Noise of Polyphase Electric Motors

by Gieras; Jacek F.

• ISBN13: 9780824723811
• ISBN10: 0824723813
• Edition: 1st
• Format: Hardcover
• Copyright: 2005-12-12
• Publisher: CRC Press

Summary

Controlling the level of noise in electrical motors is critical to overall system performance. However, predicting noise of an electrical motor is more difficult and less accurate than for other characteristics such as torque-speed. Recent advances have produced powerful computational methods for noise prediction, and Noise of Polyphase Electric Motors is the first book to collect these advances in a single source. It is also the first to include noise prediction for permanent magnet (PM) synchronous motors.Complete coverage of all aspects of electromagnetic, structural, and vibro-acoustic noise makes this a uniquely comprehensive reference. The authors begin with the basic principles of noise generation and radiation, magnetic field and radial forces, torque pulsations, acoustic calculations, as well as noise and vibration of mechanical and acoustic origin. Moving to applications, the book examines in detail stator system vibration analysis including the use of finite element method (FEM) modal analysis; FEM for radial pressure and structural modeling; boundary element methods (BEM) for acoustic radiation; statistical energy analysis (SEA); instrumentation including technologies, procedures, and standards; and both passive and active methods for control of noise and vibration.Noise of Polyphase Electric Motors gathers the fundamental concepts along with all of the analytical, numerical, and statistical methods into a unified reference. It supplies all of the tools necessary to improve the noise performance of electrical motors at the design stage.

