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Modeling and Design Optimization of Electromechanical Brake Actuator Using Eddy Currents

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Modeling and Design Optimization of Electromechanical Brake Actuator Using Eddy Currents Modeling and Design Optimization of Electromechanical Brake Actuator Using Eddy Currents by Kerem Karakoc MASc, University of Victoria, 2007 BSc, Bogazici University, 2005 A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY in the Department of Mechanical Engineering. Kerem Karakoc, 2012 University of Victoria All rights reserved. This dissertation may not be reproduced in whole or in part, by photocopy or other means, without the permission of the author. ii Modeling and Design Optimization of Electromechanical Brake Actuator Using Eddy Currents by Kerem Karakoc MASc, University of Victoria, 2007 BSc, Bogazici University, 2005 Supervisory Committee Dr. Afzal Suleman, Dept. of Mechanical Engineering, University of Victoria Co-Supervisor Dr. Edward Park, Dept. of Mechanical Engineering, University of Victoria Co-Supervisor Dr. Ned Djilali, Dept. of Mechanical Engineering, University of Victoria Departmental Member Dr. Issa Traore, Dept. of Electrical and Computer Engineering, University of Victoria Outside Member iii Supervisory Committee Dr. Afzal Suleman, Dept. of Mechanical Engineering, University of Victoria Co-Supervisor Dr. Edward Park, Dept. of Mechanical Engineering, University of Victoria Co-Supervisor Dr. Ned Djilali, Dept. of Mechanical Engineering, University of Victoria Departmental Member Dr. Issa Traore, Dept. of Electrical and Computer Engineering, University of Victoria Outside Member Abstract A novel electromechanical brake (EMB) based on the eddy current principle is proposed for application in electrical vehicles. The proposed solution is a feasible replacement for the current conventional hydraulic brake (CHB) systems. Unlike CHBs, eddy current brakes (ECBs) use eddy currents and their interaction with an externally applied magnetic field to generate braking torque. Due to their pure electrically controllable and contact free nature, ECBs have multiple advantages over the current CHB systems, such as faster response, reduced weight and number of components, ease of implementing various controllers (e.g., anti-lock braking), and reduced noise levels. However, the torque generated by a typical ECB at low speeds is insufficient to effectively and completely stop a moving vehicle. Therefore, an ECB is commonly used as an assistive brake to the CHB system in heavy vehicles, i.e. trains and trucks. In order to overcome this shortcoming, the use of AC magnetic fields is proposed to realize a stand-alone ECB system in which sufficient braking torque can be generated at low speeds. To this end, eddy currents are modeled analytically using the governing Maxwell’s equations with the consideration of time varying field application. The analytical model was validated using finite element analysis. Results show that the braking torque increases with the application of a time varying field. Various forms of time varying fields have been studied. It was found that the frequency-modulated applied field in triangular waveform results in the highest braking torque. Next, the design was optimized to maximize the braking torque and an optimum configuration was obtained using multiple pole projection areas (PPAs). Optimization results show that the braking torque significantly increases with the introduction of iv additional PPAs to the configuration, and the braking torque generation for an optimum four-PPA ECB configuration exceeds the braking requirements for current passenger vehicles. For control purposes, a dynamic model for a novel stand-alone ECB system using AC fields for automotive applications has been successfully designed and evaluated. Also, a model-based predictive controller has been developed for the optimum ECB configuration. Finally an experimental test-bed has been designed for experimentation of both DC and AC field application on ECB. Keywords: • Brake-by-wire • Eddy Current Brake • Time-varying Magnetic Fields • Analytical Modeling • Helmholtz Equations • Method of Images • Finite Element Modeling • Genetic Algorithm • Vibration Response of Human Body • Automotive Applications • Model Based Predictive Control v Table of Contents Supervisory Committee ...................................................................................................... ii Abstract .............................................................................................................................. iii Table of Contents ................................................................................................................ v List of Tables .................................................................................................................... vii List of Figures .................................................................................................................. viii Nomenclature ...................................................................................................................... x Acknowledgments............................................................................................................ xiii Dedication ........................................................................................................................ xiv 1. INTRODUCTION ...................................................................................................... 1 1.1 Overview ............................................................................................................. 1 1.2 Objectives and contributions............................................................................... 9 1.2.1 Contributions ................................................................................................ 10 1.3 Thesis Outline ................................................................................................... 11 2. ANALYTICAL MODELING OF EDDY CURRENT BRAKES WITH THE APPLICATION OF TIME VARYING MAGNETIC FIELDS ....................................... 13 2.1 Introduction ....................................................................................................... 13 2.2 Analytical modeling of eddy currents ............................................................... 14 2.3 Validation and preliminary results .................................................................... 27 2.4 Discussion ......................................................................................................... 32 2.5 Conclusion ........................................................................................................ 35 Appendix.2A. Analytical Model: DC field application ................................................ 35 3. IMPROVED BRAKING TORQUE GENERATION CAPACITY OF EDDY CURRENT BRAKE WITH TIME VARYING FIELDS: A NUMERICAL STUDY ..... 44 3.1 Introduction ....................................................................................................... 44 3.2 Eddy current brake model ................................................................................. 45 3.3 Simulation results.............................................................................................. 50 3.3.1 Validation of the FEM .................................................................................. 51 3.3.2 Time varying field application with induction effects ................................... 54 3.3.3 ECB configuration for automotive application ............................................. 57 3.3.4 Time varying field application and optimization without induction effects .. 58 3.3.5 Effects of frequency modulation on braking torque generation ................... 60 3.4 Discussion ......................................................................................................... 62 3.5 Conclusion ........................................................................................................ 67 Appendix.3A. Analytical Model: DC field application ................................................ 67 4. OPTIMIZATION OF BRAKING TORQUE GENERATION CAPACITY OF EDDY CURRENT BRAKES WITH THE APPLICATION OF TIME VARYING MAGNETIC FIELDS ....................................................................................................... 69 4.1 Introduction ....................................................................................................... 69 4.2 Eddy current brake model ................................................................................. 70 4.3 Optimization ..................................................................................................... 74 4.4.1 Definition of the problem .............................................................................. 74 4.4.2 Optimization Results ..................................................................................... 80 vi 4.4 Discussions ....................................................................................................... 82 4.5 Conclusion ........................................................................................................ 86 5. CONTROL ................................................................................................................ 87 5.1 Introduction ....................................................................................................... 87 5.2 Dynamic ECB Model ........................................................................................ 89 5.3 Dynamic model of the vehicle .......................................................................... 93 5.4 Design of a model based nonlinear
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