Magnetic Bearings (eBook)

Preface 5
Contents 7
List of Contributors 9
The Authors 11
1 Introduction and Survey 16
1.1 Principles of Magnetic Bearing Function 16
1.2 The Magnetic Bearing as a Mechatronic Product 19
1.3 The Magnetic Bearing in Transportation, Physics and Mechanical Engineering 20
1.4 Classification of Magnetic Bearings 25
1.5 Characteristics of Active Magnetic Rotor Bearings 30
1.6 Examples from Research and Industry 32
References 39
2 Principle of Active Magnetic Suspension 42
2.1 The Magnetic Bearing as a Controlled Suspension 42
2.2 Closing the Control Loop of a Magnetic Bearing 48
2.3 Feedback Control Design 66
2.4 Forced Vibration and Frequency Response 70
References 82
3 Hardware Components 84
3.1 Bearing Electromagnets 85
3.2 Permanent Magnet Biased Magnetic Bearings 110
3.3 Power Ampli.ers 112
3.4 Sensors 114
3.5 Concluding Remarks 122
References 123
4 Actuators 125
4.1 Structure 125
4.2 Amplifiuers 126
4.3 Electromagnets 129
4.4 Actuator assembly 131
4.3 Electromagnets 129
4.4 Actuator assembly 131
4.5 Examples 134
4.6 Driving Modes and Linearization 138
4.7 Response Limitations of the Magnetic Actuator 141
4.8 Measuring System Characteristics 145
References 147
5 Losses in Magnetic Bearings 149
5.1 Overview 149
5.2 Iron Losses in the Rotor 152
5.3 Aerodynamic Losses, Windage Losses 154
5.4 Determining Rotor Losses 160
5.5 Measures to Reduce Losses 161
5.6 Losses in Various Applications 162
References 164
6 Design Criteria and Limiting Characteristics 165
6.1 Load Capacity 165
6.2 Controller and Actuator 166
6.3 Speed 168
6.4 Size 172
6.5 High Temperature 172
6.6 Losses 173
6.7 Precision 175
6.8 Smart Machine Concept 175
6.9 Conclusions 176
References 177
7 Dynamics of the Rigid Rotor 180
7.1 Introduction 180
7.2 Inertia Properties 180
7.3 Natural Vibrations of a Rotor on Elastic Supports 184
7.4 In.uence of Rotor Speed and Gyroscopic E.ects 189
7.5 Static and Dynamic Unbalance 193
7.6 Rotor Excitations and Critical Speeds 195
References 202
8 Control of the Rigid Rotor in AMBs 203
8.1 The Rotor–Bearing Model 203
8.2 Feedback Control Design 205
8.3 Unbalance Control 227
References 236
9 Digital Control 241
9.1 Digital vs. Analog Control 241
9.2 Digital Control Hardware and Timing Issues 242
9.3 Basics of Discrete-Time Control 244
9.4 Control Design for Discrete-Time Systems 254
9.5 Implementation Aspects of Digital Control 257
9.6 Diagnostic Capabilities of Digitally Controlled AMBs 258
References 261
10 Dynamics of Flexible Rotors 263
10.1 Introduction 263
10.2 Je.cott Rotor – a Simple Flexible Rotor 264
10.3 Flexible Rotors with Continuous Mass and Stiffness Distribution 275
10.4 Equations of Motion Based on the Finite Element Method 279
10.5 Flexible Rotor with Active Magnetic Bearings 300
10.6 Reduction of Finite Element Models 304
10.7 Closing Remarks 307
References 308
11 Identification 310
11.1 Introduction 310
11.2 Dynamic Characteristics of Rotating Systems 311
11.3 Identification of Physical and/or Modal Parameters 312
11.4 Excitation of a Rotor by means of Magnetic Bearings 316
11.5 Applications for Identi.cation 318
11.6 Closing Remarks 328
References 329
12 Control of Flexible Rotors 330
12.1 Flexibility E.ects 330
12.2 Model Structure 339
12.3 Model Elements and Assembly 340
12.4 Simplest Control: Collocated Local PID 353
12.5 Performance Assessment 358
12.6 Non-collocated Local PID Control 363
12.7 Sensitivity 366
12.8 Non-collocated Mixed PID Control 372
12.9 H8 Norm 377
12.10 H8 Control 378
12.11 µ.Control 381
12.12 Asymmetric Example 386
12.13 Gyroscopics 388
12.14 Unbalance Control 389
12.15 Closing Remarks 394
References 395
13 Touch-down Bearings 400
13.1 A Rotor Contacting its Housing - Survey 401
13.2 Modeling of Contacts 402
13.3 Whirl Motion 407
13.4 Ball Bearings 411
13.5 Design Considerations 412
13.6 Conclusions 415
References 416
14 Dynamics and Control Issues for Fault Tolerance 418
Introduction 418
14.1 Avoiding Touchdown 418
14.2 Touch-down Dynamics 423
References 443
15 Self–Sensing Magnetic Bearings 445
15.1 Concepts 445
15.2 Motivation 447
15.3 Control Approaches 448
15.4 Remaining Technical Challenges 460
15.5 Conclusions 464
References 465
16 Self–Bearing Motors 470
16.1 Introduction 470
16.2 Self-Bearing Motor of the Type P ± 2 472
16.3 Hybrid Type Self-Bearing Motor 477
16.4 Lorentz Type Self-Bearing Motor 482
16.5 Axial Self-Bearing Motor 486
16.6 Application to Arti.cial Heart Pump 489
16.7 Concluding remarks 493
References 493
17 Micro Magnetic Bearings 495
17.1 Introduction to micro magnetic actuators and their down-scaling 495
17.2 Classification of magnetic bearing types 501
17.3 Diamagnetic rotor bearings 503
17.4 Active Magnetic Micro Bearings 506
17.5 A microbearing for 3 million rpm 507
17.6 Conclusions 510
References 511
18 Safety and Reliability Aspects 512
18.1 Psychological and Philosophical Background of Safety 513
18.2 De.nitions and Technical Aspects of Safety, Reliability and Dependability 514
18.3 The AMB as a Mechatronic Product and Failure Examples 515
18.4 Measures for Reducing Risks of Failure 516
18.5 Smart Machine Technologies 521
18.6 Conclusions 525
References 525
Index 529