Noise and vibration of permanent magnet synchronous electric motors: A simplified analytical model

Design of electric motors, especially for automotive applications where early design choices have significant impacts on the final results, in terms of both cost and performances, is a matter of primary importance, with direct consequences on the entire vehicle. Common practice lacks simple, yet reliable, analytical method to evaluate vibration and noise emission of permanent magnet synchronous motors (PMSMs), and this is the gap that the work here proposed aims to fill. In particular, electric vehicles’ noise requirements have added a design opportunity to manufacturers, which, depending on the type of costumers they are selling their products to, need to comply with different preferences. Accurately estimating noise emissions of such complex machines is a difficult matter, which can be fully exploited only at the end of the design process. The article aims to provide a simple, yet accurate enough, tool to estimate the noise emission of electrical motors at the early stage of the design, giving engineers and researchers a tool to drive their choices. An equivalent curved beam model is used for modeling the structural vibration of the stator when subjected to electromagnetic forces. The sound pressure amplitudes are analytically derived based on the acoustic solution for infinitely long cylindrical radiators. Part of the innovation lays on the fact that the contributions of both the radial and tangential forces are taken into account, and a discussion on the effect and influence of the latter on the stator acoustic emission is presented. The sound pressure radiated from the outer surface of the stator is calculated, and a unique indicator of sound emission, named sound pressure level (SPL), is determined. The proposed method is validated against data of two PMSMs from literature, showing good agreement with the experiments, proving the method is a reliable tool for electric motor designers to be used especially during the early stage of design.