Calculating the steady-state torque of PM machines using the cross-correlation of stator and rotor fields

This paper deals with the analytical calculation of torque in PM machines with surface mounted magnets. The calculation is based on the cross-correlation of stator and rotor flux density. As a consequence of the Parseval´s theorem, the magnetic cross-energy, given by a space-dependent function, is equal to the sum of the components of the spectral energy density in the frequency domain. By using the complex Fourier coefficients of the stator and rotor flux density in the air gap, the torque calculation will be completely performed in frequency domain. The presented analytical method is applied to the calculation of an eighteen slot, six pole permanent magnet exited machine, with an asymmetrical rotor construction. The results are compared to those of a finite element simulation and to measurements on a real machine.