Mechatronics: Ideas, Challenges, Solutions and Applications [1 ed.] 978-3-319-26885-9, 978-3-319-26886-6

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Advances in Intelligent Systems and Computing 414

Jan Awrejcewicz Krzysztof J. Kaliński Roman Szewczyk Małgorzata Kaliczyńska Editors

Mechatronics: Ideas, Challenges, Solutions and Applications

Advances in Intelligent Systems and Computing Volume 414

Series editor Janusz Kacprzyk, Polish Academy of Sciences, Warsaw, Poland e-mail: [email protected]

About this Series The series “Advances in Intelligent Systems and Computing” contains publications on theory, applications, and design methods of Intelligent Systems and Intelligent Computing. Virtually all disciplines such as engineering, natural sciences, computer and information science, ICT, economics, business, e-commerce, environment, healthcare, life science are covered. The list of topics spans all the areas of modern intelligent systems and computing. The publications within “Advances in Intelligent Systems and Computing” are primarily textbooks and proceedings of important conferences, symposia and congresses. They cover significant recent developments in the field, both of a foundational and applicable character. An important characteristic feature of the series is the short publication time and world-wide distribution. This permits a rapid and broad dissemination of research results.

Advisory Board Chairman Nikhil R. Pal, Indian Statistical Institute, Kolkata, India e-mail: [email protected] Members Rafael Bello, Universidad Central “Marta Abreu” de Las Villas, Santa Clara, Cuba e-mail: [email protected] Emilio S. Corchado, University of Salamanca, Salamanca, Spain e-mail: [email protected] Hani Hagras, University of Essex, Colchester, UK e-mail: [email protected] László T. Kóczy, Széchenyi István University, Győr, Hungary e-mail: [email protected] Vladik Kreinovich, University of Texas at El Paso, El Paso, USA e-mail: [email protected] Chin-Teng Lin, National Chiao Tung University, Hsinchu, Taiwan e-mail: [email protected] Jie Lu, University of Technology, Sydney, Australia e-mail: [email protected] Patricia Melin, Tijuana Institute of Technology, Tijuana, Mexico e-mail: [email protected] Nadia Nedjah, State University of Rio de Janeiro, Rio de Janeiro, Brazil e-mail: [email protected] Ngoc Thanh Nguyen, Wroclaw University of Technology, Wroclaw, Poland e-mail: [email protected] Jun Wang, The Chinese University of Hong Kong, Shatin, Hong Kong e-mail: [email protected]

More information about this series at http://www.springer.com/series/11156

Jan Awrejcewicz Krzysztof J. Kaliński Roman Szewczyk Małgorzata Kaliczyńska •

•

Editors

Mechatronics: Ideas, Challenges, Solutions and Applications

123

Editors Jan Awrejcewicz Lodz University of Technology Lodz Poland Krzysztof J. Kaliński Gdańsk University of Technology Gdańsk Poland

Roman Szewczyk Industrial Research Institute for Automation and Measurements PIAP Warsaw Poland Małgorzata Kaliczyńska Industrial Research Institute for Automation and Measurements PIAP Warsaw Poland

ISSN 2194-5357 ISSN 2194-5365 (electronic) Advances in Intelligent Systems and Computing ISBN 978-3-319-26885-9 ISBN 978-3-319-26886-6 (eBook) DOI 10.1007/978-3-319-26886-6 Library of Congress Control Number: 2015955874 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved 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, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)

Preface

Broadly perceived control, automation, robotics and measuring techniques belong to the most relevant fields of science and technology, both from the point of view of theoretical challenges and practical importance. In spite of being separate areas of research, knowledge and expertise, they are strongly related, in terms of paradigms and tools and techniques employed, as well in terms of their industrial scope of applications. Therefore, an industrial, practice-oriented perspective is an important aspect of these areas. Moreover, automation, robotics and measuring techniques have a significant innovative potential as the current industrial practice calls for a further integration of all kinds of production systems, more ecological and energy efficient solutions as well as cost- and time-effective production and manufacturing processes. Among many important problems and challenges faced by automation and control, most of which have been reflected in the scope of the papers included in this volume, one can mention, for instance, discrete systems, actuators, diagnostics and modern tools exemplified by fuzzy logic, evolutionary computation, neural networks, probabilistic approaches, etc. In robotics, in particular in its part related to the development of mobile robots, one can quote as crucial problems and challenges various problem solving tasks related to the control of walking robots, control of manipulators, motors and drivers, mechatronic systems, and tracking control. Measuring techniques and systems have to overcome, first of all, barriers implied by environmental conditions and limitations. They call for the development of novel sensors (also utilizing novel materials such as graphene), advanced signal processing and a more foundational development focused on the theory of metrology. This book presents the recent advances and developments in control, automation, robotics and measuring techniques that are trying to meet those challenges and to fulfil those technological, economic and social needs. It presents contributions of top experts in the fields, focused on both theory and industrial practice. The particular chapters present a deep analysis of a specific technical problem, which is

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Preface

in general followed by a numerical analysis and simulation, and results of an implementation for the solution of a real-world problem. We strongly believe that the presented theoretical results, practical solutions and guidelines will be useful for both researchers working in the area of engineering sciences and practitioners solving industrial problems. Warsaw July 2015

Jan Awrejcewicz Krzysztof J. Kaliński Roman Szewczyk Małgorzata Kaliczyńska

Contents

Multi-criteria Robot Selection Problem for an Automated Single-Sided Lapping System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Norbert Piotrowski and Adam Barylski Mechatronic Design Towards Investigation of the Temporo-Mandibular Joint Behaviour . . . . . . . . . . . . . . . . . . . . Victor Creuillot, Cynthia Dreistadt, Krzysztof J. Kaliński and Paul Lipinski

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Requirements for Tire Models of the Lightweight Wheeled Mobile Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Przemysław Dąbek and Maciej Trojnacki

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Simulations of Accelerations and Velocities of the Robot’s Arm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Krzysztof Dąbrowski

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The Numerical Analysis of Burnishing Process of Hollow Steel Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tomasz Dyl

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Piecewise Control Method of Oxygen Flow in PEM Fuel Cell . . . . . . . . Jerzy Garus and Adam Polak Testing the Piezoelectric Energy Harvester’s Deflection on the Amount of Generated Energy . . . . . . . . . . . . . . . . . . . . . . . . . . Dariusz Jasiulek

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Analysis of Crash Computation on a Basis of the Principle of Linear Momentum and Kinetic Energy . . . . . . . . . . . . . . . . . . . . . . 113 Krzysztof J. Kaliński, Marek Chodnicki, Barbara Kowalska and Piotr Kmita

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Contents

Modeling and Simulation of the Solar Collector Using Different Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Kazimierz Kamiński and Tomasz Krzyżyński Uncertainty Analysis of Innovative Method for Wheel Load Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Michał Kluziewicz and Michał Maniowski Designing the 40 kHz Piezoelectric Sandwich Type Ultrasonic Transducer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 Paweł Kogut, Andrzej Milewski, Piotr Kluk and Witold Kardyś Development of an Electronic Stethoscope . . . . . . . . . . . . . . . . . . . . . . 189 Olga Szymanowska, Bartłomiej Zagrodny, Michał Ludwicki and Jan Awrejcewicz Determination of Forces and Moments of Force Transmitted by the Wheel of a Mobile Robot During Motion . . . . . . . . . . . . . . . . . . 205 Maciej Trojnacki Comparative Study of Maintenance Vehicles Using Vibration Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 Ovidiu Ioan Vulcu and Mariana Arghir Correction of the Influence of not Ideal Geometric Profile on the Constant of Primary Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 Aleksander A. Mikhal, Zygmunt L. Warsza and Vladimir G. Gavrylkin Modeling and Analysis of the Hydraulic Servo Drive System . . . . . . . . 253 Piotr Woś and Ryszard Dindorf Stereoscopic Technique for a Motion Parameter Determination of Remotely Operated Vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 Bogdan Żak and Stanisław Hożyń Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

About the Editors

Prof. Jan Awrejcewicz graduated from Lodz University of Technology (LUT) in 1977 (Mechanics) and from the University of Lodz in 1978 (Philosophy). He obtained a Ph.D. in 1981, D.Sc. in 1990 and became full professor in 1997. Now he is chairperson of the Department of Automation, Biomechanics and Mechatronics, head of a 4‐years Doctoral School on Mechanics, and head of the Mechatronics Study at LUT. His research areas include nonlinear mechanics (analytical, numerical and experimental methods), continuous systems (plates, shells, beams, and structures), thermo‐elasticity, mathematical methods in mechanics, asymptotic methods, dynamics of lumped mechanical systems, bifurcation and chaos, numerical methods as well as non‐smooth and discontinuous systems. Professor Awrejcewicz is an editor of 12 books and guest‐editor of 18 journal special issues. He is the editor of the Journal of Modeling, Simulation, Identification, and Control, Columbia International Publishing, USA. He has supervised 20 Ph.D. theses. Prof. Krzysztof J. Kaliński graduated from Gdansk University of Technology (GUT) in 1980, in the area of machine tools and production devices. He obtained his Ph.D. in 1988 in scope of computer methods in applied mechanics, D.Sc. in 2002 in the field of machine building and operation, and received the Professor’s title in 2013. In 2015 he became full professor. Now he is head of Group of Mechatronics at the Faculty of Mechanical Engineering of GUT. Since 2007 he has been the main inspirer and coordinator of the Mechatronics Study in GUT. His research areas include theoretical and applied mechanics, machine dynamics, vibration engineering, dynamics of machine tools and production processes, robotics and automation, finite element methods, theoretical and experimental modal analysis, mechatronics, and biomechanics of a mandible. In 2003 he created in GUT the research team of dynamic processes surveillance, whose competences concerned vibration in high speed cutting processes, as well as—dynamics and control of manipulators and mobile robots. He performed 17 domestic research and development projects (among them, six as organiser and supervisor), six international projects (two as supervisor and coordinator) and five structural funds’

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projects (four as coordinator and the head). He is the author or co-author of 217 scientific publications (including 68 books and chapters in books, as well as 56 articles in magazines) and 151 unpublished works. He has supervised five Ph.D. theses, and the three subsequent are to be finalised soon. He was an editor of three scientific elaborations. Among them were Proceedings of Applied Mathematics and Mechanics Vol. 9 Issue 1 (December 2009). Special Issue: 80th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Gdańsk 2009. Prof. Roman Szewczyk received both his Ph.D. and D.Sc. in the field of mechatronics. He specializes in modelling of properties of magnetic materials as well as in sensors and sensor interfacing, in particular magnetic sensors for security applications. He leads the development of a sensing unit for a mobile robot developed for the Polish Police Central Forensic Laboratory and of methods of non-destructive testing based on the magnetoelastic effect. Professor Szewczyk was involved in over 10 European Union funded research projects within the FP6 and FP7 as well as projects financed by the European Defence Organization. Moreover, he was leading two regional and national scale technological foresight projects and was active in the organization and implementation of technological transfer between companies and research institutes. Roman Szewczyk is Secretary for Scientific Affairs in the Industrial Research Institute for Automation and Measurements (PIAP). He is also Associate Professor at the Faculty of Mechatronics, Warsaw University of Technology and a Vice-chairman of the Academy of Young Researchers of the Polish Academy of Sciences. Dr. Małgorzata Kaliczyńska received her M.Sc. Eng. degree in Cybernetics from the Faculty of Electronics, Wroclaw University of Technology, and her Ph.D. degree in the field of fluid mechanics at the Faculty of Mechanical and Power Engineering from the same university. Now she is Assistant Professor in the Industrial Research Institute for Automation and Measurement (PIAP) and editor of the scientific and technological magazine “Measurements, Automation, Robotics”. Her areas of research interest include distributed control systems, Internet of things, information retrieval and webometrics.

Multi-criteria Robot Selection Problem for an Automated Single-Sided Lapping System Norbert Piotrowski and Adam Barylski

Abstract Flat lapping is a crucial process in a number of precision manufacturing technologies. Its aim is to achieve extremely high flatness of the workpiece. Single-sided lapping machines have usually standard kinematic systems and are used in conjunction with conditioning rings, which are set properly between the centre and the periphery of the lapping plate. In this paper, instead of conventional single-sided lapping machine, an automated lapping cell is introduced. The object of the robotic lapping system is to provide improved means for controlling the position of conditioning rings on lapping plate, so as to enable the flatness of the plate and consequently of the workpieces to be controlled. What is more, this innovative solution allows to fully automate a single-disc lapping process. Selection of a robot is one of a number of challenges in designing automated manufacturing systems. This problem has become very demanding due to the increasing specifications and the complexity of the robots. This study aims to solve a robot selection difficulty for conditioning ring positioning, workpieces handling and loading tasks in the lapping cell. For this reason, analytic hierarchy process (AHP), which is one of the multi-criteria decision-making (MCDM) methods, is used to select the most convenient robot.




Keywords Abrasive machining Lapping kinematics Analytic hierarchy process Robot selection







Robot application




1 Introduction The lapping process is a significant technology among various precision manufacturing applications. It has a broad scope of application, mostly in technical ceramics, medical devices, electro optics, data storages, and aerospace and N. Piotrowski (&)
A. Barylski Gdańsk University of Technology, Gdańsk, Poland e-mail: [email protected] A. Barylski e-mail: [email protected] © Springer International Publishing Switzerland 2016 J. Awrejcewicz et al. (eds.), Mechatronics: Ideas, Challenges, Solutions and Applications, Advances in Intelligent Systems and Computing 414, DOI 10.1007/978-3-319-26886-6_1

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N. Piotrowski and A. Barylski

automotive industries [1]. Moreover, this type of machining can be used both in optical mirrors and lenses. Lapping process is conducted by implementing loose abrasive grains between two surfaces and causes a relative motion between them resulting in a finish of multi-directional lay [2]. Flat lapping is one of the most commonly used types of the lapping process which objective is to achieve extremely high flatness of the workpiece. Single-sided lapping machines are usually used along with conditioning rings, which are situated precisely between the centre and the periphery of the lapping plate [3]. Previously conducted studies put the main emphasis on the mechanisms of material removal, the effects of input parameters and the thermal measurements. The main aim of the research was to optimize the machining conditions in order to boost the surface quality and to improve the efficiency of the process. However, issue such as behaviour of lap flatness in lapping process when the standard input parameters— relative velocity of workpiece as well as the velocity of lapping plate—are carefully controlled, and a conventional kinematic system is changed and has not been closely scrutinized. The investigation of new kinematic systems should be continued in order to improve the flatness of lapping plate and consequently the surface quality of workpiece [4]. The main object of the automated lapping system is to provide the improved means for controlling the position of conditioning rings on lapping plate so as to enable the flatness of the plate to be controlled. This innovative solution enables an automation of a single-sided lapping process. A remarkable point in the process is a robot that helps automating the lapping process with such available options as multi-step programmable rings speed, down pressure, slurry feed as well as quick machine loading and unloading. One of the challenges in designing automated manufacturing systems is selecting a robot. This issue has become very demanding due to increasing specifications and complexity of the industrial robots. The study aims to solve a robot selection difficulty for conditioning ring positioning, workpieces handling and loading tasks in the lapping cell. To meet the mentioned requirements the author chose one of multi-criteria decision-making (MCDM) methods in order to select the most beneficial robot.

2 Robot Selection 2.1

Industrial Robots Parameters

Recent developments in information technology and information technology have been the main reason for the increased utilization of manipulators in a variety of advanced manufacturing facilities. Nowadays there are many types of industrial robots of various applications. Leading industrial robots producers are KUKA (Germany), ABB (Switzerland), Comau (Italy), Fanuc (Japan), Kawasaki (Japan).

Multi-criteria Robot Selection Problem …

3

According to the application, the engineers must be able to select the perfect robot. This is only possible, if the engineers are well known about the technical parameters of every robot. The basic technical features of such robots are: – – – – – – – – – – – – – – –

configuration of a robot, number of axes of a robot, type of control system, drive system, permissible working load (kN), total weight of a robot (kg), working volume (mm3), floor space (m3), range of joints motion (°), maximum speed (°/rad), repeatability that ensures the precision of a motion (mm), work area temperature (°C), recommended relative operating humidity (% + °C), versions of the robot installations, additional information and equipment.

Various technical features are needed in different applications. For example, machine loading need a polar, cylindrical or revolute robot with four to five axes. It should be equipped with a limited sequence or point-to-point (PTP) control system. For heavy weights the drive system must be hydraulic. Otherwise electric drive type is sufficient. In case of assembly operations a robot should be either Cartesian or revolute. It must be incorporated with three to six axes and must have an electrical drive system. Continuous path or PTP control system is required. To perform various machining process, a revolute will be the appropriate selection. The number of axes must be more or equal to five. It can have either electric or hydraulic drive system. It must possess a continuous path control system [5].

2.2

Robot Selection Methods

The selection of robots to suit a certain application and production environment form among the large number available in the market is a difficult challenge. Different approaches were used by previous researchers to solve the robot selection problem. Khouja and Booth [6] used a statistical procedure known as robust fuzzy cluster analysis that can select the robots with the best compilation of specifications based on various performance parameters. Moreover, Khouja [7] is the author for two-phase decision model for problems according to the robot selection. The first phase consists of employing data envelopment analysis (DEA) for identifying the robots with the best combination of vendor specifications with regard to the robot performance parameters. The second phase applies a multi-attribute decision-making (MADM)

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method in order to choose the best robot among those which were identified in the first phase. Revised weighted sum decision model was developed by Goh et al. [8]. The model takes into account the objective as well as subjective attributes while choosing the industrial robots. Rao and Padmanabhan [9] introduced the diagraph and matrix methods to assess and rank the alternative robots for a specific industrial application, applying the similarity and dissimilarity coefficient values. Karsak [10] is the author of a decision model for robot selection. It is based both on quality function deployment (QFD) and fuzzy linear regression methods while combining the user demands with the technical parameters of the robots. Zhao et al. [11] introduced a multi-chromosome genetic algorithm with first-fit bin packing algorithm in order to choose a robot and workstation assignment problem for a computer integrated manufacturing system. Among numerous multiple-criteria decision analysis (MCDA) or MCDM methods developed to solve real-world decision problems by supporting the subjective evaluation of a finite number of decision alternatives under a finite number of performance criteria, technique for order preference by similarity to ideal solution (TOPSIS) can be found. TOPSIS was developed by Hwang and Yoon in 1981. This ranking method is simple in conception and application. The fundamental logic of TOPSIS method is to determine the positive-ideal solution (PIS) and the negative-ideal solution (NIS). The convenient alternative is the one with the shortest distance from the positive solution and the farthest distance from the negative solution and preference order is ranked. The PIS maximizes the benefit criteria and minimizes the cost criteria, whereas the NIS maximizes the cost criteria and minimizes the benefit criteria. However, attribute values must be numeric, monotonically increasing or decreasing to apply this technique [12].

2.3

Analytical Hierarchy Process

One of the most common MCDM techniques is analytic hierarchy process (AHP). It was developed in 1970 by Thomas L. Saaty. However, AHP is still improved by other decision makers. Solving difficult decision problems using this method is based on their decomposition into components; objective, criteria (sub-criteria) and alternatives. These elements are then linked into a model with a multi-level (hierarchical structure). The goals can be found at the top of this structure and the main criteria at the first level. Criteria can be broken down into sub-criteria, and at the lowest level given are the alternatives. Another important component of the AHP method is the mathematical model that calculates the priorities of the elements that are at the same level of the hierarchical structure [13]. AHP has been used in many applications with various risks. Using this method allows to:

Multi-criteria Robot Selection Problem …

– – – – – –

5

make a selection of alternatives (e.g. robot selection), evaluate a quality (e.g. Computer software), estimate design solutions, assist financial decisions, determine the suitability of a technical equipment, introduce amendments.

General algorithm for the AHP method is shown in Fig. 1. It consists of several steps. The first one is defining the unstructured problem and criteria. Then pairwise comparisons and rating scale must be employed and relative importance weights at each level of the hierarchy must be evaluated. Next step is to check the consistency property of the matrix. Consistency index (1) and consistency ratio (2) parameters should not be greater than 0.1. Finally, the results can be made into a hierarchical structure [14]. CI ¼

kmax n  0:1 n 1

ð1Þ

CI  0:1 RI

ð2Þ

CR ¼

where: λmax—maximum eigenvalue, n—order of matrix, RI—random index (Table 1).

3 Automated Lapping System Lapping is one of the finishing methods that allows very high surface qualities, form accuracies and very close dimensional tolerances. Since now, various types of lapping machines have been developed. However, there are only two kinematic systems, which are commonly used. Plane and parallel surfaces are lapped on double-disc lapping machines with a planetary kinematic system. In case of flat surfaces machining, single-sided lapping machines are used. They are usually used in conjunction with conditioning rings. In the standard lapping machines, relative movements of lapping plate and workpieces are induced from respective rotations and reciprocal movements. Nowadays modern lapping machines became more efficient than those in the past. The basic constructions are supplied with additional components. As a result of the automation of lapping machines some of the supporting operations were eliminated. Lapping machines for flat and parallel surfaces are supplied with feeding tables, loading and unloading systems of rings, which form mini-production lines (Fig. 2). The Peter Wolters Company developed a solution for a micro lapping lines that provides greater efficiency and precision (Fig. 3). In these machines, a five-axis robot functions as a workpieces feeder. The robot is able to handle the workpieces

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Fig. 1 Analytical hierarchy process algorithm [14]

Problem definition Decision subjects determination: objective, main criteria, sub-criteria, variants Hierarchical Structure establishment

Determination of a rating scale Creation of comparisons matrices Determination of an eigenvalue λ max

Local and global prioritization Determination of priorities values

Validation Errors determination Consistency index CI

Random index RI

Consistency ratio CR

Matrix consistency check

Matrix reduction

No

CR < 0.1 and CI < 0.1

Yes Results statement Decision

Table 1 Random inconsistency indices RI [14] n RI

1 0.0

2 0.00

3 0.58

4 0.9

5 1.12

6 1.24

7 1.32

8 1.41

Multi-criteria Robot Selection Problem …

Fig. 2 Lapping machine with feeding table [15]

Fig. 3 Robot as a feeder in Peter Wolters lapping machine [15]

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Fig. 4 Idea of robotic single-sided lapping machine

from the storeroom with a magnetic or vacuum holder, put them in the conditioning rings and shift the whole ring. The system reduces the auxiliary process time, increases the flow capacity and makes the unmanned machining possible [15]. After a careful analysis of numerous offers of many lapping machines producers, it has emerged that none of them has a system where the ring is led by the manipulator, during the machining. The robot functions as a feeder in the Peter Wolters lapping machines and moreover, it can support the machining. It is complicated and in some cases impossible to create a universal mechanism that makes the ring move at any path. Thanks to the robot that moves an effector from point to point, it is possible to change the ring trajectory at any moment. Owing to this solution, it is possible to apply any lapping kinematics, which causes a regular wear of lapping disc at its ray [1–4]. The idea of how single-sided lapping machine and the robot working together is presented in Fig. 4. There is a robot 1 situated next to the lapping machine 2. Primarily sorted workpieces are handled from the table to the separator, located in conditioning ring 3. Then ring griped by the robot moves on the plate 4, which is propelled with angular velocity ωt. The machining is executed by the robot. It shifts the ring with workpieces in such a way to keep the flatness of the plate along the radius. The turning motion ω2 of the ring can be forced by the robot (same or oppositional rotational direction) or it can be affected by the friction force. After lapping process, robot shifts conditioning ring to another table and workpieces fall into the box with finished parts. Finally the flatness of the plate is controlled and fixed in case an error occurs.

Multi-criteria Robot Selection Problem …

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4 AHP Methodology for Lapping Robot Selection Application of AHP method was carried out for robot selection. An automated lapping system was examined. The selection of a robot to perform material handling tasks and lapping process were decided. After initial selection, three robots R1, R2 and R3 were chosen for further evaluation (Table 2). These articulated robots have six degrees of freedom and are powered by an electrical drive. Continuous path or PTP control system is required. Thus, the robot selection problem consists of three main criteria and nine sub-criteria. These criteria are as follows: Physical (P): weight (P1), total height (P2), Specification (S): load (S1), speed (S2), range (S3), repeatability (S4) and Cost (C): purchase cost (C1), maintenance cost (C2), insurance (C3). The first step in the AHP procedure is to make pairwise comparisons between each criterion. Results of the comparison are described in term of integer values from 1 to 9, where higher number means the chosen factor is considered more important than other factor being compared with. N × N matrix with compared criteria can be composed, where N means number of criteria. It can be noticed that the diagonal elements of the matrix are always 1. Next step is to sum every column and every row (Table 3). Each element of the matrix is divided by a sum of the corresponding column. The result is saved in new matrix (Table 4). The weights of criteria are obtained by adding all the elements in a row. Weights are allowed to develop a ranking of criteria. It may be noted that a sum of each column of the Table 4 equals 1.

Table 2 Chosen parameters for industrial robots

Parameters

R1

R2

R3

Weight (kg) Height (mm) Load (kg) Speed (°/s) Joint 1 Joint 2 Joint 3 Joint 4 Joint 5 Joint 6 Reach (mm) Repeatability ± (mm) Purchase cost (PLN) Maintenance cost (PLN) Insurance cost (PLN)

380 1564 16 360 210 125 400/∞ 240 800 /∞

130 1340.5 12 360 250 445 380 380 720

280 1630 10 160 140 160 330 330 500

1550 0.04 220,800 80,000 40,000

1420 0.08 260,000 85,000 20,000

1852 0.10 185,000 65,000 35,000

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Table 3 A pairwise comparison of criteria P S C Sum

P

S

C

Sum

1.00 7.00 5.00 13.00

0.14 1.00 0.33 1.48

0.20 3.00 1.00 4.20

1.343 11.000 6.333

Table 4 Criteria importance P S C Sum

P

S

C

Weight

Rank

0.08 0.54 0.38 1.00

0.10 0.68 0.23 1.00

0.05 0.71 0.24 1.00

0.074 0.643 0.283 1.00

3 1 2

Apart from the relative weight, consistency has to be checked. To do that, principal eigen value λmax is needed. It is obtained from the summation of multiplication products between each weights and the sum of columns of the matrix with comparison. Then conditions (1) and (2) are checked: CI ¼

3:097 3 ¼ 0:048  0:1 3 1

ð3Þ

0:048 ¼ 0:083  0:1 0:58

ð4Þ

CR ¼

In the same manner as criteria, sub-criteria are calculated. Local weights of sub-criteria are obtained by multiplying global weights by a weight of corresponding criteria. The results of the Specification (S) sub-criteria calculations are shown in Tables 5 and 6, respectively. The matrix consistency is checked as well in (5) and (6).

Table 5 A pairwise comparison of sub-criteria specification (S) S1 S2 S3 S4 Sum

S1

S2

S3

S4

Sum

1 5 3 7 16

0.20 1 1 5 7.20

0.33 1 1 3 5.33

0.14 0.2 0.33 1 1.68

1.68 7.20 5.33 16

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Table 6 Sub-criteria (S) importance S1 S2 S3 S4 Sum

S1

S2

S3

S4

Global weight

Local weight

Rank

0.06 0.31 0.19 0.44 1.00

0.03 0.14 0.14 0.69 1.00

0.06 0.19 0.19 0.56 1.00

0.09 0.12 0.20 0.60 1.00

0.060 0.190 0.178 0.573 1.00

0.038 0.122 0.115 0.369 0.643

4 2 3 1

CI ¼

4:227 4 ¼ 0:076  0:1 4 1

ð5Þ

0:076 ¼ 0:084  0:1 0:9

ð6Þ

CR ¼

In Tables 7 and 8 as example, the calculations of the Repeatability (S4) of R1, R2, R3 robots are shown. They were implemented in the same way as calculations of sub-criteria importance. Moreover, the necessary conditions are checked (7) and (8). CI ¼

3:111 3 ¼ 0:056  0:1 3 1

ð7Þ

0:056 ¼ 0:096  0:1 0:58

ð8Þ

CR ¼

Finally, the last step of robot selection with AHP method is to develop a hierarchical structure (Fig. 5). Furthermore, results were presented in Table 9.

Table 7 A pairwise comparison of repeatability (S4) S4 R1 R2 R3 Sum

R1

R2

R3

Sum

0.04 1 0.20 0.14 1.34

0.08 5.00 1 0.33 6.33

0.1 7.00 3.00 1 11.00

13.00 4.20 1.48

Table 8 Repeatability (S4) importance R1 R2 R3 Sum

R1

R2

R3

Global weight

Local weight

Rank

0.74 0.15 0.11 1.00

0.79 0.16 0.05 1.00

0.64 0.27 0.09 1.00

0.724 0.193 0.083 1.00

0.01779 0.00475 0.00205 0.025

1 2 3

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N. Piotrowski and A. Barylski

Fig. 5 Hierarchical structure of the robot selection

Robot selection for an automated lapping system

Physical (P) 0,074

Insurance (C3) – 0,021

Maintenance (C2) – 0,080

Purchase (C1) – 0,182

Repeat. (S4) – 0,369

Range (S3) – 0,115

Speed (S2) – 0,122

Load (S1) – 0,038

Height (P2) – 0,049

Weight (P1) – 0,025

Table 9 Results of robot selection

Cost (C) 0,283

Specifications (S) 0,643

R1

R2

R3

0,086

0,095

0,041

Parameters

R1

R2

R3

Weight (kg) Height (mm) Load (kg) Speed (°/s) Reach (mm) Repeatability ± (mm) Purchase cost (PLN) Maintenance cost (PLN) Insurance cost (PLN) Sum Ranking

0.00261 0.00696 0.01557 0.01644 0.00475 0.01779 0.00598 0.01118 0.00440 0.08568 2

0.01557 0.01582 0.00641 0.00598 0.00205 0.00475 0.01644 0.01118 0.01685 0.09505 1

0.00641 0.00181 0.00261 0.00217 0.01779 0.00205 0.00217 0.00224 0.00334 0.04059 3

5 Conclusion The aim of this paper is to solve the robot selection problem using one of MCDM methods. Selection problem refers to the automated lapping cell. A robot has to perform material handling tasks and assist lapping process. The most important attributes of the robot are described. The weights of the considered criteria and sub-criteria are calculated using analytical hierarchy process (AHP) method. The

Multi-criteria Robot Selection Problem …

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repeatability of robot is the leading sub-criteria in this case. According to the calculations, the ranking order of three robots is R2, R1 and R3 for the problem. However, there is not much difference between the first two robots.

References 1. Barylski, A.: Podstawy docierania jednotarczowego powierzchni płaskich. Zeszyty Naukowe Politechniki Gdańskiej. Mechanika nr 67, Gdańsk (1992) 2. Barylski, A., Gniot, M.: Analiza kinematyki docierania jednotarczowego powierzchni płaskich. Obróbka ścierna. Współczesne problemy, Katedra Technologii Maszyn i Automatyzacji Produkcji Politechnika Gdańska, Gdańsk (2011) 3. Barylski, A.: Problemy technologiczne docierania powierzchni płaskich w układach jednotarczowych. Presented at XXVI Szkoła Tribologiczna Problemy Tribologiczne w Przyrodzie i Technice oraz VI Konferencja Problemy Niekonwencjonalnych Układów Łożyskowych, Łódź-Niedzica (2003) 4. Barylski, A., Piotrowski, N.: Koncepcje niekonwencjonalnych układów kinematycznych docierania jednotarczowego z wykorzystaniem robota. XXXVII Naukowa Szkoła Obróbki Ściernej, Mechanik, nr 8-9 (2014) 5. Groover, M.P., Weiss, M., Nagel, R.N.: Industrial Robotics: Technology, Programming and Application. McGraw-Hill Higher Education, New York (1986) 6. Khouja, M., Booth, D.E.: Fuzzy clustering procedure for evaluation and selection of industrial robots. J. Manuf. Syst. 14, 244–251 (1995) 7. Khouja, M.: The use of data envelopment analysis for technology selection. Comput. Ind. Eng. 28, 123–132 (1995) 8. Goh, C.-H., Tung, Y.-C., Cheng, C.-H.: A revised weighted sum decision model for robot selection. Comput. Ind. Eng. 30, 193–199 (1996) 9. Rao, R.V., Padmanabhan, K.K.: Selection, identification and comparison of industrial robots using digraph and matrix methods. Robot. Comput.-Integr. Manuf. 22, 373–383 (2006) 10. Karsak, E.E.: Robot selection using an integrated approach based on quality function deployment and fuzzy regression. Int. J. Prod. Res. 46, 723–738 (2008) 11. Zhao, L., Tsujimura, Y., Gen, M.: Genetic algorithm for robot selection and work station assignment problem. Comput. Ind. Eng. 31, 599–602 (1996) 12. Behzadian, M., Khanmohammadi Otaghsara, S., Yazdani, M., Ignatius, J.: A state-of the-art survey of TOPSIS applications. Expert Syst. Appl. 39:13051–13069 (2012) 13. Żurek, J., Ciszak, O., Cieślak, R., Suszyński, M.: Ocena i wybór robota przemysłowego metodą AHP. Arch. Mech. Technol. Autom. 31, nr 2:201–211, Poznań (2011) 14. Downarowicz, O., Krause, J., Sikorski, M., Stachowski, W.: Zastosowanie metody AHP do oceny i sterowania poziomem bezpieczeństwa złożonego obiektu technicznego. Wybrane metody ergonomii i nauki o eksploatacji, Wydawnictwo Politechniki Gdańskiej, pp. 7–42, Gdańsk (2000) 15. http://www.peter-wolters.com. Accessed 29 Jan 2015

Mechatronic Design Towards Investigation of the Temporo-Mandibular Joint Behaviour Victor Creuillot, Cynthia Dreistadt, Krzysztof J. Kaliński and Paul Lipinski

Abstract A significant problem of the temporo-mandibular joint (TMJ) research is lack of data concerning geometry and position of TMJ discs. It leads to necessity of developing a driving method of the process optimization, which is based on chosen techniques of mechatronic design. In particular, the latter concerns a technique of experimentally supported virtual prototyping. On this stage, the research is characterized by well-verified constitutive characteristics of all components, engagement of real components of the research system, offline experimental identification of the TMJ system parameters, offline experimental determination of the appropriate parameters of the TMJ, online computation of the TMJ process of non-stationary model and assessment of the driving method’s efficiency. In case of the medium opening–closing jaw motion, results of the FEM are close to the experimental data and validate discs’ geometries and positions. Quality of the obtained solution is also verified by analysing the contact between discs and surrounding bones. In case of the immediate clenching simulation, a comparison of finite element model simulation and dental plaster mould occlusions testifies the correctly reproduced occlusal scheme. Values of the contact forces and the contact area surfaces enable calculation of the mean contact pressure values on the cranial and caudal faces of the discs. The obtained model allowed reproducing accurate anatomic mandible trajectories and also a physical occlusion.







Keywords Temporo-mandibular joint FE modelling Muscles’ motion driving Mechatronic design




V. Creuillot
C. Dreistadt
P. Lipinski (&) LaBPS, Ecole Nationale d’Ingénieurs de Metz France, 1 Route d’Ars Laquenexy, 57 078 Metz, France e-mail: [email protected] K.J. Kaliński Faculty of Mechanical Engineering, Gdańsk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland © Springer International Publishing Switzerland 2016 J. Awrejcewicz et al. (eds.), Mechatronics: Ideas, Challenges, Solutions and Applications, Advances in Intelligent Systems and Computing 414, DOI 10.1007/978-3-319-26886-6_2

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1 Introduction Temporo-Mandibular Joint (TMJ) allows the relative motion between the mandible and the maxillary. It is one of the most utilized joints in the human body. According to Kamina [1], it endures approximately 10,000 cycles per day, and by consequence, it is also one of the most symptomatic joints. Indeed, up to 35 % of the worldwide population presents TMJ disorders. In 70 % of the pathologic cases, the symptom corresponds to a disc displacement. Nowadays, causes of these dysfunctions are still misunderstood. To elucidate the origin of such pathologies, the key factor, from the biomechanical viewpoint, is the knowledge of forces acting on the TMJ discs. However, for the evident ethical reasons, the direct TMJ force measurements are unworkable in living human. Mathematical modelling of the joint appears as the best approach to correctly quantify these forces. Many 2D and 3D finite element models of TMJ have been developed during the last 15 years, see for instance [2–8]. The most finite element studies of the TMJ were performed on one side with the strong assumption of the jaw symmetry. They were dedicated to study the stress distribution in the TMJ for asymptomatic as well as pathologic cases and for different movements such as opening, closing, opening-closing cycle or jaw clenching. The first studies have been focused on healthy cases. Chen et al. [9] built a 2D model of one side of TMJ in order to establish a relationship between the condylar sagittal displacement and the stress distribution into the disc. A few years later, Tanaka et al. [10] proposed a method of geometry reconstruction based on MRI acquisitions. They developed a more realistic finite element TMJ model of a healthy person. In order to show the influence of the internal TMJ’s disorders, Tanaka et al. [3] used the same method of reconstruction to compare the stress distribution in the TMJ between subjects with and without anterior disc displacement. Since even the healthy subjects are not fully symmetric, the modelling of a complete jaw appeared necessary. Mori et al. [7] and Savoldelli et al. [8] demonstrated that the stress fields in the two discs are different, the condyle trajectories are not the same and the geometry itself of the left and right TMJs is dissimilar. Only the study of Savoldelli et al. [8] takes into account the full skull without assumption of the condyle geometry. This study simulated a 10 mm inter-incisal jaw closing and prolonged clenching. Force vectors oriented in muscular directions reproduced this simple movement. The crucial point of TMJ modelling is related to the discs description. The TMJ disc is constituted of cartilaginous tissue with collagen fibres oriented in function of their location [11]. In numerous studies [3, 7, 12], the disc geometry is retrieved from the MRI acquisitions. Otherwise, its geometry is reconstructed from the articular surfaces in the occlusal position [5, 13]. Recent studies were focused on prolonged clenching which is a current phenomenon that can appear during the sleep leading to the effect of a disc overload. A large variety of constitutive laws for the disc can be found in the literature. In the case of large movement, the disc is frequently considered as an elastic isotropic component [3],

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17

whereas in clenching simulations, it is usually regarded as viscoelastic or hyper-viscoelastic constituent. In some cases [4, 6, 13], the elevator muscles are taken into account or displacements are merely applied to the condyle. In our approach, the mandible was driven by a set of muscles. The FE software MSC MARC was used to perform simulations. However, this software does not provide elements reproducing muscles’ actions such as those elaborated by Hill [14], or improved by Zajac [15]. This kind of “actuators” is implemented in biomechanical Multibody Software such as LifeMod or OpenSim. The aim of this study is to validate an original driving method of the mandible movement by the muscular contractions reproducing muscles’ activation determined using the LifeMod code. In order to improve performance of this method classical mechatronic design techniques [16] were employed. Mechatronic approach to the design process is characterized by the fact that several components of the system/process can be designed in parallel (i.e. concurrently), provided that there will be a method for checking the compatibility of each element. The benefits of concurrent design are: shortening the design phase, simplifying and accelerating the implementation and the possibility of flexible implementation of individual functions. The correctly carried concurrent design, with careful verification of the components (virtual prototyping) allows us to avoid problems with the cooperation of the individual components of the system [17]. When all components are developed simultaneously, one can be more flexible to implement various functions of the device/process in various fields. A standard mechatronic design procedure was successfully applied in this work, similarly to that proposed by Kaliński and Buchholz [18] in scope of development of 3-wheeled mobile platform. In the paper, two simulations are presented—one reproducing a medium opening–closing movement and another mimicking clenching with large occlusal forces. The simulated condylar trajectories have been compared with experimental data of Alvarez et al. [19] to validate the driving method used in this paper. On the other hand, TMJ forces have been analysed by comparing the obtained values with data from the open literature.

2 Materials and Methods A 31-year-old female healthy volunteer with no history of present and past TMJ disorder (Skeletal class I and asymptomatic joint) has been selected for her relatively symmetrical condylar trajectories during an opening-closing movement of the mouth. The movement recording has been made by the WinJaw system Zebris GmbH and was briefly presented in Alvarez et al. [19].

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Numerical Model

A cone beam computed tomography with 0.25 mm thick slices was carried out in close mouth position on this volunteer. The segmentation and the reconstruction tasks were done using Mimics 14.12 and 3Matic 5.1 software packages (Materialise, Leuven, Belgium). Only the bone structures, maxillary and mandible can be accurately recovered with the tomography. These structures have been imported into the Hypermesh software 11 (Altair, Troy, Michigan, USA) and meshed using linear tetrahedral elements with a size variation depending on location in the mandible. The condyles and teeth have been meshed with a small element size (i.e. 0.5 mm) to increase the precision of obtained mechanical fields in these areas. The obtained mesh is illustrated in Fig. 1a, b. The model has been set in the occlusal position by comparing with dental plaster cast executed on the volunteer (Fig. 2). The computed tomography does not permit to visualize disc, so they were designed following indications from literature data,

Fig. 1 The mesh of finite element model: a global view, b details of left and right TMJs

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Fig. 2 Comparison of dental plaster and numerical occlusal positions

shape was taken from Athanasiou et al. [11] and occlusal positioning from Bumann and Lotzmann [20]. Disc volumes have been created in accordance with the data of Tanaka et al. [10]. They were meshed by using tetrahedral quadratic elements with a size of 0.5 mm. The articular capsules were modelled by using 3D truss elements representing medial and lateral parts of the capsule with a position taken from Bumann and Lotzmann [20]. Literature provides stiffness for these ligaments. Cross-sections associated to the truss elements have been defined in function of this stiffness as A¼

k
L E
n

ð1Þ

where A is the unknown ligament cross-section area, k is capsular stiffness, L is length of ligaments, n is number of parallel ligaments modelling the capsular part and E is Young’s modulus assigned to the ligaments representing the capsule.

2.2

Material Properties

Generally, bones are considered as elastic, macro-heterogeneous and anisotropic media. However, in this work, which is focused on the discs behaviour, isotropic elastic properties have been assigned to the mandible and the maxillary. Distinction between cortical and cancellous bone was not implemented in this model, because the mechanical fields in the bone are not analysed. The corresponding data is summarized in Table 1. A density of 1.4 g/cm3 has been attributed to the mandible in order to obtain a mass of 74 g in accordance with rigid body model of Alvarez et al. [19]. TMJ discs are modelled as a hyper-elastic Marlow continuum [13]. The corresponding constitutive relationship is implemented in the MSC MARC software. The constants of this law were deduced from the first cycle of the stress–strain curve from experimental data of Beek et al. [21] presented in Fig. 3.

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Table 1 Material properties of model components

Component

Young’s modulus (MPa)

Poisson’s ratio

Mandible Maxillary Disc Capsule

13,700 13,700 Data from Beek et al. [19] 0.2

0.3 0.3 0.3

Fig. 3 Experimental data describing the disc stress– strain relationship, Beek et al. [21]

As mentioned in previous section, the capsule has been modelled by elastic 3D truss elements. The last line of Table 1 specifies the corresponding elastic properties of these elements.

2.3

Contact Management

Three interacting deformable bodies, namely condyle, disc and fossa, form each temporo-mandibular joint. All these contacts are supposed frictionless as the synovial fluid plays the role of quasi-perfect lubricant; see Chen et al. [9]. Teeth have been assumed as the continuation of the maxillary and mandible bones. The upper and lower teeth arcades are considered as two deformable contact bodies in the clenching case simulation. The friction coefficient μ = 0.1 was supposed for this interaction.

2.4

Muscular Action Modelling

In numerous finite element studies, the TMJ behaviour was analysed in various configurations, but anyone used a muscular activation to drive the mandible. In this study, our intention was to drive the mandible by activation of eleven pairs of muscles, illustrated in Fig. 1. The MSC MARC was used to reproduce the motions. However, as it was mentioned in the Introduction paragraph, this general-purpose

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software does not include muscle elements. To circumvent this difficulty, the Multibody System software LifeMod was first worked to determine the simultaneous forces and elongations of all Hill-type muscles. First, experimental trajectories of the condyles and incisor point, determined by Alvarez et al. [19], for the same volunteer, have been used throughout the inverse dynamic simulation. The activation profiles of all muscles were obtained in this way. Next, during the direct dynamic analysis stage, these activation profiles were used to simulate a required cycle of mandible motion. As the output, files of the current length l(t) and force F (t) experienced by the muscles were generated. To reproduce the same behaviour of muscles, modelled by 3D truss elements in MARC, the thermal contraction capability of these elements was exploited. Let lo be the initial length of a muscle. Its total logarithmic strain eT ðtÞ is defined by its current and initial lengths: eT ðtÞ ¼ ln

lðtÞ lo

ð2Þ

The elastic part of this strain ee ðtÞ is due to the force exerted by the muscle: ee ðt Þ ¼

F ðtÞ SE

ð3Þ

where S and E are the muscle cross-section area and Young’s modulus, respectively. The muscle contraction is reproduced by the thermal expansion capability of the truss elements. The contractile strain of the muscles ec ðtÞ is calculated using the following expression: ec ðtÞ ¼ ahðtÞ

ð4Þ

where α is an arbitrarily chosen contraction coefficient and θ(t) the unknown muscle excitation. Assuming the additive decomposition of the total strain into elastic and contractile parts: eT ¼ ee þ ec

ð5Þ

and using definitions (2) to (4), the determination of the excitation profiles for all muscles of the model can be expressed as follows: hð t Þ ¼

 1 l ðt Þ ln a lo

 F ðt Þ : SE

ð6Þ

These excitation profiles were calculated for every muscle using the files of the current length and force procured by the LifeMod. The method was first verified in the case of ample opening-closing jaw motion. The comparison of the experimental and finite element trajectories of condylar centres is illustrated in Fig. 4, taken from Alvarez [22]. It validates the method proposed.

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Fig. 4 Comparison of experimental and predicted trajectories of condyles’ centres

2.5

Definition of Disc Shape and Positioning by Mean of Experimentally Supported Virtual Prototyping

Simulation model is an idealized mathematical description of real process and, because of a class of phenomena planned for investigation, is not purposed for the other classes. Thus, there is a need of creating a great number of models for simulation of various phenomena with various levels of particularity. Regardless of the software used, due to unavoidable inaccuracies of the built models and numerical calculations, it should be carried out verification of the used models, the obtained results and used design tools. The best way, as far as possible, is to experiment on a real object. Since the computed tomography achieved on the volunteer did not permit to visualize soft tissues, various discs’ geometries were created as following the method presented above. Because of the lack of data concerning the shape and occlusal position of the TMJ discs, the choice of these parameters was done in function of experimental trajectories of the condyle centres and the incisal point, i.e. the method of assurance assessment (validation) with the real object behaviour was applied. For this purpose, the offline identification of the model parameters of the TMJ was utilized. While the precise design procedure depends on the particular device or process, we can distinguish certain techniques, which enable the achievement of the mechatronic design idea. They are as follows: – virtual prototyping, – experimentally supported virtual prototyping and – rapid prototyping (i.e. real implementation) on the target system.

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It is possible to design without the use of these techniques but, in many situations, it is inconvenient or very difficult as for example in the cases when: – the monitoring system is being developed for the physically non-existent system or it is unacceptable to experiment on a working device, – the system is unstable or weakly damped, – the system is characterized by complex dynamic properties, being difficult for modelling. In the TMJ case studied here, experimentally supported virtual simulation has been used. The latter, together with simulation implemented only on computing equipment having office software (i.e. virtual prototyping), are important techniques for mechatronic design. Prediction of the results of the driving method, on a basis of computer simulation of the TMJ model commonly used in many former scientific and research works, is mainly affected by the disc parameters. Generally, the real time (RT) simulation should significantly improve precision of the prediction. However, the system/process studied is so complex that, for the reasons mentioned above, the whole system is not controllable in case of the present application. Behaviour of the TMJ is investigated in convention of open loop system. Thus, because of a lack of closed loop interaction between the measured and controlled signals, the RT simulation is not recommended in such a situation. Virtual prototyping allows for fast and low cost analysis of many alternatives of the TMJ process performance, at the demanded accuracy level. Also it consents the concurrent design, thanks to supported means of verification of correct cooperation between all components (mandible, maxillary and discs). On this stage, the research was characterized by: – – – – – –

the well-verified constitutive characteristics of all components, engagement of real components of the research system, offline experimental identification of the TMJ system parameters, offline experimental determination of the appropriate parameters of the TMJ, online computation of the TMJ process of non-stationary model, assessment of the driving method’s efficiency.

