(IPMSM flux linkage radial force torque ripple suppression control, radial force suppression control vibration suppression SR (9)

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1 VT-- Poposal of Simultaneous Suppession Contol of th Radial Foce and th Toue Ripple fo IPMSM Based on Flux Linkage Veification on No-Load Condition Masato Kanematsu, Takayuki Miyajima, Hioshi Fujimoto, Yoichi Hoi (The Univesity of Tokyo) Toshio Enomoto, Masahiko Kondou, Hioshi Komiya, Kantao Yoshimoto, Takayuki Miyakawa (Nissan Moto Co., LTD.) Abstact IPMSMs (Inteio Pemanent Magnet Synchonous Motos) ae wely used fo many industial applications. Howeve, IPMSMs cause lage noise and vibation due to toue ipple and adial foce. In this pape, simultaneous suppession contol of th ode adial foce and th ode toue ipple is poposed. Fistly, simple modelling of th adial foce is poposed based on flux-linkage. Fom this simple modelling, d-axis hamonic cuent which can suppess th ode adial foce is deived. Secondly, the analysis of the poposed simple th adial foce model shows that d-axis cuent can suppess th adial foce and -axis cuent do not cause th adial foce on no-load condition. Finally, simulations and expeiments on no-load condition ae pefomed to show the veification of simultaneous suppession contol of th ode adial foce and th ode toue ipple. (IPMSM flux linkage adial foce toue ipple suppession contol, adial foce suppession contol vibation suppession ). (Inteio Pemanent Magnet Synchonous Moto IPMSM) IPMSM IPMSM Radial Electomagnetic Foce IPMSM () () () () (5) () PWM () () SR (9) IPMSM () () () /

2 F((θ π)) F(θ) F((θ + π)) F((θ π)) F(θ) F((θ + π)) (a) (b) (c) (SP ) (d) Fig.. elationship between adial foce and natual feuency(sp concentated winding (5) F u(t) = B (t) S (5) µ θ () (5) () i =. JSOL JMAG φ u(t) () φ u(t) = ψu(t) P N P N ψ u () U U B θ (t) B (t) B (t) () Z φ u(t) = B (t)ds () U F u () Z B(t) F u(t) = ds () µ S S () () () (5) φ u(t) = B (t)s () U F u(θ) = ψ u(θ) µ SP N = Aψ u(θ) () A := µ SP N () () U ψ um U ψ ui U ψ ui ψ u(θ) = ψ um(θ) + ψ ui(θ) () PS IPMSM U ψ um(θ) (9) ψ um(θ) = ψ m cos θ + ψ 5m cos 5θ + ψ m cos θ (9) ψ 5m ψ m U IPMSM F :noload T :cog θ F :noload cos θ T :cog sin θ d L d K t i d, i A. d d i dh i dh = I d cos(θ θ d ) d UVW C uvw d U ψ ui () ψ ui ψ vi ψ wi " # 5 = C uvw L d I d cos(θ θ d ) d /

3 Table. IPMSM Paametes of IPMSM tun numbe N a pai of poles P teeth aea S [m ]. ψ m [mwb]. ψ m5 [mwb]. ψ m [mwb] -. K t [Nm/A]. L d [mh]. T :cog [Nm] -.59 F :noload [N]. L di d cos(5θ θ d ) + L di d cos(θ θ d ) = L di d cos(5θ θ d + π) + L di d cos(θ θ d π) 5 L di d cos(5θ θ d + π) + L di d cos(θ θ d π) () U ψ u(θ) () ψ u (θ) =ψ m cos θ + ψ 5m cos 5θ + L di d cos(5θ θ d ) + ψ m cos θ + L di d cos(θ θ d ) () () () F F = ψ ma j (ψ 5m + ψ m ) cos θ ff + L di d cos(θ θ d ) () K := ψ m A L d () K I θ d = [deg] I d I d = I d I d = () (5).5 K. [N/A] I. I i h i h = magnetic foce F [N] magnetic foce F [N] magnetic foce F [N]..9.. F(FEA) F(poposed model) F(fitting) I d [A] I d (θ d = ) I [A] (a) I (θ = ).. θ [deg] (b) θ (I =.5) I sin(θ θ ) d ψ ui (θ) () ψ ui ψ vi ψ wi " # 5 = C uvw d L I sin(θ θ ) LI cos(5θ θ) + LI cos(θ θ) = LI cos(5θ θ + π) + LI cos(θ θ π) 5 L I cos(5θ θ + π) + L I cos(θ θ π) () /

4 U ψ u (θ) (5) ψ u(θ) =ψ m cos θ + ψ 5m cos 5θ L I cos(5θ θ ) + ψ m cos θ + LI cos(θ θ) (5) (5) () F () F = ψ ma j (ψ 5m + ψ m ) cos θ ff () () θ = [deg] I I =.5 [A] θ 5. i = () T (θ) = K ti h (θ)+p (L d L )i dh (θ)i h (θ)+t cog(θ) () d d T θ (θ) () T θ (θ) = K ti h (θ) + T :cog sin θ () d I h (9) I = T :cog K t (9) I =. [A] () i = F :noload () I d = F :noload K () I d =. [A] F [N] T θ [Nm] 9 [%] 99 [%] (b) (h) [ ] I (c) (i). 5 mm 5 5 pm 5 Hz 5 Hz a θ 5(b) 5(h) 5(c) 5(i) 5(c) 5(f) 5(i) 5(l) d 5(h) 5(k) 5(b) 5(e) (). i = /

