Mechanical and Magnetic Pivot Roles of Tooth in Vibration of Electrical Machines

Abstract

The magnetic field including tooth effect can be calculated by the tooth harmonic permeance. However, the mechanical pivot role of tooth is always neglected in vibration analysis and the slotted stator is considered as a simple cylinder. In this article, the mechanical pivot role that the tooth plays in vibration analysis is illustrated, where the transfer function of force is proposed to represent the process of force from the top of tooth to the yoke. First, the magnetic pivot role of tooth in magnetic field analysis is described by the tooth harmonic permeance. Then the force on the top of tooth is transferred to the yoke by the transfer function of force, after that the yoke can be considered as a cylinder. Based on the pivot role of tooth, the phenomenon that the high order force can cause the low mode vibration is explained and clarified straightforwardly. Not only the fractional slot permanent magnet synchronous motor (PMSM), but also the integer slot PMSM, are analyzed to demonstrate the universality of these methods. Finally, the finite element method simulation, and the experiments on one fractional slot PM motor and one integer slot PM motor, are applied to validate the theory.