consumed energy during a face milling operation.
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2 Numerical Machine Tool Consumed Power During a cutting operation the overall electrical consumed power Pcutting system , is written as the sum of the power needed to move the table Ptable and the power needed to rotate the spindle system Pspindle as shown below: Pmachinetool (t) = Pspindle (t) + Ptable (t)
(1)
with
Pspindle (t) = Ft (t) × Vc Ptable (t) = Fx (t) × Vf
(2)
where F t (t) and F x (t) are respectively the nonlinear tangential and feed components of the cutting force. During a milling operation, the cutting forces are nonlinear. V f (mm/min) is the feed rate and V c (m/min)is the cutting speed. In the rest of this paper, we will focus on the cutting force computation in order to calculate the feed and tangential components. Two methods are illustrated in this work. The first one (given by the Sect. 2.1) considers the spindle and the table systems separately. Any coupling between the two machinery parts is considered. Two motion equations, relative to each part (table and spindle), are resolved in order to calculate the cutting force. The second method (given by the Sect. 2.2), which better describes the machinery process, considers a coupling between the table and the spindle. The equation of motion of the machine is resolved, taking account of the table and the spindle in the same time, to calculate the cutting force. 2.1 Decoupled Modeling For the first method, the cutting system is considered decoupled. To determine the cutting force, a resolution of the spindle equation of motion is performed. The spindle is discretized based on the Finite Element Method (FEM) into 15 linear beam elements (Fig. 1). The theory of Timoshenko is included to describe the shear constraints in the beam elements. In this case, the equation of motion of the spindle is as following: (3) Mspindle {¨q} + Cspindle {˙q} + Kspindle {q} = {Fc (t)} where [M spindle ], [C spindle ], [K spindle ] are respectively the mass, the damping and the stiffness spindle matrix. The vector {q} constitutes the degrees of freedom associated to various nodes and caused by elastic movements.
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Fig. 1. Schematic representation of spindle system
The total variable cutting force is described in the second member. Two operating modes are defined: the face milling operating mode and a peripheral operating mode. For a face milling operating mode, the cutting force is described by this equation (Budak 2006): ⎧ N ⎫ ⎪ ⎪ ⎪ dFX (i (t)) ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ i=1 ⎪ ⎪ ⎫ ⎪ ⎫ ⎧ ⎤⎧ ⎡ ⎪ ⎪ ⎪ ⎪ N ⎪ ⎪ cos(i (t)) sin(i (t)) 0 ⎪ N ⎨ ⎬ ⎨ dFt,i (i (t)) ⎪ ⎬ ⎪ ⎬ ⎨ FX (t) ⎪
⎥ ⎢ dFY (i (t)) = Fc (t) = FY (t) = ⎣ sin(i (t)) −cos(i (t)) 0 ⎦ dFr,i (i (t)) ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ i=1 ⎪ ⎩ dF ( (t)) ⎪ ⎭ ⎩ F (t) ⎭ ⎪ ⎪ i=1 ⎪ ⎪ 0 0 1 Z a,i i N ⎪ ⎪
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ dF ( (t)) Z i ⎩ ⎭ i=1
The parameters are shown by the following Fig. 2:
Fig. 2. Face milling parameters
(4)
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where N is the tool teeth number and i (t) is the instantaneous angular position of the ith tooth given as: i (t) = t + (i − 1) p
(5)
with is the angular speed of the spindle and Φ p is the tooth spacing angle. For peripheral operation the total cutting force is determinated as (Hentati et al. 2016): ⎧ N ⎫ N ⎪ ⎪ f ⎪ ⎪ ⎪ ⎪ dF ( (t)) ⎪ ⎪ ⎪ ⎪ ⎪ k=1 i=1 X ,i i ⎪ ⎪ ⎪ ⎪ ⎫ ⎪ ⎫ ⎧ ⎤⎧ ⎡ ⎪ ⎪ ⎪ ⎪ Nf N Nf N ⎪ ⎪ ⎪ ⎪ F (t) ⎬ ⎨ dFt,i (i (t, z)) ⎪ ⎬ ⎨
⎬ ⎨ X
⎢ −cos(i (t)) −sin(i (t)) 0 ⎥⎪ dFY ,i (i (t)) = Fc (t) = FY (t) = ⎣ sin(i (t)) −cos(i (t)) 0 ⎦ dFr,i (i (t, z)) ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ⎭ ⎪ ⎩ F (t) ⎪ ⎪ k=1 i=1 ⎪ k=1 i=1 dFa,i (i (t, z)) ⎭ ⎪ ⎪ 0 0 1 Z ⎪ ⎪ Nf N ⎪ ⎪ ⎪ ⎪
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ dFZ,i (i (t)) ⎪ ⎩ ⎭
(6)
k=1 i=1
where dF X,i , dF Y,i and dF Z,i are the differential feed, normal to feed and axial forces components expressed using dF t,i , dF r,i and dF a,i that are the tangential, radial and axial components for the ith tooth which are described as a nonlinear function of variable chip load h(Fi ) as follow: ⎧ ⎨ dF t,i (i (t)) = g(i (t))kt ap h(i (t)) (7) dF ( (t)) = kr dF t,i (i (t)) ⎩ r,i i dF a,i (i (t)) = ka dF t,i (i (t)) where the function g(Fi (t)) describes if the ith tooth is active or not, k t , k r and k a are the specific constant pressure of the cutting force and ap is the axial depth. We choose k t = 2200 (N/mm2 ), k r = 0.8 (N/mm2 ) and k a = 0.7 (N/mm2 ). During the face milling and the peripheral operations, the variable chip generated is composed of a static part named hs and a dynamic one named hd relative to the instantaneous angular position. hj (i (t)) = fz sin(i (t)) hs
+ (uX (t) − uX (t − τ ))sin(i (t)) + (uY (t) − uY (t − τ ))cos(i (t))
(8)
hd
The difference between the variable chip thickness generated by a face milling operation or peripheral operation resides on the expression of the instantaneous angular position which can be expressed with function of only the ith tool teeth number or with function of both the ith tool teeth number and disks number (k). The spindle system motion equation is resolved based on Newmark method coupled with Newton Raphson iterative method due to its non linearity. 2.2 Decoupled Modeling For the second method, the total cutting energy will be obtained from a coupling between the spindle and the table where the cutting force is determined from the equation of
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motion formed by the finite element modeling of both the table and the spindle system. In this case, the equation of motion is presented as follow: Fc (t) (9) [Mmachinetool ] {¨q} + [Cmachinetool ] {˙q} + [Kmachinetool ] {q} = −Fc (t) where [M machinetool ], [C machinetool ], [K machinetool ] are respectively the mass, the damping and the stiffness cutting system matrix expressed as following: ⎧ ⎪ Mspindle 0 ⎪ ⎪ [Mmachinetool ] = ⎪ ⎪ 0 Mtable ⎨ (10) Kspindle Kcoupling ⎪ = ] [K machinetool ⎪ ⎪ K K coupling table ⎪ ⎪ ⎩ [C ] = α[M ] + β[K ] machinetool
machinetool
machinetool
To obtain each matrix of the spindle and the table, the first step consists on developing the finite element model of the spindle structure and the table to obtain each stiffness and mass matrix. The vice and the workpiece are considered rigid in our model and they are modeled by a concentrated mass at the contact point between the spindle and the table (Fig. 3). The cutting force is placed in the contact point which corresponds to node 1 of the spindle and node 60 of the table.
Spindle Contact point
Table Fig. 3. Cutting system finite element model
The coupling is modeled by a localized rigidity k coupling added in the contact point. The equation of motion of the coupled cutting system is resolved using Newmark method coupled with Newton Raphson. The flowchart describing each step used to computing the estimated machine tool consumed power is given by Fig. 4. The temporal responses of the displacement vectors along the X, Y and Z directions of the node 1 of the spindle and the node 60 of the table are presented in these figures and show that the displacements of the two nodes are identical in terms of norm but in opposite directions. Thus, the coupling between the two systems is well modeled (Fig. 5).
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Dynamic equation resolution (eq. 9) (Newmark coupled with Newton Raphson method)
Cutting forces Fc(t)
Spindle consumed power Pspindle
Table consumed power Ptable
Output: Machine tool consumed power Pmachinetool
Fig. 4. Flowchart describing machine tool consumed power computation
Knowing the machinetool consumed power, the machinetool cutting energy can be deduced by the following equation: tcutting
Emachinetool (t)dt
Emachinetool
(11)
0
2.3 Experimental Machine Tool Consumed Power A CNC FEELER fv760 milling machine is used to elaborate an experimental study. The characteristics of the machine are given by Table 1. The used mild steel workpiece is a 150 mm length, 100 mm width and 50 mm thick. In order to calculate the total energy consumed by the cutting machine during the cutting period, both table and spindle consumed power are measured using an experimental situ. An electrical connection performed at the output of the spindle or the table drives. Then, two NI9223 data collecting cards are used to converts the signal to a digital one. The signals are recorded by a NI cDAQ9174. A LabVIEW interface is used to acquire the instantaneous power consumed by the machine (Fig. 6). Each mechanical measured power is giving by subtracting the Joule power from the total one absorbed by the spindle or the table systems. The Joule power can be determinated using the motor resistance measured by a multimeter (R = 2.42 for the spindle and R = 0.29 for the table) and the currents values per phase as expressed in the following expression: (12) PJoule = R I02 + I12 + I22
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Displacement in X direction (m)
Node 1
Node60
Time (s)
Displacement in Y direction (m)
Node 1
Node 60
Time (s)
Displacement in Z direction (m)
Node 1
Node 60
Time (s)
Fig. 5. Displacement evolution of node 1 of the spindle and node 60 of the table in direction X (a), direction Y (b) and direction Z (c)
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Spindle
Table
Parameter
Value
Maximum feed system cross travel along Z axis
510 mm
Spindle diameter
80 mm
Machine speed
1500–2000 rpm
Column  spindle axis
665 mm
Tool holder
BT 40
Maximum feed system cross travel along X axis
760 mm
Maximum feed system cross travel along Y axis
420 mm
Rapid traverse along X, Y, and Z axes
24 m/min
NI cDAQ9174
2 data collecting NI 9223
3 voltage sensor
3 current sensor
LabVIEW
Fig. 6. Setting up measuring instruments on the machine tool
The total power consumed by the tool machine during the cutting period will be then the sum of the mechanical power consumed by the spindle and the table systems. The total energy consumed by the cutting machine, FEELER fv760, will be computed by multiplying the total consumed power by the total time spent to execute the material removing. 2.4 Results and Discussion In order to improve the accuracy of our formulation, comparisons between numerical and experimental table and spindle consumed powers and energies are done. The Table 2 recapitulates the obtained results given for a face milling cutting operation and a rotational speed equal to 716 rpm. The cutting parameters for this study are: a cutting speed of 140 m/min, an axial depth of cut equals to 2 mm and a feed per tooth equals to 0.2 mm/tooth. We note a concordance between the numerical and experimental powers and energies consumed by both table and spindle. In fact, the errors between numerical and experimental powers consumed respectively by the table and the spindle are 2.44% and 3.36% and the errors between numerical and experimental energies consumed respectively by
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Table 2. Comparison between table and spindle consumes powers and energies Consumed power (W)
Consumed energy (J)
Numerical
Experimental
Numerical
Experimental
Table
14.79
15.16
105.46
101.07
Error (%)
2.44
Spindle
729.73
Error (%)
3.36
Uncoupled model
744.52
Error (%)
3.55
4.16 756.76
9140.6
771.92
9246.06
9609.4
4.9 9710.47
4.78
the table and the spindle are 4.16% and 4.9%. A good agreement is noted between experimental and numerical results showing the robustness of our modeling. For those cutting conditions, we can compute the experimental total consumed energy and the numerical total consumed energy for an uncoupled modelization. The obtained results are summarized in the Table 2 (last two lines). The numerical obtained results obtained for the uncoupled model are validated with experiments, in which the error is 3.55% and 4.78% respectively in terms of consumed power and consumed energy. Table 3. Comparison between coupled and uncoupled model Rotational speed (rpm)
1500
Coupled system
Peripheral
866.9
1147.93
Face milling
606.26
862.71
Uncoupled system
Peripheral
872.8
1188
Face milling
613.15
868.8
Error 1 (%)
Peripheral
0.7
1.10
Face milling
1.18
0.7
29.7
26.86
Error 2 (%)
2000
Puncoupled − Pcoupled × 100 Puncoupled Pperipherical − Pface milling × 100 Erreur2(%) = Pperipherical
Erreur1(%) =
(13)
In order to show the impact of the coupling in our modeling, a parametric study is elaborated for a FEELER fv 760 working in the same cutting operation parameters. A comparison between the coupled and uncoupled model results, rotating at 1500 rpm and 2000 rpm, are summarized in Table 3, giving the CN machine consumed power for two machining types (peripheral and face milling), during a single pass of each operation.
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The obtained results in Table 3 show, firstly, that the error (1) between the consumed power by the coupled and uncoupled system is between 0.7 and 1.18% for the two different rotational speeds. Thus, one concludes that there is no different between the coupled and the uncoupled system to estimate the required consumed power. Furthermore, it is clear that the consumed power consumed by the coupled system is slightly lower than the one demanded by the uncoupled system. This result is explained by the consideration of the mass, stiffness and damping matrices of the table in the motion equation which influences the outputs of the motion equation and the value of the cutting force. In addition, results prove that the peripheral operation consumes more power than the face milling. In fact, we note in the case of the uncoupled system an increase of 26.86% for the rotational speed 1500 rpm and an increase of 29.7% for the rotational speed 2000 rpm. This increase can be explained by the increase of the stress distribution in the case of peripheral machining where the contact zone will be linear while in the case of face milling machining, the contact zone will be the entire contact surface toolpiece and the stress distribution will be all along this surface.
3 Optimization of the Consumed Cutting Energy In manufacturing, the machining phase is the main electrical energy consumer (Li et al. 2016). Due to her significant part of electrical energy consumption, the CNC machining has an important negative effect on environment (Dahmus and Gutowski 2004). It is then urgent to reduce the consumed energy by the machining operation (Jin et al. 2015). The goal of this section is to develop a new model of face milling machining energy optimization. Our objective is to find the optimum cutting parameters for a single pass of face milling operation (rotational speed , feed per tooth f z and axial depth of cut ap ) to minimize the cutting energy Pmachineoutil computed as described in Sect. 2. Due to the indifferent consumed power of the machine tool, for the coupled and uncoupled model, we will use in this section the uncoupled modelization. Our optimization problem is described as following: ⎧ min(P ) ⎪ ⎪ ⎧machinetool ⎪ k s a e a p fz N ⎨ ⎪ g = ≤ Fmax ⎨ 1 πD (14) ks ae ap fz N Vc ⎪ s.c. : g2 = 60000 π D ≤ Pmax ⎪ ⎪ ⎪ ⎩ ⎩ 8k a f z V g3 = sπ 2p Dz 3 c ≤ τmax where g1 , g2 and g3 denotes functions defining constraints related respectively to the maximum cutting force F max that can be supported by the cutter tool, the maximum cutting power available on the spindle machine Pmax , and the rupture resistance condition of a milling cutter. The limit of the machine tool must be also considered as following: ⎧ min max ⎨ ≤ ≤ min max f ≤ fz ≤ fz ⎩ zmin ap ≤ ap ≤ apmax
(15)
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To resolve the optimization problem, particle swarm algorithm (PSO) is used. The resolution is repeated 10 times to decrease the random effect of PSO algorithm. The tool and the workpiece materials are respectively carbide and steel. The parameters used during the simulation are summarized in Table 4. Table 4. Optimization parameters Parameters
Value
Workpiece length (mm)
100
Tool diameter (mm)
40
Radial depth of cut (mm)
20
Axial depth of cut range of variation [ap min ap max ] (mm)
[1; 4]
Feed per tooth range of variation [f z min f z max ] (mm/tooth) Rotational speed range of variation [min max ] (rpm)
[0.1; 0.6] [397,8; 2387]
Using the PSO algorithm, the cutting parameters obtained by minimizing the cutting energy are: an axial depth of cut ap equals to 1 mm, a feed per tooth f z equals to 0.1 mm/tooth and a rotational speed equals to 802.83 rpm. For those cutting parameters, the total energy consumed by the machine tool E machinetool is equal to 319 J.
4 Conclusion This work includes the nonlinearity of the cutting force to estimate the consumed power by the machine tool cutting system. Two methods are developed to evaluate this quantity of consumed power: coupled and uncoupled cutting system. To validate the establish model, a comparison between numerical and experimental powers and energies consumed by the table and the spindle is performed. The obtained results show a concordance between the experimental and numerical results. A parametric study is elaborated in order to show the effect of the coupling consideration in the equation of motion, shows that the coupled and uncoupled cutting system consumes the same quantity of power. By comparing the consumed power for two types of milling operation, it is shown that the peripheral operation consumes more power than the face milling. This study ameliorates the background described above by including the milling cutting force nonlinear behavior to calculate the consumed power by the cutting system. In a second time, an optimization of this consumed power is formulated. Using the PSO algorithm, the optimum cutting parameters is determined which conduct to a minimal consumption of electrical energy. As perspectives, we propose to perform an optimization of the consumed energy in the case of a multi pass face milling operation.
