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The analytical methods are widely used to predict the vibration and noise of the permanent magnet motors in industry applications. In the traditional analytical method, the influence of the teeth is ignored and a large error of vibration calculation will occur in the slotted motor. In this article, a high-precision analytical method is proposed for vibration calculation of motors based on tooth modeling. First, the electromagnetic forces on each tooth of stator of the motor under no load and load are calculated. Then, the transfer function from the force acting on the teeth to the vibration on the surface of the shell is derived and verified by finite-element method (FEM). Next, the superposition method is introduced and used to superimpose the vibration excited by the force of all teeth to calculate the total vibration acceleration of the motor surface. Finally, the FEM and experiments are conducted to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 literatures has touched on this. In this article, one method by adding some permanent magnet (PM) interpoles to fill the force valley and then reduce the pole-frequency vibration for surface-mounted PM 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. Based 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 three-dimensional 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 results, two 6 poles/36 slots PM motors are manufactured and the experiments are conducted. [ABSTRACT FROM AUTHOR]

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 as effective as the mitigation of tooth harmonic electromotive force (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 finite-element method (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 the 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 pole technique. [ABSTRACT FROM AUTHOR]

The experimental modal test of the structure of the driving motor has always provided a major contribution to understand and control the vibration phenomena encountered in practice. The hammer test is a common experimental method to obtain a mathematical model of the structure and to validate the theoretical model and finite element method model. However, the hammer or the real vibration exciter will increase the test cost. In this article, an electromagnetic vibration exciter is proposed to achieve the frequency response functions and then the modal parameters can be extracted. Its principle of modal parameters estimation is presented and described in detail. The finite-element analysis and experiments of a 6p/36s permanent magnet motor have been conducted to verify the proposed method. [ABSTRACT FROM AUTHOR]

For the integer slot permanent-magnet (PM) driving synchronous motor, the zeroth-mode slot frequency vibration and noise play 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 from 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 an analytical method, while their amplitudes and caused deformations of these forces are calculated with the finite-element method (FEM). Finally, to validate the analytical and FEM results, a 6-pole 36-slot PM driving motor is manufactured and tested, and the results are in good agreement with those of the FEM results. [ABSTRACT FROM AUTHOR]

This paper focuses on the electromagnetic vibration and its reduction in PM brush dc motors. First, the air gap flux density distribution and the radial force density distribution are derived in detail, and compared with the results of the finite element method. Next, two types of vibration sources, called pulsating force and bending moment, are analyzed. Then, two passive improvement methods, called varied PM pole width in axial direction and copper ring, are proposed to reduce the magnetic forces and their vibration, and their principles of the vibration reduction are described in detail. For further explanation, a rotor-skewed motor is used for comparison, and the radial force on the motor is discussed and the influence of four different thicknesses of copper ring on the motor vibration is analyzed. Finally, three 2p/24s sample motors are manufactured and the experimental vibration results confirm the analysis and the proposed improvement technique. [ABSTRACT FROM AUTHOR]

This paper presents a PM pole with varied width in the axial direction for vibration mitigation in permanent magnet brush dc motors, which is proposed to decrease the deformation caused by radial pulsating force and bending moment together. First, the air gap flux density distribution and radial force density distribution are derived in detail. After two types of vibration modes and their reasons as pulsating force and bending moment are analyzed, the difficulty in vibration mitigation is pointed out. By investigating the change rule of the pulsating force and bending moment with PM pole width, a type of PM pole with varied width in the axial direction is proposed. Its principle of deformation reduction is presented, and the optimized pole shape is derived. A three-dimensional finite-element method is used to calculate the magnetic field, Maxwell force, modal analysis, and deformation of motors. In order to verify the effectiveness of the proposed method, the vibration of the proposed motor is compared with the other three types of traditional motors, including skewing slot or skewing pole. Finally, experimental results of two types of motors are compared to validate the proposed technique. [ABSTRACT FROM AUTHOR]