5 - - - i toue [Nm] magnetic foce [N] (a) i d, i (w/o contol) (b) T θ (w/o contol) (c) F (w/o contol) i toue [Nm] magnetic foce [N] (d) i d, i (with F contol) (e) T θ (with F contol) (f) F (with F contol) i toue [Nm] magnetic foce [N] (g) i d, i (with T θ contol) (h) T θ (with T θ contol) (i) F (with T θ contol) i toue [Nm] magnetic foce [N] (j) i d, i (with F, T θ contol) (k) T θ (with F, T θ contol) (l) F (with F, T θ contol) Fig.. Simulation esults of Japan Technical Meeting Recod, MAG--, No., pp., (in Japanese). Tao Sun, Ji-Min Kim, Geun-Ho Lee, Jung-Pyo Hong, Myung-Ryul Choi: Effect of Pole and Slot Combination on Noise and Vibation in Pemanent Magnet Synchonous Moto, Magnetics, IEEE Tansactions on, vol., no.5, pp.-, May T. Kobayashi, Y. Takeda, M. Sanada, and S. Moimoto: i Vibation Reduction of IPMSM with Concentated Winding by Making Holes, T.IEEJapan, Vol. -D, No., pp., (in Japanese). Y. Asano, Y. Honda, Y. Takeda, and S. Moimoto: Reduction of Vibation on Concentated Winding Pema- nent Magnet Synchonous Motos with Conseing Radial T. Hattoi, K. Naita, Y. Sakashita, T. Yamada, K. Stess., T.IEEJapan, Vol. -D, No., pp. 5 9, (in Japanese). 5 R. Takahata, S. Wakui, K. Miyata, K. Noma, and M. Hanaoka, and K. Akatsu: Modeling Method of Vibation Senoo: Study on Reduction in Vibations of Concen- Analysis Model fo Pemanent Magnet Moto, IEE tated Winding Pemanent Magnet Synchonous Moto by 5/

6 i acceleation [mm/s ] 5 acceleation [mm/s ] (a) i d, i (w/o contol) (b) a θ (w/o contol) (c) a (w/o contol) i acceleation [mm/s ] 5 acceleation [mm/s ] (d) i d, i (with F contol) (e) a θ (with F contol) (f) a (with F contol) i acceleation [mm/s ] 5 acceleation [mm/s ] (g) i d, i (with T θ contol) (h) a θ (with T θ contol) (i) a (with T θ contol) i acceleation [mm/s ] 5 acceleation [mm/s ] (j) i d, i (with F, T θ contol) (k) a θ (with F, T θ contol) 5 (l) a (with F, T θ contol) Fig. 5. Expeimental esults Skew Effects of Roto, T.IEEJapan, Vol. -D, No., T. Miyakawa: EV pp., (in Japanese).,, --. H. Yashio and H. Takada: Reduction of a Radial Electomagnetic M. Kanematsu, T. Miyajima, H. Fujimoto, Y. Hoi, Oscillating Foce of an Electical Moto by T. Enomoto, M. Kanayama, T. Miyakawa, and K. Yoshi- Supeposing a High Ode Cuent, Tansactions of the moto: Radial Foce Contol of IPMSM Conseing Magnetic Japan Society of Mechanical Enginees. C, Vol., No. Flux Distibution On No-Load Condition, IEE 5, pp., (in Japanese). E. Zeze, K. Akatsu: Vibation impovement by cuent of Japan Technical Meeting epot, VT, No., (in Japanese). hysteesis contol fo PM moto, JIASC, pp. III-9 M. Kanematsu, T. Miyajima, H. Fujimoto, Y. Hoi, 5 ()(in Japanese) T. Enomoto, M. Kanayama, T. Miyakawa, and K. Yoshimoto: Z.Q. Zhu, et al: Analytical modeling and finite-element Base Study on Radial Foce Reduction with d- computation of adial vibation foce in factional-slot pemanent-magnet bushless machines. Industy Applications, IEEE Tansactions on.5 (): Divandai, M.; Dadpou, A.;, Radial foce and toue ipple optimization fo acoustic noise eduction of SRM axis Cuent Conseing Magnetic Flux Distibution, JI- ASC, pp. III-5 ()(in Japanese) F. Ishibashi, S. Noda, S. Yanase, and T. Sasaki: Magnetostiction and Moto Vibation, T.IEEJapan, Vol. - A, No., pp. 59 5, (in Japanese). dives via fuzzy logic contol, Industy Applications (IN- DUSCON), 9th IEEE/IAS Intenational Confeence on, vol., no., pp.-, - Nov. /