References Li, C., Xiao, Q., Tang, Y., Li, L.: A method integrating Taguchi, RSM and MOPSO to CNC machining parameters optimization for energy saving. J. Clean. Prod. 135, 263–275 (2016)
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Peng, T., Xu, X.: An interoperable energy consumption analysis system for CNC machining. J. Clean. Prod. 140, 1828–1841 (2017) Edem, I.F., Mativenga, P.T.: Modelling of energy demand from computer numerical control (CNC) toolpaths. J. Clean. Prod. 157, 310–321 (2017) Borgia, S., Albertelli, P., Bianchi, G.: A simulation approach for predicting energy use during general milling operations. Int. J. Adv. Manuf. Technol. 90(9–12), 3187–3201 (2016). https:// doi.org/10.1007/s0017001696545 Lv, J., Tang, R., Jia, S., Liu, Y.: Experimental study on energy consumption of computer numerical control machine tools. J. Clean. Prod. 112, 3864–3874 (2016) Deng, Z., Zhang, H., Fu, Y., Wan, L., Liu, W.: Optimization of process parameters for minimum energy consumption based on cutting specific energy consumption. J. Clean. Prod. 166, 1407– 1414 (2017) Li, C., Chen, X., Tang, Y., Li, L.: Selection of optimum parameters in multipass face milling for maximum energy efficiency and minimum production cost. J. Clean. Prod. 140, 1805–1818 (2017) Hu, L., et al.: Minimizing the machining energy consumption of a machine tool by sequencing the features of a part. Energy 121, 292–305 (2017) Rief, M., Karpuschewski, B., Kalhöfer, E.: Evaluation and modeling of the energy demand during machining. CIRP J. Manuf. Sci. Technol. 19, 62–71 (2017). https://doi.org/10.1016/j.cirpj. 2017.05.003 Dahmus, J., Gutowski, T.: An environmental analysis of machining. In: Proceedings of the 2004 ASME International Mechanical Engineering Congress and RD&D Exposition, Anaheim, California, USA (2004) Budak, E.: Analytical models for high performance milling. Part I: Cutting forces, structural deformations and tolerance integrity. Int. J. Mach. Tools Manuf 46, 1478–1488 (2006) Hentati, T., Barkallah, M., Bouaziz, S., Haddar, M.: 1982. Dynamic modeling of spindlerolling bearings systems in peripheral milling operations. J. Vibroeng. 18 (2016) Mouzon, G., Yildirim, M.B., Twomey, J.: Operational methods for minimization of energy consumption of manufacturing equipment. Int. J. Prod. Res. Sustain. Des. Manuf. 45, 18–19 (2007) Jin, M., Tang, R., Huisingh, D.: Call for papers for a special volume on advanced manufacturing for sustainability and low fossil carbon emissions. J. Clean. Prod. 87, 7–10 (2015) Bhushan, R.K.: Optimization of cutting parameters for minimizing power consumption and maximizing tool life during machining of Al alloy SiC particle composites. J. Clean. Prod. 39, 242–254 (2013) Jia, S., Tang, R., Lv, J.: Therbligbased energy demand modeling methodology of machining process to support intelligent manufacturing. J. Intell. Manuf. 25, 913–931 (2014) Avram, O.I., Xirouchakis, P.: Evaluating the use phase energy requirements of a machine tool system. J. Clean. Prod. 19, 699–711 (2011) Edem, I.F., Mativenga, P.T.: Impact of feed axis on electrical energy demand in mechanical machining processes. J. Clean. Prod. 137, 230–240 (2016) Li, J.G., Lu, Y., Zhao, H., Li, P., Yao, Y.X.: Optimization of cutting parameters for energy saving. Int. J. Adv. Manuf. Technol. 70(1–4), 117–124 (2014) Ben Jdidia, A., Hentati, T., Bellacicco, A., Khabou, M.T., Rivier, A., Haddar, M.: Optimisation des conditions de coupe dans le fraisage de face en un seul passage pour une énergie de coupe, un temps, un coût et une rugosité de surface minimaux. In: Dans Advances in Materials, Mechanics and Manufacturing, pp. 214–222. Springer, Cham (2020)
Quasistatic Study of Gear Mesh Stiffness of a PolymerMetallic Spur Gear System Ala Eddin Chakroun1,2(B) , Chaima Hammami1 , Ahmed Hammami1 , Ana DeJuan1 , Fakher Chaari1 , Alfonso Fernandez2 , Fernando Viadero2 , and Mohamed Haddar1 1 Laboratory of Mechanics, Modeling and Production (LA2MP), National School of Engineers
of Sfax, BP 1173, 3038 Sfax, Tunisia [email protected], [email protected] 2 Department of Structural and Mechanical Engineering, Faculty of Industrial and Telecommunications Engineering, University of Cantabria, Avda de los Castros s/n, 39005 Santander, Spain {alfonso.fernandez,fernando.viadero}@unican.es
Abstract. Plastic gears are becoming increasingly reliable in modern industry. The study of the gear mesh stiffness can give a better understanding to their dynamic behavior. For metallic gear set, gear mesh stiffness has been widely studied. However, for plastic ones, there is still work to be done to accurately describe the impact of the material’s viscoelastic behavior on it. A quasistatic investigation can give a better understanding to a longterm gear meshing. In this study, it is proposed to perform a quasistatic simulation on a polymermetallic spur gear system. The viscoelastic behavior of the polymer is modelled using a rheological model, which is Generalized Maxwell Model (GMM). The gear materials are chosen to be steel verses nylon 6,6. For this type of gear pairs, deformation occur only on the polymer gear due to the huge difference in the materials Young’s modulus. The quasistatic speed of the pinion is selected so that the strain of the polymer gear tooth can be approximated to achieve full recovery before the beginning of the next engagement. Therefore, the gear mesh stiffness found by this quasistatic study is compared to that used in metal gear systems. Keywords: Gear mesh stiffness · Polymer · Viscoelastic behavior · Generalized Maxwell model · Quasistatic
1 Introduction Plastic gears are conquering modern industry by replacing metal gears. They are known for their lightness and low cost. They have been of interest to many researchers for many years. Polymer are known to be used as plastic gear materials. Therefore, it is interesting to study their static and dynamic behavior. To do so, many studies proposed many approaches to model the viscoelastic behavior of the said material. Rheological models are commonly used to model such behavior. In the study of (Ewoldt et al. 2008), © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 301–307, 2022. https://doi.org/10.1007/9783030849580_32
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it is mentioned that soft solids, such as polymers, are known to be characterized by viscoelastic moduli. The elastic part of the structure is the storage modulus G (w) and the viscous part of the structure is the loss modulus G (w). Those moduli are used to obtain a Fourier series of expression of the stress σ . Thus, the strain ε is extruded from a Fourier transform from the stress. Recovery (Joo et al. 2007), creep (Almagableh et al. 2008) and Stressstrain (Blanc and Ravasoo 1996) are then determined. Primitive models are also used to model viscoelastic behavior. Maxwell, KelvinVoight and their derivative models are the most common. They consist of a combination of springs and dashpots connected in series or in parallel or even a mixed connection. The choice depends on the characteristics of the material. In the study of (Jrad et al. 2013), it is mentioned that generalized models are used for more precise modelling. In this study, it is proposed to use GMM for its capability to model viscoelasticity during a steadystate harmonic excitation. In the literature, there is many mentions of modeling the gear mesh stiffness of metallic spur gears. Chaari et al. (2009) considered that a tooth of a spur gear behave as a nonuniform cantilever beam. Therefore, the gear mesh stiffness is deduced after considering bending, thread foundation and contact deflection. Finite element models are also used like the one proposed by Fernandez Del Rincon et al. (2013). Approximated models are also used. Farhat et al. (2020) modeled the gear mesh stiffness using a square signal that fluctuate around a mean value of the tooth contact stiffness. In this quasistatic study, it is considered that all deformations will occur on the polymer gear regarding that the stiffness of the latter is too small than the stiffness of the metal pinion. It is proposed to introduce a variable stress that is deduced from the sharing approach proposed by Raghuwanshi and Parey (2017). Therefore, the strain is deduced after considering the viscoelastic behavior using GMM. The meshing stiffness of each tooth of the polymer gear is resulted from the stress and the strain. Therefore, the gear mesh stiffness is the result deduced using an overlay on each of the polymer gear teeth meshing stiffness. This result is then compared to gear mesh stiffness signal used in metallic gear systems.
2 Generalized Maxwell Model (GMM) GMM (see Fig. 1(b)) are often used to model the viscoelastic behavior of polymer materials. It usually consists of several Maxwell cells connected in parallel. A spring is also added in parallel to retract the dashpots after releasing the load applied to it. The GMM is known for its ability to model the actual viscoelastic behavior when a harmonic load is applied, compared to other rheological models (Jrad et al. 2013). When a linear spring is used, the relation between stress σ and strain ε is given by the following Eq. (1). Generally, springs are often used to model elastic behavior of materials. σ = εE
(1)
Where E is the Young modulus. When a dashpot is used, the relation between stress and strain is given by the following Eq. (2). Generally, dashpots are often used to model viscous behavior of
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materials. σ =η
dε dt
(2)
Where η is the coefficient of viscosity. When a spring connected to a dashpot in series, the relation between stress and strain is given following Eq. (3). A Maxwell cell (see Fig. 1(a)) is then formed. Generally, the latter is often used to model viscoelastic behavior of materials. σ0 σ0 ε(t) = + t (3) E η
Fig. 1. (a) Maxwell cell. (c) GMM (Renaud et al. 2011)
A single Maxwell cell can only model the viscoelastic behavior when applying a constant stress. When the latter is released, the dashpot cannot retract itself. Thus, to model the viscoelastic behavior, when applying a harmonic stress, GMM is proposed. It consists of several Maxwell cells connected in parallel with an extra parallel spring. The dynamic stiffness, also known as the impedance Z, is given by Eq. (4). n jωEi ηi Z(ω) = E0 + Ei + jωηi
(4)
i=1
Where E0 is the stiffness of the single string, ω is the angular frequency, i ∈ [1 n] and n is the number of Maxwell cells.
3 Parameter Identification Method In the literature, it is mentioned that the parameters of transfer functions can be identified using different identification methods. In the study of (Renaud et al. 2011), it is mentioned that PoleZero formulation (PZF) is suitable to identify GMM parameters. It is also mentioned that in dynamics, the behavior of PZF is the superposition of the behaviors of
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Fig. 2. DMA creepstrain of pure nylon 6,6 over 30 min at different temperatures (Almagableh et al. 2008)
Pole–Zero couples. These couples are what adds a nonlinear contribution. Initial values used in GMM are taken from a Dynamic Mechanical Analysis (DMA) test done on pure nylon 6,6. Figure 2 shows the latter results as a straintime curves found by Almagableh et al. (2008). In this study, only the curve plotted at 28 °C is considered. Creep is then simulated. The simulated and the experimental graph of creep have approximately the same shape. Therefore, it is now possible to model properly the viscoelastic behavior of the polymer gear.
4 Numerical Results The parameters of the gear system are given in Table 1. Load sharing factor is considered following the study of Raghuwanshi and Parey (Raghuwanshi and Parey 2017). After considering the latter approach, the load applied on one tooth of the pinion for two cycles is plotted in Fig. 3 where T is the period of one cycle. Then, the strain is deduced after considering the viscoelastic behavior of nylon 6,6. After zooming in Fig. 4, the nonlinear behavior can be seen clearly. This is the result of the viscous character of the viscoelastic material. Considering the long period, it takes the tooth to recover, the recovery can be approximated to be total. Therefore, the behavior of the first cycle will be the same in the next coming cycles. From stress and strain curve, the mesh stiffness of on tooth is then deduced. Therefore, it now possible to consider all the pinion teeth. After considering the phase difference between the teeth, an overlay is made to deduce the overall gear mesh stiffness. Figure 5 shows the behavior of the gear mesh stiffness for two cycles. It is known that, in metallic spur gears, it is possible to model the gear mesh stiffness as a square signal. To compare it to the result found in this study, it is more or less the same. The only difference is that the shape of the polymer gear signal has a brief exponential form in the beginning of the period of two engaged teeth. In future study it is proposed to consider a dynamic study instead of a quasistatic study. Considering a nontotal recovery of polymer can lead to a totally different result.
Quasistatic Study of Gear Mesh Stiffness Table 1. Characteristics of the gear system Pinion
Gear
Teeth numbers
20
30
Material
Steel
Pure nylon 6,6
Base circle (mm) 18.8
28.2
Torque (N m)
1000
−1500
Rotation speed (rpm)
3
2
Module (mm)
2
Pressure angle
20°
Teeth width (mm)
23
Contact ratio
c = 1.6
T
Fig. 3. Stress of one tooth of the gear for on cycle
Recovery
Fig. 4. Strain of one tooth of the gear for one cycle
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Fig. 5. Gear mesh stiffness of the gear system for two successive cycles
5 Conclusion In this study, a quasistatic study of the gear mesh stiffness of a polymermetal gear pair is proposed. A new approach is proposed to model the gear mesh stiffness of polymer gears. This approach considers the use of the GMM as a rheological model of viscoelastic behavior. The identification of the GMM parameters followed the PZF method. The stiffness of the gear is then deduced from the introduced stress and the simulated strain. The shape of the latter is repeated at each cycle. Therefore, the shape of the gear mesh stiffness is not so different from that used to model metallic gears. In future work, it is proposed to make a dynamic study that takes into account the nontotal recovery. Then to compare it with the result found in this one. Acknowledgements. This paper was financially supported by the TunisianSpanish Joint Project N° A1/037038/11.
References Almagableh, A., Gupta, S., Raju Mantena, P., AlOstaz, A.: Dynamic mechanical analysis of graphite platelet and nanoclay reinforced vinyl ester, and MWCNT reinforced nylon 6,6 nanocomposites. In: International SAMPE Technical Conference (June) (2008) Blanc, R.H., Ravasoo, A.: On the nonlinear viscoelastic behaviour of nylon fiber. Mech. Mater. 22(4), 301–310 (1996). https://doi.org/10.1016/01676636(95)000453 Chaari, F., Fakhfakh, T., Haddar, M.: Analytical modelling of spur gear tooth crack and influence on gearmesh stiffness. Eur. J. Mech. A/solids 28(3), 461–468 (2009). https://doi.org/10.1016/ j.euromechsol.2008.07.007 Ewoldt, R.H., Hosoi, A.E., McKinley, G.H.: New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear. J. Rheol. 52(6), 1427–1458 (2008) Farhat, M.H., et al.: Numerical model of a single stage gearbox under variable regime Mech. Based Des. Struct. Mach. (2020) Fernandez Del Rincon, A., et al.: A model for the study of meshing stiffness in spur gear transmissions. Mech. Mach. Theory 61, 30–58 (2013). https://doi.org/10.1016/j.mechmachtheory. 2012.10.008 Joo, W., Jepsen, K.J., Davy, D.T.: The effect of recovery time and test conditions on viscoelastic measures of tensile damage in cortical bone. J. Biomech. 40(12), 2731–2737 (2007)
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Jrad, H., et al.: Experimental characterization, modeling and parametric identification of the non linear dynamic behavior of viscoelastic components. Eur. J. Mech. A/solids 42, 176–187 (2013) Raghuwanshi, N.K., Parey, A.: Experimental measurement of spur gear mesh stiffness using digital image correlation technique. Meas. J. Int. Meas. Confederation 111(November 2016), 93–104 (2017). https://doi.org/10.1016/j.measurement.2017.07.034 Renaud, F., et al.: A new identification method of viscoelastic behavior: application to the generalized maxwell model. Mech. Syst. Sig. Process. 25(3), 991–1010 (2011). https://doi.org/10. 1016/j.ymssp.2010.09.002
Combined Approach for Modeling Progressive Damage in Unidirectional CFRP Composites B. Salem1 , A. Mkaddem2 , S. Rubaiee3 , A. S. Bin Mahfouz4 , A. AlZahrani2 , and A. Jarraya1,2(B) 1 LA2MP, National School of Engineering of Sfax, University of Sfax, PO Box 1173,
3038 Sfax, Tunisia [email protected] 2 Department of Mechanical and Materials Engineering, Faculty of Engineering, University of Jeddah, PO Box 80327, Jeddah 21589, Saudi Arabia [email protected] 3 Department of Industrial and Systems Engineering, Faculty of Engineering, University of Jeddah, PO Box 80327, Jeddah 21589, Saudi Arabia [email protected] 4 Department of Chemical Engineering, Faculty of Engineering, University of Jeddah, PO Box 80327, Jeddah 21589, Saudi Arabia [email protected]
Abstract. This investigation addresses Finite Element (FE) modeling of unidirectional carbon fibre reinforced polymer (CFRP) behavior basing on uniaxial test. The progressive damage approach is specially used to predict the failure of composite laminates. Damage initiation and evolution of Carbon/Epoxy is modeled using HashinPuck combined criteria. Hashin criteria accounts for fibre tension, fibre compression and matrix tension failure modes while matrix compression mode was modeled referring to Puck criteria. In each failure mode, the initiation and evolution of damage are controlled by different internal variables. Uniaxial tension tests in transverse and longitudinal directions were simulated using VUMAT subroutine implemented upon ABAQUS/Explicit. The numerical inputs were calibrated basing on experimental data from referred literature. Stressstrain plots show high reliability of the proposed model when compared with experimental findings. Predictions exhibit physical failure modes owing to crack initiation and evolution as typically observed in experimental tests. Keywords: Hashin damage · Puck criteria · Tensile test · VUMAT · CFRP
1 Introduction In recent years, FRP composites become increasingly popular in different applications including aerospace and civil infrastructures. FRP are particularly attractive because of their high propertiestodensity ratios, good fatigue and corrosion resistances (Kassapoglou 2015). However, their damage is a very complicated phenomenon, which can take place through different failure mechanisms such as matrix cracking, delamination, © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 308–316, 2022. https://doi.org/10.1007/9783030849580_33
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and fibre breakage, combined or individually (Donadon et al. 2008; Robert et al. 2013). Computational modeling of damage initiation and failure cannot be achieved without referring to experimental calibration and validation (Khan and Sharma 2018). Hence, fine characterization looks crucial for describing the elementary mechanisms controlling the behavior of wide range of composites e.g. synthetic fibres (Solati et al. 2019), natural fibres (Ouarhim et al. 2020), FGM (Moita et al. 2020), hybrid composites (Gemi 2018), etc. This was achieved by referring to different standard tests namely, uniaxial tensile, bending (Hosseini et al. 2020), impact (Khashaba and Othman 2017; Zhang et al. 2017), static and dynamic crush tests (Kim et al. 2020) with or without temperature variation. Several damage models have been proposed (Lapczyk and Hurtado 2007). Two failure mechanisms have been proposed by (Hashin and Rotem 1973). The first is based on the failure of the fibre and the second is based on the failure of the matrix. (Puck and Schurmann 2002) developed a mechanistic theory that distinguishes between various modes of failure. This study presents a reliable prediction approach to investigate the failure modes in composite materials when uniaxial testing. By this reason, User Material Subroutine was particularly developed and implemented into ABAQUS/explicit.
2 Material Modeling 2.1 Damage Initiation Damage initiation criteria, included in the finite element code ABAQUS, are extensively used in numerical development. The quadratic failure criterion takes into account four modes of initiation of damage assumed to be decoupled. In 3D, the criterion of Hashin is applicable to the fibres in tension and in compression, and to the matrix in tension. However, the failure of the Epoxy matrix in compression yields from the criterion of Puck. Hashin’s failure criteria have been shown to predict individual damage modes well (Bakhshan et al. 2017), except for compression damage to the matrix, as the fracture can occur at an angle in the thickness of the layer. For transverse compression, a damage model has been developed by Puck (Khan et al. 2018). Fibre tension σ11 ≥ 1
Fft =
σ 11 XT
2
+
σ 12 S12
2
+
σ 13 S13
2 (1)
Fibre compression σ11 ≤ 1 Ffc
=
σ 11 XC
2 (2)
Matrix tension σ22 + σ33 ≥ 1 2 σ 22 + σ 33
Fmt
=
YT 2
σ 23 2 + σ 22 σ 33
+
S23 2
σ 12 2 + σ 13 2 + S12 2
(3)
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Matrix compression (Puck criterion) σ22 + σ33 ≤ 1 Fmc
=
σ tn A S23 + μn σ nn
2
+
σ ln S12 + μl σ nn
2
(4)
In Eqs. (1)–(3), σij , (i, j = 1, 2, 3) represents the effective stress tensor, XT and YT are the tensile failure stresses in longitudinal and transverse direction, respectively. XC and YC are the compressive failure stresses in longitudinal and transverse direction, respectively. Sij (i, j = 1, 2, 3) are components of the shear failure stresses inplane and outof plane. In Eq. (4), σ ij (i, j = l, t, n) represents the effective stress in real fracture plane.
σ ltn = T (α)σ 123 T (α)T SA 23 is the term representing the transverse shear failure stresses. The transformation matrix is written as ⎡ ⎤ 1 0 0 T (α) = ⎣ 0 cos(α) sin(α) ⎦ 0 sin(α) cos(α)
(5)
(6)
The transverse shear strength in the fracture plane is given by A S23 = Yc /2 tan α
(7)
The transverse friction coefficient is given as μtn = −1/2 tan(α)
(8)
A μln = S2 /S23 μtn
(9)
For the uniaxial compression test, experimental tests have shown that the orientation of the fracture plane is approximately 53◦ ± 2◦ from the laminate plane. 2.2 Damage Evolution To provide accurate predictions of the damage behavior of composites, the damage evolution is modeled as a gradual degradation of the material stiffness (Donadon et al. 2008). • Fibre tension
fail 0 δeq δeq − δeq
dft = fail 0 δeq δeq − δeq
(10)
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Where fail
δeq = 0 δeq
=
2Gft 0 σeq
(ε11 · LC )2 + (ε12 · LC )2 + (ε13 · LC )2 Fft
(11) (12)
The constitutive law representing tensile failure mode of the fibre are shown in Fig. 1b.
Fig. 1. (a) Fracture plane, (b) Fibre failure path in tension and compression.
The damage initiation (point A in Fig. 1b) and the fully damaged condition (point B in Fig. 1b). The equivalent displacement can be written as, δ = LC ε. • Compressive fibre
fail 0 δeq δeq − δeq
dfc = fail 0 δeq δeq − δeq
(13)
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Where fail
δeq = 0 δeq
=
2Gfc 0 σeq
(ε11 · LC )2 Ffc
(14)
(15)
• Tensile matrix
fail 0 δeq δeq − δeq
dmt = fail 0 δeq δeq − δeq
(16)
Where t 2Gm 0 σeq
(17)
(ε22 · LC )2 + (ε12 · LC )2 + (ε23 · LC )2 Fmt
(18)
fail
δeq = 0 δeq
=
• Compressive matrix failure
δfail δeq − δ0eq eq c
dm = 0 δeq δfail eq − δeq
(19)
Where c 2Gm 0 σeq
(20)
(εln · LC )2 + (εtn · LC )2 Fmc
(21)
fail
δeq = 0 δeq
=
3 Finite Element Model To accurately predict stress distributions, forces, and different damage modes in composites, the FE methods may be efficiently applied. The FE modeling offers high reliable tool for predicting mechanical responses of the real structures (Sun et al. 2020).
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In this work, Threedimensional (3D) finite element modeling techniques had been used for the strength prediction and failure process simulation. The dimensions of specimens are 200 × 20 × 1.35 mm3 in longitudinal directions and 200 × 20 × 2.25 mm3 in longitudinal directions (Donadon et al. 2008). The loading and boundary conditions are applied as similar to the experience of the tensile test. When load is applied, one end is loaded with axial displacement and the other clamped (Fig. 2).
Fig. 2. FE model used in this study.
