Influence of Different Mode-shape Functions on Analytical Calculation of Stator Natural Frequencies

In this paper, the influence of different mode-shape functions on the calculation of stator natural frequencies under free-free boundary condition is discussed. The axial components of the mode-shape functions are replaced by power polynomials, trigonometric polynomials, and Chebyshev polynomials, respectively. Based on energy method, their convergence and accuracy are verified. Finite element method results are provided for reference. It is found that the calculated stator natural frequencies of different mode-shape functions are convergent while change of polynomials fails to improve the calculation accuracy. Instead, the errors of the analytical method may come from the energy functions of the teeth.