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Permanent magnet (PM) synchronous motors (PMSMs) have been used to drive a number of vehicles. They have high torque density, high efficiency, and a wide speed range. However, the high cost of PMs is disadvantageous. This paper presents a technique for increasing the torque density by modifying the shape of the PMs and minimizing the magnet volume. The PM characteristics such as flux density, demagnetizing force, PM energy product, and the air-gap flux density are represented by a lumped magnetic equivalent circuit when the thickness and width of the PM are increased for the same volume but with different shapes. The torque, torque ripple, core loss, magnet loss, and efficiency of three interior (IPMSM) models designed by the proposed method are compared by finite element analysis. In addition, the demagnetization of the PM due to high temperature, maximum torque load angle, and an adverse field is analyzed. Finally, the analysis result is compared with that of the experiment to verify the proposed model. Index Terms-Energy product, interior permanent magnet synchronous motor (IPMSM), magnet shape, magnet volume, permanent magnet (PM), torque density.

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