Characteristic analysis of linear induction traction motor for urban rail transit

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1 ELECTRI C MACHINES AND CONTROL Vol. 14 No. 3 Mar TM 351 A X Characteristic analysis of linear induction traction motor for urban rail transit L Gang 1 3 FAN Yu 1 MA Yun-shuang 1 3 SUN Shou-guang 2 1. School of Electrical EngineeringBeijing Jiaotong UniversityBeijing China 2. School of Mechanics & Electric Control Engineering Beijing Jiaotong UniversityBeijing China 3. CSR Sifang Locomotive and Rolling Stock Co. Ltd. Qingdao China Abstract Aming to the airgap magnetic field distortion caused by end effect of linear induction motors and the calculation analysis of the normal force longitudinal end effect through equivalent electromagnetic field EMF is considered. Transverse edge effects are considered by different modified coefficients when the secondary is magnetizer or conductivityand thrust and normal force are computed. Finally the thrust and normal force are measured by a model linear induction motor under different air gap and current frequency. The experiment results show that the thrust and normal force which are computed are close to these which are measured. Key words linear induction motors thrust end effect normal force characteristic analysis RC

78 14 2 (a) v=0 3 (b) v 0 1 Fig. 1 Flux distribution 1.

e s + e + e = - E ms cosωt - E mscosωt + 2 1.

2 (a) v=0 3 (b) v 0 1 Fig. 1 Flux distribution b x t = b s x t + b + e x t = B mz sin( ωt - π x τ ) + B mzexp( + - x α ) sin( ωt - π x + δ 1 τ e ) 1 δ B mz B mz + α 1 x τ e 1 b s x t b + x t 5 e = e s + e + e = - E ms cosωt - E mscosωt k e = E + me /E ms 3 2 e = - E ms 1 - k e cosωt 4 e s e + e 3 6 k e = - k we πτ e /τ 2 k w1 1 /α π /τ B e f δ 2 mz exp- pτ e /α 1 sinh pτ e /α 1 psinh τ /α 1 5 k we sin τ π ( τ e 2m ) 1 v 0 k we = q 1 sin τ π ( τ e 2m 1 q ) sin πw 6 c ( 1 2τ ) e 5 4 f δ = 1 sinδ + π cosδ 7 ANSOFT v α 1 τ e = 0 v q 1 = z 1 /2pm 1 p w c τ e τ e = τ k we = k 6 w1 e

3 79 δ δ 0 δ π v 0 k RN v < v 0 σ Al = k RN σ Al 15 0 v v s k e = 0 k RN < 1 δ 0 = δ ke = 0 = π - arctan πα 1 /τ e v = v0 8 δ δ 0 + cv e δ 0 8 c 9 c arctan πα 1 /τ e v = v0 10 150 v v 0 v e v e = v -

3 3 79 δ δ 0 δ π v 0 k RN v < v 0 σ Al = k RN σ Al 15 0 v v s k e = 0 k RN < 1 δ 0 = δ ke = 0 = π - arctan πα 1 /τ e v = v0 8 δ δ 0 + cv e δ 0 8 c 9 c arctan πα 1 /τ e v = v v v 0 v e v e = v - v 0 v s - v 0 v s v < v 0 v e 11 v e = 0 12 β v = v π τ 18 v v s v 0 = 0 v e = v = v s 1 - s k z k z k z = 1 - g + 2τ vl i vπw 1 - exp E 1 = E k e 13 E σ Al k z 7 d h sec L i 初级铁轭 w w+2w ov B g Al t ov 6 k 10 RN v tanh β v w/2 k RN v =1 - β v w/2 1 + k t tanh β v w/2 tanh β v w ov 16 w w ov t ov d v k t β v k t t ov - d 1 d ( ) [ ] - v πw 2L g L i i Z t = Z 0Z 2 Z 0 + Z 2 20 Z 0 Z 2 13 E 1 E 1 Z e Fig. 2 Z e = 1 - k e k e Z t 21 Z e Z e Z 0 Z 2 w/2 0 w/2 v E 1 3 Z 1 2 LIM Transaction and parameter of the LIM and flux distribution v s Z 2 s m 22 F x = m k e 2 E 2 1 R 2 s - ΔF

80 14 ΔF m Laplace V 1 I 1 Z 1 Z 2 E 1 Z e Z 0 2 F mvi x 2 + 2 F mvi = 0 27 z 2 Helmholtz 2 F mvi 3 x 2 Fig.

