Magnetic Actuators and Sensors

A fully updated, easy-to-read guide on magnetic actuators and sensors The Second Edition of this must-have book for today's engineers includes the latest updates and advances in the field of magnetic actuators and sensors. Magnetic Actuators and Sensors emphasizes computer-aided design techniques—especially magnetic finite element analysis; offers many new sections on topics ranging from magnetic separators to spin valve sensors; and features numerous worked calculations, illustrations, and real-life applications. To aid readers in building solid, fundamental, theoretical background and design know-how, the book provides in-depth coverage in four parts: PART I: MAGNETICS Introduction Basic Electromagnetics Reluctance Method Finite-Element Method Magnetic Force Other Magnetic Performance Parameters PART II: ACTUATORS Magnetic Actuators Operated by Direct Current Magnetic Actuators Operated by Alternating Current Magnetic Actuator Transient Operation PART III: SENSORS Hall Effect and Magnetoresistive Sensors Other Magnetic Sensors PART IV: SYSTEMS Coil Design and Temperature Calculations Electromagnetic Compatibility Electromechanical Finite Elements Electromechanical Analysis Using Systems Models Coupled Electrohydraulic Analysis Using Systems Models With access to a support website containing downloadable software data files (including MATLAB® data files) for verifying design techniques and analytical methods, Magnetic Actuators and Sensors, Second Edition is an exemplary learning tool for practicing engineers and engineering students involved in the design and application of magnetic actuators and sensors.

