Index
AC excitation, 147–9
coordinate transformation, 173–7
three-phase, 168
two-phase, 167
Acceleration, 80
Acceleration test, 121–2
balanced, 2
induction motors, 264–70
PMS motors, 205–8
unbalanced, 2
Angular speed, 148
Applications, 14–15
Axial force, 95
Axial gap motors, 321–8
axial position regulation, 322–3
inclination control, 323–5
mechanical structure, 319–20
nonlinear characteristics, 327–8
radial damping control, 325–7
structure, 321–2
Axial position regulation, 322–3
Back electromotive force, 75
Bearing and drive, 8
Bearing motors, 8
Bearingless drives, 4–5
advantages of, 4–5
definitions of, 5
development of, 7–8
vector control theory, 169–73
Blood pump, 367–70
BPM motors See (Buried permanent magnet motors)
Brushless DC motors, 5
rotor position control, 232–7
rotor structures, 229–30
specifications, 232
suspension force, 231–2
unbalance pull force, 41
Canned drives, 361–5
Canned pumps, 361–5
Coil current, 3
Combined motor-bearing, 8
Common mode rejection ratio, 124
Compact pumps, 365–7
Consequent-pole motors, 279–81
Controllers See (Digital controllers)
Coordinate transformation, 203
DC to AC bearingless machines, 173–7
and torque regulation, 166–9
Coordinates, 86
Corn type motors, 320
coil, 3
equations of, 204–5
synchronous reluctance motors, 239–40
BPM motors, 231–2
PMS motors, 208–12
Current block, three-phase, 169
Current detectors, 37
Current driver operating area, 119–22
acceleration test, 121–2
Current feedback, 112–22
linear current controller, 113–16
nonlinear current controller, 116–19
Current-originated acceleration, 90
Damping constant, 48
Damping factor, 56
Damping-force command, 17
DC excitation, 145–7
DC motors, coordinate transformation, 173–7
Delay, 65–7
Demagnetization, 212–14
Derivative gain, 57
Design procedure, 351–60
induction motors, 351–6
PMS motors, 356–60
Differential actuator, 26–7
Differential circuit, 334
Digital controllers, 344–50
sample program, 348–50
z-domain, 347
Digital signal processing, 6–7
Diodes, 105
Direct drives, 264–70
detection from line voltage and current, 267–9
modulation block suspension current commands, 269–70
search coil method, 264–7
Direction angle error, 68
Displacement, 56
flux distributions, 171
Displacement frequency response, 55
Displacement-originated acceleration, 90
Displacement reference, 53
improvements in sensitivity, 333–6
differential circuit, 334–6
resonant circuit, 334
inductive and eddy current sensors, 336–8
principles of, 330–3
requirements for, 329–30
sensorless motors, 338–42
Displacement time response, 55
Disturbance frequency, 56
Drive systems, 284–6
switched reluctance motors, 297–301
Duty cycle, 108
DVD drives, 9
Dynamic stiffness, 53
E-core, 29–33
Eccentric displacement, 78–81
and flux density, 23–4
Electromagnetics, 16–44
Electromagnets, 7
structure and operation, 16–17
Electromotive forces, 12
induction motors, 252
EMF See (Electromotive forces)
Equation of motion, 90–4
Excitation torque, 162
Feed-forward compensator, 304–7
Feedback radial force, 76
Field orientation misalignment, 185–90
Field oriented control theory See (Vector control theory)
requirements of, 95–6
thrust magnetic bearing, 94–5
Fleming’s left-hand rule, 161
Floating actuator, 8
Flux, 17–20
and radial force, 68
Flux density detectors, 183
Flux detection, 37
relationship to current, 21
Flux path length, 18
Flywheel drives, 9
Force calculation, 25–6
Force command, 17
Force-current factor, 39
Four-axis systems, 90–4
Gate drive circuits, 122–6
waveform checking and isolation, 125–6
Gauss’ law, 136
Gyroscopic acceleration, 90
H-bridge inverter, 103–4
Hard disk drives, 9
Hastelloy, 362
High-cut filter, 114
Homopolar magnetic bearing, 274–6
Hybrid amplifier, 98
Hybrid motors, 278–9
Hysteresis current controller, 116–19
unbalance pull force, 41
