22 2 2018 2 Electri c Machines and Control Vol. 22 No. 2 Feb. 2018 1 2 3 3 1. 214082 2. 214082 3. 150001 DOI 10. 15938 /j. emc. 2018. 02. 005 TM 301. 4 A 1007-449X 2018 02-0033- 08 Research of permanent magnet motors cogging force affected by interferential magnetic field ZHAO Wen-feng 1 2 ZHAO Bo 3 XU Yong-xiang 3 1. National Key Laboratory on Ship Vibration & Noise Wuxi 214082 China 2. China Ship Science Research Center Wuxi 214082 China 3. School of Electrical Engineering and Automation Harbin Institute of Technology Harbin 150001 China Abstract Aiming at the underwater acoustical directiity of permanent magnet PM motor theoretical and numerical simulation methods are used to study radial force characteristics of fractional slot motor when ideal sine wae power and containing harmonic current power supplied. It is found that radial force of the fractional slot PM motor with ideal sinusoidal phase current periodically appears after some teeth. When phase current contains noninterfering harmonic current the radial force is aperiodic in time domain but it is still periodic in frequency domain. When harmonic current in phase current is interferential the radial force is aperiodic in both time domain and frequency domain. The aperiodic law is erified by an experiment in which phase current containing interfering harmonic current caused by pulse width modulation PWM. The radial force is the driing source of electromagnetic ibration and noise. Different forces leads to different ibrations on tooth. The aperiodic law of radial force can explain the acoustic directiity. Keywords PM motors electromagnetic force radial force electromagnetic ibration and noise harmonic interference 2016-07 - 10 863 2012AA09A306 1981 1978 1975
34 22 f t = f 0 w t + f r t 1 2 3 f w θ t = F cos p - ω 0 t - φ 1 2 f r θ t = F cos p - ω 0 t - φ 2 3 p ω 0 F F φ 1 φ 2 t A 1-2 0 B s 1 7000 1 Fig. 1 Schematic diagram of stator tooth space position t + Δt B t A 2 3 p s - 0 ω 0 Δt t + Δt B t A 3 t A 3-7 t +Δt B 2 8-11 4 12 f 0 t = F cos p 0 - ω 0 t - φ 1 f s t + Δt = F cos p s - ω 0 t - ω 0 Δt - φ 1 4 A B 1 1. 1 p s - 0 - ω 0 Δt = k 1 360 5 k 1 1 f w t f r t
2 35 6 9 z 0 p 0 z 0 = b + c 2mp 0 d = bd + c 6 d q = z = z 0 k p = p 0 k d 13 β = 360 /z 0 6 p 0 q = 7 5 8 9 = 2 3k 2 + 1 d 7 p s - 0 = ± 60 d 9 d 13 10 5 11 = 6k 2 + 1 d 10 p s - 0 = 6k 1 60 + ω 0 Δt d 11 6k 2 + 1 ω 0 Δt = ± 60 k 2 k 1 = ± k 2 11 s 0 9 9 ± 60 d ω I d f w t = F I cos p - ω I t - φ I I ω 0 Δt = ± 120 d ω 0 Δt 18 = ± 60 ω 0 Δt 60 d s t + Δt θ 0 t 12 f 0 t = f s t + Δt 12 s 0 9 60 d 1 A B Λ 13 14 p 0 t p s t + Δt 9 Λ 20 b t = f t + f t Λ θ 13 p t = b2 t 14 2 z 0 /6 Δt 60 15 z ' r = ωδt /β = z 0 /6 = p 0 q = p 0 bd + c /d p s - 0 = 3k 1 120 + ω 0 Δt d 8 2 3k 2 + 1 15 ω 0 Δt = ± 120 k 2 d z 0 2mp 0 k 1 k 1 = z 0 p 0 ± k 2 8 s 0 z 0 /m = m = 3 z 0 / 3 z 0 /6 d = p 0 15 d z r 16 z r = z ' r = bd + c 16 z 0 /6 d = 2p 0 d z r 17 ωδt = 120 z r = 2z ' r = bd + c 17 d bd + c 1. 