Analytical Calculation of Temporal and Circumferential Orders of Radial Force Density Harmonics in External-Rotor and Internal-Rotor Switched Reluctance Machines

This paper presents an analytical method to calculate the temporal and circumferential orders of the radial force density harmonics in switched reluctance machines (SRMs) without running the electromagnetic finite element analysis (FEA). The characteristics of the radial force density harmonics in several SRM topologies are investigated, including the 64, 2416, and 614 internal-rotor (IR) SRMs, and 1216 and 1824 external-rotor (ER) SRM. The study shows that the temporal and circumferential orders of the radial force density harmonics depend on the pole configuration, the rotational directions of the rotor, the phase excitation sequence, and the rotor or stator radial force density waveform. The acoustic noise of a four-phase 86 internal-rotor SRM and a three-phase 1216 external-rotor SRM was experimentally measured to validate the calculation of the temporal and circumferential orders of the radial force density harmonics. The proposed analytical method helps locate the possible radial force density harmonics of a given SRM configuration. In order to determine the dominant radial force harmonics, the proposed method should be complemented by analyzing the natural frequencies of the motor structure and the forcing frequencies of the radial force harmonics.