If the discs are not correctly shaped and positioned, there is a risk of their dislocation during the opening on the model leading to the wrong final trajectories and positions. A few adjustments on the discs shape and position were done until obtaining satisfactory trajectories of the mandible compared to the experimental records.

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3 Results 3.1

Medium Opening-Closing Jaw Motion

The jaw motion of this finite element simulation was driven using the method presented in Sect. 4, that is, the mandible trajectory was not imposed as a boundary condition but resulted from the muscular activation and contact management between discs, fossa and condyles. Figure 5 shows the condylar trajectories during a medium opening-closing jaw motion. They reflect the best solution obtained in this study and correspond to shapes and positions of disc illustrated in Fig. 1. The blue (respectively red) continuous line represents the right (respectively left) condylar trajectory obtained by using the FEM. The blue (respectively red) dotted line represents the experimental trajectory of the same condyle at the same coordinate system. Results from the FEM are close to the experimental data and validate discs’ geometries and positions. Another way of verifying the quality of the obtained solution could be done by analysing the contact between discs and surrounding bones. The MSC MARC enables the visualization of contact status. The contact status, as all mechanical fields such as stresses or strains, evolves during the motion. The results presented below were exploited for the final opening of the jaw corresponding to 22 mm inter-incisal space. Figure 6 illustrates the contact status. Red zones indicate the part of the discs in contact with fossa (cranial view) or condyles (caudal view). The areas of contact localization are not symmetric (left and right discs) and are different on cranial and caudal faces. The cranial face of the right disc is in contact with the fossa on the lateral side while the contact between the left disc and the fossa is on the posterior area. The contact between right disc and condyle is situated in the middle of the disc when for the left pair this contact is experienced rather on posterior area. The size of the contact areas is relatively limited indicating the low contact forces transmitted by the discs. The evolution of contact normal forces in the TMJ

Fig. 5 Condyle trajectories in the case of a medium opening-closing jaw motion

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Fig. 6 Contact zone on the TMJ discs during the final medium opening

is illustrated in Fig. 7. This evolution is drawn in function of the condyles antero-posterior movement. Right condyle (dotted line) demonstrates higher motion magnitude than the left one (continuous line). The maximal antero-posterior displacements are of about 6.4 mm and 5.1 mm for the right and left condyles, respectively. Maximal contact normal force was reached at the maximum opening. Similar maximal values of this force were obtained for both discs equal to 6.39 N and 6.61 N, respectively, on the right and left one. Figures 5 and 7 indicate that condyles did not come back to their initial positions and are submitted to some residual contact forces of about 1.2 N at the end of the opening-closing loop. Since during the motion discs are compressed between the condyles and fossa, the minimal eigen, or principal, stress σIII values developed in the discs are analysed

Fig. 7 Condylar contact forces evolution as a function of the condylar anterior displacement

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Fig. 8 Fields of minimal eigen stress σIII on discs for 22 mm inter-incisal space

here. These stresses are expressed in Pa. Fig. 8 shows a comparison between the right and left sides. Obviously, the contact areas identified above are submitted to the most intense compression. It can be observed that the stress concentration on the right disc is located on its lateral part while the maximum stress concentration appeared on the posterior location of the left disc. The value of the minimal principal stress exceeds locally −0.9 MPa on both discs and its mean value on the contact zones was evaluated to be −0.15 MPa.

3.2

Immediate Clenching Simulation

Figure 2, comparing the finite element model and dental plaster mould occlusions, testifies the correctly reproduced occlusal scheme. Four anatomic occlusal points were detected with the finite element simulation; one on the second right molar, one on the left canine, one on the second left premolar and one on the second left molar. The elevating muscles of the model were activated to reproduce a typical normal clenching force observed during bruxism. The evolution of this force in function of time is illustrated in Fig. 9. Also, the overloading zone proposed by Nishigawa et al. [23] is indicated in this figure. This zone is defined by maximum or threshold force of 420 N.

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Fig. 9 Occlusal force evolution during clenching

Fig. 10 Evolution of condylar contact normal forces during clenching

The evolution of the corresponding condylar contact forces is presented in Fig. 10 only for normal load zone. It can be observed that the forces grow linearly and quite symmetrically during the clenching. The maximum contact forces rise up to 88.8 N on the right condyle and 73.1 N on the left one. During the clenching process, the sum of these forces represents approximately 40 % of the clenching force. These important forces are transmitted through the disc soft tissue to the fossa bone. To estimate the risk of mechanical damage of the discs, the contact areas and stress state are analysed below for the maximal admitted clenching force of 420 N. According to Fig. 11, the contact areas on the cranial and caudal faces of the discs are more pronounced during the bruxism than during the opening-closing cycle.

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Fig. 11 Contact areas on discs at the maximal clenching state

Fig. 12 Minimal principal value of stresses on discs during the maximum clenching state

These contact areas are quite similar on both discs. However, the contact of the right disc is mainly located on its central part while that of the left one is slightly shifted in posterior direction. The surfaces of the contact areas were estimated to be 38 and 100 mm2, respectively, on the left and right cranial faces and to 35 and

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29

54 mm2 on the left and right caudal faces. The values of the contact forces and the contact area surfaces enable calculation of the mean contact pressure values on the cranial and caudal faces of the discs. They are equal to: – 0.89 and 1.04 MPa for the right disc on the cranial and caudal faces, respectively. – 1.92 and 2.09 MPa for the left disc on the cranial and caudal faces, respectively. The field of eigen stress σIII exerted in the discs is illustrated in Fig. 12. The most important compressive stress is concentrated in contact areas. Locally its value can be lower than −8 MPa for both discs on cranial and caudal sides. The mean values of this stress on contact areas are comparable with the mean contact pressures presented above.

4 Discussion The use of the finite element method for simulation of the jaw motion driven by muscular actions leads to very realistic models contrarily to the frequently presented simulations driven by the imposed mandibular displacement or force vectors. Even if the selected volunteer was a healthy case, the bone structures and mandible placement with respect to the maxillary appeared to be asymmetrical. Different initial locations and shapes of the TMJ discs reflected this asymmetry. These parameters play a crucial role on the disc contact area and contact forces during the motion and particularly for the final jaw medium opening state. In their study, Tanaka et al. [3] explained that the anterior disc dislocation has an influence on the load level transmitted by the disc. Here, for the same reason, the contact areas and pressures were found different on the left and right discs because of the differences evoked above. Nevertheless, Fig. 7 shows that these forces remain globally balanced during the all opening-closing motion, as expected for a healthy person without TMJ trouble. The residual contact forces and displacements obtained at the end of the simulated motion indicate that more than one cycle is necessary to stabilize the opening-closing loop. This fact is well confirmed experimentally [22]. The contact areas on discs obtained for the clenching load are pretty similar. In the literature [8], contact zones appeared generally on the middle part of the disc since the discs are usually constructed in occlusal position, i.e. with teeth in contact [7]. In our study, these zones are slightly posteriorly displaced. This is probably due to, the initial disc position and shape, which have been defined in rest position (with jaw slightly opened) and muscular actions were used to bring the mandible in occlusion. Significant condylar contact forces were obtained during the clenching simulation (about 80 N per disc). These forces represent approximately 40 % of the clenching load. Such a high level of compressive force can be exploited to explain the troubles and pains due to the clenching. No studies were found in the open literature analysing the contact forces on TMJ discs. Generally, the authors discuss the stress distribution in discs; see for instance Aoun et al. [13], Savoldelli et al. [8].

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In accordance with Aoun’s results, maximal compressive stress is located on the caudal face of both discs. However, in our case, the magnitude of this stress is approximately five times lower than in case of Aoun’s results. This difference is mainly due to the muscular action introduced and that is higher in Aoun’s study than in this work. At the maximum clenching, forces on the elevator muscles are 55 N and 290 N, respectively, in this study and Aoun et al. [13] simulation.

5 Conclusions and Prospects The volunteer treated in this study was identified as a person with symmetric condylar motion. However, the CT scanning revealed slight differences in morphology of the left and right TMJs. Consequently, the whole mandible with two discs and fossa was reconstructed and meshed. The general-purpose finite element software, such as ABAQUS, MARC or ANSYS, does not have the ability to model the muscle’s actions. An original method of muscular activation was developed and used to simulate two load cases, namely moderate jaw opening-closing cycle and teeth clenching. The lack of data concerning the geometry and position of TMJ discs led to an optimization process based on the well-established method of the mechatronics design. In particular, the latter concerns one technique of the mechatronic design, called “experimentally supported virtual prototyping”. Indeed, the experimentally determined condyle trajectories were used as a selection tool. The exploitation of this method enabled the optimal choice of these parameters, different for the left and right discs. The obtained model allowed reproducing accurate anatomic mandible trajectories and also a physical occlusion. Values of forces determined on the basis of a TMJ model are consistent with literature data. The results of simulations allowed for: – further improvement of the driving method and its evaluation, – the evaluation of improvement of the driving method results prediction precision. In the future works, the model can be improved by a stronger stabilization of the discs by inserting a 3D model of TMJ capsules, instead of the 1D representation of these organs. Moreover, the “experimentally supported virtual prototyping” procedure was applied in a quasi-manual manner. This task can be highly improved and accelerated basing on the following general indications. For the purpose of online computer simulations, we envisage to prototype some authorial computer programs, written in a high-level programming language (e.g. Fortran, C, C++), and being supported by commercial software used. Promising results of the simulation shall allow developing and implementing the driving method on the target system

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(i.e. the examined patient), in which all components are real. Research on the target system will enable increasing: – the performance of the driving method of the mandible motion by the method of muscular contraction, on selected volunteer, – the assessment of efficiency of the driving method during real performance of the TMJ. It is expected that the obtained results will confirm performances of the driving method in case of one TMJ of the volunteer. The solution enables the monitoring of the TMJ behaviour during routine functioning without the need for interference with the structure of the body, but only by adapting a portable bench on the mandible. Thanks to the above, the proposed solution will entail lower price in comparison with the apparatus investment.

References 1. Kamina, P.: Anatomie clinique. Tome 2. Maloine, Paris (2006) 2. Tanaka, E., Tanne, K., Sakuda, M.: A three-dimensional finite element model of the mandible including the TMJ and its application to stress analysis in the TMJ during clenching. Med. Eng. Phys. 16(4), 316–322 (1994) 3. Tanaka, E., del Pozo, R., Tanaka, M., Asai, D., Hirose, M., Iwabe, T., Tanne, K.: Three-dimensional finite element analysis of human temporomandibular joint with and without disc displacement during jaw opening. Med. Eng. Phys. 26(6), 503–511 (2004) 4. Tanaka, E., Hirose, M., Koolstra, J.H., van Eijden, T.M.G.J., Iwabuchi, Y., Fujita, R., Tanaka, M., Tanne, K.: Modeling of the effect of friction in the temporomandibular joint on displacement of its disc during prolonged clenching. J. Oral Maxillofac. Surg. 66(3), 462–468 (2008) 5. Beek, M., Koolstra, J.H., van Ruijven, L.J., van Eijden, T.M.G.J.: Three-dimensional finite element analysis of the human temporomandibular joint disc. J. Biomech. 33(3), 307–316 (2000) 6. Hirose, M., Tanaka, E., Tanaka, M., Fujita, R., Kuroda, Y., Yamano, E., van Eijden, T.M.G.J., Tanne, K.: Three-dimensional finite-element model of the human temporomandibular joint disc during prolonged clenching. Eur. J. Oral Sci. 114(5), 441–448 (2006) 7. Mori, H., Horiuchi, S., Nishimura, S., Nikawa, H., Murayama, T., Ueda, K., Ogawa, D., Kuroda, S., Kawano, F., Naito, H., Tanaka, M., Koolstra, J.H., Tanaka, E.: Three-dimensional finite element analysis of cartilaginous tissues in human temporomandibular joint during prolonged clenching. Arch. Oral Biol. 55(11), 879–886 (2010) 8. Savoldelli, C., Bouchard, P.-O., Loudad, R., Baque, P., Tillier, Y.: Stress distribution in the temporo-mandibular joint discs during jaw closing: a high-resolution three-dimensional finite-element model analysis. Surg. Radiol. Anat. 34(5), 405–413 (2012) 9. Chen, J., Akyuz, U., Xu, L., Pidaparti, R.M.V.: Stress analysis of the human temporomandibular joint. Med. Eng. Phys. 20(8), 565–572 (1998) 10. Tanaka, E., Rodrigo, D.P., Tanaka, M., Kawaguchi, A., Shibazaki, T., Tanne, K.: Stress analysis in the TMJ during jaw opening by use of a three-dimensional finite element model based on magnetic resonance images. Int. J. Oral. Maxillofac. Surg. 30(5), 421–430 (2001) 11. Athanasiou, K.A., Almarza, A.A., Detamore, M.S., Kalpakci, K.N.: Tissue engineering of temporomandibular joint cartilage. Morgan and Claypool Publishers, San Rafael (2009)

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12. Pérez del Palomar, A., Doblaré, M.: An accurate simulation model of anteriorly displaced TMJ discs with and without reduction. Med. Eng. Phys. 29(2), 216–226 (2007) 13. Aoun, M., Mesnard, M., Monède-Hocquard, L., Ramos, A.: Stress analysis of temporomandibular joint disc during maintained clenching using a viscohyperelastic finite element model. J. Oral Maxillofac. Surg. 72(6), 1070–1077 (2014) 14. Hill, A.V.: The heat of shortening and the dynamic constants of muscle. Proc. R. Soc. Lond. B Biol. Sci. 126(843), 136–195 (1938) 15. Zajac, F.E.: Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Crit. Rev. Biomed. Eng. 17(4), 359–410 (1989) 16. Hehenberger, P., Poltschak, F., Zeman, K., Amrhein, W.: Hierarchical design models in the mechatronic product development process of synchronous machines. Mechatronics 20, 864– 875 (2010) 17. Furtanato, A., Ascari, A.: The virtual design of machining centers for HSM: towards new integrated tools. Mechatronics 23, 264–278 (2013) 18. Kaliński, K.J., Buchholz, C.: Mechatronic design of strongly nonlinear systems on a basis of three wheeled mobile platform. Mech. Syst. Signal Process 52–53, 700–721 (2015) 19. Alvarez, D.A., Brosses, E.S., Mommers, X., Bonnet, A.S., Zwetyenga, N., Lipinski, P.: Asymmetric kinematics and dynamics of the temporomandibular joint without pain: a case report. Comput. Methods Biomech. Biomed. Engin. 16, 297–299 (2013) 20. Bumann, A., Lotzmann, U.: Function-oriented Evaluation of Craniomandibular Diseases. Thieme, Stuttgart (2002) 21. Beek, M., Koolstra, J.H., van Eijden, T.M.G.J.: Human temporomandibular joint disc cartilage as a poroelastic material. Clin. Biomech. Bristol Avon 18(1), 69–76 (2003) 22. Alvarez, D.A.: Réflexions sur la reconstruction prothétique de l’Articulation Temporo-Mandibulaire (ATM) à travers une étude biomécanique comparative entre sujets asymptomatique et pathologique. PhD thesis, Université de Lorraine, Metz (2014) 23. Nishigawa, K., Bando, E., Nakano, M.: Quantitative study of bite force during sleep associated bruxism. J. Oral Rehabil. 28(5), 485–491 (2001)

Requirements for Tire Models of the Lightweight Wheeled Mobile Robots Przemysław Dąbek and Maciej Trojnacki

Abstract Tire models for vehicle dynamics studies have been developed for many years to suit the needs of automobiles and the automotive industry. Recently, the growing use of advanced simulation techniques in design of wheeled mobile robots calls for analysis of the possibility to use the existing automotive tire models in the wheeled mobile robots dynamics studies. This analysis is especially important in the case of the skid-steered lightweight mobile robots, which are very common type of design, but exhibit many differences in the tire–ground system as compared to a typical car. In the present work the differences between lightweight wheeled robots and automobiles are examined in the following areas: tires, environment, maneuvers, ways of control, and vehicle systems. The influence of the found differences on the tire–ground system is examined in detail. Finally, the requirements for the tire models of the lightweight wheeled mobile robots are formulated with emphasis on the requirements different than those for tire models of the automobiles.




Keywords Wheeled mobile robot Automobile model Comparative analysis Requirements










Vehicle dynamics




Tire

1 Introduction In the process of design of wheeled mobile robots, the modern methods of computer-aided engineering analysis (CAE) become more widespread and more important. This design approach is promoted in the 2014–2020 strategic research agenda proposed by the public private partnership for robotics in Europe—SPARC [1] under the topic of “Improving Designs and Systems”. P. Dąbek (&)
M. Trojnacki Industrial Research Institute for Automation and Measurements PIAP, Warsaw, Poland e-mail: [email protected] M. Trojnacki e-mail: [email protected] © Springer International Publishing Switzerland 2016 J. Awrejcewicz et al. (eds.), Mechatronics: Ideas, Challenges, Solutions and Applications, Advances in Intelligent Systems and Computing 414, DOI 10.1007/978-3-319-26886-6_3

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Computer-aided engineering methods enable development of virtual prototypes of machines and investigation of their dynamic properties in advance of building physical prototypes. The virtual prototypes of mobile robots are based on mathematical models of dynamics, in which the key element is the model describing the effector interaction with environment. The purpose of this model is determination of forces and moments of force, which besides the gravity force, virtually alone determine motion of a robot. In case of the wheeled mobile robots, the role of effectors is played by wheels, most often equipped with rubber tires which interact with grounds of various properties. So far, the problems of modeling of the tire–ground system were tackled mainly from the point of view of requirements of automotive vehicles, which over the years resulted in development of multiple tire models with diverse capabilities [2]. However, it turns out that the wheeled mobile robots, especially lightweight robots, differ significantly from automotive vehicles in terms of applications, maneuvers performed, types of ground, vehicle design, and parameters of tires. It seems that there is very little work done so far in the field of modeling of tire–road interaction for lightweight wheeled robots. This gap is sometimes noticed by researchers as in [3], where authors observe that tire–terrain models for lightweight robots on rigid terrain are not as readily available as models for heavier vehicles. Several studies concern wheel–terrain interaction of planetary rovers, where a rigid wheel is considered [4] or a flexible wheel of special design made primarily of metal [5]. Aim of the present work is to determine specific requirements with respect to tire models of the lightweight wheeled mobile robots. This is the starting point for analysis of the existing automotive tire models from the point of view of their application in simulation studies of the lightweight wheeled mobile robots, which is planned by the authors.

2 Scope and Method of Analysis In the present work requirements for tire models of the wheeled mobile robots will be determined as a result of the analysis carried out according to the procedure outlined below. Step 1. Analysis of differences between automobiles (especially passenger cars) and lightweight wheeled mobile robots in the following areas which affect the tire–ground system: • • • • • •

tires, environment, vehicle systems, ways of control, maneuvers, allowable extreme vehicle body motions.

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The first step of the analysis is based on the literature studies, documentation of the Proteus Project [6], and consultations with the specialists from Industrial Research Institute for Automation and Measurements PIAP. Step 2. Analysis of the influence of the differences between automobiles and lightweight wheeled mobile robots identified in Step 1 on elements of the tire–ground system: • • • •

wheel hub, tire and its components, tire–ground contact, ground surface.

Step 3 Selection of those phenomena and properties of the tire–ground system which specifically pertain to the wheeled robots, and may be less relevant in case of the automobiles. In the present work, we especially seek those tire model requirements which are different than requirements for the automotive tire models. Those requirements, unique for the tire models of mobile robots, can be the basis for evaluation of the existing tire models and as a result help identify weak spots and assess if the existing tire models satisfy the needs of the mobile robots or maybe some developments are necessary. The reason for comparing the regular automobiles with the wheeled mobile robots follows from the fact that vast majority of the existing tire models was developed to satisfy requirements of the regular automobiles. Those tire models are readily available in the literature, and are used by researchers in the mobile robots community in simple simulation scenarios. The scope of the analysis in this work is limited to the rigid grounds, and the focus is on the lightweight wheeled mobile robots.

3 Tire Modeling Background In the present work the term “tire model” refers to a component of the multibody model of a full vehicle, which generates forces and moments of force in the assumed point of connection with the vehicle body (a wheel hub) depending on the operating conditions of the tire, including kinematic state of the tire and properties of the tire and the ground. This kind of “tire model” finds its application in studies of dynamics of a vehicle for the purpose of synthesis of a control system [7] or optimization of design [8]. The forces and moments of force, as well as principal kinematic quantities, typically studied in the vehicle dynamics, are listed below and shown in Fig. 1: α γ

slip angle, camber angle,

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Fig. 1 Tire coordinate systems

W

Fx Fy W Fz W Mx W My W Mz W

longitudinal tire–ground reaction force, lateral tire–ground reaction force, normal tire–ground reaction force, overturning moment, rolling resistance moment, (self-)aligning moment.

Conventionally, tire forces and moments of force depend on the kinematic state of the wheel expressed by slip ratio (or longitudinal slip) λ [2]: H

k¼

re X

vx Hv

ð1Þ

x

and lateral slip tan(α): H

tan a ¼

vy

Hv

ð2Þ

x

where Hvx and Hvy—respectively, longitudinal and lateral components of velocity of the wheel center, re—effective rolling radius, Ω—angular velocity of spin of the wheel. In case of typical automotive tires, the dependency of longitudinal force WFx on slip ratio λ has the form depicted in Fig. 2. The curve can be characterized by its initial slope, called longitudinal slip stiffness, the value of peak force at a certain slip ratio of about 10–20 %, and the value of sliding force at 100 % slip ratio.

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Fig. 2 Example of force–slip ratio characteristic

It should be emphasized that only the slip ratio equal to 100 % describes the state of full sliding of the tire tread on the road surface, and slip ratios over 0 % and below 100 % (excluding the range limits) describe the situation where part of the tire contact patch does not slide on the road (i.e., adheres to the road), and the remaining part does slide. In particular, for the small slip ratios, of the order of a few percent, the sliding is negligible. In case of typical automotive tires, the dependency of lateral force WFy on the slip angle α has similar (but not identical) nonlinear shape as the WFx(λ) dependency. Also in cases of simultaneous wheel driving/braking and turning, the shape of WFx(λ) dependency is strongly affected by the value of α, and the shape of the W Fy(α) by the value of λ; this phenomenon is associated with limited tire–ground friction force and its distribution between WFx and WFy force components. Modeling of tires for the purpose of automobile dynamics studies started in the first half of the twentieth century, and over the years resulted in several tens of automotive tire models from various authors. Many of those models are described in [2]. According to [9], the existing automotive tire models can be broadly classified into three–four categories shown in Fig. 3. The models are divided into categories according to growing complexity of formulation (e.g., number of model elements) and the frequency spectrum of input/output signals covered by the model. The first category is comprised of the models based on mathematical expressions which best fit the measurement results of real tires, e.g., a polynomial or the Pacejka model [10]. The second and third categories include models formulated based on the available knowledge of the tire, but they differ as to the complexity (analytical models). An example of the model from the second category is the Dugoff model [11], and from the third category the FTire model [12]. The fourth category comprises accurate finite element models, which, however, rarely can be used for vehicle dynamics studies due to the computational complexity. An example of this kind of model can be work [13].

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Fig. 3 Classification of the automotive tire models, following Ammon [9]

4 Analysis of Differences Between Lightweight Wheeled Robots and Automobiles In the present section discussion of differences between automobiles and lightweight wheeled mobile robots in the aspects which affect the tire–ground system is carried out, which comprises Step 1 of the analysis.

4.1

Tires

In Fig. 4 are shown examples of two types of tires used with the PIAP SCOUT lightweight robot produced in the Industrial Research Institute for Automation and Measurements PIAP [14]. Comparison of the most important mechanical design properties of robot tires with tires of other categories of vehicles is shown in Table 1. A reference custom-made robot tire (Fig. 4b), the automotive off-road tire (Fig. 5a), and the tractor tire (Fig. 5b) were chosen for comparison. The SUV tire and tractor tire were chosen because they have tread of relatively large depth. It is evident that rubber tires of the lightweight robots have several times smaller unloaded diameter than the automotive/tractor tires. Robot tires are usually Fig. 4 Tires of the lightweight PIAP SCOUT wheeled mobile robot: a 2009 version, b 2014 version

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39

Table 1 Comparison of robot tires with tires of vehicles of other categories Dimensions Width (mm) Unloaded radius UR (mm) Sidewall height (mm) Tread depth TD (mm) TD/UR ratio Construction Filling Material a 31 × 10.5 R15 SUV off-road

(A) Car tirea

(B) Tractor tireb

(C) Robot tire

272 395 267 15.2 4%

295 546 369 37 6.8 %

65 97 32 (outside: 42) 6.2 6.5 %

Pressurized gas Pressurized gas Foam (polyurethane) Composite Composite Synthetic rubber—pure tire [15], b11.2 R24 standard agricultural tire [16]

Fig. 5 Examples of off-road tires for conventional vehicles: a Open Country M/T sport utility vehicle tire—Toyo [15], b Agribib tractor Tire—Michelin [16] (sizes are not to scale)

non-pneumatic, that is, they are not filled with the gas under pressure, but contain a foam insert (Figs. 6 and 7b). Also the rubber shell of the robot tires is often not reinforced, whereas the automotive/tractor tires contain carcass and belt made of materials different than rubber. In case when robot tires are equipped with block tread (usually they are, because block tread improves obstacle climbing capabilities), the ratio of the block tread depth to the tire unloaded radius (TD/UR) is usually greater than in SUV tires, but similar as in tractor tires.

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Fig. 6 Cross section of a non-pneumatic tire of the type used in the lightweight wheeled mobile robots (source of the background image: Pro-Line racing [17])

Fig. 7 Components of the robot wheel: a wheel hub, b foam insert (visible gaps after material samples cut out for testing)

It should be noted that various very diverse tread patterns can be used with robot tires, including patterns typical for passenger car tires, SUV tires, and agricultural tires. In case of the robot tires interesting is also the asymmetric wheel hub (Fig. 7a), which is designed for tires with one sidewall of height smaller than another.

4.2

Environment

In case of automobiles their intended working environments are the outdoor environments, especially the engineered roads, hence their tires are optimized to operate on asphalt or concrete pavements.

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Lightweight wheeled mobile robots can operate in various outdoor environments, in urban and natural scenarios, in the environmental conditions similar to the automobiles. Additionally, by advantage of their small size they can operate inside buildings, especially in the areas designed for people, like office spaces or industrial passages. In Table 2 are listed some typical materials with which the rubber tire of a robot interacts by friction during normal operation. In Table 3 are shown typical shapes of the ground encountered by a wheeled mobile robot during normal operation. The shape of the ground affects the conditions of contact between the tire and the ground surface. The lightweight mobile robots are often used for reconnaissance and inspection tasks, so they must be able to operate on a broad range of grounds. Steel gratings are commonly used in the industrial environments for catwalks and decks. Their contact configurations with tires having block tread can be especially complex. The “bumps” category may include, for example, curbstones and doorsteps. Sometimes a wheeled robot must operate on extremely irregular terrain like debris, however for this kind of terrain other means of locomotion like legs might be better suited. Stairs deserve special attention because they are frequently encountered during robot inspection missions inside buildings, but are very uncommon for automobiles.

Table 2 Automobiles and lightweight wheeled robot tires interaction with materials of hard ground surfaces Material

Localization

Cars

Robots

Asphalt Concrete Polished concrete Ceramics (tiles) PVC (PVC flooring) Olefin fiber (carpet flooring) Lacquer coated wood (parquet)

Outdoor Outdoor Indoor Indoor Indoor Indoor Indoor

Typical Typical Untypical Untypical Untypical Untypical Untypical

Typical Typical Typical Typical Typical Typical Typical

Table 3 Ground shapes for motion of automobiles and lightweight wheeled robots Ground shape

Cars

Robots

Even flat surface Grating (e.g., steel grating for industrial catwalks [18]) Bump (even flat surface with a bump) Pothole (even flat surface with a hole) Stairs Irregular surface (e.g., debris)

Typical Untypical Typical Typical Untypical Untypical

Typical Typical Typical Untypical Typical Typical

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P. Dąbek and M. Trojnacki

Vehicle Systems

Table 4 presents differences between cars and lightweight robots in the vehicle systems which affect tire–ground working conditions, i.e., suspension, steering, and power train. Car suspension systems are typically equipped with springs and shock absorbers, which are not typical for the small robots. The small robots usually have suspensions with no damping capabilities. Often the axle is rigidly connected to the body without any possibility of travel. There is a big difference in the suspended mass, which is 1–2 orders of magnitude larger in case of cars than in case of small robots. This translates to smaller vertical loads of wheels in case of small robots which are about 100 N per wheel, as compared to several thousand Newtons per wheel (about 2300 N in case of cars from the European Commission A-segment, e.g., Toyota Aygo, Fiat 500). The steering systems of cars and robots differ in the number of steered wheels and the range of steering of the individual wheel. In the case of lightweight wheeled robots the most popular steering principle at the moment is the differential steering, where turning is achieved by means of a difference of speeds of wheels at the left- and right-hand side of a vehicle. This kind of design allows individual wheels not to turn with respect to vehicle body (non-steered wheels). It also permits to achieve zero-radius turns, but is not energy efficient in case of multiple non-steered wheel designs due to inherent large wheel slip during turns.

Table 4 Design parameters of cars and robots Cars

Lightweight robots

Suspension system 940 25 Body massa (kg) Rigid Untypical Typical Flexible Typical Untypical Steering system Differential steering Untypical Typical Ackermann steering Typical Untypical All-wheel steering Untypical Typical Power train and drive system Internal combustion engine Typical Untypical Electric motor Untypical Typical 51 1 Engine/motor total powera (kW) Driving/braking force at wheela (kN) 2–4 0.1 154 30 Top angular velocity of wheela (rad/s) Top speeda (km/h) 160 10 a Representative data for robots: PIAP SCOUT lightweight mobile robot [14], and for A-segment cars: Toyota Aygo [19]

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Another possibility is the steering system typical for automobiles, i.e., Ackermann steering, where individual wheels turn in relatively narrow limits with respect to vehicle body depending on the desired radius of the turn. This design is rather rare in case of wheeled robots at the moment. Common solutions of this kind of steering do not allow zero turning radius. The third possibility is all-wheel steering where individual wheels turn in wide limits with respect to vehicle body (e.g., ±90°). This design is popular in the planetary rovers, because it enables turning with zero turn radius, but is more energy efficient than differential steering with multiple wheels (skid-steering). Lightweight wheeled mobile robots are commonly powered by DC electric motors (one motor per wheel is common), in contrast to internal combustion engines used in the automobiles (one engine per whole vehicle with distribution of mechanical power to driving wheels is common). The lightweight wheeled robots require relatively low power to drive and also range between refill of energy storage is not so critical as in case of cars, so it is possible to use electric motors only and fulfill the design requirements (this is usually not possible in case of cars). As a rule each driving wheel has its dedicated electric motor, so the drivetrain system of a robot requires much simpler mechanical design than that of a car.

4.4

Ways of Control

Table 5 compares ways of motion control of robots and automobiles. In the basic (traditional) mode, both robots and cars are controlled by a human, who commands the desired motion by means of appropriate human–machine interface, i.e., steering wheel and pedals in case of a car and elements of the control panel in case of a robot. The fundamental difference lies in the position of the human with respect to vehicle. In the case of mobile robots operator is not on-board of the vehicle, and sometimes cannot even directly observe the vehicle, but must issue commands based on picture from the onboard cameras. The absence of a human on-board has profound influence on robot design starting from applications (dangerous and tedious tasks), through size and mass, to suspension system and robot body design. With advancement of technology, mobile robots are equipped with more and more complex control systems which make the work of a human operator easier in the semiautonomy mode (operator has to issue high level commands instead of manually setting motion of individual joints). From the point of view of cybernetics

Table 5 Ways of control of cars and mobile robots

Operator placement Control Manual (Semi-)autonomous

Cars

Robots

On-board

Off-board

Typical Possible

Typical Typical

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P. Dąbek and M. Trojnacki

and robotics, the ultimate design goal is to reduce the need of human supervision and control of the robot to the minimum, so that robot can perform tasks autonomously, for example, search debris and maybe rescue casualties by itself or call the rescue team to help if necessary. By having no people on-board and without need of human participation in the low-level control loop, the better performance of control can be achieved, increasing speed and accuracy of maneuvers performed by the robot to the level restricted by machine limitations rather than by human perception or motor skills.

4.5

Maneuvers

In Table 6 are summarized basic maneuvers that can be performed by automobiles and wheeled robots. Possibility of realization of a particular maneuver depends on design of the steering system of a vehicle, exclusive of the last maneuver listed in the table which is strictly associated with overall design and application of the robot. Maneuvers are commanded or initiated by the operator (the driver), or by a vehicle itself in case of autonomous vehicles. Crabbing is the kind of straight-line motion that takes place not in the longitudinal direction of a vehicle—it requires turning all wheels through the same angle, in particular by 90°, and is possible only when the vehicle is equipped with the all-wheel steering system. This kind of maneuver is generally not implemented in the contemporary automobiles, but it is usually present in planetary rovers. Ackermann turns are typical for automobiles and are characterized by turning radius greater than zero—in practical applications greater than certain minimum turning radius depending on the steering system design and vehicle wheelbase. A 90° turn is typical for wheeled robots which have the differential steering system. This kind of turn is characterized by a very small turning radius (close to zero, because sideways skid of the wheels is possible). The single one maneuver which differentiates automobiles (Ackermann steering) from wheeled robots (differential or all-wheel steering) is the turn with zero radius (or the pivot turn).

Table 6 Maneuvers of cars and robots Forward straight-line motion (regular) Sideways straight-line motion (crabbing) Ackermann turn (regular turning radius) 90° turn (very small turning radius) Pivot turn (zero turning radius) Hand throw/high-profile jump

Cars

Robots

Typical Untypical Typical Untypical Untypical Impossible

Typical Typical Untypical Typical Typical Possible

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45

The last-mentioned maneuver, that is hand throw, concerns a robot particularly designed to allow such action and to withstand the associated conditions [14]. The human operator picks up the robot using the handle on the side of the robot body and rotates himself to pass velocity to the robot, then releases it (this can be seen, e.g., in the movie [20] at 5:26 min.). The robot rotates during flight and then hits the ground, usually with one of the wheels. Another example of maneuver from this category is 1–8 m high jump performed by the Sand Flea robot of Boston Dynamics using an integrated piston actuator and onboard fuel supply [21]. Jump trajectory can be precisely controlled by changeable initial conditions and stabilization during the flight phase.

4.6

Allowable Extreme Vehicle Body Motions

During operation in real conditions, vehicle body may be subjected to large roll and pitch angles, and also tire impacts with the ground. Table 7 gives some examples of the situations, where vehicle body undergoes high to extreme roll and pitch rotation. In case of regular straight-line motion with significant speed on hilly terrain, a condition may occur when the automobile hops (looses contact of wheels with the ground), flies for a very short period of time after which wheels come to contact with the ground again. During short period of the flight, the vehicle center of mass moves along a parabolic path, and angles describing orientation of the body change only by small values. This condition is generally allowable by all automobile designs and most robots. In case when the jump has higher profile and lasts longer, vehicle body orientation may change significantly during the phase of flight resulting in impact which is damaging to the vehicle body. This situation can be sometimes seen during automobile rally championships, where the vehicle is seriously damaged after ground impact. In case of lightweight inspection wheeled mobile robots, like already mentioned PIAP SCOUT [14], the robot body by design may undergo large roll and pitch rotations without damage—for example, the ground impact after being thrown by the operator described earlier. Particularly interesting is robot immunity to rollover condition, that is, the robot body can rotate upside down about roll axis, and continue motion with no influence on its health. Table 7 Possible extreme body motions of cars and robots Low profile parabolic flight and moderate ground impact High-profile parabolic flight and severe ground impact Rollover

Cars

Robots

Allowable Not allowable Not allowable

Allowable Allowable Allowable

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5 Requirements for Tire Models of the Lightweight Wheeled Mobile Robots The presented differences between automobiles and lightweight wheeled mobile robots influence the vehicle tire–ground system in certain ways, which are not described here in detail due to space limitations. Below are presented only those findings of the analysis which are particular to the wheeled robots, especially lightweight wheeled robots. Those findings regarding tire–ground system which are common for wheeled robots and automobiles are not mentioned. The findings are formulated in the form of requirements concerning modeling and identification of the tire–ground system. One should note that in order to fully take advantage of the benefits offered by vehicle dynamics simulation of wheeled robots, a comprehensive tire model should satisfy the requirements formulated in the present section and summarized in Table 8. Table 8 Requirements specific for lightweight wheeled mobile robots, with indicated conditions when the requirement becomes important #

Requirement

Wheel hub kinematics 1 Modeling tire interaction at large slip angles (about 45°) and combined slip 2 Modeling tire interaction with emphasis on nonlinear effects Tire/ground contact 3 Modeling effects of large curvature of a small tire 4 Modeling tire shoulder and sidewall contact with the ground Ground surfaces 5 Modeling and characterization of indoor ground surfaces Tire structure design 6 Modeling tire sidewall including sidewall asymmetry 7 Modeling tire internal structure and interactions involving foam insert Tread design 8 Modeling tread flexibility and masses of tread blocks 9 Accurate modeling of tread shape including tread block sidewalls and tread pattern

Applicability conditions Steering Body system configuration

Tread

Relative importance

Skid-steering

Any

Any

High

Any

Any

Any

Moderate

Any

Any

Any

High

Any

Without manipulator

Any

Low

Any

Any

Any

High

Any

Any

Any

High

Any

Any

Any

High

Any

Any

Moderate

Any

Any

Block tread Block tread

High

Requirements for Tire Models …

5.1

47

Wheel Hub Kinematics

Requirement 1. The tire model should be accurate in the conditions of large slip angles α (about 45°) and combined slip. This requirement must be satisfied when the wheeled robot is skid-steered. In this case, during pivot turns, the robot wheel moves with approximately constant slip angle, whose value depends on robot chassis geometry, so it is a design constant. In many skid-steered robot designs the value of the angle α (Fig. 8) is about 45°. Robot tires work in the conditions of this slip angle during every pivot turn, so this is the frequently occurring condition. In contrast, automobile tires usually move with slip angles below 25°, and only occasionally reach higher values of slip angles [9]. It should be also emphasized that tires of skid-steered wheeled robots during turning always move in the condition of combined slip, that is, simultaneous longitudinal slip and lateral slip. Requirement 2. More emphasis should be put on nonlinear regions of force–slip (moment–slip) dependencies on the rigid grounds. This requirement follows from the fact that robot automatic controllers are able to utilize the friction potential existing on the ground to a larger extent than the human driver does. Realization of time-critical tasks will lead to necessity of taking advantage of the peak friction forces and possibly to explore opportunities offered by agility dynamics (controlled sliding) of the kind described in the work [22].

Fig. 8 Slip angle α of a skid-steered wheeled robot during pivot turn

48

5.2

P. Dąbek and M. Trojnacki

Tire-Ground Contact

Requirement 3. Effects of large circumferential curvature of a small-size tire should be considered in the tire model. With small tire radius, the curvature of the tire shell is relatively large, as compared with automotive tires. The large tire curvature affects the tire–ground contact conditions, the contact area being generally smaller. This leads to a situation where tire–ground contact on a rigid ground may reduce to a single tread block contact. Requirement 4. Contact of tire with rigid ground should be modeled also on tire shoulder and tire sidewall. Typically, the contact of tire with rigid grounds is restricted to the tread area. However, in case of lightweight wheeled robots without manipulator a situation of body rollover is a normal operating condition, allowed by design. Because tires are the most protruded elements of the robot body, during vehicle rollover the contact between tire and the ground occurs on the tread area, on tire shoulder and on tire sidewall.

5.3

Ground Surfaces

Requirement 5. Frictional interaction of rubber tire with ground surfaces typical for lightweight wheeled robots and nontypical for automobiles should be considered. A range of ground surfaces on which the robot usually moves, which are however not typical for automobile tires, can be indicated as in Table 2. This statement is especially true for ground surfaces found in spaces dedicated for humans, like offices. The parameters describing tire interaction with those surfaces like maximum and sliding friction coefficient, peak and sliding adhesion coefficient, coefficient of rolling resistance are usually not available in the literature.

5.4

Tire Structure Design

Requirement 6. Heights of tire sidewalls should be considered in tire modeling. Heights of tire sidewalls, together with tire width, are the basic geometric parameters which determine the shape of tire cross section. With known material properties of the tire structure including shell and internal filling, the cross-sectional shape determines tire stiffness and damping. Tire stiffness belongs to the key factors which influence the vehicle dynamics of automobiles. It should be emphasized, that in case of lightweight wheeled robot tires, the height of one sidewall can be different than the height of another one (Fig.7).

Requirements for Tire Models …

49

Requirement 7. Nontypical tire filling should be considered in tire model. Tire filling with foam inserts instead of typical gas under pressure, creates different conditions for tire structure deformation under load than in case of pneumatic tires. The influence of this nontypical tire structure on generated forces and moments of force should be analyzed in detail.

5.5

Tread Design

Requirement 8. Mass and flexibility of individual tire tread blocks should be included in the tire model. It is evident that relative depth of the tread blocks of the robot tires is greater than relative depth of tread blocks of automotive tire (Table 1). Individual tread blocks flexibility may influence the force and moment generated by the tire. This effect should be included in tire modeling and its importance should be investigated. Because of significant volume of tread blocks, the effect of masses of individual tread blocks on tire vibrations should be considered as well. Requirement 9. Tread pattern and shapes of individual tread blocks should be included in the tire model. Tire tread should be modeled at high level of detail in order to enable contact with ground surface not only on the external faces of tread blocks, but also on tread block side area. The geometry of individual tread blocks and their layout on the tire (i.e., tread pattern) should be modeled. Satisfaction of this requirement is necessary to adequately model robot tire interaction with various non-smooth, non-flat ground surfaces like stair steps or deck gratings, where gear interaction of tread with ground plays major role besides friction (Fig. 9). Fig. 9 Example of interaction of tire tread block with rigid obstacle—the tread block contacts obstacle with its side surface

50

5.6

P. Dąbek and M. Trojnacki

Required Empirical Data

There is a deficiency of empirical data characterizing the small tires form the point of view of vehicle dynamics. In order to carry out identification and verification/validation of tire models one would like to have at least the following dependencies describing tire forces and moments: normal force on normal tire deformation, longitudinal force on longitudinal tire deformation, lateral force on lateral tire deformation, longitudinal force on longitudinal slip (on various ground surfaces, especially indoor surfaces) including influence of the lateral slip (combined slip case), • lateral force on lateral slip, including influence of the longitudinal slip (combined slip case). • • • •

Attempts to obtain parameters of small robotic tires on the basis of automotive tire data using the scaling method were made for tire rotational stiffness and damping by one of the authors [23], where the conclusion was that the method of scaling may not be the most appropriate for such tires.

6 Conclusion A comparative analysis of properties of lightweight wheeled mobile robots and automobiles from the point of view of their influence on the tire–ground system was carried out. The differences found were the basis for formulation of requirements that tire models of wheeled robots must satisfy in order to get the most of the wheeled robot dynamics studies by means of computer simulation. The existing tire models, developed for the needs of the automotive industry, should be tested against those requirements to find out if they are suitable for mobile robot dynamics analysis. Research like that is planned by the authors. Verification and validation of the tire models is not possible without empirical data of the real tire. Gathering of required empirical data concerning robot tires is planned by the authors. Acknowledgments The work has been realized as a part of the project entitled “Dynamics modeling of four-wheeled mobile robot and tracking control of its motion with limitation of wheels slip.” The project is financed from the means of National Science Centre of Poland granted on the basis of decision number DEC-2011/03/B/ST7/02532.

Requirements for Tire Models …

51

References 1. SPARC: Strategic Research Agenda For Robotics in Europe. 2014–2020. http://www.eurobotics.net/cms/upload/PPP/SRA2020_SPARC.pdf 2. Pacejka, H.B.: Tire and Vehicle Dynamics. Elsevier, New York (2012) 3. Ray, L.R., Brande, D.C., Lever, J.H.: Estimation of net traction for differential-steered wheeled robots. J. Terramech. 46, 75–87 (2009) 4. Kobayashi, T., Fujiwara, Y., Yamakawa, J., Yasufuku, N., Omine, K.: Mobility performance of a rigid wheel in low gravity environments. J Terramech. 47, 261–274 (2010) 5. Heverly, M., Matthews, J., Lin, J., Fuller, D., Maimone, M., Biesiadecki, J., Leichty, J.: Traverse performance characterization for the Mars Science Laboratory rover. J. Field Robotics. 30, 835–846 (2013) 6. Proteus—Integrated mobile system for supporting anti-terrorist and crisis management operations. http://www.projektproteus.pl/en/ 7. Hendzel, Z., Trojnacki, M.: Neural network control of a four-wheeled mobile robot subject to wheel slip. In: Awrejcewicz, J., Szewczyk, R., Trojnacki, M., Kaliczyńska, M. (eds.) Mechatronics—Ideas for Industrial Applications, pp. 187–201. Springer International Publishing, Cham (2015) 8. Zboiński, M., Trojnacki, M.: Motion modeling and simulation of small robot for reconnaissance using MD Adams software (in Polish: Modelowanie i symulacja ruchu małego robota do rozpoznania terenu z zastosowaniem oprogramowania MD Adams). Pomiary Automatyka Robotyka 15(2), 454–461 (2011) 9. Ammon, D.: Vehicle dynamics analysis tasks and related tyre simulation challenges. Vehicle Syst. Dyn. 43, 30–47 (2005) 10. Bakker, E., Nyborg, L., Pacejka, H.B.: Tyre Modelling for Use in Vehicle Dynamics Studies. SAE International, Warrendale (1987) 11. Dugoff, H.: Tire performance characteristics affecting vehicle response to steering and braking control inputs. Final Report (1969) 12. Gipser, M.: FTire—the tire simulation model for all applications related to vehicle dynamics. Veh. Syst. Dyn. 45, 139–151 (2007) 13. Wilk, Ł., Trojnacki, M., Dąbek, P., Cader, M.: Modeling of non-typical tire of Scout mobile robot using CAx systems (in Polish). Mechanik 1–8 (2014) 14. PIAP SCOUT mobile robot, EOD equipment, EOD robot, surveillance robot. http://www. antiterrorism.eu/product/en/scout 15. Toyo Tires: Open Country M/T. http://toyotires.com/tire/pattern/open-country-mt-off-roadmaximum-traction-tires?cat=10 16. MICHELIN AgriBib tire: the standard size tire for all North American tractor applications. www.michelinag.com/Agricultural-tires/Tractors/MICHELIN-AGRIBIB 17. Pro-Line Racing|Most-winning RC parts and accessories!|RC Parts, Traxxas Parts, RC Crawler, RC Wheels, RC Tires, RC Bodies. http://www.prolineracing.com/ 18. PREMIUM GRATING—Professional Steel Grating Manufacturer. http://www. premiumgrating.com/ 19. New Cars, Used Cars, Hybrid Cars, Small Cars|Toyota UK. https://www.toyota.co.uk/ 20. PIAP Scout promotional movie (in Polish). www.youtube.com/watch?v=GIktOv0gqWk 21. Boston Dynamics: Dedicated to the Science and Art of How Things Move. http://www. bostondynamics.com/robot_sandflea.html 22. Yi, J., Li, J., Lu, J., Liu, Z.: On the Stability and Agility of Aggressive Vehicle Maneuvers: A Pendulum-Turn Maneuver Example. IEEE Trans. Control Syst. Technol. 20, 663–676 (2012) 23. Dąbek, P., Szosland, A.: Identification of rotational properties of a non-pneumatic tyre of a mobile robot (in Polish: Identyfikacja parametrów skrętnych opony niepneumatycznej robota mobilnego). Pomiary Automatyka Robotyka 15(2), 495–503 (2011)

Simulations of Accelerations and Velocities of the Robot’s Arm Krzysztof Dąbrowski

Abstract Project of program realizing reciprocal kinematic exercise is the entrance to researches of robots arm’s power. The C++ based program counts accelerations and velocities of robot arms based on position between the end of arm and the level of the ground. Using different versions of the inverted kinematic problems, the ranges of errors are calculated. For the demand of the user the animation of robot arms movements might be played in slow motion. Keywords Robot movement of error




Robot arm




Velocity




Acceleration




Range

1 Introduction Robotics has been developed as a science for almost a century. Every subsequent approach results in constructions being lighter and faster. It makes necessity of researches whether vibrations and forces are even more important. Each computational model introduces calculation error. Of course other mock-ups have various percentage of mistakes. Then some important questions arise more frequently. For example, how to anticipate amount of aberration? Is it possible to avoid errors? The aim of this chapter is to create a bridgehead for further research of the robot’s movements. The main part of an appropriate program is purposed for calculation of velocities, accelerations, and motion deviation. In the beginning, it is necessary to introduce number of time instants for the motion performance at every subsequent steps, having elementary time increment Δt (s). The latter shall allow us to obtain the required size of appropriate matrix used

K. Dąbrowski (&) Gdansk University of Technology, Gdansk, Poland e-mail: [email protected] © Springer International Publishing Switzerland 2016 J. Awrejcewicz et al. (eds.), Mechatronics: Ideas, Challenges, Solutions and Applications, Advances in Intelligent Systems and Computing 414, DOI 10.1007/978-3-319-26886-6_4

53

54

K. Dąbrowski

in the computer program. Thus, for expedience of computation, size of the above matrix is desired as nDt ¼ 100:

ð1Þ

For calculations it is necessary to assign relative changes in the upper arm position [1], at subsequent instant of time t, with respect to previous instant of time t − Δt. That is, to say yt y0 DyDt ¼ ; ð2Þ nDt 1 DzDt ¼

zt z0 ; nDt 1

ð3Þ

where y0 initial position of the end of the upper arm along the x coordinate axis (mm), z0 initial position of the end of the upper arm along the y coordinate axis (mm), yt final position of the end of upper arm along the y coordinate axis (mm), zt final position of the end of upper arm along the z coordinate axis (mm).

