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.

中文翻译：

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电机振动中齿的机械和磁枢轴作用


包括齿效应的磁场可以通过齿谐波磁导来计算。然而，振动分析中总是忽略齿的机械枢轴作用，将开槽定子视为简单的圆柱体。本文阐述了齿在振动分析中所起的机械枢轴作用，提出了力的传递函数来表示力从齿顶部到轭架的过程。首先，齿在磁场分析中的磁枢作用通过齿谐波磁导来描述。然后齿顶上的力通过力的传递函数传递到轭上，之后轭可以被认为是一个圆柱体。基于齿的枢轴作用，简单地解释和阐明了高阶力引起低模态振动的现象。不仅对分数槽永磁同步电机（PMSM）进行了分析，还对整数槽永磁同步电机进行了分析，以证明这些方法的通用性。最后，通过有限元法仿真，并在一台分数槽永磁电机和一台整数槽永磁电机上进行实验验证了理论。