Ideal derivative controller, 58
Inclination control, 323–5
Inclination force, 92
Inclination movement, 92
Indirect drives, 257–64
Inductance, 17–20
measurement, 149–58
switched reluctance motors, 290–1
three-phase, 154
Inductance matrix, 138–41
design procedure, 351–6
direct drives, 264–70
detection from line voltage and current, 267–9
modulation block suspension current commands, 269–70
search coil method, 264–7
indirect drives, 257–64
primitive controller, 258
force, 251–7
two-pole motors drive, 271–2
VA requirement, 192–6
Inductive sensors, 336–8
Inertia, 86
Inrush current, 125
Inset motors, 220–8
mutual interference between radial suspension forces, 221–2
rotor position control, 223
specification, 227
structure and features, 220–1
suspension force parameters, 223–8
Integrated motor bearings, 8
Integrator constant, 62
Integrators, 61–5
Interference force, 71
Interference in perpendicular axes, 67–72
Interference transfer function, 72
Interior permanent magnet motors See (Buried permanent magnet motors)
Inverter fault tolerance, 13
IPM motors See (Buried permanent magnet motors)
Lateral force motors, 8
Levitated motors, 8
Linear analogue amplifiers, 98
Linear approximation errors, 26
Linear operation, 102
Linear operator amplifiers, 101–3
Linear transistor amplifiers, 99–100
Linearization, 37–9
Load power consumption, 103
Low pass filters, 76
Magnetic attraction force, 302–4
Magnetic bearing controllers, 45–84
adjustment of PID gains, 52–67
eccentric displacement, 78–81
interference in two perpendicular axes, 67–72
one-axis magnetic suspension, 45–52
synchronized displacement suppression, 81–4
unbalance force and elimination, 72–8
Magnetic bearings, 1–3
Magnetic centre, 302–4
Magnetic co-energy, 21
Magnetic energy, 20–33
Magnetic force, 20–33
Magnetic potential, 135–8
Magnetic saturation, 197–200
synchronous reluctance motors, 247–8
Magnetically levitated train, 2
Mathematical models, 16–44
Maximum flux density, 17
Maxwell stress equation, 23
Mechanical dial gauges, 153
Mechanical dynamics, 85–96
four-axis and five-axis systems, 90–4
two-axis system, 85–90
Mechanical structure, 318–20
axial-gap motors, 319–20
radial gap motors, 318–19
Metal oxide silicon field effect transistors See (MOSFETs)
MMF See (Magneto Motive Force (MMF))
Moment, 88–9
Motor control system, 245–6
Motor drives, 1–3
Neodymium, 29
Non-linear current controller, 116–19
Non-linear magnetic characteristics, 25
force calculation, 25–6
P-pole winding, 313–16
(P±2)-pole winding, 313–16
airgap flux density, 205–8
control system configuration, 216–19
design procedure, 356–60
equations of voltage and current, 204–5
irreversible permanent magnet demagnetization, 212–14
limits of stator winding MMFs, 214–16
radial suspension force and suspension winding current, 202–4
radial suspension force for unity current, 208–12
rotor structure, 201–2
VA requirement, 196–7
Permanent magnets, 12
E- and I-cores, 29–33
positioning, 212–14
thickness, 205–12
VA requirement, 192–6
switched reluctance motors, 291–4
Phase-lead angle, 58
Phase-lead compensator, 58
Phase shift angle, 187
Phasor diagrams, 240
PMS motors See (Permanent magnet synchronous motors)
Position disturbance, 80
Position error, 58–61
Power consumption ratio, 103
Power devices, 122–6
current feedback, 112–22
gate drive circuits, 122–6
linear operational amplifiers, 101–3
linear transistor amplifiers, 99–100
low cost chopper circuit, 106–7
pulse width modulation, 107–12
switched-mode amplifiers, 103–6
Power factor, 163
Practical derivative controller, 57–61
Proportional gain, 57
gain adjustment, 56–7
influence of delay, 65–7
practical digital controller, 57–61
sample program, 348–50
steady-state position error, 61–5
z-domain, 347
analysis of RL circuit, 109–12
principles, 107–9
