14 3 2010 3 ELECTRI C MACHINES AND CONTROL Vol. 14 No. 3 Mar. 2010 1 3 1 1 3 2 1. 100044 2. 100044 3. 266111 TM 351 A 1007-449X 2010 03-0077- 06 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 100044China 2. School of Mechanics & Electric Control Engineering Beijing Jiaotong UniversityBeijing 100044China 3. CSR Sifang Locomotive and Rolling Stock Co. Ltd. Qingdao 266111China 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 0 1 2008-05 - 06 50807004 200800041040 2007RC096 1976 1954 1971 1964
78 14 2 (a) v=0 3 (b) v 0 1 Fig. 1 Flux distribution 1. 2 5 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 + 2 1. 1 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 2 1 + 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 0 1 1 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 - 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 0 0. 5v 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 1 1 - k e 13 E 1 2 2 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 1 + 1. 3 t ov - d 1 d ( ) [ ] - v πw 2L g L i i 17 19 3 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 1 1 - 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. 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 24 25 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 0 4 3 2 x + 2 F mvi = α 2 vif z 2 mvi 28 F mvi i 27 28 6 0 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 1 2 3 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 2 38 4 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 5. 1 4 k = 3 3 5 29 30 31 32 33 34 35 36 5
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. 2 50 30 Hz 40 Hz 50 Hz 0 6-50 7-100 8. 35% 6. 89% 6-300 8 Fig. 8 Experimentation vertical force F/%N 45 40 35 30 25 20 15 10 5 30 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 40 35 30 1 mm 理论值 25 20 15 10 5 2 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%%%%4.5-150 -200-250 50 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 2 1 1 2 3 0. 5 m /s
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