Design of a Magnetorheological Brake System Based on Magnetic Circuit Optimization

by

Kerem Karakoc
BSc - Bogazici University, TURKEY, 2005 A Thesis Submitted in Partial Fulllment of the Requirements for the Degree of

Master of Applied Science

in the Department of Mechanical Engineering.

Kerem Karakoc, 2007 University of Victoria All rights reserved. This thesis may not be reproduced in whole or in part, by photocopy or other means, without the permission of the author.

ii

Supervisory Committee

Dr. Edward Park, Supervisor (Dept. of Mechanical Engineering, University of Victoria)

Dr. Afzal Suleman, Supervisor (Dept. of Mechanical Engineering, University of Victoria)

Dr. Zuomin Dong, Member (Dept. of Mechanical Engineering, University of Victoria)

Dr. Farid Golnaraghi, External Examiner (School of Engineering Science, Simon Fraser University)

iii Supervisors: Dr. Edward Park and Dr. Afzal Suleman

Abstract
Conventional hydraulic brake (CHB) systems used in automotive industry have several limitations and disadvantages such as the response delay, wear of braking pad, requirement for auxiliary components (e.g. hydraulic pump, transfer pipes and brake uid reservoir) and increased overall weight due to the auxiliary components. In this thesis, the development of a novel electromechanical brake (EMB) for automotive applications is presented. Such brake employs mechanical components as well as electrical components, resulting in more reliable and faster braking actuation. The proposed electromagnetic brake is a magnetorheological (MR) brake. The MR brake consists of multiple rotating disks immersed into an MR uid and an enclosed electromagnet. When current is applied to the electromagnet coil, the MR uid solidies as its yield stress varies as a function of the magnetic eld applied by the electromagnet. This controllable yield stress produces shear friction on the rotating disks, generating the braking torque. This type of braking system has the following advantages: faster response, easy implementation of a new controller or existing controllers (e.g. ABS, VSC, EPB, etc.), less maintenance requirements since there is no material wear and lighter overall weight since it does not require the auxiliary components used in CHBs. The MRB design process included several critical design steps such as the magnetic circuit design and material selection as well as other practical considerations such as cooling and sealing. A basic MRB conguration was selected among possible candidates and a detailed design was obtained according to a set of design criteria. Then, with the help of a nite element model (FEM) of the MRB design, the magnetic eld intensity distribution within the brake was simulated and the results were used to calculate the braking torque generation.

iv In order to obtain an optimal MRB design with higher braking torque generation capacity and lower weight, the key design parameters were optimized. The optimization procedure also consisted of the FEM, which was required to calculate the braking torque generation in each iteration. Two dierent optimization search methods were used in obtaining the minimum weight and maximum braking torque: (i) a random search algorithm, simulated annealing, was rst used to nd an approximate optimum design and (ii) a gradient based algorithm, sequential quadratic programming, was subsequently used to obtain the optimum dimensional design parameters. Next, the optimum MRB was prototyped. The braking performance of the prototype was tested and veried, and the experimental results were shown. Also, experimental results were compared with the simulation results. Due to the lack of accurate material property data used in the simulations, there were discrepancies between the experimental and the simulation results. Other possible sources of errors are also discussed. Since the prototype MRB generates much lower braking torque compared to that of a similar size CHB, possible design improvements are suggested ton further increase the braking torque capacity. These include the relaxation of the optimization constraints, introduction of additional disks, and the change in the basic magnetic circuit conguration.

Dr. Edward Park, Supervisor (Dept. of Mechanical Engineering, University of Victoria)

Dr. Afzal Suleman, Supervisor (Dept. of Mechanical Engineering, University of Victoria)

Dr. Zuomin Dong, Member (Dept. of Mechanical Engineering, University of Victoria)

Dr. Farid Golnaraghi, External Examiner (School of Engineering Science, Simon Fraser University)

vi

Contents
Supervisory Committee Abstract Table of Contents List of Figures List of Tables Nomenclature 1 Introduction 1.1 Thesis Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Modeling of MR Brake 2.1 Vehicle Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Required Braking Torque Calculation . . . . . . . . . . . . . . 2.2 Analytical Model of MR Brake . . . . . . . . . . . . . . . . . . . . . 3 Design of MR Brake 3.1 Conceptual Design Selection . . . . . . . . . . . . . 3.2 Magnetic Circuit Design . . . . . . . . . . . . . . . 3.3 Material Selection . . . . . . . . . . . . . . . . . . . 3.3.1 Magnetic Properties of Materials . . . . . . 3.3.2 Selection According to Magnetic Properties 3.3.3 Selection According to Structural Properties 3.3.4 Selection According to Thermal Properties . 3.4 Sealing . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii iii vi viii x xi 1 6 8 10 10 14 15 18 21 21 26 26 31 33 34 35 37

CONTENTS 3.6 3.7 3.8 3.9 3.10 Working Surface Area . . . Viscous Torque Generation . Applied Current Density . . Additional Disk Attachment MR Fluid Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii 39 42 48 49 52 55 56 57 62 64 71 71 72 75 76 76 77 82 85 85 86 94

4 FEA and Design Optimization 4.1 Finite Element Model of MRB . . 4.2 Optimization Problem Denition 4.3 Optimization Methods Used . . . 4.4 Optimum Design . . . . . . . . .

5 Experimentation 5.1 Experimental Setup . . . . . . . . . 5.1.1 MRB Prototype . . . . . . . 5.1.2 MRB Test-Bed . . . . . . . 5.2 Validation of the MRB prototype . 5.2.1 Experimental Problems . . . 5.2.2 Experimental Procedure and 5.3 Discussion . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . Results . . . . .

6 Conclusion and Future Works 6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Maxwell Equations

viii

List of Figures
1.1 1.2 2.1 2.2 3.1 3.2 3.3 3.4 3.5 Comparison of a CHB system and an electromechanical brake (EMB) system on a passenger type car [1] . . . . . . . . . . . . . . . . . . . . Cross section of an MRB actuator design [34, 38] . . . . . . . . . . . Free body diagram of a wheel . . . . . . . . . . . . . . . . . . . . . . Friction coecient versus slip ratio for dierent road surfaces [41] . . Chosen MRB conguration based on the design criteria . . . . . . . . Dimensional parameters related to magnetic circuit design . . . . . . Four candidate designs . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetic circuit representation of the MRB . . . . . . . . . . . . . . B-H curve of a typical ferromagnetic material (L) and varying permeability of a ferromagnetic material with respect to applied magnetic eld intensity (R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hysteresis cycle of Steel 1015 simulated by Hodgdon Model [47] . . . B-H curve of Steel 1018 for initial magnetic loading . . . . . . . . . . Dierent seals on proposed MRB design . . . . . . . . . . . . . . . . Iron particle alignment without magnetic eld application . . . . . . Alignment of iron particles with magnetic eld application between non-ferromagnetic casing and shear disk (L) and ferromagnetic casing and shear disk (R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . Couette ow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental ow patterns developed by a rotating disk within a static enclosure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Velocity prole for a segment away from 0.12 m from the center of the disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Viscous torque versus the gap thickness of MR uid (at 60 kph) . . . Wire conguration in a coil . . . . . . . . . . . . . . . . . . . . . . . Surface plots with one (top) and two (bottom) rotating shear disks attached to the shaft . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 7 11 13 19 20 22 24

3.6 3.7 3.8 3.9 3.10

28 30 32 36 41

3.11 3.12 3.13 3.14 3.15 3.16

41 43 44 46 47 49 51

LIST OF FIGURES 3.17 Shear stress versus magnetic eld intensity for MRF-132DG (top) and MRF-241ES (bottom) . . . . . . . . . . . . . . . . . . . . . . . 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 Magnetic eld intensity distribution Plot generated by COMSOL . . Magnetic ux density plot generated by COMSOL . . . . . . . . . . . Process of computing the cost function for a random design . . . . . . MRB optimization process . . . . . . . . . . . . . . . . . . . . . . . . Optimum MRB design . . . . . . . . . . . . . . . . . . . . . . . . . . i) Magnetic eld intensity distribution and ii) Magnetic ux density within optimum MRB design . . . . . . . . . . . . . . . . . . . . . . Shear stress distribution within optimum MRB . . . . . . . . . . . . Braking torque generation simulation results . . . . . . . . . . . . . . MRB CAD model (L) and cross-section of the MRB CAD model with bearings, screw holes and seal beds (R) . . . . . . . . . . . . . . . . . MRB prototype (L) and coil assembly (R) . . . . . . . . . . . . . . . Picture of experimental setup . . . . . . . . . . . . . . . . . . . . . . Viscous torque versus velocity . . . . . . . . . . . . . . . . . . . . . . Torque (Tb ) versus current applied . . . . . . . . . . . . . . . . . . . . Torque (Th ) generated due to magnetic eld (without viscous and friction torques) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison between experimental and simulation results @ 200 rpm Simulation plot of braking torque (TH ) generated with respect to the number of disks (N ) (@ 1.8 A) . . . . . . . . . . . . . . . . . . . . . . An MRB with dierent magnetic circuit conguration (L) and corresponding simulation plot of braking torque (TH ) vs. applied currents (R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

54 58 59 61 65 67 68 69 70 72 73 75 78 80 81 81 83

84

List of Tables
1.1 2.1 2.2 3.1 3.2 3.3 3.4 4.1 4.2 5.1 5.2 Disadvantages of a CHB and the potential advantages of an EMB . . Parameters for the quarter car model . . . . . . . . . . . . . . . . . . Required braking torque values for dierent vehicles . . . . . . . . . . Examples of ferromagnetic and non-ferromagnetic materials Properties of SS304, STEEL 1018 and Al 6061-T1 . . . . . . Current densities for coils of wires with dierent sizes . . . . Properties of MRF-132DG and MRF-241ES . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 14 15 32 33 50 53 62 66 74 79

Inner diameters of wheels of dierent sizes . . . . . . . . . . . . . . . Optimum design parameters . . . . . . . . . . . . . . . . . . . . . . . MRB prototype specications . . . . . . . . . . . . . . . . . . . . . . Torque generated under various magnetic eld intensities . . . . . . .

xi

Nomenclature
A Aws dbrake f0 fs Ff FL Fn Fr g h hc g Hcore Hdisk Hgap HM RF i I Ie Iw Iy k kcon kT kW Kv l Cross-sectional area of medium [m2 ] Working surface area [m2 ] Outer diameter of MRB [m] Speed eect coecient Basic coecient Friction force [N ] Transfer of weight caused by braking [N ] Normal force [N ] Rolling resistance force [N ] Gravitational acceleration [ms2 ] MR uid gap thickness [m] Height of the center of gravity [m] Magnetic eld intensity on magnet core [A/m] Magnetic eld intensity on disk section [A/m] Magnetic eld intensity on electromagnet gap that includes Hdisk and HM RF [A/m] Magnetic eld intensity on MRF [A/m] Current applied to the coil [A] Total moment of inertia [kgm2 ] Engine inertia [kgm2 ] Wheels inertia [kgm2 ] Inertia of brake disks [kgm2 ] Linear coecient relates intensity to yield stressgenerated on MRF Thermal conductivity [W/m K] Weighting coecient for torque Weighting coecient for weight Conversion factor (m/s to mph) [mph(m/s)1 ] Length of medium [m]

NOMENCLATURE lbase Wheel base [m] lcore Length of magnet core [m] ldisk Length of total disk section [m] lgap Length of electromagnet gap that includes ldisk and lM RF [m] lM RF Length of total MRF section [m] mt Quarter vehicle mass [kg] mv Vehicle mass [Kg] mw Wheel mass [Kg] n Number of wire turns in coil N Number of disks Q Heat transferred [Cal] r Radius of shear disk [m] rz &rj Outer and inner radii of the shear disk [m] Rw Wheel Radius [m] sr Slip ratio S Heat transfer surface [m2 ] T Magnetic torque generated in MRB, i.e. TH [N m] T Temperature gradient [K/m] T Viscous torque [N m] Tb Braking torque [N m] TH Torque generated due to applied eld [N m] Tref Reference torque value [N m] u Linear uid velocity [m/s] w Angular velocity [rad/s] W Weight of MRB [N ] Wref Reference weight value [N ] x Horizontal distance travelled [m] x Linear velocity, [m/s] x Linear acceleration [m/s2 ] y Vertical distance [m] d Dimensional design parameters vector B Magnetic ux density vector [T ] D Electric displacement [C/m2 ] E Electric eld intensity [N/C] J Current density vector [A/m2 ] H Magnetic eld intensity vector [A/m]

xii

NOMENCLATURE

xiii

Greek Symbols
f p r 0 H Angular acceleration [rad/s2 ] Angular Distance [rad] Electric charge density [C/m3 ] Friction coecient Gear ration Magnetic permeability [H/m] Magnetic reluctance [turns/H] Plastic viscosity [kg/m.s] Power coecient that relates intensity to yield stressgenerated on MRF Relative magnetic permeability Shear rate [Hz] Total shear stress [P a] Vacuum permeability [H/m] Yield stress of MRF due to applied eld [P a]