The model was implemented in the ABAQUS/Explicit calculation code via a VUMAT routine. For the generation of mesh the integral solid element reduced to 8 nodes (C3D8R) is adopted. Mechanical properties used are summarized in Table 1 (Donadon et al. 2008). Table 1. Laminates mechanical properties Parameters
Value
E11
100.00 GPa
E22 = E33
8.11 GPa
G12 = G23 = G31 3.88 GPa ν12 = ν13 ν23
0.36
Xt
1800 MPa
Xc
800 MPa
Yt = Z t
74.1 MPa
Yc = Z c S12 = S13
160 MPa
S23
26 MPa
Gft
100 KJ/m2
Gfc
25 KJ/m2
t Gm Gfc
2 KJ/m2
Gs
2 KJ/m2
0.038
60 MPa
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4 Results and Discussion The uniaxial tensile response of unidirectional CFRP is described by stress–strain curves in longitudinal and transverse directions and a comparison between the results obtained numerically and experimentally is presented in Fig. 3. From Fig. 3.a it is clear that the numerical model and the experimental have similar major stress and the numerical major strain is less than the experimental major strain. This is due to that the Young´s modulus E11 for numerical simulation is greater than experimental. From Fig. 3.b, it is clear that the numerical model and the experimental have similar major strain and the numerical major stress is less than the experimental major stress. This is attributed to the fact that the tensile strength value in transverse direction, used in numerical simulation, is slightly smaller than experimental value.
Fig. 3. Stressstrain plots obtained from tensile tests. (a) Longitudinal Tension and (b) Transverse Tension.
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It is worth to note the discrepancy between experimental and numerical peaks obtained is about 5.8%, which is reasonably acceptable. Predictions of Fig. 3.b reflects high reliability of the model proposed irrespective to the uncertainties on the inputs data considered for calculations. Predicted failure (Fig. 4) shows good agreement with the physical cracking in both longitudinal and transverse fibre directions. The model appears able to simulate cracks initiation and crack evolution during loading. Physical failure mechanisms seem to be accurately reproduced.
Fig. 4. Predicted vs. experimental failure modes obtained in tensile tests. (a) Fibre direction, and (b) transverse direction.
5 Conclusions In this study, the tensile test behavior of fibre reinforced polymer composites is simulated using finite element ABAQUS/Explicit code. The proposed approach, combining Hashin and Puck failure modes, was found efficient to simulate the tensile behavior in both longitudinal and transverse directions. Predictions show high reliability in producing failure modes as observed in experimental tests.
References Bakhshan, H., Afrouzian, A., Ahmadi, H., Taghavimehr, M.: Progressive failure analysis of fiberreinforced laminated composites containing a hole. Int. J. Damage Mech. 1, 1–16 (2017). https:// doi.org/10.1177/1056789517715088 Donadon, M.V., Iannucci, L., Falzon, B.G., Hodgkinson, J.M., Almeida, S.F.M.: A progressive failure model for composite laminates subjected to low velocity impact damage. Comput. Struct. 86, 1232–1252 (2008). https://doi.org/10.1016/j.compstruc.2007.11.004 Gemi, L.: Investigation of the effect of stacking sequence on low velocity impact response and damage formation in hybrid composite pipes under internal pressure. A comparative study. Compos. PartB 153, 217–232 (2018). https://doi.org/10.1016/j.compositesb.2018.07.056
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Hashin, Z., Rotem, A.: A fatigue failure criterion for fiber reinforced materials. J. Compos. Mater. 7, 448–464 (1973). https://doi.org/10.1177/002199837300700404 Hosseini, M.R., TaheriBehrooz, F., Salamattalab, M.: Mode II interlaminar fracture toughness of woven Eglass/epoxy composites in the presence of mat interleaves. Int. J. Adhesion Adhes. 98, 1–8 (2020). https://doi.org/10.1016/j.ijadhadh.2019.102523 Khan, S.H., Sharma, A.P.: Progressive damage modeling and interface delamination of cross ply laminates subjected to low velocity impact. J. Strain Anal. Eng. Des. 53, 435–445 (2018). https://doi.org/10.1177/0309324718780598 Khashaba, U.A., Othman, R.: Lowvelocity impact of woven CFRE composite sunder different temperature levels. Int. J. Impact Eng. 108, 1–14 (2017). https://doi.org/10.1016/j.ijimpeng. 2017.04.023 Kassapoglou, C.: Modeling the Effect of Damage in Composite Structures Simplified Approaches. Wiley, Hoboken (2015) Kim, J., Jeong, M., Böhm, H., Richter, J., Modler, N.: Experimental investigation into static and dynamic axial crush of composite tubes of glassfiber mat/PA6 laminates. Compos. PartB 181, 1–16 (2020). https://doi.org/10.1016/j.compositesb.2019.107590 Lapczyk, I., Hurtado, J.A.: Progressive damage modeling in fiberreinforced materials. Compos. PartA 38, 2333–2341 (2007). https://doi.org/10.1016/j.compositesa.2007.01.017 Moita, J.S., Araújo, A.L., Correia, V.F., Mota Soares, C.M., Herskovits, J.: Buckling behavior of composite and functionally graded material plates. Eur. J. Mech. A/Solids 80, 1–10 (2020). https://doi.org/10.1016/j.euromechsol.2019.103921 Ouarhim, W., Essabir, H., Bensalah, M.O., Rodrigue, D., Bouhfid, R., Qaiss, A.: Hybrid composites and intraply hybrid composites based on jute and glass fibers: A comparative study on moisture absorption and mechanical properties. Mater. Today Commun. 22, 1–9 (2020). https://doi.org/ 10.1016/j.mtcomm.2019.100861 Puck, A., Schurmann, H.: Failure analysis of FRP laminates by means of physically based phenomenological models. Compos. Sci. Technol. 62, 1633–2166 (2002). https://doi.org/10.1016/ S02663538(01)002081 Robert, D.C., Stephen, B.C., Caglar, O.: Experimental and computational investigation of progressive damage accumulation in CFRP composites. Compos. PartB 48, 59–67 (2013). https:// doi.org/10.1016/j.compositesb.2012.12.005 Solati, A., Hamedi, M., Safarabadi, M.: Combined GAANN approach for prediction of HAZ and bearing strength in laser drilling of GFRP composite. Opt. Laser Technol. 113, 104–115 (2019). https://doi.org/10.1016/j.optlastec.2018.12.016 Sun, J., Jing, Z., Wu, J., Wang, W., Zhang, D., Zhao, J.: Strain rate effects on dynamic tensile properties of openhole composite laminates. Compos. Commun. 19, 226–232 (2020). https:// doi.org/10.1016/j.coco.2020.04.004 Zhang, C., Duodu, E.A., Gu, J.: Finite element modeling of damage development in crossply composite laminates subjected to low velocity impact. Compos. Struct. 173, 219–227 (2017). https://doi.org/10.1016/j.compstruct.2017.04.017
Impact of Venturi Shape on Performance of Solar Chimney Power Plant Haythem Nasraoui1 , Abdallah Bouabidi1,2(B) , Zied Driss1 , and Hedi Kchaou1 1 Laboratory of ElectroMechanic Systems (LASEM), National School of Engineers of Sfax
(ENIS), University of Sfax (US), B.P. 1173, km 3.5 Soukra, 3038 Sfax, Tunisia [email protected], [email protected] 2 National Engineering School of Gafsa (ENGA), University of Gafsa, Sidi Ahmed Zarroug University Campus, 2112 Gafsa, Tunisia
Abstract. Solar Chimney Power Plant (SCPP) presents significant contributions to the energy production in the high radiations zones. The optimization of the SCPP design is an essential process to obtain an economic profitability. In this work, a chimney with venturi design is investigated. Three venturi designs were studied for the chimney configuration. Added to the standard SCPP, the venturi shape was employed at the bottom, at the center and at the top of the system. For this end, a specific dimensionless factor ratio (HV) defined as the fraction between the venturi altitude and the chimney height, was varies from 0 to 1 by using CFD method. The numerical method used to predict the air flow behavior was presented. The flow characteristics were analyzed for the different considered designs. Outcomes show that the performance of system with venturi design presents an efficient solution comparing to the typical system. In fact, the air velocity and the pressure drop through the chimney reached the double values of the cylindrical chimney for HV = 0.016. The maximum power output was achieved when the venturi localized at the chimney center. Numerical model was optimized and validated with the experimental data of a reference model taken from the literature. Keywords: Renewable energy · Solar chimney power plant · Thermodynamics · CFD · Airflow · Venturi effect
1 Introduction Nowadays, renewable energy systems, particularly, solar devices, are the wildest increasing sources of electrical power in the high solar radiations countries (El Ouederni et al. 2019). SCPP is one of the simple solar setup. It consists of three main compounds; collector, chimney and turbine. Its role was considered in the conversion the solar radiations into electricity by passage way of thermal energy through the collector. In the literature, the SCPP principle was widely investigated and confirmed by several prototypes. The first experimental prototype of solar chimney was built in Manzanares of Spain by Schlaich Bergermann (Schlaich et al. 2005). This prototype can produce 50 kW of electrical power. An experimental and theoretical study of the different parts © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 317–325, 2022. https://doi.org/10.1007/9783030849580_34
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of the Manzanares prototype was developed by Haaf et al. (1984). The feasibility of the solar chimney was analyzed by Nizetic et al. (2008). The influence of different geometrical parameters was established numerically by Tingzhen et al. (2006), based on the Manzanares system. The main disadvantage of the solar chimney is its low thermodynamic efficiency and its high investment cost. Thus, the optimization of the SCPP geometry is required. Kasaeian et al. (2014) carried out numerical and analytical models to improve the different geometrical considerations. They confirmed that the chimney diameter and the chimney height are the most influential parameters on the system efficiency. Bouabidi et al. (2019) carried out numerous simulations by varying the angle between chimney and collector of small SCPP. Their results showed that the efficiency of the solar chimney is related to the value of this angle. Ayadi et al. (2017) noted that the chimney height is one of the main factors responsible on the fluctuation of the depression in the chimney. The impact of the chimney height on the performance of a solar chimney power plant was presented in their work. Kasaeian et al. (2017) analyzed the influence of the turbine blades number. They indicated that the power output is related to the turbine blades number. Nasraoui et al. (2020) performed 3D simulations of different collector layouts. They noted that a double passes counter flow collector presents an efficient solution for improved the SCPP performance. Zhou et al. (2016) proposed a new concept of sloped solar collector constructed on the upper mountain slope. This idea is focused on the heat extracting from the solar radiation received by the lower bare mountain slope. They noted that the proposed system is an applicable solution to enhance the performance and the cost of the SCPP. Ghalamchi et al. (2016, 2017) presented an accurate experimental test for optimizing the thermodynamic performance of the SCPP setup. They studied the impact of the different SCPP dimensions based on an experimental process. A system with positive collector roof was developed by Gholamalizadeh and Kim (2016). They revealed that the air velocity rises with the collector roof due to the more creation of the natural convection near to the chimney. Pretorius (2007) carried out a numerical study of the shape and the characteristics of the collector roof and presented a system with double glazing collector. These authors confirmed that the height of the collector roof and its shape affect directly the power output of the solar chimney. Li et al. (2012) reported a comprehensive model for solving the thermal balance equations in the collector to study the collector radius effect on the SCPP potential. Results revealed that the raise of the collector radius enhances the overall potential, but there is a limit radius while the potential trend becomes slower. Toghraie et al. (2018) investigated the effect of different geometric parameters on the SCPP performance. They noted that practically, all SCPP dimensions have a positive relationship with the power output. Elwekeel et al. (2019) investigated the effect of the roughness shapes of the collector roof on the SCPP performance. Several collector shapes with smooth, triangular, square and curved grooves were predicted. They noted that the collector with triangular grooves gives the optimal performance. Najm and Shaaban (2018) presented an optimization process of the solar chimney and the power density. They changed the collector radius, the chimney height, the turbine pressure drop and the operating conditions. Zhou et al. (2009) determined the power output by calculating the temperature variation along the chimney. The
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authors claimed that there is a maximum chimney height where equilibrium of the air temperature appears. The chimney design presents critical impacts on the output power and thus the choice of the chimney shape required an accurate analysis. In recent years, the chimney shape has received much attention in the SCPP optimization. Hu et al. (2017a) studied the solar chimney with angle divergence of the chimney. Results showed that the divergent chimney design is an efficient technique for raise the SCPP profitability. In other work, Hu et al. (2017b) compared the power output generated from several concepts of the divergent SCPP. They combined between cylindrical and divergent chimney when change the divergence from inlet to chimney outlet. The impact of the angle divergence on the flow behavior was investigated by Nasraoui et al. (2019). Xu et al. (2018) carried out numerical simulations of divergent systems based on total pressure potential impact. They found that when the divergence value is important, the boundary layer separation and backflow will occur. Bouabidi et al. (2019) studied the effect of the chimney diameter on the flow behavior. They noted that a large chimney can gives an optimum velocity with respect the ratio between the height and the diameter of the chimney. Nasraoui et al (2019a, b) proposed a novel chimney with hyperbolic divergence in order to extract the maximum kinetic energy. They noted that a hyperbolic chimney is able to raise the power output of conventional SCPP by 295%. According to the above works, the divergent chimney was widely investigated in the literature. However, no author in our knowledge was studied the chimney with venturi profile. In this paper, a novel chimney design with venturi shape is proposed. Four configurations with different venturi heights are analyzed.
2 Computational Method The model of the radiations source and the heat transfer into the solar chimney power plant is carried out using the CFD code ANSYS Fluent 17.0 (Bouabidi et al. 2018). 2.1 Governing Equations The physical quantities are described basing on the continuity, the momentum and the energy equations. These equations are written respectively in the cylindrical coordinate: Continuity equation: ∂ ∂ρ 1 ∂ + (rρu) + (pw) = 0 ∂t r ∂z ∂z
(1)
The momentum equations: u ∂(ρu) 1 ∂(ρuu) ∂(ρVw) d(u) ∂p 1 ∂ d(u) ∂ μ + + =− + μr + − 2μ 2 ∂t r ∂r ∂z ∂r r ∂r dr ∂z dz r (2) ∂(ρw) 1 ∂(ρuw) ∂(ρVw) ∂p 1 ∂ d(w) + + =− + μr ∂t r ∂r ∂z ∂z r ∂r dr
+
∂ d(w) μ ∂z dz
− (ρ0 − ρ)g
(3)
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The energy equation: λ ∂(T) ∂ λ ∂(T) ∂(ρT) 1 ∂(rρuT) ∂(ρwT) 1 ∂ r + + + = ∂t r ∂r ∂z r ∂r cp ∂r ∂z cp ∂z
(4)
The standard kε turbulence model is incorporated for describing the airflow turbulence. The discrete ordinate (DO) is chosen to compute the incident solar irradiations on the collector surface. 2.2 Geometrical Arrangement A 2D simulation is performed to study the efficiency of venturi design. The geometrical parameters and metrological data are similar to the reference geometry considered by Ghalamchi et al. (2016). The computational domains and its several dimensions are recorded in Fig. 1. The standard dimensions of the collector and the chimney are keeping constant and the venturi height is varied. The chimney height is Hch = 3.04 m, the collector diameter is Dc = 3.82 m and the collector height is Hc = 0.029 m. The modification between the four presented shapes consists on the chimney profiles. The first shape is a conventional chimney. The suggested shapes are characterized by a specific distance x which varies for the second, the third and the fourth case. Figure 2 displays a schematic of the suggested shapes in the present work.
Fig. 1. Main dimensions of the proposed configurations
Table 1 summarizes the different boundary conditions.
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Fig. 2. The proposed configurations
Table 1. Description of boundary conditions. BC
Type
Value
Collector roof
Convection
h = 5 W.m−2 . K−1 and T = 302 K G = 1000 W/m2
Absorber
Convection
h = 5 W.m−2 . K−1 and T = 302 K
Chimney
Heat flux
Q = 0 W.m−2
Collector entrance
Pressure inlet
p = 0 Pa and T = 302 K
Chimney exit
Pressure outlet
p = 0 Pa
3 Model Optimization and Validation 3.1 Meshing Effect The meshing independence is carried out comparing the numerical outcomes with the experimental data of the reference case. Four structured mesh have been investigated to choose the appropriate mesh size. Table 2 gives the different parameters for each case, mesh density, nodes number and cells number. Table 2. Meshing parameters. Mesh density
Coarsest
coarse
fine
Very fine
Nodes number
4850
18501
33604
49912
Cells number
4400
17600
31573
48411
A comparison of the temperature profiles along the collector centerline is depicted in Fig. 3. The temperature profile is closer to the experimental results when the mesh
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becomes finer. A mesh convergence is appeared at the third case while the finer and the very finer meshes present the same behavior. Experimental (Ghalamchi et al, 2016) coarest fine coarse
T (K)
322
312
302 0.1
0.4
0.7 r (m)
1
1.3
Fig. 3. Meshing effect
4 Computational Results In this part, the effect of the venturi height is discussed. The distributions of the local temperature, the velocity and the static pressure are plotted at the axisymmetric plane. Figure 4a compares the four profiles of the temperature in the collector. The deepest temperature values emerge with the standard chimney. But, the high values emerge in the chimney with HV = 0.93. This fact shows an raise of the mass flow under the collector, due to thermal balance in the collector and because the heat transfer coefficient is considered as constant in all cases. Furthermore, it can be estimated from these results that the raise of the venturi height in the chimney raises the mass flow rate. In the meantime, the air velocity rose significantly under the venturi and then shows a downward trend near the chimney exit for the three other cases. This fact is confirmed by Fig. 4b which presents a comparison between the velocity profiles along the chimney axis. Otherwise, the maximum velocity diminished with raising in HV. The significant velocity is shown in the second case (HV = 0.016) and reached V = 5.31 ms−1 . Figure 4c shows the profiles of the static pressure along the chimney axis. A gradient of the static pressure emerges along the chimney. In the conventional configuration, the static pressure raises gradually as the air is growing inside the chimney. Besides, it raises and drops in the venturi shapes. A depression zone, characteristic of the minimum values, emerges near the venturi region, while at the chimney outlet, a compression zone, characteristic of the maximum values was created, which it ensures the outflow of air. In these conditions, the low pressure value reaches p = 5.846 Pa for HV = 0, p = − 18.33 Pa for HV = 0.016, p = −5.346 Pa for HV = 0.5, p = −14.83 Pa for HV = 0.93. From the comparison of these results with the velocity profile, it is concluded that the
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static pressure evolves contrary to the magnitude velocity, presenting an acceleration zone. In these conditions, the static pressure is minimal. Figure 4d shows the variation of the power output with increasing in the ratio HV. When assumed that the turbine is installed at the venturi zone, the power output can be defined by the extracted kinetic energy and expressed as follows: Po =
1 2 3 ρ π Rv Vv 2
(5)
Where Rv and Vv are respectively the chimney radius and the air velocity at the venturi altitude. HV=0
HV=0.016
HV=0
HV=0.016
HV=0.5
HV=0.93
HV=0.5
HV=0.93
335
6
330
5 V (m.s1)
325 T (K)
320 315 310
3 2 1
305 300
4
0
0.5
1
0
1.5
0
1
r (m)
(a) Temperature profiles HV=0 HV=0.5
0 5 p (Pa)
3
(b) Velocity profiles
HV=0.016 HV=0.93
10
Po = 109,85 (HV)3 + 497,07 (HV)2  134,31 HV  144,03 R² =0.99
1200
Power output (103 W)
5
2 z (m)
800
400
15
0
20 0
1
2 z (m)
(c) Static pressure profiles
3
0
0.016
0.5 HV
(d) Power output
Fig. 4. Effect of the venturi height on the aerodynamic characteristics
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The power output presents a parabolic tendency over the specific ratio HV. A peak value emerges for the third configuration with HV = 0.5 when the venturi shape is located at the chimney middle. In this case, the turbine site is taken at a high altitude which has another negative effect on the global performance of the system. Therefore, the second venture design (HV = 0.016) is the efficient design. This shape can enhance the power output by 600% comparing to the standard solar chimney.
5 Conclusion In this work, a new chimney design with a venturi shape was proposed. Three different venturi designs were studied based on CFD methodology. Numerical results were validated with the experimental data of a reference model taken from the literature. The findings show that, the performance of the solar chimney with venturi design presents a good agreement comparing to the typical solar chimney. The chimney with HV = 0.5 (the venturi is located at the chimney middle) presents the high power output. The maximum air velocity in the configuration HV = 0.016 reached 200% of that in the standard chimney. Moreover, the air velocity rises with the raise in HV. In term of overall performance, a SCPP with venturi system localized at the chimney bottom presents the best configuration. In the future, we propose to study new others parameters like a helicoidally chimney profile.
