End-effect of the permanent-magnet spherical motor and its influence on back-EMF characteristics

The permanent-magnet(PM) spherical motor has special configuration and complicated distribution of electromagnetic field.The spatial distribution of the effective flux density produced by permanent magnets is obtained,and the end-effect of the permanent magnets is analyzed.In the 3-dimensional(3-D) finite element(FE) analysis,the calculation of Back-EMF charac-teristics of the PM spherical motor needs to be conducted by steps,which leads to large computational burden.A novel ana-lyzing method to quantize the end-effect of the PM spherical motor is proposed,that is,the end-effect coefficient of the PM spherical motor is calculated to revise the back-EMF waveform obtained from the 2-D FE model.Under different outer radii of the stator coil and different pole arc coefficients of the PM spherical motor,the revised 2-D results are validated by the results obtained from the 3-D FE model and the experimental results.With this method,the special structural feature of the PM spherical motor is fully considered;the pure 3-D calculation of electromagnetic field is conducted only once;higher precision and less computational burden can be achieved.The method provides a new approach to investigating the back-EMF charac-teristic of the PM spherical motor.