Acronynms
ABS AISI AWG CAD CHB EMB EPB FEA FEM LB mmf MR MRB MRF PID SA SQP UB VSC Anti-lock Brake System American Iron and Steel Institute American Wire Gauge Computer Aided Design Conventional Hydraulic Brake Electro-Mechanical Brake Electronic Parking Brake Finite Element Analysis Finite Element Model Lower Boundary Magnetomotive Force Magnetorheological Magnetorheological Brake Magnetorheological Fluid Proportional-Integral-Derivative Simulated Annealing Sequential Quadratic Programming Upper Boundary Vehicle Stability Control

xiv

Acknowledgements
I would like to thank Dr. Edward Park and Dr. Afzal Suleman for giving me the opportunity to be a part of their research team. Also, I would like to thank them for sharing their academic expertise and life experience with me. Special appreciation to Patrick Chang for the help in setting up the experiment. His eort, availability, patience and know-how were very valuable. Special thanks to Rodney Katz and Ken Begley for the help with the machining of the parts and for helping me to gain valuable experiences in terms of manufacturing processes and drawings. I also thank Casey Keulen for his help in understanding the existing experimental setup at the beginning of my program. I give thanks to Luis Falco da Luz for his previous work with the experimental setup and Dilian Stoikov for his previous work related to control. I would also like to thank Sandra Makosinski for all the help and sincerity. Thanks for always being there when I needed help. Also, I would like to express my appreciation to Art Makosinski for his logistic support and for sharing his immense practical knowledge. Special thanks to Kelly Sakaki and Dan Kerley. They made me feel like a Canadian and made the lab a pleasant place to work. I also thank to Jung Keun Lee, William Liu, Vishalini Bundhoo, Ricardo Paiva, Andre Carvalho, Casey Keulen, Adel Younis and others for their friendship. I would like to express my gratitude to Dr. Mehmet Yildiz, for his innite support, help and encouragement. I thank Kerem Gurses for accompanying me in this journey. It has been my pleasure to share the same apartment and the same name. I also thank Dr. Emre Karakoc, my brother, for his support and directions. He

xv was the one who oered me to apply for a Masters position at UVic. I thank him for helping me to set my future goals by sharing his experience in life with me. A nal word of gratitude has to go to my parents for their continuous support and faith in me. I know there is no way to repay my debt, but all I can do is to make them proud. Without their support and love, I would not be able to succeed.

xvi

To my family...

Chapter 1 Introduction
Automotive industry is changing everyday. Billions of dollars are invested in research and development for building safer, cheaper and better performing vehicles. One such investment is the x by wiretopic which has been introduced to improve the existing mechanical systems on automobiles. This term means that the mechanical systems in the vehicles can be replaced by electromechanical systems that are able to do the same task in a faster, more reliable and accurate way than the pure mechanical systems. This thesis work is concerned with the topic of braking in the vehicles. Nowadays, conventional hydraulic brakes (CHB) are being used in order to provide the required braking torque to stop a vehicle. This system involves the brake pedal, hydraulic uid, transfer pipes and brake actuators (disk and drum brakes). When the driver presses on the brake pedal, the hydraulic brake uid provides the pressure in the brake actuators that squeezes the brake pads onto the rotor. The basic block diagram of this type of brake is shown in Figure 1.1 (right). However, the CHB has a number of disadvantages. First of all, when the driver

CHAPTER 1. INTRODUCTION

Figure 1.1: Comparison of a CHB system and an electromechanical brake (EMB) system on a passenger type car [1]

CHAPTER 1. INTRODUCTION

pushes the pedal, there is a latency in building up the pressure necessary to actuate the brakes. Also, since CHBs employ a highly pressurized brake uid, there is the possibility of leakage of the brake uid that would cause fatal accidents, and this uid is harmful to the environment as well. Another problem seen in CHBs is that this type of brake uses the friction between brake pads and the brake disk as its braking mechanism, leading to the brake pad wear. Due to both the material wear and the friction coecient variation in high speeds, the brake performs less optimally in high speed region, as well as with the increased number of usage cycles. Thus, the brake pads must be changed periodically in order to get the optimum braking performance. Finally, another disadvantage of this type of brake system is that it is bulky in size, when both auxiliary components and brake actuators are considered. Nowadays in addition to the use of the CHB, pneumatically actuated drum brakes (i.e. air brakes) are being used for trucks and other heavy vehicles that need more braking torque. Similar to the CHB, in this type of brake, pneumatic pumps and pipes are used to transfer the air pressure to the brake actuators. However, with the introduction of x by wire technologies, electromechanical brakes (EMB) have appeared in the industry. In this conguration, some of the pure mechanical components of the conventional brakes are replaced by electromechanical components. Figure 1.1 (left) shows a typical EMB system. A simple example of such brake system is the drum brakes used in trailers where less braking torque is required. These brakes are actuated by an electromagnet installed in the drum brake instead of a hydraulic mechanism that attracts a magnetic rotating disks onto a stator. The friction generated between the stator and the rotor results in braking. Electric calipers developed by Continental [1] and Delphi [2] are also examples where the hydraulic actuators are replaced with electromechanical ones. There are also eddy

CHAPTER 1. INTRODUCTION

current retarders being used for trucks, buses, trains and garbage collectors. This type of brake basically works in conjunction with the main hydraulic brakes, in order to decrease the braking load [3]. Eddy current brakes [4, 5, 6, 7] cannot be used alone due to their performance loss (i.e. low braking torque generation) in the low speed region. In Table 1.1, the disadvantages of a CHB and the potential advantages of an EMB are listed.

Table 1.1: Disadvantages of a CHB and the potential advantages of an EMB Disadvantages of CHB The Potential Advantages of EMB - Slow response due to - Faster response pressure build-up - Control that requires additional - Easy implementation of control electrical components systems - Signicant Weight of the - Reduced number of components overall system and wiring - Brake pad wear - Less maintenance due to elimination of pads - Risk of environmentally - Elimination of hazardous hazardous brake uid leakage brake uid - Simple software-based brake parameter adjustment depending on the driving conditions

In this thesis work, an EMB based on magnetorheological uids (MR uid or MRF), i.e. a magnetorheological brake (MRB), is presented. MRB is a friction based brake like a CHB. However, the method of the friction generation in an MRB is entirely dierent. In the CHB, when the braking pressure is applied, the stator and rotor surfaces come together and friction is generated between the two surfaces, resulting in the generation of the braking torque. But in the MRB, MRF is lled between the stator and the rotor, and due to controllable rheological characteristics

CHAPTER 1. INTRODUCTION of the MRF, shear friction is generated (thus the braking torque).

MR uids are created by adding micron-sized iron particles to an appropriate carrier uid such as oil, water or silicon. Their rheological behavior is almost the same as that of the carrier when no external magnetic eld is present. However, when exposed to a magnetic eld, the iron particles acquire a dipole moment aligned with the applied magnetic eld to form linear chains parallel to the eld [8, 9]. This reversibly changes the liquid to solid-like that has a controllable yield strength, which its magnitude depends directly on the magnitude of the applied magnetic eld. There is a number of companies producing MR uids, e.g. Lord Corporation, for various applications such as clutches, dampers, brakes, as well as for medical and seismic applications. Although the studies on MRFs started around the late 1800s and early 1900s, the rst relevant patent was issued to Jacob Rabinow [10, 11] in 1940s [12]. The interest in MR technology rose in the late 1980s and since then, a number of commercial and research devices have appeared: e.g. hydraulic systems [13], damping systems and seismic devices [14, 15, 16, 17, 18], clutches [10, 19, 20], prosthetic devices [21, 22], haptic devices [23], cancer treatment equipments [24] and exercise equipments [25, 26]. Also, a study on possible applications of MRF devices was done by Carlson et al. in [27]. The main contribution of this thesis work is the development of a new MRB conguration for automotive application. The MRB is a pure electronically controlled actuator and as a result, it has the potential to further reduce the braking time (thus, braking distance), as well as easier integration of existing and new advanced control features such as anti-lock braking system (ABS), vehicle stability control (VSC), electronic parking brake (EPB), etc. (see Table 1.1). The idea of using the friction generated by aligned magnetic materials under

CHAPTER 1. INTRODUCTION

magnetic eld in brakes was rst introduced by Eddens [28, 29, 30]. He devised a brake which contains small magnetic particle powder and when magnetic eld is applied, the powder aligns in the direction of applied magnetic eld and generates a resistance against motion. With the subsequent introduction of MRFs, the dry magnetic particle powder has been replaced by these uids as the source of friction for braking purposes. The literature presents a number of MRF based brake designs, e.g. [31, 32, 33, 34, 35], and modeling, design, optimization and control issues of MRBs were also considered in a few previous works [34, 36, 37, 38]. The basic conguration of a MRB proposed by Park et al. [34] for the automotive application is shown in Figure 1.2. In this conguration, a rotating disk (3) is enclosed by a static casing (5), and the gap (7) between the disk and casing is lled with the MR uid. A coil winding (6) is embedded on the perimeter of the casing and when electrical current is applied on the coil, due to the generated magnetic elds, the MR uid in the gap becomes solid-like instantaneously. The shear friction between the rotating disk and the solidied MR uid provides the required braking torque. Unlike previous works, in this work, a new MRB is designed with a focus on magnetic circuit design and material selection.

1.1

Thesis Objective

The main objective of this thesis is to develop an MRB specically for automotive application, with the potential advantages listed in Table 1.1. Within this main objective, the thesis has the following sub-objectives: 1. Creating an accurate electromagnetic nite element model (FEM) of the MRB that simulates the braking behavior;

CHAPTER 1. INTRODUCTION

Figure 1.2: Cross section of an MRB actuator design [34, 38]

CHAPTER 1. INTRODUCTION

2. Selection of proper materials for the MRB with adequate structural, thermal and magnetic properties; 3. Detailed design of the MRB with considerations to sealing and cooling as well as applied current density, viscous torque generation and the number of shear disks; 4. Optimization of the magnetic circuit in the MRB for higher braking torque capacity; and 5. Validation of the nite element simulations with an experimental prototype.

1.2

Thesis Outline

In Chapter 2, the dynamic model of a typical passenger vehicle is introduced and the braking torque requirements are calculated for dierent vehicles (i.e. a fully loaded car, a sport motorbike and a scooter). After the required braking torque values are obtained, the analytical model of an MRB is presented. The behavior of MR uid is modeled using the Bingham plastic model. Then, by using this model, the total braking torque generated is analytically described in terms of the magnetic eld intensity applied and the viscosity of the uid. In Chapter 3, the design process of an MRB is explained in detail. The proposed MRB is designed considering the design criteria such as the number of disks used, the dimensional design parameters, the materials used and the conguration of the magnetic circuit. There are also some additional practical considerations that are included during the design process, e.g. sealing of the MR uid, cooling the MRB and the viscous torque generated within the MRB due to MR uid viscosity. However, the main focus of the design process is on magnetic circuit design and material selection.