References El Ouederni, A.R., Wahabi, A., Dhahri, H.: Design and simulation of a low cost mini solar concentrator. In: Advances in Materials, Mechanics and Manufacturing, pp 94–102 (2019) Ayadi, A., Driss, Z., Bouabidi, A., Nasraoui, H., Bsisa, M., Abid, M.S.: A computational and an experimental study on the effect of the chimney height on the thermal characteristics of a solar chimney power plant. In: Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering (2017). https://doi.org/10.1177/095440891771 9776 Bouabidi, A., Nasraoui, H., Ayadi, A., Driss, Z., Abid, M.S.: Numerical analysis of chimney diameter effect on the fluid flow and the heat transfer characteristics within the solar tower. Energy Sources Part A Recovery Utilization Environ. Effects 1–13 (2019) Bouabidi, A., Ayadi, A., Nasraoui, H., Driss, Z., Abid, M.S.: Study of solar chimney in Tunisia: effect of the chimney configurations on the local flow characteristics. Energy Build. (2018) Elwekeel, F.N., Abdala, A.M., Rahman, M.M.: Effects of novel collector roof on solar chimney power plant performance. J. Solar Energy Eng. 141(3), 031004 (2019) Ghalamchi, M., Kasaeian, A., Ghalamchi, M., Mirzahosseini, A.H.: An experimental study on the thermal performance of a solar chimney with different dimensional parameters. Renew. Energy 91, 477–483 (2016) Gholamalizadeh, E., Kim, M.H.: CFD (computational fluid dynamics) analysis of a solarchimney power plant with inclined collector roof. Energy 107, 661–667 (2016) Ghalamchi, M., Kasaeian, A., Ghalamchi, M., Fadaei, N., Daneshazarian, R.: Optimizing of solar chimney performance using electrohydrodynamic system based on array geometry. Energy Convers. Manage. 135, 261–269 (2017) Haaf, W.: Solar chimneys: part II: preliminary test results from the Manzanares pilot plant. Int. J. Sustain. Energ. 2(2), 141–161 (1984)
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Hu, S., Leung, D.Y., Chan, J.C.: Impact of the geometry of divergent chimneys on the power output of a solar chimney power plant. Energy 120, 1–11 (2017a) Hu, S., Leung, D.Y., Chan, J.C.: Numerical modelling and comparison of the performance of diffusertype solar chimneys for power generation. Appl. Energy 204, 948–957 (2017b) Kasaeian, A., Ghalamchi, M., Ghalamchi, M.: Simulation and optimization of geometric parameters of a solar chimney in Tehran. Energy Convers. Manage. 83, 28–34 (2014) Kasaeian, A., Mahmoudi, A.R., Astaraei, F.R., Hejab, A.: 3D simulation of solar chimney power plant considering turbine blades. Energy Convers. Manage. 147, 55–65 (2017) Li, J., Guo, P., Wang, Y.: Effects of collector radius and chimney height on power output of a solar chimney power plant with turbines. Renew. Energy 47, 21–28 (2012) Nasraoui, H., Driss, Z., Kchaou, H.: Novel collector design for enhancing the performance of solar chimney power plant. Renew. Energy 145, 1658–1671 (2020) Nasraoui, H., Driss, Z., Ayadi, A., Bouabidi, A., Kchaou, H.: Numerical and experimental study of the impact of conical chimney angle on the thermodynamic characteristics of a solar chimney power plant. In: Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering (2019a). https://doi.org/10.1177/0954408919859160 Nasraoui, H., Driss, Z., Ayedi, A., Kchaou, H.: Numerical and experimental study of the aerothermal characteristics in solar chimney power plant with hyperbolic chimney shape. Arab. J. Sci. Eng. 44(9), 7491–7504 (2019b). https://doi.org/10.1007/s1336901903821x Najm, O.A., Shaaban, S.: Numerical investigation and optimization of the solar chimney collector performance and power density. Energy Convers. Manage. 168, 150–161 (2018) Nizetic, S., Ninic, N., Klarin, B.: Analysis and feasibility of implementing solar chimney power plants in the Mediterranean region. Energy 33(11), 1680–1690 (2008) Pretorius, J.P.: Optimization and control of a largescale solar chimney power plant. University of Stellenbosch, Stellenbosch (2007) Schlaich, J., Bergermann, R., Schiel, W., Weinrebe, G.: Design of commercial solar updraft tower systems—utilization of solar induced convective flows for power generation. J. Solar Energy Eng. 127(1), 117–124 (2005) Tingzhen, M., Wei, L., Guoliang, X.: Analytical and numerical investigation of the solar chimney power plant systems. Int. J. Energy Res. 30(11), 861–873 (2006) Toghraie, D., Karami, A., Afrand, M., Karimipour, A.: Effects of geometric parameters on the performance of solar chimney power plants. Energy 162, 1052–1061 (2018) Xu, Y., Zhou, X.: Performance of divergentchimney solar power plants. Sol. Energy 170, 379–387 (2018) Zhou, X., Xu, Y., Huang, Y.: Novel concept of enhancing the performance of sloped solar collector by using natural anabatic winds. Int. J. Heat Mass Transf. 102, 1356–1361 (2016) Zhou, X., Yang, J., Xiao, B., Hou, G., Xing, F.: Analysis of chimney height for solar chimney power plant. Appl. Therm. Eng. 29(1), 178–185 (2009)
Parametric Analysis of Steel Cutting Using Johnson and Cook Model Nouha Kamoun1(B) , Nabih Feki1,2 , Hamdi Hentati1,3 , and Mohamed Haddar1 1 Research Laboratory of Mechanics, Modeling and Manufacturing (LA2MP), National
Engineering School of Sfax, University of Sfax, Sfax, Tunisia 2 Higher Institute of Applied Sciences and Technology of Sousse, University of Sousse,
4003 Sousse, Tunisia 3 Higher School of Sciences and Technologies of Hammam Sousse, University of Sousse,
Sousse, Tunisia
Abstract. Many manufacturing applications involve high temperatures and high strain rate deformations. Experimental tests are very expensive to study those problems. For that, it is very important to use numerical analysis. The main goal of those studies is to determine the stress state in manufacturing processes, to elaborate characterization tests and to compute the studied process. In this paper, we focus to cutting process of AISI 1045 steel in which a thermomechanical model is developed. The Johnson and Cook’s law was used for the behavior of workpiece. Its five parameters may be easily found in literature for AISI 1045 steel material. We start by determine the triaxiality, the temperature and stress fields in cutting process with continuous chip. This study allows us to develop the characterization tests from negative to positive triaxialities. After that, a numerical examination is carried out to study the influence of cutting parameters on the variation of temperature, cutting force and max Von Mises stress in workpiece. The interaction of cutting speed and feed and the interaction of all the two cutting parameters have significant influence on cutting force, temperature and max Von Mises stress fields. Hence, in the turning process optimization, we focus on choosing an appropriate combination of cutting parameters that are principally the cutting speed and feed. Keywords: FEM · Cutting process · Triaxiality · Johnson Cook model
1 Introduction Metal cutting is a very recognized manufacturing process. An accurate model of the machining operation is not yet presented. The main reason is that different thermomechanical phenomena such as friction, heating, large strains and high strain rates related with this process are very complex to predict. Many research works, such as (Barge et al. 2005; Rao et al. 2013; Ozel and Zeren 2005) were developed in order to study the influence of the cutting process parameters on the numerical results in terms of temperature, cutting forces, geometry of chip. They have simulated the cutting with continuous chip. Otherwise, a few works use the Johnson and Cook model (Johnson and Cook 1983) to model the cutting processes and study the evolution of the triaxiality parameter. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 326–332, 2022. https://doi.org/10.1007/9783030849580_35
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The Johnson Cook law allows taking into account the simultaneous effect of temperature, strain rate and strain. Moreover, the field of validity of this law covers the zone of different plastic strain (several units), the strain rate (to 105 s−1 ) and the temperatures (which can reach 60% of the melting temperature of workpiece material) in machining. In mechanicalmathematical modeling approach, the material’s strain and ductile fracture strongly depends on the existing state of stress in individual areas of the material being strained. Stress and failure mechanisms in the JohnsonCook material modelling compute fracture strain as a function of triaxiality, strain rate and temperature field. The formulation is relatively simple to implement because of the independency between behavior and damage descriptive equations. JohnsonCook models’ is used in the simulation of metal cutting and forming processes (Moakhar et al. 2019a, b, c; Hentati et al. 2015; Abushawashi et al. 2017; Moakhar et al. 2021) involving high strain rates and temperatures. It is very important to optimize the cutting parameters of any machining operation. In manufacturing processes, the cutting forces, damage, temperature fields and the obtained surface are directly influenced by cutting parameters such as cutting speed, feed tool geometry and material properties of workpiece. This is for understanding of the abovementioned problems would improve the choice of optimum cutting conditions, especially in engineering applications such machining and shearing processes. In this work, the simulation of this model provides a set of results in term of cutting forces, von Mises stress and temperature. Hence, the main objective of this paper is to analysis the influence of the cutting speed and feed on computed cutting force, temperature and triaxiality of the workpiece.
2 Material Properties and Behavior Law of Workpiece The creating of cutting process is strongly conditioned by the relevance of the behavior model that describes the main phenomena in the cutting process and their different coupling. The choice of mechanical behavior bank on the phenomena occurring during the cutting process. Plasticity is the main factor causing the formation of the chip. Viscosity is essential to the study of the cutting speed influence and thermal factor has an essential role in the variations of the mechanical characteristics of the machined workpiece. In the cutting model, the material of the part is given by Johnson Cook’s law: • ε T − Tamb m n 1− (1) 1 + CLog • σeq = A + Bε Tf − Tamb ε0 This model includes the involvement of Von Mises stress, equivalent plastic strain, temperature and strain rate. In the secondary shear zone, the workpiece is the seat of strain reaching some units, strain rate reaching 105 s−1 and temperature that can be greater than 1000°K. In addition, another advantage of using the Johnson Cook model is that a database of material behavior for studied material can directly implement in the commercial finite element software.
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The workpiece is made of steel C45. The mechanical and thermal properties of the material and the coefficients of the behaviour law are listed in the Tables 1, 2 and 3 below. Table 1. Mechanical properties of workpiece material (Moakhar et al. 2019a, b, c) Density (Kg/m3 )
Young modulus (MPa)
Poisson’s ratio
Expansion
7800
2.08 105
0.3
11 10−6
Table 2. Thermal properties of workpiece material (Moakhar et al. 2019a, b, c) Conductivity (W/m°C) Specific heat (J/Kg°C) 47
433
Table 3. Johnson Cook constants’ for the AISI1045 (Moakhar et al. 2019a, b, c) A B n [MPa] [MPa] 553
600
C
˙E0 [s−1 ] m Tm [C°] T0 [C°]
0.234 0.0134 1
1
1480
20
We can determine the behavior model’s parameters experimentally. In fact, we can release different tensile tests in quasistatic and dynamic conditions.
3 Numerical Model of Steel Cutting Process Accurate prediction remains difficult by the reason of the complexity of the cutting processes. The finite element method (FEM) has been used as a solution to give a good prediction model in machining. Our numerical model is developed in the finite element framework using the Abaqus/Explicit software. The numerical model consists of rigid tool and workpiece as shown in Fig. 1. This work deals with the problem of machining in plane strain. The workpiece is modeled, as a deformable rectangular solid, the length and the width are respectively equal to 15 mm and 10 mm. Several choices already exist in literature for the modeling of the cutting tool. The majority of the works focuses on the workpiece and the formation of the chip and considers the cutting tool as a rigid material. This assumption is justified by the behavior of the cutting tool material which is harder than the workpiece. The tool cutting edge radius is equal to 0.05 mm. The rake and clearance angle are respectively equal to 10° and 11°.
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Fig. 1. FE model of cutting
In this work, the used elements in the mesh are quadrilaterals with firstorder reduced integration adapted to thermo mechanical coupling and plane strain conditions (CPE4RT). The “Adaptive Mesh” option is used to make a remeshing of the workpiece without the suppression of elements in chip forming. The basic idea is to modify the coordinates of the nodes in order to avoid the distortion of the element. The contact phenomenon and the friction between the part and the cutting tool have a significant influence on the final geometry of the chip and the final quality of the machining surface. The friction conditions between the tool and the chip are complex and depend on the cutting conditions. In our cutting model, the secondary shear zone are the seat of a friction of Coulomb type with a coefficient μ = 0.1. Left and bottom boundary nodes of the workpiece are fixed in both U1 and U2 directions. The initial temperature of the workpiece is equal to 20 °C.
4 Numerical Results The existence of different stress states in the workpiece during the deformation. The stress triaxiality is used to identify the state of stress. It is a dimensionless ratio. It is given by the following equation: η=
σm σeq
(2)
Where σm is the hydrostatic stress and σeq is the Von Mises equivalent stress. The stress triaxiality is known as a significant parameter to control damage process through critical failure strain in cutting processes. The ductile fracture of steels depends
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on hydrostatic stress. We investigate the state of the stress, through the stress triaxiality in machined workpiece. The results in terms of Von Mises stress, equivalent plastic strain, temperature and triaxiality in workpiece obtained by using the code ABAQUS/Explicit are shown on Fig. 2.
Fig. 2. Evolution Von Mises stress, equivalent plastic strain, temperature and triaxiality in workpiece
The simulation shows the formation of continuous chip and the variation of Von Mises stress (S), equivalent plastic strain (PEEQ), temperature field (TEMP) and the triaxiality (TRIAX) in the workpiece. The maximum temperatures reached during the simulation are produced in primary and secondary areas of cutting. We show that in the shear zones, we obtain various stress states: from compression (negative triaxiality) to tension (positive triaxiality) with a shearing stress state (close to zero triaxiality). In addition, we illustrate in Fig. 3 the influence of temperature, cutting force and max Von Mises stress. It can be observed that the both cutting parameters, which are cutting speed and feed, have significant influence on temperature, cutting force and max Von Mises stress. In
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Fig. 3. Variation of temperature T (◦ C), cutting force F(KN ) and max Von Mises stress σmax (MPa) in function of cutting speed Vc (m/ min) and feed f (mm/tr)
fact, the temperature field decreases with the feed. Nevertheless, it increases with cutting speed like the cutting force.
5 Conclusion Many parameters have an effect on the numerical results of the machining process, such as temperature, material properties and cutting parameters. These parameters are related together. A thermomechanical FE model is defined with the ABAQUS code to simulate the cutting process in plane strain. The Johnson Cook law is used to model the workpiece behavior and the tool is considered rigid. Furthermore, we try to improve the cutting parameters by studying the influence cutting speed and feed on the evolution of temperature, cutting force and max Von Mises stress. We have observed through the numerical study of variance that feed and cutting speed have significant influence on the different cutting results.
References Barge, H.H., Rech, J., Bergheau, J.M.: Numerical modelling of orthogonal cutting: influence of numerical parameters. J. Mater. Process. Technol. 164–165, 1148–1153 (2005)
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Johnson, W.H.C.: A constitutive model and data for metals subjected to larges trains, high strain rate, and temperatures. In: International Symposium on Ballistics, The Hague, The Netherlands, pp. 1–7 (1983) Ozel, E.Z.: FE modelling of stresses induced by high speed machining with round cutting tools (2005) Rao, C.J., et al.: Influence of cutting parameters on cutting force and surface finish in turning operation. Procedia Eng. 64, 1405–1415 (2013) Moakhar, S., et al.: Evaluation of AW6082 aluminium bar shearing simulation. In: Chaari, F., et al. (eds.) Advances in Materials, Mechanics and Manufacturing. LNME, pp. 142–149. Springer, Cham (2020). https://doi.org/10.1007/9783030242473_16 Moakhar, S., Hentati, H., Barkallah, M.: Modeling of the ductile damage  Application for bar shearing. Materialwiss Werkstofftech 50, 1–11 (2019). https://doi.org/10.1002/mawe.201800 128s Hentati, H., Naceur, I.B., Bouzid, W., Maalej, A.: Numerical analysis of damage thermomechanical models. Adv. Appl. Math. Mech. 7(5), 625–643 (2015). https://doi.org/10.4208/ aamm.2014.m517 Abushawashi, Y., Xinran, X., Viktor, A.: Practical applications of the “energytriaxiality” state relationship in metal cutting. Mach. Sci. Technol. 21(1), 1–18 (2017). https://doi.org/10.1080/ 10910344.2015.1133913 Moakhar, S., Hentati, H., Barkallah, M., et al.: Parametric study of aluminum bar shearing using JohnsonCook material modeling. In: Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture (2021). https://doi.org/10.1177/095440542199 5621 Moakhar, S., Hentati, H., Barkallah, M., Louati, J., Haddar, M.: Influence of geometry on stress state in bulk characterization tests. C.R. Mec. (2019). https://doi.org/10.1016/j.crme.2019. 10.003
Experimental Study and Measurement of Vehicle Interior Vibration Hichem Hassine1,2(B) , Hadil Chaeib2 , Maher Barkallah1 , Jamel Louati1 , and Mohamed Haddar1 1 Laboratory of Mechanics, Modelling and Production (LA2MP), Sfax, Tunisia 2 Higher Institute of Transport and Logistics, University of Sousse, Sousse, Tunisia
Abstract. In recent years, the automotive sector has experienced increasing competition between different manufacturers. It is in this sense that interior comfort represents one of the areas for improvement to meet customer needs. The level of comfort can be assessed at all stages of vehicle use: Whether stationary or moving at low or high speed, whether driver or passenger. Vehicle occupants can always estimate the comfort of their location. The interior comfort of vehicle is related to some phenomena such as: noise, vibration. Vibration is one of the major sources of discomfort. The main goal of this paper is to study vehicle interior vibration. We present experimental study and measurement of vehicle interior vibration by referring to some parameters: Vehicle characteristics, speed and traffic conditions. The experimental procedure has taken place in two different sites: an urban segment and a rural segment using a vehicle type Citroen C4. The vibration acceleration signals were measured in three dimensions (xaxis, yaxis, zaxis). Measurement results demonstrate that engine is the main source of vibration and in the other hand the speed as an important parameter that influence the vehicle interior comfort quality. Also, the vibration level changes with the position of accelerometers in the vehicle. Keywords: Passenger’s comfort · Vibration measurement · Accelerometer · Vehicle characteristics · Speed
1 Introduction Car manufacturers are constantly improving their offerings to customers in order to increase the degree of confidence. Customer satisfaction automatically involves meeting their needs as well as the quality of the products presented (Stein et al. 2011). User comfort is one of the major pillars to guarantee good quality in the automotive sector. This comfort is linked to several factors such as: noise pollution and vibrations. It is in this sense that several researchers have sought the integration and control of these aspects from the design phase. Comfort depends on many criteria, such as the car’s handling, its ability to filter out external stresses, or even the ergonomics, materials and thermal regulation of its interior. These elements are often studied separately, whereas the assessment of comfort is strongly dependent on the overall perception of the environment. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 333–341, 2022. https://doi.org/10.1007/9783030849580_36
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Several studies have been developed in this context to theoretically model or experimentally measure vibrations (Auersch 2017). These studies have shown the following sources of vibration: the engine or mechanical intermediary between the engine and the wheels; the turn of the wheel; the ground which imposes on the wheel’s movements whose composition in frequencies. The engine is considered as the most important source of noise and vibration in interior car. There fore, the first studies in this field were taked into account vibrations generated by the engine and powertrain (Panza 2015; Wang 2010). Also, other sources of vibration are detected such as: the gearbox, the differential and the structural vibrating modes of the exhaust system (Cerrato 2009; Cerrato and Goodes 2011). To study vibration transmission, researchers tried to study the vehicle suspension system (Horne et al. 2020; Hamza et al. 2020). In the same context, many authors tried to couple sound and vibration in order to ameliorate vehicle interior comfort (Amman et al. 2007; Bellmann 2005; Genuit 2001; Lakuši´c et al. 2011). Based on the literature review, variation of vehicle interior vibration depends on some factors such as: passenger’s position in the car, the source, type of vehicle, type of contact with road, speed and acceleration. The main goal of this paper is to present an experimental study of vehicle vibrations in order to exploit the effect of some parameters such as: speed, position in the car, vehicle characteristics… The remaining content of this paper is organized as follows: Sect. 2 presents the methodology and procedure used to measure vehicle interior vibration. Section 3 is reserved to detail experimental results. Finally, conclusions of this study are summarized in Sect. 4.
2 Description of the Used Procedure to Measure Vehicle Interior Vibration Vibration represent one of the undesirable phenomena that decrease the degree of user’s satisfaction. We propose to study vehicle interior vibration in two different site and different traffic conditions. To assess vibration, we started with the choice of sites, the identification of instruments, measurement procedures, location of sensors and then, the analysis of results in order to detect the influence of each studied parameters. In this paper, two sites were studied in Sousse cityTunisia which represents a rural segment and an urban segment. Then, 4 accelerometers type ADXL 335 were placed in different locations: motor, front dashboard, rear dashboard and in the car floor. This procedure is applied to vehicle, type “Citroen C4” with the following technical characteristics: – The vehicle power is 6 CH, – The fuel type is the petrol, – The number of cylinders is 3.