Preface to the First Edition XX Preface to the Second Edition XX List of Examples XX PART I MAGNETICS 1 1. Introduction 3 1.1 Overview of Magnetic Actuators 3 1.2 Overview of Magnetic Sensors 4 1.3 Actuators and Sensors in Motion Control Systems 5 1.4 Magnetic Actuators and Sensors in Mechatronics X References 2. Basic Electromagnetics 7 2.1 Vectors 7 2.2 Ampere’s Law 12 2.3 Magnetic Materials 15 2.4 Faraday’s Law 18 2.5 Potentials 22 2.6 Maxwell’s Equations 24 Problems 26 References 28 3. Reluctance Method 29 3.1 Simplifying Ampere’s Law 29 3.2 Applications 32 3.3 Fringing Flux 36 3.4 Complex Reluctance 36 3.5 Limitations 37 Problems 37 References 37 4. Finite–Element Method 39 4.1 Energy Conservation and Functional Minimization 39 4.2 Triangular Elements for Magnetostatics 40 4.3 Matrix Equation 42 4.4 Finite–Element Models 44 Problems 48 References 49 5. Magnetic Force 51 5.1 Magnetic Flux Line Plots 51 5.2 Magnetic Energy 56 5.3 Magnetic Force on Steel 57 5.4 Magnetic Pressure on Steel 60 5.5 Lorentz Force 62 5.6 Permanent Magnets 62 5.7 Magnetic Torque 66 5.8 Magnetic Volume Forces on Permeable Particles XX Problems 67 References 67 6. Other Magnetic Performance Parameters 69 6.1 Magnetic Flux and Flux Linkage 69 6.2 Inductance 72 6.3 Capacitance 75 6.4 Impedance 77 Problems 80 References 80 PART II ACTUATORS 83 7. Magnetic Actuators Operated by Direct Current 85 7.1 Solenoid Actuators 85 7.2 Voice Coil Actuators 96 7.3 Other Actuators Using Coils and Permanent Magnets 97 7.4 Proportional Actuators 98 7.5 Rotary Actuators 101 7.6 Magnetic Bearings and Couplings XX 7.7 Magnetic Separators XX Problems 104 References 105 8. Magnetic Actuators Operated by Alternating Current 107 8.1 Skin Depth 107 8.2 Power Losses in Steel 108 8.3 Force Pulsations 113 8.4 Cuts In Steel 116 Problems 122 References 123 9. Magnetic Actuator Transient Operation 125 9.1 Basic Timeline 125 9.2 Size, Force, and Acceleration 125 9.3 Linear Magnetic Diffusion Times 128 9.4 Nonlinear Magnetic Infusion Time 132 9.5 Nonlinear Magnetic Effusion Time XXX 9.6 Pulse Response of Nonlinear Steel Problems 138 References 142 PART III SENSORS 143 10. Hall Effect and Magnetoresistive Sensors 145 10.1 Simple Hall Voltage Equation 145 10.2 Hall Effect Conductivity Tensor 146 10.3 Finite–Element Computation of Hall Fields 149 10.4 Hall Sensors for Position or Current XX 10.5 Magnetoresistance 159 10.6 Magnetoresistive Heads for Hard–Disk Drives 161 10.7 Giant Magnetoresistive Spin Valve Sensors  XX Problems 162 References 162 11. Other Magnetic Sensors 165 11.1 Speed Sensors Based on Faraday’s Law 165 11.2 Inductive Recording Heads 167 11.3 Proximity Sensors Using Impedance 169 11.4 Linear Variable Differential Transformers 174 11.5 Magnetostrictive Sensors 177 11.6 Flux Gate Sensors 179 11.7 Chattock Coil Field and Current Sensor XX 11.8 SQUID Magnetometers XX 11.9 Magnetoimpedance and Miniature Sensors  XX 11.10 MEMS Sensors  XX Problems 186 References 186 PART IV SYSTEMS 189 12. Coil Design and Temperature Calculations 191 12.1 Wire Size Determination for DC Currents 191 12.2 Coil Time Constant and Impedance 194 12.3 Skin Effects and Proximity Effects for AC Currents 195 12.4 Finite–Element Computations of Temperatures 199 Problems 206 References 206 13. Electromagnetic Compatibility 209 13.1 Signal–to–Noise Ratio 209 13.2 Shields and Apertures 210 13.3 Test Chambers 215 Problems 220 References 220 14. Electromechanical Finite Elements 223 14.1 Electromagnetic Finite–Element Matrix Equation 223 14.2 0D and 1D Finite Elements for Coupling Electric Circuits 225 14.3 Structural Finite–Element Matrix Equation 228 14.4 Force and Motion Computation by Time–Stepping 232 14.5 Typical Electromechanical Applications 234 Problems 242 References 244 15. Electromechanical Analysis Using Systems Models 247 15.1 Electric Circuit Models of Magnetic Devices 247 15.2 VHDL–AMS/Simplorer Models 254 15.3 MATLAB/Simulink Models 258 15.4 Including Eddy Current Diffusion Using a Resistor 264 15.5 Magnetic Actuators Systems for 2D Planar Motion xx 15.6 Optimizing Magnetic Actuator Systems xx Problems 268 References 268 16. Coupled Electrohydraulic Analysis Using Systems Models 271 16.1 Comparing Hydraulics and Magnetics 271 16.2 Hydraulic Basics and Electrical Analogies 272 16.3 Modeling Hydraulic Circuits in SPICE 274 16.4 Electrohydraulic Models in SPICE and Simplorer 277 16.5 Hydraulic Valves and Cylinders in Systems Models 283 16.6 Magnetic Diffusion Resistor in Electrohydraulic Models 292 16.7 Optimization of an Electrohydraulic System XX 16.8 Magnetic Actuators for Digital Hydraulics xx Problems 296 References 297 Appendix A: Symbols, Dimensions, and Units xx Appendix B: Nonlinear B–H Curves xx Appendix C: Final Answers for Odd–Numbered Problems Index 301

JOHN R. BRAUER, PhD, PE, is Adjunct Professor in the Department of Electrical Engineering and Computer Science at the Milwaukee School of Engineering. A Life Fellow of the IEEE, he received their Third Millennium Medal in 2000 for his service, and has served on the boards of the Applied Computational Electromagnetics Society and the International Compumag Society. In addition, Dr. Brauer has published 160 technical papers and contributed to several books.