CHAPTER 1. INTRODUCTION

In this chapter, corresponding dimensional design parameters are introduced and the MRB that is designed in detail according to the above design criteria is presented. In Chapter 4, in order to calculate the total braking torque generation, a FEM of the MRB is created solving the magnetic eld intensity distribution within the brake. A commercial FEA software package, Comsol Multiphysics , is used for this purpose. Then, the MRB is optimized for higher braking torque and lower overall weight using the FEM created. An optimization problem is dened and proper search methods are selected to solve for optimal torque and weight. At the end of this chapter, an optimum MRB design is found and presented, with the optimum dimensional design parameter. Then, the magnetic eld intensity, the magnetic ux density and the shear stress distribution plots of the optimum design are shown. Finally, using the FEM, the braking torque generation is simulated at various current values applied to the coil. Chapter 5 presents the experimental results. A CAD model of the optimized MRB is generated using a 3-D CAD software, Pro/E. In order to verify the simulation results obtained in the previous chapter, a prototype made based on the CAD model. Then, the prototype is mounted on an experimental test-bed, which consists of a torque source (i.e. servo motor) and a torque sensor. Braking torque generation at various applied currents is recorded and a comparison between the simulation results and the experimental results is made. At the end of this chapter, some concluding remarks are presented comparing the results obtained and the original design requirements. The conclusions of this work are presented in Chapter 6. In addition, possible improvements that can be made in order to design a higher torque MRB are discussed here as part of future works.

10

Chapter 2 Modeling of MR Brake

As mentioned in the previous chapter, a magnetorheological brake (MRB) is proposed in this work as a possible substitute for CHBs. In this chapter, before modeling the MRB, the vehicle dynamics are studied in order to calculate the required amount of braking torque for stopping a vehicle. Then, required braking torque values of different vehicles are calculated using the dynamic vehicle model. Finally, an analytical model of the MRB itself, required to obtain the braking torque generation, is derived.

2.1

Vehicle Dynamics

In this work, the motion of a vehicle is described using the quarter vehicle model [39]. This model is needed to calculate the required braking torque that a brake should provide. The basic assumption of this model is that the mass of the vehicle is divided equally between four wheels. In Figure 2.1, a free body diagram of a wheel rotating clockwise is shown. During braking, a torque is applied by the brake, Tb , and Fr , Ff , Fn and FL are the rolling resistance force, the friction force, normal force and the

CHAPTER 2. MODELING OF MR BRAKE

11

transfer of weight caused by braking of the vehicle. Lets denote I as the total mass moment of inertia and is the angular acceleration of the vehicle. The radius of the wheel is Rw and x is the distance traveled by the vehicle.

Figure 2.1: Free body diagram of a wheel

According to the quarter vehicle model, the mass that the wheel carries can be calculated as: 1 mt = mv + mw 4 (2.1)

where mv is the mass of the vehicle and mw is the mass of the wheel. The total mass moment of inertia can be dened dened by: 1 I = Iw + 2 Ie + Iy 2 (2.2)

CHAPTER 2. MODELING OF MR BRAKE

12

where Iw is the wheels inertia, Ie is the engine inertia, is the gear ratio and Iy is the inertia of the brake disks. The eective inertia of the engine, 2 Ie , is divided by 2 in order to account for the distribution of the inertia of the engine to each of the driving wheels. The rolling resistance force against the motion of the wheel is dened as [39]: Fr = f0 + 3.24fs (Kv x)2.5 (2.3)

where Kv is a conversion factor that is used for converting the speed value from m/s to mph, fs and f0 are the basic coecient and the speed eect coecient. This equation was developed by the Institute of Tech. in Stuttgart for rolling on a concrete surface [40]. The friction force acting on the wheel is dened in terms of the normal force and the friction coecient between the tire and the surface, i.e. Ff = f Fn Fn = mt g mv hcg x = mt g FL lbase (2.4) (2.5)

where lbase is the wheel base and hcg is the height of the center of gravity and the friction coecient, f , is a function of the slip ratio, sr , which is the relative proportion of the rolling to slipping, i.e. sr = x Rw w x (2.6)

where w is the angular velocity of the wheel. The correlation between the slip ratio and the coecient of friction is illustrated in Figure 2.2 for dierent types of surfaces.

CHAPTER 2. MODELING OF MR BRAKE

13

Figure 2.2: Friction coecient versus slip ratio for dierent road surfaces [41]

CHAPTER 2. MODELING OF MR BRAKE Finally, the equations of motion for the wheel can be written as: mt x = Ff = f mt g + f mv hcg x lbase

14

(2.7) (2.8)

I = Tb + Rw Ff Rw Fr = Tb + f Rw Fn Rw Fr

Eq (2.7) is the force equilibrium equation in the direction of motion and Eq. (2.8) is the moment equilibrium equation around the wheel axis. Then, the required braking torque, Tb , can be found by solving these two equations.

2.1.1

Required Braking Torque Calculation

In this section, required braking torque values for various vehicles were calculated using the above dynamic model of the vehicle. However, in order to solve for the braking torque, the parameters in the equations have to be known. These parameters were taken from Will et al. [42] and are listed in Table 2.1.

Table 2.1: Parameters for the quarter Wheel Radius Wheel Base Center of Gravity Height Wheel Mass 1/4 of the Vehicle Mass Total Moment of Inertia of Wheel and Engine Basic Coecient Speed Eect Coecient Scaling Constant

car model Rw 0.326 m lbase 2.5 m hcg 0.5 m mw 40 kg mv /4 415 kg It 1.75 kg.m2 fo 10e-2 fs 0.005 Kv 2.237

Approximate required braking torque values for a sport motorbike and a scooter were also calculated. Due to the lack of information on some property values (i.e. f0 ,

CHAPTER 2. MODELING OF MR BRAKE

15

fs and Kv ), the braking torque requirement for these vehicles were calculated assuming that the whole kinetic energy of the vehicle is dissipated in the brake actuators. With such an assumption, the eects of rolling friction and the friction between the tire and the road were omitted. In Table 2.2, the data used for the required braking torque calculations are summarized.

Table 2.2: Required braking torque values for dierent vehicles Properties Passenger Vehicle Sport Motorbike Scooter Mass (Total-loaded) (kg) 1820 (mw = 40) 370 250 Wheel Size (inch) 13 17 12 Wheel Radius (m) 0.3226 0.305 0.237 Number of Brake Actuators 4 2 2 Assumptions: Road Surface Dry, smooth concrete Initial Speed 60 mph (26.82 m/s) Deceleration (m/s2 ) 5.8 m/s2 Braking Torque (Nm) 560 321 171

The above study was carried out in order to determine the braking torque that a comparable MRB should generate. Table 2.2 gives us an idea about how much braking torque must be generated by an MRB.

2.2

Analytical Model of MR Brake

In order to model an MRB, the behavior of the MR uid under magnetic eld application has to be modeled. The idealized characteristics of the MR uid can be described eectively by using the Bingham-Plastic Model [8, 36, 43, 44, 45]. According to this

CHAPTER 2. MODELING OF MR BRAKE model, the total shear stress is: = H sgn( ) + p

16

(2.9)

where H is the yield stress due to applied magnetic eld intensity, p is the no-eld plastic viscosity of the uid and is the shear rate. The rst term in the right side of the equation is a magnetic term related to the applied magnetic eld intensity whereas the second term is a viscous term related to the viscosity of the MR uids. The use of the sgn function guarantees that the magnetic term will always be added to the viscous term no matter what the direction of the shear rate is. Then, using Eq. (2.9), the braking torque can be dened as follows for the geometry shown in Figure 1.2: Tb =
Aws z

rdAws = 2N
j

(H sgn( ) + p )

(2.10)

where Aws is the working surface area (the domain where the uid is activated by applied magnetic eld intensity), z and j are the outer and inner radii of the disk, N is the number of disks used in the enclosure and r is the radius of the disk. If the MR uid gap in Figure 1.2 is very small (i.e. gap thickness << radius of the disk), the shear rate can be obtained by: = rw h (2.11)

which assumes linear uid velocity distribution across the gap and no slip conditions. In Eq. (2.11), w is the angular velocity of the disk and h is the thickness of the MR uid gap. In Eqs. (2.9) and (2.10), the yield stress, H , can be approximated in terms of the magnetic eld intensity applied specically onto the MR uid, HM RF , and the

CHAPTER 2. MODELING OF MR BRAKE constant parameters, k and , i.e.

H = kHM RF

17

(2.12)

where the parameters can be calculated using the shear stress versus applied magnetic eld intensity plot published in the specs of the MR uid. The MR uid selection and detailed information about the selected MR uid will be discussed in Sec. 3.10. By substituting Eqs. (2.11) and (2.12), the braking torque equation in Eq. (2.10) can be rewritten as:
z

Tb = 2N
j

(kHM RF sgn( ) + p

rw 2 )r dr h

(2.13)

Then, Eq. (2.13) can be divided into the following two parts:
z

TH = 2N
j

(kHM RF sgn( ))r2 dr

(2.14)

T =

4 4 N p w(rz rj ) 2h

(2.15)

where TH is the torque generated due to the applied magnetic eld and T is the torque generated due to the viscosity of the uid. Since the magnetic eld intensity distribution within the MRB is a function of the radius, the results of the integrations cannot be simplied. Then, nally, the total braking torque is Tb = T + TH . From the design point of view, the parameters that can be varied to increase the braking torque generation capacity are: the number of disks (i.e. N ), the dimensions and conguration of the magnetic circuit (i.e. rz , rj , and other dimensional design parameters shown in Figure 3.2), and HM RF , which is related to the applied current density in the electromagnet and materials used in the magnetic circuit.

18

Chapter 3 Design of MR Brake

In this chapter, the proposed MRB is designed considering the design parameters addressed at the end of the previous chapter (see Sec. 2.2). There are also some additional practical considerations that are included during the design process, e.g. sealing of the MR uid, cooling the MRB and the viscous torque generated within the MRB due to MR uid viscosity. Below, the main design criteria considered for the brake are listed, which will be discussed in detail in the subsequent subsections: 1. Magnetic Circuit Design 2. Material Selection 3. Sealing 4. Cooling 5. Working Surface Area 6. Viscous Torque Generation

CHAPTER 3. DESIGN OF MR BRAKE 7. Applied Current Density 8. Additional Disks attached to the shaft 9. MR Fluid Selection

19

Amongst the various design criteria, the main focus of our design process is on the magnetic circuit design and material selection. Note that Figure 3.1 shows the cross section of the basic MRB conguration which is improved according to the listed design criteria. This is the conguration that will be considered for nite element analysis and design optimization in the subsequent chapter. The corresponding dimensional design parameters are shown in Figure 3.2.

Figure 3.1: Chosen MRB conguration based on the design criteria

Before explaining the above design criteria in detail, a brief discussion on the conceptual design selection procedure, which led to the selection of the basic conguration

CHAPTER 3. DESIGN OF MR BRAKE

20

Figure 3.2: Dimensional parameters related to magnetic circuit design

CHAPTER 3. DESIGN OF MR BRAKE presented in Figure 3.1, is given in Sec. 3.1.

21

3.1

Conceptual Design Selection

The selected basic conguration of the proposed MRB is presented in Figure 3.1. This selection was made amongst the four candidate conceptual designs shown in Figure 3.3. In this gure, the rst design (a) is the selected design with the electromagnet coil embedded into the stator. The second one (b) is slightly dierent from the rst one in terms of the coil cross-sectional area. Unlike (a), the magnetic eld intensity generation is increased by increasing the area occupied by the coil is installed. However, this design does not have a magnetic ux focus region and the intensity is generated mostly due to coil eld. The third one (c) is a totally dierent design from the others with the coil installed on the rotating shear disk. Last one (d) is another design with a dierent magnetic circuit conguration and magnetic focus region. Unlike the others, this design has two separate coil regions, where the coils are wound around the C-shaped magnetic part used to focus the magnetic ux on both sides. Based on our initial analysis (using FEA), the design (c) is the one that can generate the most braking torque. However, since the coil is installed on the rotating shear disk, it can not be easily manufactured. Therefore, the rst design, (a), whose cross-section was shown in Figure 3.1, was selected mainly due to manufacturability.

