Modeling of Zero-Order Radial Electromagnetic Force for Integer-Slot Permanent Magnet Synchronous Motor Using Lumped Parameters

The zero-order radial electromagnetic force is the main cause of integer-slot winding interior permanent magnet synchronous motor (PMSM) stator vibration. In this article, a zero-order radial electromagnetic force analytical model explicitly containing current is established. Taking flux as the key correlation variable, the relationship between air-gap flux density and current is revealed by reasonably selecting lumped parameters. Incremental inductance is used to establish the relationship between current and flux. Apparent inductance is used to separate the permanent magnet (PM) and armature part of flux density. The stator leakage inductance is used to obtain the air-gap armature flux. The flux density distribution characteristic is further refined by considering the influence of stator and rotor structure. By analyzing the relationship between distributed and lumped parameters, the zero-order radial concentrated force on the tooth is derived. Some new lumped parameters are defined to build the analytical model and the extraction strategy based on finite element analysis (FEA) is established. The analytical model can intuitively express the relationship between current, lumped parameters, and zero-order radial electromagnetic force. Finally, through FEA and experiment verification, the analytical model has high accuracy under both sinusoidal and harmonic excitations.