Table of Contents

1 Generation and Radiation of Noise in Electrical Machines	1	(20)
1.1 Vibration, sound, and noise	1	(1)
1.2 Sound waves	1	(4)
1.3 Sources of noise in electrical machines	5	(2)
1.3.1 Electromagnetic sources of noise	5	(2)
1.3.2 Mechanical sources of noise	7	(1)
1.3.3 Aerodynamic noise	7	(1)
1.4 Energy conversion process	7	(2)
1.5 Noise limits and measurement procedures for electrical machines	9	(4)
1.6 Deterministic and statistical methods of noise prediction	13	(4)
1.7 Economical aspects	17	(1)
1.8 Accuracy of noise prediction	18	(3)
2 Magnetic Fields and Radial Forces in Polyphase Motors Fed with Sinusoidal Currents	21	(44)
2.1 Construction of induction motors	21	(2)
2.2 Construction of permanent magnet synchronous brushless motors	23	(2)
2.3 A.C. stator windings	25	(3)
2.4 Stator winding MMF	28	(8)
2.4.1 Single-phase stator winding	28	(4)
2.4.2 Three-phase stator winding	32	(1)
2.4.3 Polyphase stator winding	33	(3)
2.5 Rotor magnetic field	36	(1)
2.6 Calculation of air gap magnetic field	37	(8)
2.6.1 Effect of slots	37	(3)
2.6.2 Effect of eccentricity	40	(3)
2.6.3 Effect of magnetic saturation	43	(1)
2.6.4 Effect of rotor saliency	44	(1)
2.7 Radial forces	45	(13)
2.7.1 Production of radial magnetic forces	45	(3)
2.7.2 Amplitude of magnetic pressure	48	(1)
2.7.3 Deformation of the stator core	49	(1)
2.7.4 Frequencies and orders of magnetic pressure	50	(1)
2.7.5 Radial forces in synchronous machines with slotted stator	51	(3)
2.7.6 Frequencies of vibration and noise	54	(4)
2.8 Other sources of electromagnetic vibration and noise	58	(7)
2.8.1 Unbalanced line voltage	58	(1)
2.8.2 Magnetostriction	58	(4)
2.8.3 Thermal stress analogy	62	(1)
2.8.4 FEM model	62	(3)
3 Inverter-Fed Motors	65	(12)
3.1 Generation of higher time harmonics	65	(1)
3.2 Analysis of radial forces for nonsinusoidal currents	66	(5)
3.2.1 Stator and rotor magnetic flux density	67	(1)
3.2.2 Stator harmonics of the same number	68	(1)
3.2.3 Interaction of stator and rotor harmonics	69	(1)
3.2.4 Rotor harmonics of the same number	70	(1)
3.2.5 Frequencies and orders of magnetic pressure for nonsinusoidal currents	70	(1)
3.2.6 Interaction of stator harmonics of different numbers	70	(1)
3.2.7 Interaction of switching frequency and higher time harmonics	71	(1)
3.2.8 Interaction of permeance and magnetomotive force (MMF) harmonics	71	(1)
3.2.9 Rectifier harmonics	71	(1)
3.3 Higher time harmonic torques in induction machines	71	(2)
3.3.1 Asynchronous torques	71	(1)
3.3.2 Pulsating torques	72	(1)
3.4 Higher time harmonic torques in permanent magnet (PM) brushless machines	73	(1)
3.5 Influence of the switching frequency of an inverter	73	(2)
3.6 Noise reduction of inverter-fed motors	75	(2)
4 Torque Pulsations	77	(30)
4.1 Analytical methods of instantaneous torque calculation	77	(1)
4.2 Numerical methods of instantaneous torque calculation	78	(1)
4.3 Electromagnetic torque components	79	(1)
4.4 Sources of torque pulsations	80	(1)
4.5 Higher harmonic torques of induction motors	80	(1)
4.6 Cogging torque in permanent magnet (PM) brushless motors	81	(13)
4.6.1 Air gap magnetic flux density	82	(2)
4.6.2 Calculation of cogging torque	84	(3)
4.6.3 Simplified cogging torque equation	87	(1)
4.6.4 Influence of eccentricity	88	(4)
4.6.5 Calculation and comparison with measurements	92	(2)
4.7 Torque ripple due to distortion of EMF and current waveforms in permanent magnet (PM) brushless motors	94	(5)
4.8 Tangential forces vs. radial forces	99	(3)
4.9 Minimization of torque ripple in PM brushless motors	102	(5)
4.9.1 Slotless windings	102	(1)
4.9.2 Skewing stator slots	103	(1)
4.9.3 Shaping stator slots	103	(1)
4.9.4 Selection of the number of stator slots	104	(1)
4.9.5 Shaping PMs	104	(1)
4.9.6 Skewing PMs	104	(1)
4.9.7 Shifting PM segments	104	(1)
4.9.8 Selection of PM width	104	(1)
4.9.9 Magnetization of PMs	105	(1)
4.9.10 Creating magnetic circuit asymmetry	105	(2)
5 Stator System Vibration Analysis	107	(20)
5.1 Forced vibration	107	(3)
5.2 Simplified calculation of natural frequencies of the stator system	110	(2)
5.3 Improved analytical method of calculation of natural frequencies	112	(8)
5.3.1 Natural frequency of the stator core	112	(2)
5.3.2 Natural frequency of a frame with end bells	114	(1)
5.3.3 Natural frequency of a stator core–frame system	115	(1)
5.3.4 Effect of the stator winding and teeth	116	(1)
5.3.5 Analytical calculation of natural frequencies for a stator core-winding-frame system	117	(3)
5.4 Numerical verification	120	(7)
5.4.1 FEM modeling	120	(2)
5.4.2 Comparison of analytical calculations with the FEM	122	(5)
6 Acoustic Calculations	127	(48)
6.1 Sound radiation efficiency	127	(2)
6.2 Plane radiator	129	(12)
6.2.1 Infinite plates	130	(3)
6.2.2 Finite plates in bending motion	133	(8)
6.3 Infinitely long cylindrical radiator	141	(4)
6.4 Finite length cylindrical radiator	145	(21)
6.4.1 Acoustically thin shells	147	(2)