3.2

Magnetic Circuit Design

The main goal of the magnetic circuit analysis performed in this work is to direct the maximum amount of the magnetic ux generated by the electromagnet onto the MR

CHAPTER 3. DESIGN OF MR BRAKE

22

Figure 3.3: Four candidate designs

CHAPTER 3. DESIGN OF MR BRAKE

23

uid located in the gap. This will allow the maximum braking torque to be generated. As shown in Figure 3.4, the magnetic circuit in the MRB consists of the coil winding in the electromagnet, which is the magnetic ux generating source (i.e. by generating magnetomotive force or mmf ), and the ux carrying path. The path provides resistance over the ux ow, and such resistance is called reluctance (). Thus, in Figure 3.4, the total reluctance of the magnetic circuit is the sum of the reluctances of the core and the gap, which consists of the MR uid and the shear disk (see Figure 3.1). Then, the ux generated () in a member of the magnetic circuit in Figure 3.4 can be dened as: = where: = l A (3.2) mmf ni = (3.1)

In Eq. (3.1), n is the number of turns in the coil winding and i is the current applied; in Eq. (3.2), is the permeability of the member, A is its cross-sectional area, and l is its length. Recall that in order to increase the braking torque, the ux ow over the MR uid needs to be maximized. This implies that the reluctance of each member in the ux path of the ux ow has to be minimized according to Eq. (3.1), which in turn implies that l can be decreased or/and and A can be increased according to Eq. (3.2). However, since the magnetic ux in the gap (gap ) and in the core (core ) are dierent, the magnetic uxes cannot be directly calculated as the ratio between the mmf and the total reluctance of the magnetic circuit. Note that magnetic ux can

CHAPTER 3. DESIGN OF MR BRAKE

24

Figure 3.4: Magnetic circuit representation of the MRB

CHAPTER 3. DESIGN OF MR BRAKE be written in terms of magnetic ux density B: =

A

25

B ndA =
A

H ndA

(3.3)

where n is the normal vector to the surface area A. Eq. (3.3) implies that the magnetic ux is a function of the magnetic eld intensity as well as and A of the member. Note that H in Eq. (3.3) can be obtained by writing the steady-state Maxwell-Amperes Law (see Eq. 4.1) in an integral form, i.e. |H| dl = ni (3.4)

which implies that H depends on the mmf (or ni ) and l of the member. Since maximizing the ux through the MR uid gap is our goal, Eq. (3.4) can be rewritten as: |HM RF | dlM RF = ni |Hcore | dlcore |Hdisk | dldisk (3.5)

where |Hcore |, |Hdisk | and |HM RF | are the magnitudes of eld intensity generated in the magnet core, shear disk and MR uid respectively and lcore , ldisk , and lM RF are the length/thickness of the corresponding members. In Eq. (3.5), the negligible losses due to the surrounding air and non-magnetic parts are omitted. Hence, in order to maximize the ux through the MR uid, the magnetic circuit should be optimized by properly selecting the materials (i.e. ) for the circuit members and their geometry (l and A).

CHAPTER 3. DESIGN OF MR BRAKE

26

3.3

Material Selection

The material selection is a critical part of the MRB design process. Materials used in the MRB have crucial inuence on the magnetic circuit (i.e. determines ) as well as the structural and thermal characteristics. Here, the material selection issue is discussed in terms of the (i) magnetic properties, (ii) structural properties and (iii) thermal properties.

3.3.1

Magnetic Properties of Materials

Before starting the discussion on the material selection for the proposed MRB, the background information regarding the magnetic characteristics of materials is rst given here [46]. The main parameter that denes a materials magnetic characteristics is its permeability (). It is the ratio between the applied magnetic eld intensity (H ) and magnetic ux density (B ) due to H through the material (See Eq. (3.6)). It is the ability of the material to transfer magnetic ux over itself. In the literature, relative permeability (r ), which is the ratio between the materials permeability and vacuums permeability (i.e. 0 = 4 10(7) H/m ), is commonly used (see Eq. 3.7). Throughout this thesis, whenever the permeability of a material is mentioned, it refers to its relative permeability. B = H B = r 0 H (3.6) (3.7)

Materials are classied in three groups according to their permeability values: i) ferromagnetic materials, ii) paramagnetic materials and iii) diamagnetic materials. Materials that are strongly attracted by the applied magnetic eld are ferromagnetic materials. They have permeabilities of higher than 1. Iron, nickel, cobalt and many

CHAPTER 3. DESIGN OF MR BRAKE

27

alloys of these three materials are examples of ferromagnetic materials. The materials that are attracted weakly by the applied magnetic eld are paramagnetic materials and their permeabilities are close to 1, most of the paramagnetic materials have permeabilities between 1 and 1.001. Many salts of iron, rare earth families, platinum and palladium metals, sodium, potassium, oxygen and the ferromagnetic materials above the Curie point1 are examples of paramagnetic materials. Note that the permeabilities of the above materials are either independent of temperature or decrease with the increasing temperature. The last group of materials is the diamagnetic materials, which are repelled by the applied magnetic eld. These materials have a tendency to move toward the weaker eld. They have permeabilities smaller than 1. Many of the metals and non-metals other than those mentioned above as examples of the other two categories belong to this group. In this thesis, the main focus will be on ferromagnetic materials and the term non-ferromagneticwill be used to imply the diamagnetic and paramagnetic materials. When a ferromagnetic material is brought closer to a magnetic eld source (i.e. a permanent magnet, electromagnet or a current carrying wire), the induced magnetization (B ) on the materials can be dened as a function of applied magnetic eld (H ) and the proportionality coecient is the magnetic permeability of the material (see Eq. 3.6). In Figure 3.5-(L), a B-H curve is shown for a typical ferromagnetic material and in Figure 3.5-(R), the change of magnetic eld permeability of a ferromagnetic material with increasing applied magnetic eld intensity is illustrated. As can be seen from Figure 3.5-(R), permeability is not a constant, but varies with increasing magnetic eld intensity. Figure 3.5-(L) shows that as H increases, B approaches to a nite limit due to saturation. This can also be seen in Figure 3.5-(R)
A ferromagnetic material property that is the temperature above which it loses its characteristic ferromagnetic ability
1

CHAPTER 3. DESIGN OF MR BRAKE

28

Figure 3.5: B-H curve of a typical ferromagnetic material (L) and varying permeability of a ferromagnetic material with respect to applied magnetic eld intensity (R)

CHAPTER 3. DESIGN OF MR BRAKE

29

as the permeability value converges to that of the vacuum. Thus, once the saturation ux density is reached a ferromagnetic material behaves as a paramagnetic material with permeability close to 1. In addition to the change with the applied magnetic eld intensity, permeability of a ferromagnetic material is also a function of temperature too. It decreases with increasing temperature and also materials lose their magnetic properties after a nite temperature is reached, which is called the Curie Point. Whenever a material is heated up to its curie temperature, its permeability will converge to 1, thus it will behave as a paramagnetic material. For instance, the curie point of iron is around 770. Figure 3.5-(L) also shows another characteristic of ferromagnetic materials known as magnetic hysteresis. When a ferromagnetic material is magnetized in one direction, it does not relax back to its initial starting point after the magnetizing eld is removed. Figure 3.6 shows the B-H curve of AISI 1015, low carbon steel, modeled using Hodgdon Model [36, 47]. Magnetic ux generation will grow towards the saturation value through curve 1. If the applied eld intensity is subsequently decreased, the ux generation will follow curve 2. When the intensity is zero, magnetic ux has a positive value, which is a residual ux on the material. When the intensity is again reversed, point (a) is reached where residual magnetic eld is zero. In addition to these characteristics, when a ferromagnetic material is magnetized by an external eld, its ends carry magnetic poles which cause a magnetic eld within the material in the opposite direction of the applied eld. Thus, these elds are called demagnetizing elds. Also when magnetic eld is applied, the dimensions of the material changes too, however it does not exceed a few parts per million. This behavior of ferromagnetic materials is called magnetorestriction. Finally, magnetic properties of single crystal materials changes with the direction of measurement,

CHAPTER 3. DESIGN OF MR BRAKE

30

Figure 3.6: Hysteresis cycle of Steel 1015 simulated by Hodgdon Model [47]

CHAPTER 3. DESIGN OF MR BRAKE

31

which is referred as magnetic anisotropy. In many materials, methods of fabrication such as rolling cause regularity in the orientations that will cause anisotropy. Because of highly non-linear magnetic characteristics of ferromagnetic materials due to hysteresis cycle, saturation, demagnetizing elds, magnetorestriction and magnetic anisotropy, it is hard to measure magnetic properties of a ferromagnetic material accurately and, in general, expensive and highly sensitive equipment is required for such measurements [48].

3.3.2

Selection According to Magnetic Properties

As discussed in the previous section, permeability () of a ferromagnetic material is highly nonlinear and varies with temperature and applied magnetic eld intensity (e.g. saturation and hysteresis). In Table 3.1, a few candidate examples of ferromagnetic and non-ferromagnetic materials are listed. As for ferromagnetic materials, there is a wide range of alloy options [48] that are undesirably costly for the automotive brake application. Therefore, a more cost-eective material with required permeability should be selected. In addition, since it is dicult to accurately measure the permeability of materials, in this work, only materials with known properties were considered as possible candidates. Considering the cost, permeability and availability, a low carbon steel, AISI 1018 was selected as the magnetic material in the magnetic circuit (i.e. the core and disks). Corresponding B-H curve of Steel 1018 with the saturation eect is shown in Figure 3.7.

CHAPTER 3. DESIGN OF MR BRAKE

32

Table 3.1: Examples of ferromagnetic and non-ferromagnetic materials Ferromagnetic Non-Ferromagnetic Materials (r > 1.1) Materials (r < 1.1) Alloy 225/405/426 Aluminum Iron Copper Low Carbon Steel Molybdenum Nickel Platinum 42% Nickel Rhodium 52% Nickel 302-304 Stainless Steel 430 Stainless Steel Tantalum Titanium
r is the relative permeability

Figure 3.7: B-H curve of Steel 1018 for initial magnetic loading

CHAPTER 3. DESIGN OF MR BRAKE

33

3.3.3

Selection According to Structural Properties

In terms of structural considerations, there are two critical parts of MRB that must be considered: the shaft which carries the brake and transfers the torque generated by the MRB, and the shear disk where the braking torque is generated. The shaft should be non-ferromagnetic in order to keep the ux far away from the seals that enclose the MR uid (to avoid from MR uid being solidied in the vicinity of the seals, see Sec. 3.4 for details). From Table 3.1, it can be easily seen that for the shaft, 304 stainless steel is a suitable material due to its high yield stress and availability. For the shear disk material, low carbon steel was selected since it is a part of the magnetic circuit and its yield stress is high. Since the remaining parts are not under any considerable loading, the choice of material selection in terms of structural considerations is very exible. In Table 3.2, the properties of 304 stainless steel and 1018 low carbon steel are shown.

Table 3.2: Properties of SS304, STEEL 1018 and Al 6061-T1 Property Composition SS304 Cr-18/20%, Ni-8/10.5%, Mn-2%, Si-1%, C-0.08%, P and S Tensile Strength (MPa) 515 Yield Strength (MPa) 205 Hardness Rockwell B 88 Density (kg/m3 ) 8000 Modulus of Elasticity (GPa) 193 Thermal Conductivity (W/m-K) 16.2 Specic Heat (J/kg-K) 500 STEEL 1018 Al T-6061 C-0.15/0.2%, Mg-0.8/1.2%, Mn-0.6/0.9%, Si-0.4/0.8%, P and S Cu-0.15/0.4%, Fe, Cr, Ti and Zn 634 124 386 55.2 197 30 7700-8030 2700 190-210 68.9 51.9 180 486 896

CHAPTER 3. DESIGN OF MR BRAKE

34

3.3.4

Selection According to Thermal Properties

Another factor that makes the material selection an important step is the thermal properties of the materials. Due to the temperature dependent permeability values of the ferromagnetic materials and the MR uid viscosity, heat generated in the actuator should be removed as quickly as possible. In order to understand the heat ow, Eq. (3.8) below which is the law of conduction, Fouriers Law, is briey considered. This equation is a constitutive equation that depends on the thermal conductivity kcon : Q = kcon t T dS (3.8)

where Q is the heat transferred, T is the temperature gradient between the ambient and heat source and S is the area where the heat ows through. According to Eq. (3.8), in order to increase the rate of heat transfer from the MRB, the ambient temperature can be lowered which will increase temperature gradient, T . In order to decrease the ambient temperature, a cooling mechanism should be introduced. Possible mechanisms that can be used for heat removal from the brake will be discussed in Sec. 3.5. In addition, in terms of thermal considerations, in order to increase the heat removal from the MRB, a material with high conductivity and high convection coefcient has to be selected as the material used for the non-ferromagnetic brake components. Aluminum (Al 6061-T1) is a good candidate material based on the thermal considerations. In Table 3.2, thermal properties of stainless steel 304, low carbon steel 1018 and Al 6061-T1, which are the materials that were selected to be used in the MRB prototype, are presented.

