Electromagnetic noise is a key barrier to the broader application of electric machines, mainly caused by radial forces on the stator. Conventional methods such as finite element or boundary element analysis involve high computational cost and make it difficult to directly establish the relationship between vibration behavior and stator parameters. Analytical models often rely on artificial springs to impose boundary conditions due to limitations of the chosen basis functions. To overcome these challenges, a forced vibration model based on the weak-form quadrature element method (QEM) is developed. This approach employs physical degrees of freedom and interpolation polynomials, enabling flexible and accurate treatment of various boundary conditions. Given the small lengthto- diameter ratio of the motor, which leads to significant end effects in the radiated sound field, the motor is modeled as a finite-length cylindrical acoustic radiator. The radiated sound field is efficiently computed in the wavenumber domain using fast Fourier transform (FFT). Validation is performed through both experimental measurements and numerical simulations. The results indicate that variations in stator tooth geometry significantly affect vibration but have a limited impact on acoustic radiation. Increasing the thickness-to-diameter or length-to-diameter ratio of the stator surface area effectively reduces radiation efficiency.
Huang et al. (2026) studied this question.