Calculation procedure.

Abstract

A two-dimensional non-linear time-stepping finite element method was employed to calculate the magnetizing inductance of an induction motor as a function of torque. Time-stepping analysis was chosen in order to take account of the effects of the geometry variation, i.e. the movement of the rotor with respect to the stator. Furthermore , magnetic saturation and skin effect were taken into account in calculations. The electromagnetic field of the motor in the Cartesian plane may be described in terms of magnetic vector potential A as J A A =       ∂ ∂ + ∇ ∇ t σ ν , (1) where ν is the magnetic reluctivity, σ is the electric conductivity , t is time and J is the current density. In order to account for the end winding effects, (1) is coupled with the circuit equation t t i L Ri u d d d d ew ψ + + = , (2) where u and i are the voltage and the current of the winding , R is the resistance of the stator winding, ψ is the flux linkage associated with the two-dimensionally modelled magnetic field and L ew is the end winding leakage induc-tance. The circuit equations for the rotor cage were constructed using the rotor network, i.e. two adjacent rotor bars were connected by the end-ring resistances and in-ductances and by the inter-bar resistances along the axial length of the rotor. FE-calculations were performed for several load conditions starting from the no-load condition and increasing the load until the breakdown torque of the motor was reached. From each stable solution the instantaneous rotor and stator currents and the air-gap flux density were extracted. The flux density distribution may be selected from any time instant. No averaging was needed since Lentz's law guarantees that the fundamental component of the flux linkage does not change due to the geometry changes caused by rotation. This was observed by selecting several calculation points for the same load condition. The results for the main flux were equal. The stepped magneto-motive force curve of the stator was then constructed by multiplying the instantaneous stator currents by the number of turns of the corresponding slot. The magneto-motive force curve of the rotor was constructed using a similar technique. The fundamental component and phase angle of the stator and rotor magneto-motive force were calculated using Fourier analysis. For example, the spatial magneto-motive force curves of the rotor and the stator along the stator bore and the corresponding fundamental components are shown in Fig. 2.