CHAPTER 3. DESIGN OF MR BRAKE

35

3.4

Sealing

Sealing of the MRB is another important design criterion. Since the brake employs an MR uid, it has to be sealed properly against a possible leakage, which will cause the loss of braking. Because MR uids are highly contaminated due to iron particles which makes sealing a critical issue. In addition, in the case of the dynamic sealing required between the static casing and the rotating shaft, there is a greater possibility of sealing failure when the MR uid is repetitively solidied (due to the repetitive braking) around the vicinity of the seals. In order to decrease the risk of sealing failure, the dynamic seals have to be kept away from the magnetic circuit in the brake. This will decrease the magnetic eld intensity that is generated in the vicinity of the seals during braking, thus avoiding the on/o cycle of the MR uid. Also, since the uid is contaminated, surface nishes and the sealing method itself are of a great importance. In this work, the dynamic seals were kept away from the magnetic circuit by introducing a non-ferromagnetic shaft and shear disk support outside the circuit which holds the magnetic shear disks (see Figure 3.1). Also the surface nishes were improved and the tolerances were kept tight for better interface between the seals and the counterpart surfaces. In Figure 3.8, the sealing types used in the MRB and their locations are shown. In the MRB proposed, Viton O-rings were used for both static and dynamic applications. In addition, as a sealant, Loctite 5900 Flange Sealant, was also used.

CHAPTER 3. DESIGN OF MR BRAKE

36

Figure 3.8: Dierent seals on proposed MRB design

CHAPTER 3. DESIGN OF MR BRAKE

37

3.5

Cooling

The heat ow within the basic MRB conguration, which was presented in Figure 1.2, was investigated by Falcao da Luz [38]. Transient and steady state heat ow analyses were done assuming that the MR uid employed was MRF-132DG and the heat was removed by forced convection from the casing of MRB as well as the conduction between the brake components. A braking schedule, that consists of 15 cycles each comprising a 28 s acceleration period followed by a 0.3 g deceleration from 120 kph to a full stop, was adopted and according to this study, after 15 cycles, the temperature within the brake reached 100 which is still in the operating range of the selected MR uid. But, with more severe repetitive braking, the temperature will exceed the operating range eventually. In this work, heat ow analysis was not included in the FEA, as the main focus lied on the braking torque generation capacity of the MRB. However, an eective and fast heat removal from the brake is crucial, since the MR uid properties (i.e. viscosity) and the magnetic properties (i.e. ) of the materials employed are dependent on the temperature. Especially, due to the existence of a carrier uid in MR uids, their operating range (see Sec. 3.10) is quite limited. In addition, in braking applications, the kinetic energy of the vehicle is transformed into heat within brakes and a CHB can reach over 600. The same will be valid for the MRB as well, and thus the heat has to be removed from it as fast as possible. There are various methods of cooling the brakes which can be divided into two categories: active and passive cooling. As passive cooling, in addition to selecting thermally conductive materials with high convection coecients (see Sec. 3.3.4), ns can be introduced which will increase the convection surface on the MRB and this method of cooling was suggested in [38]. However, these methods will not increase

CHAPTER 3. DESIGN OF MR BRAKE

38

the heat ux considerably. Therefore, an additional active cooling system should be introduced. In active cooling, the heat ux is increased by the introduction of a forced heat transfer uid (i.e. water, air, coolant, etc). The term forced is used to imply that, in active cooling, additional components such as pumps and fans are used to help the heat transfer from the system to the ambient environment by circulating the heat transfer uid between these mediums. The analyses in [38] were carried out by assuming that there was forced convection between the brake casing and the ambient air when the vehicle is moving. For the MRB heating problem, since this is an automotive application, similar to an active engine cooling system, a water cooling system can be included to the design. In addition, a fan can also be attached to the shaft which will cool the MRB. Another method that can also be used is to consider the MR uid itself as a cooling uid. An MR uid reservoir for each brake can be included into the system which has an active cooling system introduced. The idea is similar to the way of cooling the water, that cools the engine, in the radiator. Since the main concern is the temperature of the MR uid, a reservoir will be ecient to keep the MR uid temperature within the operation temperature. But, on the other hand, a reservoir will need a pump or an active system that helps the MR uid circulation and introduction of new components will increase the overall weight of the actuator as well as the cost of the brake. But as mentioned previously, since the main concern of this thesis lies in the brake torque capacity of the MRB for the automotive application, the eects of adding active or passive cooling systems were not studied. This remains as an important future work that must be addressed (see Sec. 6.2).

CHAPTER 3. DESIGN OF MR BRAKE

39

3.6

Working Surface Area

As mentioned previously, a working surface is the surface on shear disk(s) where the MR uid is actuated by applied magnetic eld intensity. Basically, it is the surface where the magnetic shear, H , is generated, thus the braking torque. Working surface is another important design factor. Since the braking torque is generating on this surface, torque has a direct dependence on the surface area. From Sec. 2.2, Eq. (2.10) shows that the braking torque is the area integral of the shear of the MR uid. If the surface area is increased then generated torque would be increased too. There are multiple ways to increase the working surface area. The rst way to increase the working surface area is to enlarge the surface area of the pole caps. But by enlarging it, the ux will be distributed over the cross section and in the working surface, there will be less magnetic ux density. However, the main concern is the change in the braking torque generated, so the ux ow over the uid, not over the surface area of the pole caps. Due to nonlinear behavior of magnetic properties, one cannot conclude that the braking torque will increase by enlarging pole caps surface area and it will decrease by reducing it. Therefore, the surface area of the pole caps has to be optimized for maximum braking torque generation by using proper optimization method and constraints. Another way of enlarging the working surface is to modify the magnetic circuit itself. As was mentioned in Sec. 3.2, in order to modify the magnetic circuit, the materials used, the conguration of the magnetic circuit and the dimensional design parameters can be changed. Since there are not many material in the literature with known (published) detailed magnetic properties, changing the material makes the subsequent MRB design and analysis dicult. However, by modifying the conguration of magnetic circuit and changing the dimensional design parameters, magnetic

CHAPTER 3. DESIGN OF MR BRAKE

40

ux generated can be focused onto uid and the working surface area can be enlarged. One must be careful when modifying the basic conguration of the magnetic circuit. In relation to the working surface area issue, the alignment orientations of the iron particles in the MR uid must be considered. For more eective braking torque generation, a magnetic circuit has to be designed in such a way to align the iron particles in the MR uid perpendicular to the working surfaces. Figure 3.9 and Figure 3.10 shows three cases of possible particle alignment in the MR uid. Figure 3.9 shows the distribution of the iron particles without magnetic eld application and thus no angular velocity. The static casing is the upper working surface and the lower working surface is the shear disk surface. Figure 3.10 represents two dierent cases when the external magnetic eld is present. In Figure 3.10-(L), the static casing and the shear disk are made of non-ferromagnetic materials. Since the permeability of the MR uid is higher than that of the surrounding materials, particles will align parallel to the working surfaces due to the parallel ux ow through the MR uid gap. Recall that the magnetic ux will ow over a medium in which the permeability is higher. This parallel alignment of the iron particles will result in layers of parallel chains throughout the MR uid gap thickness. Since the bond between the layers is weak, they will be subjected to slipping during braking. However, when ferromagnetic materials are used for static casing and the shear disk, the magnetic ux will prefer to ow through them instead of the MR uid. In order to complete the magnetic circuit, the ux will ow perpendicular to the static casing and shear disk surfaces which will result in a perpendicular alignment of the iron particles. This can be seen in Figure 3.10-(R), the resistance against the motion of the shear disk will be increased due to the formation of the perpendicular chains. In this case, slipping between the layers would not occur. Another way that helps to increase the working surface area is the introduction

CHAPTER 3. DESIGN OF MR BRAKE

41

Figure 3.9: Iron particle alignment without magnetic eld application

Figure 3.10: Alignment of iron particles with magnetic eld application between nonferromagnetic casing and shear disk (L) and ferromagnetic casing and shear disk (R)

CHAPTER 3. DESIGN OF MR BRAKE of additional shear disks, which will be discussed in more detail in Sec. 3.9.

42

In our MRB design, the dimensional parameters were optimized for higher braking performance and also ferromagnetic layers were installed on the static casing in order to achieve the perpendicular alignment of the iron particles in the MR uid when the external magnetic eld is applied.

3.7

Viscous Torque Generation

The gap between the stator and the rotor is lled with the MR uid, which generates some amount of braking torque, i.e. viscous torque, even without the magnetic eld application. The viscous torque is generated due to the viscosity of the MR uid, which cannot be removed completely. However, it can be decreased to a reasonable value. There are multiple ways to decrease the amount of viscous torque generated. The very rst thing that should be done is to select an MR uid with a low viscosity value, which will be addressed in Sec. 3.10. Viscous torque can also be decreased by decreasing the shear rate value. Eq. (2.11) gives the shear rate as a function of uid velocity and the thickness of the gap, with the assumptions of no slip conditions, thin uid gap thickness and linear velocity distribution of uid ow over the uid gap thickness. This equation tells us that, in order to decrease the shear rate, the thickness of the gap, which is lled with the MR uid, should be increased. In order to show the eect of a change in the uid gap thickness on the viscous torque generation, the MR uid ow was briey studied. A laminar Couette ow analysis was carried out in order to simulate the ow between the static casing and a rotating disk. A Coquette ow, shown in Figure 3.11, is a simple viscous parallel plate ow of a Newtonian uid, developed between a stationary plate and a moving

CHAPTER 3. DESIGN OF MR BRAKE

43

plate. Newtonian uid is the one in which shear stress is distributed proportionally to the velocity gradient in the direction perpendicular to the direction of shear plane.

Figure 3.11: Couette ow

For this type of ow, a shear stress is generated between the uid and the plate, and this shear stress is directly related with the viscosity of the uid. Basically, uid resists the ow in the direction of motion and this resistance is a function of the viscosity and derivative of the velocity with respect to thickness. This relationship is shown in Eq. (3.9) for the geometry specied in Figure 3.11. Moreover, for calculating the braking torque, the shear stress is multiplied by the area and the moment arm. In Eq. (3.10), the general torque equation in cylindrical coordinates is given (similar to Eq. (2.15) dened for the MRB). du dy

= p

(3.9)

CHAPTER 3. DESIGN OF MR BRAKE

44

T =
j 0

r2 ddr

(3.10)

where u is the linear velocity in x direction, p is the plastic viscosity, and is the angle that the radius makes with the horizontal. Figure 3.12 shows the actual picture of the problem, in which a disk rotating within a static enclosure. As it can be seen from the gure, there are two types of ow motion: one is in the radial direction and the other is in the tangential direction. In addition, the ow motion does not depend on the angle, , which implies that the motion is same everywhere on an arbitrary circle in the uid.

Figure 3.12: Experimental ow patterns developed by a rotating disk within a static enclosure

The following assumptions were made in regards to the MR uid ow problem:

CHAPTER 3. DESIGN OF MR BRAKE 1. Newtonian Flow. 2. Steady and incompressible ow. 3. No radial ow. 4. No change of velocity in the tangential direction. 5. No pressure gradient and gravitational eects on the ow. With the above assumptions, the ow problem becomes a 1-D problem: d2 u =0 dy 2

45

(3.11)

which is an idealized case that should be sucient for our purpose. By solving the above Navier-Stokes equation, the ow prole between the stationary casing and the rotating disk is shown in Figure 3.13. This is the ow that is expected for the Couette Flow. With the above velocity prole between the stationary and the rotating parts, the shear stress and the torque can be calculated by just using the slope of the curve and the viscosity. Lord Corporationss MRF-132DG was selected and used in the ow analysis, which has the plastic viscosity of 0.09 Pa-s. Figure 3.14 shows the change in the viscous torque with respect to the changing uid gap thickness. In this plot, the results were multiplied by a factor of 4 to obtain the total sum of the viscous torque when 4 MRBs are used in a car. According to the plot, for a gap of 1 mm between the static enclosure and the disk, a viscous torque of around 13 Nm is generated purely due to the viscosity of the MR uid in each brake (around 50 Nm for 4 brakes) while the car is moving at 60 kph. An additional load that the engine has to overcome while the car is traveling.