Pulse width modulation inverter, 339
Push-pull amplifiers, 97–126
linear operator, 101–3
linear transistor, 99–100
switched-mode, 103–6
Push-pull transistors, 98
PWM See (Pulse width modulation)
Radial damping control, 325–7
Radial displacement, 43
density, 36
errors in direction, 68
synchronous reluctance motors, 241
two-pole bearingless motors, 131–2
Radial force interference, 185–90
Radial gap motors, 318–19
Radial interference, 67–72
unbalance pull force, 41–2
winding configuration, 309–11
Radial position loops, 188
Radial sensor output, 90
Radial suspension force See (Suspension force)
Recoil permeability, 30
Resonant circuit, 334–6
Revolving magnetic field, 147–9
RL circuit, 109–12
Rotary encoder, 344
Rotor magnetic potential, 136–8
BPM motors, 232–7
inset motors, 223
Rotor radial movement, 92
BPM type, 229–30
inset type, 220–1
PMS type, 201–2
synchronous reluctance type, 238–9
Samarium, 30
Satellite reaction wheels, 14
Self bearing motors, 8
Semiconductor processing, 371–3
Sensor target, 79
Sensorless motors, 338–42
Short-pitch differential winding, 14
Single-phase inverter, 103–6
Speed regulation, 169
Spindle motors, 370–1
SPM motors See (Surface-mounted permanent magnet motors)
Spring-force command, 17
Spring-mass-damper system, 47–52
Squirrel-cage induction motors See (Induction motors)
Static displacement, 48
Static stiffness, 53
inset type, 227
PMS type, 214–16
winding configurations, 13
switched reluctance type, 288–9
synchronous reluctance type, 238–9
Steady-state position error, 61–5
Step disturbance suppression, 189
Step response, 70
Stepping motors, 7
Suspension control system, 244–5
mutual interference, 234
nonlinear magnetic characteristics, 234–7
unity current, 231–2
variations in, 232–4
induction motors, 251–7
inset motors, 223–8
mutual interference, 221–2
suspension winding current, 202–4
unity current, 208–12
Suspension winding current, 202–4
Swinging motors, 15
Switched-mode amplifiers, 103–6
Switched-mode operation, 102–3
Switched-mode PWM amplifier, 98
drive system, 297–301
feed-forward compensator, 302–7
inductances, 290–1
permeances, 291–4
stator windings, 288–9
suspension force and torque, 295–6
suspension force generation, 288–9
Synchronized displacement suppression, 81–4
Synchronous disturbance elimination, 74–8
flux paths, 322
magnetic saturation, 247–8
motors control system, 245–7
radial forces, 241
rotor and stator, 238–9
suspension control system, 244–5
test machine, 248–9
torque, 240–1
unbalanced magnetic pull, 242–4
voltage and current, 239–40
System block diagrams, 177–83
five-axis active suspensions, 94–5
Time constant, 49
excitation, 162
generation, 11–12
induction motors, 252–3
regulation, 166–9
switched reluctance motors, 295–8
synchronous reluctance motors, 240–1
Transfer function, 79
Translational force, 92
Two-axis active magnetic suspension, 9
Two-axis system, 85–90
Two stage push-pull amplifier, 100
Unbalance force, 75
Unbalance mass, 73
Unbalance pull force, 40–2
analysis in C- and I-cores, 41
analysis in radial magnetic bearing, 41–2
Unbalanced force, 72–8
Unbalanced magnetic pull, 242–4
bearingless motors, 169–73
induction motors, 261–3
Vibration, 72–8
synchronous disturbance elimination, 74–8
Volt-ampere (VA) requirement, 190–7
induction-type bearingless motors, 192–6
permanent magnet type bearingless motors, 196–7
equations of, 204–5
synchronous reluctance motors, 239–40
Waveform checking and isolation, 125–6
Winding back-EMFs, 190
induction motors, 353
modified radial magnetic bearings, 309–11
P-pole and (P2)-pole, 313–16
short-pitch, 14
split winding motors, 311–13
switched reluctance type, 288–9
synchronous reluctance type, 238–9
Winding current, 22
Winding structures, 13–14
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