Permanent magnet synchronous machines (PMSM) are becoming an essential technology for applications, such as home appliances, industrial tools, and electrical vehicles. Consumer demand regarding noise and vibration of products are increasing, and studies on the noise and vibration characteristics of motors that generate power are actively being conducted. One of the factors contributing to noise and vibration is rotor eccentricity, which may be a result of the manufacturing process of the motor. Rotor eccentricity indicates that the center of the rotor deviates from the center of the stator, implying that the air-gap is not uniform. The rotor eccentricity interrupts the uniform distribution of magnetic flux to the stator, resulting in an increased cogging torque and unbalanced magnetic force. Because the cogging torque and unbalanced magnetic force are generated by the use of permanent magnets, the impact on the magnetic field distribution due to permanent magnets must be analyzed using a model in which eccentricity is applied. Although it is necessary to confirm the occurrence of eccentricity through a numerical analysis technique, such as the finite element method (FEM), it is difficult to understand the direct physical relationship between the eccentricity and design variables. However, it is easy to analyze the characteristic variation according to the eccentricity and design variables by using an analytical model that calculates an analytical solution from the electromagnetic governing equations.
In this study, we proposed an analytical model for permanent magnet machines in which rotor eccentricity is applied. We simplified the analysis model through several assumptions and modeled the magnetization. Based on electromagnetic field theory and the perturbation theory, the governing equations were derived in the air-gap region. Furthermore, the relationship between the magnetic vector potential in each region and the appropriate boundary conditions is used to obtain the undefined coefficients to derive the magnetic flux density characteristics in each region. The validity of the analytical results was verified by comparing them with the results of the two-dimensional (FEM) and those of the experiments.