27 3 Vol.27 No.3 Oct. 27 27 1 Proceedings of the CSEE 27 Chin.Soc.for Elec.Eng. 258-813 (27) 3-92-5 TM33 A 47 4 1 1 2 (1 2129 2 NC 28223-1 ) 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 /
3 93 [17] 2 5 12 169 [11-15] f=cnp/6 n p c c=1 c=2 [18-2] 23 24 3 [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 2 2 2 B(x) 1
94 27 2 S B(x) 1 2 3 4 5 6 7 8 9 1 19 2 1 2 1 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 ( ) + = 1 1 1 g( t + ) = g( t + ) = G( t) (6) = 1 = G(t) T c =T/ f c f = 1/ T = / T = f (7) c c 2 2 3 3 ( =3) 3 3 2 6 1 1 2T 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 1 6 4 3 4 3 2T 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
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) 1 2 2 2 1 1 2 1 (11) 2 1 1 K 3 3.1 1 p 1 1 2 1 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 1996 21-28 [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) 77-83 [3] [J]22 22(12) 47-49 Zou Jibin Xu Yongxiang Yu Chenglong A novel detecting ethod of the rotor position of PMSM[J] Proceedings of the CSEE 22
96 27 22(12) 47-49(in Chinese) [4] [J]23 23(2) 88-93 Chen Shuo Tsuji Mineo YaadaEiji On-line identification of stator resistance for sensorless vector control syste of induction otors [J] Proceedings of the CSEE 23 23(2) 88-93(in Chinese) [5] [J]25 25(17) 121-126 Liu Yi He Yiang Qin Feng et al Investigation of rotor saliency-tracing based sensorless vector control drive for ps [J] Proceedings of the CSEE 25 25(17) 121-126(in Chinese) [6] [J] 25 25(22) 136-141 Zhang Qianfan Pei Yulong Cheng Shuang Position sensor principleandaxialexciting coilef ofaxialand racialair gaphybrid agnet circuit ulti-coupling otor[j] Proceedings of the CSEE 25 25(22) 136-141(in Chinese) [7] [J]25 25(23) 163-166 Wan Jun Wang Jianhai Ma Yanbing et al Speed sensorless vector control syste basedon utual ras schee[j] Proceedings of the CSEE 25 25(23) 163-166(in Chinese) [8] [J]1978 (3) 7 Zhang Wenhai A ethod for testing rotary speed of dc icro otor[j] Radio 1978(3) 7(in Chinese) [9] [J]1999 32(1) 36-37 Chen Zhiwen A novel ethod for speed easureent of dc icro otor[j] Microotor 1999 32(1) 36-37(in Chinese) [1] [J]1999 32(3) 33-34 36 Chen Zhiwen Iproving speed easureent precision of dc otor by using frequency spectra[j] Microotor 1999 32(3) 33-36(in Chinese) [11] - [J] 21 28(2) 49-53 Huang Jin Huang Jianhua Chen Dun et al Measureent of DC otor torque-speed charac- teristic based on wavelet analysis[j] S& M Electric Machines 21 28(2) 49-53(in Chinese) [12] [J]21 16(5) 64-67 Wei Yunbing Huang Jin Huang Jianhua Reoving noises fro signals of otor easureent by wavelet pacet[j] Transactions of China Electrotechnical Society 21 16(5) 64-67(in Chinese) [13] [J] () 23 37(2) 235-238 Chen Tun Huang Jin Ma Jian et al Application of wavelet pacet transfor in otor perforance test[j] Journal of Zhejiang University(Engineering Science) 23 37(2) 235-238(in Chinese) [14] [D] 23 Chen Tun The applications of wavelet analysis theory in the doain of otor test[d] Hangzhou Zhejiang University 23(in Chinese) [15] [J]26 21(4) 122-126 Niu Faliang Huang Jin Instantaneous frequency extraction of asyptotic signal and its applica- tions in otor perforance test[j] Transactions of China Electrotechnical Society 26 21(4) 122-126(in Chinese) [16] [J] 1985 13(3) 31-33 Lu Daoing Wang Xiaoing A ethod of ea- suring rotary speed of dc icro otor[j] Sall & Special Electrical Machines 1985 13(3) 31-33(in Chinese) [17] [J]1997(3) 4-42 Zhang Wenhai Special approach to test rotary speed of dc otor [J] Electrotechnical Journal 1997(3) 4-42(in Chinese) [18] Tobias G Method for deterining the frequency of the current ripple in the arature current of a coutated DC otor[p] United States Patent. NO 2498213 May 2 24 [19] Thoas L Thoas F Method for detecting the rotational position of the drive shaft a dc otor[p] United States Patent NO 2312251 23-7-3 [2] Tobias G Method for correcting the deterination of the rotational position of a coutated DC otor drive shaft[p] U S Patent NO 24125 24-5-27 [21] Hilairet M Auger F Sensorless speed easure- ent using current haronic spectral estiation in a DC- otor[c] Proceedings of International Syposiu on Power Electronics Electrical Drives Autoation and Motion SPEEDAM26 26 Taorina Sicily Italy S28/14-19 27-4-6 (1946 ) bgyuan@8189.net (1945 ) ( )