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【正文】 ed by new material. This new part material tends to resist a sudden increase in flux peration and only allows a gradual buildup of the flux density in air gap. Eddy current in the entry or exit end of secondary plate will be produced because of a sudden change of magic flux. This inductive current will prevent the change of air gap magic field (Sung and Nam, 1999). Considering the dynamic end effect, the effective length of linear motor’ primary is supposed as l, and the secondary parameter is converted into the primary’s. At the entry end of secondary core, the eddy current increases promptly, and the increasing rate can be decided by T1=Lr1/Rr (Lr1 is the secondary leaking inductance converted into the primary’s, Rr is the secondary equivalent resistance converted into theprimary’s). Because T1=Lr1/Rr is very small and can be neglected, the secondary eddy current can reach the primary exciting current Im rapidly, while the phase of eddy current is contrary with primary current. The time constant of secondary eddy current decrease can be described as T2=(Lm+Lr1)/Rr=Lr/Rr (Lm is the mutual inductance of LIM). At the exit of secondary plate, the eddy current increases to Im promptly, and then decreases with the time constant T1. The transient process is shown in . Based on the above analysis, the end effect can be added into the equivalent circuit. 13 The relative velocity between the primary and secondary decides the distribution of magic flux along air gap. Suppose v is the primary velocity, in T2 time the primary moves a length of vT2. The time of the primary passing a point on the secondary is Tv=l/v. (1) Then normalize the motor length Q=l/(vT2)=vTv/(vT2)=Tv/T2=lRr/[(Lm+Lr1)v], (2) where Q is a dimensionless parameter representing the motor length on the normalized time scale. The average value of secondary eddy current is ? ?? ??? Q Qmxmea QeIdxeQII 02 1 (3) Equivalent exciting current is ? ?? ?QeIIII Qmeamma /112 ?????? (4) where Imea is the equivalent exciting current considering the dynamic end effect. The demagizing effect can be reflected by amending the exciting current, so the total exciting current is： 14 ? ?? ?QeL Qm /11 ??? (5) The virtual value of the secondary eddy current at entry is QeIdxeQIIQmQ xmer 2120222 ?? ??? ? (6) The eddy current loss at entry end is QeRIRIPQrmrere nt r y 212222???? (7) The eddy current loss at exit end is ? ? ? ?QeRIT eILP QrmQmre x i t 2121 222 ?? ????? (8) The total loss of the secondary is ? ? QeRIPPP Qrme x i te nt r ye dd y /12 ????? (9) The eddy current loss can be described as a series resistance (Rr(1?e?Q)/Q) in exciting circuit. Suppose f(Q)=(1?e?Q)/Q, the Ttype equivalent circuit considered the end effect is shown in . MODEL OF LIM CONSIDERING END EFFECT
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