2 Notation At the beginning, it is important to introduce all needed angles, lengths, and characteristic points (Fig. 1). lD lG

length of lower arm of the robot (mm), length of upper arm of the robot (mm),

Fig. 1 Scheme of the notation

Simulations of Accelerations and Velocities …

55

A, B, C, D kinematic pairs, αt1, αt2, αt3, αt4 angles describing mutual rotations (°).

3 Exact Method The exact method enables comparison of the other approximate methods [2]. Using trigonometry relationships (4) and (5) and introducing the law of cosines (11) it is possible to calculate angles αt2 and αt3 (Fig. 2). Additional notation, α β Φt2, Φt3

angle between the lower arm and line from the beginning of coordinate system to the end of upper arm (°), angle between the base and line from the beginning of coordinate system to the end of upper arm (°), auxiliary angles (°).

As a result of applying the method based on elementary trigonometry relationships, we obtain [1] tgb ¼

Fig. 2 Scheme of the exact method variables

zt yt

ð4Þ

56

K. Dąbrowski

tga ¼

lG
sin ht3 lD þ lG
cos ht3

ð5Þ

The next step is to calculate the auxiliary angles, on the basis of following relationship: tght2 ¼ tgða þ bÞ ¼

tga þ tgb : 1 tga
tgb

ð6Þ

Then lG
sin ht3 zt þ lD þ lG
cos ht3 yt ; tght2 ¼ lG
sin ht3 zt
1 lD þ lG
cos ht3 yt tght2 ¼

ð7Þ

yt
lG
sin ht3 þ zt ðlD þ lG
cos ht3 Þ : yt ðlD þ lG
cos ht3 Þ zt
lG
sin ht3

ð8Þ

yt ¼ lD
sin at2 þ lG
cos at3 ;

ð9Þ

Because

zt ¼ lD
cos at2

lG
sin at3 ;

ð10Þ

and using the law of cosines y2t þ z2t ¼ l2D þ l2G

2
lD
lG
cosð180

ht3 Þ;

ð11Þ

we get y2t þ z2t l2D l2G ; 2
lD
lG

ð12Þ

yt
lG
sin ht3 þ zt ðlD þ lG
cos ht3 Þ : yt ðlD þ lG
cos ht3 Þ zt
lG
sin ht3

ð13Þ

ht3 ¼ arccos ht3 ¼ arctg

Finally, the appropriate configuration angles are as follows:

at3 ¼ ht3

at2 ¼ 90

ht2 ;

ð90

ht2 Þ ¼ ht3

ð14Þ ht2 :

ð15Þ

Simulations of Accelerations and Velocities …

57

4 First Approximate Method The first approximate method is also based on trigonometry relations (16) and (17) and law of cosines (20). The difference with respect to the exact method is that two unknown configuration angles αt2, αt3 are calculated solving a set of two nonlinear Eq. (23). This method is based on trigonometry relationship (Fig. 3) c ¼ arctg

zt : yt

ð16Þ

Using law of sinuses, sin b sinð180 ð90 at2 Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ lG y2t þ z2t b ¼ arcsin

lG
sinð180 ð90 at2 Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi y2t þ z2t at2 ¼ 90

y2t þ z2t ¼ l2D þ l2G

Fig. 3 Scheme for the first approximate method’s application

at3 Þ

c

ð17Þ

at3 Þ

ð18Þ ð19Þ

b

2
lD
lG
cosð180

ð90

at2 Þ

at3 Þ

ð20Þ

58

K. Dąbrowski

at2

at3 ¼ arcsin

y2t þ z2t l2D l2G 2
lD
lG

ð21Þ

Additional notation, β angle between the lower arm and line from the beginning of coordinate system to the end of upper arm (°), γ angle between the base and line from the beginning of coordinate system to the end of upper arm (°). It is necessary to define, on a basis of Eqs. (20) and (21), a set two nonlinear equations [1] 

f1 ðat2 ; at3 Þ ¼ 0 f2 ðat2 ; at3 Þ ¼ 0

ð22Þ

The requested configuration angles αt2, αt3 can be calculated as solution of the set of two nonlinear equations with two unknown variables. 8 >  > > < 90 > > > :

arctg yztt at2

arcsin

at3

lG
cosðat2 at3 Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi y2t þ z2t

at2 ¼ 0

y2 þ z2t l2D l2G arcsin t ¼0 2
lD
lG

ð23Þ

5 Second Approximate Method The second approximate method depends on the solution of a set of two nonlinear equations [1] 8 xt > > < at2 ¼ arccos > y > : at3 ¼ arcsin t

lG
cos at3 lG lD
sin at2 lG

ð24Þ

6 Movement Simulations In order to check correctness of the described methods of calculations, the MATLAB (MATrix LABoratory) environment was used. The software has been developed by the MathWorks company since 1985. The main aim of the program is

Simulations of Accelerations and Velocities …

59

Fig. 4 Scheme of the MATLAB arms simulations

to simplify calculations and simulations. In Fig. 4 a proper view of robot’s arms is shown. At first, the Newton–Raphson method was planned to use, but results were different than in the rest of methods.

7 Program The next step was creating the C++ based program with the use of Visual Studio 2008. It was the longest part of the project, mainly because of many problems with data conversions and forms issues. View of the main window is shown (Fig. 5). User has to input time of operation. Subsequently, one may input primary angles or position of final point of the arm. After that the program will calculate appropriate lengths and angles. Then the user has to type final positions of robot upper arm. While writing this article the only type of movement that was possible to use was linear interpolation. Later will be available the additional types, e.g., circular, A-spline, B-spline, and C-spline (Fig. 6). In order to create animation of the arms movement, the SFML (Small and Fast Media Library) graphic engine was used. This is open-source project which was launched in 2005. The usage of SFML is very convenient, because of many ready-to-use classes. The size of files—around megabyte—makes the programs easy to distribute.

60

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Fig. 5 View of the program Fig. 6 Scheme of the program arms simulations

8 Velocities In next point the velocities are calculated. The process must be performed for every piece of the nDt matrix and for difference in time Dt, i.e., xD;t ¼

Dat2;t ; Dt

ð25Þ

Simulations of Accelerations and Velocities …

61

Fig. 7 Results of the velocities’ simulations

xG;t ¼ xD;t þ

Dat3;t : Dt

ð26Þ

Results of every method were the same and were illustrated (Fig. 7). The results for both arms are nonlinear. The upper arm is of a strongly increasing character.

9 Accelerations By the other transformation of the reciprocal dynamic theory accelerations of robot arms can be determined (Fig. 8).

eD;t ¼

DxD;t ; Dt

eG;t ¼ eD;t þ

DxG;t : Dt

ð27Þ ð28Þ

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K. Dąbrowski

Fig. 8 Results of the accelerations’ simulations

10

Duration of Operations

Beside robots arms simulations, times of operations were calculated. At first we used the MATLAB (Fig. 9), later—the C++ program (Fig. 10). The MATLAB environment generates application being even 50 % slower than the C++ one. Note,

Second approximate method

0,146

Exact method

1,840

Approximate method

8,144

0

2

4

6 time [s]

Fig. 9 Time of operation and charts generation with the use of MATLAB

8

10

Simulations of Accelerations and Velocities …

Second approximate method

63

0,107

Exact method

1,840

Approximate method

5,931

0

1

2

3 4 time [s]

5

6

7

Fig. 10 Time of operation and charts generation with C++

that when we apply the C++ program, solution of the second approximate method of nonlinear equations will appear 17 times faster than using the exact method. Generated results match expectations [3].

Fig. 11 Results of the range of error simulations

64

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K. Dąbrowski

Range of Errors

The last point of the chapter concerns calculation of ranges of errors between all the methods. The biggest range of error expresses the second approximate method. The difference between the results of subsequent steps is shown (Fig. 11). The line of range of error stabilizes after 14 iterations. The first approximate method appeases after five steps, but it is 40 times slower.

12

Conclusion

Using approximate methods, it is likely to save up to 92 % of the calculation time. Using the MATLAB environment, it is possible to skip first 15 % of iterations, in order to obtain the results with range of error smaller than 0.001 %. Using the C++ program, it is possible to skip first 25 % of iterations, in order to obtain the results with range of error smaller than 0.001 %. Acknowledgements The author acknowledges Prof. Krzysztof J. Kaliński of Gdańsk University of Technology, for his conceptual supervision and tutorship.

References 1. Kaliński, K.J.: Nadzorowanie procesów dynamicznych w układach mechanicznych (2012) 2. De Luca, A.: Zero dynamics in robotic systems. http://link.springer.com/chapter/10.1007% 2F978-1-4757-2135-5_5 (1991) 3. Kiang, C.T., Spowage, A., Yoong, C.K.: Review of control and sensor system of flexible manipulator. http://link.springer.com/article/10.1007/s10846-014-0071-4 (2015)

The Numerical Analysis of Burnishing Process of Hollow Steel Tubes Tomasz Dyl

Abstract This paper presents numerical research of burnishing process of hollow steel tubes. The internal surfaces of the tubular elements are treated, among others, by burnishing process. The type of force can be divided into static and dynamic burnishing. The kinematics can be divided into sliding and roller burnishing. Occurrence of moving parts in direct contact with the material qualifies for the group process of burnishing rolling. The sliding burnishing design element property is part of the work surface burnished permanently attached to the handle. Theoretical analysis of the burnishing is carried out numerically. For the calculations were used commercial software Forge based on the finite element method. After burnishing modeling was found intentionally controlled state of stress and strain in the tubular elements to ensure the intended technological quality.





Keywords Numerical analysis Finite element method Steel tubes hollow State strain State stress Forge








Burnishing process


1 Introduction In advanced manufacturing, it is important to obtain good quality products. Therefore, it is used to carry parts up during completion of machinery manufacture. The most common burnishing internal cylindrical surfaces used are in serial productions of machine components. The burnishing process is a finishing machining of hollow tube, having a number of advantages. This treatment increases the dimensional accuracy of holes and the surface roughness parameters decreases, increasing the hardness of the surface layer with formation of compressive residual stresses. It is also important that the burnishing technology allows machining holes with a lack of straightness of the axis. The advantages of burnishing may also be T. Dyl (&) Gdynia Maritime University, Gdynia, Poland e-mail: [email protected] © Springer International Publishing Switzerland 2016 J. Awrejcewicz et al. (eds.), Mechatronics: Ideas, Challenges, Solutions and Applications, Advances in Intelligent Systems and Computing 414, DOI 10.1007/978-3-319-26886-6_5

65

66

T. Dyl

considered with high performance and relatively easy technological instrumentation. The tools used for processing by the burnishing special broaches plungers in a variety of shapes and steel balls such as bearing. The beneficial effect of treatment holes burnishing process by the state of the surface layer and the accuracy of the machined holes are obtained for products made of unalloyed steel, steel alloys and stainless steel, copper alloys, and titanium alloys. Burnishing process is most often used for machining of circular cross-section holes with a diameter from a few tenths of millimeter’s to about one hundred. In the papers [1–3] confirmed the usefulness of burnishing process (ballizing process) as a finishing hole machining sliding bearings. It is important that the burnishing technology sets were prepared special burnished elements in the form of beads used as a tool for broaching. At the yield point of the piece-part material, the surface is plastically deformed by the cold flowing of subsurface material. The result is a mirror-like finish and tough, hardened surface. The pressure required for roller burnishing depends on various factors, such as tensile strength of the material, surface toughness before and after burnishing, ductility, shape of the rollers, and diameters. Developed using artificial neural networks [3] model of stress distribution in the surface layer of workpieces can be used to expand the burnishing process control system, which may advantageously influence the quality of the machined elements used for the machine construction. As part of the many works defining numerical elastoplastic model of plastic surface treatment has been made a number of theoretical analyses using the finite element method to determine the state of stress and strain at the interface of two bodies pressed against [1, 4–8]. On the surface of the contact elements cooperating with one another to determine the status of stress and strain using a Forge MES [9]. This commercial packet Forge is used for simulation different plastic works: rolling, forging and pressing, drawing and other simulated [5, 6, 10–13]. As an innovative application of the program is to use it to burnishing process. Determination of the state of stress in the surface layer is particularly an important issue due to the possibility of the projections at the relevant technological parameters of the mechanical condition of machine components. It takes into account the fact of burnishing force spread out over a contact surface of the spherical tool and the workpiece in the half elastic–plastic. Plastic forming surface modeling consists in determining the impact of the rigid tool predefined curvature of the deformable object, which is the Hertz model, which is a modification of the Bussinesqa model [14, 15].

2 Methodology and Numerical Analysis The numerical study was conducted for C45 steel samples. The samples were in the form of hollow steel tubes. Internal diameters of samples from each set were made by boring in three dimensions. The largest internal diameter of a set of samples was about 0.1 mm smaller than the diameter of the tool. Two more samples from a given

The Numerical Analysis of Burnishing Process …

67

Fig. 1 Schema of burnishing process, D—external diameter tube, d—outer diameter of the ball, d0—diameter inner tube before burnishing, d1— diameter inner tube after burnishing, w—reduction ratio, Δd—absolute plastic strain, Δds—absolute elastic strain

set of internal diameters were smaller than the ball diameter by 0.2 and 0.3 mm. In Fig. 1 is shown schema burnishing process by ball. Burnishing process is performed using the balls bearing steel 20CrMo4 through the hole. Computer simulations of burnishing were carried out at ambient temperature. The computer simulations were carried out with C45 steel. The temperature of materials was 20 °C. The external diameter D = 30–45 mm and internal diameter d0 = 15.56–33.22 mm. The diameter of balls bearing was d = 15.86–33.32 mm. The coefficient of sliding friction of steel on steel is 0.1. The use of a computer program Forge, which is based on the finite element method and has built-in thermomechanical models, requires defining the boundary conditions. The boundary conditions are properties of a material, the conditions of friction, kinetic parameters, and thermal properties and tools. Forge® commercial software uses a model consisting of a finite element mesh, whose base element is a triangle. The friction forces been model on the basis of the solution Tresca are determined from the equation [9, 10, 16]: s¼

  r0 m pffiffiffi 3

ð1Þ

68

T. Dyl

where τ—vector of unitary friction forces (MPa), σ0—base flow stress (MPa), m— friction factor. The relative plastic deformation for burnishing sliding is expressed by the formula [16]: en ¼

d

d0 d0


100 %

ð2Þ

where d—outer diameter of the ball, d0—diameter inner tube before burnishing. For the computer simulation, the input data are as follows: the initial temperature is the ambient temperature, the heat exchange coefficient between the workpiece and the tool is 3000 W/Kmm2, the heat exchange coefficient between the material and the air is 100 W/Kmm2. Due to limitations of the software used movable third element in the form of a thin disk sliding burnishing tubes. The use of moveable tubes on the beads did not affect the accuracy of the calculations and only affect the calculation time by increasing the number of elements in the node which calculations are performed. Computer simulations were carried out in a three-dimensional reference system. Mechanical state of the deformed material is described by a law Norton–Hoff [9, 10, 16–20]: Sij ¼ 2K0 ðe þ e0 Þn0
eð

b0
T Þ

pffiffiffi m0 3 e_ i

1

e_ ij

ð3Þ

where Sij—stress tensor deviator, e_ ij —strain rate tensor, e_ i —strain rate intensity, ε—strain intensity, ε0—based strain, T—temperature, K0, m0, n0, β0—material constants specific to the material considered. Table 1 shows examples of the geometrical parameters for the steel tubes after burnishing process. The strain hardening of the material structure of the surface layer is obtained by cold plastic deformation, this improves the fatigue strength. Processing of

Table 1 Geometrical parameters and strain ratio of the tube hollows after burnishing process No.

D (mm)

d1 (mm)

d (mm)

d0 (mm)

w (mm)

εn (%)

Δd (mm)

Δds (mm)

4511 4512 4513 3521 3522 3523 3031 3032 3033

45 45 45 35 35 35 30 30 30

33.28 33.29 33.29 21.97 21.97 21.97 15.84 15.82 15.83

33.32 33.32 33.32 22.00 22.00 22.00 15.86 15.86 15.86

33.22 33.12 33.02 21.90 21.80 21.70 15.76 15.66 15.56

0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3

0.3 0.6 0.9 0.5 0.9 1.4 0.6 1.2 2.0

0.06 0.17 0.27 0.07 0.17 0.27 0.08 0.16 0.27

0.04 0.03 0.03 0.03 0.03 0.03 0.02 0.04 0.03

The Numerical Analysis of Burnishing Process …

69

burnishing provides the creation of a surface layer of large compressive stress, so very often it is observed with the increase of materials treated by burnishing fatigue resistance (surface and volume). Resistance to fatigue is one of the exploitation properties of machines, changing preferably by burnishing. Can be determined based on the relationship between the parameters and the strain and stress state in the surface layer material. It is therefore important to determine the stress and strain state in the tubular elements widely used in the metallurgical industry, machinery, and shipbuilding. The source of heat evolved in the deformation zone is the work of plastic deformation. In practice, about 10 % of this energy is converted in the area of plastic deformation in the heat. With intensive surface treatment process in the surface layer forming material at the interface with the tool of the present temporary increase in temperature, it is caused not only by the work of deformation, but also by the occurrence of the friction surface of the tool with the workpiece, and the effect on the temperature in the deformation zone of the technological parameters are of the burnishing process. Figure 2 shows the effective strain and strain rate and stress tensor and pressure distributions substitute for computer simulation of the burnishing ball diameter d = 33.32 mm burnishing reduction ratio 0.3 mm.

Fig. 2 The distribution of the effective strain (a); and strain rate (b); and stress tensor (c); and pressure (d) for ball diameter d = 33.32 mm of the reduction ratio w = 0.3 mm for burnishing

70

T. Dyl

Fig. 3 The distribution of the effective strain (a); and strain rate (b); and stress tensor (c); and pressure (d) for ball diameter d = 22.00 mm of the reduction ratio w = 0.3 mm for burnishing

Figure 3 shows the effective strain and strain rate and stress tensor and pressure distributions substitute for computer simulation of the burnishing ball diameter d = 22.00 mm burnishing reduction ratio 0.3 mm. Figure 4 shows the effective strain and strain rate and stress tensor and pressure distributions substitute for computer simulation of the burnishing ball diameter d = 15.86 mm burnishing reduction ratio 0.3 mm. Because of nature of the burnishing shown axisymmetric distributions of selected strains and stresses in the middle of the tube hollow on the longitudinal section. Based on the results shown in Figs. 2, 3 and 4, it can be concluded that the effective strain and strain rate and stress intensity depend on the outer diameter of the ball. For smaller diameters balls of stress take the greatest value. It can be concluded that the intensity of the deformation in the outer layer of the hollow tube from inside of contact with the ball increases with the reduction ratio. Conversely, the intensity is proportional dependence of the deformation and the diameter of the balls. Similarly it occurs in the event of deformation. For larger values of the diameter of the balls as well as the intensity of deformation strain rate values take smaller and smaller diameter of the balls reach the higher values. This character of stress and

The Numerical Analysis of Burnishing Process …

71

Fig. 4 The distribution of the effective strain (a); and strain rate (b); and stress tensor (c); and pressure (d) for ball diameter d = 15.86 mm of the reduction ratio w = 0.3 mm for burnishing

strain distribution is determined by the average stress values increase with decreasing diameter of the balls. This is directly related to the decrease in the surface area of contact deformation element burnishing the inner wall of the hollow tube. Depending residual stress as a function of: the outer diameter of the ball, absolute and relative plastic deformation for the burnishing set within 50 μm from the machined surface of the tube hollow and is shown in Figs. 5 and 6. With the increase in the value of the diameter of the ball burnishing strain value decrease. Such nature of the deformation state is directly dependent on the state of stress occurring in the outer layer of the tube hollow subjected to burnishing. Based on the analysis results shown in Figs. 5 and 6 it can be concluded that the residual stresses are numerically calculated dependent on two variables: the outer diameter of the balls and the predetermined strain for burnishing. It can be concluded that the higher relative plastic deformation and with the increase of the reduction ratio, while reducing the diameter of the ball there is an increase the absolute value of the compressive residual stress in the inner surface layer of the tube hollow.

72

T. Dyl

σmax, [MPa]

Fig. 5 Residual stress—σmax, as a function of d the outer diameter of the ball and εnp—relative plastic deformation for burnishing

σmax, [MPa]

Fig. 6 Residual stress—σmax, as a function of d—outer diameter of the ball and w—reduction ratio for burnishing

The Numerical Analysis of Burnishing Process …

73

In order to determine the depth of the zone of plastic deformation used in numerical analysis based on the finite element method. The paper was determined as a numerical solution for contact and deformation of bodies on the basis of the theory of plasticity and elasticity. Based on numerical analysis of the equations for calculating the depth of plastic deformation zone. For the required boundary conditions and specific areas of research, determined on the basis of their own numerical sliding burnishing the relationship between the depth of the zone of plastic deformation and the deformation and reduction ratio shown by the equation: hd ¼ 0:756w1:667

ð4Þ

where hδ—depth of deformation zone, w—reduction ratio. After burnishing sliding surface layer are compressive residual stress resulting from the increased specific volume of the material in a plastic state. The maximum absolute value stresses occur near the surface subjected to burnishing. The presence of compressive stresses in the surface layer is preferred due to improved performance, especially the increase in fatigue strength of machine parts, but also to tribological wear.

3 Summary The paper presents the effect of burnishing process on the state of stress and strain of the hollow steel tubes. Burnishing is a technology of surface plastic forming of machine parts. Burnishing is used as a finishing strengthens, and smoothness, can be realized on the universal machine tools and machining centers, effectively replaces the machining operations, such as grinding, reaming, honing, and lapping. The numerical analysis is determining that the reduction ratio has significantly influenced on the state strain and state stress of the inner tube holes after burnishing process. An increase in the value of reduction ratio, the value of the effective strain increases. After burnishing simulations can be concluded that the most intense nature of the surface of an elastically deformable material contact with the ball is the state of effective strain and strain rate. The values of the deformation tensor gradient propagate into the material. Examined the cross-section of the tube hollow can be seen that the area is characteristic of the occurrence of deformation tensors maximum value at a certain depth from the surface of the workpiece, but not more like half of the wall thickness of the tubes. After burnishing is constituted compressive residual stresses in the surface layer that result from increased specific volume of the material in a plastic state. The maximum absolute value stresses occur near the surface of the treated burnishing. After burnishing numerical studies determines the relationship between the depth of the zone of plastic deformation and the deformation and reduction ratio.

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After analysing the numerical computer simulations of burnishing can be conclude that can effectively specify state of strain and state of stress required for planning finishing machining abrasive tube for the piece production and small lot production. It has been determined that it is possible to intentionally form state of stress and strain in the tubular elements intended to provide technological quality while maintaining the required strength and the exploitation properties surface layer of the workpiece.

References 1. Dyl, T.: Ballizing process impact on the geometric structure of the steel tubes. Solid State Phenom. 199, 384–389 (2013) 2. Fattouh, M.: Some investigation on the Ballizing process. Wear 134, 209–219 (1989) 3. Lipski, J., Zaleski, K.: Modelling of residual stresses distribution in workpiece past Ballizing process. Maint. Reliab. 4, 18–21 (2004) 4. Dyl, T., Stradomski, G., Rydz, D.: Effect of the reduction ratio on the state strain of the steel tubes after burnishing broaching process. In: 23rd International Conference on Metallurgy and Materials, METAL 2014, Brno Czech Republic, EU, 21.05, 23 May 2014 5. Garstka, T., Dyl, T.: Circumferential residual stresses in tubes estimated by means of deflection method. Arch. Metall. Mater. 51(2), 199–203 (2006) 6. Chen, D.C., Chen, W.J., Lin, J.Y., Jheng, M.W., Chen, J.M.: Finite element analysis of superplastic blow-forming of Ti-6Al-4V sheet into closed ellipcylindrical die. Int. J. Simul. Model. 9(1), 17–27 (2010) 7. Rodriguez, A., Lopez de Lacalle, L.N., Celaya, A., Lamikiz, A., Albizuri, J.: Surface improvement of shafts by the deep ball-burnishing technique. Surf. Coat. Technol. 206, 2817– 2824 (2012) 8. Sayahi, M., Sghaier, S., Belhadjsalah, H.: Finite element analysis of ball burnishing process: comparisons between numerical results and experiments. Int. J. Adv. Manuf. Technol. 67, 1665–1673 (2013) 9. FORGE® Reference Guide Release. Transvalor S.A., Parc de Haute Technologie Sophia— Antipolis (2002) 10. Rydz, D.: The optimal conditions for production of bimetallic plate St36K + 0H13J in asymmetrical hot rolling. J. Mater. Process. Technol. 157–158, 609–612 (2004) 11. Mróz, S., Szota, P., Koczurkiewicz, B.: Modelling of rolling and cooling processes of the bulb bars HP220. In: Materials Processing and Design: Modeling, Simulation and Applications, AIP Conference Proceedings, vol. 908, pp. 1243–1248 (2007) 12. Dyja, H., Sobczak, K., Kawałek, A., Knapiński, M.: The analysis of the influence of varying types of shape grooves on the behaviour of internal material discontinuities during rolling. Metalurgija 52, 35–38 (2013) 13. Stradomski, G., Niepsuj, P.: Use of numerical modelling in the burnishing technology. Plast. Deformation Met. 2, 86–90 (2014) 14. Korzyński, M.: Sliding Burnishing. WNT Publisher, Warsaw (2007) 15. Niezgodziński, M.E., Niezgodziński, T.: Formulas Graphs and Tables the Strength. WNT Publisher, Warsaw (1996) 16. Dyl, T.: Numerical and Experimental Analysis of Burnishing Process Using the Theory of Elasticity and Plasticity, Monographs. Gdynia Maritime University, Gdynia (2014) 17. Norton, F.H.: The Creep of Steel at High Temperatures. McGraw-Hill, London (1929)

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18. Hoff, N.J.: Approximate Analysis of Structures in the Presence of Moderately Large Creep Deformations. Quart. Appl. Match. 12(1), 49 (1954) 19. Lochegnies, D., Gelin, J.C.: A mixed variational formulation fort the solution of Norton-Hoff viscoplastic flows. Comput. Struct. 65(2), 177–189 (1997) 20. Kolmogorov, V.L., Fedotov, V.P., Gorshkov, A.V.: Three-dimensional analysis of the stress-strain state in the process of plastic deformation of metals. J. Mater. Process. Technol. 95, 55–64 (1999)

Piecewise Control Method of Oxygen Flow in PEM Fuel Cell Jerzy Garus and Adam Polak

Abstract The paper presents a method of control of an oxygen flow in the PEM fuel cell without recirculation. The proposed procedure of finding an optimal value of the oxygen flow basis on comparing a current voltage of the cell with a reference one obtained from a static model of the PEM fuel cell. Simulation results show that such value of the flow is obtained for a limited number of steps. It allows to reduce the oxygen usage assuring safe operation of the fuel cell. Keywords PEM fuel cell


Oxygen flow
Control

1 Introduction Nowadays renewable energy sources are intensively searched. This approach has its roots in the belief of scientists and industry representatives on the imminent exhaustion of fossil fuels and environmental safety. Fuel cells are the perfect solution to both of these issues. They are completely ecologically clean and do not require fossil fuels to work [1, 2]. An evidence of the growth of interest in this source of energy in last decades is the increasing number of scientific publications as well as implementations of the power supply systems which have found a variety of applications, including electric energy sources for unmanned vehicles, cars, submarines, space objects, etc. [1–3].

J. Garus (&)
A. Polak Faculty of Mechanical and Electrical Engineering, Polish Naval Academy, Gdynia, Poland e-mail: [email protected] A. Polak e-mail: [email protected] © Springer International Publishing Switzerland 2016 J. Awrejcewicz et al. (eds.), Mechatronics: Ideas, Challenges, Solutions and Applications, Advances in Intelligent Systems and Computing 414, DOI 10.1007/978-3-319-26886-6_6

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There are many types of the fuel cells, but the most promising one seems to be the proton exchange membrane (PEM) fuel cell. It requires providing hydrogen and oxygen for correct operation and produces electricity, heat, and water as products. One of the main subsystems responsible for proper operation of the fuel cell system is an oxygen supply subsystem. Most often oxygen is obtained from the atmospheric air and the oxygen supply subsystem consists of a blower or a compressor [4] causing the air flow through a cathode channel of the fuel cell and providing the sufficient amount of oxygen for the oxidation reaction and removal of produced water, and sometimes also the excess heat. In the case of lack of access to the air, pure oxygen is used and the oxygen supply subsystem is constructed in two different ways [3]. In the first one, oxygen is circulated through a closed loop by an oxygen recirculation pump. It needs to use a controller responsible for maintaining a constant gas pressure in the cathode channel and providing a continuous circulation of oxygen in the system. An advantageous of such a solution is possibility of complete oxygen utilization, but disadvantageous a need of additional equipment like the oxygen recirculation pump and dryers or water condensers increasing a total weight and size of the system. The second solution is the oxygen supply subsystem with an open cathode, wherein the excess oxygen is blown out of the cell. In such a way, part of oxygen is not used causing a loss in the overall balance of the fuel cell system operation but there is no need for installation of any additional equipment. However, in such a case control of the oxygen flow is more complicated because not only a proper amount of the oxygen for the reaction has to be provided but also a sufficient flow of the oxygen in the cathode must be ensured in order to remove water being the reaction product. Therefore, it is necessary to apply a control procedure allowing to choose the flow of oxygen depending on an operating state of the fuel cell. This case is considered in the paper. The work consists of six sections. A mathematical model of the PEM fuel cell is written in section two. Then in next two sections a behavior of the fuel cell for different oxygen flows and a proposed control strategy are described. In section five some simulation tests and obtained results are presented. Conclusions are given in the last section.

2 PEM Fuel Cell Mathematical Model PEM fuel cells obtain the energy from electrochemical reaction that take place inside them. Separating the half reaction to anode and cathode it is possible to harness the released energy to do electric work. The reactions that take place inside fuel cells are as follows:

Piecewise Control Method of Oxygen Flow in PEM Fuel Cell

79

2H2 ! 4H þ þ 4e

ð1Þ

O2 þ 4e þ 4H þ ! 2H2 O

ð2Þ

2H2 þ O2 ! 2H2 O

ð3Þ

An overall reaction is:

Electric energy generated by the fuel cell comes from a difference between the Gibbs free energy of formation of the product (water) and the Gibbs free energy of formation of the reactants (oxygen and hydrogen) [1]: 2DG ¼ Gproduct

Greactants

ð4Þ

It is convenient to analyze the energy equation in the molar notation, hence the formulae (4) takes a form: Dg ¼ gproduct

greactants

ð5Þ

During the chemical reaction that take place in the PEM FC one mole of molecular hydrogen and half a mole of molecular oxygen are consumed by the cell per one mole of the produced water. Therefore (5) for PEM FC can be expressed as follows: gH 2 O

gH2

1 gO 2 2

ð6Þ

For a mole of reacting hydrogen, 2N of electrons flow through an external electric circuit (N—the Avogadro constant) and charge transferred between the electrodes is equal to: 2Ne ¼

2F

ð7Þ

where: e—the charge of a single electron, F—the Faraday constant. The electric work Wel, related to transferred charge, done by the fuel cell is equal to: Wel ¼

2FE

where E is the electromotive force of the fuel cell.

ð8Þ

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Assuming that the cell operates without losses, the electric work would be equal to the change of the Gibbs free energy of formation: Wel ¼ Dg

ð9Þ

Hence, the electromotive force E, of the hydrogen fuel cell operating in standard pressure, can be expressed by the following equation: E¼

Dg 2F

ð10Þ

However, there is also a dependency between the Gibbs free energy of formation and the pressure of the reactants and the products. For PEM FC, it is taken into account in the Nernst equation and is expressed as [1, 2]: 1

RTop PH2 PO2 2 E¼E þ ln 2F PH2 O 0

!

ð11Þ

where E0 is the electromotive force of the fuel cell at standard pressure, Top is the operating temperature of the cell and PH2 ; PO2 ; PH2 O are the partial pressure of hydrogen, oxygen, and produced water, respectively. Modeling of the PEM FC operation it is required to take into account voltage losses which occur during operation. The losses are distinguished according to their causes, but generally, they are regarded as: activation losses, concentration losses, and ohmic losses [2, 4, 5].

2.1

Activation Losses

The activation losses are caused by the limited speed of reactions that take place on the electrodes. A part of the generated electric energy is used to maintain the speed of the reaction which is determined by the load current. These losses are described by the empirical equation introduced by Tafel in 1905 and used since now by researches [6]: DVact

  i ¼ A ln i0

ð12Þ

where: i0—exchange current density, A—coefficient which depends on the catalyst material and the reactants composition.

Piecewise Control Method of Oxygen Flow in PEM Fuel Cell

81

In the hydrogen fuel cell, the activation losses existing on the cathode are much greater than losses appearing on the anode, thus in practical applications the last ones are neglected. Also losses associated with the fuel crossover, because of their insignificant effect on the operating voltage, are omitted [1].

2.2

Ohmic Losses

The ohmic losses are proportional to the current and the internal resistance of the fuel cell according to the following formulae [1]: Vohmic ¼ IR

ð13Þ

The resistance R can be treated as a sum of the resistance of the path through which the electrons flow, (i.e., electrodes and bipolar plates), and the ionic resistance of the PEM. The Eq. (13) can be written in current density terms as follows: DVohmic ¼ ir

ð14Þ

where: i is the current density in mA/cm2, and r is the area-specific resistance given in kΩ cm2.

2.3

Concentration Losses

The mass transport losses, also named the concentration losses, are caused by reactants pressure gradient appearing in gases supply manifolds, flow channels, and gas diffusion layers once a current is being drawn from the cell. A decreased partial pressure of the reactants at the catalyst site leads to the reduction of the fuel cell voltage. There are many theoretical approaches presenting models of the transport losses, but the following one is lately regarded to be of the most value [1, 7]: DVtrans ¼ m exp ni

ð15Þ

The constants m and n in (15) depend not only on a construction of the gas flow channels and diffusion layers but also a composition of the reactants.

2.4

Operating Voltage Equation

Taking into account all the voltage losses, the operating voltage of the fuel cell at given current density can be calculated as follows [6, 8, 9]:

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V ¼E

DVohmic

DVact

DVtrans

ð16Þ

Substitution (12), (14), and (15) into (16) gives the expression: V ¼E

  i A ln i0

ir

m exp ðniÞ

ð17Þ

Excluding the constant i0 from the activation losses (12) and including it into the constant value of the real open circuit voltage Eoc: Eoc ¼ E þ A lnði0 Þ

ð18Þ

leads (17) to the dependency: V ¼ Eoc

ir

A lnðiÞ

m exp ðniÞ

ð19Þ

The above theoretical form of the polarization curve is quite simple and easy to implement into a control system of the PEM FC. An operating voltage of a whole fuel cell stack Vst can be calculated from the following expression: Vst ¼ Ncell
V

ð20Þ

where Ncell is the number of cells in the stack. The parameters of the Eq. (19) are obtained with help of the identification method described in [10]. The equations with the obtained parameters have a form:

Fig. 1 PEM fuel cell steady-state model (polarization curve)

Piecewise Control Method of Oxygen Flow in PEM Fuel Cell

U ¼ 1:01

47  10

6

i

0:0347  lnðiÞ

2  10

83 4

 expð4:9  10

3

 iÞ ð21Þ

and it’s graphical representation is shown in Fig. 1.

2.5

Fuel Cells Behavior in Different Oxygen Flows

PEM fuel cell for proper operation requires sufficient amount of oxygen delivered successfully to the positive electrode of the cell. The amount of the consumed oxygen is dependent on the cell current and results directly from the reaction (3) occurring in the cell. Dependency (22) presents the oxygen usage to perform the reaction in the cell [1] O2;usage ¼

1 i
AFC ¼ 4F 4F

ð22Þ

where I is the fuel cells’ current, AFC is the fuel cell’s active area (cm2). The Eq. (22) depicts the amount of oxygen, which is used to maintain the chemical reaction inside the cell at the rate determined by the cell’s current. In the PEM fuel cell, the additional amount of oxygen flow is required to flush the produced water out of the cell before it starts to condense. Therefore, the total oxygen flow required for the proper operation of the cell can be expressed as follows: m_ O2 ;mol ¼ k
O2;usage

ð23Þ

where: k is the oxygen flow coefficient and m_ O2 ;mol is the actual oxygen flow expressed in mol/s. In the reviewed literature, there was not found the analytical way to determine the optimal oxygen flow coefficient that ensures safe and stable operation of the cell. It is significant aspect especially in fuel cell systems that do not use the oxygen from air but use the oxygen from any storage devices. However, the minimal and at the same time safe for fuel cell oxygen flow coefficient, was experimentally estimated. Depending on the size of the fuel cell, the current density, the temperature, and the reactants partial pressure inside the cell, as well as the architecture of the oxygen flow channels of the cell, the optimal oxygen flow coefficient varies from 1.1 to 4 [11, 12]. In order to use a simulation means to validate the control method it is necessary to model the fuel cell response to different oxygen flows. For that purpose the

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Voltage [mV]

780 770 760 750 740 730 0

100

200 Time [s]

300

400

Fig. 2 PEM fuel cell response to low oxygen flow (from k = 2 to k = 1.1); blue line—measured data, black line—linear interpolation)

790

Voltage [mV]

780 770 760 750 740 730 0

10

20

30

40

Time [s] Fig. 3 PEM fuel cell response to the change of the flow coefficient from k = 1.1 to k = 2 (blue line —measured data, black line—linear interpolation)

experimentally gathered data from the PEM fuel cell system was used. The measurements of voltage change of the PEM fuel cell and its linearization during low oxygen flow (oxygen flow coefficient set to 1.1) are presented on Fig. 2. The response to increased oxygen flow was also recorded and is presented on Fig. 3. The oxygen flow was increased from k = 1.1 to k = 2. From the measurements of the fuel cell response to a different oxygen flows it is possible to determine the general dependencies describing the voltage change in case of different oxygen flows. The equation for estimation the DU (the voltage change in discrete time intervals T) in case of different oxygen flow coefficients presents dependency (24)

Piecewise Control Method of Oxygen Flow in PEM Fuel Cell

DU ¼ a
T

85

ð24Þ

where: a is the voltage change coefficient, T is the assumed time interval. The a coefficients for the data presented on Figs. 2 and 3 are a = −0.108 mV/s, a = 1.118 mV/s respectively. For the modeling purpose, the possible values of the oxygen flow coefficient were limited to the range k 2 h 1; 5i. Moreover, according to the laboratory tests the optimal oxygen flow coefficient was estimated to the value of kopt = 1.345. Furthermore, the linear relationship of the parameter from Eq. (24) and the oxygen flow coefficient was assumed. For those assumptions the parameter a is calculated as follows: 8 < 0:44
k 0:592 for 1\k\kopt and Uact U  0 ð25Þ a ¼ 1:707
k 2:296 for k  kopt and Uact U\0 : 0 for k  kopt and Uact U ¼ 0

where Uact and U are the current voltage of the cell and the calculated voltage of the cell from (21), respectively.

3 Control Strategy for Oxygen Flow The oxygen flow control algorithm should deliver to the fuel cell sufficient amount of oxygen for the reaction and for the product water removal. For the optimal usage of oxygen it is necessary to continuously track the actual current and the voltage of the cell and set the oxygen flow to the minimal value that will guarantee the proper operation of the cell, which will be assessed by comparison of the voltage of the fuel cell with the reference one obtained from the model. Due to the high inertia of the fuel cell and the air supply subsystem for fuel cell that is operating at constant current, for control of oxygen flow a method of successive approximations at regular intervals can be implemented. The control method involves: – by any change of the electric current drawn from the cell to set the predefined initial value of oxygen flow coefficient k0, – finding the optimal value of the oxygen flow coefficient by method of successive approximations in fixed intervals T, – completion of the search for the optimal oxygen flow when the step reaches a value less than assumed ε. The search for the optimal flow rate of oxygen is accomplished by changing the value of the oxygen flow coefficient in the steps obtained from the following Eq. (25):

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ki ¼

(

kj

1

kj

1

þ

k0 pj k0 pj

for Uact

U\0

for Uact

U¼0

ð26Þ

where: j is the number of the current iteration, p is the constant control coefficient.

4 Simulation Tests and Results The simulation tests of the proposed control strategy of the oxygen flow through the cathode of the PEM fuel cell were performed in MATLAB/Simulink environment. Figure 4 presents the simulation model. The model allows to run the tests for different initial oxygen flow, and for different control coefficient. It also allows to visualize the change of the oxygen flow, the oxygen usage and the current voltage of the cell. The tests were performed for the conditions presented in Table 1. Simulations were performed for different values of the control coefficient, so it is possible to rate the control method of the oxygen flow for various values of this coefficient. The results of the simulations are presented on Figs. 5, 6, 7, 8, 9 and 10. From results of the simulation it can be concluded that the selection of the appropriate value of the control coefficient has a significant impact on the quality of the obtained results of the regulation.

Oxygen flow coefficient

In1

p Control coefficient p

1/s

k0 Initial oxygen flow coefficient k

In2

Out1

Oxygen usage

In1

0

Out1 In3

f(u) Static model of PEM fuel cell

Current voltage

In2

Oxygen flow controller

Fuel cell model dependent on the oxygen flow

Current density

Fig. 4 Oxygen flow control system of the PEM fuel cell—simulation model created in MATLAB/Simulink environment

Table 1 Parameters of the performed simulations

Parameters

Units

i p

mA/cm –

k0 T

– s

Values 2

300 1.25, 1.5, 1.75, 2, 2.2, 2.4, 2.6, 2.8, 3 1.7, 2 100

Piecewise Control Method of Oxygen Flow in PEM Fuel Cell

87

Fig. 5 Oxygen flow coefficient and voltage at the output of the PEM fuel cell for p = 1.25

The quality of the regulation is measured as an accuracy of setting the oxygen flow coefficient. Setting the control coefficient on a too low value causes that the regulation steps are very small, therefore the adjustment time is greatly extended. On the other hand, small value of the control coefficient allows for accurate adjustment of the oxygen flow coefficient. Conversely, if the control coefficient is too high, the regulation steps are large, which can also cause the proposed regulation method never come close enough to the optimal oxygen flow. This phenomenon is dangerous in two ways. In the case of setting a value less than the optimum value, it would lead to water condensation inside the cathode channel of

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Fig. 6 Oxygen flow coefficient and voltage at the output of the PEM fuel cell for p = 1.5

the fuel cell and in consequence a significant reduction of the cell voltage and even the failure of the cell. In contrast, setting the flow to a much higher value than the optimum result in excessive oxygen consumption and consequently low oxygen utilization. Also, the initial oxygen flow has an influence on the results of the proposed control algorithm. For the same control coefficient and for the different initial oxygen flows, the results of the simulations differ each other. Figure 10 presents the results of the simulation for the initial oxygen flow coefficient set to 1.7 and the

Piecewise Control Method of Oxygen Flow in PEM Fuel Cell

89

Fig. 7 Oxygen flow coefficient and voltage at the output of the PEM fuel cell for p = 2

control coefficient set to 2.4. Comparison the results presented on Figs. 8 and 10 shows the influence of the initial oxygen flow on the value of the oxygen flow coefficient at the end of regulation, which in the case presented on Fig. 10 is tuned for higher value.

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Fig. 8 Oxygen flow coefficient and voltage at the output of the PEM fuel cell for p = 2.4

Piecewise Control Method of Oxygen Flow in PEM Fuel Cell

Fig. 9 Oxygen flow coefficient and voltage at the output of the PEM fuel cell for p = 3

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Fig. 10 Oxygen flow coefficient and voltage at the output of the PEM fuel cell for p = 2.4 and the initial oxygen flow coefficient set to 1.7

5 Conclusions The main task of the oxygen subsystem of the PEM fuel cell is to deliver oxygen in an amount which assures maintaining speed of the oxidation reaction at level determined by the electric current drawn from the cell. Another important task is to flush out water being the product of the reaction. Both of them are achieved by setting the oxygen flow rate at the proper value. Most often that value is calculated as a product of the amount of oxygen consumed in the oxidation reaction and the oxygen excess flow coefficient k. The oxygen flow is usually overestimated due to the value of the coefficient is constant in time.

Piecewise Control Method of Oxygen Flow in PEM Fuel Cell

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The paper presents a method of determination of the oxygen flow taking into account that the coefficient k is varying in time. In every step of the control procedure a new value of the coefficient k is calculated. Performed simulations confirmed the correctness of the proposed procedure for estimating the proper value of the oxygen flow coefficient. The results showed that the most significant impact on the quality of control has the initial value of oxygen flow coefficient k0. The further investigations will focus on the verification of the effectiveness of the described control method by means of experiment on the real PEM fuel cell.