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Finally, collect data and analysis of results was done based on electronic card type “Arduino”. The used materials and the procedure of measurement can be described using the following Fig. 1.
Fig. 1. Materials and measurement procedure
3 Results and Discussion This section is devoted to the presentation of the results of vibration measurements in the two studied sites. The vibration measurements were carried out on September 2020 using Citroën C4 as a type of vehicle. The vibration acceleration signals were measured in three dimensions (xaxis, yaxis, zaxis) using ADXL 335 type accelerometers. Figure 2 describes the orientation of the used axes during the measurement process. 3.1 Site 1: A Rural Segment The first studied site is a rural segment in Sousse region (Tunisia) where the speed is limited to 90 km/h. Figure 3 provides a graphic representation of the measurement of motor vibration accelerations in the Citroën C4 vehicle on 3 axes on the first site. The acceleration of vibrations on the x axis was between −40 and 12 m/s2 . On the y axis which vibration was between −8 and 6 m/s2 and finally the vibrations recorded on the z axis were between −14 and 7 m/s2 .
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Fig. 2. Description of the adopted axes
Fig. 3. Evolution of motor vibration in site 1
Referring to Fig. 4, the variation of the accelerations of the vibrations of the front dashboard on the x axis are between −2.8 and 1.4 m/s2 . The recording on the y axis of the acceleration of vibrations are between −2.8 and 3.5 m/s2 and between −1.3 and 2.7 m/s2 on the z axis. For the back dashboard, results show that the variation of the vibration on the x and z axis were between −2.3 and 4 m/s2 and on the y axis it varies between −2.5 and 1.8 m/s2 (Fig. 5). Referring to results shown by Fig. 4, we note that the change in vibration on the Citroën C4 vehicle in the car floor is between −1.5 and 2.3 m/s2 on the two axes x and y, and it varies between 0 and 2.8 m/s2 on the z axis (Fig. 6). The presented results demonstrate that the engine is the most source of vehicle vibrations.
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Fig. 4. Evolution of front dashboard vibration in site 1
Fig. 5. Evolution of back dashboard vibration in site 1
3.2 Site 2: An Urban Segment We also measured the acceleration of vibrations in the Citroën C4 vehicle in an urban segment in Sousse city. We obtained a significant variation on the x axis (between −28 and 15 m/s2 ) and a less important variation for the other two axes: between −7 and 5 m/s2 for y axis and also on the z axis which was between −10 m/s2 and 8 m/s2 (Fig. 7).
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Fig. 6. Evolution of car floor vibration in site 1
Fig. 7. Evolution of motor vibration in site 2
Based on Fig. 8, we note that the variation is high on the x axis of the front dashboard (between −3.5 and 1.5 m/s2 ) and on the y axis given (between −4 and 2.5 m/s2 ) but it is weak on the z axis (between −0.6 and 0.9 m/s2 ). The analysis of vibration of the back dashboard demonstrates an important variation on the two axes x and y (between −1.5 and 1.8 m/s2 ). The vibration acceleration measured on the z axis was between −1.3 and 1.3 m/s2 .
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.
Fig. 8. Evolution of front dashboard vibration in site 2
The recordings on the x axis and the y axis given by Fig. 9 show the same variation in accelerations which were varied between −1.2 and 7 m/s2 . In the other hand, the variation of vibration on the z axis was between −0.8 and 12 m/s2 . .
Fig. 9. Evolution of car floor vibration in site 2
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Experimental results demonstrate an important change in the car floor vibration compared to those obtained in site 1. But engine still represents the most important source of vehicle vibrations.
4 Conclusion In this paper, an experimental study of vehicle interior vibration was presented. The main objective was the analyze of the impact of three parameters in the interior comfort of vehicle: type of vehicle, position of the passenger and traffic condition. The experimental measure was carried out on Sousse city (Tunisia) in two type of sites: a rural and urban segment. Measurements results demonstrates an important level of vibration in the motor and it can be considered as the most source of vibration noise in different type of sites. In the other hand, the change of the traffic conditions especially the speed of vehicle, has an important influence in the car floor vibration. As a perspective of this study, future work can be oriented to the theoretical modelling of vehicle interior noise based on experimental measure and also the study of the possibility of the optimization of vibration by the use of metaheuristic such as particle swarm optimization (PSO) and genetic algorithm (GA).
References Amman, S., Mouch, T., Meier, R.: Sound and vibration perceptual contributions during vehicle transient and steadystate road inputs. Int. J. Veh. Noise Vib. 3(2), 157 (2007) Bellmann, M.: Perception of wholebody vibrations: from basic experiments to effects of seat and steering wheel vibrations on the passenger’s comfort inside vehicles. Dissertation, University of Oldenburg, Germany (2005) Horne, D., Jashami, H., Monsere, C.M., Kothuri, S., Hurwitz, D.S.: Evaluating invehicle sound and vibration during incursions on sinusoidal rumble strips. Transp. Res. Rec. 2675, 154–166 (2020) Cerrato, G.: Automotive sound quality – powertrain road and wind noise. Sound Vibr. 43, 16–24 (2009) Cerrato, G., Goodes, P.: Practical approaches to solving noise and vibration problems. Sound Vibr. 45, 18 (2011) Stein, G.J., Chmúrny, R., Rosík, V.: Compact vibration measuring system for invehicle applications. Meas. Sci. Rev. 11(5), 154 (2011) Genuit, K.: The interaction of noise and vibration inside vehicles. In: NOISECON, Hong Kong, China (2001) Genuit, K.: Vehicle interior noise  a combination of sound, vibration and interactivity. In: 8th International Congress on Sound and Vibration, Dearborn (2008) Hamza, G., et al.: An analytical approach for modeling a multibody system during predesign with application to the railway system. In: Chaari, F., et al. (eds.) Advances in Materials, Mechanics and Manufacturing. LNME, pp. 150–157. Springer, Cham (2020). https://doi.org/10.1007/9783030242473_17 Auersch, L.: Simultaneous measurements of the vehicle, track, and soil vibrations at a surface, bridge, and tunnel railway line. Shock Vibr. 2017, 1–18 (2017). Article ID 1959286
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Panza, M.A.: A review of experimental techniques for NVH analysis on a commercial vehicle. Energy Procedia 82, 1017–1023 (2015) Lakuši´c, S., Brˇci´c, D., Lakuši´c, V.T.: Analysis of vehicle vibrations – new approach to rating pavement condition of urban roads. Traffic Transp. 23(6), 485–494 (2011) Trent, J.W.: Experimental acute renal failure. Dissertation, University of California (1975) Wang, X.: Vehicle Noise and Vibration Refinement. Woodhead Publishing, Cambridge (2010)
Design Discussion of a Mobile and Intelligent Infrared Detector for the Measurement of the Air Quality Index Mohamed Abdessamia Chakchouk1,2(B) , Abdelkhalek El Hami1 , Wajih Gafsi2 , and Mohammed Haddar2 1 LMN  Laboratory of Mechanics of Normandy (LMN), The National Institute of Applied
Sciences of Rouen (INSA – Rouen), Rouen, France [email protected] 2 Mechanics, Modeling and Productics Laboratory (LA2MP), The National School of Engineers of Sfax (ENIS), Sfax, Tunisia [email protected], [email protected]
Abstract. Continued air pollution has severely affected the health of humans around the world, according to the World Health Organization (WHO) air pollution kills an estimated seven million people worldwide each year [WHO18]. From the smog hovering over cities to the smoke inside the home, air pollution poses a major threat to health and the climate. The combined effects of indoor (outdoor) and domestic air pollution cause an estimated seven million premature deaths each year, largely due to increased mortality from strokes, heart disease, illnesses. Chronic obstructive pulmonary disease, lung cancer and acute respiratory infections. Multiple technological solutions are in progress to confront this problem. The quality of air in heavily populated areas become a more and more important subject that governments around the world try to monitor, for this end several projects are lunched based on scientific research given the complexity and diversity of the processes involved in the atmosphere, three complementary approaches are used; laboratory studies, modelization and observation. This paper will present a project idea that belongs to the observation domain, hence the optimization of the use of an IR (Infra – Red) detector mounted on drones to do the mapping of the air quality index in a given area. Keywords: Drone · Infrared sensors · Air pollution · Optimization · Design
1 Introduction WHO sounds the alarm about air quality that humans are respirating, in fact most of cities worldwide fails to meet the WHO guidelines for safe levels of pollution [YAN18]. This paper presents an initiative to participate in the ongoing effort to limit the impact of pollution on the environment and the health of humans by developing a digital design and realization a mobile infrared (IR) detector on a drone. It is an intelligent mobile © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 342–352, 2022. https://doi.org/10.1007/9783030849580_37
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mechatronic system, to observe and measure the intensity and IR absorption profile of molecules present in a given environment. The application is for the observation and characterization of atmospheres and environments concerning: – Pollution monitoring in urban areas or in the perimeter of industrial areas at risk. – The characterization of a given environment with its physiochemical composition and its physical parameters. This system will be based on the development of two connected and communicating drones. The whole could eventually be extended to a network of drones in the form of a flotilla that can be operated remotely. The server implemented in the ground base will be equipped with realtime and timeshared processing software. These smart drones are equipped with the Infrared sensor system based on DLaTGS or DTGS operating at room temperature, the use of onboard FTIR (Fouriertransform infrared spectroscopy) is not listed in systems already used on Drone. The system will be designed using the methods of the RBDO (ReliabilityBased Design Optimization). The aim is to improve and optimize from the design stage, the measurement and analysis device by choosing the layout of the measurement elements and the analysis algorithms. This paper will give a hent about similar works done and present some primary results.
2 Present Model The use of drones has gradually increased over the past decade and has started to be regarded today as a standard research tool for acquiring images and other ondemand information on a field of interest. In this project the drone will be equipped with an FTIR spectrometer, in the next sections a presentation of MEMS and drone system that are going to be used. 2.1 Infrared Spectroscopy Nowadays, infrared absorption spectroscopy is considered as an analytical method which allows to identify a large number of chemical species in an unambiguous environment because all molecular chemical compounds, possess a vibrationrotation spectrum which their own and which can be analyzed by suitable models. Different types of detectors ranging from DTGS (deuterated triglycine sulfate) or DLaTGS (deuterated Lalanine doped triglycine sulfate) usable at room temperature or MCT (Mercury Cadmium Telluride) [DAH21]. For this project an FTIR spectrometer will be used but in a miniature size to be mounted on a drone, this is the novelty proposed in this project regarding the high capacity of an FTIR engine to analyze a large part of the IR spectra this will give provide the method with a high accuracy, coupled with the use of a miniature spectrometer (MEMS) that will make the method more flexible and economical.in the next section a brief introduction to the MEMS instruments.
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2.2 Principle of the Envisaged IR Spectrometer Solution in the Context of a MEMS MEMS are chipbased electromechanical elements that are developed with techniques inherited from semiconductor micromanufacturing technologies. The electromechanical designs are printed on masks first, these masks are used to model the design on silicon wafers by photolithography, the patterns are then etched using batch process, and finally the chips are diced and packaged. Over the past few decades, MEMS chips have revolutionized several industries to the point that today MEMS chips are found in a multitude of electronic devices. The goal is to integrate all optical and mechanical components integrated into a single MEMS chip, enabling chipwide FTIR functionality [CHA20]. 2.3 Application of Remotely Piloted Aircraft Systems for the Detection of Air Quality Based on Cooperative Multidrone Communication Unmanned Aerial Vehicles (UAVs) are flexible observation platforms designed to cover inaccessible areas on demand. 2.3.1 Architecture for an AirGround Air Quality Detection System The system used in multiple references consists of four layers, namely the detection layer, the transmission layer, the processing layer and the presentation layer. The function of the detection layer is to collect realtime air quality data. It is carried out by detection devices installed near the ground or mounted on a mobile drone [HU19]. The function of the transmission layer is to enable twoway communications between the detection layer and the processing layer. It is supported by the infrastructure of current wireless communication networks. The function of the processing layer is to record the data from the detection layer and submit the results. The complexity of the processing layer depends on the amount of data collected and the protocols of data fusion used this is linked primarily to the number of drones used and in the case of multi drone system to the topology of the drone system [SHA19]. 2.3.2 Multidrone Systems Team members can exchange sensor information, collaborate to track and identify targets, perform detection and surveillance activities, or even act cooperatively in tasks such as hauling loads [FU19]: • Several simultaneous interventions are possible. A single autonomous vehicle is limited at any time to detect or actuate at a single point. • Mission execution time can be reduced when using multiple vehicles simultaneously.
3 Results As said previously to make the design feasible we need to have a multidisciplinary optimization approach from the solidworks conception to the data base through the
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mission profile introduction to this approach will be presented in this section starting with a risk analysis that guided to a certain topology for the drone and then a first step to optimize the mission profile by introducing the speed stability simulation done with scilab and in the end a database. 3.1 Risk Analysis One of the major first tasks to tackle when handling a project is to do the risk analysis this will provide a broader evaluation of the design in terms of its reliability and allows to capture systemlevel risk (Table 1). Table 1. Main absorption areas in IR Description
Severity Occurrence Criticality Prevention 1–4 1–4
Repair
Very low gas concentrations (very restricted pollutant chamber)
3
3
9
Optimize the volume of the pollutant chamber and extend the measurement time as much as possible
Wavelength Modulation Spectroscopy (WMS) or second harmonic detection
The fragile 3 nature of the fibers and the feedback of the laser which reduces the signal to noise ratio
2
6
Isolate the devices from any type of accidental exposure to high temperature
Low loss hollow core waveguides (HCW) for transmission of midIR beams
Angular divergence contributes to noise in the spectra
3
6
The intrferogram obtained will be difficult to interpret and it will create problems of interpretation
Choice of entry and exit aperture for the laser beam to restrict the amount of light passing through
2
(continued)
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Description
Severity Occurrence Criticality Prevention 1–4 1–4
Repair
The presence of 2 water vapor in the medium to be studied
2
4
Get an idea about the amount of water vapor that exists in the medium
Use of the wavelengthmodulated spectroscopy technique to differentiate the spectral characteristics of H2 O by completely eliminating interference
Higher 4 temperatures lower the precision levels of species concentrations
1
4
Monitor the sensor temperature
Continuous cooling of the sensor devices
The accuracy of 2 the measurement
2
4
Repeating the Control the bandwidth scan of the IR in which we will act spectrum
The Fluctuating loads, temperatures, variability in material properties, and uncertainties in analytical models all contribute to making optimum design performance different from that expected. RBDO allows us to take into account the evolution of the safety margin, which leads to finding the best compromise between cost and the required reliability. A reliability analysis can be carried out via simulation methods, coupled with the Kriegeage model to move to an associated reliability analysis in the optimization process, in order to improve the performance and reliability of the structural design of the device sensor and analysis. 3.2 Drone Conception Choosing the quadcopter came after a comparison of different drone types (helicopter, fixed wings, hybrid) For the type of drone most useful for our thesis application, we find that the use of multirotor drone seems the most suitable, we need a hover for the determination of the quality index of the air in one point we will also have more ease of use thanks to the use of multidrone. The solid works software will be used to do the conception of the different parts of the drone and the assembly (Fig. 1).
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Fig. 1. The drone conception
3.2.1 Conception Choices Justification • use of six fins to guarantee the maximum possible propulsion. • Landing device designed with six supports for a safe landing. • the top cover of the drone will serve as a cold plate which guarantees the cooling of the sensor and the electronic board (still in consideration in the final work: additional load problem). • Design made with the aim of keeping the center of gravity of the drone in the same plane as the fins. 3.2.2 Future Ameliorations • Landing device designed with six supports for a safe landing. • the top cover of the drone will serve as a cold plate which guarantees the cooling of the sensor and the electronic board. • Antenna for transmission. • Design made with the aim of keeping the center of gravity of the drone in the same plane as the fins. 3.2.3 Vertical Flight Simulation Consider the vertical flight of a quadcopter drone. Only the ‘z’ dimension is taken into account. The drone is subjected to its weight ‘P’ (we take g = 10) and to the vertical traction of its 4 propellers T’. Its mass is “M” estimated by 5.2 kg from the solidworks mass simulator. It also undergoes a viscous aerodynamic force proportional and in the opposite direction to its vertical speed. F = − Kv ∗ V
(1)
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– Differential equation of vertical motion;
M z¨ + Kv z˙ + M ∗ g = T
(2)
– Linearization around static equilibrium; Around the position of equilibrium, we can say that the action of the fins T tends towards the weight P and can be written in the form; T = P + T = Mg + T
(3)
If we inject this equality into the differential equation of motion, we get an equation with terms that all depends on Z (vertical motion we take only the Oz axis), we can say that the equation is linearized: T = M z¨ + Kv z˙ . Let us now write the transfer function between T and Z which will later allow to design a regulator, it is thus important to write the transfer function in the form: A(P) 1+A(p)∗B(P)
T = M ∗ s2 + Kv ∗ s ∗ Z, we have then; Z=
1 1 ∗ s Ms + K
(4)
We will simulate the evolution of speed in function of the altitude and see the impact of changing our parameters on the stability of the speed, in fact this means the stability of our drone which is primordial to make the measurement. This simulation saves time and we will prevent accidents dealing with the drone going to the field with very close values of P, I and D. We know that V = s * z (Laplace transform Speed of vertical rise) we can therefore deduce that the first order gives the form of V. We can see the existence of a zero pole at the denominator, the stability condition for the system is if and only if its transmission poles all belong to the left halfplane and therefore all strictly negative, we can say that this function transfer rate is unstable. We will therefore try directly with a PID (proportional–integral–derivative), we first went with the values mentioned in drone forums and simulate it using SCILAB (Fig. 2). We notice that the speed does not show any stability criterion if we change the size of the figure before the simulation, we can see that the speed does not find a stability value.
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Fig. 2. The first scilab simulation
There is no such thing as the perfect PID, it’s all about compromise. After a number of tries to limit the choice of the values of P, I and D (taking I = 0 from the start because we have an integrator in the transfer function introduced by the 1/s) (Fig. 3). With its values we notice that the speed finds a certain stability after a short period of time. 3.3 Detection and Analysis of IR Data Data analysis will be one of the key elements of the smart mobile detector. It is based on comparison using numerical optimization methods. The specific characteristics of IR absorptions of chemical bonds will constitute a database allowing the comparison of the measurement data with known data. The following Fig. 4 show the main absorption zones that delimit the detection of IR sensors to be implemented on drones.
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Fig. 3. Simulation with PID
For example, methyl groups have valence vibration bands located around 2962 cm−1 and 2904 cm−1 and strain vibration bands located around 1413 cm−1 followed by a small band at 1440 cm−1 and a significant band at 1258 cm−1 . The kriging technique will be used to optimize analysis time and an artificial intelligencetype approach based on the neural network algorithm will be implemented to identify the different elements present in the medium being probed, again by comparison with data from a database. Under suitable assumptions on the priors, kriging gives the best linear unbiased prediction of the intermediate values. Interpolating methods based on other criteria such as smoothness, the aim is to predict the air quality index in a certain point based on the information taken from similar points that the mission profile of the drone passed through. Thus we will obtain an AQI mapping of the area.
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Wave Length (µm)
% Transmittance
Absorption Bands & Identification of possible structures in IR spectroscopy.
Wave Number (cm1)
Fig. 4. Example of IR absorption bands linked to specific bonds [DAH 18]
Conclusion Despite the promise of UAVs, there are many issues that need to be addressed before full realization of a UAV network. The effective use of UAVs depends on many aspects; The design, implementation and configuration are an important part of any UAV’s. the coming works related to this thesis will focus on these topics. • The optimization of the drone design chosen for the application using ANSYS software. • Make measurement campaigns in a test environment and in the open to compare the results obtained numerically. • Studying the reliability of the infrared detector based on the risk analysis.
