Air Gap Flux Density Waveform Design of Surface-Mounted Permanent Magnet Motor Considering Magnet Shape and Magnetization Direction

The flux density waveform in the air gap of a surface-mounted permanent magnet motor demonstrates key design information such as the back electromotive force, cogging torque and torque waveform. To achieve a sinusoidal back electromotive force waveform, zero cogging torque and zero total ripple torque, the most important point to be considered is the elimination of higher harmonics in the air gap flux density. In this paper, the harmonics of the air gap flux density waveform is reduced by designing the magnet shape and magnetization direction using the level set based design optimization method. Multiple level set functions are employed to express several magnet segments with different magnetization directions. To control geometry complexity and improve the ease of manufacturing, a modified phase field model is implemented. The reaction-diffusion equation is solved to update the level set functions by the design sensitivity. A practical example shows that the optimal shapes of a permanent magnet with different magnetization directions can effectively mitigate the harmonics of the air gap flux density waveform.