References 1. Larminie, J., Dicks, A.: Fuel cell systems explained. Willey, London (2003) 2. Barbir, F.: PEM fuel cells: theory and practice. Elsevier, California (2005) 3. Grzeczka, G., Polak, A.: Fuel cells for autonomous underwater vehicles. Solidstate Phenomena 198, 84–89 (2013) 4. Pukrushpan, J., Stefanopoulou, A., Peng, H.: Control of fuel cell power systems. Advances in industrial control. Springer, Verlag (2004) 5. Haraldsson, K., Wipke, K.: Evaluating PEM fuel cell system models. J. Power Sources 126, 88–97 (2004) 6. Żak, B., Hożyń, S.: Fuzzy control of reactant supply system in PEM fuel Cell. Solid State Phenom. 180, 11–19 (2012) 7. Al-Dabbagh, A.W., Lu, L., Mazza, A.: Modelling simulation and control of a proton exchange membrane fuel cell power system. Int. J. Hydrogen Energy 35, 5061–5069 (2010) 8. Rowe, A., Li, X.: Mathematical modeling of proton exchange membrane fuel cells. J. Power Sources 102:82–96 (2001) 9. Garus, J.: Modeling of fuel cell energy system for use in AUV. Int. J. Arts Sci. 6(3), 15–22 (2013) 10. Garus, J., Polak, A.: Simulation model of PEM fuel cell operating at hydrogen and oxygen. Adv. Intell. Syst. Comput. 317, 31–39 (2015) 11. Boyer, C., Gamburzev, S., Appleby, A.J.: Evaluation of methods to increase the oxygen partial pressure in pem fuel cells. J. Appl. Electrochem. 29, 1095–1102 (1999) 12. Niknezhadi, A., Allué-Fantova, M., Kunusch, C., Ocampo-Martínez, C.: Design and implementation of LQR/LQG strategies for oxygen stoichiometry control in PEM fuel cells based systems. J. Power Sources 196, 4277–4282 (2011)

Testing the Piezoelectric Energy Harvester’s Deflection on the Amount of Generated Energy Dariusz Jasiulek

Abstract On the market of energy harvesting devices, there are more and more solutions, what means strong development of this relatively new part of industry. In the case of underground mining industry, it is not possible to use the typical solutions and they must be properly adopted. Part of the project results associated with a development of wireless, self-supplying sensor networks for operation in underground mines are given. The results of the measurement of voltage generated by piezoelectric energy harvester (PEH) for of free mounting and installation in the housing, limiting its deflection, are given. Tests were conducted in the laboratory conditions, using a vibrating table. The measurement results indicate a significant reduction of energy generated by PEH when it is installed in the casing, confining its movement. Simulated operation of wireless sensor powered by PEH in a casing and without casing is also presented. Keywords Energy harvesting Vibration energy Piezoelectric energy harvester Wireless sensor node










1 Introduction Progress in the monitoring and automation systems of mining machinery and equipment enable the development and implementation of newer diagnostic and control technology. In the case of explosive atmosphere of methane and/or coal dust, implementation of state-of-the-art technologies is associated with special safety requirements of Directive 94/9/EC (ATEX). The need of meeting the requirements of the Directive and the limited mining market means that the number

D. Jasiulek (&) KOMAG Institute of Mining Technology, Gliwice, Poland e-mail: [email protected] © Springer International Publishing Switzerland 2016 J. Awrejcewicz et al. (eds.), Mechatronics: Ideas, Challenges, Solutions and Applications, Advances in Intelligent Systems and Computing 414, DOI 10.1007/978-3-319-26886-6_7

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of available sensors and communication systems adapted for use in potentially explosive atmosphere of methane and/or coal dust are limited. Control systems of machines and mining equipment, based on industrial networks, e.g., on CANopen bus [1] becomes more and more popular. Industrial networks are aimed at reducing the number of wires (in practice it is necessary to conduct a network cable and power cord, often in one cable). There are the sensors that communicate using a wireless network, but it is necessary to use power wire or battery power supply. Cable routing, especially in the case of mobile mining equipment and large machine systems—such as powered longwall complexes, is troublesome. Damage of cables connecting the machine communication system is the reason of costly downtime. Legal requirements significantly restrict the ability of modifying the existing control systems of machines and devices operating in the underground mines. Especially in the case of mobile mining machinery, such as roadheading machines and loaders manufactured before 2004, the introduction of additional components to the control system makes it necessary to carry out the costly process of recertification of equipment for conformity with the Directive. Bearing in mind the needs of underground mining, the work aiming at development of wireless networks of self-supplying and self-organized sensors in the machines operating in areas threatened by methane and/or coal dust explosion hazard, was undertaken. In the market there are the systems of dispersed pressure sensors, which organize communication with use of wireless network, supplied from batteries [2, 3], what generates the problems associated with time of sensor operation and frequency of measuring data transfer. Current systems offer the ability of transferring the information about pressure with frequency 1 Hz ensuring the battery-powered system uptime of 1 year. Replacement of batteries in the conditions of underground mines can be troublesome, if not impossible, due to the limitations of the space in which the machine works. Batteries are usually replaced during the machine repair. In the last decade the intensive progress of work on wireless sensor networks, which do not require the typical power source, are observed [4–11], while there are no such solutions designed for operation in underground mines. Self-powered sensor networks can be used in various applications, such as monitoring the machine’s operating parameters, environmental parameters, animal behavior [10] or transport infrastructure [5, 6]. In the area of wireless sensor networks, investigations are conducted in the following three main areas: – in the organization of radio communications, especially related to the auto network configuration and operation of the network under emergency conditions. Projects on development of swarm algorithms, which recreate behavior of animals [12, 13], – minimizing the energy consumption of electronic components, – sources of power, including the development of miniature generators based on renewable energy or energy loss [14–16].

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Work regarding the power sources is focused on the development of devices for energy storage—batteries, rechargeable batteries, supercapacitors, and on the development of mini generators powered by renewable energy or energy loss [8, 9, 16, 17]. In the field of renewable energy, mini generators of electricity, based on the conversion of solar or wind energy into electricity are popular. Solar energy can not be used in underground mining plants, but the energy of the air flow can be used. Mine workings are ventilated to provide fresh air to the areas where people work Example of the structure of a self-powered sensor node supplied by energy of air flow is shown in [18]. It was assumed that the sensors used in the network would be equipped with micro power generators supporting or replacing the battery power supply [4, 19–22]. Available sources of energy [23–25] possible to be used in constructing the sensors being a part of wireless network were analyzed, assuming that it is possible to use energy from the temperature difference [12, 26], hydraulic pressure fluctuations [27, 28], airflow [18], and mechanical vibrations [8].

2 Sources of Energy Available in Underground Condition Considering specific character of the processes realized in hard coal mines, the sources of energy, which can be used to supply components of self-supplying and wireless network of sensors, were identified. Sources of energy available in underground mining plants are as follows [23–25]: – Sources of mechanical energy: • • • •

vibrations of machines [8, 29], rotary movement, energy of braking, human motion [8, 30, 31],

– Sources of thermal energy [26, 32]: • temperature of machines and equipment (energy of losses) [26], • temperature of human body, • temperature of rock mass, – Sources of energy coming from electromagnetic radiation: • electric motors, transformers, • power cables, – Sources of energy coming from the air flow [18]: • flow of air in vetube fans, • flow of air ventilating the mine workings,

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– Sources of energy coming form the hydraulic systems [27, 28]: • hydraulic pressure fluctuations, • liquid flow. There are the following popular methods for energy conversion, which can be applied in underground mining plants: – electromagnetic, which uses Faraday’s law saying that electromotive force is induced in a conductor placed in an alternating magnetic field. Alternating magnetic field is most often generated by moving magnets, and systems of coils playing a role of conductor [33, 34]. – piezoelectric, which uses the phenomenon consisting in generation of electric charges on the surface of piezoelectric material under mechanical stresses. Piezoelectric component is placed in a device in a way ensuring maximal use of energy of mechanical phenomena occurring in the device [17, 35]. – electrostatic, which includes conversion of kinetic energy of vibration into electric energy with use of variable capacitor, which is polarized by operation of electrets (a dielectric material that has a quasi-permanent electric charge or dipole polarization). Electret generates external electric field and is the electrostatic equivalent of a permanent magnet [33]. – magnetostriction, which is based on the phenomenon of deformation of ferromagnetic materials in magnetic field. Villari effect is the inverse effect. Change of dimensions under magnetic field can have a linear or volumetric character [33]. – thermoelectric, which is based on recuperation of thermal energy [32]. To convert, e.g., thermal energy to electricity, the thermogenerators are used. These devices produce electricity as a result of temperature difference and stream of thermal energy. There are two main types of thermogenerators–based on Seebeck effect (Peltier Cells) and using the phenomenon occurring in Stirling engine. Peltier Cells are based on Seebeck thermoelectric phenomenon (Seebeck effect), which consists in generation of electromotor force (also called thermoelectric force) in a circuit consisting of two different materials, contacts of which have different temperatures [26, 32]. It is the result of relationship between the contact potential difference between materials and the temperature. Contact potential is generated in a result of diffusion through the contact surface of electrons, from one material to another [32].

2.1

Energy of Mechanical Vibration

Machines operating in underground workings generate vibrations from rotating components, toothed gears of electric motors, etc., in a result of mining and transportation of run-of-mine.

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It is possible to use the energy of vibrations to supply the sensors measuring the following parameters: – temperature at any place by changing the sensor position during machine operation, – pressure of medium in a hydraulic system, – vibrations (vibrodiagnostics), – tension of flight-bar conveyor’s chain, – illuminance of mine railways (suspended monorails and floor-mounted railways). Mechanical vibration energy can be converted to electricity, interalia, through the use of piezoelectric transducers. They are available in the form of a film or ready-to-use components—Piezoelectric Energy Harvester (PEH) [36], prepared for mechanical installation. Analysis of literature sources indicate that this is an efficient energy conversion method [4] but it has some limitations due to requirement of encapsulation and tuning the transducer to a specific oscillation [36–41]. The paper presents results of tests on PEH MIDE V21BL-ND, installed within the electronic system simulating the debiting, corresponding to the sensor network. We analyzed two versions of PEH, without housing and with housing limiting deflection of the transducer within ±2.75 mm. The tests were carried out in the laboratory and accepted conditions regarding the frequency and amplitude of vibration correspond to the selected mining machine with a diesel engine.

2.2

Piezoelectric Energy Harvester MIDE V21BL-ND

Piezoelectric components (piezoelectric transducers, PEH) and electromagnetic generators are the most often used components, which convert the energy of mechanical vibrations into electricity. These components have to be tuned to the machine’s vibrations or automatic tuning has to be applied. Available piezoelectric components most often are adapted to the operation within the range 40–250 Hz. Amplitude of vibrations also affects the generated power. After the initial laboratory test [24], the PEH MIDE V-21BL-ND (Fig. 1) was selected for further tests associated with the use of piezoelectric components in the process of supplying the sensors [24]. V21BL-ND transducer has a narrow range of resonance frequency and it is tuned by adding the weight at its end. Voltage generated by the transducer changes, depending on operational frequency and transducer articulation. Relationship between power and voltage at operational frequency 50 Hz is presented in Fig. 2. The weights that should be used to load the transducer as well as amplitude of articulation, at which a specified output voltage can be reached, are defined in the catalog card of the transducer. Schematic overview of a vibration harvester is presented in Fig. 3.

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Fig. 1 Piezoelectric energy harvester MIDE V21BL-ND [36]

Fig. 2 Piezoelectric energy harvester MIDE V21BL-ND operational characteristics at 50 Hz [36]

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Fig. 3 Schematic overview of a vibration harvester [16]

3 Tests Objectives Determination of the impact on installation of (PEH) MIDE V21BL-ND PEH (Fig. 4) in the housing limiting the maximum deflection of ±2.75 mm on the amount of generated energy was the test’s objective. Tests were carried out on a vibrating table (Fig. 6) which allows changing the oscillation frequency. It was assumed that the frequency of vibration to which PEH are adapted is 50 Hz. PEH was loaded with 2.4 g seismic mass, according to the data sheet [36]. Voltage generated by two PEHs was measured. The first PEH1 was installed in housing without limiting deflection. The second PEH2 transducer was installed in the housing limiting the maximum deflection to ±2.75 mm [36]. PEH2 installed in the housing is shown in Fig. 4. The tests were conducted to determine the impact of housing on the amount of energy generated by the PEH, in the case of amplitude of the vibration acceleration of 36 m/s2. The tests were conducted in two stages. In the first stage, the signal generated by the transducers without the load by receiving system, relation to the table vibration of frequencies 46, 48, 50, 52, and 54 Hz was recorded. Determination of the effect of limiting the deflection of PEH2 on operation of the electronic system with load simulating wireless sensor node was the next stage of tests. It was assumed that to estimate the energy demand of the sensor, the sensor should take measurement and send signal with frequency as 1 Hz. The load was simulated by 3.3 kΩ resistor. The supply voltage was 3.3 V and the current was 1 mA. In real conditions, load is changeable. Typical scenario for the power consumption of sensor node is presented in [16] (Fig. 5). The largest current, of order 15 mA, is at the time of sending a radio signal.

102 Fig. 4 Piezoelectric energy harvester MIDE V21BL-ND installed in the housing [24]

Fig. 5 A typical scenario for the power consumption of a sensor node [16]

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Fig. 6 Vibration table

3.1

Test Rig

The tests were conducted on a test setup, whose schematic diagram is shown in Fig. 7. PEH1 and PEH2 transducers with ICP vibration sensor were mounted on the vibrating table shown in Fig. 6. The vibration frequency of the table was controlled by change of supplying voltage of DC motor. The signals were recorded using an oscilloscope. The energy required to power the sensor was stored in the capacitor CIN included in the electronic system responsible for the energy management [24]. List of symbols VPEH1 VPEH2 CIN VCIN PGOOD T1 T2 ICP VICP

the voltage generated by PEH without housing, the voltage generated by PEH built inside the housing limiting deflection of ±2.5 mm, energy storage capacitor with a capacity of 480 μF, the voltage measured on the capacitor CIN, signal confirming the availability of the system, the capacitor voltage VCIN ≥ 2.7 V, the time from starting the test system to generation of signal about its availability PGOOD, the time measured from connection load simulating the sensor operation to the UCIN < 2.7 V capacitor discharge, vibration sensor Hansford Sensors HS-100F9995408, the voltage generated by the vibration sensor.

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Fig. 7 Diagram of the test bench

UICP

Seismic mass PEH2

PEH1 ICP Vibration generator

Power supply UPEH2 UPEH1

PGOO D

Electronic circuit

UCIN

Recorder

CIN

3,3kΩ

4 Test Results 4.1

Comparative Tests of the Signal Generated by PEH1 and PEH2

In Figs. 8, 9, 10, 11 and 12 the voltage time curves of VPEH1 and VPEH2 recorded during the tests, with settings 46, 48, 50, 52, and 54 Hz are presented. Spectrum of vibrations recorded for the vibrating table, set to 50 Hz is given in Fig. 13. Amplitudes of voltage signal generated by PEH1 and PEH2 are specified in Table 1. Analysis of the results indicate that installation of PEHs in the housing, which limits their deflection reduces the amount of generated energy. In cases where the vibration frequency of the table was equal to 50 Hz, amplitude of the voltage generated by the PEH1 was 43 V and by the PEH2 was 13 V. The recorded voltage amplitude affects the CIN capacitor charging time and the maximum voltage to which the capacitor is charged.

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Fig. 8 The time curves of voltages VPEH1 and VPEH2–46 Hz

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Fig. 9 The time curves of voltages VPEH1 and VPEH2–48 Hz

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Fig. 10 The time curves of voltages VPEH1 and VPEH2–50 Hz

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Fig. 11 The time curves of voltages VPEH1 and VPEH2–52 Hz

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Fig. 12 The time curves of voltages VPEH1 and VPEH2–54 Hz 4.0 3.5 3.0

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Fig. 13 Vibration frequency spectrum of −50 Hz Table 1 Result of tests

The oscillation frequency (Hz) Amplitude VPEH1 Amplitude VPEH2

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Determination of Standby Time T1 in the Case of PEH1 and PEH2

In Fig. 14, the time curve of the CIN capacitor charging is shown. Charging time is calculated from the start up of vibrating table to generate the PGOOD signal by the electronic circuit board. PGOOD signal is generated when the CIN capacitor voltage is above 2.7 V. The measurements were taken at a vibration frequency of 50 Hz of the vibrating table. Time after which the system was ready to work when charging voltage of PEH VPEH1 was T1PEH1 = 7 s. When charging voltage was VPEH2, time was T1PEH2 = 40 s—Fig. 15. The measurements were taken without the load simulating the receiving system.

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Fig. 14 CIN capacitor charging process in the case of power supply by UPEH1

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Fig. 15 CIN capacitor charging process in the case of power supply by UPEH2

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CIN Capacitor Discharge T2 Time

After the voltage stabilization on the capacitor CIN, which in the case of PEH1 was UCIN = 10 V and in the case of PEH2 was UCIN = 4.2 V, the load is connected to the system to simulate the receiver with constant current 0.3 mA. Vibrating table was still active, what caused charging of the capacitor. Figure 16 presents the curve of the capacitor CIN discharge after charging it to the maximum possible voltage with VPEH1. This time it was T2PEH1 = 212 s. When capacitor was charged by voltage VPEH2, the discharge time was T2PEH2 = 11 s—Fig. 17. 12

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Fig. 16 CIN capacitor discharge time below 2.7 V during supply by the PEH1 4.5 4 3.5

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Fig. 17 CIN capacitor discharge time below 2.7 V during supply by the PEH2

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5 Conclusions and Future Work The results of comparison of energy generated by MIDE V21BL-ND PEH with housing in accordance with the guidelines of the data sheet (PEH2) and without housing (PEH1) were presented. Tests were carried out on a vibration table, vibration frequency was between 46 and 54 Hz and amplitude of vibration acceleration was 36 m/s2. The results indicate that PEH1 without housing is able to generate more power, however, the amplitude of deflection exceeds allowable value ±2.25 mm. Energy generated by PEH affects the capacitor charging time and its maximum charge level. In case of testing PEH1, the capacitor charged to voltage above 2.7 V during T1PEH1 = 7 s, while for PEH2 T1PEH2 = 40 s. The capacitor voltage stabilized at UCIN = 10 V for PEH1 and UCIN = 4.2 V for PEH2 what after connecting the load 100 μW allowed for continuous operation for a period of T2PEH1 = 212 s and T2PEH2 = 11 s. On the basis of the obtained results, it can be concluded that in the case of vibration amplitude exceeding the values specified in the data sheet, it is necessary to design different type of housing that guarantees better use of the PEH or use of another type of PEH. In further research work, it is planned to analyze characteristics of PEH operation for vibration frequency of 50 Hz and amplitude of vibration acceleration of 36 m/s2. It has been assumed that energy is stored in a capacitor of capacitance CIN = 480 μF. This has resulted in continuous long-time operation (11 or 212 s). In further work, it would be necessary to select the capacitor enable reducing the charging time and to gather the amount of energy required to operate the sensor at specified intervals. The required frequency of the sensor signal generation is at least 0.1 Hz. In the market of energy harvesting devices, there are more and more solutions, what means strong development of this relatively new part of industry. This development is possible mainly due to introduction of electronic circuits with low power consumption. In the case of underground mining industry, i.e., occurrence of areas threatened by methane and/or coal dust explosion hazard, it is not possible to use the typical solutions and they must be properly adopted.

References 1. Bartoszek, S., Jagoda, J., Jura, J.: System diagnostyczny ładowarki bocznie wysypującej bazujący na iskrobezpiecznej magistrali CAN (in Polish). Szybkobieżne Pojazdy Gąsienicowe (32) nr 1, Ośrodek Badawczo-Rozwojowy Urządzeń Mechanicznych OBRUM sp. z o.o., Gliwice (2013) 2. Catalogue card of Elgór-Hansen EH-PressCater system (www.elgorhansen.com) 3. Catalogue card of Famur FAMAC RSPC system (www.famur.com.pl) 4. Zhu, D., Beeby, S.P., Tudor, M.J., Harris, N.R.: A credit card sized self powered smart sensor node. Sens. Actuators A 169(2), 317–325 (2011)

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5. Sazonov, E., Li, H., Curry, D., Pillay, P.: Self-powered sensors for monitoring of highway bridges. IEEE Sens. J. 9(11) (2009) 6. Wischke, M., Masur, M., Kröner, M., Woias, P.: Vibration harvesting in traffic tunnels to power wireless sensor nodes. Smart Mater. Struct. 20(8) (2011) 7. Lee, M., Bae, J., Lee, J., Lee, C.-S., Hong, S., Wang, Z.L.: Self-powered environmental sensor system driven by nanogenerators. Energy Environ. Sci. 4, 3359–3363 (2011) 8. Mitcheson, P.D., Rao, G.K., Green, T.C.: Energy harvesting from human and machine motion for wireless electronic devices. Proc. IEEE 96(9) (2008) 9. Theophylus Yusuf, S., Halim, Y.M.A., Samosir, A.S., Abdulkadir, M.: Mechanical energy harvesting devices for low frequency applications: revisited. ARPN J. Eng. Appl. Sci. 8(7) (2013) 10. Sudevalayam, S., Kulkarni, P.: Energy harvesting sensor nodes: survey and implications. IEEE Commun. Surv. Tutorials 13(3) (2011) 11. Wang, Z.L.: Self-powered nanosensors and nanosystems. Adv. Mater. 24(2), 280–285 (2011) 12. Stankiewicz, K.: Metoda samoorganizacji roju w monitorowaniu i sterowaniu urządzeń w warunkach wyrobisk podziemnych (in Polish). Maszyny Górnicze nr 4, 10–13 (2011) 13. Arabshahi, P., Gray, A., Kassabalidis, I., Das, A., Narayanan, S., Sharkawi, M., El Marks, R. J.: Adaptive routing in wireless communication networks using swarm intelligence. In: AIAA 19th Annual Satellite Communications System Conference, Toulouse, France (2001) 14. Buchacz, A., Wróbel, A.: Modelling of complex piezoelectric system by non-classical methods. J. Achievements Mater. Manufact. Eng. 35, 63–70 (2009) 15. Buchacz, A., Płaczek, M., Wróbel, A.: Control of characteristics of mechatronic systems using piezoelectric materials. J. Theor. Appl. Mech. 51(1), 225–234, Warsaw (2013) 16. Vullers, R.J.M., van Schaijk, R., Doms, I., Van Hoof, C., Mertens, R.: Micropower energy harvesting. Solid-State Electron. 53, 684–693 (2009) 17. Chen, X.-R., Yang, T.-Q., Wang, W., Yao, X.: Vibration energy harvesting with a clamped piezoelectric circular diaphragm. Ceram. Int. 38, 271–274 (2012) 18. Sardini, E., Serpelloni, M.: Self-powered wireless sensor for air temperature and velocity measurements with energy harvesting capability. IEEE Trans. Instrum. Measur. 60(5) (2011) 19. Sardini, E., Serpelloni, M.: Passive and self-powered autonomous sensors for remote measurements. Sensors 9, 943–960 (2009) 20. Gilbert, J.M., Balouchi, F.: Comparison of energy harvesting systems for wireless sensor networks. Int. J. Autom. Comput. 05(4), 334–347 (2008) 21. Zuo, L., Tang, X.: Large-scale vibration energy harvesting. J. Intell. Mater. Syst. Struct. 24 (11), 1405–1430 (2013) 22. Roundy, S., Wright, P.K., Rabaey, J.: A study of low level vibrations as a power source for wireless sensor nodes. Comput. Commun. 26, 1131–1144 (2003) 23. Jasiulek, D., Stankiewicz, K., Jagoda, J.: Możliwości zastosowania czujników samozasilających się przeznaczonych do pracy w podziemiach kopalń (in Polish). Mechanizacja i Automatyzacja Górnictwa. Nr 8(519), 73–80 (2013) 24. Jasiulek, D.: Alternative sensors power source used in mining. ITG KOMAG Gliwice (not published) (2012) 25. Jasiulek, D.: Propozycje zastosowania czujników samozasilających się w przemyśle wydobywczym (in Polish). Przegląd Górniczy 1 (2014) 26. Woszczyński, M., Świder, J.: Use of the system for energy recuperation and control in diesel machines. Mach. Dyn. Res. 38(1) (2014) 27. Wang, D.-A., Pham, H.-T., Chao, C.-W., Chen, J.M.: A piezoelectric energy harvester based on pressure fluctuations in Kármán Vortex Street. In: World Renewable Energy Congress, Linkoping, Sweden, 8–13 May 2011. Hydropower Applications (2011) 28. Cunefare, K.A., Skow, E.A., Erturk, A., Savor, J., Verma, N., Cacan, M.R.: Energy harvesting from hydraulic pressure fluctuations. Smart Mater. Struct. 22 (2013) 29. Żólkiewski, S.: Vibrations of beams with a variable cross-section fixed on rotational rigid disks. Latin Am. J. Solids Struct. 10, 39–57 (2013)

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30. Bai, P., Zhu, G., Lin, Z.-H., Jing, Q., Chen, J., Zhang, G., Ma, J., Wang, Z.L.: Integrated multilayered triboelectric nanogenerator for harvesting biomechanical energy from human motions. ACS Nano 7, 3713–3719 (2013) 31. Prabaharan, R., Jayaramaprakash, A., VijayAnand, L.: Power harvesting by using human foot step. Int. J. Innov. Res. Sci. Eng. Technol. 2(7) (2013) 32. Stankiewicz, K., Woszczyński, M.: Metody odzyskiwania i przetwarzania energii cieplnej (in Polish). Maszyny Górnicze nr 1, 39–46 (2010) 33. Jaworski, B., Dietłaf, A., Miłkowska, L.: Kurs fizyki. T. II: Elektryczność i magnetyzm (in Polish). Warszawa: Państwowe Wydawnictwo Naukowe (1984) 34. Glynne-Jones, P., Tudor, M.J., Beeby, S.P., White, N.M.: An electromagnetic, vibration-powered generator for intelligent sensor systems. Sens. Actuators A 110, 344–349 (2004) 35. Shena, H., Qiu, J., Balsi, M.: Vibration damping as a result of piezoelectric energy harvesting. Sens. Actuators A, 169, pp. 178–186 (2011) 36. Catalogue card of MIDE V21BL-ND transducer (www.mide.com) 37. Aboulfotoha, N.A., Arafab, M.H., Megahed, S.M.: A self-tuning resonator for vibration energy harvesting. Sens. Actuators A 201, 328–334 (2013) 38. Radkowski, S., Lubikowski, K., Piątak, A.: Vibration energy harvesting in the transportation system: a review. Diagnostyka—Appl. Struct. Health Usage Condition Monit. 4(64) (2012) 39. Challa, V.R., Prasad, M.G., Fisher, F.T.: Towards an autonomous self-tuning vibration energy harvesting device for wireless sensor network applications. Smart Mater. Struct. 20 (2011) 40. Tang, X., Zuo, L.: Simultaneous energy harvesting and vibration control of structures with tuned mass dampers. J. Intell. Mater. Syst. Struct. 23(18), 2117–2127 (2012) 41. Jia, Y., Seshia, A.A.: An auto-parametrically excited vibration energy harvester. Sens. Actuators A 220, 69–75 (2014)

Analysis of Crash Computation on a Basis of the Principle of Linear Momentum and Kinetic Energy Krzysztof J. Kaliński, Marek Chodnicki, Barbara Kowalska and Piotr Kmita

Abstract The article shows the calculation of a vehicle crash with a fixed pile, modelled by the finite element method. They were compared during the crash simulation changes in kinetic energy, as well as—changes in linear momentum and its derivative, with respect to time. Calculations were made in the HyperWorks CAE software environment. The obtained results show influence of various body parts and devices of the deceleration on the vehicle during crash. Keywords Crash method


Simulation
Linear momentum
Energy
Finite element

1 Introduction Car accidents are dramas of thousands of people all over the world. They became one of the main social problems, whose significance is becoming greater with increasing a number of vehicles and their performance. Providing safety for users then became one of the priorities for present designers work.

K.J. Kaliński (&)
M. Chodnicki
B. Kowalska Gdańsk University of Technology, Gdańsk, Poland e-mail: [email protected] M. Chodnicki e-mail: [email protected] B. Kowalska e-mail: [email protected] P. Kmita Des Art Sp. z o.o, Gdynia, Poland e-mail: [email protected] © Springer International Publishing Switzerland 2016 J. Awrejcewicz et al. (eds.), Mechatronics: Ideas, Challenges, Solutions and Applications, Advances in Intelligent Systems and Computing 414, DOI 10.1007/978-3-319-26886-6_8

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Modern engineering solutions require executing the numerous products analysis to define their behaviour under specified conditions. Newly implemented ideas must be tested especially in terms of loads, which reflect the real exploitation conditions. The same recommendations are also advised to vehicles intended for common use. They should therefore be in a particularly rigorous fulfilment of safety requirements. One of the types of tests is called “crash tests.” Previous studies associated with the crash tests, using models representing approximately the whole car structure (instead of only selected parts), were focused mostly on reconstructions of occurred collisions. There were mutual collisions of two vehicles as well as collisions with stationary obstacles. Their purpose was, for example, verification of the methods used for accidents’ reconstructions [1], retrieving crash process based on deformation of the construction [2, 3], studying the impact of a number of factors on a size of human injuries [4–6]. Vehicle collisions with wall, pile or lamppost were intended to demonstrate influence of using different materials on extent of the damage. Course of these studies were mostly focused on testing the materials of the piles, for example, to increase their impact energy absorption [7]. Also materials used in car constructions were analysed from the point of view of reducing mass of the vehicle and simultaneous maintaining of its hardness during collision [8]. Research with pile crash impact performed by V. Sharma and the others finally attempted to show stresses and deformations of the modelled car [9]. However, the model was extremely simplified. Also, there were presented only approximate external modes of the vehicle. During subsequent stages of a collision, no real-part behaviour has been presented. The article shows the simulation results of a vehicle crashing with stationary pile, and modelled with the use of finite element method and principle of linear momentum and kinetic energy. There are presented successive stages of a collision to demonstrate the influence of selected parts of the vehicle on its slowdown. It is also possible to observe behaviour of the parts and their stress distribution based on simulated computational model.

2 Simulations First step of simulation depended on importing the CAD model of the vehicle into a computer simulation programme. Also obstacles were modelled, to which the car has hit; in this case, it was a stationary pile. Simulated system is illustrated in Fig. 1. For simulation purposes, chosen simple model contains the most important elements, such as the body, bumper, radiator, engine, wheels, stringers, and beams. Generally, it consists of 26 components (Fig. 2).

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Fig. 1 Model of the vehicle and the pile

The next step was mesh generation of the model, i.e. division of the geometry into finite elements (Fig. 3). After applying the mesh, the model consists of 4586 8-node isoparametric finite elements and 4755 nodes. There were determined and specified material properties, including mass densities, Young’s modules, Poisson’s coefficients and defined the types of connections between parts of the vehicle. There were three kinds of materials, i.e. glass, rubber and steel. Appropriate properties of the specified materials are shown in Table 1. In all cases, the simulated material models were of Johnson–Cook [10]. Initial speed was 100 km/h. In this simulation, the engine was treated as rigid body, which was not subject to deformations, and the brakes were not being used. It was also not taken into account interaction between the tyres and the road. The crash history is shown in Fig. 4. It may be noticed how under the impact of the stationary pile, different parts of the car behave. The bumper is the first part of the structure, which sustains deformation. Along with the successive stages of the simulation, we can observe also large deformations of the hood, fenders and other

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(a)

(b)

(c)

Fig. 2 Collocation of car components, without windows and hood (a, b) and without fender (c)

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Fig. 3 Model of car and pile with the finite element mesh

Table 1 Properties of used materials Initial mass density (kg/m3) Young’s modulus (MPa) Poisson’s coefficient (−) Yield stress (MPa) Hardness parameter (MPa) Hardness exponent (−)

Glass

Rubber

Steel

2.5 × 103 76,000 0.3 192 200 0.32

2 × 103 200 0.49 1 – 1

7.9 × 103 210,000 0.3 200 450 0.5

elements. The impact causes also wheel axle deflection. It can therefore be concluded that the simulation in a very realistic way reflects the behaviour of the crash. Next steps of the crash, together with the calculated reduced stress according to hypothesis of Huber-von Mises, are shown in Fig. 5. Figure 6 shows also the behaviour of internal components of the vehicle. We can see how different parts of the structure are moving with the crash development. The latter facilitates interpretation of the obtained characteristics.

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(a)

(b)

(c)

(d)

Fig. 4 Crash simulation. a Beginning of collision, b destruction of the bumper and radiator, c destruction of the hood and motor collision with the pile, d wheel axle and stringers deflection

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(a)

(b)

(c)

(d)

Fig. 5 Crash simulation with reduced stress distribution, according to hypothesis of Huber-von Mises

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(a)

(b)

(c)

(d)

Fig. 6 Crash simulation with reduced stress distribution inside the vehicle, according to hypothesis of Huber-von Mises

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3 Computational Model Complex geometry of the structure is mapped using volumetric 8-node isoparametric finite elements described in global Cartesian coordinate system x, y, z. This system is common to all of the finite elements and does not depend on their position in space [11]. Nodes of element no. e were respectively labelled 1e, 2e, 3e, 4e, 5e, 6e, 7e and 8e, whereas their coordinates—xie, yie, zie, i = 1, …, 8. At the instant of the collision of the car with a pile occurs the deformation of finite elements (Fig. 7). Vector of generalised displacements of selected point of the finite element with coordinates x, y, z is described by equation: qðx; y; zÞ ¼ X ðx; y; zÞ
a

ð1Þ

wherein 2

 ðx; y; zÞ X X ðx; y; zÞ ¼ 4 0 0

0  ðx; y; zÞ X 0

 ðx; y; zÞ ¼ ½ 1 X

z

3 0 5 0  ðx; y; zÞ X

ð2Þ

yz xyz Š

ð3Þ

where x

y

xy

xz

while a ¼ ½a1 . . . a24 ŠT

Fig. 7 Deformation of 8-node isoparametric finite element no. e

ð4Þ

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is a vector of unknown coefficients. The number of coefficients of the vector a is equal to the number of all components of vector of nodal displacements qe of finite element number e, which are the boundary conditions. Vector of coefficients a is determined from the equation qe ¼ X nod
a

ð5Þ

qe ¼ colðqðx1e ; y1e ; z1e Þ; . . .; qðx8e ; y8e ; z8e ÞÞ

ð6Þ

where

It is a vector of generalised displacements of finite element no. e, corresponding to its nodes. Now, on the basis of Eq. (2), we obtain the following matrix: 2

3 Xðx1e ; y1e ; z1e Þ 6 7 .. ¼4 5 .

ð7Þ

qðx; y; zÞ ¼ N e ðx; y; zÞ
qe

ð8Þ

1 N e ðx; y; zÞ ¼ X ðx; y; zÞ
X nod

ð9Þ

Xnod

Xðx8e ; y8e ; z8e Þ

Thus is obtained the relation

where

is the matrix of shape functions of finite element no. e. Equation (9) allows to determine generalised displacements for any point inside the isoparametric finite element, as functions of nodal displacements of the element. Inertia matrix of the isoparametric finite element describes its properties related to the storage of kinetic energy. The matrix of inertia of the element no. e is determined by the following equation [11]: Z M e ¼ qe ðx; y; zÞN Te ðx; y; zÞ
N e ðx; y; zÞdV ð10Þ V

where: qe —density of the material of isoparametric finite element. The kinetic energy of the finite element no. e is a variable value during the simulation from time t0 to tmax. At instant of time t, we get: 1 Te;t ¼ q_ Te;t M e;t q_ e;t 2 whereas, at instant of time t + Δt

ð11Þ

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1 Te;t þ Dt ¼ q_ e;t þ Dt T M e;t þ Dt q_ e;t þ Dt 2 where Te;t Te;t þ Dt

123

ð12Þ

kinetic energy of finite element no. e at instant of time t, kinetic energy of finite element no. e at instant of time t þ Dt;

Fig. 8 Procedure for calculating whole kinetic energy of the system composed of ie finite elements in a time domain

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q_ e;t q_ e;t þ Dt M e;t M e;t þ Dt

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vector of nodal velocities of finite element no. e at instant of time t, vector of nodal velocities of finite element no. e at instant of time t þ Dt; inertia matrix of finite element no. e at instant of time t, inertia matrix of finite element no. e at instant of time t þ Dt:

A block diagram of the procedure for calculating in the time domain the whole kinetic energy of the system composed of ie isoparametric elements, is shown in Fig. 8. Linear momentum of the system at instant of time t, we compute by equation pt ¼ M t q_ t

ð13Þ

where Mt ¼

ie X e¼1

c M e;t

ð14Þ

is matrix of inertia of the whole system with m degrees of freedom and q_ t is vector of generalised velocities of this whole system. Structures of local matrices M e;t and q_ e;t of finite element no. e are illustrated in Fig. 9, while distributions of their components over areas of global matrices c M t and q_ t —in Fig. 10. A block diagram of the procedure for calculating, in the time domain, vector of linear momentum of the system composed of ie isoparametric finite elements, is shown in Fig. 11.

Fig. 9 Structure of local matrices of finite element no. e

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Fig. 10 Distribution of components of local matrices of finite element no. e over areas of the global matrices

4 Results of simulations Equations (1)–(14) show that the basis for applying the principle of linear momentum and principle of kinetic energy is the knowledge about the mass and velocity of the object under consideration. They are constant at the starting point of simulation and determine the initial value of the linear momentum and energy, whose changes we intend to observe. Although the mass is constant during the simulation, the volume of each finite element, as a consequence also density, will vary with time. Therefore, the linear momentum and kinetic energy will change due to changes of speed or deceleration of the vehicle, as well as changes in the matrix of inertia, due to changes in geometry of the finite elements. That is why we are going to observe the above concerning body parts and other equipment of the vehicle. Figure 12 shows simulation in time domain, the course of values of the linear momentum of the system. There are marked in the plot four subsequent important steps of a collision (i.e. from A to D). Hence you can observe a very distinct decline in value of the linear momentum, which represent the clash of next elements of the car. The first significant change can be observed near time-instant 0.009 s, when the cooler hits in the pile. Earlier stage has rather gentle course because striking the bumper suffers considerable deformation and its influence on characteristics of the linear momentum is small. Collision with the engine is of great importance, because its impact causes the loss of about half of the linear momentum. It can be seen for 0.023 s of the simulation.

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Fig. 11 Procedure for calculating vector of linear momentum of the whole system composed of ie finite elements, in a time domain

Further, course of plot reflects the impact among other components of hood and stringers, as well as the engine hits to cabin wall. At time-instant about 0.048 s is shown again a rapid decrease in the linear momentum. It is caused by beam to which is mounted the engine. Deformation runs along its construction, so that it results in relatively rapid (albeit small) deceleration of the vehicle. Above observations and course of the linear momentum in time domain, confirms computation of derivative of the linear momentum in time domain. In Fig. 13 is shown the time-variable numerical value of linear momentum derivative of the whole system, which is equal to the resultant force acting on the centre of mass of the vehicle, in accordance with the principle and the linear momentum

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A

B

C

D

Fig. 12 Linear momentum value of the whole system in time domain

A D

B

C

Fig. 13 Linear momentum derivative of the whole system in time domain

kp_ t k ¼ FC;t

ð15Þ

A similar conclusion can be reached by analysing the plots of the kinetic energy and the internal energy (Fig. 14). The curve showing the kinetic energy is similar to the plot of a linear momentum decreasing. A significant decrease in the kinetic energy occurs at time of impact on the radiator and the engine. For the same time-instants increase of internal energy,

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A B

D C

Fig. 14 Kinetic energy and internal energy of the whole system in time domain

which is almost equal relative to the decrease in kinetic energy. Noticeable differences in the final values are due to conversions of kinetic energy into deformation energy.

5 Summary Crash simulations of vehicles using computer software are becoming a necessary tool of modern engineering. Their utility during study of the structural behaviour under different conditions is wide indeed. Thanks to the performed simulations; it is possible to observe an influence of every element of the vehicle during the collision process, as well as the scale and type of the formed damages. The obtained results may be used for structural improvements on a stage of virtual prototyping. It is possible to find the weak points of the structure and make their appropriate modifications, what will have an unquestionable influence on safety improvement. Besides the construction optimisation, this kind of research can be used to define a degree of safety of the vehicle under specified operating conditions. Skilfully executed simulations give the opportunity to define, for example, acceptable speed range when the vehicle will preserve its safety properties relative to the driver and passengers. This has a huge practical meaning due to safety improvement and reduction in mortality in the case of an accident. An unquestionable advantage is also a significant time reduction while implementation of the new construction, because on the design and optimisation stage it is possible to perform numerous simulations instead of building and studying real structures. The number of real tests is limited to minimum, they bring up only for

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confirmation of the simulation results. That allows for huge cost reduction. Using the obtained results of subsequent simulations, it is possible to optimise the structure increasingly, until achieving its most passable form. The tests using models created by the finite element method give relatively high precision for calculations. Furthermore, for effective and clear result presentation, it is possible to create an animation using post-processing tools; also whole object behaviour may be observed in various perspectives, in dependence of the necessity. These studies are just an illustrative example of the potential that crash the tests provided, with usage of the finite element method. For more accurate and actual results, it is intended to perform simulations using definitely more complex model, which would give the actual structure largely.

References 1. Gidlewski, M.: Badania zderzeń bocznych samochodów osobowych w ruchu – ślady powstające na skutek zderzenia, istotne dla jego rekonstrukcji. Zeszyty Naukowe Instytutu Pojazdów 4(90), 43–60 (in Polish) (2012) 2. Zhang, X., Jin, X., Qi, W., Guo, Y.: Vehicle crash accident reconstruction based on the analysis 3D deformation of the auto-body. Adv. Eng. Softw. 39, 459–465 (2008) 3. Prochowski, L., Żuchowski, A.: Comparative analysis of frontal zone of deformation in vehicles with self-supporting and framed bodies. J. KONES Powertrain Transp. 18(4) (2011) 4. Sobhani, A., Young, W., Logan, D., Bahrololoom, S.: A kinetic energy model of two-vehicle crash injury severity. Accid. Anal. Prev. 43, 741–754 (2011) 5. Tolouei, R., Maher, M., Titheridge, H.: Vehicle mass and injury risk in two-car crashes: a novel methodology. Accid. Anal. Prev. 50, 155–166 (2013) 6. Prochowski, L., Żuchowski, A., Zielonka, K.: Analiza wpływu prędkości uderzenia w przeszkodę na obciążenia dynamiczne osób w samochodzie z ramową konstrukcją nośną. Archiwum Motoryzacji, 3/2011, Warszawa 2011 (in Polish) 7. Yehia, A.: Abel-Nasser: Frontal crash simulation of vehicles against lighting columns using FEM. Alexandria Eng. J. 52, 295–299 (2013) 8. Ambati, T., Srikanth, K.V.N.S., Veeraraju, P.: Simulation of vehicular frontal crash-test. Int. J. Appl. Res. Mech. Eng. (IJARME) 2(1) (2012). ISSN: 2231–5950 9. Sharma, V., Bansal, R., Sharma, R.B., Pupadhyay, Y.: Simulation of generic sports utility vehicle-to-pole front crash analysis using a CAE based methodology. Int. J. Automobile Eng. Res. Develop. (IJAuERD) 3(1), 47–56 (2013). ISSN 2277-4785 10. Kang, W.J., Cho, S.S., Huh, H., Chung, D.T.: Modified Johnson-Cook model for vehicle body crashworthiness simulation. Int. J. Veh. Des. 21(4–5), 424–435 (1999) 11. Kaliński, K.J.: A surveillance of dynamic processes in mechanical systems, (in Polish). Poland, Gdańsk University of Technology Publishers, Gdańsk (2012)

Modeling and Simulation of the Solar Collector Using Different Approaches Kazimierz Kamiński and Tomasz Krzyżyński

Abstract This paper presents numerical and experimental investigation of a flat-plate solar collector. Fluid flow and heat transfer in the collector panel are studied by means of distributed-character modeling method (D-C) and computational fluid dynamics (CFD) calculations. Further, experimental investigations of the solar collector panel are carried out. The solar collector thermal efficiency is determined according to EN ISO 9806:2013 standard and the absorber temperature distribution is measured through the back side of collector panel. The measured collector thermal efficiency and absorber temperature distribution are compared with the results from two different numerical models. The paper is summarized by discussion about utility value of tested numerical models in various research areas. Nomenclature A c d D Gsun g V W L Q v T q

Area (m2) Heat capacity (J kg−1 K−1) Inner diameter (m) Outer diameter (m) Solar radiation (W m−2) Thickness (m) Volume (m3) Width (m) Length (m) Power output (W) Velocity (m s−1) Temperature (°C) Heat flux (W)

K. Kamiński (&)
T. Krzyżyński Faculty of Technology and Education, Koszalin University of Technology, Koszalin, Poland e-mail: [email protected] T. Krzyżyński e-mail: [email protected] © Springer International Publishing Switzerland 2016 J. Awrejcewicz et al. (eds.), Mechatronics: Ideas, Challenges, Solutions and Applications, Advances in Intelligent Systems and Computing 414, DOI 10.1007/978-3-319-26886-6_9

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a k ðsaÞ m_ r S q e g g0 a1 a2 T m Nu Re Pr Γ

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Heat transfer coefficient (W m−2 K−1) Thermal conductivity (Wm−1 K−1) Transmittance–absorbtance product Mass flow rate (kg s−1) Stefan-Boltzman constant (W m−2 K−4) Surface area (m2) Density (kg m−3) Emissivity Efficiency Optical efficiency Heat loss coefficient (W m−2 K−1) Temperature dependence of a1 (W m−2 K−2) Reduced temperature difference (m2 K W−1) Nusselt number Reynolds number Prandtl number Diffusive coefficient

Subscripts a p f m in out amb

Absorber Pipe Fluid Middle Inlet Outlet Ambient

1 Introduction A flat-plate solar collector is a low-cost and the easiest-to-fabricate device which can effectively transform solar energy into useful heat. For the same reason, solar collectors are often used in domestic water heating systems, agriculture drying applications, and industrial heat processing. Figure 1 shows a typical, commonly used flat-plate solar collector. The energy conversion, which occurs inside solar collector, is carried out by a flat-plate, high conductive metal sheet called as the absorber plate. Useful heat, collected in the absorber plate, is taken away by working fluid, pumped through the flow channels which are welded to the absorber plate. This type of absorbers is called fin-and-tube and can be made in two basic configurations. The first one is a serpentine-tube absorber, where flow is driven through only one, specially formed

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Fig. 1 Solar flat-plate collector: 1 collector housing; 2 glass cover; 3 absorber; 4 thermal insulation

flow channel. Because of quite a complicated fabrication process this type of solar collector is often priced similarly to evacuated heat pipe solar collectors. The second type, more widespread and cheaper, is parallel tube solar collector. In this type of collector, flow of working fluid is driven through a number of straight flow channels, mounted to inlet and outlet manifolds. Figure 2 shows basic flow channels configurations applied in commonly used solar flat-plate collector. In most cases, solar flat-plate collectors are simple devices which consist of thermal isolated assembly of flat metal sheet connected to flow pipes. During the last few decades, this simple design has been well optimized and improved. However, there is still an interest in more effective solutions and design

Fig. 2 Basic configuration of solar collector absorber flow channels configurations: a serpentine-tube (meander); b parallel tube (harp)

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optimizations. This improvement process needs to be carried out with appropriate numerical models and experiments. In order to estimate the thermal performance of the solar collector, which is operated in specific climate conditions, many different models presented in literature can be used. The differences between those approaches basically depend on complexity and established assumptions and simplifications. It is important to know which one can be used to achieve the required calculation goal.

2 Solar Flat-Plate Collector Modeling In general, it is quite difficult to numerically obtain comprehensive information about heat exchange process and thermal behavior of a solar collector. This is mainly because of the complexity of this problem and high number of parameters affecting it. In spite of these difficulties, several useful numerical approaches have been developed. A part of these methods are based on the well-known Hottel-Whillier-Bliss theory [1], which is suitable for almost every kind of solar collectors. These methods provide quite simple form of differential equations, with distributed character (D-C), which can be solved with the finite differences method. Another group of solar collector modeling approaches, highly developed during the last years, are CFD numerical methods [2]. In order to compare the results from these two types of modeling approaches, the simplified distributed-character model was built and CFD modeling procedure using Ansys Fluent 13 was carried out.