References [WHO18] Delivering on Air Quality, Climate Change and Health a World Health Organization, UN Environment, World Meteorological Organization partnership, supported by the Climate and Clean Air Coalition [YAN18] Yang, Y.: Realtime profiling of finegrained air quality index distribution using UAV sensing (2018) [FU19] Fu, Z.: Pollution source localisation based on multiUAV cooperative communication (2019) [SHA19] Shakeri, R., et al.: Design challenges of multiUAV systems in cyberphysical applications: a comprehensive survey, and future directionsREVIEW (2019) [HU19] Hu, Z.: UAV aided aerialground IoT for air quality sensing in smart city: architecture, technologies and implementation (2019) [KON15] Kona, H., Burde, A., Zanwar, D.R.: A review of traveling salesman problem with time window constraint (2015) [HAM20] Hamdani, H.: Métamodèles pour l’étude fiabiliste des systèmes mécatroniquesTHESIS (2020)
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[CHA20] Chai, J., et al.: Review of MEMS based fourier transform spectrometersreview (2020) [LAK17] Lakhlifi, A., Dahoo, P.R., Meis, C., Gale, J.D.: Investigating CH4 thermal activation in clathrate nanocages. J. Phys.: Conf. Ser. 936(1), 012071 (2017). 6th International Conference on Mathematical Modelling in Physical Sciences, 28–31 August 2017, Pafos, Cyprus, 2017 [LAK17a] Lakhlifi, A., Dahoo, P.R., Chassefière, E.: Potential infrared relaxation channels calculated for CO2 clathrate hydrates. J. Quantit. Spectrosc. Radiat. Transf. 187, 124–134 (2017) [DAH21] Dahoo, P.R., Lakhlifi, A.: Infrared Spectroscopy of Symmetric and Spherical Tops for Space Observation. Volume 3  Infared Spectroscopy SET Coordinated, 248 p. ISTE – Wiley (2021). In press [DAH18] Dahoo, P.R., Lakhlifi, A.: Infrared Spectroscopy of Triatomics for Space Observation. Volume 2  Infared Spectroscopy SET Coordinated, 236 p. ISTE – Wiley (2018). ISBN 9781786303936
ElectroThermomechanical Modelling of a BGA Assembly Subjected to a Damaging Displacement and to Random Vibrations Sinda Ghenam1,2(B) , Abdelkhalak Elhami1 , Ali Akrout2 , Wajih Gafsi2 , and Mohamed Haddar2 1 Laboratory of Mechanics of Normandy (LMN), National Institute of Applied Sciences of
Rouen (INSA – Rouen), Rouen, France [email protected], [email protected] 2 Laboratory of Mechanics, Modelling and Production (LA2MP), National School of Engineers of Sfax (ENIS), University of Sfax, Sfax, Tunisia [email protected], [email protected], [email protected]
Abstract. A multiphysic system is the current tendency of the latest upcoming electronic devices of these recent years. In this context, many researchers have focused their work on the mechanisms of failure of these systems in order to study their reliability, their lifetime and the influence of external factors on them and how well they work. In a response to this wave, a numerical modeling using the Multiphysics finite element method of Ansys Workbench is carried out to study the electrothermomechanical modeling of the Ball Grid Array (BGA) mounted on a printed circuit board (PCB) and attached with the solder joints, which are the main subject of this paper, and the effect of the random vibrations on this system. That is to say that following an electrical excitation (an applied current), the system heats up which causes a thermal gradient and stress due to the difference of the thermal expansion coefficients (CTE) which generates unwanted displacements, strains and mechanical stresses as a final result. This coupled field system is also subjected to random vibrations, which causes, because of a gradual and repeated charge over a long period of time, the system to fail due to the phenomenon of fatigue. These obtained results are shown in this paper and discussed in order to avoid the root of this failure mechanisms. Keywords: Electrothermomechanical modeling · Random vibrations · Thermal expansion coefficients · Mechanical stresses
1 Introduction The highspeed development of the mechatronics sector results from the inclusion of electronics into mechanics, which allows manufacturers in this sector to minimize the volume, mass, consumption and cost of onboard systems and hence save on the costs. To meet this set of requirements, the manufacturer has to guarantee a high level of performance and proper operation under increasingly severe operating conditions and © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 353–364, 2022. https://doi.org/10.1007/9783030849580_38
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over increasingly long operating periods. However, a poor risk assessment can produce equipment that may not perform well under the conditions of use, it can increase nonconformities during warranty periods and have a negative impact on the profitability of their industrial activities. Almost all electronic components, are subject to daily stresses that can cause failures. Microsystem failure mechanisms can be divided into two categories: wear mechanisms and overload mechanisms. Many researchers have worked on these phenomenons. We can cite mainly the work of (Hamdani 2019) and (Jannoun 2017). For the wear mechanisms, which imply that the failure action is gradual and repeated over a long period of time to cause the system to fail. This may occur even at lower stress levels. In this context, we cite the work of (Assif 2013) who worked on the drop test. For the overload or stress mechanisms occur in a single event, where the stress exceeds the strength or capacity of the component and causes a system failure. Many researchers have worked on this failure mechanism since it is well known, mainly, the work of (Yaich et al. 2017) and (Halouani et al. 2020a). Among the mechanisms of existing failures such as thermal fatigue, fragile fracture, plastic strain and delamination, another type of failure was chosen: it is the break of the joints of brazing by unpredictable and random vibrations. Random vibration analysis enables to determine the response of structures to vibration loads that are random in nature. For our example, it would be the response of a sensitive electronic component mounted in a car subjected to the vibration from the engine. Loads such as the acceleration caused by this type of vibration are not deterministic. Hence, it is not possible to predict precisely the value of the load at a point in its time history. Such history load, however, can be characterized statistically (mean, root mean square, standard deviation). The frequency content of the time history (spectrum) is captured along with the statistics and used as the load in the random vibration analysis. This spectrum is called Power Spectral density (PSD). Before starting this part, a numerical simulation of harming displacements exercised over the flea in silicon was made with the intention of validating the numerical model of electrothermomechanical coupling.
2 State of the Art and ElectroThermomechanical Modeling 2.1 Software Used: Ansys Workbench ANSYS, Inc. is a software company specializing in digital simulation. ANSYS develops, promotes and supports its simulation software to predict the behavior of a product in its environment. Its major products are software that implements the finite elements method, in order to solve previously dissected models. In numerical analysis, the finite element method (MEF) is used to digitally solve equations with partial derivatives. For example, these can represent analytically the dynamic behavior of certain physical systems (mechanical, thermodynamic, acoustic, etc.). ANSYS Structural: This product allows mechanical simulations to be performed in the calculation of structures. Its main capabilities are: Static analysis/Modal analysis/Harmonical analysis (forced response)/Time analysis/Management of different nonlinear situations (contacts, plasticity materials, large displacements or large deformations).
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2.2 Mathematical Multiphysics Modeling A Multiphysics system is a system that depends on several fields such as mechanics, electricity and thermics. In this paper, we will treat an electronic component called BGA: Ball Grid Array subjected to stresses which will be simulated thanks to the numerical method of the Multiphysics finite elements. As an example, for this paper, I will use the BGA component cited in the article of (Halouani 2020b). The assembly of the BGA component is composed of a Printed Circuit Board composed of two basic layers: the FR4 and the Copper. The component is mounted with a grid of 9 (3 × 3) solder balls. The weld balls are modelled by balls of 2 mm in diameter. The FR4 resin layer is 15 mm × 15 mm × 5 mm, the copper layer has the same dimensions as the FR4 layer except it has 1 mm thick. The component, made with silicon, has a square shape with a stop 13 mm and a height h = 2 mm. Here’s below the geometry of this system (Fig. 1):
Solder material
Fig. 1. Geometry of the BGA assembly
Considering the importance of the impact of the difference between the materials in the electrothermomechanical simulation of the system, it is imperative to focus on the material properties of each part of the assembly. Based on the work of (Halouani 2020c), the table below summarizes, for each material, the isotropic values of the electrical, thermal and mechanical material properties. The assignment of materials to each component of the assembly is done primarily on ANSYS WORKBENCH. The BGA assembly is meshed with tetrahedral finite elements. The mesh size is refined at the level of the solder balls. 2.2.1 Initial Conditions The initial temperature T0 is assumed to be homogeneous in any part of the field. The goal is to solve the electrothermomechanical problem in the field of study . The formulation of this problem is given as follows: ⎧ U = 0V ⎨ T = 22 ◦ C = Tamb ⎩ D = 0 mm
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Copper
Solder
Silicon
λ
0.3
400
55
130
α
18.10−6 17.10−6
2,3.10−5
2,6.10−6
Cp
1369
385
180
700
E
22
110
48
170
ρ
1900
8960
7360
2330
ν
0.28
0.35
0.35
0.28
1,7. 10−8
45. 10−8
4. 103
ρ élec 8. 1011
2.2.2 Boundary Conditions We assume that materials have a linear behaviour. Electrical Field As a simplified hypothesis, it is assumed that the electrical conduction is mainly vertical according to the zaxis. Thermal Field • The selfheating of the BGA assembly chip is neglected • We neglect the phenomenon of convection • It is assumed that the side surfaces are adiabatic
Mechanical Field • It is assumed that there is no relative displacement of any component under any external excitation • It is assumed that the BGA assembly is mechanically isolated from the rest of the motherboard of the overall system in order to be able to focus on only the effect of the electrothermomechanical coupling on such an assembly. To solve the mathematical equations describing the electrothermomechanical coupling, it is necessary to determine the equations connecting the electrical, thermal and mechanical quantities. The multiphysical simulation is based on equations developped by (Makhloufi et al. 2020). These equations are mentioned in details in the next paragraph.
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2.2.3 Mathematical Formulation of ElectroThermal Coupling By applying the principle of virtual work to heat flow equations, we obtain the following matrix: t ˙ t T {Q} + {Qp } C [0] K [0] {T}
(1) = + ˙ {I} Kϑt Kϑ [0] Cϑ {V} V
2.2.4 Mathematical Formulation of ThermoMechanical Coupling By applying the principle of the stresses due to the virtual work and the equation of conservation of the thermal flow coupled with the equations of thermoelasticity, one obtains the following matrix: {˙u} {u} {¨u} {F} [M] [0] [K] Kut [C] [0]
+ tu t + = (2) {Q} C C [0] [0] [0] Kt {T} T˙ T¨
2.2.5 Mathematical Formulation of ElectroThermomechanical Coupling The objective of the weak coupling of the electrothermomechanical modelization is to determine the electric voltage field, the temperature field and finally the displacement. By taking into consideration the previous equations, we obtain the following matrix equation of the electrothermomechanical coupling: ⎫ ⎫ ⎡ ⎤⎧ ⎤⎧ ⎡ [M ] [0] [0] ⎨
{¨u} ⎬ [0] [0] ⎨ {˙u} ⎬ [C] ⎣ [0] [0] [0] ⎦ + ⎣ C tu C t [0] ⎦ T˙ T¨ ⎩ ⎭ ⎩
¨ ⎭ V˙ V [0] [0] C ϑ [0] [0] [0] tu ⎫ ⎧ ⎫ ⎡ ⎤⎧ [K] K [0] ⎨ {u} ⎬ ⎨ {F} ⎬ + ⎣ [0] K t [0] ⎦ {T } = {Q} (3) ϑt ϑ ⎩ ⎭ ⎩ ⎭ {V } {I } K [0] K
2.3 Random Vibrations 2.3.1 Random Process A random vibration, as defined in (Yaich et al. 2017) and (Jannoun et al. 2017) articles, is a motion which is nondeterministic. It means that future behavior cannot be precisely predicted. In a random vibration study, the loadings are statistically described by power spectral density (PSD) functions. The power spectral density units are those of the load squared and divided by frequency as a function of frequency. For example, the units of a power spectral density curve are (psi) 2/Hz versus frequency in Hz. If the process f(t) has units of meters, and the frequency f (the independent variable) has units of Hz then the units of the PSD is m2 /Hz. Alternatively, if the angular frequency ω = 2πf is the independent variable, then the units of the PSD is m2 /(rad/s). So, to
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convert between frequencies f and ω, the value of the PSD needs to be scaled as well: (ω)dω = 2π (f)df. The random response of a structure subjected to random vibrations is represented by a random stochastic process. Let’s suppose that we record a parameter characterizing a physical phenomenon n time. The set of all these functions {f (t)} is called random process. We can calculate for this process the mean value, the variance, the autocorrelation function and the covariance matrix. This stochastic process must be a Gaussian stationary ergodic process that means that its statistical properties are invariable with time and if its overall statistical properties are equal to the temporal properties of any taken sample. 2.3.2 Power Spectral Density The power spectral density can be defined as the Fourier transform of the autocorrelation function of a random process. ∞ f (f ) =
R (τ )e−j2π f τ d τ
(4)
−∞
Let’s suppose that we record a parameter characterizing a physical phenomenon n time. The set of all these functions {f (t)} is called random process. Power spectral density describes how the energy of the random process is distributed in the frequency representation. 2.3.3 The Statistical Properties of the Random Vibration Process As mentioned in the article of (Yaich et al. 2017), the statistical properties of the random vibrations are expressed as follows: • The mean value:
E[f(t1 )] =
• The variance:
+∞ −∞
f(t1 ).p(f(t1 ))df
σf 2 = E f 2 − (E[f])2
(5)
(6)
• The autocorrelation function: Rf (t1 , t1 + τ) = E[(f(t1 )).(f(t1 + τ))T ]
(7)
• The covariance Matrix: f
T (t1 , t1 + τ) = E[(f(t1 ) − f(t1 )). f(t1 + τ) − f(t1 + τ) ]
(8)
It’s called a Gaussian stationary ergodic process if all its statistical properties are invariable with time and if its overall statistical properties are equal to the temporal properties of any taken sample.
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3 Preliminary Numerical Results In this paper, an electrothermomechanical coupling is provided by ANSYS workbench which brings together the electrical, stationary thermal modules and finally the static structure module. This simulation is based on the matrices mentioned before. The first field to study is the electrical field considering that it generates the input of the coupling algorithm. Further to the application of several numerical tensions, they acquired a limit tension beyond of which there is risk of mechanical break. A progressive imposed displacement is then applied to this component. 3.1 Stationary Electrical Conduction Study Given an electrical input of the system and taking into account the resistivity of each material, a digital simulation on the BGA assembly is made. Then, we can obtain the total electric field intensity. Then, the total current density can be derived for an applied voltage equal to 4 V (see Fig. 2).
Fig. 2. Total current density
3.2 Stationary Thermal Study The joules effect produced by the heating of the system following the flow of current in the BGA assembly creates a temperature gradient (see Fig. 3). The intensity of the heat flow is mainly seen in the copper layer and in the FR4 layer. 3.3 Static Structure Study Besides the load imported from the previous module, other inputs for this module have been added such as the fixing of a support which is the underside of the PCB and a small
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Fig. 3. Total heat flow
displacement imposed on the component and which is added as a risk factor which can cause the failure of the BGA assembly. For this fact, one observes displacements, the equivalent stress of Von mises output and the equivalent elastic strain. The results of the shape of the solder joints are presented in Figs. 4, 5 and 6.
Fig. 4. Total displacement: Dmax = 4,826 mm, Dmin = 0 mm
So, following the equivalent stress of Von Mises and the equivalent elastic stain, there is a tendency to break between the brazing joints and the copper sole as results of the movements imposed as inputs to the mechanical module. This coupled system is subjected also to random vibrations which will ultimately generate fatigue.
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Fig. 5. Equivalent elastic strain: εmax = 1.366, εmin = 6,1 e−3
Fig. 6. Von Mises equivalent stress: σmax = 1,64 e5 MPa, σmin = 472,9 MPa
4 Numerical Study of Random Vibration In the random vibration analysis, since the inputs excitations are statistical in nature, so are the output responses such as displacements, stresses and strains. • Modal analysis: Six eigenfrequencies are considered as inputs for the system (see Table 2).
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Modes
1
2
3
4
5
6
Eigenfrequencies (Hz)
31834
71564
82411
685135
91191
1,0064e+005
• Random vibrations The excitation is applied in the form of a power spectral density. This PSD is a table of spectral values vs. frequency. The PSD captures the frequency and mean square amplitude content of the time history of the load. The base excitation could be an acceleration PSD, velocity PSD or displacement PSD (Table3). As inputs we’ve: PSD displacement and PSD acceleration. As outputs, we’ve: normal elastic strain, elastic shear strains and equivalent stress (Figs. 7, 8 and 9). • Inputs: Table 3. Inputs of random vibration module Frequency
1 2 3 4 5 6
PSD acceleration 1 2 4 6 8 10 2
[(mm/s2 ) /Hz]
• Outputs:
Fig. 7. Normal elastic strain: εmax = 7,667 e−8, εmin = 4,14 e−12
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Fig. 8. Equivalent stress: σmax = 0.015 MPa, σmin = 2,225 e−5 MPa
Fig. 9. Total displacement: Dmax = 2,127 e−7 mm, Dmin = 0 mm
5 Conclusion In this paper, we have studied the impact of coupling the three main domains on the behavior of the BGA assembly. As well as the submission of the system to a damaging displacement. Finally, we’ve studied the effect of the random vibration because the random excitation is more damaging than the deterministic excitation. The failure appears at a reduced number of cycles compared to the deterministic excitation. This is why it was imperative to study the response of the system to random vibrations through numerical simulation by ANSYS WORKBENCH.
Appendix: Notations [C t ]: Elementary specific heat matrix, [C ϑ ]: Elementary dielectric permittivity matrix, [K t ]: Thermal conductivity matrix, [K ϑ ]: Elementary electrical conductivity matrix,
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[K ϑt ]: Matrix of elementary Seebeck coefficients, [Q]: Elementary heat density vector, [Qp ]: Peltier effect heat flux vector, [C tu ]: Thermoelastic damping matrix, [K ut ]: Thermoelastic stiffness matrix, E: Strain, σ: Stress, F: heat flux, P: power in Watt, hf : exchange coefficient in W.m−2 m−2 .K −1 , dt/dx: the temperature gradient in K.m−1 , dt: basic time in s,T 0 : initial temperature of the system, λ: thermal conductivity of the material in W.m−1 .K −1 , T: temperature in K, Q: dissipated power in J, ϕ→ : Heat density vector in W.m−2 , K: coefficient of plastic resistance, M: exponent of strain hardening.
