Exact Air Gap Magnetic Field Calculation of a Short Primary Single-sided Linear Induction Motor Considering Coupling Effects of Slot Harmonics and Longitudinal Dynamic End Effect

Short primary single-sided linear induction motor (SP-SLIM) exhibits promising potential in maglev rail transit and other fields. However, due to the magnetic field distortion caused by the discontinuous iron core, conventional field analysis models typically neglect the influence of slotting effects on spatial harmonics in both normal and transverse air gap flux density. In practical, however, the slot harmonics exert non-negligible impacts on output characteristics such as thrust fluctuations and vibration noise. Unfortunately, few studies have analyzed the spatial harmonics in SP-SLIMs. To investigate the coupling effects of slot harmonics and longitudinal dynamic end effect in slotted SP-SLIMs, this paper proposes an analytical method for calculating the exact normal and transverse air gap magnetic field under synchronous operation. First, considering the large air-gap of SP-SLIMs, the complex relative permeance is improved by using the finite-slot-depth Schwarz-Christoffel transformation. Second, an equivalent method is constructed, which applies Laplace’s equation, Cauchy-Riemann conditions and 2D slotless magnetic field to acquire the analytical expressions for the exact normal and transverse air gap flux density. Additionally, a spatial harmonic frequency analytical model of SP-SLIM is established. The analytical solutions are compared with finite element method (FEM) results, verifying the effectiveness of the proposed analytical method. Based on the investigations, the major findings include the following:1) For SP-SLIM with large air gaps, the finite slot depth must be considered under some specific conditions; 2). There are four major spatial frequencies in the slotted field, predominantly determined by pole pitch and slot pitch; 3) The thrust ripple can be calculated more precisely by the proposed magnetic field compared with conventional method.