Finite Element Based Optimal Commutation Under Multiple Objective Functions for Magnetically Uncoupled Linear Variable Reluctance Motors with Different Airgap Geometries

Abstract

Optimal commutation of magnetically uncoupled linear variable reluctance motors depends on their geometry and phase current limits. When subjected to the same phase current limits, tooth geometry differences in these motors lead to significant differences in their maximum force output. This is true for various objectives to maximize force or minimize copper losses with or without constraints on the amount of force ripple. This study uses a finite element data based nonlinear model of a group of linear variable reluctance motors with magnetically uncoupled ux paths to determine the optimal commutation for each motor design that would achieve a specified objective function. Varying tooth widths at constant tooth pitch distinguish the motors in the study. Force ripple is measured by the 2-norm of the force ripple waveform. The results presented provide a basis for identifying which motor tooth geometries are more favorable given an intended application, be that an application where force ripple is tolerated, constant force (minimum ripple) is necessary or copper loss minimization is most important. A subset of tooth geometry shapes is identified as generally favorable, and a new expression for tooth shape factor is introduced to help in analysis and design studies by constraining choices from the range of feasible tooth geometries to this favorable subset.