References Yaich, A., et al.: Local multiaxial fatigue damage estimation for structures under random vibrations. Finite Elem. Anal. Design 132(15), 1–7 (2017). https://doi.org/10.1016/j.finel.2017.04.003 Halouani, A., et al.: Modeling and experimentation of creepfatigue and failure of lowprofile quad flat package under thermal cycle. J. Mech. Eng. Sci. 234(21), 2020 (2020a). https://doi. org/10.1177/0954406220920680 Halouani, A., Cherouat, A., Miladi Chaabane, M., Haddar, M.: Modeling and experimental investigation of damage initiation and propagation of LQFP package under thermal cycle. Microsyst. Technol. 26(9), 3011–3021 (2020b). https://doi.org/10.1007/s00542020048849 Jannoun, M., et al.: Probabilistic fatigue damage estimation of embedded electronic solder joints under random vibration. Microelectron. Reliabil. 78, 249–257 (2017). https://doi.org/10.1016/ j.microrel.2017.08.005 Makhloufi, A., et al.: Study on the thermomechanical fatigue of electronic power modules for traction applications in electric and hybrid vehicles (IGBT). In: El Hami, A. (ed.) Embedded Mechatronic Systems, vol. 1 (2020) Darveaux, R., et al.: Reliability of plastic ball grid array assembly. In: Lau, J. (ed.) Chapter Ball Grid Array Technology. McGrawHill (1995) Assif, S.: Reliability and optimization of mechanical structures in uncertain parameters: application to electronic cards. Doctoral thesis, INSARouen (2013) Halouani, A.: Multiphysics modeling and simulation for the reliability of electronic components. Doctoral thesis, University of Technology of Troys (2019) Hamdani, H.: Metamodels for the reliability study of mechatronic systems. Doctoral thesis, INSARouen (2019) Jannoun, M.: Reliability of structures in random vibrations  application to embedded mechatronic systems. Doctoral thesis, INSARouen (2018) Bendaou, O.: Thermomechanical characterization, modeling and reliability optimization of electronic packages. Doctoral thesis, INSARouen (2017) Adams, P.J.: Thermal fatigue of solder joints in microelectronic devices. M.S thesis, Department of Mechanical Engineering, MIT, Cambridge (1981) Makhloufi, A., et al.: Probabilistic assessment of thermal fatigue of solder joints in mechatronic packaging. In: Proceedings of the1st International Symposium on Uncertainty Quantification and Stochastic Modeling, Maresias, Brazil (2012) Babahammou, A., Benamar, R.: Geometrically nonlinear free vibrations of simply supported rectangular plates connected to two distributions of rotational springs at two opposite edges. In: Chaari, F., et al. (eds.) Advances in Materials, Mechanics and Manufacturing. LNME, pp. 166–174. Springer, Cham (2020). https://doi.org/10.1007/9783030242473_19
Predicting of Particle ExhaustEmissions from Urban Road Traffic Using Artificial Neural Networks (ANNs) Ines Belkacem1(B) , Ali Helali2(B) , Salah Khardi3 , and Khalifa Slimi4 1 Laboratory of Thermal and Energy Systems Studies (LESTE), National Engineering School,
University of Monastir, Monastir, Tunisia 2 Mechanical Laboratory of Sousse, Higher Institute of Transport and Logistics, University of
Sousse, Sousse, Tunisia 3 Contact and Structure Mechanics Laboratory LaMCoS, Campus LyonTech La Doua  INSA
Lyon 27bis, Avenue Jean Capelle, 69621 Villeurbanne Cedex, France 4 Laboratory of Thermal and Energy Systems Studies (LESTE), Higher Institute of Transport
and Logistics, University of Sousse, Sousse, Tunisia
Abstract. Nanoparticles generated from urban areas have remarkable effect on environment, climate change and human health including cardiovascular and respiratory problems, among others. Compared to the high cost and difficulty of realtime measurements, statistical models are the most recommended alternative to forecast the exhaust particle number concentrations (PNCs) from urban road traffic. The goal of this research is to forecast vehicle exhaust PNCs using two different methods of Artificial Neural Networks (ANNs) namely, MultiLayer Perceptron (MLP) and Generalized Regression Neural Network (GRNN), based on continuous realtime measurements. In fact, these measurements were measured using a native algorithm based on the GRIMM analyzer, series 1.108 Portable Aerosol Spectrometer. Besides, this study tends to compare the two chosen methods (GRNN and MLP) in order to distinguish the most suitable method for estimating vehicle exhaust PNCs. The estimated models efficiency was determined by statistical metrics in testing and training phases. The results revealed that GRNN provided the best performance as compared to MLP model, with coefficient of determination R2 equal to 0.98 and 0.80 respectively. In addition, the results are robust enough for correct and accurate next day forecasting of vehicle exhaust PNCs on French urban areas and ensure a sustainable environment and mobility. Keywords: Generalized regression neural network · Artificial Neural Networks (ANNs) · Multilayer perceptron · Particle number concentrations · Modeling · Environment
1 Introduction Nanoparticles have dangerous effects on ambient air quality (Watson 2002), human health (Belkacem et al. 2021; Tang et al. 2017) and environmental impact (Silva et al. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 365–373, 2022. https://doi.org/10.1007/9783030849580_39
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2021). Nanoparticles recorded a remarkable increase in recent years. Dieselpowered vehicles reveal the major source of road vehicle pollution in the European Union. Urban road traffic areas engender various human activity and pollution that reveals considerable adverse environmental impacts. (Belkacem et al. 2020; Stone et al. 2017). Particles with small size diameter displaying a larger specific surface area and reveal a high disposition fraction in the respiratory system (Giechaskiel et al. 2015). According to Epidemiological analyses a pronounced relationship among pollution, the number of cardiovascular and respiratory tract disease victims and particle number concentrations (PNCs). (Kim et al. 2012). The objective of this research is to predict vehicle exhaust PNCs using two different methods of Artificial Neural Networks (ANNs) namely, MultiLayer Perceptron (MLP) and Generalized Regression Neural Network (GRNN), based on continuous realtime measurements. Exhaust emissions being generated from tailpipes as a result of incomplete fuel combustion inside the engine chamber. This is because, modeling ambient air pollutants and PNCs is a critical research area for mitigating road transport emissions on environment. ANNs were frequently applied for the simulation of the ambient air pollution and environment induced from road traffic. (Saggar et al. 2020; Benedetti et al. 2016; Khayatian et al. 2016) demonstrated great potential for predicting and modeling. However, restricted research has been focused to simulate continuous real time PNCs from road traffic using ANNs. (Antonopoulos et al. 2017; Vakili et al. 2017) and differentiate complex patterns in database without understanding required of the interconnectivity among input and output variables (Lu et al. 2016). ANNs accuracy do not depends only to the quantity of data but also on the quality of data. The number of hidden layers and the architecture are the major factors that influences on the performance of the model. But, it is difficult to make decision of the most appropriated architecture of a particular circumstance. PNCs were recorded in Lyon (France) using Grimm analyzer series 1.108. The locations and instantaneous speed profiles were simultaneously gathered by the global positioning system 747 Pro (GPS). After that, we make the simulation of PNCs from urban road traffic by ANNs, MLP and GRNN. The model efficiency is assessed by applying statistical parameters; mean absolute percentage error (MAPE), coefficient of determination, (R2 ) and Root mean squared error (RMSE). Finally, this study tends to compare the performance among the two chosen ANNs methods. The remainder of this paper is structured as follows; the next section describes the followed methodology for estimating the vehicle exhaust PNCs. Then, Sect. 3 presents the most important results and discussion. Finally, some concluding remarks are presented in the latest section.
2 Experimental Protocol 2.1 Study Area and Data Measurements took place during July 2019 in urban (BronMeyzieu) – France (Fig. 1). Lyon is France’s second largest conurbation and third largest city. The National Institute of Statistics and Economic Studies (INSEE) has predicted the population at 515,695 as of 2016, with location coordinates of 4°50 32 East 45°45 35 North.
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Fig. 1. Field area
2.2 Methodology This study started by obtaining the exhaust emissions of PNCs under continuous real time measurements using the Grimm. At the same time, vehicle speed was measured by the GPS (747 Pro). Grimm outputs were used as target for the two selected ANNs methods (GRNN and MLP). The methodology that was followed to model the continuous vehicle PNCs is summarized in Fig. 2 based on real experimental data.
Fig. 2. Flow chart methodology
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2.3 Artificial Neural Networks (ANNs) ANNs are among the most efficient computational models that practically approximate the same behaviour as human brain. ANNs have been extensively applied for forecasting and predicting in ambient air pollution, due to their accuracy and reliability to estimate any nonlinear function. (Nielsen et al. 2015). MLPs are among the most applied architectures of the feedforward networks employed by researchers (Maier et al. 2010). In this research, the GRNN and MLP were chosen to model and predict PNCs. 2.3.1 General Regression Neural Networks (GRNN) GRNNs based on a standard statistical technique known as kernel regression (Specht 1991). GRNNs comprise of four main layers including; output, summation, pattern and input layers from right to left (Fig. 3).
Fig. 3. Standard architecture of general regression neural network (GRNN)
2.3.2 Multilayer Perceptron (MLP) The input variables produce input signals, then they transferred to the network starting from the left side (Input layer) to the right side of the GRNN architecture (output layer) passing by the pattern layer. The input vector is multiplied by weights vector. This information has been recapitulates by the neuron in the patter layer, which includes bias. (Fig. 4). y0 =
n
wi × xi + b
(1)
i=1
The nonlinearity of model produces when it is proceeding through the transfer or activation function. f (x) =
1 1 + e−x
(2)
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Then y0 = f
n
369
wi × xi + b
(3)
i=1
Where, y0 = output, wi = weight vector, xi = scaled input vector, b = bias, f = transfer function and x = total sum of weighted inputs.
Fig. 4. Standard architecture of multilayer perceptron
2.3.3 Comparison Between GRNN and MLP The two selected techniques considered in this research have their illustrated capabilities and features. The techniques incompatible from each other specifically for the structure of the network and the type of used function. The comparison of GRNN and MLP is shown in Table 1. Table 1. Comparison between GRNN and MLP (Swain and Das 2014) MLP
Number of On the basis of On the basis of Sigmoid, step input variables nonlinearity of complexity of and pure linear the system the problem function
GRNN Number of data points
Number of data Single hidden points layer
Number of neurons in the hidden layer
Normal Spread value distribution and distance function
2.4 Performance Indicators The GRNN and MLP efficiency were concluded based on the statistical performance indexes and the performance indicators. The accuracy of measurement evaluates with
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values varied between 0 and 1. In fact, an efficient model was chosen when the assessed results are nearby to 1 as well as the error rate is close to zero. Performance indicators that were selected are: n 2 i=1 (Target i − Output i 2 (4) R =1− n 2 i=1 Target i
2 1 n RMSE = (5) Target i − Output i i n 1 n (Target i − Output i (6) MAPE = t=1 n Target i
3 Results and Discussion 3.1 ANN Architecture The standard ANNs model architecture is constituted by output layer, one/more hidden layers and input layer (Khoshnevisan et al. 2014). In the present research, two different architectures have been considered (GRNN and MLP). GRNN model was based on two input variables including vehicle speed and vehicle Acceleration/Deceleration maneuvers, one hidden layer, a spread value equal to 0.7 and a single output node (particle number concentration) (2, 0.7, 1) (Fig. 5a). MLP was based on the same output and inputs of GRNN as well as one hidden layer with three neurons (Fig. 5b).
Fig. 5. Architectures of MLP and GRNN
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3.2 Efficiency of the Predicted Models The 70 sets of sampling were divided randomly as follows: 49 (about 70%) for training, 11 (about 15%) for validation and 10 (about 15%) for testing data. The performance of the trained networks was evaluated, using several statistical parameters which are; RMSE, R2 , and MAPE. These parameters and coefficients are estimated using MATLAB® package (Table 2). Table 2. The performances of each model. Models RMSE (p/cm3 ) R2
MAPE (%)
MLP
4.8 104
0.80 20.4
GRNN
3.9 103
0.98
1.08
The measured and predicted PNCs by GRNN and MLP models are shown in Fig. 6. Comparison results demonstrated that MLP model gives lower accuracy than GRNN model as found by (e.g. Abdullah et al. 2019; Chen et al. 2018). This can also be clearly observed. 5
x 10 4
Measured vs. Predicted PNCs
Measured PNCs (p/cm3)
MLP 3
2
1
0 5
x0 10
5
Measured PNCs (p/cm3)
4
10 Predicted PNCs(p/cm3)
15 4
x 10
Measured vs. Predicted
GRNN 3
2
1
0 0
0.5
1
1.5 2 2.5 Predicted PNCs (p/cm3)
3
3.5
Fig. 6. Comparison between MLP and GRNN models
4 5
x 10
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Testing and training results revealed that ANN techniques performed superior to the regression models. The GRNN method was created to have the finest method for forecasting particle number exhaust emissions in urban road traffic. This result is coherent with other pertinent literature. Comparison results of GRNN with several other ANNs models showed that GRNN model furnish accurate and efficient results (Antanasijevi´c et al. 2015). MLPs are among the best ANNs, which appears a noticeable performance, since the selected model could be specified by iterant settings calibration after adaptation in the model (Safari et al. 2016). The issue of overtraining frequently reliability, because a wide number of biases and weights is induced from many iterations. However, GRNN model is a one pass learning network and does not required a repetitive strategy like MLP models. Indeed, GRNN is able to solve overfitting issue to a wide margin. In conclusion, the GRNN model can be preferred over the MLP model for estimating PNCs induced from urban road exhaust emissions.
4 Conclusion In this research, ANNs (MLP and GRNN) are applied to predict PNCs from French urban road traffic based on real time measurements. The performance of observation models was evaluated and compared by statistical indexes of RMSE, MAPE and R2 . The performance of the GRNN model is strongly better than MLPs. The analysis of GRNN and MLP models justified that vehicle speed and vehicle Acceleration/Deceleration maneuvers have an important effect on PNCs. Furthermore, results proved that GRNNs characterized by significant potential to predict PNC of exhaust emissions from urban road traffic. This is because the statistical models need more attention, since they are powerful tools to evaluate the particle exhaust emissions engendered from urban road traffic giving new insights into consideration of vehicle technologies’ conception and ensure a sustainable mobility and environment. In addition, with this prediction, authorities can inform communities of hazardous levels of PNCs, then they can limit their exposure inlow air quality and to mitigate outdoor activities.
References Abdullah, S., Ismail, M., Ahmed, A.N., Abdullah, A.M.: Forecasting particulate matter concentration using linear and nonlinear approaches for air quality decision support. Atmosphere 10(11), 667 (2019) Antonopoulos, V.Z., Antonopoulos, A.V.: Daily reference evapotranspiration estimates by artificial neural networks technique and empirical equations using limited input climate variables. Comput. Electron. Agric 132, 86–96 (2017) Antanasijevi´c, D., Pocajt, V., Risti´c, M., Peri´cGruji´c, A.: Modeling of energy consumption and related GHG (greenhouse gas) intensity and emissions in Europe using general regression neural networks. Energy 84, 816–824 (2015) Benedetti, M., Cesarotti, V., Introna, V., Serranti, J.: Energy consumption control automation using artificial neural networks and adaptive algorithms: proposal of a new methodology and case study. J. Appl. Energy 165, 60–71 (2016) Belkacem, I., Khardi, S., Helali, A., Slimi, K., Serindat, S.: The influence of urban road 722 traffic on nanoparticles: Roadside measurements. Atmos. Environ 242, 117786 (2020)
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Belkacem, I., Helali, A., Khardi, S., Chrouda, A., Slimi, K.: Road traffic nanoparticles characteristics: sustainable environment and mobility. Geosci. Front. (2021). https://doi.org/10.1016/j. gsf.2021.101196 Chen, Z., Ye, X., Huang, P.: Estimating carbon dioxide (CO2) emissions from reservoirs using artificial neural networks. Water 10(1), 26 (2018) Giechaskiel, B., Riccobono, F., Vlachos, T., et al.: Vehicle emission factors of solid nanoparticles in 448 the laboratory and on the road using portable emission measurement systems (PEMS). 447449 Front. Environ. Sci. 3, 82 (2015) Kim, S.Y., Peel, J.L., Hannigan, M.P., et al.: The temporal lag structure of shortterm associations of fine particulate matter chemical constituents and cardiovascular and respiratory hospitalizations. Environ. Health Perspect. 120, 1094–1099 (2012) Khayatian, F., Sarto, L., Dall’O’, G.: Application of neural networks for evaluating energy performance certificates of residential buildings. J. Energy Build 125, 45–54 (2016) Khoshnevisan, B., Rafiee, S., et al.: Prediction of potato yield based on energy inputs using multilayer adaptive neurofuzzy inference system. Measurement 47, 521–530 (2014) Lu, F., Chen, Z., Liu, W.Q., Shao, H.B.: Modeling chlorophylla concentrations using an artificial neural network for precisely ecorestoring lake basin. Ecol. Eng. 95, 422–429 (2016) Maier, H.R., Jain, A., Dandy, G.C., Sudheer, K.P.: Methods used for the development of neural networks for the prediction of water resource variables in river systems: current status and future directions. Environ. Model. Softw. 25, 891–909 (2010) Nielsen, M.A.: Neural Networks and Deep Learning. Determination Press, USA (2015). http:// neuralnetworksanddeeplearning.com/. Accessed 29 Dec 2017 Tang, G., Zhao, P., Wang, Y., et al.: Mortality and air pollution in Beijing: the longterm relationship. Atmos. Environ. 150, 238–243 (2017) Vakili, M., SabbaghYazdi, S.R., Khosrojerdi, S., Kalhor, K.: Evaluating the effect of particulate matter pollution on estimation of daily global solar radiation using artificial neural network modeling based on meteorological data. J. Clean. Prod 141, 1275–1285 (2017) Saggar, M., Nasr, A., Bouraoui, C.: Initiation life prediction method for defective materials. In: Chaari, F., et al. (eds.) Advances in Materials, Mechanics and Manufacturing. LNME, pp. 17–25. Springer, Cham (2020). https://doi.org/10.1007/9783030242473_3 Safari, M.J.S., Aksoy, H., Mohammadi, M.: Artificial neural network and regression models for flow velocity at sediment incipient deposition. J. Hydrol. 541, 1420–1429 (2016) Silva, L.F., Pinto, D., Neckel, A., Oliveira, M.L.: An analysis of vehicular exhaust derived nanoparticles and historical Belgium fortress building interfaces. Geosci. Front 11(6), 2053–2060 (2021) Stone, V., Miller, M.R., Clift, M.J.D., et al.: Nanomaterials versus ambient ultrafine particles: an opportunity to exchange toxicology knowledge. Environ. Health Perspect. 125(10), 106002 (2017) Swain, A., Das, M.K.: Artificial intelligence approach for the prediction of heat transfer coefficient in boiling over tube bundles. Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 228(10), 1680– 1688 (2014)
Thermohydraulic Study of an Air/R22 Tubular Evaporator: Application of the Superposition Model Lazhar Ayed1,2(B) 1 Laboratory of Applied Fluids Mechanics, Process and Environment Engineering, National
School of Engineers of Sfax, University of Sfax, Sfax, Tunisia [email protected] 2 National School of Engineers of Gafsa, University of Gafsa, Gafsa, Tunisia
Abstract. In order to dimension and evaluate the performance of the heat exchanger (airrefrigerant R22), this work presents a simulation and calculation method to study the influence of different external parameters such as temperature and speed of air and the flow configuration. The heat exchanger used is a countercurrent horizontal tubular evaporator, allowing the refrigerant R22 to evaporate internally by a hot fluid which is air. For hydraulic calculation, we choose the MullerSteinhoger and Heck method. For thermal computation, we use correlations from the literature. For the calculation of internal coefficient of convection, the superposition model “Gunger and Winterton method” is used. Based on the sizing method of the heat exchanger and after having predicted the convective exchange coefficients, a thermal study has been performed. Numerically obtained results of the thermohydraulic analysis were presented and compared with those predicted by Comsolmultiphysics software model. These results show a good agreement in the global exchange coefficient. The calculation of the evaporator is carried out by considering a saturated state of the refrigerant. This imposed a large dependence of the overall heat exchange coefficient of the internal convective exchange coefficient and a small variation with the inlet temperature of the hot fluid. Keywords: Heat exchanger · Numerical modeling · Flow configuration · Evaporator · Convection coefficient
1 Introduction The heat exchange between two fluids at different temperatures and separated by a solid wall occurs in many industrial applications (Mihailovi´c et al. 2019). The device used to carry out this exchange is called heat exchanger, it is very frequently found in chemical processes, it is also used in air conditioning systems, in special machines and in the energy production plant, etc. This device is also intended for extremely diverse uses despite the same basic general function, which is the transfer of heat from the hot fluid to the cold one. This diversity of © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 374–387, 2022. https://doi.org/10.1007/9783030849580_40
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applications has led to a proliferation of geometric shapes of exchangers (tubular, plate, finned, etc.) (McQuiston 1978). The different configurations for liquid/vapor flow in a uniformly heated horizontal tube depend on the flow rate of the fluid entering the tube. They are represented in Fig. 1. We observe configurations relatively close to those of the vertical tubes. However, in nucleated boiling, bubbles emitted around the entire periphery of the tube rise to the top of the tube by the action of gravity and come together to form pockets of vapour separated by plugs of liquid. As the thermodynamic titer (vapourfraction) in the twophase liquidvapour mixture increases, an asymmetric annular flow appears with a thin liquid film at the top and thicker one at the base of the tube. The film of liquid in the upper part is the first to disappear, giving way to a stratified flow often with the presence of droplets within the core of the flow (Monisha 2009; Delhaye 1990). Often, heat exchangers are found in industries in the form of interstage coolers, evaporators, etc. where air at high pressure is used for heat transfer from one fluid to another (Delhaye 1990). The thermalhydraulic study of the flow as well as the performance of the evaporator by studying the influence of the various external parameters is the object of this work. The goal is to simulate the behavior of a fluid in the process of evaporation, from its liquid state at the inlet of the tube to its vapourstate in the outlet. For this purpose, a model is designed and introduced in a MATLAB calculation program and in COMSOL Multiphysics software package. COMSOL has the ability to solve multiple non linear PDE’s simultaneously and the models can be generated and solved in one, two or even three dimensions (Shubhneet 2010).
2 Algorithm of the Calculation The flow chart presented in Fig. 2 rigorously shows the stages of calculation of the evaporator. The hydraulic and thermal calculations taking place are based mainly on the thermalhydraulic regimes which occur during the phase change of the refrigerant circulating in the inner tube (Fig. 1).
