Statistical analysis on the additional torque ripple caused by magnet tolerances in surface-mounted permanent magnet synchronous motors

In surface-mounted permanent magnet synchronous motors, two types of magnet tolerances: magnet misplacements and magnetisation errors, cause additional torque ripple harmonic components and lead to the dispersion of torque ripple in mass production of motors. This paper analyses the effects of the magnet tolerances on torque ripple and estimates the statistical values of the magnitudes in each harmonic of additional torque ripple resulting from Gaussian distributed magnet tolerances. By using synthesis method, the analytical expressions are derived which reveal the relationship between the magnet tolerances and the magnitudes of the additional torque ripple harmonics. Based on the analytical expressions, the statistical values of each harmonic's magnitude are predicted. The expected values and standard deviations of the harmonics' magnitudes are calculated and verified by both the simulations and experiments.