2.1

Distributed-Character Model

The solar collector thermal efficiency is strongly correlated with the internal temperature distribution. In order to form highly accurate numerical model with proper heat losses, the spatial absorber temperature needs to be obtained. Since the single-capacitance models are not able to predict the inside collector temperature distribution, the distributed-character modeling method was used. The proposed distributed-character model is suitable for almost every kind of solar collector design. It allows obtaining a lot of useful information about modeled heat exchanging process. The elaborated model consists of M nodes perpendicular to the flow direction (e.g., absorber discrete elements, flow channels, and working fluid) and N nodes in flow direction. As a result, the N × M system of ordinary differential equations is obtained and solved with the finite difference method. Similar forms of models were presented by Kimminga [3] and de Ron [4]. Schnieders [5] presented also a validation with evacuated tubes solar collector. Himler et al. [6] presented a wide overview of partial differential equations calculation methods and validation with unglazed collector used for heating public outdoor swimming pool. One of the most advanced distributed-character models,

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Fig. 3 The absorber fin discretization sketch

which can be used to obtain spatial temperature distribution inside the collector, was presented by Oliva et al. [7]. The model prepared to use in this paper assumes equal mass flow rate in each flow channel of solar absorber so there is only one fin section of absorber taken into consideration. Figure 3 shows the absorber fin divided into control volumes. For each collector component, in this case absorber plate, flow channel and working fluid, energy balance equations were derived. The energy balance equation of heat fluxes in control volume of the absorber plate is formulated in cross-section of the absorber fin (Fig. 4). Energy balance equation for the absorber plate is formulated as qacc ¼ Dqx  qloss þ qa

ð1Þ

where qacc, Δqx, qloss, and qa are energy fluxes of accumulation, conduction, heat loses, and absorbed solar radiation, respectively. The absorber taken into consideration is the assembly of a flat-plate sheet metal with pipes welded into the uninsulated side of plate. The expanded form of absorber plate energy equation is written as follows [1]: q a ca V a

dTa ¼ ds



 dTa  dTa  ka ga  k g a a dx x dx x þ Dx " #
 Ta 4  aamb ðTa  Tamb Þ þ rea Gsun ðsaÞ Dx 100

where αamb is the heat loss coefficient determined experimentally.

ð2Þ

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Fig. 4 Energy balance of absorber plate

In Eq. (2), spatial derivatives dTa/dx are replaced by forward differential quotients   Ti  Tp dTa  Ti  Ti þ 1 dTa  ; ¼ ¼   dx i¼0 Dx dx x¼Wa =2 Dx

Thermal energy generated in the absorber plate is conducted into fluid channels through the homogeneous bonds. Figure 5 shows fluid channel energy balance. The energy balance equation for the fluid pipe is formulated as qacc ¼ Dqy  qloss þ qap

ð3Þ

where qacc, Δqy, qloss, and qa−p are heat fluxes of accumulation in the flow channel, conduction in the flow channel, heat losses to ambient, and conduction between the absorber plate and the flow channel, respectively. The final form of flow channel energy balance is written as follows: dTp ¼ qp cp Vp ds



 dTp  dTp  ka pSp  ka pSp dy y dy y þ Dy      aamb pDp Tp  Tamb þ ka ga ðTp  Ta Þ Dy

ð4Þ

Working fluid is heated by the walls of flow channels. In practice parts channels near to the absorber plate are hotter than bottom parts. This model assumes uniform temperature distribution in the cross section of the flow channel, equal to the temperature of the bond (Fig. 6).

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Fig. 5 The energy balance of fluid channel

Fig. 6 Energy balance of working fluid

The energy balance for working fluid was formulated as q f cf V f

   dTf  ¼ mf cf Tf y  mf cf Tf y þ Dy þ apf pdp ðTp  Tf ÞDy ds

ð5Þ

where αp−f is the heat transfer coefficient on the boundary between pipes and working fluid, determined on the basis of Nusselt number, given by Heaton [1]: apf ¼

Nuf kf dp

ð6Þ

where:

1:66 d 0:00172 Re Pr Lp Nuf ¼ 4:4 þ

: d 1:29 1 þ 0:00281 Re Pr Lp

ð7Þ

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CFD Model

The second approach of solar collector simulation methods, often used to determine the efficiency of solar collectors, are CFD models built with CFD simulation software. Fan et al. [8] presented CFD solar collector model verified with experimental outdoor data. In this paper, the solar collector is modeled with assumption of uniform energy generation in the absorber tube and considering only a convective heat loss coefficient, calculated using external software SolEffs and set as an input for the CFD calculations. The comparison between calculated results and experimental data shows good agreement, especially in high flow rates. Furthermore, the authors show nonuniformity of the mass flow rate in absorber flow channels and discuss the influence of flow nonuniformity on the collector performance. Selmi et al. [9] presents 3D simulation of a flat-plate solar collector using the commercial CFD software CFD-ACE. The numerical results compared with experimental data, show good agreement in the analysed temperature profiles. Turgut and Onur [2] perform a numerical CFD analysis to determine the average heat transfer coefficients for forced convection air flow over a flat-plate solar collector surface. To compare this method with the previously shown distributed-character modeling method, a simplified CFD model was built using code Fluent 12. The calculation domain of the proposed CFD solar collector model consist of the same physical components representation as previously: an absorber plate, fluid channels, and working fluid. However, in this case, all geometrical details of the absorber were taken into consideration. Figure 7 shows the geometric details of the calculation domain. Collector chasing is represented by convective and radiative heat loss from the absorber to ambient. The heat loss coefficient is estimated during thermal experiments of average absorber surface temperature and ambient collector temperature (Table 1).

Fig. 7 CFD solar collector geometric model

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139

Table 1 Solar collector KSH-2.0 technical specification Technical parameters

KSH-2.0

Manufacturer/brand Collector type/gross area Absorber type Absorber material: plate/tubes Absorber connection method Number of working channels Number of manifolds Working channels inner/outer diameter Manifolds inner/outer diameter Absorber coating/selectivity index Cover glass number/thickness Thermal insulation: bottom/sides

KOSPEL inc./KSH-2.0 Flat-plate/2 (m2) Parallel tube (harp) Copper/copper Ultrasonic welding 9 2 ϕ8/ϕ7 (mm) ϕ18/ϕ16 (mm) Blue Tec eta plus/19 1/3.2 (mm) 45/20 (mm)

Using the geometrical absorber model, the unstructured mesh was generated with the ICEM-CFD mesh tool. The absorber plate was meshed with hexahedron type of volume elements and all fluid channels and fluid domain were meshed with tetrahedral type cells. Solar energy absorbed by an absorber was determined as qa ¼ Gsun ðsaÞ

ð8Þ

where Gsun is the solar irradiance (W/m2) and ðsaÞ is effective transmittance– absorption product (Fig. 8).

Fig. 8 Mesh setup of solar absorber model

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In default operation conditions, a solar collector works in laminar flow conditions, so that a laminar flow model was used. In this case, Fluent will solve the governing conservation equations of mass, momentum, and energy. The governing equations are represented by a conservation equation for transport of a scalar quantity ϕ, written in an integral form for an arbitrary control volume V as follows [8]: I A

q/v
dA ¼

I

C/ r/
dA þ

A

Z

S/ dV

ð9Þ

V

H ! R ! H where q/! v
d A , C/ r/
d A , V S/ dV stand for change of parameter ϕ by convection, diffusion, and generation, respectively. In the presented numerical approach, the natural-convection flow was taken into account by setting the fluid density ρ as a function of temperature, using the Boussinesq approximation

Fig. 9 Outdoor solar collector experimental setup

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q ¼ q0 ð1  bDT Þ

ð10Þ

where β is the fluid thermal expansion coefficient and ρ0 is constant density of the flow (Fig. 9). Calculation was performed in transient mode with pressure staggering option PRESTO and second-order upwind method for discretization of the momentum equations. The semi-implicit method (SIMPLE) was used to treat the pressure-velocity coupling. Calculation was considered converged when the scaled residuals for continuity equation, momentum equations, and energy equations fall below 1.0 × 10−4, 1.0 × 10−4, and 1.0 × 10−7, respectively.

3 Experimental Work Thermal measurements have been carried out with a 2 m2 parallel tube flat-plate solar from KOSPEL Inc., Poland. Technical specification of tested collector is given in Table 2. Collector was tested in steady-state and transient conditions with artificial and natural solar radiation. Working fluid water was used. The inlet and outlet water temperature and ambient temperature was measured with RTD platinum sensors (Pt 100). The circulation of working fluid was forced by pump and the mass flow rate was measured using ENCO MPP-6 flow meter. Solar irradiance at collector front plane was measured with LP PYRA 02 pyranometer. The absorber surface temperature was measured during indoor test with thermocouple type “K”. The position of measuring points is schematically shown in Fig. 10. The data collection from RTD sensors, pyranometer, flow meter, ambient temperature sensor, and surface temperature sensor was executed by NI CompactDAQ data acquisition system and LabVIEW-2012 software. The accuracy of the measuring equipment is given in Table 3. During the outdoor measurements, the incidence angle of solar radiation on collector surface was maintained manually in the range of 0° ≤ Θβ ≤ 5°, using solar pointer shadow. This angle correction rate was tested experimentally and the result shows a negligible effect on the thermal efficiency of the solar collector. The absorber surface temperature, during an indoor test, was measured with artificial solar radiation. To simulate the solar radiation, a system of 28 metal-halide radiation sources was used. Radiation sources were embedded inside the aluminum luminaries on the tilting panel. To obtain uniform distribution of the radiation intensity at the collector mounting surface, several attempts have been carried out (Fig. 11). Each time, the power of radiation and distance between collector surface Table 2 CFD model mesh parameters

Model component

Element type

Number of elements

Absorber plate Flow channels Working fluid

Hex Tetra Tetra

5.12 × 105 3.73 × 106 6.76 × 106

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Fig. 10 Solar simulator radiation distribution measurement

Table 3 Accuracy of measuring equipment Measured value

Measuring device

Accuracy

Inlet and outlet working fluid temperature Total solar irradiation Mass flow rate Surface absorber temperature Ambient temperature

RTD—Pt 100 LP PYRA-02 ENCO MPP-6 Thermocouple type K RTD—Pt 100

±0.1 K ±2 % ±1 % ±0.5 K ±0.5 K

Tout

Ta

Gsun 1000

90

900

80

800

70

700

60

600

50

500

40

400

30

300

20

200

10

100

0

0 1

2

3

4

5

6

7

8

9

Time τ x 103 [s] Fig. 11 Steady-state indoor measurement time graph

10

11

12

13

14

15

Gsun[W/m2]

T [˚C]

Tin 100

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and solar simulator ware modified and measured in 80 points. The collimation procedure was stopped when the difference between extreme values and average value of radiation flux was smaller than 5 %.

4 Results and Discussion To compare the results of numerical simulations and experiments, several measurements have been carried out. Firstly, the thermal efficiency characteristic η(T ⋅ m) was determined in a steady-state indoor test. According to EN ISO 9806:2013 standard, the second-order efficiency curve was statistically fitted to the values of collector efficiency measured for four different reduced temperature values T ⋅ m. Each test point represents the average value of thermal efficiency from 30 min measurement period, with constant radiation and inlet fluid temperature value. The actual useful power Q_ u , for each test point, was calculated from Q_ u ¼ m_
cf
DTf

ð11Þ

where m_ was obtained from volumetric flow rate measurement with density determined for the temperature of fluid in flow meter. Thermal efficiency g for each test point was calculated from gi ¼

Q_ u Aa
Gsun

ð12Þ

Test data were correlated by curve fitting using least square method to obtain the thermal efficiency function of the form (Table 4) g ¼ g0  a1 ðT
mÞ  a2 Gsun ðT
mÞ2

ð13Þ

After the experiment, the numerical calculation was performed. Each step of steady-state measurement points was treaded separately. Boundary conditions for each steady-state point were represented by average values of mass flow rate, inlet fluid temperature, ambient temperature, and solar radiation flux which recorded Table 4 Steady-state outdoor experiment data Tin (°C)

Tout (°C)

Ta (°C)

Gsun (W/m2)

_ (kg/h) m

T ⋅ m (m2K/W)

ηi

25.1 41.5 59.6 79.0

32.8 49.4 67.0 85.6

21.8 22.1 23.4 23.6

980 990 984 987

139.9 140.0 139.5 140.0

0.00 0.02 0.04 0.06

0.74 0.68 0.62 0.53

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0.9

0.8

η

0.7

0.6

0.5

0.4 0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

T m [W/m2K]

Fig. 12 The results of steady-state thermal efficiency measurement and numerical calculations

Table 5 Second-order efficiency curve η coefficients

Based on absorber area

ηo

a1 (W/m2 K)

a2 (W/m2 K)

η—experiment η—D-C model η—CDF model

0.76 0.74 0.76

2.9 2.8 3.0

0.017 0.02 0.021

during corresponding measurements. The results of numerical calculations between D-C and CFD models compared with the experiments are shown in Fig. 12. As shown in Fig. 12, the results of numerical calculations using D-C and CFD models are in good agreement with the experiment. In case of CFD model result, the correlation with the experiment around the low values of T · m is almost perfect (Table 5). The values of optical efficiency η0, determined by experiment and CFD calculations, are the same with accuracy of two decimals. With increasing T · m value, the convergence of CFD model results and experiments decreases. The reason of divergence in results within high values of T · m can be caused by underestimation of heat loss coefficient. In case of D-C model, the calculated efficiency curve goes below all measured values in similar distance from each measured points. This can be caused by simplification of absorber construction characteristics, contained in the model. To investigate the relationship between the absorber design and the heat exchange process, the absorber surface temperature was measured experimentally and calculated with D-C and CFD models. The absorber surface temperature was measured through the back side of collector housing. During the surface temperature measurements, the inlet fluid temperature was set to meet the least heat loss conditions

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Fig. 13 Absorber temperature measurements

Tin þ DT=2 ffi Ta

ð14Þ

The absorber surface temperature was measured in four different profiles. Each profile consisted of 19 temperature points, measured one by one. The profiles and measure point distribution are shown in Figs. 10 and 13. All measured temperature values in each profile were imposed on numerically determined absorber temperature surface calculated with D-C model. As shown in Fig. 15 middle section of the absorber has temperature comparable to calculated values in this region. The agreement of the result is especially high for the absorber plate, measured between flow pipes, whereas flow pipe wall temperature seems to be higher than calculated results. Higher fluid wall channel temperature can be caused by not exactly laminar flow regime and higher heat transfer coefficient in near wall fluid zones. Those differences can be reduced by tuning the model parameters. The most important is that the agreement of numerical and experimental results is much lower for the edge zones of the absorber. The absorber temperature measured in edge zones is often more than 20 % higher than the calculated values (Fig. 14). The reason for results disagreement, in the side edge zones of absorber, lies in different geometry of marginal fins. In this particular solar collector, the edge fins of absorber are larger than the middle ones. This means that the first and last fluid pipe cooperates with a larger absorption surface, than the others. This geometric feature

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Fig. 14 Absorber surface temperature calculated using D-C model, with experimentally measured temperature points

(a)

D-C model

55

Experiment

(b)

45 35 25

35 25

15 0

20

40

60

15

80 100 Wa x 10-2[m]

0

20

40

P1 profile

(c)

D-C model

55

60

80

100 Wa x 10-2[m]

P2 profile Experiment

(d)

D-C model

Experiment

60

45

50 T [˚C]

T [˚C]

Experiment

45 T [˚C]

T [˚C]

D-C model

55

35 25

40 30

15 0

20

40

60

P3 profile

80

100 Wa x 10-2[m]

20 0

20

40

60

80

100 Wa x 10-2[m]

P4 profile

Fig. 15 The result of absorber temperature investigation with experimental measurements and D-C model simulation

of this particular solar absorber is shown in Fig. 7. As a result, the conduction of heat flux from the edge zone of the absorber plate has a longer distance to cover, which causes heat energy damming in edge regions of the absorber. This effect can be clearly seen in Fig. 15, where measured temperature points and calculated temperature values are presented in each profile.

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Fig. 16 The result of absorber surface temperature distribution from CFD model with experimentally examined cross sections marked

For the same collector working conditions, the CFD analysis was carried out. As it was mentioned before, all geometrical details of the absorber were considered and fluid local density was approximated. The results of the absorber temperature values, obtained from CFD model, were compared with the previously collected experimental data. In Fig. 16, the result of the absorber surface temperature distribution is shown. The CFD simulation result shows the consequences of geometric irregularity of marginal absorber fins. Observed experimental high-temperature values on the edge of the absorber, has been mapped with good agreement with experiment. The comparison of measured temperature points values and CFD calculated temperature values, in each profile, are presented in Fig. 17. The CFD analysis has proved a strong dependency between the geometrical details of absorber design and heat exchanging process. Measurement data is in better agreement in comparison with D-C modeling method. Both methods were also compared to experimental data from long-term outdoor test. This investigation was performed to verify which method is more suitable for long-term efficiency calculations. In order to examine both approaches for transient states, strongly dynamic conditions of experimental data were selected (Fig. 17). The result of experimentally measured useful power Q_ u , extracted from collector and numerical results from D-C and CFD models are shown in Fig. 18. Based on numerical and experimental results, the root mean square values of useful energy Q_ uRMS , extracted from solar panel were determined as follows:

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K. Kamiński and T. Krzyżyński CFD model

(b)

Experiment

CFD model

60

65

50

55

40

45

T[˚C]

T[˚C]

(a)

30 20 0

20

40

60

35 25

80 100 Wa x 10-2[m]

0

20

40

P1 profile

60

80 100 Wa x 10-2[m]

P2 profile

CFD model

(d)

Experiment

CFD model

65

70

55

60 T[˚C]

T[˚C]

(c)

Experiment

45

Experiment

50 40

35

30

25 0

20

40

60

0

80 100 Wa x 10-2[m]

20

P3 profile

40

60

80 100 Wa x 10-2[m]

P4 profile

Fig. 17 The result of absorber temperature investigation with experimental measurements and CFD model simulation

Qu - D-C model

Qu - Experiment

Qu - CFD model

1800

Qu [W]

1400

1000

600

200 0.0E+0

5.0E+2

1.0E+3

1.5E+3

2.0E+3

2.5E+3

3.0E+3

Time τ [s] Fig. 18 Measured experimentally and calculated useful energy Qu extracted from solar collector during outdoor test, with mass flow rate m_ c ¼ 140 kg=h

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Table 6 RMS values of experimental and calculated useful energy Q_ u Q_ uRMS (W)

Experiment

D-C model

CFD model

1212.3

1191.3

1181.7

Table 7 Correlation coefficients for D-C and CFD model results in relation to the experiment Res

D-C model

CFD model

0.968

0.951

Q_ uRMS

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n 1X ¼ ðQ_ ui Þ2 n i¼1

ð15Þ

where i—is the measuring sample (Table 6). In order to quantify the convergence of experimental and simulation results, the multidimensional correlation coefficients Re−s were determined as follows (Table 7): Res

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn ðQui  QuEx Þ2 ¼ 1  Pni¼1 2 i¼1 ðQuEx  QuAV Þ

ð16Þ

The results of useful energy Qu obtained using proposed simulation methods are satisfactorily accurate. In both cases, the value of calculated RMS energy gain differs from the experiment of less than 3 %. The correlation coefficient R sums to confirm a good result agreement. In light of this analysis, proposed numerical simulation methods can be used to estimate the energy yield from flat-plate solar collector in variable insolation conditions, with high accuracy.

5 Conclusion Two different numerical simulation methods of flat-plate solar collectors’ heat exchanging process are presented in this paper. All calculated results were compared with experimental steady-state and transient data. The absorber surface temperature, obtained with tested numerical models, was verified by contact temperature measurements through the back side of collector housing. The steady-state indoor investigation shows good agreement between calculated and measured results. Determined numerical solar collector efficiency curves η(T · m) were sufficiently similar to EN ISO 9806 standard test result, which means that the basic exploitation parameters, like optical efficiency η0 and heat loss coefficients, can be found with high accuracy. The difference between these approaches is noticeable if time consumption is taken into evaluation. The D-C

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simulation model can be formulated quite fast and the solution can be found using standard PC in short time, while CFD modeling method requires much larger computational effort. Therefore, in order to quantify the solar collector efficiency, low-cost distributed-character modeling method is suggested. Because of wide simplifications of lumped capacitance, D-C solar collector models it is difficult to analyze the construction design and optimize its geometric and structural configurations. For this research area, CFD method seems to be essential. Presented in this work, CFD analyses of KSH-2.0 solar collector allowed to detect some design misstatements, identified by high temperature values in the edges of absorber plate. The local temperature of the absorber plate is the authoritative determinant of the local heat removal factor. Detected high temperature of marginal fins will cause greater heat loss to the ambient, and consequently, marginal fins will have lower thermal efficiency. Higher temperature of fluid in marginal fins will also cause greater inequality of mass flow rate in other pipes, which contributes to the reduction of solar collector performance. Similar analysis could not be done with distributed-character model without an edge correction factor. Long-term investigations, with various environmental conditions show good agreement of experimental and calculated results. However, to optimize the energy yield during operations in any working conditions, in order to optimize the regulation criteria for control systems, fast modeling method is needed. Universal CFD modeling method can be used, in many applications, were result resolution and accuracy are more important than calculation time. The optimization process which often involves looped model start-up, D-C modeling method is suggested.

References 1. Duffie, J.A., Beckman, W.A.: Solar engineering of thermal processes, 3rd edn. Wiley Interscience, New York (2006) 2. Turgut, O., Onur, N.: Three dimensional numerical and experimental study of forced convection heat transfer on solar collector surface. Int. Commun. Heat Mass Transfer 36(3), 274–279 (2009) 3. Kamminga, W.: The approximate temperatures within a flat-plate solar collector under transient conditions. Int. J. Heat Mass Transf. 28(8), 433–440 (1985) 4. de Ron, A.J.: Dynamic modeling and verification of a flat-plate solar collector. Sol. Energy 24 (2), 117–128 (1980) 5. Schnieders, J.: Comparison of the energy yield predictions of stationary and dynamic solar collector models and the model’s accuracy in the description of a vacuum tube collector. Sol. Energy 61, 179–190 (1997) 6. Hilmer, F.,Vajen, K., RatkaA., Ackermann, H., Fuhs, W., Melsheimer, O.: Numerical solution and validation of dynamic model of solar collectors working with varying flow rate. Sol. Energy 65(5), 305–321 (1999) 7. Oliva, A., Costa, M., Perez Segarra, C.D.: Numerical simulation of solar collectors: the effect of nonuniform and nonsteady state of the boundary conditions. Solar Energy 47(5), 359–373 (1991)

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8. Fan, J., Shah, L., Furbo, S.: Flow distribution in a solar collector panel with horizontally inclined absorber strips. Sol. Energy 81(12), 1501–1511 (2007) 9. Selmi, M., Al-Khawaja, M., Marafia, A.: Validation of CFD simulation for flat plate solar energy collector. Renew. Energy 33, 383–387 (2008)

Uncertainty Analysis of Innovative Method for Wheel Load Measurements Michał Kluziewicz and Michał Maniowski

Abstract The estimation process of uncertainty of rotating wheel loads measuring system is presented. The mentioned device is developed to determine friction forces between tire and road surface, based on measured internal reaction forces in wheel suspension mechanism. The combined standard uncertainty is calculated in accordance with the law of propagation of uncertainty. Different sources of uncertainty are described along with their interference and impact on final measurement result.




Keywords Vehicle dynamics Vehicle modeling wheel Measurement uncertainty





Measuring loads on a rotating

1 Introduction Modeling of vehicle motion requires implementing the characteristics of the examined tires [2]. Among the known methods of tire characteristics estimation, the measurements can be conducted either on test benches or in the real road conditions using a test vehicle [5]. The author’s research is focused on the development of a tire-to-loose-surface interaction model, which can be applied in a rally car dynamics analysis [4, 6]. In a view of the best representation of tire work conditions, it is crucial to conduct appropriate road tests on a real gravel surface (Fig. 1). Featured test vehicle is a front wheel drive, fully rally-prepared Citroen Saxo VTS (Fig. 1). The main advantages of using rally car are increased crew safety, ease of sensors assembly, and simplicity of setup adjustments. Multicomponent wheel hubs for direct load measuring are commercially available, but extremely expensive, not suitable for tough working conditions, and result in change of suspension system parameters. M. Kluziewicz (&)
M. Maniowski Cracow University of Technology, Krakow, Poland e-mail: [email protected] © Springer International Publishing Switzerland 2016 J. Awrejcewicz et al. (eds.), Mechatronics: Ideas, Challenges, Solutions and Applications, Advances in Intelligent Systems and Computing 414, DOI 10.1007/978-3-319-26886-6_10

153

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Fig. 1 Test vehicle sideslipping on a gravel surface

Therefore, an innovative measuring system enabling indirect tire characteristics estimation has been proposed by the authors [4]. This system exploits existing front wheel suspension of Macpherson strut type. A single mechanism will perform various roles such as wheel guiding, shock absorbing, and measuring reaction forces in suspension joints (Fig. 2).

Fig. 2 Front wheel suspension strut of Citroen Saxo

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155

The described approach bases on measurement of internal forces (using strain gauges and load cells) and suspension mechanism configuration coordinates (mechanical and optical displacement sensors) [4]. Relations between input and output data are described by kinetostatic model of the mechanism using Jacobian matrix and spatial transformations. Computer algorithm was implemented in MATLAB environment. The main goals of this paper are: – definition of load measurement procedure, – verification of the suspension kinematic characteristics, – estimation of possible measurement uncertainties using error propagation principle, – identification of significant sources of inaccuracies, suitability evaluation of the proposed solution, which is being designed and prototyped.

2 Estimation of Tire Model Parameters Tire model generates forces (F) and torques (M) in a contact patch (C in Fig. 3) between the tire tread and road surface in relation to different parameters, which can be expressed as in Fig. 4, Fig. 3 Kinematic model of Citroen Saxo MacPherson strut suspension

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Fig. 4 Diagram of tire model

where Fx, Fy Fz M x, M y, M z γ α sx Tb surface par. model par.

longitudinal and lateral forces; vertical force; torques: overturning, rolling resistance, bore; wheel camber angle; tire slip angle; longitudinal tire slip; tire tread temperature; friction coefficient, loose layer depth, particle size; with physical or nonphysical meaning.

There are various tire models describing the aforementioned relation using physical and/or empirical approaches [2]. According to the model complexity, the number of its parameters varies from several to hundreds. The process of model parameters estimation can be carried out when a set of inputs and outputs (Fig. 4) is known from measurements, which is ought to be conducted in a most similar to real work conditions. There are kinematic and load states to be measured. This paper is focused on load states measurements only.

3 Indirect Measurement of Wheel Spatial Load In order to measure a tire load, the wheel suspension mechanism was adapted. A kinematic model of MacPherson strut suspension (Fig. 3) with rack-and-pinion steering system was formulated according to the following assumptions: – the wheel knuckle is joined by spherical pairs with: lower wishbone (in B1), tie rod (in B3), and top mount (in A4) in the strut end; – two degrees of the wheel knuckle mobility correspond to the wheel bounce (controlled by the strut height h) and turn motions (controlled by the steering rack displacement p); – the lower wishbone, due to a special design, can be treated as a composition of two rods (B1A1 and B1A2) with spherical pairs at its ends; – direct kinematic task is solved using a vector method [1]; – joints and links are ideal;

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– internal reactions in the suspension are determined under static conditions; – following vector transformations are written instantaneously with respect to the wheel reference system. The Cartesian coordinates (k) of the wheel reference system (Fig. 3) are the following: 3 bx 6 by 7 6 7 6 bz 7 7 k¼6 6 bx 7 6 7 4 by 5 bz 2

ð1Þ

where b = [bx by bz] position vector of the wheel center [m]; β = [βx βy βz] vector of the wheel orientation angles [rad]. According to the considered suspension kinematic structure (Fig. 3), the wheel knuckle is constrained by the following coordinates: 3 d1 6 d2 7 7 6 6 d3 7 7 6 q¼6 7 6 a4x 7 4 a4y 5 a4z 2

ð2Þ

These coordinates (2) describe blocked motions, due to constant lengths of the three rods (di, i = 1…3) and unchangeable position of the top mount spherical pair (a4x, a4y, a4z). Each rod (i = 1…3) of the wheel suspension is described by the following vectors: d i ¼ bi

ai

ð3Þ

di ¼ kdi k½mŠ

ð4Þ

di d^i ¼ di

ð5Þ

with the length

and the unit vector

Kinematic relation between virtual changes of Cartesian (1) and constraints (2) coordinates can be written as [3]:

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@q ¼ J@k

ð6Þ

Jacobian matrix (J) of parallel mechanism can be defined as the twist coordinates (each row) of the constraints, as follows: 2 h iT d^ 6 h 1i 6 T 6 d^2 6 6 h iT J¼6 6 d^3 62 6 1 6 44 e z ey

h

ez 1 ex

ey ex 5 1

iT 3

iT 7 7 7 7 h iT 7 7 ^ b3  d 3 7 7 7 7 5 ½~a4 Š h

3

b1  d^1 b1  d^2

ð7Þ

66

where 2

0 ~ a4 ¼ 4 a4;z a4;y

3 a4;y a4;x 5 ðskew symmetric matrixÞ 0

a4;z 0 a4;x

ex ; ey ; ez —small deviation angles [rad] of force sensor orientation in the top mount (around x, y, and z axes accordingly). Jacobian matrix (7) depends on the mechanism geometry and is determined for a specific suspension travel (bz) and steering rack position (p). Forces and torques generated in the tire tread patch are collected in a spatial load vector: W t ¼ ½ Fx

Fy

Fz

Mx

My

Mz ŠT

ð8Þ

This load (8) for quasi-static conditions can be transferred to the wheel center, by the formula: W ¼ HW t   ½1Š33 ½0Š33 H¼ ½~rŠ33 ½1Š33 2

3 0 ~r ¼ 4 0 5 rd

ð9Þ ð10Þ

ð11Þ

rd—dynamic tire radius [m]. According to the assumed constraints (2) in the suspension mechanism, there are six reaction forces (Fig. 3), which are grouped in the vector:

Uncertainty Analysis of Innovative Method for Wheel Load …

R ¼ ½ R1

R2

R3

R4

R5

159

R6 ŠT

ð12Þ

where R1—force in the front rod [N]; R2—force in the rear rod [N]; R3—force in the steering rod [N]; R4, R5, R6—longitudinal, lateral, and vertical reactions in strut top mount [N]. Applying the virtual work principle, which describes the balance of works done by external and internal loads, it can be stated as W T @k ¼ RT @q

ð13Þ

Transforming Eq. (13) by applying kinematic relations (6), the static task can be written as W ¼ JTR

ð14Þ

Equation (14) describes linear relations between unknown external wheel load (W) and the mechanism internal load (R) that can be measured.

4 Verification of the Suspension Kinematic Model For the purposes of kinematic analysis, the spatial model of MacPherson suspension of Citroen Saxo test car was implemented into MATLAB software. The mechanism was strictly measured and the gathered geometric data were entered in. At this stage, with the aim of verifying kinematic relations, following values were measured as a function of suspension travel (bz): camber angle (βx) [°], toe (βz) [mm], and track width change [mm] [4]. Front wheels were set on turntables to avoid the influence of tangent forces. The front axle was supported with a jack and loaded with weights of total 300 kg. A measuring plate with four cable sensors was mounted on the rim (Fig. 5) [1]. One of the cables was attached to the car body in order to measure the suspension travel. Other three cables were fixed to the solid pillar. By measuring the displacements of equilateral triangle’s vertices, aforementioned value changes were obtained [4]. Measured real suspension characteristics were compared to the corresponding ones received from the kinematic model (black) (Figs. 6 and 7). Presented functions of track width change and toe change computed using the model are closely matching the real traces. On this basis, it can be concluded that the kinematic model is properly specified. To obtain improved results, steering rod length should be measured more precisely.

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Fig. 5 Measuring adapter with four cable sensors attached to the wheel

Fig. 6 Wheel toe angle (βz) change as a function of suspension travel (bz)

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Fig. 7 Half track width change as a function of suspension travel (bz)

5 Uncertainty of Load Measurement System Every measurement is subject to some uncertainty. A measurement result is complete only if it is accompanied by a statement of the uncertainty in the measurement. When the uncertainty in a measurement is evaluated and stated, the fitness for purpose of the measurement can be properly judged [7]. As a part of measuring system preparation, it is crucial to predict the influence of constituents on the final measuring result. Thereby the usefulness of the designed solution can be assessed and further improvements can be introduced. The developed method for wheel load measurement has an indirect character. First, internal load (R) in the suspension mechanism is directly measured (using strain gauges and load cells). Then, the acquisition results are further transformed by the Jacobian matrix in the formula (14). This matrix is calculated on the basis of the suspension kinematic model, which relies on the mechanism dimensions and current position. The chain of possible uncertainty accumulation is fairly long in this case. Therefore, the measurement system components ought to be carefully designed. The most significant sources of inaccuracy in the load measurement system are reviewed (Table 1). These sources can be classified as related to the following phenomena.

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Table 1 Spreadsheet of the assumed uncertainty sources No.

Source of uncertainty

U-uncertainty (99.7 % confidence interval = 3σ)

Standard deviation (σ)

Force sensor in rods (strain gauges) 1 R1

±1 %

2

R2

±1 %

3

R3

±1 %

10 N 3 kN 10 N 3 kN 10 N 3 kN

Top mount three-component force sensor (load cell) ±0.5 % 4 R4 5 6

R5 R6

Suspension mechanism coordinates (chassis side) 7 a1x 8 a1y 9 a1z 10 a2x 11 a2y 12 a2z 13 a3x 14 a3y 15 a3z 16 a4x 17 a4y 18 a4z (wheel side) 19 b1x 20 b1y 21 b1z 22 b3x 23 b3y 24 b3z Orientation of the three-component force sensor 25 εx 26 εy 27 εz Dynamic wheel radius 28 rd Computing algorithm (mechanism model, friction and backlashes in the joints, mechanism compliance, dynamic effects)

(for force) (for force) (for force)

5 N (for 3 kN force)

±0.7 % ±0.5 %

5 N (for 3 kN force)

±0.002 ±0.002 ±0.002 ±0.002 ±0.002 ±0.002 ±0.005 ±0.005 ±0.005 ±0.005 ±0.005 ±0.005

m m m m m m m m m m m m

U/3

±0.005 ±0.005 ±0.005 ±0.005 ±0.005 ±0.005

m m m m m m

U/3

±0.02 rad ±0.02 rad ±0.02 rad

U/3

±0.005 m ?

U/3

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• Measuring instruments (No. 1–6 in Table 1) Six sensors are utilized for measuring internal forces. Axial forces in the suspension rods (R1, R2, R3) will be measured using strain gauges with expected uncertainty ±1 %. The three-component force sensor is used for the dynamic and quasi-static measurements of the three orthogonal components of any force acting in the suspension strut top mount (R4, R5, R6). The sensor contains three pairs of quartz plates, of which one is sensitive to pressure in the z direction and the two others to shear forces in the x and y directions. Measurement takes place practically without displacement. The force to be measured is introduced via a special washer to the base plate and transmitted through static friction. Top plate abuts with a uniball adapter. Immobility of the measuring chain is provided with preload bolt. According to the sensor producer, its measurement uncertainty is ±0.05 %. • Measurement and calculations process (No. 7–28 in Table 1) The process of data transformation will be affected by inaccurate determination of the suspension model components. The suspension model coordinates can be measured with accuracy dependent on the applied apparatus. Some of the joints are built in and barely reachable, i.e., steering rack coordinates cannot be simply evaluated with measuring tape or ruler. The harder the access to the joint in straight line, the bigger the inaccuracy of measurement. For the purposes of basic tests, measuring tape tool has been used. Estimated accuracy of this method varies from 2 to 5 mm depending on the ease of measurement. All the measurements of links coordinates on the wheel side have to be conducted in the same, known suspension travel (bz) and steering rack position (p). For improved measurement precision, it is considered to use a portable measuring arm. • Measured item (not included in Table 1) During on-road measurements, the tire tread wear and temperature, and tire inflation pressure should be controlled. Tread temperature will be measured continuously with pyrometer gauge. • Calibration uncertainty (not included in Table 1) The proposed measurement method will be calibrated on a static test bench, where a selected load will act on the car wheel. Due to a force shunt caused by a preloading bolt, it is recommended to conduct a calibration after sensor installation, to determine the sensitivity of the complete measuring arrangement. • Environment (not included in Table 1) The effects of temperature and humidity are significant with respect to the road surface conditions. It is also relevant to observe surface relief, e.g., ruts, banks, mounds. Multiple repetitions of same maneuver will lead to substantial change of arrangement of gravel and thereby wheel loads. In order to analyze the influence of the considered uncertainty sources (Table 1) on accuracy of the determined wheel load (13), a linear law of uncertainty

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propagation [7] is further utilized. Let us consider a general function with many variables: y ¼ f ð xÞ

ð15Þ

x ¼ ½ x1 x2 . . . xn Š T

ð16Þ

where

There are the following assumptions: – variables follow random processes with normal distribution (described by mean value and standard deviation); – random variables are independent; – the variables deviations are small enough to be linearized. Under the mentioned assumptions, standard deviation (σ) of the function (15) output (y) can be evaluated as the following function of standard deviations of the function variables: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n X rð yÞ ¼ ½wi rðxi ފ2

ð17Þ

i

where wi ¼

@y @xi

ð18Þ

wi —uncertainty scaling factor as partial differential. Concerning the measurement system uncertainty, the most significant sources of inaccuracy (Table 1) are analyzed by analytical calculation of partial derivatives (18) of (14) with respect to (according to Table 1): x ¼ ½ R1

R2

R3

R4

R5

R6

a1x

a1y

. . . rd ŠT128

ð19Þ

The following numerical examples show the importance of individually measured 28 components (19) on the estimated load vector (14). Results are presented as Pareto charts of uncertainty scaling factors (18) for three different load states. In the examples, standard deviations (σ) of the sensors and the suspension dimensions are assumed in accordance with Table 1. Final measurement uncertainty is calculated separately as an effect of: (i) force sensors components uncertainty and (ii) entering to (14) inexact mechanism coordinates.

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165

Longitudinal Force

Considering the longitudinal force, the spatial load vector (8) in tire tread patch of the left front wheel (Fig. 3) is assumed as: W t ¼ ½ 3000; 0; 0; 0; 0; 0ŠT

ð20Þ

The obtained uncertainty scaling factors (18) for load sensors only (Table 1, i = 1, 2, …, 6) are ranked in Fig. 8. The greatest influence on a final result deviation will have measurements of x-force (R4) in a top mount and reaction in the rear rod (R2). Standard deviation (σ) of load component (20) as an effect of the load sensors uncertainty is equal to: rðFx ; lÞ ¼ 8:1½NŠ ðfrom load sensorsÞ

ð21Þ

The obtained uncertainty scaling factors (18) for geometrical inaccuracies only (Table 1, i = 7, 8, …, 28) are ranked in Fig. 9. The most significant elements are: (i = 7) x-component of A1 point, (i = 10) x-component of A2 point, (i = 11) ycomponent of A2 point, (i = 19) x-component of B1 point. These coordinates should be measured with increased accuracy. Standard deviation (σ) of load component (20) due to geometrical inaccuracies is equal to:   r Fx;g ¼ 12:2½NŠ ðgeometrical inaccuraciesÞ

ð22Þ

Fig. 8 Pareto ranking of uncertainty scaling factors (wi) of load sensors for longitudinal force application

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Fig. 9 Pareto ranking of uncertainty scaling factors (wi) of geometrical inaccuracies for longitudinal force application

Altogether, net standard deviation as an effect of uncertainty from the load sensors and the geometrical inaccuracies for load of Fx = 3000 N is evaluated as follows: rðFx Þ ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rðFx;l Þ2 þ rðFx;g Þ2

ð23Þ

and it gives rðFx Þ ¼ 14:6½NŠ

ð24Þ

Therefore, the force (20) can be measured with 99 % confidence interval (equal to 3σ) of ±43.8 N, what represents ±1.46 % of 3000 N force.

5.2

Lateral Force

While the 3000 N lateral force is acting on the left front wheel of vehicle in the point of contact between the tire and surface, the spatial load vector (8) is stated as: W t ¼ ½0;

3000; 0; 0; 0; 0ŠT

ð25Þ

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Fig. 10 Pareto distribution of uncertainty scaling factors (wi) of load sensors for lateral force application

The obtained uncertainty scaling factors (18) for load sensors only (Table 1, i = 1, 2, …, 6) are ranked in Fig. 10. Measurements of forces in front rod (R1), rear rod (R2), steering rod (R3), and y-force (R5) in top mount load have nearly equal impact on the final result deviation. Standard deviation (σ) of load component (20) as an effect of the load sensors uncertainty is equal to:   r Fy ; l ¼ 16:8 N ðfrom load sensorsÞ

ð26Þ

  r Fy;g ¼ 1:7 N ðgeometrical inaccuraciesÞ

ð27Þ

  r Fy ¼ 16:9 N

ð28Þ

The obtained uncertainty scaling factors (18) for geometrical inaccuracies only (Table 1, i = 7, 8, …, 28) are ranked in Fig. 11. The most significant elements are similar to the previous example. Standard deviation (σ) of load component (20) due to geometrical inaccuracies is equal to:

Evaluated net standard deviation as an effect of uncertainty from the load sensors and the geometrical inaccuracies for load of Fx = 3000 N is equal to:

In this case, the force (25) can be measured with 99 % confidence interval (equal to 3σ) of ±50.7 N, what represents ±1.69 % of 3000 N force.

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Fig. 11 Pareto distribution of uncertainty scaling factors (wi) of geometrical inaccuracies for lateral force application

5.3

Normal Force

Considering the example of a car standing still, laden only by its own weight, equivalent to 3000 N on each front wheel, the spatial load vector (8) in tire tread patch (Fig. 3) is assumed as: W t ¼ ½0; 0; 3000; 0; 0; 0ŠT

ð29Þ

The obtained uncertainty scaling factors (18) for load sensors only (Table 1, i = 1, 2, …, 6) are ranked in Fig. 12. The greatest influence on a final result deviation will have a measurement of z-force (R6) in the top mount. The other meaningful component is a reaction in the steering rod (R3). Standard deviation (σ) of load component (20) as an effect of the load sensors uncertainty is equal to:   r Fz;l ¼ 5:1 N ðfrom load sensorsÞ

ð30Þ

The obtained uncertainty scaling factors (18) for geometrical inaccuracies only (Table 1, i = 7, 8, …, 28) are ranked in Fig. 13. The most significant elements are first of all: (i = 9) z-component of A1 point, (i = 21) z-component of B1 point and also (i = 25) x-component of force sensor orientation, (i = 12) z-component of A2

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Fig. 12 Pareto distribution of uncertainty scaling factors (wi) of load sensors for normal force application

Fig. 13 Pareto distribution of uncertainty scaling factors (wi) of geometrical inaccuracies for normal force application

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point. These coordinates should be measured with increased accuracy. Standard deviation (σ) of load component (20) due to geometrical inaccuracies is equal to:   r Fx;g ¼ 5:8 N ðgeometrical inaccuraciesÞ

ð31Þ

rðFx Þ ¼ 7:7 N

ð32Þ

Altogether, net standard deviation as an effect of uncertainty from the load sensors and the geometrical inaccuracies for load of Fz = 3000 N is equal to:

Therefore, the force (20) can be measured with 99 % confidence interval (equal to 3σ) of ±23.1 N, what represents ±0.77 % of 3000 N force.

6 Conclusions The innovative method of measuring the wheel load using the suspension mechanism is described. Forces and torques acting on a rotating wheel are estimated based on internal forces and configuration coordinates of the suspension mechanism. The relationship between the aforementioned input and output data featuring Jacobian matrix is presented along with equation derivation and evaluation procedure. Adequacy of kinetostatic model is verified via the comparison of simulated and measured kinematic relations such as: camber angle, toe, and track width change with respect to suspension travel. Uncertainty estimation of the designed measuring system is shown. Sources of expected uncertainties are listed together with their expected influence on final measurement result. Few numeric examples for different load states are presented as Pareto charts. Accuracy of the developed estimation method is desired to be at the level of 3 %. Thereby system can be successfully used for tire characteristics measurement and tire model development. According to the uncertainty analysis carried out, specified accuracy is very probable to be achieved. Having in regard the outcome of error analysis, further improvements in measuring system construction, sensors calibration, and computational model can be applied. Further steps will be targeted in a complete assembly of measuring system, on-site calibration on a test bench, and basic road tests.

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References 1. Góra, M., Maniowski, M.: Verification of 6DOF platform with wire-based sensors for spatial tracking. Arch. Mech. Eng. 58(2), 157–174 (2011) 2. Pacejka, H.B.: Tyre and vehicle dynamics. Butterworth-Hienemann, SAE (2002) 3. Knapczyk, J., Maniowski, M.: Elastokinematic modeling and study of five-rod suspension with subframe. Mech. Mach. Theor. 41, 1031–1047 (2006) 4. Kluziewicz M., Maniowski, M.: Estimation of wheel load state by using suspension joints reactions. In: Badania pojazdów, praca zbiorowa pod redakcją Władysława Mitiańca, opracowanie monograficzne, Kraków, pp. 61–71 (2014) 5. Kluziewicz, M., Maniowski, M.: Porównanie efektywności wyścigowej i rajdowej techniki pokonania łuku samochodem przednionapędowym. Czasopismo techniczne 5-M/2012, Zeszyt 10, Rok 109 (2012) 6. Kluziewicz, M., Maniowski, M.: Stany nadsterowności podsterownego samochodu z przednim napędem. Zeszyty Naukowe Instytutu Pojazdów Politechniki Warszawskiej 1(77), 169–177 (2010) 7. Sobczyk, M.: Statystyka. Wydawnictwo Naukowe PWN. Warszawa (2007)

Designing the 40 kHz Piezoelectric Sandwich Type Ultrasonic Transducer Paweł Kogut, Andrzej Milewski, Piotr Kluk and Witold Kardyś

Abstract Ultrasonic sandwich type transducers (also known as Langevin transducers) are widely used in welding and cutting systems. The efficiency of such system is particularly important due to the increasing interest in the ultrasonic welding field. Optimal design of the transducer allows meeting those requirements. Designing process requires considering problems of the material selection, geometry optimization, and mechanical endurance. During the past years many aspects of the designing and manufacturing process have been studied, however, there is little information about the transducer aging. Aging has shown that stress relaxation after bolt prestressing had significant influence on its final transducer parameters. Authors conclude that optimal design of the transducer with FEM and analytical analysis yields experimental results with good convergence after proper assembling and aging. Since transducer parameters are strongly influenced by the bolt stiffening and aging authors claim that corrections of the dimensions should be done on a relaxed transducer. Keywords Ultrasonic modeling Aging







Transducer




Piezoelectric




FEM




Mathematical

1 Introduction Sandwich type ultrasonic transducer is a well-known electromechanical converter, widely used in high power applications such as ultrasonic welding or cleaning. It consists of a piezoceramic stack coupled between two metal pieces known as an emitter and a reflector. Metal and piezoceramic parts are connected together through

P. Kogut (&)
A. Milewski
P. Kluk
W. Kardyś Tele and Radio Research Institute, ITR, Warsaw, Poland e-mail: [email protected] © Springer International Publishing Switzerland 2016 J. Awrejcewicz et al. (eds.), Mechatronics: Ideas, Challenges, Solutions and Applications, Advances in Intelligent Systems and Computing 414, DOI 10.1007/978-3-319-26886-6_11

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Fig. 1 High power sandwich ultrasonic transducer, e, r, p—emitter, reflector, piezoceramic stack, u—displacement, h—length

a bolt screw. This allows achieving high acoustic intensities and electro-acoustic efficiency. Geometry is axially isotropic, which is optimal for excitation of a standing longitudinal acoustic wave in axial direction. Transducer is therefore designed to operate in the first harmonic of axial vibration mode. In this vibration mode, standing wave is formed, when total length of the transducer is equal to half-wavelength (λ/2). Sandwich type transducers were invented by Paul Langevin. Simplified model of such transducers were presented in [1], where authors distinguished symmetrical (nodal point located in the middle part of the piezoceramic stack) and unsymmetrical transducers. The high power transducers were discussed in [2–5]. Proposed model is presented in Fig. 1, where parts of the transducer were numbered as follows, 1—emitter 2—reflector, 3—electrode, 4—isolation tube, 5—bolt, and 6— piezoceramic.

