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Simulation of Magnetization Errors Using Conformal Mapping Field Computations

Due to their production and magnetization process, rare earth magnets, e.g. NdFeB, exhibit deviations from the targeted ideal remanent magnetic flux-density. As a consequence, the calculation of cogging torque, load torque and force computations of a permanent-magnet synchronous machine by means of finite-element analysis are at best in fair agreement to measurements, since the mentioned variations of the magnet material are not covered by standard simulation models. Actual solutions to consider these variations in the simulation of a permanent-magnet synchronous machine consist either in a full-factorial Monte-Carlo simulation or advanced stochastic analysis techniques such as the creation of polynomial-chaos meta-models. Even meta-model techniques result in an exponential growth of repetitive finite element simulations for a rise in the used polynomial's degree or an increment of the input variables. In order to reduce computation time, this paper unveils a methodology to build the magnet rotor field distribution with consideration of magnet faults semianalytically for calculating arbitrary machine operation points. For this purpose a conformal mapping approach is extended to be applicable to stochastic variations. It is shown, how the conformal mapping assumption of symmetrical field conditions can be overcome. As a result, the proposed approach is applied to the calculation of cogging torques for stochastic varying magnetizations in a permanent synchronous machine.