CHAPTER 3. DESIGN OF MR BRAKE

46

Figure 3.13: Velocity prole for a segment away from 0.12 m from the center of the disk

CHAPTER 3. DESIGN OF MR BRAKE

47

Figure 3.14: Viscous torque versus the gap thickness of MR uid (at 60 kph)

CHAPTER 3. DESIGN OF MR BRAKE

48

In order to decrease the amount of viscous torque that impedes with the free shaft rotation of MRB, MR uid with a low viscosity value was selected, and the uid gap thickness was optimized along with the other dimensional parameters for better brake performance.

3.8

Applied Current Density

The electromagnet coil is another important design criterion, as it is the source (i.e. the magnetomotive force or mmf ) in the magnetic circuit. The current density that can be applied to the electromagnet coil is limited, which depends on the cross-sectional area of the wire, its material, and the saturation ux densities of the magnetic materials used in the MRB. When the saturation ux value of a magnetic material, especially that of the electromagnet core material, has been reached, it will behave as non-magnetic material (i.e. r becomes 1), aecting the corresponding reluctance in the magnetic circuit which will result in a change in the magnetic circuit, and consequently the amount of ux ow through the MR uid. Thus, it is benecial to keep the ux in the unsaturated region for that material. In order to maximize the amount of applied current density, the dimensional space where the coil is located needs to be optimized along with the other dimensional parameters. In addition, a wire size, with the highest current density capacity was selected. In order to nd the most ecient wire in terms of the current density carrying capacity, a coil with a winding conguration of Figure 3.15 was studied. By drawing an equilateral triangle, the eective cross sectional area of the wire can be calculated within the triangular area and the corresponding current density application capacity was calculated by dividing the mmf by the calculated triangular area. The mmf was calculated by using the maximum current carrying capacity of the wire.

CHAPTER 3. DESIGN OF MR BRAKE

49

Figure 3.15: Wire conguration in a coil

Table 3.3 shows the corresponding current densities that can be applied to the coils made of dierent sizes of wires. According to this study, the most ecient wire size is the AWG 21. More current density can be applied to the MRB using this wire size, which means that the magnetic eld intensity generated within the brake will increase. Note that, from Eq. (2.14), the amount of the magnetic torque generated will be increased with the increasing magnetic eld intensity. Therefore, in this work, the AWG 21 size copper wire was used to wind the coil of the MRBs electromagnet.

3.9

Additional Disk Attachment

In order to increase the amount of braking torque generated in the brake, additional brake disks can be attached to the shaft to increase the working surface area. By attaching additional disks, additional working surfaces would be introduced (see Sec. 3.6 for other ways to increase the working surface area). In Figure 3.16, two brake cross sections are shown: one with only one shear disk attached to the shaft and the other

CHAPTER 3. DESIGN OF MR BRAKE

50

Table 3.3: Current densities for coils of wires with dierent sizes awg gauge diameter ohms per km current density (mm) (A/mm2 ) 7 3.665 1.634 2.587 8 3.263 2.060 2.610 9 2.905 2.598 2.607 10 2.588 3.276 2.594 11 2.303 4.132 2.619 12 2.052 5.208 2.558 13 1.828 6.569 2.563 14 1.628 8.282 2.578 15 1.450 10.443 2.588 16 1.290 13.172 2.574 17 1.150 16.609 2.538 18 1.023 20.942 2.543 19 0.911 26.407 2.508 20 0.812 33.292 2.630 21 0.723 41.984 2.653 22 0.645 52.939 2.561 23 0.574 66.780 2.563 24 0.510 84.197 2.564 25 0.454 106.173 2.561 26 0.403 133.856 2.564 27 0.360 168.821 2.565 28 0.320 212.872 2.556 29 0.287 268.402 2.559 30 0.254 338.496 2.550 31 0.226 426.728 2.562 32 0.203 538.248 2.553 33 0.180 678.632 2.565 34 0.160 855.752 2.533

CHAPTER 3. DESIGN OF MR BRAKE

51

one with two disks attached. In the latter, the working surface area is increased but also the magnetic resistance (reluctance) in the circuit is increased.

Figure 3.16: Surface plots with one (top) and two (bottom) rotating shear disks attached to the shaft

The braking torque generated is calculated by using Eq. 2.10, integrating the shear stress over the working surface area. The working surface area in Figure 3.16(bottom) is doubled and the amount of torque generated in two disk design is expected to be roughly twice as much as the torque generated in the one disk design. Due to

CHAPTER 3. DESIGN OF MR BRAKE

52

the nonlinearity of the material properties and the dependence on the geometry, the amount of change in braking torque can only be estimated accurately using an adequate nite element analysis. Hence, the proposed MRB has two shear disks (N = 2) attached to the shaft for higher braking torque generation.

3.10

MR Fluid Selection

There is a number of commercially-available MR uids sold by Lord Corporation. In terms of selecting the uid that is most suitable for braking purposes, there are multiple properties that have to be considered. Viscosity of the uid without magnetic eld application is one of those properties. Since the gap between the stator and rotor is lled with the uid, viscous torque is present in the MRB. Thus in order to keep the viscous torque low, a uid with a low viscosity has to be selected. Another important property of MR uid is the operating temperature range. Since we are considering a brake actuator, the kinetic energy of the car will be transferred as heat in the MRB, and it will heat up while braking. Since the magnetic properties of the materials in the MRB and the MR uid viscosity depends on the temperature, the uid with a broader operating temperature range has to be selected in order to maintain the braking performance at higher operation temperatures. The shear stress gradient with respect to the applied magnetic eld intensity is another important property of the MR uid. By keeping the shear stress gradient high, the amount of braking torque that could be generated by the brake will also increase. According to Falcao da Luz [38], MRF-132DG is the best candidate for the automotive braking application due to its broad operating temperature range (-40 to 130). However, the shear stress gradient of MRF-132DG is lower than that

CHAPTER 3. DESIGN OF MR BRAKE

53

of MRF-241ES which has an operating temperature range from -10 to 70. In Table 3.4, the properties of MRF-132DG and MRF-241ES are summarized and the relationships between the magnetic eld intensity and the shear stress generated for both uids are shown in Figure 3.17.

Table 3.4: Properties of MRF-132DG and MRF-241ES Property MRF-132DG MRF-241ES Base Fluid Hydrocarbon Water Operating Temperature -40 to 130 -10 to 70 Density 3.09 g/cc 3.8-3.92 g/cc Color Dark gray Dark Gray Weight Percent Solid 81.64 % 85 % Coef. of Thermal Expansion (Unit Volume per ) 0 to 50 5.5e-4 0.226e-3 50 to 100 6.6e-4 100 to 150 6.7e-4 Specic Heat at 25 0.80 j/g 0.94 j/g Thermal Conductivity at 25 0.25-1.06 w/m 0.85-3.77 w/m Flash Point > 150 > 93 Viscosity slope between 800 Hz 0.09( 0.02)Pa-s and 500 Hz at 40 10 Hz 10.8 1.5 Pa-s 50 Hz 2.2 0.4 Pa-s k 0.269 Pa-m/A 0.467 Pa-m/A 1 1

However, even though the shear shear generation capacity of MRF-132DG is approximately only a half of that of MRF-241ES , MRF-132DG was chosen for having a broader temperature range. In addition, MRF-132DG does not contain water which may result in corrosion of the MRB.

CHAPTER 3. DESIGN OF MR BRAKE

54

Figure 3.17: Shear stress versus magnetic eld intensity for MRF-132DG (top) and MRF-241ES (bottom)

55

Chapter 4 FEA and Design Optimization

The analytical MRB model was derived in Sec. 2.2. As shown by Eq. (2.13), the total braking torque Tb generated is a function of the material properties (i.e. viscosity of the uid, k and coecients) and the magnetic eld intensity distribution on the MR uid (HM RF ). While the material properties are given by the manufacturers specications, however, the magnetic eld intensity distribution has to be calculated within MRB. In order to obtain this, a nite element model (FEM) of the MRB was created and using nonlinear magnetic properties of materials employed, the magnetic eld distribution within the MRB was calculated. In this chapter, the FEM generated for the MRB is presented. In addition to the generation of the FEM, the nite element software used also described. The resulting magnetic ux and magnetic eld intensity distribution plots for the selected design shown in Figure 3.1 are also included in this chapter. After the FEM was created for the proposed MRB design, it was optimized for the maximum braking torque generation and minimum weight. For the optimization process, an MRB optimization problem was dened with a corresponding objective

CHAPTER 4. FEA AND DESIGN OPTIMIZATION

56

function and a set of constraints. Then, existing optimization methods were used in order to solve for the optimum MRB dimensional design parameters.

4.1

Finite Element Model of MRB

To solve Eq. (2.13), the magnetic eld intensity distribution in the MRB has to be calculated. For this purpose, a nite element analysis (FEA) was carried out using a commercial FEA package, COMSOL Multiphysics . The following governing magnetostatic equations [49], that were derived from Maxwells equations (see Appendix A), are used by the COMSOL Electromagnet Module: H=J B=0 (4.1) (4.2)

where H is the magnetic eld intensity, B is the magnetic ux density and J is the electric current density. By solving these equations over a dened domain with proper boundary conditions, the magnetic eld intensity distribution (H) generated by the modeled MRB can be calculated. Subsequently, the braking torque in Eq. (2.14) can be calculated. In order to solve the above magnetostatic equations, a 2-D MRB nite element model (FEM) was created. The FEM is a quasi-static magnetic model, which simulates the in-plane induction currents and vector potentials, needed to obtain the magnetic eld intensity distribution (H) over the dened MRB geometry. First, the geometry of the proposed MRB was generated using the sketch function in COMSOL and the nonlinear material properties of the MR uid and AISI 1018 were dened as functions of the magnetic ux density B. Then, a magnetically isolated boundary

CHAPTER 4. FEA AND DESIGN OPTIMIZATION

57

that includes the MRB geometry was selected. After the mesh was generated, the FEM was solved using a parametric nonlinear solver and the magnetic eld distribution onto the MR uid (i.e. HM RF which is equal to the magnitude of the magnetic eld distribution, |H|) was obtained. Finally, the braking torque in Eq. (2.13) was calculated using a boundary integration post processing function in COMSOL that integrates the shear, that is calculated by the magnetic eld intensity distribution, over the shear disk surfaces. The FEM accounts only for the magnetic eld distribution. Fluid ow dynamics and heat transfer models were not included in the FEM. In Figure 4.1 and Figure 4.2, the simulations of the magnetic eld intensity and the ux density in the MRB are shown.

4.2

Optimization Problem Denition

As a next step, the revised design in Figure 3.1 was optimized for higher braking torque and lower weight. In setting up an optimization problem for the MRB, a cost function was dened by including the braking torque and the weight as functions of the magnetic circuit design parameters, (see Figure 3.2). The objective function of the MRB optimization problem is dened as: f (d) = W T (4.3)

where d = [d1 , d2 , ..., d12 ]T is the design variable vector that consists of the dimensional parameters shown in Figure 3.2, W (N) is the weight of the actuator and T (Nm) (equal to TH in Eq. (2.14)) is the braking torque generated due to applied magnetic eld. But there is a conict between terms since these terms have dierent units in

CHAPTER 4. FEA AND DESIGN OPTIMIZATION

58

Figure 4.1: Magnetic eld intensity distribution Plot generated by COMSOL

CHAPTER 4. FEA AND DESIGN OPTIMIZATION

59

Figure 4.2: Magnetic ux density plot generated by COMSOL

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60

Eq. (4.3). Higher term will dominate over the other and the minimum value and the optimized variables will be deviated from the exact solution. In order to overcome this problem a reference value can be set for each function separately and dividing the terms by the reference will give dimensionless values which can be compared. Thus, the cost function becomes: f (d) = T W Wref Tref (4.4)

where the values with the subscript ref are the reference values for the functions. In this form, the cost function is dened and can be optimized. But if one of these functions, weight or braking torque, is wanted to be dominated over the other in the optimization process, weighting coecients should be introduced. Every term will be multiplied by coecients and these coecients are estimated in accordance with the importance of the term in the optimization process. For MRB optimization problem, the braking torque generated has a considerably important role compared to the weight of the actuator, because main goal of the optimization process is to nd the design which can generate maximum torque in accordance with the constraints. Therefore, the coecient of weight function should be less than the coecient of the braking torque function. Final form of the optimization function will be: Minimize : f (d) = kW T W kT Wref Tref (4.5) (4.6) (4.7) (4.8)

kW + kT = 1 subject to : W < 18 dbrake < 240

where kW and kT are the weighting coecients. The FEM was used to obtain W and T in the cost function for various brake designs. The block diagram in Figure 4.3

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61

shows the process of calculating W and T via COMSOL in the cost function for an arbitrary design.