2 Mathematical Modeling Theoretical studies were divided into two parts, derivation of the analytically simplified transducer model without bolt and a complete FEM model. In mathematical analysis, following materials parameters were assumed: emitter Y = 72.6 GPa,

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ρ = 2.82 g/cm3, σ = 0.34, bolt and reflector Y = 199 GPa, ρ = 7.85 g/cm3, σ = 0.29, piezoceramic PZT8 parameters published in [6, 7], where, Y—Young modulus, σ— Poisson ratio, ρ—density.

2.1

Analytical Modeling

Electromechanical coupling factor keff and mechanical displacement gain coefficient ku are of particular importance in transducer optimization, and can be calculated as follows [1, 8], 2 keff ¼1

ku2 ¼

u2e u2r


2 1 þ Zrp
¼ 2 1 þ Zep

fs2 ; fp2

 1 sin2 ðkr hr Þ  ; 1 sin2 ðke he Þ

ð1Þ

Zep ¼

Ze ; Zp

Zrp ¼

Zr ; Zp

ð2Þ

where fs, fp—series and parallel resonant frequencies, ue,r—mechanical displacement (see Fig. 1), Ze,r,p—characteristic acoustic impedance, he,r,p—axial length, ke,r,p—wave number, of e—emitter, r—reflector, and p—piezoceramic medium. Equation (2) shows that mechanical gain coefficient relies on material parameters and geometry. This means that a sandwich transducer can be optimized due to material parameters and geometry. In material parameters optimization beside the gain factor, emitter and reflector materials should also satisfy the impedance matching criterion. High power ultrasonic transducers are designed to achieve the highest acoustic transmission. This is fulfilled when transducer materials meet the Chebyshev relation [2, 8], Zp ¼

pffiffiffiffiffiffiffiffiffi Zr Ze :

ð3Þ

From (2) appears that gain factor is approximately proportional to the quotient of Zr/Ze value. In high power applications most commonly used piezoceramic is PZT8. It has good piezoelectric parameters, low dielectric and mechanical losses, and relatively stable parameters due to high external voltage/stress loading and temperature changes. Reflector and emitter materials have been selected in reference to (2) and (3). Results of the selection are presented in Tables 1 and 2. The best matched set were tungsten–magnesium alloys, with very high gain factor. This set

Table 1 Acoustic impedances of selected materials Zc (MRayl)

Aluminum Pa9

Magnesium AZ91D

Steel 50Hs

Tungsten HD17

Piezoceramic PZT8

14.3

9.0

39.5

68.5

29.9

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Table 2 Selected materials comparison

Materials reflector/emitter

Zr/Ze

Steel/Aluminum Tungsten/Magnesium

2.76 7.61

pffiffiffiffiffiffiffiffiffi Zr Ze Zp 0.79 0.83

was also most expensive and that is why it was decided to use cheaper steel/aluminum set. Transducer axial dimensions and resonant frequencies can be calculated from the following analytical equation, Zel ¼ Zx ¼

 1 1 jxC0S

1þ

 2 k33 Zx ; k p hp

  Zep tanðke he Þ þ Zrp tanðkr hr Þ þ 2 tan 12 kp hp

Zep tanðke he Þ þ Zrp tanðkr hr Þ tanðkp hp Þ

Zep Zrp tanðke he Þ tanðkr hr Þ

ð4Þ ;

where: Zel—electrical impedance, k33—piezoceramic longitudinal coupling factor, CS0 —input static capacitance. Equation (4) presents a more general approach than presented in [1], where authors derived eigenvalue equation for parallel resonant only, which can be easily obtained from (1) assuming Zel → ∞. It was derived under the assumption of the one-dimensional (planar) acoustic wave propagation in cylindrical bar, with thin bar sound speed approximation. This assumption is fulfilled only for resonators with the diameter D length less than 2, which now can be recalculated by substituting Ta in (7) with Tv value, 63 MPa 425 MPa þ  0:46 ) nf  2:18: 600 MPa 1200 MPa

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Such fatigue safety factor leads to a conclusion that 50 MPa of static prestress is in the range of designed transducer capabilities.

3 Assembling the Transducer In order to achieve the assumed static prestress value, it is needed to assemble the transducer with proper screwing torque momentum. This can be analytically calculated or experimentally controlled by measuring the static charge inducted during bolt clamping [2, 14]. If we assume that mean stress in piezoceramic is proportional to the inducted electric charge, then loading pressure can be calculated as follows: P¼

C
U ¼ a
U: n
S
d33

ð8Þ

Transducer clamping was conducted with the following steps, 1—transducer was connected in parallel to high capacity (Cx ≈ 26.8 μF), 2—transducer was screwing with calibrated dynamometric key, and 3—after each screwing momentum step transducer was discharged. Assembling process was shorter than one hour, to avoid errors in conducted measurements caused by the stress relaxation. Voltage and transducer static capacitance was measured by multimeter, results are presented in Figs. 8 and 9. As it is seems measured voltage is proportional to the torque

Fig. 9 Measured voltage and input capacitance versus torque momentum

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Fig. 10 Measured series frequency and impedance changes in function of loading pressure

momentum. This means that the same portion of stress results in the same voltage (charge), which leads to the conclusion that piezoelectric constant d33 does not vary significantly under 30–50 MPa preloading. Series impedance decreases and resonant frequencies increase due to the increasing mechanical coupling, which was discussed in [15], as a change of effective contact between transducer elements under bolts clamping. Static capacitance in range of small stress values first decrease and then increases reaching expected value of 6 nF for preloading value >35 MPa. This can be influenced by the boundary conditions changes, where transducer capacitance vary between capacitance measured for static strain and stress conditions. After assembling the transducer was exposed to aging in the oven with temperature set to 60 °C for 24 h. During aging, the transducer electrical inputs were short circuit, to prevent piezoceramic from partial depolarization (Fig. 10).

4 Measurements Before and after aging transducer was subjected to impedance characteristics measurements. Results are presented in Table 3 and in Fig. 11. Experimental analysis was conducted with experimental set discussed in [16, 17].

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Fig. 11 Experimental and simulated impedance characteristics, taken for relaxed and aged transducer

5 Conclusions From Fig. 11 and Table 3 it seems that conducted simulations and experimental characteristics show very good agreement after aging and transducer relaxation. During relaxation piezoceramic rings slowly set up their final position. This probably changes the effective surface contact between the transducer elements, which also takes place during transducer assembling. Transducer has to be properly aged before involving any experimental corrections. Acknowledgments We gratefully acknowledge the financial support of the National Center for Research and Development, Poland, under grant number PBS2/B9/19/2013.

References 1. Dominquez, R., Ranz, C.: Sandwich transducer, simplified mathematical model (I), (II). Acoustica 29, 156–167 (1973) 2. Abdullah, A., Shahini, M., Pak, A.: An approach to design a high power piezoelectric ultrasonic transducer. J. Electroceram. 22, 369–382 (2008) 3. Abdullah, A., Pak, A.: Correct prediction of the vibration behavior of a high power ultrasonic transducer by FEM simulation. Int. J. Adv. Manuf. Technol. 39, 21–28 (2008)

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4. Safari, A., Akdogan, E.K.: Piezoelectric and Acoustic Materials for Transducers Applications. Springer Science + Busines Media, LLC, 2008, Chapter 3.11 5. Radmanović, M.Đ., Mančić, D.D.: Designing and modeling of the power ultrasonic transducers. MPI, Switzerland (2004) 6. Berlincourt, D., Krueger, H.H.A.: Properties of Piezoelectricity Ceramics, Morgan Electro Ceramics. Technical Publication TP-226 7. Noliac.: Piezo materials specification 8. Gudra, T., Właściwości i zastosowanie przetworników ultradźwiękowych do pracy w ośrodkach gazowych, OWPWr, 2005, Chapters 4, 5 (in Polish) 9. Kim, M., Kim, J., Cao, W.: Electromechanical coupling coefficient of an ultrasonic array element. J. Appl. Phys. 99, 074102 (2006) 10. Lierke, E.G., Littmann, W., Morita, T., Hemsel, T.: Various aspects of the placement of a piezoelectric material in composite actuators, motors, and transducers. J. Korean Phys. Soc. 57, 933–937 (2010) 11. Radzimovsky, E.I.: A New Approach to Strength Calculations for Bolts Subjected to Periodically Changing Loads. Machine design, pp. 135–146, (1952) 12. Oberg, E., Jones, F.D., Horton, H.L., Ryffel, A.H.: Machinery’s Handbook, 26th edn, pp. 197– 200 and 1490–1491. Industrial Press, INC (2000) 13. Xu, L.R., Bhamidipati, V.: An Efficient Method to Estimate the S–N Curves of Engineering Materials, SEM (2002) 14. Bo, F., Ting, L., Hemsel, T.: A simple pre-stress estimating method of Langevin transducers, pp. 324–327. IEEE, SPAWDA (2008) 15. Arnold, F.J., Mühlen, S.S.: The mechanical pre-stressing in ultrasonic piezotransducers. Ultrasonics 39, 7–11 (2001) 16. Kluk, P., Milewski, A., Kardyś, W., Kogut, P., Michalski, P.: Measurement system for parameter estimation and diagnostic of ultrasonic transducers. Acta Phys. Pol. A 124(3), 468–470 (2013) 17. Kogut, P., Milewski, A., Kluk, P., Karyś, W., Karyś, W., Nafalski, L.: Piezoelectric transducer impedance measurement circuit. Elektronika 54, 16–19 (2013). (In Polish)

Development of an Electronic Stethoscope Olga Szymanowska, Bartłomiej Zagrodny, Michał Ludwicki and Jan Awrejcewicz

Abstract This paper presents the development of an electronic stethoscope which acquires auscultation results and transfers them to the computer where they can be immediately processed, analyzed, and replayed. The prototype based on the redesign of already existing stethoscope supplemented with data acquisition element (electret microphone connected to the computer sound card) as well as dedicated software for data acquisition and processing is presented. The developed device has an advantage over a commercial product used for the comparison, i.e., it allows for simultaneous auscultation and monitoring the recorded signal with time–amplitude plot or spectrogram as well as enables sound acquisition with much higher sampling frequency, which can be essential in detailed heart and lung analyses. Keywords Stethoscope Biomechanics Analysis Microphone Applications LabVIEW
















1 Introduction The development observed in technology and science leads to the creation of new applications, such as telemedicine aimed at medical data sharing to improve health care (see [1]). The urge for improvement and digitization of existing diagnostic methods constantly arises. Not only individual fields of science have been O. Szymanowska
B. Zagrodny (&)
M. Ludwicki
J. Awrejcewicz Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, Lodz, Poland e-mail: [email protected] O. Szymanowska e-mail: [email protected] M. Ludwicki e-mail: [email protected] J. Awrejcewicz e-mail: [email protected] © Springer International Publishing Switzerland 2016 J. Awrejcewicz et al. (eds.), Mechatronics: Ideas, Challenges, Solutions and Applications, Advances in Intelligent Systems and Computing 414, DOI 10.1007/978-3-319-26886-6_12

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undergoing noticeable progress but also new, cross-disciplinary sciences such as biomechanics or bioelectronics have evolved. What should be noted is that proceeding digitalization of information made some of the commonly used methods of medical diagnosis insufficient in specific situations. This, in turn, imposed the improvement of existing passive medical devices in order to either amend the quality of diagnosis or use the aforementioned devices in new situations. Sound plays an important role in diagnosing numerous disorders occurring in human body (see for example [2]). Sound waves used in medical examination are either generated by external source (e.g., ultrasounds) or created by organs such as the heart, lungs or bowel as well as by movement of bones in joints. Listening to the sound generated by a human body is called an auscultation and most commonly is conducted with the aid of devices called stethoscopes. A. The heart One of the most frequently examined and most crucial organs that can be subjected to an auscultation is the heart. The importance of proper diagnosis of heart (cardiovascular) diseases can be explained by taking into consideration the data of the World Health Organization (WHO). According to Global Health Observatory (GHO) being a part of the WHO (see [3]), cardiovascular diseases are the major cause of about half of all deaths in Poland, considering noncommunicable diseases (NCDs)––chronic diseases that cannot be passed to other person. It gives about 180,000 deaths annually. Taking the problem globally––3 in 10 deaths, this is ca. 17.5 million (in 2012), result from CVDs. The heart has four chambers––two atria located in its upper part and two ventricles in the lower one (see Fig. 1). The main task of the atria is to receive the blood delivered to the heart by large veins and then pass it to the ventricles. Ventricles are the heart’s pumps that keep the blood flowing around the body by means of ejecting the blood to the arteries (see for example [4]). At each atrium–ventricle as well as ventricle–artery interface a two or three-leaflet fibrous valve can be found which is responsible for ensuring the one-way flow of blood and preventing its reflux. Heartbeat is triggered by heart’s conduction system consisting of nodes and fibers propagating electrical impulse. The electric shock causes contraction of the heart at the average pace of 70–90 beats per minute. The condition when the heartbeat exceeds 100 bpm is referred to as ‘tachycardia’, and when the heart beats at the pace lower than 60 bpm, ‘brachycardia’ is said to occur (see for example [4]). During heart contraction (referred to as ‘systole’) and relaxation (diastole) the closure of the valves accompanied by contraction of particular areas of the heart leads to turbulent flow of blood that during auscultation corresponds to a specific ‘lub-dub’ sound. The first of these two major heart tones (see Fig. 2), termed S1 (‘lub’), is caused by the closure of mitral and tricuspid valves while the second, S2 (‘dub’), by the closure of pulmonary and aortic valves (see for example [4, 5]). The aforementioned tones are easily distinguishable since they differ in frequency and duration: S1 lasts for 140 ms and its frequency equals to 35–50 Hz while S2 lasts

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Fig. 1 Internal anatomy of the heart (anterior view) (from Texas Heart Institute website)

for 110 ms and has higher frequency––50–70 Hz. In children and adolescents, the third tone, S3, is also present. What is also worth mentioning is that heart sounds usually fall within the range of 20–650 Hz; however, it has been proved that the most diagnostically crucial are those between 70 and 120 Hz [6]. Abnormalities in the functioning of the valves can be noticed by the analysis of the heart tones. If some dysfunction is present, the amplitude of the sound changes as well as extension or splitting of the tone can be observed. What is more, also heart murmurs of the amplitude often comparable to the one of S1 and S2 tones are noticeable [5]. B. Stethoscope history The first stethoscope was created in 1816 by a French physician, René Théophile Hyacinth Laennec (see for example [8–11]) and revolutionized the auscultation by introducing its mediate form, this is by eliminating the need of placing one’s ear directly on the chest of a patient. Employing an auscultation instrument improved also the quality of the sound coming to the doctor’s ears. The device presented by Laennec was a wooden hollow tube with detachable brass-based chest piece and differed significantly in form from the stethoscopes used nowadays. The design of Laennec’s stethoscope has undergone a number of modifications initiated in 1828 by Pierre Piorry, who changed the shape of this medical device to trumpet-like. One of the most revolutionizing redesigns––changing the instrument from mono to binaural was introduced in 1840s. The new device was made of two

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Fig. 2 Normal and abnormal heart sounds (related to different disorders) with S1–3 sounds during heart cycle [7]

bent pipes connected to the wooden chest piece. Elastic rubber tubing was presented in 1851 by Arthur Leared, however, the first commercially useable stethoscope was created a year later, in 1852, by George Camman. Apart from the aforementioned, modifications covered various improvements of the chest piece, including introduction of the diaphragm (1851, Marsh), combined bell-diaphragm (1925, Sprague) as well as dual-frequency chest pieces (late 1970s, Littmann). Nowadays, two major types of stethoscopes are used by physicians. In the so-called Y-tube stethoscope a single tube is connected to the chest piece and then branched into two, where each of the branches is ended with an earpiece. In the second type of the stethoscope, Sprague Rappaport-type, each earpiece is connected to the chest piece by means of separate tubes. The tubes are held together by metal clips.

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The present development of the auscultation instruments is mostly based on finding better materials and improvement of the acoustics which follows better understanding of sound conduction. Apart from this, electronic stethoscopes have been developed which allowed for recording the sound and its further processing and analysis. Features of electronic stethoscopes facilitate training of new doctors as well as expand telemedicine abilities by possible saving and sharing auscultation results (see for example [12–14]). The main objective of this article is to present the proposition of practical solution of the stethoscope characterized with the function of recording and play back the sound of, among others, the heart or lungs accompanied by the proposition of analysis and interpretation methods of acquired recordings.

2 Construction of the Electronic Stethoscope An ordinary Sprague Rappaport type stethoscope was employed for the purpose of developing the electronic stethoscope and was dedicated for redesign. Both of the tubes were cut off at the distance that enables comfortable grip and use of the chest piece (approximately 6 cm from the chest piece) (see Fig. 3). In order to reuse the binaural of the stethoscope the Y-connector was used. One of its branches was put into one of the elastic tubes connected to the chest piece. The other two branches of the Y-connector were connected to the tubes of stethoscope’s headset. The second tube of those permanently linked with the chest piece was supplemented with the electret microphone. The microphone followed by a shielded cable and a mini jack connector enables connecting the stethoscope to the Fig. 3 Prototype of the electronic stethoscope

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computer by means of sound card’s microphone input. Such a redesign gives a possibility to easily implement a microphone in commonly used classical stethoscopes.

3 Advantages of the Construction Presented solution has an important advantage: it allows auscultating and, at the same instance, observing recorded signals on the computer by means of time– amplitude plot or spectrogram (see Fig. 4). For this purpose, a dedicated program developed in LabVIEW environment is used. Alternatively free (GNU license) software––Thinklabs Phonocardiography can be also employed. In both of the programs it is possible to record and analyze the signal after auscultation. Observation of plots during blood pressure test based on the Korotkoff method (see Fig. 5) allows to obtain more precise results comparing to ordinary auscultation.

Fig. 4 Filtered signal acquired from the stethoscope during heart auscultation, time–amplitude plot, spectrogram

Fig. 5 Raw signal acquired from the stethoscope during blood pressure test (Korotkoff sounds), time–amplitude plot, spectrogram

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Thus, such a construction has also a didactic purpose––it is possible to record signals and play them back in the class in the real time or post process them after auscultation. In addition, as it was mentioned in Sect. 2, each type of stethoscope can be supplemented with an electret microphone.

4 Professional Electronic Stethoscope To verify the recording’s quality, a professional middle-class electronic stethoscope was used. It provides audio recording feature and also (not real-time) transferring the audio file to dedicated software through PCs IrDA (infrared) communication port. Two reference sounds were prepared. Sound of silent to check the noise level and professional 150 Hz reference source (RTF Elektrodynamischer Eichtisch 11032). This frequency is in the range of real heartbeat sounds. Mentioned sounds were recorded using both stethoscopes. The recordings were then analyzed using Audacity audio software (GNU license), including waveform, offset, and FFT analysis. Basic waveform analysis showed that the professional stethoscope records sound with low sampling frequency (only 8 kHz) while the construction proposed in this paper can record the sound with sampling frequency up to 96 kHz. In typical medical practice, high sampling frequency is not important. It matters in some hiss detection in lungs, detailed heart valves analysis and also in accuracy of automatic heartbeat parameters detection algorithms. Figure 6 presents FFT plots of silence recordings using both stethoscopes. The noise level of about −50 to −80 dB for both microphones is acceptable as for

Fig. 6 Comparison of FFT analysis of silence recordings

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Fig. 7 Comparison of FFT analysis of recorded reference 150 Hz sound (marked by vertical dashed line)

nonprofessional audio recordings. This level depends on the place where the sound is recorded as well as on the environment sounds. Some frequencies can be selected as louder in both stethoscopes, but it will not stand out stronger than in other one. Figure 7 shows similar FFT analysis but of 150 Hz reference sound recordings. Both stethoscopes record this frequency perfectly, but the professional one records 78 Hz at maximal dB level and 157 Hz in a set of higher harmonics. It should be emphasized that this inaccuracy is negligible in same basic analysis but plays an important role in more advance measurements when high frequency sounds should be detectable correctly.

5 Acquisition and Analysis Software Originally developed software was created in National Instruments LabVIEW package to record and analyze the signal from the stethoscope or previously recorded audio files. The key implemented features include: acquisition of the sound with simultaneous monitoring; replay mode; amplitude normalization; signal filtering; graphical representation of the signal; automatic peak detection; and heartbeat frequency analysis. Additionally, it is also possible to simultaneously measure and analyze other biological signals, e.g., blood pressure level, using dedicated sensor and acquisition hardware, not presented in this paper. Acquisition algorithm is based on the standard LabVIEW Sound Input/Output Vis (Visual Instruments) that uses Microsoft DirectX system libraries. Sound card driver sends raw data to the LabVIEW where the signal is properly conditioned,

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Fig. 8 LabVIEW acquisition, filtering and recording algorithm

filtered, and stored in chosen audio file (in WAV format). This part of the program shows Fig. 8. Similar procedure is followed in record and monitor mode. Audio data is stored in the file and simultaneously sent to the sound card driver. Replay mode reads WAV audio file from the hard drive. Recorded signal is played back and also showed as a waveform plot. A. Filtering modes A user can chose between several filtering modes: (i) original mode—no filtering is applied, the user hears exactly what the microphone collects, (ii) heart 1 mode—applies band-pass filter with cut off frequencies equal to 20 Hz and 650 Hz which determine the range of heart sounds frequency, (iii) heart 2 mode—applies band-pass filter with cut off frequencies equal to 70 and 120 Hz; the passband is equal to the frequency range of the most crucial heart sounds, (iv) lungs 1 mode—band-pass filter applied in this mode passes the frequencies lying in the range 70–2000 Hz corresponding to the literature frequency range of lung sounds, (v) lungs 2 mode—band-pass filter passes the frequencies from 200 to 600 Hz range––this is from the range carrying the most of diagnostically important information, (vi) Korotkoff mode—20–50 Hz frequencies are passed by the band-pass filter. What is more, the amplification of the signal can be set by rotating the knob. Change of parameters results in immediate change of the output.

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B. Automatic heartbeat analysis Created software analyses recorded mono audio material with standard parameters of sampling frequency 44,100 Hz but it can be adapted to different sound qualities. Additionally, recording with proper SNR (signal-to-noise) parameter is required. If the noise amplitude is too high, there is no guarantee that the analysis will be correct. Good quality of the microphone, preamplifier, and sound card is in this case significant. The automatic analysis of heartbeat sound signal is realized in six steps (a) selecting part of the signal to be analyzed; (b) selecting peak detection minimal value and minimal peak width; (c) automatic peak detection using LabVIEW Peak Detector VI, that finds S1 and S2 peaks in whole selected sample; (d) separating proper S1 and S2 peaks; (e) calculating period between each successive S1 and also S2 peaks; (f) calculating mean values, standard deviations, and drawing plots of the period versus time. Parts of the program (steps of calculation) are presented in Fig. 9. The first part (a) depicts automatic peak detection VI, which creates an array of time positions and values of each found peak. This data is filtered (b) to delete some noise peaks between S1 and S2. Two consecutive peaks are treated as correct if time gap between them is greater than delta variable. This step creates three arrays: numbers of correct peaks, correct peaks values, and its time position. Assuming that only S1 and S2 peaks passed the filtering algorithm, odd and even data are separated (c) to two arrays containing S1 and S2 peaks time positions. Periods are also calculated in this step. After that the mean value and standard deviation are calculated. C. Graphical User Interface The user interface of created program consists of (see Fig. 10): (i) text field with file open dialog box to select WAV audio file from the computer memory; (ii) normalized waveform plot of loaded WAV file, amplitude versus time; (iii) two sliders to select starting and ending time position of the analysis sample. This feature is helpful if the loaded audio material contains irrelevant data at the start or at the end; (iv) the similar plot after trimming and automatic peak detection procedure, amplitude versus time. A red horizontal line is used to trigger minimal amplitude level to be detected during analysis; (v) two plots showing peaks S1 and S2 periods versus period number to present stability of the heartbeat period during each heartbeat; (vi) the user can also trigger minimal time interval between peaks to omit irrelevant noise peaks placed between S1 and S2, etc.; (vii) the results, mean value and standard deviation are shown for each S1 and S2 and mean value for whole heartbeat period.

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Fig. 9 a Peak detector VI and its configuration, b cleaning-up unwanted noise peaks, c selecting proper S1 and S2 peaks

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Fig. 10 Graphical user interface of the LabVIEW analysis software

6 Algorithm Verification To verify if the S1 and S2 peaks are detected correctly, simultaneous sound acquisition and ECG measurements were performed. According to Wiggers diagram presented in Fig. 11, the first audio peak should be detectable at the same time instant as the beginning of the first peak in ECG. S2 peak starts nearby (i.e., right after) the second maximum on the ECG plot. The third peak is not detectable. Presented comparison (in Fig. 12) shows the correspondence of the obtained results to the aforementioned theoretical assumptions and positively verifies the measurement method.

Fig. 11 Wiggers diagram. (part of Wiggers_Diagram.svg from Wikimedia, CC 2.5 licence)

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Fig. 12 Comparison of ECG (electrocardiograph) electrical signal and recorded stethoscope audio signal

7 Results An exemplary analysis and results were performed on typical, normal heartbeat signal recorded for one person, using presented stethoscope supplemented with electret microphone and is showed in Fig. 13. One can see S1 (lower amplitude), S2 (higher amplitude) peaks, and barely visible S3 in several periods. Figure 14 depicts waveform signal after processing. Horizontal line (just above zero) shows minimal amplitude value that is used for the detection of each peak. Additionally, peak detector width variable sets precise limit to the width of every

Fig. 13 Recorded heartbeat signal

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Fig. 14 Recorded heartbeat signal, peak minimal detected value (horizontal line just above zero) and detected peaks (points just before each peak)

peaks to be detected. Each qualified peak is marked with small dot above its time position. For this paper seven volunteers were examined by stethoscope auscultation and, in addition, one was examined by simultaneous measurement with professional ECG system. ECG comparison results were presented in sixth section. Resulting duration of the recording, detected heart beats, mean values of intervals between them, and its standard deviations for all analyzed audio signals are presented in Table 1. Mean values are repetitive, which is correct as for the recording of persons with no diagnosed heart diseases. Generally, in healthy adults the heartbeat range covers 60–90 beats per minute [15] which correspond to about 0.66–1.0 s-long periods. Relatively high value of the standard deviations can suggest an arrhythmia. During construction and testing of the electronic stethoscope the following observations were made: (i) It is very important to use high quality microphone capable of low frequencies recording. Furthermore, both mechanical and electronic parts should be also of good quality. (ii) For the purpose of automatic peak detection algorithm higher (more than standard 44,100 Hz) sampling frequency of the recording gives better results.

Table 1 Results of automatic heartbeat analysis Probe no

Probe length (s)

Number of detected heartbeats

Heartbeat period mean value (s)

SD

1 2 3 4 5 6 7

16 17 16 28 60 18 15

16 17 17 33 76 11 12

0.898 0.941 0.906 0.832 0.786 1.236 1.053

0.0262 0.0269 0.0341 0.0232 0.1377 0.0643 0.0267

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(iv) (v) (vi) (vii)

(viii)

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If the frequency is too low, detected peaks positions can increase standard deviation value. The system should be resistant to different types of interferences (including electrical ex. net signal and mechanical ex. noise from the environment). This requirement can be met by proper grounding and shielding of the electrical circuits. Computer power supply type as well as its general condition influences the output by means of generating electrical noise. The user should avoid positive feedback during simultaneous auscultation and play back of the sound through speakers. S3 sound peaks were sometimes visible on the plot but were barely audible. Playback of the recordings requires a speaker set including subwoofer due to low frequencies that usually are not transmitted through computer’s built-in speakers. Headphones can be also used. LabVIEW package is powerful software for this type of application. Additional specialized hardware and plugins for sound recording and analysis are also available.

8 Concluding Remarks Taking all the results into consideration, several conclusions can be drawn. First of all, electret microphones connected to computer sound cards can be used for biological sounds acquisition. It has been shown that the electronic stethoscope can be successfully used for acquisition of heart, lung, and Korotkoff sounds. It can be also stated that an electronic stethoscope can be used in telemedicine to record, analyze, and share medical data or for educational purpose to record, play back (in real time), and real-time presentation of the graphical results during normal auscultation during a class. What is more, real-time filtration of the signal improves the ability of recognizing sounds. Commercial electronic stethoscopes are available on the market but their advantages over presented simply modified normal stethoscope are significant only when the expensive dedicated software is used. In general, the comparison of the presented device with a commercial one showed that the noise level in both devices is comparable and both of them properly detect the reference frequency. However, the commercial stethoscope detects the reference frequency in a set of higher harmonics while the device being the subject of this paper records this frequency at maximal dB level. Last but not least, the system enables to record the sound with much higher sampling frequency than the used commercial product and this fact can be meaningful in detailed heart and lungs analysis. Additionally following modifications are planned: (i) Redesign of the stethoscope in such a manner that it will be possible to operate with or without the cable.

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(ii) Adding a preamplifier to minimize the interferences on the way microphone– computer and filter out unwanted frequencies before post processing. (iii) Testing the system with physicians and patients with already diagnosed disorders resulting in change of sound waveform. (iv) Testing better preamplifiers and microphones with higher audio quality to eliminate more noises from the recording process.

References 1. World Health Organization: Telemedicine—opportunities and developments in Member States, report on the second global survey on eHealth 2009. Global Observatory for eHealth Series. Healthcare Inf. Res. 18(2), 153–155 (2012) 2. Beach, K., Dunmire, B.: Medical acoustics. In: Rossing, T.D. (ed.) Springer Handbook of Acoustics, pp. 83–898. Springer Science+Business Medium, New York (2007) 3. World Health Organization: Noncommunicable diseases. Fact sheet. Jan 2015 4. Saladin, K.S.: Anatomy and Physiology—The Unity of Form and Function, 5th edn. McGraw-Hill, New York (2009) 5. Wilk, B.: Wirtualny stetoskop do badania tonów podstawowych serca. Pomiary, Automatyka, Kontrola 53(12), 46–47 (2007) 6. Bankaitis, A.U.: Amplified stethoscope options for professionals with hearing loss. Audiol. Online http://www.audiologyonline.com/articles/amplified-stethoscope-options-forprofessionals-860 7. Congenital Heart Defects (modified): http://www.boundless.com/physiology/textbooks/ boundless-anatomy-and-physiology-textbook/the-cardiovascular-system-18/heart-disorders-andclinical-cases-178/congenital-heart-defects-894-1808 8. Fang, C.: It was almost called the cylinder (& other who-knew facts about the stethoscope). Clin. Correlations The NYU Langone Online J. Med. 10 Oct 2014 9. Welsby, P.D., Parry, G., Smith, D.: The stethoscope: some preliminary investigations. Postgrad. Med. J. 79(938), 695–698 (2003) 10. Roguin, A.: Rene Theophile Hyacinthe Laënnec (1781–1826): the man behind the stethoscope. Clin. Med. Res. 4(3), 230–235 (2006) 11. Geddes, L.A.: Birth of the stethoscope. Eng. Med. Biol. Mag. 24(1), 84–86 (2005) 12. Bhaskar, A.: A simple electronic stethoscope for recording and playback of heart sounds. Adv. Physiol. Educ. 36(4), 360–362 (2002) 13. Wang, H., Chen, J., Hu, Y., Jiang, Z.: Heart sound measurement and analysis system with digital stethoscope. In: 2nd International Conference on Biomedical Engineering and Informatics, Tianjin (China), 17–19 Oct 2009 14. Sound Strategy: The story behind the development of 3 M™ Littmann Electronic Stethoscopes. http://multimedia.3m.com/mws/media/749312O 15. Simmers L.: Diversified Health Occupations, 2nd edn, p. 157. Cengage Learning (1988)

Determination of Forces and Moments of Force Transmitted by the Wheel of a Mobile Robot During Motion Maciej Trojnacki

Abstract This paper is concerned with a mechanical system for determination of forces and moments of force transmitted by a wheel of a mobile robot during its motion. At the beginning, the importance of the knowledge of forces and moments of force acting on a wheel of the vehicle are highlighted. Such knowledge may be useful during designing and optimizing the construction of a vehicle and also can be the basis for development of tire models which are used, for example, in vehicle dynamics simulations. Next, the concept of a solution enabling determination of forces and moments of force transmitted by the wheel of a robot is described in detail. The method of determination of those forces and moments of force takes into account the motion of the vehicle and properties of the drive units. The developed solution is based on the measurement of the forces transmitted by force sensors located near bearings mounted on the axle of each wheel. Finally, implementation of the proposed system in the four-wheeled mobile robot with independently driven nonsteered wheels is presented. Keywords Mobile robot surement Force sensor





Robot wheel
Drive unit
Force and torque mea-

1 Introduction Forces and moments of force acting on vehicle wheels have critical impact on its motion and durability of its structure. For this reason, knowledge of these forces and moments of force is important in the process of designing and optimization of mechanical structures of the wheeled mobile robots. Optimization of the design can be aimed at guaranteeing, for example, the required strength of the chassis while keeping the minimum mass or the adequate damping of structural vibrations. M. Trojnacki (&) Industrial Research Institute for Automation and Measurements PIAP, Warsaw, Poland e-mail: [email protected] © Springer International Publishing Switzerland 2016 J. Awrejcewicz et al. (eds.), Mechatronics: Ideas, Challenges, Solutions and Applications, Advances in Intelligent Systems and Computing 414, DOI 10.1007/978-3-319-26886-6_13

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Knowledge of the phenomena associated with robot motion, in particular, the occurring forces and moments of force, is also the foundation for the development of dynamic models of this kind of system. Models like that can be useful both in the process of robot design and in the synthesis of algorithms for control of its motion, especially when the designed controller relies on robot dynamics model (e.g., adaptive control or robust control). The developed models of dynamics of the mobile robots enable simulation of their motion. In the case of robots moving in conditions of wheel slip, it is necessary to consider the so-called tire model in the model of robot dynamics. Models like that have been developed for automobiles for many years, which is reflected, for instance, in the works [1, 2], whereas they are rarely used in the case of mobile robots. As pointed out in the work [3], tire models should be taken into account especially in the case of robots with nonsteered wheels, called skid-steered robots. Tire models take into account the phenomena in the tire-ground interface, including forces and moments of force, and in the case of more advanced models also the tire structure is included. In order to develop or validate a tire model, the knowledge of robot motion parameters as well as the forces and moments of force acting on wheels is necessary. Particularly difficult is the measurement of forces and moments of force acting on wheels during robot motion. Commercial solutions to this problem are not available at the moment. In the case of automobiles, solutions using the so-called multiaxis wheel force transducers [4, 5] are available. In the case of small-wheeled robots, because of their size and lack of standards concerning the wheel geometry, it would be difficult to use them with existing robot designs. After taking into account the above considerations, in this work a concept of measurement system and method enabling determination of forces and moments of force acting on the wheel of a small mobile robot during motion will be presented.

2 Wheeled Mobile Robot The object of the research is a small four-wheeled mobile robot called PIAP GRANITE. The robot has all wheels driven independently by DC servomotors with gear units and encoders. A visualization of the robot is shown in Fig. 1a, and its kinematic structure as well as illustration of reaction forces acting in the wheel–ground plane of contact is presented in Fig. 1b. It is possible to distinguish the following main components of the robot: 0— body with frame for installation of the research equipment, 1–4—wheels with toothed belt pulleys, and 5–6—toothed belts. The drive transmission in each drive unit can be decoupled, which permits obtaining the following configurations of the robot chassis: – driving of front or rear wheels only,

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Fig. 1 Four-wheeled mobile robot: a visualization of the robot, b kinematic structure of the robot and illustration of reaction forces acting in the wheel-ground plane of contact

– driving of front or rear wheels and transmission of the drive to the remaining wheels using the toothed belts, – independent driving of all wheels. The following designations for the ith wheel have been introduced in the robot model: Ai is the geometrical center, ri is the radius, θi is the rotation angle (i = {1, …, 4}). The most important robot parameters are: – dimensions: L = 0.425 m, W = 0.553 m (where L = A1A3 = A2A4, W = A1A2 = A3A4, see Fig. 1b), ri = r = 0.0965 m, – masses of the components: m0 = 40 kg, mi = 1 kg, m5 = m6 = 0.18 kg. The robot is equipped with: – a laptop computer for control and data acquisition purposes, – iNEMO sensors module with 3-axis MEMS accelerometer, gyro, and magnetometer for determination of motion parameters of the robot [6], – a GNSS receiver and antenna for robot navigation [7], – a 2D laser scanner for localization in known environment [8], – bumpers for obstacles detection, – router and USB modem for Internet connection, – video cameras and lights for robot teleoperation. The robot drives are DC servomechanisms. The mechanical power from the motor is transmitted by means of the gear unit to the axle of the wheel, which is illustrated in Fig. 2. It is assumed that version of the robot with independent driving of all 4 wheels is analyzed in this paper.

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Fig. 2 Schematic diagram of the robot drive unit and wheel

3 Method of Determination of Forces and Moments of Force Transmitted by the Wheel of a Mobile Robot During Motion To the described robot will be applied the method allowing determination of forces and moments of force transmitted by its wheels. The method of determination of those forces and moments of force takes into account the vehicle motion and properties of a drive units. The idea of the solution relies on measurement of forces carried by flexible pressure sensors, which are placed between axle bearings and the supporting frame inside the measuring head. Forces and moments of force are then transmitted from the wheel via bearings to particular force sensors placed between bearings and the supporting frame which, based on the force measurements on those sensors, enables determination of forces and moments of force carried by the wheel, which in the end allows determination of forces and moments of force resulting from interaction of the wheel with the ground. The schematic diagram of the system for the left front wheel is shown in Fig. 3. Forces and moments of force acting on a wheel are transmitted to the axle and then to the two bearings denoted B and C in Fig. 3, and finally via force sensors to Fig. 3 Schematic diagram of the system for measurement of forces and moments of force carried by the axle of robot wheel

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Fig. 4 Illustration of forces and moments of force acting on robot wheel

the robot body. In the analyzed system occurs also the interaction at the point D, that is, in the gears contact area. In general case, on the wheel act forces and moments of force resulting from the gravity force of this wheel, inertia forces, driving torque, and contact of the wheel with the ground. As a result, from the axle to which the wheel is mounted, reaction forces and reaction moments of force acting on the wheel appear as well. All forces and moments of force acting on the wheel excluding gravity force are shown in Fig. 4. External reaction forces and moments of force acting at the point of contact of the wheel with the ground T, that is, FT = [FTx, FTy, FTz]T and TT = [TTx, TTy, TTz]T can be reduced to the agreed-on point of mounting of this wheel, i.e., to the point A, according to the following relationships: FA ¼ FT ;

T
A ¼ rT  FT þ T
T ;
ex ey ez



0 0 r

¼ ½FTy r; FTx r; 0ŠT ; r T  FT ¼

FTx FTy FTz


ð1Þ

where FA = [FAx, FAy, FAz]T, TA = [TAx, TAy, TAz]T, rT = [xT, yT, zT]T are the vectors that determine the position of the point of contact T with respect to the point A of the wheel which is also the origin of the coordinate system of this wheel, ex, ey, ez are unit vectors of the axes.

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For the wheel, the following dynamic equations of motion can be written in the matrix-vector form: ðWÞ

mW aA ¼ FA þ RA þ mW g;

ð2Þ

      ðWÞ € þ h_ A þ u_  IW h_ A þ u_ ¼ TA þ MðWÞ ; IW € hA þ u A þs

ð3Þ

where mW is the mass of the wheel, IW is the inertia tensor of the wheel (3 × 3 matrix), and aA is the vector of acceleration of the wheel geometric center, h_ A ¼ _ 0ŠT ; € ½0; h; hA ¼ ½0; € h; 0ŠT are the vectors of angular velocity and angular accel€ ¼ ½€ € y; u € z ŠT —vectors of angular eration of wheel spin, u_ ¼ ½u_ x ; u_ y ; u_ z ŠT ; u ux ; u velocity and angular acceleration of the spin of the mobile platform, g = [gx, gy, gz]T—gravitational acceleration vector, FA = [FAx, FAy, FAz]T, TA = [TAx, TAy, TAz]T—vectors of force and moment of force resulting from the contact of the wheel with the ground reduced to the point A, τ(W) = [0, τ, 0]T—driving torque vector, ðWÞ ðWÞ ðWÞ ðWÞ ðWÞ ðWÞ ðWÞ ðWÞ RA ¼ ½RAx ; RAy ; RAz ŠT ; MA ¼ ½MAx ; MAy ; MAz ŠT —vectors of reaction force and moment of force acting on the wheel. Those equations enable determination of internal reaction forces and moments of force acting on the wheel in the agreed-on point of its mounting to the axle. It is assumed that all parameters of motion of the system are known, that is, they are measured and/or determined during robot motion. Forces and moments of force acting on the axle of the wheel (after reduction of the forces acting on the wheel to the point A), the gear, and the bearings are shown in Fig. 3. Based on this figure, it is possible to write the following dynamic equations of motion for the wheel axle: ðSÞ

ðSÞ

ðSÞ

mS aS ¼ FA þ RB þ RC þ RD þ mS g;

ð4Þ

ðSÞ € Þ þ ðh_ A þ uÞ _  IS ðh_ A þ uÞ _ ¼ TA þ MBðSÞ þ MðSÞ IS ð€ hA þ u C þ MD þ rCM  mS g;

ð5Þ where mS is the mass of the system: axle, wheel, toothed belt pulley, gear and bearings, IS is the inertia tensor for the system calculated with respect to the reference system of origin at the point A, based on the known inertia tensor IS with respect to the mass center of this system using the parallel-axis theorem (Steiner’s theorem) [9], rCM is the vector describing position of the mass center of the system with respect to the point A, aS is the vector of acceleration of the mass center of the system, ðSÞ ðSÞ ðSÞ ðSÞ ðSÞ ðSÞ ðSÞ ðSÞ ðSÞ ðSÞ ðSÞ ðSÞ RB ¼ ½RBx ; RBy ; RBz ŠT , RC ¼ ½RCx ; RCy ; RCz ŠT , MB ¼ ½MBx ; MBy ; MBz ŠT , ðSÞ

ðSÞ

ðSÞ

ðSÞ

MC ¼ ½MCx ; MCy ; MCz ŠT are the vectors of reaction forces and moments of force of ðSÞ

ðSÞ

ðSÞ

ðSÞ

ðSÞ

ðSÞ

ðSÞ

ðSÞ

the bearings, RD ¼ ½RDx ; RDy ; RDz ŠT , MD ¼ ½MDx ; MDy ; MDz ŠT are the vectors of reaction force and moment of force acting on the spur gear.

Determination of Forces and Moments of Force …

211

It is assumed that the current i consumed by the motor driving the wheel is known. On this basis, knowing the torque constant and transmission gear ratio and after assuming certain efficiency, it is possible to determine the torque acting on the axle of the wheel from the following relationship: s ¼ gD nD kM i;

s ¼ ½0; s; 0ŠT ;

ð6Þ

where ηD is the efficiency of the gear transmission, nD is the gear ratio of the transmission from the motor to the wheel axle, and kM is the torque constant of the motor. ðSÞ The force RD can be projected both on the directions of axes of the adopted coordinate system, and on the directions: tangent, normal, and binormal of the natural coordinate system associated with the driven gear and of origin at the point D; that is, in the point of contact of the gears. Between those projections, the following relationships hold true: ðSÞ

ðSÞ

RD ¼ ½RDs sin d

ðSÞ

ðSÞ

ðSÞ

RDn cos d; RDb ; RDs cos d

ðSÞ

RDn sin dŠT ;

ð7Þ

where the angle δ describes the position of the point D (Fig. 3), δ = 45° for the right wheel and δ = 135° for the left one. ðSÞ Between the tangent and normal components of the force, RD is the valid relationship resulting from the pressure angle ζ, which enables determination of the normal component of the force: ðSÞ

ðSÞ

ðSÞ

ðSÞ

RDs =RDn ¼ tgf ) RDn ¼ RDs =tgf:

ð8Þ

In turn, the binormal component of the force depends on the coefficient of friction between the gears μD, that is: ðSÞ jRDy j  lD

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðSÞ ðSÞ ðRDx Þ2 þ ðRDz Þ2 :

ð9Þ

The friction coefficient for the interacting gears is in the interval μDs ≥ μD ≥ μDk. In the case of the spur gears, the value of this coefficient is small enough for the longitudinal component of the force to be small compared to the remaining components. For this reason, in the following considerations, it is assumed that this component is approximately equal to zero. It should be noted that the driving torque τ acting on the wheel is equivalent to the moment carried by the driven gear, that is: ðSÞ

ðSÞ

ðSÞ

s ¼ MDy ¼ RDs rD ) RDs ¼ s=rD ; where rD is the radius of the driven gear (equal to half of its pitch diameter).

ð10Þ

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M. Trojnacki

Fig. 5 Arrangement of force sensors and related notation

So, eventually the vector of force carried by the driven gear located on the axle of the wheel reads: ðSÞ

RD ¼ ½s=rD ðsin d

cos d=tgfÞ; 0; s=rD ðcos d

sin d=tgfފT ;

ð11Þ

whereas the vector of the moment of force is equal to: ðSÞ

ðSÞ

ðSÞ

ðSÞ

MD ¼ rD  RD ¼ ½RDz yD ; RDx zD

ðSÞ

RDz xD ;

ðSÞ

RDx yD ŠT ;

ð12Þ

where rD ¼ ½xD ; yD ; zD ŠT ¼ ½rD cos d; d; rD sin dŠT , d is the distance of the gear plane from the wheel plane, sign “+” is for the right wheel, and “−” is for the left one. Around each bearing, six pressure sensors are mounted. Their arrangement is presented in Fig. 5. Sensors measuring the axial component of the reaction force are situated at the opposite sides of the bearings. It is assumed that the nominal operating point of all sensors is in the middle of their range; i.e., all sensors are pre-stressed. It prevents the situation when, due to existence of clearances, effects of impact on the surfaces of sensors occur during robot motion. On the basis of known forces acting on the sensors, it is possible to determine the forces carried by the bearings B and C using the following relationships: ðSÞ

RB ¼

6 X j¼1

ðSÞ

RBj ;

ðSÞ

RC ¼

6 X

RCj

ð13Þ

j¼1

RB ¼ ½ RB2 þ RB4 ;  ðRB5 þ RB6 Þ; RB1 þ RB3 ŠT ;

ð14Þ

Determination of Forces and Moments of Force …

213

ðSÞ

RC6 Þ; RC1 þ RC3 ŠT ;

RC ¼ ½ RC2 þ RC4 ;  ð RC5

ð15Þ

where sign “+” is for the right wheel whilst “−” is for the left one. In turn, the reaction moments of force of the bearings B and C are, respectively, equal to: ðSÞ

ðSÞ

ðSÞ

ðSÞ

ð16Þ

ðSÞ

ðSÞ

ðSÞ

ðSÞ

ð17Þ

MB ¼ rB  RB ¼ ½RBz yB ; 0; RBx yB ŠT ; MC ¼ rC  RC ¼ ½RCz yC ; 0; RCx yC ŠT ;

where rB = [xB, yB, zB]T = [0, ± b, 0]T, rC = [xC, yC, zC]T = [0, ±c, 0]T, b and c are distances of the geometric centers of the bearings B and C from the point A of the wheel, sign “+” is for the right wheel while “−” is for the left one. Knowing the geometric and inertial parameters, parameters of motion of the system and estimated values of the driving torques, it is finally possible to determine forces and moments of force carried by the robot wheels. To this end, one should determine the unknown quantities for each robot drive unit in the following sequence: 1. value of the driving torque on the basis of the measured current consumption for the robot drive and knowing the parameters of the motor and transmission— Eq. (6): s ¼ gD nD kM i;

s ¼ ½0; s; 0ŠT ;

2. vectors of reaction force and moment of force carried by the driven gear mounted on the wheel axle—relationships (11)–(12), on the assumption that δ ≈ const ðSÞ

RD ¼ ½s=rD ðsin d ðSÞ

cos d=tgfÞ; 0; s=rD ðcos d ðSÞ

ðSÞ

MD ¼ ½RDz yD ; RDx zD

ðSÞ

sin d=tgfފT ;

ðSÞ

RDz xD ; RDx yD ŠT ;

3. vectors of reaction forces and moments of force of the bearings B and C (Fig. 3) on the basis of measurements from the pressure sensors—relationships (14)–(17) ðSÞ

RB ¼ ½ RB2 þ RB4 ;  ðRB5 þ RB6 Þ; RB1 þ RB3 ŠT ; ðSÞ

ðSÞ

ðSÞ

ðSÞ

MB ¼ rB  RB ¼ ½RBz yB ; 0; RBx yB ŠT ;

214

M. Trojnacki ðSÞ

RC6 Þ; RC1 þ RC3 ŠT ;

RC ¼ ½ RC2 þ RC4 ; ð RC5 ðSÞ

ðSÞ

ðSÞ

ðSÞ

MC ¼ rC  RC ¼ ½RCz yC ; 0; RCx yC ŠT ; 4. vectors of forces and moments of force acting on the wheel, reduced to the point A (Fig. 3) on the basis of dynamic equation of motion for the wheel axle— resulting from Eqs. (4) to (5): FA ¼ mS aS

ðSÞ

ðSÞ

ðSÞ

ðRB þ RC þ RD þ mS gÞ;

€ Þ þ ðh_ A þ uÞ _  IS ðh_ A þ uÞ _ TA ¼ IS ð€ hA þ u

ðSÞ

ðSÞ

ðSÞ

ðMB þ MC þ MD þ rCM  mS gÞ;

where

rCM



ex
 mS g ¼ mS

0
gx

ey yCM gy


ez

0

¼ ½gz yCM ; 0; gx yCM ŠT gz


5. vectors of external reaction forces and moments of force acting on the point of contact of the wheel with the ground, resulting from relationship (1) FT ¼ FA ;

TT ¼ TA

rT  FT :

In the initial approximation, for simplicity, it is possible to neglect the parameters of system motion occurring in Eqs. (4)–(5) and consequently the resulting inertia forces. This assumption is particularly justified during steady-state motion of the robot.

