For the integer slot permanent magnet (PM) driving synchronous motor, the zeroth mode slot frequency vibration and noise plays a significant vibroacoustic role in the low frequency domain. For conventional analysis in literature, it is usually assumed that the zeroth mode vibration is caused by the zeroth-order radial force harmonic. But in this paper, the genuine reason for zeroth mode vibration is proposed and discussed in detail, which is different with the conventional analysis. The teeth chopping effect is proposed and demonstrates that the slot number order radial force is the root of the zeroth mode vibration of the motor. After the analysis of the zeroth mode vibration in existing research work is presented, the teeth chopping effect is introduced and described. The amplitudes of the zeroth-order and slot number order forces are compared with analytical method, while their amplitudes and caused deformations of these forces are calculated with finite element method (FEM). Finally, to validate the analytical and FEM results, a 6 poles 36 slots PM driving motor is manufactured and tested, and the results are in good agreement with those of the FEM results.

In traditional analysis, several studies have discussed the vibration behavior of electric machines from the point of view of radial force. With the increasingly strict vibroacoustic index, the tangential force effects on the vibration are analyzed and investigated, and it shows the contribution of tangential force on electromagnetic vibration cannot be ignored. However, these studies are based mainly on finite element multi-physics models, and experiments are not conducted. Furthermore, the mechanism of tangential force is not clearly explained. In this paper, a special motor stator structure is proposed to explore the effect of tangential force on vibration. First, the analytical calculation of the tangential force and the tangential effect on motor vibration are described. Next, the Theorem of Translation of A Force is introduced to convert the effective tangential tooth force to a radial force couple acting on the stator yoke. Then, a novel motor stator is proposed to investigate the vibration characteristics caused only by tangential force, and the simulation is analyzed. Finally, a vibration test of the prototype is conducted and the result shows the tangential force can induce the radial vibration with corresponding order.

The electromagnetic vibration of permanent magnet brush DC (PMBDC) motors has its distinct feature, where only slot-frequency related components exist. Skew slot technique is naturally recalled to mitigate the slot-frequency vibration. Unfortunately, the straight skew slot normally used is not so effective as the mitigation of tooth harmonic EMF or cogging torque. First, in this paper, the principle of vibration mitigation by straight skew is discussed and compared with mitigation of tooth harmonic EMF and cogging torque. The reason for poor effect of straight skew slot is illustrated by a specifically-designed experiment and FEM simulation. In order to solve this problem, the zigzag skew PM pole technique is proposed for PMBDC motors for the first time, which overcomes the disadvantage of straight skew slot. The pulsating radial force and bending moment, two main causes of electromagnetic vibration, are derived and analyzed analytically and by three-dimensional FEM for zigzag skew PM poles. At last, the experiments on two PMBDC motors, one with straight skew slots and the other with zigzag skew PM poles, are conducted to verify the effectiveness of the zigzag skew PM pole technique.

Because the root of pole-frequency vibration is the fundamental component of magnetic field, which is the basis of electromechanical energy conversion, by now no effective reduction method of pole-frequency vibration has been proposed, even few literature has touched on this. In this paper, one method by adding some permanent magnet (PM) interpoles to fill the force valley and then reduce the pole-frequency vibration for surface-mounted permanent magnet (SPM) synchronous machines, is proposed and verified by experiments on prototype motors. First, a general expression of radial force density, including the amplitude, frequency and spatial order, of a PM motor is investigated in detail. Basing on this, the deep reason of pole-frequency vibration is ascribed as the valley of force density and the zero-crossing area of magnetic flux density. To fill the force valley and reduce the vibration, some PM interpoles are arranged between original main PM poles and its principle of vibration reduction is presented. A 3-D weak-coupling electromagnetic- mechanical finite element model is built to simulate the radial force and the vibration of the PM motors. Finally, to validate the proposed method and Finite Element Method (FEM) results, two 6 poles/36 slots PM motors are manufactured and the experiments are conducted.

The common method to mitigate the slot-frequency vibration and noise of the permanent magnet (PM) motors is skewing the stator slot or skewing the PM. However, the limitation of this method in pole-frequency vibration reduction exists. In this article, one method by adopting the piecewise stagger PM pole with a continuous skew edge is proposed to reduce the pole-frequency and slot-frequency vibration for surface-mounted permanent magnet (SPM) synchronous machines. First, the analysis of the radial force acting on the stator teeth is conducted. Basing on this, the limitation of the skewing slot method in reducing the vibration is revealed. In order to solve this problem, a piecewise stagger PM pole with a continuous skew edge for pole-frequency and slot- frequency vibration reduction is proposed and its principle of vibration reduction is presented in detail. The finite element models of three 6-pole/36-slot SPM motors are built to simulate the radial force. Finally, two 6-pole/36-slot SPM motors are manufactured and the experimental results validate the effectiveness of the proposed method.

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.