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 characteristics of the PM spherical motor needs to be conducted by steps, which leads to large computational burden. A novel analyzing 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 characteristic of the PM spherical motor.