I am working on an model of a permanent magnet synchronous machine. Right now I am stuck with calculating the eddy current losses caused by the harmonics of the stator magnetic field in the electrical steel of the rotor. Or to put it differently. How do I calculate the eddy current in electric steel at high frequencies and low flux density?
I would like to use something very simple like $$P_{ec} = \sum\limits_\nu \sigma_{ec} (f(\nu-1))^2 B^2_\nu m_\nu$$ were $P_{ec}$ are the eddy current losses in watts. $\sigma_{ec}$ are the specific eddy current losses for the material, but I don't know if they are any good for frequencies above 2000Hz and I would like to calculate the losses up to 100kHz if that is even possible. $f$ is the fundamental frequency an $\nu$ is the ordinal of the harmonics. $B_\nu$ is the respective flux density and $m_\nu$ is the mass.
Now there are two big questions. I know the amplitude of the flux density in the air gap (above the surface) but how do I calculate the flux density in the lamination (electric steel: M330-35A). Apparently I have to consider the skin depth, but I have no values for the permeability at such high frequencies and comparably low flux densities. And also, how do I calculate the mass? $$m_\nu = A \delta \rho$$ ($A$ - surface of the rotor , $\delta$ - skin depth, $\rho$ - density of the electric steel) If I take the same flux density as in the air gap and calculate the masses like above, I obtain losses that are so low, that I am pretty sure they can't be right.
Does anyone have an idea how to solve this problem by adjusting the described or with another approach. I don't need a 100% accurate result. If I am 50% off that is still ok. Any references to text books or papers are also very much appreciated.