4 Practical Realization of Measuring System Within the present work, a practical realization of the measuring system allowing determination of forces and moments of force acting on the robot wheel will be presented. It is the patent pending solution [10]. In Fig. 6 mechanical design of the robot drive unit is shown, and in Fig. 7, the realized structure. The drive unit contains 2 measuring heads shown in Fig. 8. Both heads enable measurement of forces carried by the bearings, which are marked B and C in Fig. 3.

Determination of Forces and Moments of Force …

215

measuring head

Fig. 6 Mechanical design of the robot drive unit

measuring head Fig. 7 Realization of the robot drive unit

Through both measuring heads passes the axle driven by the motor on which the wheel is mounted. According to Fig. 8, the measuring head consists of bearing 1 which transmits the forces and moments of force acting on the axle, bearing housings 2 and 3, the supporting frame 4, six flexible pressure sensors 7 and fine-pitch screws 5 which allow calibration of the head measuring system.

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M. Trojnacki

Fig. 8 Mechanical design of the measuring head

5 Conclusions Within the work, the method of determination of forces and moments of force transmitted by the wheel of a mobile robot during its motion is presented. The proposed method of calculations will enable determination of those quantities in the experimental investigations of motion of the robot. Also the practical implementation of the proposed system developed for the four-wheeled robot with independently driven nonsteered wheels is presented. The proposed solution will enable verification of the tire models used in the simulation investigations of the lightweight wheeled mobile robots.

Determination of Forces and Moments of Force …

217

Acknowledgements The work has been realized as a part of the project entitled “Dynamics modeling of a four-wheeled mobile robot and tracking control of its motion with limitation of wheel slips”. The project is financed from the means of National Science Centre of Poland granted on the basis of decision number DEC-2011/03/B/ST7/02532.

References 1. Pacejka, H.B.: Tire and Vehicle Dynamics, 2nd edn. SAE International and Elsevier (2005) 2. Wong, J.Y.: Theory of Ground Vehicles, 3rd edn. Wiley, New York (2001) 3. Trojnacki, M.: Dynamics Modeling of Wheeled Mobile Robots. OW PIAP, Warszawa (2013) (in Polish: “Modelowanie dynamiki mobilnych robotów kołowych”) 4. Vehicle onboard measuring system: Tokyo Sokki Kenkyujo Co., Ltd., 19 Feb 2015. Available on: http://www.pcb.com/auto/MultiAxis_Wheel_Force_Transducer.aspx 5. Multi-Axis Wheel Force Transducer for Automotive Road Load Data Measurement Applications: PCB® Piezotronics, 19 Feb 2015. Available on: http://www.tml.jp/e/product/ automotive_ins/automotive_ins_sub/automobile.html 6. Trojnacki, M., Dąbek, P.: Determination of motion parameters with inertial measurement units. part 2: algorithm verification with a four-wheeled mobile robot and low-cost MEMS sensors. In: Mechatronics: Ideas for Industrial Applications, Series: Advances in Intelligent Systems and Computing, pp. 253–267. Springer International Publishing, Berlin (2015) 7. Perski, A., et al.: GNSS receivers in engineering practice. Introduction to Global Navigation Satellite Systems, Pomiary Automatyka Robotyka 17(3/2013), 103–111 (in Polish: “Odbiorniki GNSS w praktyce inżynierskiej. Wprowadzenie do systemów GNSS”) 8. Jaroszek, P., Trojnacki, M.: Localization of the wheeled mobile robot based on multi-sensor data fusion. J. Auto. Mobile Robot. Intell. Syst. (submitted) 9. Craig, J.J.: Introduction to Robotics: Mechanics and Control, 2nd edn. Pearson/Prentice Hall, Upper Saddle River (2005) 10. Trojnacki, M., Kajder, Ł., Zboiński, M.: A device for measurement of forces and moments of force transmitted by the vehicle wheel. Patent application No. P.406966, 27.01.2014, (in Polish: Urządzenie do pomiaru sił i momentów sił przenoszonych przez koło jezdne pojazdu)

Comparative Study of Maintenance Vehicles Using Vibration Analysis Ovidiu Ioan Vulcu and Mariana Arghir

Abstract This article justifies the importance of vehicles maintenance throughout their entire running. According to this purpose, we have done a comparative study of vibrational behavior of two vehicles of the same type but different manufacturing years. For both cars, there were made experimental measurements of vibrations on the stand for three significant measurement points: the screw at the cover cleats, the bodywork, and the seat. The results are justified by the history of repairs and maintenance operations. Keywords Vehicles maintenance


Vehicles vibration
Vehicle wear

1 Introduction Transportation is one field of economic and social activity through which the movement in space is made of people and goods in order to meet the material and spiritual needs of the society. The inspection operations, troubleshooting, repair, improvement, etc., which allows ensuring continuity of use, safely, an optimal overall cost of a vehicle, constitute maintenance vehicles [1]. Maintenance of vehicles is a necessity, because the technical condition significantly affects comfort, road safety, and vehicle endurance as a whole. The main maintenance operations for means of transport are: replacement of worn parts, refilling working fluids, regulating components, and removal of wear factors (vibration, water, dust, acids, etc.). The efficiency of conveyance maintenance is mainly determined by minimizing the costs of maintenance and repair, by the achievement of the higher running times O.I. Vulcu (&)
M. Arghir Technical University of Cluj-Napoca, Cluj-Napoca, Romania e-mail: [email protected] M. Arghir e-mail: [email protected] © Springer International Publishing Switzerland 2016 J. Awrejcewicz et al. (eds.), Mechatronics: Ideas, Challenges, Solutions and Applications, Advances in Intelligent Systems and Computing 414, DOI 10.1007/978-3-319-26886-6_14

219

220

O.I. Vulcu and M. Arghir

Fig. 1 Operating regime curve of a vehicles [2]

between failures and the maintenance of high ecological parameters. This requires close and continuos observation of the technical condition of cars and periodic testing and diagnosis of these processes in order to detect faults, even the minor ones and determining the most effective intervention solutions. Inadequate operation and maintenance of the vehicle (using improper maintenance and repair materials, not following the periodicity of technical maintenance and current repairs, inappropriate adjustments, thermal regimes and overly high mechanical stress etc.) determines an accelerated wear of parts and subassemblies vehicle, but with similar features to the normal wear processes. The maintenance of the transport means, especially motor vehicles, is represented by means of the operating regime curve (Fig. 1). According to the curve shown in Fig. 1, maintenance actions are carried out at certain times and at certain values of vibration levels. It is observed that when the vehicle is new, it is normal to have high levels of vibration. During the period of running, this level decreases to a value that will remain approximately constant during the exploitation period. Significant increase in vibration parameters indicate a fault and there will be needed a remedial intervention. There is a vibration level value that indicates the vehicle is out of order and the repair is mandatory [2].

2 Vibration Sources of the Vehicles The most important vibration sources that occur while driving a vehicle are: propulsion engine, transmission organs, air resistance to the advance of the vehicle, and road surface quality [3]. During running, the most disturbing are the vibrations

Comparative Study of Maintenance Vehicles …

221

coming from the engine compartment or from the car decks. There are some possible causes of producing vibrations [4]: 1. Irregular functioning of the engine caused by insufficient air or fuel or faulty ignition received due to spark plugs, which may lead to mechanical vibration transmission throughout the car. 2. The precarious state suspension increases the level of vibration. Also, vibrations may occur due to the wear of rubber backing. 3. All vehicles have rotating components that are manufactured in tolerance class in sliding regime to function properly. If one of the axles is even slightly distorted, then it may cause vibration along the car. In this case, vibration increases while intensifying the running speed. 4. The vibrations are intensified when brake discs are slotted. 5. The vibrations caused by the deformation of wheels appear quite often. 6. Another reason for the occurrence of vibration is due to the tires. In general, if there are low-quality tires, they deform in time or suffer irregular wear and produce vibrations when running with certain speeds.

3 Experimental Method In the transport means maintenance and diagnosis on the items using experimental determination of vibration involves the establishment of the measuring device, depending on the parameter to be measured, the measurement points (items) where to put the accelerometer and method of the results analysis. We used as a measuring instrument SVAN 958 vibrometer, and the data obtained will be processed and analyzed using PC software SVAN++ [5].

3.1

Description of the of Passenger Cars Whose Vibration Was Measured

To highlight the vibrator response of a transport means, it was determined that vibration sources are elements of two cars Volkswagen Caravelle with identical characteristics, in the normal state, but with different years of manufacture. The first vehicle, the Volkswagen brand, shown in Fig. 2, for which measurements were made, has the following technical characteristics (as per registration certificate): – – – – –

manufacturing year: 2002; registration number: AB 07 WNT; number of seats: 8 + 1; power source: Diesel; maximum mass: 2800 kg;

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O.I. Vulcu and M. Arghir

Fig. 2 Vehicle with AB 07 WNT registration number

Fig. 3 Vehicle with CJ 47 ZEK registration number

– power: 75 kW; – engine capacity: 2461 cm3; – total running: 428,988 km. The second vehicle, the Volkswagen brand, for which measurements were made, is shown in Fig. 3. Technical characteristics (according to the registration certificate) of the vehicle from Fig. 3 are: – – – – – –

manufacturing year: 1999; registration number: CJ 47 ZEK; number of seats: 8 + 1; power source: Diesel; maximum mass: 2800 kg; power: 75 kW;

Comparative Study of Maintenance Vehicles …

223

– engine capacity: 2461 cm3; – total running: 575,366 km.

3.2

The Measurement of the Vibration

The measurement was carried out according to the following conditions: – measurements were performed on ITP stand (Periodic Technical Inspection); – vehicles had a normal operating condition; – measurement points for both vehicles were: (1) P1—screw the cover cleats (rocker arms); (2) P2—the bodywork under the windshield; (3) P3—front driver’s seat. – mounting accelerometers in the three measuring points was performed using special magnetic elements; – measurement axes were complied according to ISO 8002: 1994 standard. This standard presents analytical parameters and the presenting results method of vibration measurements for land vehicles.

4 Vibration Measurement Results Obtained for the Two Vehicles 4.1

Results Obtained for the First Vehicle

Vibration measurement mode, in the P1 first measurement point is illustrated in Fig. 4. According to Fig. 4, the measurement axes of vibrations have the following correspondence with accelerometer measuring channels: – Oz axis measurement for channel 1 is Ch1; – Oy axis measurement for channel 2 is Ch2; – Ox axis measurement for channel 3 is Ch3. Table 1 contains the effective values of vibration acceleration, type Peak, Peak-to-Peak (P-P), Maximum and RMS (Root Mean Square), obtained in P1 measuring point, determined experimentally on the 3 coordinate axes. The numerical values in Table 1 are presented by graphical form in Fig. 5. From Table 1 and Fig. 5, it is observed that the highest values of vibration acceleration are along the Ox horizontal direction.

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O.I. Vulcu and M. Arghir

Fig. 4 Location vibration measuring system for P1 measurement point

Table 1 Effective vibration accelerations obtained on the three channels, in P1 measurement point

Measurement canal

Acceleration (mm/s2) PEAK P-P

MAX

RMS

Ch1 Ch2 Ch3

98.288 103.872 106.537

20.701 20.630 20.989

19.838 19.792 20.091

184.289 196.562 198.609

Fig. 5 Chart of effective vibration acceleration measured on the three channels, from the P1 measuring point

For example, the maximum RMS acceleration along the Ox horizontal direction is 20.09 mm/s2. This is confirmed by the oscillogram given in Fig. 6. Vibration measurement mode, in the P2 measurement point is illustrated in Fig. 7. According to Fig. 7, the measurement axes of vibrations have the following correspondence with accelerometer measuring channels: – Oz axis measurement for channel 1 is Ch1; – Oy axis measurement for channel 2 is Ch2; – Ox axis measurement for channel 3 is Ch3.

Comparative Study of Maintenance Vehicles …

225

Fig. 6 Oscillogram of RMS acceleration from the P1 measuring point

Fig. 7 Location vibration measuring system for the P2 measurement point

Table 1 contains the effective values of vibration acceleration, type Peak, Peak-to-Peak (P-P), Maximum and RMS (Root Mean Square), obtained in P2 measuring point, determined experimentally on the three coordinate axes. The numerical values in Table 2 are presented in a graphical form in Fig. 8. From Table 2 and Fig. 7, it is observed that the highest values of vibration acceleration are along the Ox horizontal direction. For example, the maximum RMS acceleration along the Ox horizontal direction is 19.88 mm/s2. This is confirmed by the oscillogram given in Fig. 9.

226 Table 2 Effective vibration accelerations obtained on the three channels in the P2 measurement point

O.I. Vulcu and M. Arghir Measurement canal

Acceleration (mm/s2) PEAK P-P

MAX

RMS

Ch1 Ch2 Ch3

88.614 89.743 112.720

20.370 20.441 20.725

19.521 19.656 19.884

177.215 178.443 201.372

Fig. 8 Chart of effective vibration acceleration measured on the three channels from the P2 measuring point

Fig. 9 Oscillogram of RMS acceleration from the P2 measuring point

Comparative Study of Maintenance Vehicles …

227

Fig. 10 Location vibration measuring system for the P3 measurement point

Vibration measurement mode, in the P3 measurement point, is illustrated in Fig. 10. According to Fig. 10, the measurement axes of vibrations have the following correspondence with accelerometer measuring channels: – Ox axis measurement for channel 1 is Ch1; – Oy axis measurement for channel 2 is Ch2; – Oz axis measurement for channel 3 is Ch3. Table 3 contains the effective values of vibration acceleration, type Peak, Peak-to-Peak (P-P), Maximum and RMS (Root Mean Square), obtained in P3 measuring point, determined experimentally on the three coordinate axes. The numerical values in Table 3 are presented in graphical form in Fig. 11. From Table 3 and Fig. 11, it is observed that the highest values of vibration acceleration are along the Oz vertical direction. For example, the maximum RMS acceleration along the Oz vertical direction is 641.95 mm/s2. This is confirmed by the oscillogram given in Fig. 12. Analyzing the results of vibration obtained in the three measuring points of the first vehicle, it follows that the acceleration is greatest at the P3 point, i.e., the front seat, along the vertical direction. Also acceleration values obtained for the first two measurement points are very close.

Table 3 Effective vibration accelerations obtained on the three channels in the P3 measurement point

Measurement canal

Acceleration (mm/s2) PEAK P-P

MAX

RMS

Ch1 Ch2 Ch3

977.237 869.961 1144.195

447.198 377.138 652.379

437.019 366.438 641.948

1634.933 1663.413 2282.969

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O.I. Vulcu and M. Arghir

Fig. 11 Chart of effective vibration acceleration measured on the three channels from the P3 measuring point

Fig. 12 Oscillogram of RMS acceleration from the P3 measuring point

4.2

Results Obtained for the Second Vehicle

Vibration measurement mode, in the first measurement point P1, is illustrated in Fig. 13. According to Fig. 13, the measurement axes of vibrations have the following correspondence with accelerometer measuring channels:

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229

Fig. 13 Location vibration measuring system for the P1 measurement point

– Oz axis measurement for channel 1 is Ch1; – Oy axis measurement for channel 2 is Ch2; – Ox axis measurement for channel 3 is Ch3. Table 4 contains the effective values of vibration acceleration, type Peak, Peak-to-Peak (P-P), Maximum and RMS (Root Mean Square), obtained in P1 measuring point, determined experimentally on the three coordinate axes. The numerical values in Table 4 are presented in graphical form in Fig. 14. From Table 4 and Fig. 15, it is observed that the highest values of Peak-to-Peak and Max vibration accelerations are along the Oy transversal direction, 209.4 and 19.8 mm/s2, respectively. RMS acceleration is higher along the Ox horizontal direction, valued at 18.5 mm/s2. This is confirmed by the oscillogram given in Fig. 15. Vibration measurement mode, in the second measurement point is illustrated in Fig. 16. According to Fig. 16, the measurement axes of vibrations have the following correspondence with accelerometer measuring channels: – Ox axis measurement for channel 1 is Ch1; – Oy axis measurement for channel 2 is Ch2; – Oz axis measurement for channel 3 is Ch3.

Table 4 Effective vibration accelerations obtained on the three channels in the P1 measurement point

Measurement canal

Acceleration (mm/s2) PEAK P-P

MAX

RMS

Ch1 Ch2 Ch3

104.954 104.954 103.633

19.770 19.792 20.022

18.450 18.450 18.535

192.309 209.411 190.766

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O.I. Vulcu and M. Arghir

Fig. 14 Chart of effective vibration acceleration from the P1 measuring point

Fig. 15 Oscillogram of RMS acceleration from the P1 measuring point

Table 5 contains the effective values of vibration acceleration, type Peak, Peak-to-Peak (P-P), Maximum and RMS (Root Mean Square), obtained in P2 measuring point, determined experimentally on the three coordinate axes. The numerical values in Table 5 are presented in a graphical form in Fig. 17. From Table 5 and Fig. 17, it is observed that the highest values of vibration acceleration are along the Oz vertical direction. For example, the maximum RMS

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231

Fig. 16 Location vibration measuring system for the P2 measurement point

Table 5 Effective vibration accelerations obtained on the three channels in the P2 measurement point

Measurement canal

Acceleration (mm/s2) PEAK P-P MAX

RMS

Ch1 Ch2 Ch3

99.655 96.939 96.383

16.943 16.866 17.080

181.134 179.887 184.289

18.030 18.009 18.281

Fig. 17 Chart of effective vibration acceleration measured in the P2 measuring point

acceleration along the Oz vertical direction is 17 mm/s2. This is confirmed by the oscillogram given in Fig. 18. Vibration measurement mode, in P3 measurement point is illustrated in Fig. 19.

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Fig. 18 Oscillogram of RMS acceleration from the P2 measuring point Fig. 19 Location vibration measuring system for the P3 measurement point

According to Fig. 19, the measurement axes of vibrations have the following correspondence with accelerometer measuring channels: – Ox axis measurement for channel 1 is Ch1; – Oy axis measurement for channel 2 is Ch2; – Oz axis measurement for channel 3 is Ch3. Table 6 contains the effective values of vibration acceleration, type Peak, Peak-to-Peak (P-P), Maximum and RMS (Root Mean Square), obtained in P3 measuring point, determined experimentally on the 3 coordinate axes.

Comparative Study of Maintenance Vehicles … Table 6 Effective vibration accelerations obtained on the three channels in the P3 measurement point

233

Measurement canal

Acceleration (mm/s2) PEAK P-P MAX

RMS

Ch1 Ch2 Ch3

710.395 732.825 573.456

244.343 291.407 188.582

1345.860 1380.384 1026.833

257.040 318.787 197.015

Fig. 20 Chart of effective vibration acceleration measured in the P3 measuring point

The numerical values in Table 6 are presented in graphical form in Fig. 20. From Table 6 and Fig. 20, it is observed that the highest values of vibration acceleration are along the Oy transversal direct. For example, the maximum RMS acceleration along the Oy transversal direction is 291.4 mm/s2. This is confirmed by the oscillogram given in Fig. 21. Analyzing the results of vibration obtained from the three measuring points of the second vehicle, it follows that the acceleration is highest at the P3 point, i.e., the front seat, along the Oy transversal direction. Also acceleration values obtained for the first two measurement points are very close.

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Fig. 21 Oscillogram of RMS acceleration from the P3 measuring point

5 Maintenance Operations History of the Two Vehicles Knowing the maintenance operations history, it is necessary to make a correct analysis of the results as vibration measurements in order to make a diagnosis by comparing the values obtained. To prevent technical failures and restoring regular working capacity of vehicles is performed a number of periodical works with preventive or corrective character, by various complexity. Routine maintenance is characterized by typology, periodicity, and planning. Preventative car maintenance and routine inspections can go a long way when it comes to keeping the car in peak condition. Following the manufacturer’s car maintenance schedule will save time and money. When it adheres to vehicle maintenance guidelines, it is necessary to take action against unwelcomed damage and future costly repairs. Periodicity of maintenance work is expressed in traveled units, namely equivalent kilometers and it is established by normative function of vehicle and maintenance type. Repairs have different degrees of complexity. These are the following: (a) current repair: technical corrective interventions and troubleshooting applied during operation; (b) average repairs: technical corrective interventions consisting of partial disassembly, repair, or replacement of aggregates and other review;

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(c) major repairs: complex technical interventions that involve complete disassembly of motor vehicles and reconditioning of all components so as to achieve initial operating parameters (parameters set in the factory). Table 7 contains the history of the first vehicle maintenance operations for the last 7 years. Table 8 contains the history of the first vehicle maintenance operations for the last 3 years. From Tables 7 and 8 are observed that in both vehicles were respected periodic maintenance periods and current repairs and media interventions were performed. Table 7 The first vehicle maintenance operations Type of intervention

Date

Indicated km

Replace distribution system Change engine oil and filter Change clutch kit: disc, pressure bearing, pressure plate Change rotule (upper and lower) Change alternator belt Change gas oil filter Change return hose (injectors) Change engine oil and filter Change gearbox oil Change right steering power link and bellows Change engine oil and filter Change pollen filter Change brake pads, front Change distribution system: rollers, water pump, belts, valves, cleats Change engine oil and filter Change alternator bearings Change brake pads, rear left Change air filter Change engine oil and filter Change two tires, front Change 4 rotule (2 inferior, 2 superior), head straight bar 4 bushings steering box, torsion bar bushings. Change power steering oil Setting direction Change clutch kit: disc, pressure bearing, pressure plate, flywheel Change engine oil and filter Change front brake pads Change engine oil and filter

25.07.2007 29.08.2007 01.02.2008 01.02.2008 01.02.2008 06.04.2008 06.04.2008 11.04.2008 11.04.2008 17.05.2008 09.09.2008 09.09.2008 12.09.2008 04.02.2009

158,000 160,000 166,820 166,820 166,820 175,000 175,000 175,000 175,000 178,300 196,399 196,399 197,000 205,000

06.07.2009 06.07.2009 07.07.2009 20.07.2009 29.07.2009 29.07.2009 12.08.2009

212,331 212,331 225,000 225,250 226,770 226,770 229,900

12.08.2009 12.08.2009 10.09.2009 28.09.2009 06.11.2009 22.12.2009

229,900 229,900 236,400 240,629 244,000 253,240 (continued)

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Table 7 (continued) Type of intervention

Date

Indicated km

Change gas oil filter Change airflow Change air filter Replace distribution system Change engine oil and filter Replace belts, accessories Change tensioner belt accessories Change pollen filter Change front tire Change engine oil and filter Change engine oil and filter Change brake pads, front and rear Repair steering box Change engine oil and filter, air filter Change front tire Change engine oil and filter Change pollen and airs filters, distribution system, bellows, belt, drive shaft Change telescopes Change engine oil and filter, air filter, gas oil filter Change front brake pads and pollen filter Change engine oil and filter and air filter Change brake pads and bearing, rear Change vacuum pump, tires, gas oil filter, stabilizer bar bushings, anti-roll connecting rods Change engine oil and filter Change engine oil and filter Change distribution system, water pump, compressor bearing Change rear brake pads Change engine oil and filter and air filter Change pivots, bushings, gearbox support Change engine oil and filter and air filter Change alternator bearings, brushes, coil collectors Change engine oil and oil filter, air filter, gas oil filter, brake sleeves Change engine oil and oil filter, air filter, gas oil filter, brake sleeves

22.12.2009 22.12.2009 20.03.2010 22.03.2010 15.04.2010 26.04.2010 30.05.2010 30.05.2010 21.06.2010 25.06.2010 20.12.2010 23.12.2010 20.01.2011 22.03.2011 01.06.2011 09.07.2011 25.07.2011

253,240 253,240 262,580 263,000 267,020 271,000 273,000 273,000 276,214 279,300 293,000 296,700 300,000 302,500 311,000 317,800 319,450

21.09.2011 31.10.2011 10.03.2012 05.04.2012 06.06.2012 12.11.2012

325,500 333,626 344,825 345,500 35,200 366,295

20.12.2012 22.06.2013 26.06.2013 10.10.2013 09.11.2013 04.12.2013 03.03.2014 28.05.2014 28.05.2014

371,000 382,359 382,441 392,000 393,434 395,000 404,146 414,339 414,339

27.08.2014

426,000

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Table 8 The second vehicle maintenance operations Type of intervention

Date

Indicated km

Change engine oil and filter Change clutch kit: disc, pressure bearing, pressure plate Change engine oil and filter Change engine oil and filter Change engine Change engine oil and oil filter, air filter, gas oil filter Change engine oil and filter Change tire Change rear and front brake pads Change engine oil and filter Change pollen filter, air filter Replace distribution system Change engine oil and filter, air filter Change clutch kit: disc, pressure bearing, pressure plate Change engine oil and oil filter, air filter Change rear and front brake pads Change engine oil and filter, air filter Change pollen filter, air distribution system, bellows, drive shaft, belt Change engine oil and filter, air filter, gas oil filter Replace distribution system Change rear and front brake pads Change engine oil and filter, air filter Change pollen filter, air filter, distribution system Change engine oil and filter Change clutch kit: disc, pressure bearing, pressure plate Change engine oil and filter Change rear and front brake pads Change tire Change engine oil and filter, air filter, gas oil filter

22.06.2012 30.07.2012 01.09.2012 18.09.2012 14.12.2012 14.12.2012 18.02.2013 03.03.2013 09.05.2013 17.07.2013 27.08.2013 27.08.2013 12.09.2013 12.09.2013 28.11.2013 28.11.2013 19.12.2013 20.01.2014

402,300 407,700 425,000 429,500 445,000 445,000 459,000 461,000 476,000 489,000 405,000 405,000 416,900 416,900 430,000 430,000 442,000 452,300

07.03.2014 20.04.2014 05.05.2014 02.06.2014 16.07.2014 01.08.2014 01.08.2014 05.11.2014 23.10.2014 23.10.2014 12.12.2014

476,000 481,200 492,000 508,700 522,000 535,000 535,000 549,300 551,100 551,100 562,800

6 Comparative Analysis of Results Comparing the results obtained by measuring vibration in three points, for two vehicles of the same brand but different years manufacturing can be observed the following: – the first car is newer with 3 years to the second; – the second car has a total running of more than 146,378 km than the first vehicle;

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– the vibration values measured for the first vehicle are higher although it is newer than the second. This can be explained by the fact that the engine of the second car was changed in the last period of operation. – the acceleration values obtained in the front seat, i.e., P3 measuring point, where the first vehicle is double the other case. Distribution belts and water pump were replaced following the analysis of the data obtained and the specialist recommendation for the first vehicle.

7 Conclusions After the comparative study of maintenance by using vibration measurements, the following can be concluded: – the vibration behavior of vehicles differ according to the measuring point; – the vibratory behavior of the vehicle depends on how their maintenance and repairs carried out especially during the operation; – the maximum acceleration values are mainly along vertical direction, i.e., along the piston engine movement direction; – because the engine of the second vehicle was replaced, it explains that the first vibrating higher. At the same time, we can say that the first motor vehicle engine shows superior vibration in the second case.

References 1. Booth, E., Kantros, E., Pyle, B., Linders, W.: Automobile Vibration Analysis, MAE 3600 System Dynamics Project Fall 2009. University of Missouri-Columbia (2009) 2. Boham, T.D.: Vehicle Dynamics Engine (VDE) (2006). www.bandedsoftware.com 3. Giraud, L.: La maintenance. État de la connaissance et étude exploratoire, Publication IRSST— Canada (2008). www.irsst.qc.ca/files/documents/PubIRSST/R-578.pdf 4. Rill, G.: Vehicle dynamics. FH Regensburg, University of Applied Sciences, Germania (2004). http://homepages.fh-regenburg.de 5. http://www.sensidyne.com/Support%20Library/sound-and-vibration/Sensidyne_Svantek-SVAN958.pdf

Correction of the Influence of not Ideal Geometric Profile on the Constant of Primary Cell Aleksander A. Mikhal, Zygmunt L. Warsza and Vladimir G. Gavrylkin

Abstract The principle of operation and metrological model of the Ukrainian primary standard of electrolytic conductivity (EC) is presented. The equations for calculating the cell constant and the budget of unknown errors for estimation of the uncertainty B-type are given. Strategies: how to minimize components of this uncertainty are proposed and obtained results, verified by Key Comparisons, are given. Keywords Conductivity


Primary cell
Geometric errors
Uncertainty

1 Introduction The electrical conductivity of solutions is measured in chemistry, biology, medicine, environment and sea monitoring, electrotechnology industry, and many other fields. Reliable and comparable results of these measurements are obtained by creation of national metrological system with the traceability, calibration, and international comparison regulations. Several countries, including Ukraine, have established national standards of the electrolytic conductivity (EC). In the world practice different ways to implement this standard are used, however, the principle A.A. Mikhal (&) Institute of Electrodynamics, National Academy of Science of Ukraine (NANU), Peremogy av. 56, 03680 Kiev, Ukraine e-mail: [email protected] Z.L. Warsza Industrial Research Institute of Automation and Measurements PIAP, Al. Jerozolimskie 202, 02-486 Warsaw, Poland e-mail: [email protected] V.G. Gavrylkin Ukrmetrteststandard, Metrologichna Str. 4, 03143 Kiev, Ukraine e-mail: [email protected] © Springer International Publishing Switzerland 2016 J. Awrejcewicz et al. (eds.), Mechatronics: Ideas, Challenges, Solutions and Applications, Advances in Intelligent Systems and Computing 414, DOI 10.1007/978-3-319-26886-6_15

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of its operation is almost the same—the “absolute,” i.e., direct method of reproduction of a unit of physical quantity [1–3]. This “absolute” method is based on the measurement of the resistance of liquid column in the conductivity cell and on the calculation of the EC from the known length and cross-sectional area of this column. The EC primary standard of Ukraine as basic components includes the four-electrode cell with calculated constant K, special high precision conductivity AC bridge, thermostat with temperature control at 25 °C and precision digital temperature meter. Value k of EC is determined as k ¼ GK ð1 þ a t25 Þ

ð1Þ

where G is the conductance of liquid column; K is the cell constant calculated from its geometric dimensions; α is the temperature coefficient for conductivity of the solution; t25 is the temperature deviation from 25 °C. On the example of this EC standard the method of estimation and minimizing the uncertainty of type B is presented.

2 Measurement System for Reproduction of the EC Unit The instrumental part of EC standard is an information measuring system and it consists of several subsystems: SSR EC—subsystem of EC reproduction, SST EC —subsystem of EC transmission, SST MC—subsystem of thermostabilization, subsystem of the preparation of solutions, subsystem of control and processing of the results of measurement. The main element of the EC standard is the subsystem SSR EC. Their simplified functional diagram is shown in Fig. 1. The main element of the conductivity sensor is the tube with internal diameter D, which is filled with electrolyte solution. Typically, this is a solution of potassium chloride. The tube is used to fix the geometry of the liquid conductor and it consists of three parts. The central part of the tube 1 has length L and two side portions 2 have the same length l. The ends of the central portion of the tube 1 are coated with circular potential electrodes 4. Their width corresponds to the tube wall thickness. At the edges of the tube two discs 3 are fixed. Inner surface of the discs is coated with metallic film 5 and are current electrodes. Discs 3 have central holes 6 of the diameter d, which serve for filling liquid. Inner disc surface has the form of cone with an angle α. Such configuration is intended to facilitate the removal of air bubbles when filling cell with the liquid. The tube and the discs are made of quartz glass which has good insulating properties, temporal stability, and minimum coefficient of thermal expansion. The cell electrodes are made from platinum which has a minimum polarization effect. These electrodes, in its four points a, b, c and d, are connected to the AC bridge (left side of Fig. 1), which measures the

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Fig. 1 Sketch of the primary conductivity cell and its connections

conductance G = Ucd/Iab of liquid column between a and b electrodes. This automatic high precision AC bridge is not a standard one, but it is designed specifically for the EC standard. The admittance components of the parallel two-element equivalent circuit of the conductivity cell are measured by this bridge. The voltage comparison circuit is also used in it. That allows to eliminate the influence of impedances which occur on the border of electrolyte with current and potential electrodes of the conductivity cell.

3 Uncertainty of Conductivity and Budget of Systematic Errors One of the major metrological parameters of this standard is the uncertainty uk of the EC unit reproduction (here referred only as type B standard uncertainty). Upon absence of correlation between the parameters of the Eq. (1), the combined standard uncertainty uk is calculated in accordance with GUM: s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2  2  2 @k @k @k uG þ uK þ ut uk ¼ @G @K @t

ð2Þ

where uG, ut are standard uncertainties of measurement the conductance G and temperature t correspondingly and uK uncertainty of the constant K calculation. Uncertainties uG, uK, and ut will depend on the errors from the sets of various  factors x 2 xi ; xj ; xn . The major factors x are metrological characteristics of measuring devices and instruments, errors of calibration standards, methodological errors of calculation models, manufacturing accuracy of calculated elements, environmental conditions, parameters of power supply, etc. The usage of relative values on the stage of preliminary evaluation gives us the possibility to compare contribution of each

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error component and to estimate a reasonable amount of errors upon budget formation. Thus, to estimate the relative uncertainty uk ¼ uk =k from the budget of the limited relative errors diG ¼ DGi =G of conductance G measurement, limited relative errors djK ¼ DKi =K of the constant K calculations and dnt of the maximum temperature increment Dta, we obtain the following formula: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N H M  X uX 2 X uk ¼ t ðAnt dnt Þ2 AjK djK þ ðAiG diG Þ2 þ j¼1

i¼1

ð3Þ

n¼1

where the influence coefficients of limited errors are δiG, δjK, δnt CiG

@Gðxi Þ  AiG ; @xi

CjK

@Kðxj Þ  AjK ; @xj

Cnt

@tðxn Þ  Ant @xn

ð4Þ

Coefficients CiG, CjK, Cnt depend on the probability distributions of the relevant errors. Type B uncertainty of the measurement system including several instruments is almost entirely dependent on the estimation of unknown values of systematic errors. Therefore, a complete set or budget of systematic errors of the EC standard is basic to assess the quality and adequacy of the mathematical model describing the accuracy of any standard. In Eq. (1), two parameters only (conductance G and temperature increment nt) are measured directly with instruments. In this case the main methods of reducing uncertainty are well-known techniques of calibration and temperature stabilization of these instruments. The third parameter (cell conductivity constant K) is calculated. Therefore, the estimation of its uncertainty needs the increased attention. The budget (“tree”) of systematic errors under calculation constant of the conductivity cell is shown in Fig. 2. The cell constant is determined by calculating the ratio of the length of the tube 1 to the cross-sectional area. However, this definition is true for an idealized object of measurements with uniform distribution of current flow lines. Distortion of such lines will be due to the presence of air holes in the solution filling; the form of current electrodes and the presence of potential electrodes; nonideal profile of the inner tube 1 in Fig. 1. Therefore, the calculations constant K have errors. The error budget for the constant calculation of the cell, shown in Fig. 2, can be written as a set of uncorrection systematic relative errors: uK 2 fdSt ; dCal ; dGeom ðdTec ; dPE Þg

ð5Þ

where δSt is an error due to the accuracy of measurement standards and measuring instruments to determine the length and diameter of the tube; δCal is an error due to the deviation of the calculation model for the cell constant in real conditions relative to the idealized model; δGeom is an error in assessment of geometrical dimensions. Each argument of set (5) has several components. Let us consider them in detail.

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Fig. 2 Tree (budget) of systematic errors δjK

Minimizing the error δSt is limited by the level of metrological assurance for measurements of tube length and diameter. It is defined by the metrological parameters of the standards and instruments for length measurement. An error δCal has two components: an error δAC due to alternating current measurement and an error δCH due to discontinuity of an electric field in the cell because of its finite dimensions and design features. Analysis of all δCal components is described in detail in [4–6]. Geometric error δGeom also has two components: δTec is an error due to manufacturing technology for the tube sections and their assemblage; δPE is an error due to the presence of potential electrodes. The latter component of the error depends on the finite thickness of potential electrodes and on changing position of a singular point of potential electrodes upon assemblage. This component is related to the calculation of the electric field inside the cell. It will be considered in other papers. In this paper, we examine the component of an error δTec. This error is due to the deviation of actual profile of the inner surface of the tube 1 (Fig. 1) from the ideal profile of the tube. The latter one is presented as rectangle along the longitudinal section and as circle in cross section. It should be mentioned that the cost of tube production from a monolithic quartz crystal is extremely high. As a rule, tubes are manufactured from workpieces (preform) which undergo precision machining. If precision machining of the inner surface is too deep, the mechanical resistance of the tube will reduce significantly. Tubes of less than 1 mm in thickness will crack (fracture) under elastic forces (adhesive polymerization, temperature differences). Therefore, grinding of the workpiece inner profile should be of minimum depth. On the other side, the workpiece inner surface can have wedge-like cracks which are parallel to the axis of the workpiece. These cracks are due to manufacturing techniques of workpiece production and depend on the quality of nozzles through which the workpiece is pulled itself. Therefore, due to the lack of deep machining of tubes, we can observe

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deviation from circle in cross section along the entire profile. The second reason of nonideal profile may be the precession of the grinding tool. During processing, quality control of the tube is practically impossible. After final grinding, the tube profile may differ from the ideal rectangle. As a result there is a systematic error that cannot be completely excluded. Let us consider in detail this component of error.

4 Manufacturing Errors To determine the actual profile of the tube, its diameter and length should be measured according to the following algorithm. Uniformly by circle, p measurements of tube length are made in different directions L. Conventionally, uniformly along the length, the tube is divided into m sections. To define the diameter, its n measurements are made in the cross section of each part of the tube in different directions. As a result, we obtain n × m measurements of the tube diameter and p values of the tube length. The constant can be determined from the results of measurements through average values of diameter Dav and tube length Lav. K¼

4Lav pD2av

ð6Þ

Modern technologies for processing of quartz glass are those that it is much easier to manufacture a tube with stable length value than a tube with stable internal diameter. From the experimental data we observe distortions of the internal profile of two types. The first one is a deviation of the tube profile from rectangle along the longitudinal section due to precession of the grinding tool. The second one is a deviation of the tube profile from circle in cross section due to the presence of wedge-like cracks on the inner surface of work pieces. The geometric dimensions of the actually manufactured tube can be measured much more accurately than the error of profile. Measurement of the parameters is generated with a device with LSB 0.1 μm. A random component of the device has not exceeded 0.5 LSB, while deviations of the actual profile from the ideal one have exceeded LSB of the device tenfold. Therefore, the following expression can be taken as a metrological model for the constant calculation: K ¼ K0 ð1 þ dK Þ;

rK ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2r2D þ r2L

ð7a; bÞ

where K0 is the true value of the constant which is determined by the actual profile of the tube inner surface; δK is a systematic relative error of the constant calculation; rK , rD , and rL are standard deviations of the mean cell constant, diameter, and length of the tube correspondingly. Then, an error due to manufacturing δTec has two components: systematic δK and random σK. Then the mean value of tube

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diameter has the standard deviation (SD). The diameter and its SD for each ith section of the tube are determined from the expressions: Pm Pn Di;av j¼1 Dij i¼1 ¼ Dav ¼ m
n m vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n  X u 1 2 riD ¼ t Dij Di;av nðn 1Þ j Pm

i¼1

ð8Þ

ð9Þ

where Di,av—mean diameter in the ith section of the tube, Dij is jth mean diameter in the ith section of the tube. The value SD from m section can be expressed as: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m X 1 r2 rD ¼ mðm 1Þ i iD

4.1

ð10Þ

Error in the Longitudinal Section

The measuring results for the mean diameter of one of the sections of the tubes upon n = 8 and m = 10 are shown in Fig. 3. Represented data indicate that the average diameters in Sects. 1 and 6 differ almost by 20 μm. In general, the profile of the tube internal section can be expressed through arbitrary function D(x). The measuring results for average diameters along the length of the tube (Fig. 3) show that this dependence has clearly determinate character. The discrete nature of the data allows us to use linear interpolation for the function D(x). The results are shown in the following formula: 4 K¼ p

ZL 0

Fig. 3 Profile along the axis of the tube

m 4X ¼ DðxÞ2 p i¼0

dx

ZDXi 0

dx

ð11Þ

ðax þ bÞ2

10.175

Di,av mm

10.17 10.165 10.16 10.155 10.15 1

2

3

4

5

6

7

section number, m

8

9

10

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Fig. 4 Influence of linear interpolation on the level of SDM (σiD)

where a and b are linear interpolation coefficients; ΔXi is the length of the area between ith and i + 1 section. Polynomial coefficients are expressible as: a¼

Di þ 1 Di ; DXi

b ¼ Di

ð12a; bÞ

After simple transformations, the expression for calculating the constant with the proposed correction takes the form: K¼

4X DXi p Di;av Di þ 1;av

ð13Þ

If we use procedure for the classical averaging of the diameter measuring results, Eqs. (8–10), we receive significant rises in the standard deviation. Let us show on one figure the graphs for SDM of diameter measuring results without deterministic component and with deterministic component by using linear interpolation (Fig. 4). As it can be seen from Fig. 4, SDM of the diameter measuring results, taking into account deterministic component, is close to almost one value and has a very small scatter of results compared with the case where the deterministic component is ignored and the average diameter value is calculated according to Eq. (8). As a result of correction, change of SDM along the cross section is reduced by 10–15 times. SDM of diameter with correction, calculated according to formula (10) is less than 0.0004 mm. This parameter without correction is 3 times larger. For the Eq. (13), we obtain an error reduction by two times. It should be noted that such correction method shifts the average value of the diameter. Thus, the constants calculated by the formulas (6) and (13) for the tube 1 in Fig. 1, differ by 0.027 %. This is the rate by which systematic relative errors δK (7a) differ when calculating the cell constant with and without correction.

Correction of the Influence …

4.2

247

Error in the Cross Section

Let us consider another tube for which the values of mean radius in each of the sections are grouped along the virtually horizontal line. However, in each individual section the surface profile differs from the circle. Example of the function for the deviation from the mean Diav (represented on Fig. 5 by the circle 0.5 Dav = 4.569 mm) in four of the sections with number m = 1, m = 3, m = 6, and m = 9 is shown in Fig. 5a–d. In all ten sections of m = (1–10) we observe triangular runouts along the lines 3– 11 and 6–14 (see Fig. 5). Such character of profile distortions allows using a method of the equivalent triangles. This method involves assessment of the effective area Sief of the tube section and subsequent diameter corrections. The algorithm for calculation is to replace diameter values in Sects. 3 and 6 with the values of

Fig. 5 Real profile—broken line (blue) across the axis of the tube for four sections (m = 1, 3, 6, 9) and its equivalent polygon (red) of the average circle diameter 0.5Dav = 4.569 mm

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mean diameter Dav, then to use standard formula for calculation of the basic mean diameter Dbias and basic area of the tube section Sbias. . Sbias ¼ pðDbias Þ2 4

ð14Þ

Next, we calculate the correction value in each section separately. It is represented as areas of triangles: ð15Þ

Si ¼ ci hi =2

where ci is the base of assumed triangle in direction 3, 11 or 6, 14 (Fig. 5); and hi is the height of assumed triangle in direction 3, 11 or 6, 14 (Fig. 5). We take into account the influence of the deterministic component by forming the effective area of each section. It is expressed as: Sief ¼ Sbicr þ 2

X

Si ¼ Sbicr þ 2

X

ð16Þ

c i hi

i¼3;6

i¼3;6

According to the following formula, we calculate the corrected Dicor which is put in the Eq. (13) instead of Diav. Dicor ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4Sief =p

ð17Þ

Deviation, mm

The difference between SDM values of the measured result of diameter Diav before correction and of the mean diameter Dicor after correction is shown in Fig. 6. As it can be seen from Fig. 6 that SDM with the correction of deterministic component is by 2.5–3 times less than one without correction. The use of an algorithm of effective areas shifts the mean diameter value. The constants calculated by formulae (6, 8) and (6, 17) differ by 0.015 %. Just as is in the previous case, this value represents the difference of systematic errors (7a) in calculations of the cell constant K.

0.0005 0.0004 0.0003 0.0002 0.0001 0

D iav D icor 1

2

3

4

5

6

7

8

9

section number m Fig. 6 SDM (σiD) without correction Diav and with correction Dicor

10

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249

5 Experimental Results Both above methods were used to calculate the corrections to the cell constant K [7, 8]. For the primary EC standard of Ukraine, the several measurement cells were made. The two types of EC cell are shown in Figs. 7 and 8. Correctness, sufficiency, and adequacy of the selected models of correction of the cell nonideal profile are confirmed by international comparisons (P22, P47, K36), which involved the primary standard of Ukraine (laboratory UkrCSM). The best results were obtained in international comparisons CCQM-K36 [9].

Fig. 7 Construction of the EC cell with additional protective tubes

Fig. 8 The design of the measuring cell without protective tubes

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Table 1 Final values of parameters of the Ukrainian primary EC standard at the value 0, 5 S/m Source of uncertainty

Sensitivity coefficient, (3)

Standard uncertainty

Contribution to standard uncertainty

Parameter Conductivity G Constant cell K Temperature t,

@k=@i 297 1/m 1.7E−3 S 1.01E−2 S/m °C

Ui 2.2E−7 S 4.0E−2 1/m 0.005 °C

ui(k) 6.5E−5 6.8E−5 5.1E−5

Errors described in Sects. 4.1 and 4.2 are used for corrections systematic errors. After accounting these and some other corrections, obtained are parameter values of primary Ukrainian EC standard as listed in Table 1. Hence, the value of combined uncertainty uk from Eq. (2) is equal to qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uk ¼ ð6:5E 5Þ2 þ ð6:8E 5Þ2 þ ð5:1E 5Þ2  1:1E 4 This result is put as final in the statement of international comparisons of CCQM-K36 [9]. According to the results of comparisons the CMC (calibration and measurement capabilities) of Ukraine in the field of EC measurements are added to the BIPM database.