3 Mathematical Modeling 3.1 Conservation Equations by Phase The mathematical modelling of a tubular heat exchanger with phase change requires hydraulic and thermal studies. These two studies can be effective only after having understood phenomenologically what occurs inside the tube carrying the flow of the fluid seat of the phase change. According to Delhaye et al. (1990), the various balances can be put in the following general form (Lemonnier 2006) (Table 1): ∂(ρK ψK ) − → + ∇ ρK ψK ϑK + ∇.JK − ρK ϕK dV + ∂t K=1, 2V (t) K (1) . mK ψK + JK − n→ K +ϕi = 0 Ai (t) K=1,2
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Fig. 1. Different flow patterns during evaporation (Delhaye 1990)
Fig. 2. Flow chart of the modeling steps
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Table 1. Definition of the variables for the generalized twophase balance equations according to Delhaye et al. (Delhaye 1990). Balance
1
Momentum equation
vk
k
r
vk
Total energy
uk
1 2 vk 2
k
.R
qk
k
r
.vk
Fk
F k . vk
qk Tk
sk
i
Fk
k
Angular momentum equation
Entropy
Jk
k
Mass
k
i
k
3.2 Relations Used for Thermal and Hydraulic Calculation 3.2.1 Thermal Calculation The number of transfer unit method/Efficiency method is used for the calculation. This method is based on data from the inlet temperatures of the two fluids and the flow rates, the purpose of which is to determine the outlet temperatures of the fluids. – Calculation of the heat transfer coefficient on the refrigerant side hint The convection coefficient of the internal fluid calculated by the superposition method is given by the formula of Gunger and Winterton (Chen 1999; MullerSteinhagen and Heck 1986; Lallemand 1998; Yannick 1999). The internal exchange coefficient is a contribution of two coefficients: that of nucleated boiling and that of convective boiling of the liquid phase. hint = S2 hen + F2 h
(2)
hen : The nucleate boiling exchange coefficient. It is given by Cooper’s formula hCooper = 55Prb (−LogPr )−0.55 M −0.5 q0.67
(3)
where Pr , M and q are respectively the reduced pressure, the molar mass and the heat flux density. Pr =
Psat Pcrit
b = 0.12 − 0.2Log(RP )
(4) (5)
h : The exchange coefficient of the liquid phase. For turbulent flow, the most suitable correlation is that of Dittus and Boelter (Delhaye 1990): 0.4 NU = 0.023Re0.8 Pr
(6)
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Pr =
where, Re =
μ Cp λ
(7)
D(1 − x)G μ
(8) •
•
Where G is the mass velocity of the liquid, G = m A with ml is the mass flow of liquid and A is the free passage section for the liquid. The suppression factor S2 and the correction factor F2 are calculated respectively by: S2 = S1 S
(9)
F2 = F1 F
(10) (0.1−2Fr )
0.5 where, S1 = Fr and F1 = Fr
Fr is the Froude number of the liquid phase such that: Fr =
(11) G gdi ρ2
−1 S = 1 + 1.15 × 10−8 Re1.17 1 0.86 F = 1 + 24000Bo1.16 + 1.37 χ tt
(12) (13)
where Bo and χtt the boiling number and the Martinelli parameter given respectively by: Bo =
q hv G
where hv is latent heat of vaporization 1 − x 0.9 ρv 0.5 μ χtt = x ρ μv
(14)
(15)
In correlation (6), the physical properties are evaluated at the socalled film temperature (T + TP ) 2, where TP is the wall temperature. • Calculation of the heat transfer coefficient on the hot fluid side hint The air convection coefficient is given by the following correlation: hext =
Nuair λair de
(16)
Nu air is calculated in studied case by the Schmidt correlation (Schmidt 1945) Nuair = 0.23Re0.625 Pr0.33
(17)
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• Calculation of the global heat exchange coefficient U The overall heat transfer coefficient is the ability of a series of resistive materials or boundaries to transfer heat (Chen 1966; Kunta and Kiatsiriroat 2002; Apreaa and Grecob 2003). U =
1 Sint hext Sext
+
Sint de 2π λL Ln di
+
1 hint
(18)
3.2.2 Hydraulic Calculation In this part of the work, the expressions for calculating pressure losses in the inner and outer tube are formulated with reference to the literature. The calculation of the pressure drops in a tube becomes complicated when the fluid undergoes a change of physical state “in the case of boiling in the tubes of the evaporator”. The pressure drop (pressure losses), in a straight tube for a twophase flow, is the sum of three terms which are: static losses (Ps ), losses due to friction on the walls Pf and dynamic losses (Pa ). If there are losses due to elbows or bends, they should be added to the dynamic losses (Moreno Quiben 2005). Pint = Pf + Ps + Pa
(19)
The losses due to the static pressure are calculated by the following relation (Lallemand 1998): Ps = g(ερV + (1 − ε)ρ ) sin θ
(20)
where g: Gravity acceleration. ρ l : The density of the liquid phase. ρ v : The vapor phase density. ε: Vacuum rate given by the following relation (Moreno Quiben 2005)
−1 x 1.18(1 − x)(gσ (ρ − ρV ))0.25 x 1−x + ε= + 1 + 0.12(1 − x) ρV ρV ρ G 2 ρ0.5 (21) x: Steam title G: Mass velocity (Kg/m2 s)
Tsat 11/ 9 σ : Surface tension (N /m). It is given by: σ = σ0 1 − T0
(22)
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where σ0 = 61.23 × 10−3 *The value of Ps is generally zero (for a horizontal tube). *The losses due to the acceleration Pa are calculated from the following relation (Yannick 1999):
x2 (1 − x)2 2 + Pa = G (23) ρV ε ρ (1 − ε) To calculate the pressure losses due to the friction, one can consider the phaseseparated model; the MullerSteinhoger and Heck method is used: Pf = F(1 − x)1/ 3 + P V x3
(24)
F = P + 2(PV − P )x
(25)
where:
P = 2f
G2 di ρ
(26)
PV = 2fV
G2 di ρV
(27)
f = fV =
0.079 R0.25 e 0.079 R0.25 eV
(28) (29)
where, P and PV are the pressure drops due to the friction of the two phases: liquid and vapor. f and fV are the pressure losses coefficients due to the friction of the two phases: liquid and vapor. Re and ReV are Reynolds numbers of the two phases: liquid and vapour, x is the vapor titer (thermodynamictiter) and F is the sum of the pressure drops. This method proposed a correlation of the pressure losses due to the friction in two phases which is an empirical interpolation between the liquid flow rate and the vapor flow rate. This is the easiest and fastest method to use. 3.2.2.2 Pressure drops on the external fluid side The pressure drop in the external tube is given by the Darcy formula (Moreno Quiben 2005). Pe =
4fVE2 DH 2gL
(30)
where DH is the hydraulic diameter; VE is the average speed of external fluid and f is the friction coefficient.
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4 Numerical Results and Discussion 4.1 Studied System The studied heat exchanger characteristics are given in Table 2. The evaporator is a tube in tube heat exchanger of 10 m length. The inside diameters of inner tube and outer one are respectively D1 = 2.4 mm and D2 = 5 mm. The refrigerant flow (R22) enters from the origin section of abscissaaxis (z = 0) and the hot fluid is entering from the other side of the device (z = L). Table 2. Heat exchanger characteristics Name Value
Description
R1
0.0012 m
Inner radius
R2
0.0025 m
Outer radius
L
10 m
Length
Ds
0.001 m
Thin interface thickness
Dext
0.001 m
Outer tube thickness
T1
283.15 K
Inner inlet temperature
T2
353.15 K
Outer inlet temperature
mfr1
0.01426 kg/s
Inner mass flow rate
mfr2
1.7475E− 4 kg/s Outer mass flow rate
pA1
4E5 Pa
Inner outlet absolute pressure
pA2
1E5 Pa
Outer outlet absolute pressure
Rtol
0.001
Solver relative tolerance
4.2 Internal and External Convective Exchange Coefficients  Global Exchange Coefficients A calculation program developed by the Matlab programming language made it possible to plot the variations of the convective exchange coefficients on the inner tube side (R22) and on the outer tube side (air) as well as the overall exchange coefficient as a function of the absolute inlet temperature of the hot fluid. The numerical simulation in Fig. 2 and Fig. 3 show the effect of the temperature of the hot fluid (the air circulating in the outer tube) on the external and internal convective heat exchange coefficient. Based on the superposition model, for the calculation of the convective heat exchange coefficient on the inner tube side, it can be seen that this temperature has no effect on this coefficient. Figure 4 show that the overall heat transfer through the separating wall of the two fluids is slightly amplified following the increase in the temperature of the hot fluid.
382
L. Ayed 595
479
590 478.5
hint (W/m K)
580
478
2
2
hext (W/m K)
585
575
477.5
570 477
565 560 300
320
340
360
380
400
T abs (K)
476.5 300
320
340
360
380
400
Tabs (K)
Fig. 3. External hext and internal hint convective heat exchange as a function of the outside temperature 477.9335
477.9325
2
U (W/m K)
477.933
477.932
477.9315
477.931 300
320
340
360
380
400
Tabs (K)
Fig. 4. Global heat exchange coefficient as a function of the outside temperature
4.3 Heat Exchanger Effectiveness and Pressure Losses Calculated Based on Superposition Model Figure 5 shows that the efficiency of the evaporator is independent of the inlet temperature of the hot fluid (air) and is E = 0.535. It can be noted that the pressure losses decrease with the hot fluid velocity (air). The efficiency of the heat exchanger calculated on the basis of the stacking model (E = 0.538) compared to that obtained by Comsol Multiphysics (E = 0.587), shows a difference of 0.049. This result shows the importance of the superposition model for the study of an evaporator in steady state conditions.
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Fig. 5. Heat exchanger effectiveness and pressure losses
4.4 Hot Fluid and Refrigerant Temperature Evolutions in Terms of the Longitudinal Abscissa Twophase flows modeling in pipes are of great interest to study the thermohydraulic behavior of heat transfer fluids in exchangers with phase change. This modeling cannot be applied in an absolute way to all configurations and it needs to be completed by closure equations, generally empirical. Based on Comsol  multiphysics the temperature profiles of hot fluid (external tube) and the Refrigerant (internal tube) are plotted.
Fig. 6. Temperature profile of R22 as a function of axial coordinate
Figure 7 shows the evolution of the temperature of the hot fluid (air) as function of the abscissa (z). The downstream section of abscissa z = 10 m corresponds to the outlet of the refrigerant at a pressure of 4 bar (Fig. 8) and a temperature of 283.85 K (superheated vapor state). At the same section, the air at a pressure P = 1.16 bar (Fig. 9) enters countercurrently. At the upstream section of abscissa z = 0 m, the refrigerant at the pressure P = 7 bar (Fig. 8) and at the temperature T = 283.15 K (Fig. 6) (saturated liquid state) enters and the air leaves at a temperature T = 283.8 K and a pressure of 1 bar.
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L. Ayed
Fig. 7. Temperature profile of air as a function of axial coordinate
These results show a high value of pressure drop on the refrigerant side and a low pressure drop on the air side. This observation is explained by the fact that the model of the separated phases, used for the calculation of the pressure drop on the refrigerant side, incorporates the viscous friction losses due to the presence of the liquid and vapor phases. Additionally, this high pressure drop is enhanced by the dominance of the liquid phase at the inlet of the heat exchanger and the decrease in its presence rate during the change of physical state. The latter is explained by the fact that the flow is 100% gaseous only for the extreme portion of the inner tube of length approximately equal to 1 m. Hence, the pressure drop value in the refrigerant side is greater than that of the hot fluid circulating in the outer tube. The slight fluctuation in the temperature of the liquid vapor mixture in the evaporator is due to high pressure drops between the upstream and the downstream side of the inner tube (Fig. 8). Figure 4 shows that the global heat transfer coefficient increases with the increase of air temperature. At the same steam pressure and same flow rates, U(z = 10) is larger than U(z = 0 m) and the reason for this is that a higher amount of heat is transferred in the downstream part of the tube as that is where a phase change is taking place and since latent heat of R22 is very large,
Fig. 8. Refrigerent (R22) pressure profile of as a function of axial coordinate
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Fig. 9. Air pressure profile as a function of axial coordinate
Fig. 10. R22axial velocity profile as a function of axial coordinate
The axial velocity of the refrigerant, as shown in Fig. 10, fluctuates slightly at the inlet of the inner tube (0 < z < 2 m), becomes practically constant in the zone of statechange since the pressure is practically constant which is not justified by the hydraulics model of Comsol Multiphysics. At the downstream part (8 < z < 10) and when the fluid is in the superheated vapor state, it still resumes fluctuations but with a higher amplitude.
Fig. 11. Air axial velocity profile as a function of axial coordinate
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Figure 11 shows the profile of the axial component of air velocity that varies along z coordinate. This is due mainly to the variation of the density of the fluid whose thermophysical properties (density, viscosity, expansion coefficient, etc.) are modelled by polynomial functions of the temperature.
5 Conclusion Difficulties are encountered in choosing the correlations of convective heat exchange coefficient and pressure losses as well as the model chosen for the calculation taking into account the flow configurations for the purpose of data analysis. Indeed, the complexity of heat transfer phenomenon arises mainly for twophase flow i.e. between the two liquid and vapour phases and between the flow and the wall. The performance study of the evaporator is the improvement of the overall heat transfer coefficient. The simulation results show that the temperature of hot fluid is of great importance because it influences the phenomenon of convective transport through its effect on the thermophysical properties of the fluid. In the present study, physically realistic boundary conditions of fluid to fluid heat transfer were used. The difference obtained based on the efficiency of the heat is due to the difference of the empirical correlations shown in the Comsolmultiphysics software and those used when applying the superposition model, as well as in the calculation of the thermophysical properties of hot fluid (air). Nevertheless the deviation remains acceptable and it can show that the superposition model can be adopted for the calculation of the evaporators. Finally this work can be extended by an experimental study to be further validated.
References Mihailovi´c, M., Milovanˇcevi´c, U., Geni´c, S., Ja´cimovi´c, B., Otovi´c, M., Kolendi´c, P.: Air side heat transfer coefficient in plate finned tube heat Exchangers. J. Exp. Heat Transf. 33(4), 388–399 (2019). https://doi.org/10.1080/08916152.2019.1656298 McQuiston, F.C.: Correlation of heat, mass and momentum transport coefficients for plate–fin–tube heat transfer surfaces with staggered tubes. ASHRAE Trans. 84, 294–309 (1978) Monisha, M.M.: Nigam experimental study on pressure drop and heat transfer of turbulent flow in tube in tube helical heat exchanger. Ind. Eng. Chem. Res. 48(20) (2009). https://doi.org/10. 1021/ie9002393 Delhaye, J.M.: Transferts de chaleur: ébullition ou condensation des corps purs. Techniques de l’ingenieur, 1560–1583 (1990) Shubhneet, K.S.: COMSOL Assisted Modeling of a Climbing Film Evaporator, A Major Qualifying Project Report (2010) Lemonnier, H.: une introduction aux écoulements diphasiques, Version du 20 décembre (2006) Chen, J.C.: A correlation for boiling heat transfer to saturated fluids in convective flow Ind. Eng. Chem. 5, 322–329 (1966) MullerSteinhagen, H., Heck, K.: A simple friction pressure drop correlation for twophase flow in pipes. Proc. Chem. Eng. 20, 297–308 (1986) Lallemand, M.: Transferts en changement de phases, Ebullition convective, technique de l’ingénieur, traite Génie énergétique, volume BE 8236 (1998)
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Yannick, M.: Transfert de chaleur dans un mélange constitué de fluide frigorigène et d’huile, thèse 13 Octobre 1999 Schmidt (Thesis) la production calorifique des surfaces munies d’ailettes annexe G5 (1945–1946) Kunta, U., Kiatsiriroat, K.: Boiling heat transfer coefficient of R22 refrigerant and its alternatives in horizontal tube: small refrigerator scale (2002) Apreaa, C., Grecob, A., Vanolic, G.P.: Condensation heat transfer coefficients for R22 and R407C in gravity driven flow regime within a smooth horizontal tube. Int. J. Refrig. 26, 393–401 (2003) Moreno Quiben, J.: Experimental and analytical study of towphase pressure drops during evaporation in horizontal tubes, these 2005
Aluminum Alloy Chips Regeneration by Sintering Ameny Ketata1(B) , Awatef Guidara2 , Anas Bouguecha1 , Jamel Bouaziz2 , and Mohamed Haddar1 1 Laboratory of Mechanics, Modeling and Manufacturing (LA2MP), National School of
Engineers of Sfax, Sfax, Tunisia [email protected], [email protected] 2 Laboratory of Advanced Materials, National School of Engineering of Sfax, Sfax, Tunisia
Abstract. The foundry process was aluminum reuse path to which we are accustomed. However, the contemporary idea consists on aluminum chips valorization to obtain finished parts with significant height change. Therefore, the approach of metal waste regeneration is based on direct use of machining chips into consolidated pellets by sintering. This paper assessed the influence of the grain size on the sintering of compacted EN AW 5083 aluminum alloy chips. In particular, it investigates the structural and mechanical properties of sintered samples that are not only depending on particle size distribution but also on implementation’ conditions such as the compacting pressure and the thermal treatment. Indeed, in order to highlight the compacting machine kinematics influence, the behavior of compacted pellets at two different pressures will be compared. Added to that, from pellets’ mechanical response, a characterization model is deduced to predict mechanical behavior for other subsequent uses more complex. This model is named Dracker–Prager Cap which is one of the families of plasticity models. It describes the aluminum shaving’s behavior in which the yield behavior depends on the equivalent pressure stress. Thus, this material modeling is applied in the numerical simulation based on the finite element calculation (FE) which allows a significant role in describing the compacting as well as sintering processes. Keywords: Chips · Compacting · Sintering · Aluminum · Recycling · Mechanical properties · Simulation · Modeling
1 Introduction Sintering is recently attracting a distinguish attention for the waste aluminum regeneration. This thermal treatment leads to the consolidation of compacted powdery agglomerate grains. The obtained sintered product can be used for many purposes according to its mechanical properties. The later depend on various parameters related to the compacting and sintering processes as well as the material grain size (Khadraoui 2017). The realization of this process requires going through many stages: the aluminum chips collection, the pellet manufacturing and the sintering (Fig. 1) (Bhouri and Mzali 2017). © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 M. Ben Amar et al. (Eds.): A3M 2021, LNME, pp. 388–395, 2022. https://doi.org/10.1007/9783030849580_41
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Fig. 1. The manufacturing and sintering aluminum chip pellets’ operations
The present work deals with the regeneration of EN AW 5083 aluminum machining chips via compacting and sintering processes. Given the diversity of parameters, we had concerns relating to breaking strength and durability. Thus, mechanical tests, in particular diametral and uniaxial compression tests were performed on pellets shaped from chips with different grain size and pressed under 100 and 150 MPa. The produced samples are in two forms: the pellets of 20 mm diameter and 4 mm thickness are intended for the diametrical compression. While, the cylindrical ones with a diameter of 10 mm and a length of approximately 15 mm are assigned to the uniaxial compression. In these tests, the load was slowly increased with a constant displacement velocity on the upper tool until the pellet broke. During loading, the displacement and the applied load were registered. The experiments were permitted thanks to the universal machine available in the laboratory shown in Fig. 2. The Young modulus of samples was determined from the elastic zone of the conventional curve which was deduced from the diametral test values. While, the breaking strength is equal to the maximum stress encountered in the plastic zone. In order to verify the performance of the chip pellets following the sintering process, material modeling was carried out. This method provides analytical tools to predict the actual mechanical behavior of a product by virtually testing.
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Fig 2. The “LLyod» universal testing machine available at the ENIS
2 Material Modeling To obtain the descriptive compressive behavior of aluminum shavings at distinct grain sizes, the Drucker Prager model is the means of numerical study, which describe the properties of porous materials for finite element simulation (Fig. 3).
Fig. 3. An illustration of Drucker  Prager Cap model (Krok et al. 2014)
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The elasticity surface is composed of an elliptical hardening cap and a straight line of failure between the hydrostatic pressure and the V. Mises equivalent stress. The evocative equations of these two quantities are quoted above (Jurgen 2014). Fk = p − pa
2
+ R2q
1/2
− R(d + pa tan β) = 0
Fv = q − p tan β − d = 0
(1) (2)
Whereabout: R represents the eccentricity of the elliptical cap, and Pa the pressure value giving the merging point between the failure line and the hardening cap. Shear Lines of the DPC Model In this work, the linear shear line is experimentally determined with diametral and uniaxial compression tests (Fig. 4) carried out on specimens with different grain sizes. The diametral compression test involves applying a force only on two points which are diametrically opposed where the object is split in half. This test indirectly measures the tensile property of a material as long as the material’ particles are pushed apart in opposite direction (Procopie et al. 2003). As for the uniaxial compression test, it frequently produces larger deformations without sample’s breaking. It determines the resistance of a sample when it is crushed in one direction during a triaxial test without any lateral stress (Hassan et al. 2012).
Fig. 4. The compression tests
Therefore, from the obtained tensile strength, the equivalent Von Mises stress and the hydrostatic pressure were determined using the mathematical formulas (Keirnan et al. 2013). Table 2 summarizes the chips grain size values and the calculated equivalent Von Mises stress along with hydrostatic pressure (Table 1). At least three specimens were tested for each test condition. An average of the values was then calculated. The diametral compression test contributes to the tracing of the shear lines given in Fig. 5. The inelastic deformation may sometimes be associated with frictional mechanisms such as sliding of particles across each other or the entanglement of aluminum shaving which increases with increasing length.
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Test
Diametrical compression
Strain (σ )
2F πde
√
Von Mises stress (q) Hydrostatic pressure (p)
Uniaxial compression 4F π d2
σ
13σ
2/3σ
1/3σ
Table 2. Shear lines’ descriptive values of DPC model Diametrical compression
Uniaxial compression
Grain size
p
q
p