Analytical model to calculate radial forces in permanent-magnet synchronous machines

Abstract

In permanent-magnet synchronous machines (PMSMs) electromagnetic forces are identified as the principal source of vibrations and noises. In this article, first of all the sources of magnetic forces in PMSMs are analyzed. Then, an analytical method for the calculation of radial forces on the base of the stator tooth created by electromagnetic sources in PMSMs is presented. Finally finite element method (FEM) is used to corroborate analytical results.

Optimum Slot and Pole Design for Vibration Reduction in Permanent Magnet Synchronous Motors

“…where F k is the amplitude of the kth magnetomotive force (MMF) wave and ω k is its rotational frequency in rad/s, which is ω k = k p Ω for the kth harmonic, where Ω is the rotational frequency of the rotor in rad/s, and p is the number of pole pairs. If the slots of the machine are taken into account, the air-gap permeance variation due to the slots must be considered, which is usually represented by a Fourier series [24][25][26][27]:…”

Analytical model to calculate magnetic flux density in permanent magnet synchronous machines with static eccentricity

“…As it is explained in [1] the coefficients of the Fourier series are computed taking into account the fringing effect. Including this effect more realistic spatial distribution of the flux density is obtained and in this way the accuracy of the results is increased.…”

“…As it is stated in [1] to include the variation of the permeance due to the slots in the model, first of all, the permeance of a slot must be computed. This effect is obtained in [18], [21] through a conformal transformation from Z to W plane, but this calculus was firstly introduced by Zhu in [22].…”

“…In this article an analytical model for the analysis of superficial permanent magnet synchronous machines (PMSMs) with static eccentricity is presented. The model is a continuation of [1] and it is based on Fourier time-space series formulated in 2-D coordinates. Besides, the equations of the model only use design parameters of the machine.…”

“…Finally, both flux densities are superimposed in order to obtain the overall flux density at load conditions with eccentricity. Since this model is based on [1], a previous article, only the necessary mathematical expressions will be stated.…”