6 Conclusions Described methods for the cell constant correction (method of linear interpolation and method of equivalent triangles) allowed us to solve two problems. First, the value obtained for lab. UkrCSM klab, practically coincides with the value kref [9]. This is the value of electrolytic conductivity, which reproduced the leading countries of the world. Results achieved by minimizing systematic error (Eq. 7a). Second, by minimizing the random component of the error (Eqs. 7b, 10), it was obtained minimum value of uncertainty u(klab).

References 1. Shreiner, R.H., Pratt, K.W.: Standard Reference Materials: Primary Standards and Standard Reference Materials for Electrolytic Conductivity. NIST Special Publication, pp. 260–142, (2004) 2. Mariassy, M., Pratt, K.W., Spitzer, P.: Major applications of electro-chemical techniques at National Metrology Institutes. Metrologia 46, 199–213 (2009) 3. Brinkmann, F., et al.: Primary methods for the measurement of electrolytic conductivity. Accred. Qual. Assur. 346–353 (2003) doi:10.1007/s00769-003-0645-5

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4. Hlukhenky, A.I., Miкhal, A.A.: Analysis of circular conductor impedance component within AC measurement. Tehnichna Elektrodynamika 1, 15–22 (2010, in Russian). Available online at http://www.techned.org.ua 5. Hlukhenky, A.I., Miкhal, A.A.: Error estimation of standard conductometric cell conditional on non-equipotentiality of electrode fase. Tehnichna Elektrodynamika 1, 76-82 (2011, in Russian). Available online at http://www.techned.org.ua 6. Gavrylkin, V.G., Glukhenkiy, A.I., Miкhal, A.A.: An analysis of the error when determining the constant of the primary standard conductometric cell. Meas. Tech. 56(8), 935–941 (2013) 7. Mikhal A.A., Warsza Z.L.: Influence of geometric uncertainties on the accuracy of calculated constant of the primary conductivity cell. In: CD Proceedings of 11th TC 24 IMEKO International Symposium ISMQC on Measurement and Quality Control, p. 87. Cracow-Kielce, Poland (2013) 8. Mikhal, A.A., Warsza, Z.L.: Geometric part of uncertainties in the calculation constant of the primary four electrode conductivity cell. ACTA IMEKO 4(2), 18–21 (2015) 9. Jensen, H.D.: Final report of Key Comparison CCQM-K36. Aug 15 2006, available at http:// kcdb.bipm.org/AppendixB/appbresults/ccqm-k36/ccqm-k36_final_report.pdf

Modeling and Analysis of the Hydraulic Servo Drive System Piotr Woś and Ryszard Dindorf

Abstract In the hydraulic servo drive appear structural nonlinearities which cause that designing nonlinear control of the position and power system is hampered. In the article a mathematical model of the servo drive hydraulic control was described. It is useful for the synthesis algorithms in the simulation model. The calculation diagram of the hydraulic servo drive model consisting of the double-acting cylinder with one-sided piston rod and directional control valve was presented. There were presented characteristics of: displacement, velocity, acceleration and pressures as well as the displacement of spool valve at mass load. An algorithm of control the nonlinear object was adapted by using the linearization method of the model process. Simulation examinations will serve for developing the control algorithm which will enable the compensation influences of disruptions such as: friction and changeable load powers mass. Keywords Hydraulic servo system feedback linearization


Nonlinear dynamic model
Input–output

1 Introduction Control of the hydraulic servo drive has already been an object of examinations in different centers of education and research for many years [1, 2]. Nonlinear dynamic characteristics of the hydraulic actuator as well as servo valve are caused by large inertia of the movement, friction forces, deformations and springiness of mechanical elements, compressibility of working fluid, and characteristic flows P. Woś (&)
R. Dindorf Faculty of Mechatronics and Machine Design, Kielce University of Technology, Kielce, Poland e-mail: [email protected] R. Dindorf e-mail: [email protected] © Springer International Publishing Switzerland 2016 J. Awrejcewicz et al. (eds.), Mechatronics: Ideas, Challenges, Solutions and Applications, Advances in Intelligent Systems and Computing 414, DOI 10.1007/978-3-319-26886-6_16

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[3, 4]. Changes in dynamic parameters of hydraulic servo drive are associated with load and velocity of the movement, maladjustment of the control structure, and influence of many other factors associated with characteristics of working fluid and exploitation parameters. They all have a significant influence on reducing the resistance of control system. Frequent maladjustment of the control structure results from large forces or load moments of the servo drive hydraulic system. Moreover, requirements concerning high accuracy of control positional and velocity in wide scope cannot be fulfilled, because these conditions are often changeable in time depending on the external load. Turbulent character of the fluid flows in valves and appearance of structural nonlinearities, such as saturation pressure or rate of fluid flow, zone of overlap caused by positive windows overlap of the control slider as well as hysteresis caused by magnetizing the armature of control slider. They all cause that the process of physical phenomena in unknown states in all hydraulic systems can be described only in the nonlinear way. Model of the hydraulic servo drive should include dynamic characteristics of the hydraulic actuator or hydraulic engine, flow characteristics of the servo valve or proportional valve, characteristics of electromechanical converters, compressibility (capacity) hydraulic in distinguished servo drive areas, friction forces appearing in elements of the system, efficiency of hydraulic elements, and other factors like the accuracy of carrying slide steam, accuracy of the filtration as well as characteristics of the working fluid [5]. We should pay attention to nonlinear static characteristics of the control valve. Proportional control valves can have positive or negative overlap [6]. In amplifiers, valve sliders are applicable with the value of overlap to 5 % nominal jump, which takes about 0.5 mm up to 1.0 mm. Edges of the spool valve and cornet cooperating with it are carried out with the lower tolerance from ±2.5 μm [6, 7]. It allows for keeping the nonlinear scope in the vicinity of zero for about ±3 % of jump. In this range, the movement of slider may change the rate of strengthening the valve to 200 % of its value appearing at normal opening the valve. Such large changes of control parameters may lead to the unstable work of servo drive, e.g., during positioning of the hydraulic actuator or hydraulic engine. Slight leakages that appear in the valve are caused by inaccuracies of making the spool and valve body, which corresponds to the negative overlap. Such a situation also appears, when the control system is unable to hold a slider in the position corresponding to turning off the hydraulic actuator from the power supply. Also, the work instability can be caused by pollutants, which block the flow of the valve. It causes the delays of valve action as at positive overlap. Disadvantageous feature is also appearing of losses caused by leakages, and they cause the movement of the piston at the zero control signal. The value of control signal must then change even in the steady state, at the lack of spool valve movement. Also, undervalued cause of the nonlinearity of hydraulic servo valves is friction between the spool valve and the sleeve valve. The threshold of insensitivity causes that to the coil of valve must be given the minimal intensity of current in order to trigger corresponding slider movement and flow of working fluid. The friction force as well as action of the well-proportioned electromagnet introduces the hysteresis into static characteristics of the control valve and electromechanical converter [8–10].

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255

2 Dynamic Model of the Hydraulic Servo System The mathematical model of occurring physical phenomena in the studied drive system was created after assuming the following [7, 8]: volume module of the oil compressibility is fixed in the entire scope of change pressures and temperatures in the hydraulic system, the ps pressure in the crowded wire of pump is permanent during the system work, hydraulic control valve has zero overlap, output pt pressure from the control valve into the container is negligibly small toward pressures in the cylinder chambers, leaks of pressures between the pump and control valve are being omitted, temperature and viscosity of the oil are established during the system work, and delay time of the control valve is equal to zero. Calculation diagram of the hydraulic servo drive model, consisting of the double-acting cylinder with one-sided piston rod and directional control valve, is presented in Fig. 1. Marked parameters presented in the mathematical model of analyzed hydraulic servo drive were compared in Table 1. Considering such nonlinearities as evolution characteristics of the flow, friction, and stiffness of working fluid in cylinder chambers from the position, such equations were determined in the following form:

Fig. 1 Scheme of the hydraulic servo model

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Table 1 Markings presented in the model Mark

Term

xp, xs vp, vs p1, p2, ps, pt V1, V2 A1, A2, Au mp, ms Qi F, Fe Ftc, Fts Ftp, Ftl, Ftk, Ftu cs, cp fl, fs, fu

Displacement of the piston, spool valve Velocity of the piston, spool valve Pressures Volumes of the individual cylinder chambers Surfaces of the piston and cross section of seals Total mass on the piston, mass of the spool valve Volumetric flow rate Load external power, electromagnet power of the valve Friction force in the cylinder and in the valve Components of the friction forces: adhesion, sticky friction, kinetic, sealing

Eol Kq Ke Cq ρ μ d kw1, kw2

Stiffness of the valve spring and stiffness of the cylinder Coefficients of sticky friction in the cylinder and valve as well as rates of friction insulating the cylinder Reduced substitute module of working fluid Coefficient of flow through the valve Coefficient of the strengthening in the electromechanical converter of the valve Coefficient of resistance flow through the valve Oil density Dynamic rate of oil viscosity Diameter of the spool valve Coefficients of leakages in the cylinder

– equation of the movement of piston 8 < dx p ð t Þ ¼ v p ð t Þ dt : dvp ðtÞ ¼ 1 ½A1 p1 ðtÞ mp dt

A2 p2 ðtÞ

Ftc

FŠ

ð1Þ

– equation of flow through control inter space of the valve for xs ðtÞ [ 0 (

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi QR1 ðtÞ þ ¼ Kq xs ðtÞ jps p1 ðtÞj pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi QR2 ðtÞ þ ¼ Kq xs ðtÞ jp2 ðtÞ pt j



pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pt j QR1 ðtÞ ¼ Kq xs ðtÞ p jpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ðt Þ QR2 ðtÞ ¼ Kq xs ðtÞ jps p2 ðtÞj

for xs ðtÞ\0

ð2Þ

ð3Þ

Modeling and Analysis of the Hydraulic Servo Drive System

257

– equation of pressures in the cylinder chambers for xs ðtÞ [ 0 8 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   Eol < dp1 ðtÞ ¼ p1 ðtÞj A1 vp ðtÞ Qw1 ðtÞ V1 þ A1 xp ðtÞ Kq xs ðtÞ jps dt pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  Eol : dp2 ðtÞ ¼ K x ð t Þ jp2 ðtÞ pt j þ A2 vp ðtÞ þ Qw1 ðtÞ q s V A x ð t Þ 2 2 p dt

for xs ðtÞ\0

8 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   Eol < dp1 ðtÞ ¼ K x ð t Þ jp1 ðtÞ pt j A1 vp ðtÞ þ Qw1 ðtÞ q s V A x ð t Þ 1 1 p dt pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  Eol : dp2 ðtÞ ¼ Kq xs ðtÞ jps p2 ðtÞj þ A2 vp ðtÞ Qw1 ðtÞ V2 þ A2 xp ðtÞ dt

Qw2 ðtÞ

 ð4Þ

Qw2 ðtÞ



ð5Þ

Flow coefficient Kq through the valve is determined as sffiffiffi 2 Kq ¼ Cq pd q

ð6Þ

where d is the diameter of the spool valve, Cq is the coefficient of resistance flow through the valve, and q is the oil density. Leakages appearing in the cylinder are proportions to the difference of pressures in the cylinder chambers: for xs ðtÞ [ 0 

Qw1 ðtÞ þ ¼ kw1 ðp1 ðtÞ Qw2 ðtÞ þ ¼ kw2 p2 ðtÞ

p2 ð t Þ Þ



Qw1 ðtÞ ¼ kw1 ðp2 ðtÞ Qw2 ðtÞ ¼ kw2 p2 ðtÞ

p1 ð t Þ Þ

ð7Þ

for xs ðtÞ\0 ð8Þ

where kw1 ; kw2 are the coefficients of leakages in the cylinder equation of the spool valve movement: 8 < dxs ðtÞ ¼ v ðtÞ s dt ð9Þ : dvs ðtÞ ¼ 1 ð Fts ðtÞ cs xs ðtÞ þ Fe ðtÞÞ ms dt

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where force of the sticky friction is Fts ðtÞ ¼ fs vs ðtÞ

ð10Þ

and the force of the electromagnet spool valve is [5] Fe ðtÞ ¼ Ke ð0:3uðtÞ þ 6:5Þ

ð11Þ

In the simulated system a friction force appearing in the hydraulic cylinder was taken into account: Ftc ðtÞ ¼ Ftl ðtÞ þ Ftz ðtÞ

ð12Þ

Friction in servo-hydraulic drives is a phenomenon causing standbys of the movement and reducing the efficiency of system as well as at the same time influences on attenuation mechanical oscillation [8]. The fundamental element of Eq. (12) is the sticky friction force, which has a primary importance in the modeling of dynamics drive system: Ftl ¼ fl vp ðtÞ

ð13Þ

The coefficient of sticky friction is determined by the relation fl ¼ lA h where A is the total area of the joint, h is the layer of the oil film (value of float), and l is the dynamic coefficient of the oil viscosity. Dry friction force Ftz and factor of the sticky friction fl were appointed stimulating the system of constant tension uðtÞ and measuring the pressure p1 ðtÞ as well as p2 ðtÞ in the cylinder chambers of in the equilibrium of velocity vp what allows for calculating the total force of friction. During the movement of the piston rod with the total constant velocity, friction force Ftc is expressed as Ftc ¼ fl
vp þ Ftz

ð14Þ

Value of the friction force Ftz appearing in the system is determined by Eq. (15) according to the Stribeck model [8]:     Ftz ðtÞ ¼ Ftk þ Ftp sgn vp ðtÞ þ Ftu

ð15Þ

where Ftk ¼ ftk FN is the kinetic friction force, ftk is the coefficient of the kinetic friction, and FN is the normal force. Friction appearing in sealing is determined in following relation (16) [8]: Ftu ¼

fu A u ðp1 ðtÞ þ p2 ðtÞÞ 2

ð16Þ

Modeling and Analysis of the Hydraulic Servo Drive System

259

where fu is the coefficient of the friction, Au ¼ pdl is the surface of the sealing, and d and l are the diameter of the piston and length of the sealing.

3 Designing the Control System—Linearization with Feedback In examining and designing hydraulic servo drive, computer simulation of the model played an important role. Natural way to adapt algorithms of control the nonlinear object is to use the classic method of linearization model process around the point of work and use the linearization of model algorithm. Applying the linearization toward the nonlinear system, the algebraic transformation is explored which eliminates nonlinearities of the object. Therefore, it is necessary to apply the so-called input–output feedback linearization [9]. Nonlinearities are being eliminated (entirely or partly) from the object so that after closing the system was linear. In effect of the linearization carried out according to the scheme [7], obtained function of coupling the valve for displacement of the spool valve xs ðtÞ is as follows:   x s ð t Þ ¼ f p1 ; p2 ; x p ; v p ; v ð17Þ for xs ðtÞ [ 0 

xs ðtÞ ¼ a0 xp ðtÞ þ a1 vp ðtÞ þ a2

ðp1 ðtÞA1

p2 ðtÞA2 Þ m

! # A1 A2 Eol ðV2 ðtÞ þ V1 ðtÞÞ     þ vðtÞp mðtÞ
a þ ðtÞ mp V1 þ xp ðtÞA1
V2 þ xp ðtÞA2     mp V1 ðtÞ þ xp ðtÞA1
V2 ðtÞ þ xp ðtÞA2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a þ ðtÞ ¼     Eol Kq ðA1 jps p1 ðtÞj V2 ðtÞ xp ðtÞA2 þ A2 jp2 ðtÞ pt j VðtÞ1 þ xp ðtÞA1 Þ

ð18Þ

for xs ðtÞ\0  ðp1 ðtÞA1 xs ðtÞ ¼ a0 xp ðtÞ þ a1 vp ðtÞ þ a2

p2 ðtÞA2 Þ m

! # A1 A2 Eol ðV2 ðtÞ þ V1 ðtÞÞ     þ vp ðtÞ vðtÞ
a ðtÞ mp V1 ðtÞ þ xp ðtÞA1
V2 ðtÞ þ xp ðtÞA2     mp V1 ðtÞ þ xp ðtÞA1
V2 ðtÞ þ xp ðtÞA2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a ðt Þ ¼   Eol Kq ðA1 jp1 ðtÞ pt j V2 ðtÞ xp A2 þ A2 jps p2 ðtÞj V1 ðtÞ þ xp ðtÞA1 ð19Þ

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Table 2 Simulation parameters

8 MPa 1.256 × 10−3 m2 0.69 900 kg/m3 0.6

Ps A κ ρ Cd

0.28 kg 172 MPa 6 × 10−3 20–125 kg 1500 N/m

ms Eol d mp cs

1.4

1.0 0.8

Trajectory Displacement

0.6 0.4

V e lo c ity v p [m m ]

D is p la c e m e n t x p [ m m ]

0.3 1.2

0.2

0.1

0.2

0.0

0.0 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.1

1.0

0.2

0.3

0.4

time[s]

p1

6

5x10

0.5

0.6

0.7

0.8

0.9

1.0

0.7

0.8

0.9

1.0

time[s]

0.2

6 6

5x10

A c c e le r a t io n a p [m m ]

Pressure p1. p2 [bar]

5x10

6

5x10

6

5x10

6

5x10

6

5x10

6

5x10

6

5x10

p2

6

5x10

6

5x10

0.1

0.0

-0.1

-0.2

6

5x10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.1

1.0

0.2

0.3

0.4

0.5

0.6

time[s]

time[s] -4

3.0x10

-4

2.0x10

-4

1.0x10

-4

-4

5.0x10

Velocity xs [mm]

D is p l a c e m e n t x s [ m m ]

6.0x10

-4

4.0x10

-4

3.0x10

-4

2.0x10

-4

1.0x10

0.0 -1.0x10

-4

-2.0x10

-4

-3.0x10

-4

0.0 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

time[s]

Fig. 2 Dynamic characteristics of the model

0.1

0.2

0.3

0.4

0.5

0.6

time[s]

0.7

0.8

0.9

1.0

Modeling and Analysis of the Hydraulic Servo Drive System

 where v ¼ ks xref p

261

 xp , xref p is the set signal, and a0 ; a1 ; a2 are the parameters of

the model [8]. For the simulation purposes, constant values of parameters were implemented, see Table 2. In Fig. 2, the chosen dynamic characteristics such as displacement xp ðtÞ, velocity vp ðtÞ, acceleration ap ðtÞ, pressures in individual chambers p1 ðtÞ and p2 ðtÞ as well as displacement the spool valve xs ðtÞ, and velocity vs ðtÞ at mass load 100 kg received as a result of the simulation model are presented.

4 Conclusions The considered solution regards algorithms of the control hydraulic servo drive for which characteristics do not change in time. The accepted theoretical description does not change during the system work. In such assumption, we may accept the sufficient theoretical description only once and select parameters of the adjuster in the course of enforcing the movement drive. Unfortunately, the disadvantage of presented solution is the large sensitivity to mistakes appearing in the description of the controlled object. A lack of the system resistance to interferences appears in case of the parametric model uncertainty [2]. Additionally, all variables of the state must be available for analysis. Since the values of many parameters are not possible to be appointed by direct measurements, they must be appointed as a result of the parametric identification of created mathematical model of the examined object. It is a difficult and laborious process, often loaded by a large dose of the uncertainty. As a result, to assure the right regulation during the work, we must adopt parameters of control process.

References 1. DeRose, D.: Proportional and servo valve technology. Fluid Power J. 4, 8–12 (2003) 2. Wos, P., Dindorf, R.: Adaptive control of the electro-hydraulic servo-system with external disturbances. Asian J. Control 15(4), 1–16 (2013) 3. Wang, Z., Shao, J., Lin, J., Han, G.: Research on controller design and simulation of electrohydraulic servo system. In: Proceeding of the International Conference on Mechatronic and Automation, pp. 380–338. IEEE Xplore Press, Changchun, 9–12 Aug (2009). doi:10. 1109/ICMA.2009.5245095 4. Zeng, H., Sepehri, N.: Tracking control of hydraulic actuators using a LUGRE friction model compensation. J. Dyn. Syst. Measur. Control 130, 1–7 (2008). doi:10.1115/1.2807181 5. Ziaei, K., Sepehri, N.: Modeling and identification of electrohydraulic servos. Mechatronics 10, 761–772 (2000). doi:10.1016/S0957-4158(99)00042-2

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6. Katalog, B., Rexroth, A.G.: Industrial Hydraulics Hydraulic and Electronic Components, RE 00208/08.04 (2013) 7. Milecki, A.: Model serwozaworu z elektrycznym sprzężeniem zwrotnym. Archiwum Technologii Maszyn i Automatyzacji, No. 2 (2000) 8. Dindorf, R.: Modelowanie i symulacja nieliniowych elementów i układów regulacji napędów płynowych. Wydawnictwo Politechniki Świętokrzyskiej, Kielce (2004) 9. Jelali, M., Kroll, A.: Hydraulic Servo Systems—Modelling, Identification and Control. Springer, Berlin (2003) 10. Zulfatman, R.A., Rahmat, M.F.: Modeling and controller design of electro-hydraulic actuator. In: Proceeding of the 2nd International Conference on Control, Instrumentation and Mechatronic Engineering, pp. 225–231. UTM Publisher, Malacca, Melaka, Malaysia, 9–9 June 2009

Stereoscopic Technique for a Motion Parameter Determination of Remotely Operated Vehicles Bogdan Żak and Stanisław Hożyń

Abstract The aim of this study was to describe and examine stereoscopic technique for a motion parameter determination of remotely operated vehicles (ROVs). We focused on geometrical restriction on a stereo vision system for various velocities of a vehicle. For the purpose of analysis, the stereo rig consist color submergible W/Effio-E DSP cameras equipped with SONY EXVIEW HAD Ultra High Sensitivity was used. Our results show that the parameters of the stereo vision rig have a strong impact on motion determination performance. For that reason, the demand distance to a bottom and velocity of vehicle should be included in calculation of stereo vision system parameters. Keywords Stereoscopic technique calibration Triangulation





Motion parameter determination
Camera

1 Introduction There is a considerable interest in vision systems for understanding of the underwater word. One of the predominant fields in this matter concerns underwater observation. Nowadays, the surveillance and inspection of underwater objects are carried out by trained operators, who control a remotely operated vehicle (ROV) with cameras mounted over it. This is a tedious, time-consuming, and expensive task. Therefore, a lot of effort into developing more autonomous solutions has been made. For example, techniques for implementing computer vision for cable tracking [1], sea bed inspection [2], maintenance proposes [3], mine detection [4], wreck localization [5], and station keeping [6] have been researched. B. Żak (&)
S. Hożyń Polish Naval Academy, Gdynia, Poland e-mail: [email protected] S. Hożyń e-mail: [email protected] © Springer International Publishing Switzerland 2016 J. Awrejcewicz et al. (eds.), Mechatronics: Ideas, Challenges, Solutions and Applications, Advances in Intelligent Systems and Computing 414, DOI 10.1007/978-3-319-26886-6_17

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For all these applications, knowledge of accurate vehicle motion parameters is vital for all underwater operations. Unfortunately, underwater vehicles designed for underwater inspections are rather low-cost devices and additional cost to equip them with navigation sensors is not desirable. Due to these limitations, some research in recent years has focused on using vision systems for a positioning purpose [7–9]. It is very convenient, because every ROV is equipped with at least one camera. Overland applications based on computer vision very often use a stereo vision system, which is capable of making accurate, precise, and noninvasive measurements. Stereo vision is a technique for inferring the 3D position of objects from two (or more) simultaneous views of the scene. It offers a cheap solution for 3D reconstruction of an environment using passive sensor and thus it does not introduce interferences with other sensor devices. In order to be used for accurate measurement, stereo vision system must be geometrically calibrated. Additionally, its geometrical parameters have very strong impact on performance. In view of these limitations, some researches have addressed the problem of geometrical restriction on measuring error in overland applications [10, 11]. Unfortunately, we had not found any examination of this problem for underwater applications. Therefore, the purpose of this study is to describe and examine stereoscopic technique for a motion parameter determination of ROVs. We focus on geometrical restriction on a stereo vision system for various velocities of a vehicle. However, an important part of stereo vision field concerning detection and matching invariant features in images was not investigated in this study. Considering its complexity in underwater applications, it will be addressed in the future work. The paper is organized as follows: Sect. 2 describes the underwater imaging conditions. In Sect. 3 the motion parameter determination of underwater vehicles is introduced. Section 4 is about the stereo vision system, Sect. 5 shows the experimental results, and Sect. 6 comes to the conclusions.

2 Underwater Imaging An underwater imaging process strongly depends on underwater environment conditions. Many variables can affect the levels of light penetration including the clarity of water, turbidity, depth, and surface conditions. Considering an impact on an image quality, three factors should be taken into consideration: scattering, attenuation, and image distortion. Scattering is a result of suspended particles or bubbles in water deflecting photons from their straight trajectory between the light source and the object viewed. The scattering can be divided into two different types: backscatter and forward scatter. Backscatter is the reflection of light from the light source back to the lens of the camera. It results in bright points appearing on the images, sometimes referred to as marine snow, strongly affecting image contrast and the ability to

Stereoscopic Technique for a Motion …

265

extract features during image processing. Forward scatter occurs when the light from the light source is deflected from its original path by a small angle. It can result in reducing image contrast and blurring of object edges. Therefore, the first part of every feature detection algorithm is focused on image enhancement technique. The most popular methods for underwater images contain image filtrations, histogram equalization, and contrast stretching. Additionally, due to the higher pressures associated with deep-sea exploration, there is a need for using depth rated lens. Imperfections in the manufacturing of the tough lens can lead to nonlinear distortion in the images. Moreover, the refraction of light at the water/glass and glass/air can result in nonlinear image deformation. To account for this distortion, the intrinsic parameters of cameras must be found through the calibration process using radial and tangential models of the lens distortion [12].

3 Motion Parameter Determination The concept established for solving a motion parameter determination problem is graphically presented in Fig. 1. An underwater vehicle moving along a bottom captures images of viewed parts of bottom using a stereo vision system. The captured images are used for extracting and matching features between them. The performance of extracting features method strongly depends on visibility and constitutes a very difficult problem in underwater environment. This difficulty is also connected with rather plane structure of the bottom. Therefore, our work was focused only on a stereo vision system for a motion parameter determination. The problem of features extraction in underwater environment will be included in future research.

Fig. 1 An underwater vehicle with cameras

h

α l

B. Żak and S. Hożyń

266 Fig. 2 Motion determination algorithm

START

Capture left and right images l1, r1

Extract and match features between them, Triangulate

Capture new left and right images li, ri

Extract and match features between them, Triangulate

Compare left image li with previous left image li-1, Determine movement

In our approach, we established knowledge about corresponding feature points in the left and right images and in successive frames of the left camera. Only three noncoincident and noncollinear features are essential to compute the change of position of a vehicle. The graphical representation of established algorithm is presented in Fig. 2. Considering a camera moving with vehicle velocity v, where v ¼ ðvx ; vy ; vz ; xx ; xy ; xz Þ

ð1Þ

and, vi is the translational velocity in ith direction, and xi is the rotational velocity about ith axis, the velocity of the point relative to the camera frame is P_ ¼

xP

ð2Þ

v

which can be rewritten in scalar form as X_ ¼ Yxz Z xy Y_ ¼ Zxx Xxz Z_ ¼ Xxy Yxx

vx vy

ð3Þ

vz

The perspective projection for normalized coordinates is x¼

X Y ;y ¼ Z Z

ð4Þ

Stereoscopic Technique for a Motion …

267

and the temporal derivative, using the quotation rule: x_ ¼

_ XZ

X Z_ Z2

; y_ ¼

_ YZ

Y Z_

ð5Þ

Z2

Substituting (3), X ¼ xZ and Y ¼ yZ it can be written in matrix form


 x_ ¼ y_

1 Z

0

0 1 Z

x Z y Z

xy

ð1 þ xÞ2

1 þ y2

xy

1 vx C !B B vy C C y B v B zC B x x B xC C @ xy A xz 0

ð6Þ

The normalized image plane coordinates are related to pixel coordinates by u¼

f f x þ u0 ; v ¼ y þ y 0 qu qv

ð7Þ

qu q  u; y ¼ v v f f

ð8Þ

which can be arranged as x¼

where  u ¼ u u0 and v ¼ v v0 are pixel coordinates relative to the principal point. Considering the above, Eq. 6 can be given as 1 vx 0 1 B vy C B C
 f 2 þ q2u u2 qu uv 1 u B vz C  0 v  u_ Z qu f f B C @ qu Z A ¼ 2 2 2 B C  f þ q v   u v q f v v v v_ u B xx C 0 qv Z Z qv f f |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} @ xy A Jp xz 0

ð9Þ

and reduced to the concise matrix form

p_ ¼ J p v

ð10Þ

where J p is the Jacobian matrix for a feature point. The motion of three points may be considered by stacking the Jacobians

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268

1 u_ 1 B v_ 1 C 0 1 B C J p1 B u_ 2 C B C ¼ @ J p Av 2 B v_ 2 C B C J p3 @ u_ 3 A v_ 3 0

ð11Þ

The matrix will be non-singular as long as the points are not coincident or collinear. The above equation can be reverted 1 u_ 1 0 1 1 B v_ 1 C B C J p1 B u_ 2 C B C @ A v ¼ J p2 B v_ 2 C B C J p3 @ u_ 3 A v_ 3 0

ð12Þ

and solved to get velocities of a vehicle [13].

4 Stereo Vision System In computer vision, it is common to use the central perspective imaging model as shown in Fig. 3. The rays converge on the origin of the camera frame and a noninverted image is projected onto the image plane z ¼ f . Using similar triangles, we can show that

Fig. 3 Perspective camera model

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269

a point at the world coordinates P ¼ ðX; Y; ZÞ is projected to the image plane p ¼ ðx; yÞ by x¼f

X ; Z

y¼f

Y ; Z

z¼f

ð13Þ

Camera parameters Computer vision algorithms reconstructing 3D structure of a scene need equations linking the coordinates of points in 3D space with coordinates of their corresponding image points. For this purpose it is often assumed that [13] – the camera reference frame can be located with respect to some other, known as reference frame; and – the coordinates of the image points in the camera reference frame can be obtained from pixel coordinates, only those directly available from the image. The relationship between the coordinates of a point P in the world and the camera frame, Pw and Pc , respectively, is presented below [14]: Pc ¼ RðPw

TÞ

ð14Þ

where R is the rotation matrix and T is the translation vector. The intrinsic parameters can be defined as the set of parameters needed to characterize the optical, geometric, and digital characteristics of the viewing camera. For a pinhole camera, three sets of intrinsic parameters are needed, specifying, respectively, [14] – a perspective projection, for which the only parameter is the focal length f; – a transformation between camera frame coordinates and pixel coordinates; and – geometric distortions introduced by the optics. Neglecting any geometrical distortions, it is convenient to assume that a CCD array is made of rectangular grid of photosensitive elements, so we have x¼ y¼

ðxu ðyu

ox Þsx oy Þsy

ð15Þ

where ox , oy are the coordinates in the pixel of the image center; and sx , xy are the effective sizes of the pixel (in millimeters) in horizontal and vertical directions, respectively. Usually, the pinhole model is the basis that is extended with some corrections for the systematically distorted image coordinates. The most commonly used correction is for the radial lens distortion that causes the actual image points to be displaced radially in the image plane [13]. The radial distortion can be approximated using the following expression:

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270

xu 1 þ k1 þ k2 r 4 þ k5 r 6 yu yv ¼ 2 1 þ k1 r þ k2 r 4 þ k5 r 6 2 r ¼ x2v þ y2v xv ¼

r2

ð16Þ

where k1 ; k2 ; k5 are the intrinsic parameters of camera defining radial distortion; xu , yu are the ideal pixel coordinates; and xv , yv are the distorted coordinates. Another common distortion type is tangential distortion. It is caused by not strictly collinear surface of lens and is usually written in the following form [15]: yt ¼ k3 ðr 2 þ 2yu Þ þ 2k4 xu yu xt ¼ 2k3 xu yu þ k4 ðr 2 þ 2x2u Þ

ð17Þ

where k3 , k4 are the tangential distortions; and xt ; yt are the distorted coordinates. After including lens distortion, the new point coordinate (xd ; yd ) is defined as follows: xd ¼ xv þ xt yd ¼ yv þ yt

ð18Þ

Camera calibration Camera calibration is the essential step towards proper moving underwater vehicle parameter determination. There are many ways to solve the camera parameters. In our work Zhang’s method for focal length calculation and Brown’s method to determine the distortion parameters were used. This approach was adopted because of the well-developed and easy to implement function available in the OpenCV library. OpenCV proposes to use a chessboard pattern to generate the set of 3D scene points required for calibration. This pattern creates points at the corners of each square, and since this pattern is flat, we can freely assume that the board is located at Z ¼ 0 with the X and Y axes well aligned with the grid. In this case, the calibration process simply consists of showing the chessboard pattern to the camera from different viewpoints. In practice, 10–20 chessboard images are sufficient, but these must be taken from different viewpoints at different depths. The two important outputs of this function are the camera matrix and the distortion parameters. Stereoscopic acquisition system The geometry of stereo is shown in Fig. 4. The figure shows two pin hole cameras, their projections centers Ol and Or , and image planes pl and pr . The focal lengths are denoted by fl and fr . The vectors Pl ¼ ½Xl ; Yl ; Zl Š and Pr ¼ ½Xr ; Yr ; Zr Š refer to the same 3-D point P. The vectors pl ¼ ½xl ; yl ; zl Š and pr ¼ ½xr ; yr ; zr Š refer to the projection of point P onto the left and right image planes, respectively. The reference fames of the left and right cameras are related via the extrinsic parameters. These define a rigid transformation in 3-D space, described by a translation vector

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271

Left camera plane Left centre point

Left epipole

Ol

el

Left epipole lines

Right centre point

Right epipole

Base line

Or

er

∏e

pl ∏l

Right camera plane

pr ∏r

Pl

Pr

Right epipole lines

P

Fig. 4 The epipolar geometry

Fig. 5 Canonical stereoscopic system

P

Z XR

XL

ΠR

oL

ΠL

pL

OL

b

oR

f

pR

OR

T ¼ ðOr Ol Þ and rotation matrix R. For a given point P in space, the relation between Pl and Pr can be formulated as Pr ¼ RðPl

TÞ

ð19Þ

Canonical stereoscopic system A canonical stereoscopic system is presented in Fig. 5. Considering similar triangles DpL oL OL and DPXOL , as well as DpR oR OR and DPXOR , the formula for horizontal disparity Dx ðpl ; pr Þ between two points pl and pr can be obtained as

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272

Dx ðpl ; pr Þ ¼ pr

pl ¼ x L

xR ¼

bf Z

ð20Þ

where the points pl ¼ ½ pl1 pl2 ŠT , pr ¼ ½ pr1 pr2 ŠT are images of a certain point 3-D point p, b is the base distance between the cameras, f is the camera focal length, and Z is the distance from point P to the baseline. Image rectification Stereo image rectification is a process of image transformations in such way that the corresponding epipolar lines in both images become collinear (Fig. 6). A very important feature of the stereo setups is an inherent constraint of the search space to one dimension only. This is a very desirable feature from the computational point of view. The rectification transformation can be described as a composition of the following transformations: – Rotation of the left and right camera planes in such a way that the epipoles go to infinity. This rotation is described by a rotation matrix Q. – Rotation of the right camera according to the transformation described by a matrix R. Additionally, without loss of generality, the following assumptions were established: – the focal length f of the two cameras is the same and – the origin of the local camera coordinate system is the camera principal point.

Fig. 6 Stereo image rectification

P

pl1

Π l1

pr 1

Πl0

pr 0

pl 0

Ol

Or

Π rl

Πr 0

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The matrix Q can be found by considering three mutually orthogonal unit vectors: q1 , q2 , and q3 . The vector q1 is collinear with the translation vector T between the focus points of the two and is given as q1 ¼

T kT k

ð21Þ

The vector q2 is orthogonal to the vector q1 . Because ½ Ty

0 Š
½ Tx

Tx

Tz ŠT ¼ 0;

Ty

ð22Þ

q2 takes the form q2 ¼

T ½ Ty Tx 0 Š qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ty2 þ Tx2

ð23Þ

The third vector q3 has to be simultaneously orthogonal to the vectors q1 and q2 . Therefore, it can be set to the vector product q3 ¼ q1  q2

ð24Þ

The vectors q1 , q2 , and q3 determine the following rotation matrix Q: 2

qT1

3

6 7 Q ¼ 4 qT2 5 qT3

ð25Þ 33

Triangulation For the estimated feature points in the left and right images, the point P lies at the intersection of the two rays from ol through pl and from or through pr , respectively (Fig. 7). Fig. 7 Triangulation with non-intersecting rays

r

l P

pr

pl

w

ol

or

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274

Because of approximate camera calibration parameters and a target location, the two rays will not actually intersect in the space, and their intersection can only be estimated as the point of the minimum distance from both rays (Fig. 7). Assuming apl be the ray l, T þ bRT pr be the ray r and w be the vector orthogonal to both l and r, the triangulation problem reduces to determining a midpoint of segment parallel to w and joins l and r. It can be computed solving the linear system of equations [16] apl þ bw ¼ T þ cRT pr

ð26Þ

for a, b, and c. Geometric restriction in distance measurement using a stereo vision system Distance measurement strictly dependent on geometric parameters of a stereo vision system. Accuracy of measurement decreases with increase in distance between a stereo rig and a target. This tendency is caused by the following parameters [17]: – focal length, – distance between cameras, and – CCD resolution. The geometrical dependences among above parameters are shown in Fig. 8. Using triangle similarity theorem, the equation describing geometrical dependence can be formulated as follows [18]: R¼

rZ 2 fb rZ

ð27Þ

where r is the pixel size, Z is the distance measurement, R is the measurement uncertainty, and b is the distance between cameras.

Fig. 8 Distance reconstruction using a stereo vision system

f

b

r

Z

R

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5 Results In order to obtain a reconstruction of the scene depth in the Euclidean space, it is necessary to determine the camera parameters. The classic calibration methods are based on a specially prepared calibration pattern with known dimensions and a position in a certain coordinate system [11]. For the purpose of obtaining the cameras’ parameters, the calibration pattern with 289 markers was used. The calibration procedure (presented in detail in [11]) was conducted. Considering conception presented in Fig. 1, it is obvious that velocity of vehicle, distance to bottom h, camera angle a, camera focal length f , distance between cameras b, and viewed surface l should be carefully established for a correct movement parameters determination. However, in the underwater environment, camera calibration and stereo rectification are also very important for the water influence compensation. In our experiment, the stereo rig with two color submergible W/Effio-E DSP cameras equipped with SONY EXVIEW HAD Ultra High Sensitivity image sensor was used (Fig. 9). The calibration process was performed in a swimming pool using a chessboard pattern. The following results for cameras (Table 1) and stereo vision Fig. 9 Stereo vision rig

Table 1 Camera calibration parameters Focal length x (pixels) Focal length y (pixels) Focal length (mm) Principal point u (pixels) Principal point v (pixels) Distortion coefficients

Left camera

Right camera

770 769 48 367 348 [−0.36, 0.41, 0.002, 0.002, −0.55]

761 761 47.6 366 323 [−0.32, 0.24, 0.002, −0.003, −0.13]

B. Żak and S. Hożyń

276 Table 2 Stereo vision rig parameters

Rotation R

Translation T

Left image

0:99 0:1 0:1 5:36

0:09 0:98 0:15 0:04

0:03 0:14 0:99 0:1

Right image

Fig. 10 Captured images

rig (Table 2) were obtained. The estimated parameters were essential for removing distortion from images and for rectification. The impact of mentioned steps on processed images can be observed below. Figure 10 shows images captured by cameras, while Fig. 11 presents obtained effect. It should be noted that though calibration and rectification steps are essential for measurement, they also substantially reduce usable parts of images. Further experiments were concentrated on finding influence of relationship between separate parameters of the stereo vision system on a motion parameter determination. Very important aspect in this matter concerns possibility to extract and track invariant features between images. In this matter, the following assumptions were made:

Left image

Fig. 11 Undistorted and rectified images

Right image

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– the distance between cameras b and the distance between the vehicle and the bottom h (Fig. 1) should assure 75 % visibility of the corresponding region in both images, and – the velocity of the vehicle in the x direction, distance to the bottom h, and the frame rate of image acquisition system should assure 75 % visibility of the same regions in the consecutive frames. Another aspect concerned accuracy of the distance measurement using a stereo vision system. As was mentioned in Sect. 4, the distance measurement error is directly connected with the following parameters: the focal length, the distance between cameras, CCD resolution, and the distance to the bottom. An correct measurement is an important part of movement parameter determination because it has strong impact on calculation. However, reduction of a measuring error by extending stereo rig base line b reduces visibility of the same regions in left and right images. It also increases a minimal distance possible to measure by stereo system. Therefore, for assessing impact of individual parameters for measurement performance, following graphs presenting relations between parameters were drawn (Figs. 12, 13, 14, 15, 16, 17, 18 and 19).

9 b=500 [mm] b=400 [mm] b=300 [mm] b=200 [mm] b=100 [mm]

8

Relative Depth Error [%]

7 6 5 4 3 2 1 0

0

5

10

15

Distance to bottom [m]

Fig. 12 Relative depth estimation errors for cameras with f = 47.5 mm and image size of 768 × 576 pixels, for different baselines

B. Żak and S. Hożyń

278 9 1280x960 [pixels] 768x576 [pixels] 480x360 [pixels] 320x240 [pixels] 160x120 [pixels]

8

Relative Depth Error [%]

7 6 5 4 3 2 1 0

0

5

10

15

Distance to bottom [m]

Fig. 13 Relative depth estimation errors for cameras with baseline = 300 mm and f = 47.5 mm, for different image sizes

1.4 b=500 [mm] b=400 [mm] b=300 [mm] b=200 [mm] b=100 [mm]

Minimum Distance [m]

1.2

1

0.8

0.6

0.4

0.2

0

0

20

40

60

80

100

120

Focal Length [mm]

Fig. 14 Minimum measured distance for cameras with image size of 768 × 576 pixels, for different baselines and focal lengths

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100

Corresponding region visibility [%]

90 80 70 60 50 40 30 b=500 [mm] b=400 [mm] b=300 [mm] b=200 [mm] b=100 [mm]

20 10 0

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Distance to bottom [m]

Fig. 15 Corresponding region visibility for cameras with f = 47.5 mm and image size of 768 × 576 pixels, for different baselines

100

Corresponding region visibility [%]

90 80 70 60 50 40 30 f=62.5 [mm] f=50 [mm] f=37.5 [mm] f=25 [mm] f=12.5 [mm]

20 10 0

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Distance to bottom [m]

Fig. 16 Corresponding region visibility for cameras with baseline = 300 mm and image size of 768 × 576 pixels, for different focal lengths

B. Żak and S. Hożyń

280 100

Corresponding region visibility [%]

90

80

70

60

50

40

30

f=10 [Hz] f=8 [Hz] f=6 [Hz] f=4 [Hz] f=2 [Hz]

20

10

0

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Distance to bottom [m]

Fig. 17 Corresponding region visibility for cameras with baseline = 300 mm, velocity = 1 m/s, and image size of 768 × 576 pixels, for different acquisition rates

100

Corresponding region visibility [%]

90 80 70 60 50 40 30 v=2.5 [m/s] v=2 [m/s] v=1.5 [m/s] v=1 [m/s] v=0.5 [m/s]

20 10 0

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Distance to bottom [m]

Fig. 18 Corresponding region visibility for cameras with baseline = 300 mm and image size of 768 × 576 pixels, for different velocities of the vehicle

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100

Corresponding region visibility [%]

90

80

70

60

50

40

30

α=60° α=45° α=30° α=15° α =0°

20

10

0

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Distance to bottom [m]

Fig. 19 Corresponding region visibility for cameras with baseline = 300 mm, focal length = 47.5 mm, velocity = 0.5 m/s, and acquisition rate = 5, for different camera angles

It can be observed that decreasing distance to the bottom is beneficial for distance measurement accuracy improvement, but simultaneously strongly worsen corresponding region visibility. In this case, considering constant value of focal length, it became very important to set baseline value meeting the requirement of small distance error value and high correspondent region visibility. Another important parameter is a resolution of the image. Lower resolution decreases the corresponding region visibility but simultaneously decreases computational load during features detection and matching. The computation load was not taken into consideration in this work, but it is obvious that the smaller image matrices can be processed more quickly than the bigger ones. Therefore, the impact of image acquisition rate on corresponding region visibility was calculated. It should be noted that feature detection and matching algorithm will determine acquisition rate value and it is expected that the demand time for calculation will range from 50 to 500 ms. For the longer period of calculation time, the 75 % visibility of the corresponding region in both images could be achieved by reducing the distance to the bottom. The distance to the bottom should be also reduced for the higher speed of the vehicle.

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6 Conclusions The problem of a motion parameter determination using stereoscopic technique was studied. We have focused on geometrical restriction on a stereo vision system for various velocities of a vehicle. For the purpose of the analysis, the stereo rig consists of color submergible W/Effio-E DSP cameras equipped with SONY EXVIEW HAD Ultra High Sensitivity has been used. Our results show that the parameters of stereo vision rig have a strong impact on motion determination performance. For this reason, the demand distance to bottom and velocity of vehicle should be included in the calculation of stereo vision system parameters. Because of high complexity of image invariant feature detection and matching for underwater applications, we have not included this issue in our investigation. Therefore, the future work will focus on invariant feature detection and matching in underwater images.

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14. Cyganek, B., Siebert, P.: An Introduction to 3D Computer Vision Techniques and Algorithms. Willey, Chippenham (2009) 15. Trucco, E., Verri, A.: Introductory Techniques for 3D Computer Vision. Prentice-Hall, New Jersey (1998) 16. Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge (2003) 17. Żak, A.: Motion parameters calculation in 3D space using stereoscopic images. Pol. J. Environ. Stud. 19(4A), 124–128 (2010) 18. Żak, A., Stereoscopy in object’s motion parameters determination. Int. J. Comput. 5(2), pp. 175–182 (2011)

Author Index

A Arghir, Mariana, 219 Awrejcewicz, Jan, 189 B Barylski, Adam, 1 C Chodnicki, Marek, 113 Creuillot, Victor, 15 D Dąbek, Przemysław, 33 Dąbrowski, Krzysztof, 53 Dindorf, Ryszard, 253 Dreistadt, Cynthia, 15 Dyl, Tomasz, 65

Kowalska, Barbara, 113 Krzyżyński, Tomasz, 131 L Lipinski, Paul, 15 Ludwicki, Michał, 189 M Maniowski, Michał, 153 Mikhal, Aleksander A., 239 Milewski, Andrzej, 173 P Piotrowski, Norbert, 1 Polak, Adam, 77 S Szymanowska, Olga, 189

G Garus, Jerzy, 77 Gavrylkin, Vladimir. G., 239

T Trojnacki, Maciej, 33, 205

H Hożyń, Stanisław, 263

V Vulcu, Ovidiu Ioan, 219

J Jasiulek, Dariusz, 95

W Warsza, Zygmunt L., 239 Woś, Piotr, 253

K Kaliński, Krzysztof J., 15, 113 Kamiński, Kazimierz, 131 Kardyś, Witold, 173 Kluk, Piotr, 173 Kluziewicz, Michał, 153 Kmita, Piotr, 113 Kogut, Paweł, 173

Z Zagrodny, Bartłomiej, 189 Ż Żak, Bogdan, 263

© Springer International Publishing Switzerland 2016 J. Awrejcewicz et al. (eds.), Mechatronics: Ideas, Challenges, Solutions and Applications, Advances in Intelligent Systems and Computing 414, DOI 10.1007/978-3-319-26886-6

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