Figure 4.3: Process of computing the cost function for a random design

In order to solve the objective function, kw was set to be 0.1 and kT was set to be 0.9, as the maximum torque generation is of our primary concern. In addition, the reference weight value was obtained considering the overall system weight of the CHB that consists of the on wheel components as well as the extra weight contributed by

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62

the hydraulic components: the master cylinder, brake uid lines, and pump. Since an MRB would not have these extra components, each MRB can potentially have heavier on-wheel weight than that of a CHB. Moreover, since the braking torque generated by the proposed conguration of the MRB is comparably less than that of the CHB, Tref was selected to be 20 Nm. This reference torque value was selected by checking a number of random designs which satised the constraints. As the constraints for the optimization problem, the weight of the actuator was set to be smaller than the weight of the CHB, i.e. W < 18 kg. Since the brake should t into a standard automobile wheel, the diameter of the MRB is set to be smaller than the inner diameter of the wheel. The diameter constraints for various sizes of wheels are shown in Table 4.1, for example, 13 wheel, the inner diameter is 240 mm, thus dbrake < 240 mm.

Table 4.1: Inner diameters of wheels of dierent sizes Wheel Size (in.) Inner Wheel Diameter (mm) 13 240 14 260 15 278 16 308 17 325 18 355

4.3

Optimization Methods Used

The MRB objective function and constraints are dened in previous section. As a next step, optimization methods that were used were selected. Before introducing the methods selected in order to solve the MRB optimization problem, brief back-

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63

ground information about the optimization methods in general will be benecial to understand the method selection process. Optimization methods can be classied as gradient based methods, random search algorithm and iteration search algorithms which are the combinations of random search and gradient based methods. Gradient based algorithms are capable of nding the exact optimum solution since the gradient of the cost function is used to determine the search direction and step sizes. Gradient based optimization algorithms are started with an initial guess. Using the gradient information, the search direction and the step size are calculated and according to them, the optimum can be found. Unlike gradient based algorithms, random search methods do not need the gradient information in order to determine the iteration direction. Iterations are made according to a random search algorithm dened for every method separately. Since the search is random, nite number of iterations is made. This results in a solution which is dierent from the exact optimum solution. For a random search algorithm, a domain of optimization variables has to be dened and the algorithm will search the space for the minimum value of the cost function dened as a function of optimization variables specied. Although gradient based methods give the exact minima, that minima may not be the global minima depending on the nonlinearity of the cost function and number of local minimas and maximas. Since gradient methods will converge to a minimum which is close to the initially dened point, it could converge to a local minimum instead of the global minimum. Therefore, in order to solve MRB problem, a random search algorithm was used. Among dierent methods of random search, simulated annealing method [50, 51] was selected in order to solve the MRB optimization problem. There are also other methods like neural nets, iterated searches, genetic algorithmsetc, but simulated an-

CHAPTER 4. FEA AND DESIGN OPTIMIZATION

64

nealing was selected due to its statistical guarantee to converge global optimum point and also it was selected due to its simplicity. SA simulates the statistical crystal growth process using material annealing to converge to the absolute minimum internal energy conguration of the crystal. With enough given time to run and enough number of iterations, such algorithm is capable of nding the global optimum for a nonlinear problem. But since this method is a random search method, nite number of iterations is made and because of that, the design that is going to be found by simulated annealing method is not going to be the exact global minimum. In order to nd the exact global optimum, a gradient based algorithm was run after solving the problem by using a random search algorithm, simulated annealing form MR Brake problem. After solving the problem by using simulated annealing, results of the algorithm were used to initiate a gradient based method, which is Sequential Quadratic Programming (SQP), in order to nd the optimum design. The block diagram for the MRB optimization process is shown in Figure 4.4. In order to solve the MRB optimization problem using SA, a design domain was specied as the possible solution space (lower and upper boundaries of this space were dened). Then, the solution of SA initiated a SQP algorithm which searches the optimum using the gradient information and the solutions were updated with the supplied step size and search direction data until the optimum design was found.

4.4

Optimum Design

The optimum dimensional parameters for the magnetic circuit are given in Table 4.2, the corresponding illustration of the optimum design cross-section is shown in Figure 4.5.

CHAPTER 4. FEA AND DESIGN OPTIMIZATION

65

Figure 4.4: MRB optimization process

CHAPTER 4. FEA AND DESIGN OPTIMIZATION

66

Parameter d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 d12

Table 4.2: Optimum design parameters Optimum Value (mm) LB - UB (mm) 17.11 20 - 80 18.05 5 - 15 1.03 2-4 47.34 10 - 80 5.08 5 - 10 14.57 4 - 15 2.07 2 - 20 10.00 10 - 30 10.34 5 - 20 3.08 3 - 10 0.91 0.91 - 3.79 2.04 1-4

LB: Lower Boundary and UB: Upper Boundary

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67

Figure 4.5: Optimum MRB design

CHAPTER 4. FEA AND DESIGN OPTIMIZATION

68

In addition, using FEA, magnetic eld intensity and magnetic ux density distribution within the MRB were plotted. Figure 4.6 shows the corresponding distributions of eld intensity and ux density.

Figure 4.6: i) Magnetic eld intensity distribution and ii) Magnetic ux density within optimum MRB design

By using the data plotted in Figure 4.6 and using the analytical model of the MRB (see Bingham Plastic Model, Eq. (2.9)), shear stress distribution generated only due to the magnetic eld application within the MRB was illustrated in Figure 4.7. One can easily notice the similarity between the magnetic eld intensity and the shear stress distribution plots. Since, the shear stress generated on MR uid is approximated with a linear function (see Eq. (2.12)), both plots are quite similar in terms of the distribution. Then, using Eq. (2.14), the braking torque generation was calculated at various current application. The relationship between the applied current and the simulated braking torque generation is shown in Figure 4.8. Since the results do not include the viscous term, the relationship starts from the origin (T = 0 @ 0 A). According to the simulation results, the relationship is almost linear and at 1.8 A, the magnetic

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69

Figure 4.7: Shear stress distribution within optimum MRB

CHAPTER 4. FEA AND DESIGN OPTIMIZATION braking torque generated is around 23 Nm.

70

Figure 4.8: Braking torque generation simulation results

71

Chapter 5 Experimentation
In this chapter, the proposed MRB was prototyped for experimenting its braking performance. The optimum design found in the previous section was used and a prototype was manufactured. This prototype was then mounted onto an experimental test-bed, which included a torque source and a torque sensor to measure the torque generation. The braking torque generated by the MRB prototype was measured at various current density applications to the coil and the results are shown in this chapter.

5.1

Experimental Setup

In order to set up an experiment to measure the braking torque capacity of the proposed design, the optimum MRB design was manufactured and it was mounted to a test-bed. Here, in this section, the overview of the experimental setup is divided into two subsections: i) MRB prototype and ii) MRB test-bed, which contains the sensors and actuators used to test the braking performance of the MRB prototype.

CHAPTER 5. EXPERIMENTATION

72

5.1.1

MRB Prototype

After an optimum design was found in the previous chapter by solving the dened optimization problem for the MRB, a 3-D CAD model was generated using Pro/E (see Figure 5.1 (L)). The MRB was slightly modied for ease of manufacturing and additional details such as bearings, seals and the surface nishes were dened. As mentioned in Sec. 3.4, standard Viton O-rings were used for the static and dynamic sealing purposes. In addition, angular ball bearings, 7004 LLB (double sealed and non-contact type), were used. Corresponding seal and bearing locations are shown in Figure 5.1 (R).

Figure 5.1: MRB CAD model (L) and cross-section of the MRB CAD model with bearings, screw holes and seal beds (R)

Also in Figure 5.1 (R), the location of the screw holes and the MR uid inlet are shown. In the MRB prototype, 38 screws of various sizes (stainless steel screws were used to assemble the parts that are not parts of the magnetic circuit) were used, and also for the MR uid inlet, 3 NPT holes were drilled, in order to ll the MRB properly without introducing an air gap.

CHAPTER 5. EXPERIMENTATION

73

Then, the MRB prototype components were manufactured according to the 3-D CAD model generated using Pro/E. Then, the parts were assembled and the prototype that is ready for testing is shown in Figure 5.2 (L). The most challenging part of the assembly was the coil, which has to be placed within the MRB static casing that forms the electromagnet i.e. core. The coil has to be one piece for easy installation, thus, a custom bobbin was machined to wind the coil and then the coil wound around the bobbin was installed onto the MRB. In Figure 5.2 (R), the coil and bobbin assembly is shown, which is installed in the MRBs electromagnetic core. Another hole was drilled onto the electromagnetic core for the terminals of the coil (see Figure 5.2 (L)). In addition, in order to measure the temperature of the MR uid within the MRB, a K-type thermocouple was bonded onto one of the NPT taps, using a high temperature resistant and highly conductive epoxy, OMEGA OB-200.

Figure 5.2: MRB prototype (L) and coil assembly (R)

The specications of the MRB prototype is given in Table 5.1.

CHAPTER 5. EXPERIMENTATION

74

Table 5.1: MRB prototype specications Weight Diameter Number of Disks Amount of MR Fluid used Coil Wire Size Number of Turns Max. Current Applied Max. Current Density Applied Seals Used Magnetic Materials Used Non-Magnetic Materials Used Max. Braking Torque 11.8 kg 239.9 mm 2 205 cm3 AWG 21 236 2 turns 1.8 A 2.54e6 A/m2 Viton O-rings and Loctite 5900 Flange Sealant Steel 1018 Al T-6061 and SS 304 23 Nm @ 1.8 A

CHAPTER 5. EXPERIMENTATION

75

5.1.2

MRB Test-Bed

The MRB prototype was then installed into the experimental setup shown in Figure 5.3. A servo motor from CMC Inc. with a continuous torque of 45.4 lb.in and with rotational speed of 5445 rpm was used to generate the continuous torque. Since the torque generation capacity of the servo motor is relatively low, an ALPHA 0755MC1-7 gear reducer (7:1) was used. The servo motor was connected to a Futek torque sensor (TRS605) which is a shaft-to-shaft rotary torque sensor with a torque measuring capacity up to 1000 Nm. The other end of the torque sensor was connected to the MRB prototype. An Inertia Dynamics magnetic clutch was installed between the torque sensor and the servo motor in order to release the load on the servo motor generated by the brake. In order to connect the various components, exible couplings were used. In addition, an OMEGA SMCJ-K, analog amplier, was used to amplify the output of the K-type thermocouple that was installed to measure the temperature of the MR uid.

Figure 5.3: Picture of experimental setup

The servo motor was controlled with a PID controller and the rotational speed of

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the brake was veried using the encoder embedded in the torque sensor. All input and output signals were connected to a dSPACE control board (DS1104). The control signal from the dSPACE board to the servo was amplied using an Advanced Motion Control Brushless PWM servo amplier. In addition, a low-pass lter circuit was implemented into the setup in order to reduce the high frequency noise in the torque sensor readings. During the experiments, the rotational speed was kept constant at various values and current was applied to the coil using an Agilent Technologies high current power supply (N5766A). Whenever the brake was actuated, since the system was at steadystate, the relative torque measured between the shafts on each side of the torque sensor was recorded as the braking torque generated by the brake prototype. After the braking torque data was obtained, the magnetic clutch was turned on in order to release the torque load on the servo motor.

5.2

Validation of the MRB prototype

After the experimental test-bed was physically set up, some sample tests were carried out in order to identify any problems with the data acquisition and signal processing. There were some issues that appeared during these tests, which had to be xed before the actual data could be collected for the MRB prototype. Then, the MRB was tested and the corresponding results were recorded.

