Analytical and Experimental Investigation of Static-Eccentricity-Induced Electromagnetic Force Waves in a Permanent-Magnet Motor for Electric Vehicles

Static rotor eccentricity distorts the air-gap magnetic field of permanent-magnet (PM) traction motors and may aggravate electromagnetic vibration and noise in electric vehicles. The equivalent remanence method (ERM) is an established eccentric-field modeling strategy; this study does not claim ERM itself as new. Instead, it extends the framework to link a prescribed static-eccentricity ratio to equivalent-remanence harmonics and low-order radial electromagnetic-force waves. Fourier decomposition is used to obtain the radial air-gap flux density, and the Maxwell stress tensor is used to calculate and decompose the radial electromagnetic-force density. The analytical magnetic field is evaluated against finite element method (FEM) results over relative eccentricity ratios from 0.16 to 0.80, and the first-order resultant force is further compared with measurements from a 4-pole, 24-slot prototype operating at 2000 r/min under open-circuit no-load conditions. Static eccentricity introduces first-, second-, and third-order force waves in addition to the fourth-order component under a uniform air gap; the first-order component is the dominant additional low-order force. The measured first-order force increases from approximately 300 to 675 N as eccentricity increases, while FEM and analytical predictions reproduce the same nonlinear trend. The FEM and analytical mean absolute percentage errors relative to experiment are 3.78% and 8.55%, respectively. The analytical overprediction is attributed mainly to idealized assumptions such as neglected local saturation, end leakage, and manufacturing deviations. The formulation is therefore suitable for harmonic interpretation and preliminary force prediction under no-load or weakly saturated conditions.