Modeling of Teeth Forces in Electrical Machines - A Comparison between different types of machines

Abstract

Electromagnetic forces are the primary excitation sources of vibration and noise in electrical machines. Their generation mechanisms and transmission processes are closely related to pole–slot combinations, winding configurations, and structural characteristics of the machine. This thesis investigates permanent-magnet synchronous machines (PMSMs) with different pole–slot configurations, focusing on the characteristics of electromagnetic (EM) forces and their associated vibration and noise mechanisms. A comparative study is conducted between an integralslot distributed-winding interior permanent-magnet synchronous machine (ISDW IPMSM) and fractional-slot concentrated-winding surface-mounted permanent-magnet synchronous machines (FSCW SPMSMs), highlighting their differences in electromagnetic fields, electromagnetic forces, torque ripple, and vibro-acoustic performance. First, from a theoretical perspective, analytical models of radial and tangential airgap electromagnetic fields and lectromagnetic forces are established under both slotless and slotted conditions. The influence of different pole–slot combinations on air-gap flux density distributions and the spatio-temporal harmonic characteristics of electromagnetic forces is systematically analyzed. Based on these models, the effects of electromagnetic forces on cogging torque and load torque ripple in different machines are investigated, clarifying the impact of pole–slot combinations on torque performance. Second, to address the discontinuous nature of force transmission from air-gap electromagnetic forces to stator tooth forces, a theoretical model of the mechanical modulation effect of stator teeth is developed. By analyzing the force transmission process from the perspectives of distributed forces and concentrated forces, the sampling and modulation characteristics exhibited by stator teeth during force transformation are revealed. The differences of this effect among various machine structures and its role in reshaping the tooth force spectrum are also clarified. In terms of numerical simulations, two-dimensional (2D) finite-element electromagnetic simulations are employed to obtain electromagnetic field distributions, electromagnetic force waves, and torque characteristics under no-load and load conditions. Three-dimensional (3D) finite-element models are used to perform modal analysis of the stator and housing, yielding their natural frequencies and mode shapes. Furthermore, the electromagnetic forces obtained from 2D simulations are mapped onto 3D structural models to conduct coupled multiphysics harmonic response analyses. Equivalent radiated power (ERP) is used to evaluate vibration and noise responses over the entire operating speed range. Finally, by combining modal analysis and harmonic response results, the generation mechanisms and evolution of vibration and noise in PMSMs with different pole–slot configurations over the full speed range are systematically elucidated. The dominant electromagnetic force components and their coupling with structural modes are identified. This thesis establishes a complete physical chain from electromagnetic force generation, through stator tooth mechanical modulation, to structural vibration and noise radiation, providing theoretical foundations and engineering guidance for the low-vibration and low-noise design of PMSMs with different pole–slot combinations.