An accessible, comprehensive guide on magnetic actuators and sensors, this fully updated second edition of *Magnetic Actuators and Sensors* includes the latest advances, numerous worked calculations, illustrations, and real-life applications. Covering magnetics, actuators, sensors, and systems, with updates of new technologies and techniques, this exemplary learning tool emphasizes computer-aided design techniques, especially magnetic finite element analysis, commonly used by today's engineers. Detailed calculations, numerous illustrations, and discussions of discrepancies make this text an invaluable learning tool for practicing engineers and engineering students.

**PREFACE xi**

**PREFACE TO THE FIRST EDITION xiii**

**LIST OF 66 EXAMPLES xv**

**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 7

References 8

**2 Basic Electromagnetics 9**

2.1 Vectors 9

2.2 Ampere’s Law 14

2.3 Magnetic Materials 17

2.4 Faraday’s Law 22

2.5 Potentials 25

2.6 Maxwell’s Equations 28

Problems 29

References 31

**3 Reluctance Method 33**

3.1 Simplifying Ampere’s Law 33

3.2 Applications 37

3.3 Fringing Flux 40

3.4 Complex Reluctance 41

3.5 Limitations 41

Problems 42

References 42

**4 Finite-Element Method 43**

4.1 Energy Conservation and Functional Minimization 43

4.2 Triangular Elements for Magnetostatics 45

4.3 Matrix Equation 46

4.4 Finite-Element Models 49

Problems 53

References 53

**5 Magnetic Force 55**

5.1 Magnetic Flux Line Plots 55

5.2 Magnetic Energy 60

5.3 Magnetic Force on Steel 61

5.4 Magnetic Pressure on Steel 65

5.5 Lorentz Force 66

5.6 Permanent Magnets 67

5.7 Magnetic Torque 72

5.8 Magnetic Volume Forces on Permeable Particles 73

Problems 75

References 76

**6 Other Magnetic Performance Parameters 79**

6.1 Magnetic Flux and Flux Linkage 79

6.2 Inductance 82

6.3 Capacitance 86

6.4 Impedance 88

Problems 91

References 91

**PART II ACTUATORS 93**

**7 Magnetic Actuators Operated by DC 95**

7.1 Solenoid Actuators 95

7.2 Voice Coil Actuators 106

7.3 Other Actuators Using Coils and Permanent Magnets 108

7.4 Proportional Actuators 109

7.5 Rotary Actuators 112

7.6 Magnetic Bearings and Couplings 114

7.7 Magnetic Separators 117

Problems 125

References 127

**8 Magnetic Actuators Operated by AC 129**

8.1 Skin Depth 129

8.2 Power Losses in Steel 130

8.3 Force Pulsations 135

8.4 Cuts in Steel 139

References 145

**9 Magnetic Actuator Transient Operation 147**

9.1 Basic Timeline 147

9.2 Size, Force, and Acceleration 148

9.3 Linear Magnetic Diffusion Times 150

9.4 Nonlinear Magnetic Infusion Times 156

9.5 Nonlinear Magnetic Effusion Time 164

9.6 Pulse Response of Nonlinear Steel 169

Problems 171

References 174

**PART III SENSORS 175**

**10 Hall Effect and Magnetoresistive Sensors 177**

10.1 Simple Hall Voltage Equation 177

10.2 Hall Effect Conductivity Tensor 179

10.3 Finite-Element Computation of Hall Fields 182

10.4 Hall Sensors for Position or Current 190

10.5 Magnetoresistance 193

10.6 Magnetoresistive Heads for Hard Disk Drives 194

10.7 Giant Magnetoresistive Spin Valve Sensors 195

Problems 198

References 198

**11 Other Magnetic Sensors 201**

11.1 Speed Sensors Based on Faraday’s Law 201

11.2 Inductive Recording Heads 203

11.3 Proximity Sensors Using Impedance 206

11.4 Linear Variable Differential Transformers 210

11.5 Magnetostrictive Sensors 213

11.6 Fluxgate Sensors 215

11.7 Chattock Coil Field and Current Sensor 219

11.8 Squid Magnetometers 222

11.9 Magnetoimpedance and Miniature Sensors 223

11.10 MEMS Sensors 224

Problems 225

References 226

**PART IV SYSTEMS 229**

**12 Coil Design and Temperature Calculations 231**

12.1 Wire Size Determination for DC Currents 231

12.2 Coil Time Constant and Impedance 234

12.3 Skin Effects and Proximity Effects for AC Currents 235

12.4 Finite-Element Computation Of Temperatures 239

Problems 246

References 246

**13 Electromagnetic Compatibility 249**

13.1 Signal-To-Noise Ratio 249

13.2 Shields and Apertures 250

13.3 Test Chambers 255

Problems 260

References 260

**14 Electromechanical Finite Elements 263**

14.1 Electromagnetic Finite-Element Matrix Equation 263

14.2 0D and 1D Finite Elements for Coupling Electric Circuits 266

14.3 Structural Finite-Element Matrix Equation 272

14.4 Force and Motion Computation by Time Stepping 273

14.5 Typical Electromechanical Applications 275

Problems 286

References 286

**15 Electromechanical Analysis Using Systems Models 289**

15.1 Electric Circuit Models of Magnetic Devices 289

15.2 VHDL–AMS/Simplorer Models 296

15.3 MATLAB/Simulink Models 301

15.4 Including Eddy Current Diffusion Using a Resistor 307

15.5 Magnetic Actuator Systems for 2D Planar Motion 312

15.6 Optimizing Magnetic Actuator Systems 313

Problems 324

References 325

**16 Coupled Electrohydraulic Analysis Using Systems Models 327**

16.1 Comparing Hydraulics and Magnetics 327

16.2 Hydraulic Basics and Electrical Analogies 328

16.3 Modeling Hydraulic Circuits in Spice 330

16.4 Electrohydraulic Models in Spice and Simplorer 334

16.5 Hydraulic Valves and Cylinders in Systems Models 341

16.6 Magnetic Diffusion Resistor in Electrohydraulic Models 348

16.7 Optimization of an Electrohydraulic System 352

16.8 Magnetic Actuators for Digital Hydraulics 353

Problems 357

References 357

**APPENDIX A: SYMBOLS, DIMENSIONS, AND UNITS 359**

**APPENDIX B: NONLINEAR B–H CURVES 361**

**APPENDIX C: FINAL ANSWERS FOR ODD-NUMBERED PROBLEMS 367**

**INDEX 371**