2 18 F I I 5 Δt 19 k 3 ω I Δt = k 3 360 ± 60 ω I Δt = k 3 } 360 ± 120 19 ω 0 Δt = ± 60 d ω 0 Δt = ± 120 d ω I = 6k 3 ± 1 ω 0 ω I = 3k 3 ± 1 ω 0 } 20 ω 0 Δt 0 s ω 0 Δt 0 s 20 ω 0 Δt
36 22 ω I Δt I = ± 60 d ω I Δt I = ± 120 d 18 14 21 ω I s 0 20 ω I 21 F I11 F I22 ω I1 + 20 ω 0 Δt ω I2 F I F ω I - ω 0 19 ω I - ω 0 = ω I1 + ω I2 ω I bd + c 1 2 0 I Λ 2 2 0 I I1 1 2 I I2 1 F I cos p - ω I t - φ I + F cos p - ω 0 t - φ 2 2 Λ 2 = F 2 Iν cos2 p - ω I t - φ I + F 2 cos2 p - ω 0 t - φ 2 + 2F I11 F I22 cos 1 p - ω I1 t - φ I1 cos 2 p - ω I2 t - φ I2 + 2 2F 1 F 2 cos 1 p - 1 ω 0 t - φ 2 cos 2 p - 2 ω 0 t - φ 2 + 2 2 2. 1 F I F cos p - ω I t - φ I cos p - ω 0 t - φ 2 PMSM Δt = 0. 004 167 s ωδt = 120 9 z = 12 2p = 8 q = 1 /2 d bd + d c = 1 30 60 d 120 1 200 r /min 2 ωδt = 120 21 1 2 3 0. 000 83 0. 005 0. 009 16 s 2. 2 bd + c = 1 1 2 3 2 ~ 4 1 2 120 z = 12 2p = 8 1 2 3 30 80 Hz 330 Hz 3 4 20 Fig. 2 2 Toothflux densities of PMSM with ideal sinusoidal phase current
2 37 3 Fig. 3 Air gap magnetic field of PMSM with ideal sinusoidal phase current 4 Fig. 4 Radial force of PMSM with ideal sinusoidal phase current 5 ωδt = 120 Fig. 5 5 Toothflux densities of PMSM with noninterference phase current 6 7 1 2 3 330-80 = 250 410 Hz 330 + 80 = 410 6 Fig. 6 Air gap magnetic field of PMSM with noninterference phase current phase current 8 250 Hz 7 Fig. 7 Radial force of PMSM with noninterference
38 22 bd + c 2. 3 z = 12 2p = 8 80 Hz 160 Hz 8 2 s 0 ω 0 Δt = 120 Fig. 8 Radial force amplitude of PMSM with noninterference phase current ω 0 Δt 20 160 Hz 20 9 10 11 ω I 20 Fig. 9 9 Toothflux densities of PMSM with interference phase current 10 Fig. 10 Air gap magnetic field of PMSM with 11 interference phase current Fig. 11 Radial force of PMSM with interference phase current 12 3 80 Hz 160 Hz 3 z = 12 2p = 8 4 3 80-160 = 13 80 ω I 20 14
2 39 PWM 15 A 15 1 200 r /min A Fig. 15 Aphase current at speed 1 200 r /min 12 Fig. 12 Radial force amplitude of PMSM with interference phase current 16 1 200 r /min A Fig. 16 Spectrum map of A phase current at speed 1 200 r /min Fig. 13 bd + c = 1 17 13 Schematic diagram of sensor position ω I 20 PWM Fig. 14 14 Test loading installation diagram 16 A 800 Hz 80 Hz 160 Hz 320 Hz 160 Hz 17 80 Hz 240 Hz Fig. 17 Amplitude of ibration acceleration on different 320 Hz 80 Hz teeth 240 Hz
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