Design considerations when developing a 50000 rpm high-speed high-power machine
In this paper, an analytical procedure is presented, how to predict the AC resistance of litz-wire windings considering air gap fringing fields. For this purpose, an equivalent complex permeability model is derived for hexagonally packed wires. It is shown, how the realas well as the imaginary part of the complex permeability can be determined with the copper filling factor as a parameter. An analytical 2D model is deduced to describe the air gap fringing fields of gapped inductors. Accordingly, the proximity losses of the litz-wire winding are determined correctly and the AC resistance of practical inductors can be predicted over a wide frequency range with high accuracy. This offers the opportunity to optimize such components. Finally, the influence of various parameters on the copper losses is investigated and verified by means of experimental data drawn from impedance measurements.