Fast Calculation of Detent Force in PM Linear Synchronous Machines With Considering Magnetic Saturation

The detent force of permanent magnet (PM) linear synchronous machines is the main source of thrust ripple. Its calculation becomes significant, especially under different load conditions. By using frozen permeability (FP) method, it can be obtained based on either the integral of Maxwell stress tensor or the virtual work principle. However, the calculated result from the former has nonzero average value, and the latter is complicated with general commercial finite element (FE) packages. For fast calculation and high precision, a hybrid FE-analytical method based on d-q axis flux linkage model is proposed, which only needs to calculate the thrust force and the flux linkage of two FE models. One is the nonlinear model with both PM and armature current excitations, and the other is the linear model with armature current only by using the FP method. The predicted result is compared with those of two existing approaches, which validates that the detent force can be calculated properly under different load conditions by the proposed method.