6.4.2 Acoustically thick shells	149	(5)
6.4.3 Modal radiation efficiencies of acoustically thick shells	154	(3)
6.4.4 Modal averaged radiation efficiency	157	(4)
6.4.5 Validity of using an infinite length model	161	(3)
6.4.6 Effects of boundary conditions on the radiation efficiency	164	(2)
6.5 Calculations of sound power level	166	(9)
6.5.1 Sound power radiated from a stator	167	(1)
6.5.2 Total sound power of an induction motor	168	(3)
6.5.3 Permanent magnet synchronous motors	171	(4)
7 Noise and Vibration of Mechanical and Aerodynamic Origin	175	(12)
7.1 Mechanical noise due to shaft and rotor irregularities	175	(1)
7.2 Bearing noise	176	(4)
7.2.1 Rolling bearings	176	(4)
7.2.2 Sleeve bearings	180	(1)
7.3 Noise due to toothed gear trains	180	(1)
7.4 Aerodynamic noise	181	(3)
7.5 Mechanical noise generated by the load	184	(3)
8 Acoustic and Vibration Instrumentation	187	(44)
8.1 Measuring system and transducers	187	(2)
8.2 Measurement of sound pressure	189	(8)
8.2.1 Choice of microphones	189	(1)
8.2.2 The sound pressure sensor–condenser microphone	189	(4)
8.2.3 Sound level meter	193	(3)
8.2.4 Acoustic calibrator	196	(1)
8.2.5 Level recorder	197	(1)
8.3 Acoustic measurement procedure	197	(3)
8.3.1 Effect of the operator on measurement results	197	(1)
8.3.2 Measurement position	198	(1)
8.3.3 Standing waves	198	(1)
8.3.4 Measurements of ambient sound pressure levels	198	(1)
8.3.5 Corrections for background sound during source measurements	199	(1)
8.3.6 Polar plots	200	(1)
8.4 Vibration measurements	200	(13)
8.4.1 Theory of operation of vibration-measuring transducer	201	(6)
8.4.2 Characteristics of piezoelectric accelerometers	207	(4)
8.4.3 Other vibration transducers	211	(2)
8.5 Frequency analyzers	213	(1)
8.6 Sound power and sound pressure	214	(1)
8.7 Indirect methods of sound power measurement	215	(2)
8.7.1 Determination of sound power in an anechoic/semianechoic room	215	(1)
8.7.2 Reverberation room	216	(1)
8.7.3 Juxtaposition principle using a reference sound source	217	(1)
8.8 Direct method of sound power measurement — sound intensity technique	217	(7)
8.8.1 Historical perspective	217	(1)
8.8.2 Theoretical background	217	(2)
8.8.3 Sound intensity probe	219	(2)
8.8.4 External noise suppression	221	(1)
8.8.5 Error considerations	221	(2)
8.8.6 Dynamic capability and pressure-intensity index	223	(1)
8.9 Standard for testing acoustic performance of rotating electrical machines	224	(7)
8.9.1 Background	224	(2)
8.9.2 Acoustic tests on an induction motor	226	(5)
9 Numerical Analysis	231	(26)
9.1 Introduction	231	(1)
9.2 FEM model for radial magnetic pressure	232	(7)
9.2.1 Induction motor	233	(4)
9.2.2 Permanent magnet synchronous motor	237	(2)
9.3 FEM for structural modeling	239	(4)
9.4 BEM for acoustic radiation	243	(12)
9.4.1 Governing equation and boundary conditions	243	(4)
9.4.2 FEM	247	(1)
9.4.3 BEM	248	(1)
9.4.4 Radiating sphere	248	(2)
9.4.5 Application to the prediction of radiated acoustic power from an inverter-fed induction motor	250	(5)
9.5 Discussion	255	(2)
10 Statistical Energy Analysis	257	(44)
10.1 Introduction	257	(2)
10.2 Power flow between linearly coupled oscillators	259	(8)
10.2.1 Two coupled oscillators	259	(2)
10.2.2 Three series coupled oscillators	261	(3)
10.2.3 Energy exchange between groups of oscillators	264	(3)
10.3 Coupled multimodal systems	267	(14)
10.3.1 General SEA equations	267	(2)
10.3.2 SEA model establishment	269	(3)
10.3.3 SEA parameters	272	(6)
10.3.4 Limitations of SEA	278	(3)
10.4 Experimental SEA	281	(9)
10.4.1 General theory	282	(3)
10.4.2 Recent developments	285	(5)
10.5 Application to electrical motors	290	(11)
10.5.1 Subsystems of a motor structure	291	(1)
10.5.2 Internal and coupling loss factors	292	(1)
10.5.3 Input power to the stator	293	(2)
10.5.4 Sound power radiated from the motor structure	295	(6)
11 Noise Control	301	(18)
11.1 Mounting	301	(6)
11.1.1 Foundation	301	(2)
11.1.2 Principles of vibration and shock isolation	303	(3)
11.1.3 Vibration limits	306	(1)
11.1.4 Shaft alignment	306	(1)
11.2 Standard methods of noise reduction	307	(4)
11.3 Active noise and vibration control	311	(8)
11.3.1 Principles of active noise control	311	(2)
11.3.2 Induction motor acoustic noise reduction	313	(2)
11.3.3 Active vibration isolation	315	(4)
Appendix A Basics of Acoustics	319	(8)
A.1 Sound field variables and wave equations	319	(2)
A.2 Sound radiation from a point source	321	(2)
A.3 Decibel levels and their calculations	323	(2)
A.4 Spectrum analysis	325	(2)
Appendix B Permeance of Nonuniform Air Gap	327	(6)
B.1 Permeance calculation	327	(1)
B.2 Eccentricity effect	328	(5)
Appendix C Magnetic Saturation	333	(4)
Appendix D Basics of Vibration	337	(10)
D.1 A mass—spring—damper oscillator	337	(2)
D.2 Lumped parameter systems	339	(3)
D.3 Continuous systems	342	(5)
Symbols and Abbreviations	347	(6)
Bibliography	353	(16)
Index	369