Analytical Modeling for Calculating Cogging Torque in Interior Permanent Magnet Machine With Multi Flux-Barriers

Abstract

This paper presents a new analytical model for estimating the cogging torque in a multi flux-barrier interior permanent magnet machine (IPM). The model is based on a lumped circuit that considers the saturated bridge in the rotor's iron core. Finally, the cogging torque waveform of a multi flux-barriers IPM can be effectively predicted with the assistance of both the proposed virtual permanent magnet concept and the superposition principle. Utilizing the proposed concept, an IPM containing multi flux-barriers may be recognized as a multiple surface permanent magnet machine (SPM) having zero height and unit relative permeability. After decomposing the flux density of air-gap <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$({\rm B}_{\rm g})$</tex></formula> in the IPM into multiple air-gap flux densities for a virtual SPM, the model is used for estimating the individual cogging torques which will be added or subtracted to the total cogging torque. For validation of our proposed concept, finite element analysis (FEA) was used. From the analysis results, it is shown that the proposed concept is practically effective in terms of finding optimal position, peak cogging torque, and waveform.