4 80 14 ΔF m Laplace V 1 I 1 Z 1 Z 2 E 1 Z e Z 0 2 F mvi x F mvi = 0 27 z 2 Helmholtz 2 F mvi 3 x 2 Fig. 3 The equivalent circuit considering end effects F z F za H mvi E mvi A mvi v F zr x y z F z = F za - F zr 23 α vi F za = B2 mz 4μ 0 A F zr = B mx B mz F x + ΔF m A B mx 1 B mx = μ 0 H mxg x = 0 z = g = μ 0 A my M 14 k Al β M 13 A my 26 4 B x 4 g d hsec x + 2 F mvi = α 2 vif z 2 mvi 28 F mvi i z g H mxg = 1 M 14 - A my e - jβx k [ Al ] β M 13coshβ z - g - W 13 sinhβ z - g A my = m 1 槡 2 I 1 k w N 1 τp β = π τ M 14 = k Al β M 13coshβg + W 13 sinhβg x x z 4 4 W 14 = W 13 coshβg + k Al β M 13sinhβg M 13 = k Fe M k 12 coshk Al d + μ re W 12 sinhk Al d Al W 13 = μ re W 12 coshk Al d + k Fe k Al M 12 sinhk Al d M 12 = β k Fe coshk Fe h sec + 1 μ re sinhk Fe h sec 1 W 12 = 1 coshk μ Fe h sec + β sinhk re k Fe h sec 37 Fe y z k Al = 槡 jsωμ 0 σ Al + π /τ k Fe = Fig. 4 Multilayer electromagnetic model of SLIM 槡 jsωμ Fe σ Fe + π /τ 2 39 N 1 I 1 τ k w μ re 1 z σ Al x 2 k k =

3 81 7 5 Fig. 5 Photo of experimentation vehicle v/(m s -1 ) 7 Fig. 7 Experimentation trust vs. air gap 8 8 380 V 4. 2 cm 4. 2 m /s 2 1 2. 57 cm 2 216 A /cm 1 35 N 5.

5 Fig. 5 Photo of experimentation vehicle v/(m s -1 ) 7 Fig. 7 Experimentation trust vs. air gap V 4. 2 cm 4. 2 m /s cm A /cm 1 35 N Hz 40 Hz 50 Hz % 6. 89% Fig. 8 Experimentation vertical force F/%N Hz 实测值 40 Hz 实测值 50 Hz 实测值 30 Hz 理论值 40 Hz 理论值 50 Hz 理论值 0%%%%0.5%%%%1%%%%1.5%%%%2%%%%%2.5%%%%3%%%%3.5%%%%4%%%%4.5 v/(m s -1 ) 6 Fig. 6 Experimentation trust 8 Fx/%N Fz/%N mm 理论值 mm 理论值 2.2 mm 理论值 2.5 mm 理论值 2 mm 实测值 1 mm 实测值 2.5 mm 实测值 2.2 mm 实测值 0 0%%%%0.5%%%%1%%%%1.5%%%%2%%%%%2.5%%%%3%%%%3.5%%%%4%%%% Hz 理论值 30 Hz 理论值 20 Hz 理论值 30 Hz 实测值 40 Hz 实测值 50 Hz 实测值 0%%%0.1%%0.2%%0.3%%0.4%%0.5%%0.6%%0.7%%0.8%%0.9%%%1 v/(m s -1 ) 9 50 Hz m /s

6 82 14 Fz/%N 6 3NONAKA SHIGUCHI T. Design of single-sided linear induction 50 1 motor for urban transit J. IEEE Transactions on Vehicular Technology LV GangLI QiangLIU Zhiminget al. The analytical calculation of the thrust and normal force and force analyses for linear induction motorc / /9th International Conference on Signal Processing October BeijingChina YAMAMURA S. Theory of Linear Induction MotorsM. New 0%%%%0.5%%%%1%%%%1.5%%%%%2%%%%2.5%%%%3%%%%3.5%%%%4%%%%4.5 York Wiley1972. v/(m s -1 ) 1 斥力 ;2 引力 ;3 合力 6GIERAS J FEASTHAM A RDAWSON G E. Performance calculation for single - sided linear induction motors with a solid steel 9 reaction plate under constant current excitation J. IEE Proceedings Fig. 9 Two parts of the normal force B Electric Power Applications lectrical Engineering in Japan OOI B TWHITE D C. Traction and normal forces in the linear induction motor J induction motor J J LV GangFAN YuLI Guoguoet al. Normal force adaptive optimal control for linear induction motor based on decoupling strategy J. Proceedings of the CSEE HIRASA TISHIKAWA SYAMAMURO T. Equivalent circuit of linear induction motors with end effect taken into account J. E- 8PAI P MBOLDEA INASAR S A. A complete equivalent circuit of a linear induction motor with sheet secondary J. IEEE Transactions on Magnetics IEEE Transactions on Power Apparatus and Systems1970PAS YAMAZOE H. Analysis and experiments of single-sided linear 2. Applications J LV GangFAN YuLI Guoguo. Hybrid nonlinear autoregressive neural networks for permanent-magnet linear synchronous motor i- dentification J. Control Theory & Applications Electrical Engineering in Japan YAMAMURA S ITO H ISHULAWAY. Theories of the linear induction motor and compensated linear induction motor J. IEEE Transactions on Power Apparatus and Systems1972PAS 12DUACAN J. Linear induction motor-equivalent-circuit model J. IEE Proceedings B Electric Power Applications KANG G NAM K. Field-oriented control scheme for linear induction motor with the end effect J. IEE Proceedings-Electric Power

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