Calculation of rotor losses in PM machines with retaining sleeves using transfer matrices

Accurate calculation of rotor losses in permanent magnet (PM) synchronous machines can be critical because these losses tend to be very small relative to others in the machine. Numerical methods, such as finite element analysis (FEA), can now provide accurate estimates of these losses, but they, especially 3D-FEA, can be time consuming. Analytical methods therefore remain very useful as quick tools for estimating losses at the early design stages. This study presents a new improved analytical method for the calculations of rotor eddy current losses in PM machines using a reformulation of the current sheet model into transfer matrices to solve Helmholtz's diffusion equation. Such methodology reduces the complexity of the problem significantly, particularly in machines with retaining sleeves, and simplifies the numerical evaluation of the resulting equations. A high-speed PM machine with a retaining sleeve is presented as a case study. The analytical results are verified using FEA.