Effect of Counter EMF on Ripple Frequency of Current in DC Motor

Transcript

1 27 3 Vol.27 No.3 Oct Proceedings of the CSEE 27 Chin.Soc.for Elec.Eng (27) TM33 A ( NC ) Effect of Counter EMF on Ripple Frequency of Current in DC Motor YUAN Bao-guo 1, CAO Zhen-rong 1, WANG Sheng-Guo 2 (1. Shanghai Second Polytechnic University, Pudongxin District, Shanghai 2129, China; 2. University of North Carolina at Charlotte, Charlotte, 28223, USA) ABSTRACT: The frequency of the current ripple in the DC otor caused by its counter-emf is analyzed. It is proved that this frequency is deterined not only by its rotation speed, but also by the nuber of windings in series, the nuber of pole-pairs, and the nuber of parallel paths in which current ripple waves do each other. It does not have direct linage with the nuber of brush-pairs, the nuber of coutator bars, and the nuber of arature slots. This result provides an analytic basis for the sensorless speed estiation of. DC otor. KEY WORDS: sensorless speed estiation; DC otor; counter-emf; superposition of signal (sensorless) [1-7] (XSX142) ( ) 1978 [8] [9-1] FFT SFFT [11-15] ( ) [8-1, 16] f=2n/ 6 f=n/6 n / [8] 2 5 [9-1] 2 12 [16] 2 3 [17] f=2n/6 f=n/6 n /

2 3 93 [17] [11-15] f=cnp/6 n p c c=1 c=2 [18-2] [21] 26 f = nn / pf sh r r n r f N r p [21] p [21] p=1 [8,1] [17] [11-14] [14] [21] (rotor slot haronics) 2 1 1(a) 2 1 A X B 1 B 2 exa = Bθ lv B θ θ l v e XA B θ 1(b) e XA B θ 1(c) B1 B2 e B1B2 1(d) B 1 B 2 N S + (a) B e AX e B1B2 (b) (c) (d) 1 Fig. 1 The operation principle schee of the siplest two poles DC otor B(x) 1

3 S B(x) Fig. 2 DC otor which has 1 winding eleents in series under each pole 1 e= e i i= 1 e i e 2 2 g() t = g( t + T) (1) T f=1/t (1) gt ( + ), {,1,, 1} (2) g(t) g( t + / ) g( t + ) g( t T) = + + (3) G(t) = G(t) N 1 Gt () = gt ( + ) (4) G(t) 1 g(t) T g() t = g( t + T) (4) G(t) T c =T/ (5) g() t = g( t + T) 1 Gt ( + Tc) = gt ( + + Tc) = = 1 ( + 1) T gt ( + ) = gt ( + ) = = = 1 1 gt ( + T) + gt ( + ) = gt ( ) + = g( t + ) = g( t + ) = G( t) (6) = 1 = G(t) T c =T/ f c f = 1/ T = / T = f (7) c c ( =3) T 1 EMF T 1 f 1 =1/T 1 1 T c =T 1 /=T 1 /3 f 1 =1/T c =/T 1 =f 1 =3f 1 3 2T T 1 6 T 1 f 1 =1/ T 1 ( u 3 3 Fig. 3 The result of superposition of the EMF ripple waves for 3 windings in series t

4 3 95 u t 4 3 Fig. 4 The result of superposition of the EMF ripple waves for 3 unevenly distributed windings in series 3 ) g ( t), {,1,, 1} g() t = Ag( t + φ), {,1,, 1} (8) A φ G(t) -1 G(t)= g ( t) = A g( t + φ ) (9) = -1 = -1-1 Gt () = Agt ( + ) + [ Agt ( + φ) = = Ag( t + / )] (1) 1 = A=A φ = -1-1 Gt () = Agt ( + ) + [ AKgt ( + φ) = = 1 Ag( t + / )] (11) (11) K p p 2p n / 1 f = 2 pn/6(hz) 3.2 f = 2 pnj /6 j f n p j 1 2( )=2 4 f n p j 1 [1] Schidt P B Wijenayae A H Sensorless control of a peranent agnet synchronous achine down to near zero speed applied to position otion control[c] Proc of IEEE IAS San Diego CA Oct [2] Harnefors L Nee H A general algorith for speed and position estiate of ac otors[j] IEEE Trans. on Industrial Electronics 2 47(1) [3] [J]22 22(12) Zou Jibin Xu Yongxiang Yu Chenglong A novel detecting ethod of the rotor position of PMSM[J] Proceedings of the CSEE 22

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