5.2.1

Experimental Problems

During the initial experimentation of the MRB prototype, a number of problems arose. The main problem was the electrical noise interference in the torque sensor

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and the thermocouple signals, caused by a ground loop within the electrical circuitry. Most of the noise interference was removed by improving the circuitry and by shielding the system properly. The remaining high frequency noise was removed by using a physical low pass lter, a simple RC circuit, and a nonlinear software lter, which was a Butterworth 6th order lter, designed using Matlab-Simulink Filter Design Toolbox. Another issue was the leakage of the MR uid, which was mentioned in Sec. 3.4. Due to the high contamination of the uid and the loss of exibility due to the on/o cycle of the MR uid by applied magnetic eld in the vicinity of the seals, the seals had to be properly installed. In the rst trial, due to low surface nish quality of the sealing surfaces, leakage occurred. Experiment was repeated after the surface nishes were improved. In addition to these, a minor problem was the heating of the prototype and also the servo motor. Between two consecutive readings, the temperature of the uid and the MRB was increased due to applied current and shear friction generation in the MRB. After a set of data was taken, the brake was cooled down to room temperature by using external fans. In addition, since brake generates a torque load against the servo motor, the motor was also heating up. Therefore, between experiments, the servo motor and the MRB prototype were cooled down which prolonged the time duration of the experiments.

5.2.2

Experimental Procedure and Results

First we measured the no-eld torque generated by the viscosity of the MR uid (plus the mechanical friction torque). In Figure 5.4, the torques generated due to viscosity of the uid at various rotational speeds are shown. The relation between the viscous

CHAPTER 5. EXPERIMENTATION torque and speed is linear, as described by Eq. (2.15).

78

Figure 5.4: Viscous torque versus velocity

After the viscous torque was calculated, current was applied to the electromagnet coil and corresponding change in the torque readings were recorded. Corresponding torque readings at various currents applied are shown in Table 5.2. Figure 5.5 shows the total braking torques (Tb ) generated with respect to the increasing speeds. The dierence between the three torque curves is directly due to the varying viscous torques (Figure 5.4) at dierent speeds. The plots shown in Figure 5.5 contain the viscous eects and the frictional eects. In order to compare the experimental results with the simulation results, the viscous and the friction eects have to be subtracted from the experimental data. The resulting plots between the torque (TH ) generated due to the applied magnetic eld and the current applied is shown in Figure 5.6. Three plots are almost identical, which shows that this quantity is not speed dependent, as described by Eq. (2.14).

CHAPTER 5. EXPERIMENTATION

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Table 5.2: Torque generated under various magnetic eld intensities Torque Generated(Nm) Torque Generated(Nm) (total) (magnetic term) Current Current Values Density 100rpm 200rpm 300rpm 100rpm 200rpm 300rpm (A) (A/m2 ) 0 0 0.426 1.269 2.051 0 0 0 0.2 281677.7 1.329 2.212 3.055 0.903 0.943 1.003 0.4 563355.4 3.316 3.858 4.500 2.890 2.589 2.448 0.6 845033.1 3.898 4.781 5.624 3.472 3.512 3.572 0.8 1126711 6.286 6.848 7.491 5.860 5.579 5.439 1 1408389 8.755 9.478 9.899 8.329 8.209 7.847 1.2 1690066 11.404 12.147 12.468 10.97 10.878 10.416 1.4 1971744 14.575 15.217 15.739 14.149 13.948 13.687 1.6 2253422 17.947 18.394 18.990 17.521 17.125 16.938 1.8 2535099 21.699 22.663 22.944 21.273 21.394 20.892

CHAPTER 5. EXPERIMENTATION

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Figure 5.5: Torque (Tb ) versus current applied

CHAPTER 5. EXPERIMENTATION

81

Figure 5.6: Torque (Th ) generated due to magnetic eld (without viscous and friction torques)

Figure 5.7: Comparison between experimental and simulation results @ 200 rpm

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82

Finally, the simulation and the experimental results are compared in Figure 5.7. While the initial (at 0 A) and nal (at 1.8 A) values match, there is deviation in the middle values (104% dierence at 0.2 A and 12% dierence at 1.6 A). The main reason behind this deviation is probably due to the lack of accurate information on the material properties that were used in the simulations. Another minor factor is the heating in the experimental brake which was not modeled in the FEM. Since temperature rise has an eect on both the magnetic properties and the viscosity of the uid, either the heating of the brake has to be avoided during the experiment or the FEM has to account for temperature eects.

5.3

Discussion

Note that in order to stop a vehicle (e.g. a 1000 kg passenger vehicle) with an deceleration of 6 m/s2 (which is the typical requirement for measuring braking performance of a fully loaded passenger vehicle with burnished brakes), each brake has to generate over 500 Nm (see Sec. 2.1.1). The prototyped MRB can generate only 5% of this braking torque. In order to further increase the braking torque a number of improvements can be made: 1. In Figure 5.8, the simulated improvement in the braking torque with additional disks is shown for the same design conguration proposed in this work. However, still, only 20% of the required torque can be generated with an MRB with 7 disks. 2. Another way of increasing the braking torque generation is to change the basic magnetic circuit conguration. In Figure 5.9(L), an MRB with a completely dierent magnetic circuit conguration is shown without considering the sealing

CHAPTER 5. EXPERIMENTATION

83

Figure 5.8: Simulation plot of braking torque (TH ) generated with respect to the number of disks (N ) (@ 1.8 A)

CHAPTER 5. EXPERIMENTATION

84

problem that was discussed in Chapter 3. The magnetic braking torque generation for this conguration at various applied currents is shown in Figure 5.9(R). In this case, 10% of the required braking torque can be generated with only one disk.

Figure 5.9: An MRB with dierent magnetic circuit conguration (L) and corresponding simulation plot of braking torque (TH ) vs. applied currents (R)

3. The braking torque capacity can also be increased by relaxing the size and the weight constraints dened in Eqs. (4.7) and (4.8). Note from Table 5.1 that the weight of the prototyped MRB is still lighter than that of the overall CHB system. With a combination of these improvements, there is a potential to further increase the braking torque capacity of an MRB for the automotive application.

85

Chapter 6 Conclusion and Future Works

6.1 Conclusion

In this work, a magnetorheological brake (MRB) is introduced as a possible substitute for the conventional hydraulic brake (CHB). Since MRB is an electromechanical device, it has several advantages over CHB, such as the reduced actuation delay, ease of software control implementation and lower system weight. In this work, the design process was started with an analytical model of the proposed MRB. Then, the MRB was designed in detail with a focus on magnetic circuit optimization and material selection. After the candidate MRB design was selected, in order to conduct further optimization analysis, a 2-D nite element model (FEM) of the MRB was created, which simulates the steady-state magnetic ux ow within the MRB domain. This was carried out using COMSOL Electromagnetic Module, which solves for the magnetic eld intensity distribution within the FEM of the MRB. The FEM was then used to optimize the magnetic circuit in order to maximize the braking torque and minimize the weight of the MRB. The MRB optimization problem was solved using an integrated optimization code that included simulated annealing and sequential

CHAPTER 6. CONCLUSION AND FUTURE WORKS

86

quadratic algorithms. A 3-D CAD model of the optimum MRB design was then generated and an MRB prototype of the optimum design was manufactured. The MRB braking performance was tested using an experimental setup that consisted of a torque sensor and a servo motor. The experimental results showed that the braking torque is increased with applied current, reaching more than 20 Nm at 1.8 A, verifying our theoretical predictions. There were discrepancies with respect to the simulation results due to inaccurate material property modeling in the simulations. Thus, in our future work (see Sec 6.2 for more detail), the simulation model will be improved by including the temperature eects and more accurate description of the material properties. In addition, this work showed that the proposed MRB conguration cannot supply enough braking torque to stop a vehicle. Therefore, an improved MRB will be designed with an increased number of disks and a modied magnetic circuit conguration.

6.2

Future Works

The very rst thing that has to be done is to improve the correlation between the simulation and the experimental results. The simulation results can be improved to match the experimental data by using a more detailed model of the material properties and by including the temperature eects in the simulation. As was mentioned previously in Chapter 1, the main objective was to design an EMB which can be used as a substitute for CHB. However, the braking torque generation capacity of the MRB proposed in this work is not high enough for a typical passenger vehicle. Therefore, the braking capacity of the MRB must be improved by relaxing the constraints dened for the MRB optimization problem, i.e. by increasing the number of disks attached and by changing the magnetic circuit conguration (see

CHAPTER 6. CONCLUSION AND FUTURE WORKS Sec. 5.3). This improved MRB then has to be prototyped and tested.

87

One of the major concerns with the actual implementation of an MRB into a car is the high temperature eect on the MR uid. In practice, the proposed MRB would likely require a physical (e.g. active or passive) cooling system to alleviate the heating problem in the MR uid and thus improving the braking performance. Since, the brake actuator transforms kinetic energy into heat, all kinetic energy of the car will be converted into heat in the MRB. As mentioned previously in the material selection section (Sec. 3.3) of this thesis, the magnetic properties are highly dependent on the temperature of the MR uid (the viscosity varies with temperature). Hence, heat transfer analysis has to be included in future studies. After the modied MRB is tested, a closed-loop controller has to be designed in order to remove the residual ux generated due to the hysteresis characteristics of the magnetic materials employed in the MRB. This controller will be then combined with other controllers such as an antilock braking controller that avoids slipping of the tires during braking. Then, the MRB and the controllers will be tested on a dynamometer to simulate real road conditions. As the nal step, the MRB will be mounted on for a vehicle and tested for on-road performances.

88

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[9] S. Genc and P.P. Phule, Rheological properties of magnetorheological uids, Smart Materials and Structures, 11, p140-146, 2002. [10] J. Rabinow , The magnetic uid clutch, AIEE Transactions, 67, p1308-1315, 1948. [11] J. Rabinow. Magnetic uid torque and force transmitting device, US Patent 2,575,360, United States Patent Oce, November 20, 1951. [12] Lord Corporation, Magnetorheological (MR) Solutions, Cary, NC, 2007. Available: http://www.lord.com [13] J. H. Yoo and N. M. Wereley, Design of a high-eciency magnetorheological valve, J. Intel. Mat. Syst. And Structures, 13(10), p679-685, October 2002. [14] R. Gilbert and M. Jackson. Magnetic ride control, GM Tech Link, 4(1), p1-2, January 2002. [15] J. D. Carlson, Controlling vibration with magnetorheological uid damping, Sensors, 19(2), February 2002. [16] S.J. Dyke, B.F. Spencer Jr., M.K.Sain and J.D. Carlson, Modeling and control of magnetorheological dampers for seismic response reduction, Smart Materials and Structures, 5, p565-575, 1996. [17] L. M. Jansen and S. J. Dyke, Semi-active control strategies for MR dampers: A comparative study, ASCE Journal of Engineering Mechanics, 126(8), p795803, August 2000. [18] Z. D. Xu, Y. P. Shen and Y. Q Guo, Semi-active control of structures incorporated with magnetorheological dampers using neural networks, Smart Materials and Structures, 12, p80-87, 2003.

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Appendix A Maxwell Equations

In 1873, the infamous Scottish scientist James Maxwell wrote Treatise on Electricity and Magnetism, in which he summarized the relationship between electrical and magnetic elds that was derived by Faraday, Ampere, Gauss, Coulomb and others. His main purpose was to explain Faradays ideas into a universal mathematical form. His main contribution was to include the displacement current (that results from the change in the electrical ux intensity (or electric displacement) D) in Amperes Law (see Eq. A.2) [49]. The eld equations known as Maxwells Equations are: B t D t

E=

(A.1) (A.2) (A.3) (A.4)

H=J+ D= B=0

where E is the electric eld intensity, H is the magnetic eld intensity, B is the magnetic ux density, J is the electric current density and is the charge density.

APPENDIX A. MAXWELL EQUATIONS

95

Eq. (A.1) is known as Faradays Law of Induction which states that any change in the magnetic eld results in the ow of charges in a conductive medium. Eq. (A.2) is the Maxwell-Amperes Law which states that electric current owing through a closed loop results in magnetic eld generation. Eqs. (A.3) and (A.4) are known as Gauss Law. Eq. (A.3) states that the divergence of electrical ux density is equal to the charge density and Eq. (A.4) states that the divergence of magnetic ux density is always zero for a closed surface dened.

PARTIAL COPYRIGHT LICENSE

I hereby grant the right to lend my thesis to users of the University of Victoria Library, and to make single copies only for such users or in response to a request from the Library of any other university, or similar institution, on its behalf or for one of its users. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by me or a member of the University designated by me. It is understood that copying or publication of this thesis for nancial gain shall not be allowed without my written permission. Title of Thesis:

Design of a Magnetorheological Brake System Based on Magnetic Circuit Optimization

Author: Kerem Karakoc

Date