# Analysis on circumferential natural frequencies of stator in permanent magnet synchronous motor

## Shuangshuang Zhong1, Shenbo Yu2

1, 2School of Mechanical Engineering, Shenyang University of Technology, Shenyang, P. R. China

1Corresponding author

Journal of Vibroengineering, Vol. 21, Issue 2, 2019, p. 431-449. https://doi.org/10.21595/jve.2018.19857
Received 2 April 2018; received in revised form 11 September 2018; accepted 26 September 2018; published 31 March 2019

Copyright © 2019 Shuangshuang Zhong, et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Abstract.

Accurate calculation on circumferential natural frequencies of stator structure in permanent magnet synchronous motor (PMSM) is very important for predicting the vibration and noise of PMSM. The analytical modal formula for the stator structure in PMSM is proposed, starting from the mathematical displacement model of cylindrical shell, then deriving the analytical formula for the stator structure. Firstly, finite element method (FEM) is applied to analyze the circumferential natural frequencies of cylindrical shells with different length, wall thickness, mean diameter, diameter-thickness ratio, size and installation position of terminal box. The influences on circumferential natural frequencies of cylindrical shells are studied. Furthermore, a new analytical formula considering diameter-thickness ratio for calculating circumferential natural frequencies of cylindrical shells is developed. Compared with the results of FEM, the correctness of the analytical formula is verified. Then, novel analytical formulas considering stiffness errors are proposed to calculate the circumferential natural frequencies of stator core and motor case. Compared with the results of FEM, the effectiveness of analytical method is validated. Finally, a new analytical formula considering diameter-thickness ratio, stiffness errors, existence of terminal box and mutual constraints is presented to calculate the circumferential natural frequencies of stator structure. Compared with the results of FEM and experimental method, the relative errors are respective within |4.43 %| and |3.38 %|. The validity of analytical formula is confirmed.

Keywords: cylindrical shell, circumferential natural frequencies, diameter-thickness ratio, stiffness error, mutual constraints, finite element method, analytical method, experimental method.

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