On-Load Cogging Torque Calculation in Permanent Magnet Machines

This paper investigates the on-load cogging torque calculation in permanent magnet (PM) machines. The vast majority of existing methods for calculating the cogging torque, no matter whether analytical or numerical methods, neglect the influence of load, or are inappropriate in considering the influence of load. Without using the frozen permeability method, the torque calculated by the virtual work principle includes the magnetic energy due to the armature field. When using the frozen permeability method, the resultant torque based on the Maxwell stress tensor with the on-load PM field only has nonzero average torque and, hence, is not the on-load cogging torque. A new on-load cogging torque calculation method is proposed in this paper based on the combination of the virtual work principle and frozen permeability method. For its implementation, an improved frozen permeability method, which makes the magnetic energy with on-load PM field that can only be calculated according to the B–H curve, is also developed. By using the new method, all the shortcomings of existing methods can be avoided and, hence, the on-load cogging torque can be calculated appropriately in both linear and nonlinear cases.