Electrical machines that are produced in mass production suffer from stochastic deviations introduced during the production process. These variations can cause undesired and unanticipated side-effects. Until now, only worst case analysis and Monte Carlo simulation have been used to predict such stochastic effects and to reduce their influence on the machine behavior. However, these methods have proven to be either inaccurate or very slow. This paper presents the application of a polynomial chaos metamodeling at the example of stochastically varying stator deformations in a permanent-magnet synchronous machine. The applied methodology allows a faster or more accurate uncertainty propagation with the benefit of a zero-cost calculation of sensitivity indices, eventually enabling an easier creation of stochastic insensitive, hence robust designs.Index Terms-Electrical machines, production tolerances, spectral stochastic finite element method, uncertainty quantification.

Model order reduction methods, like the proper orthogonal decomposition (POD), enable to reduce dramatically the size of a finite element (FE) model. The price to pay is a loss of accuracy compared with the original FE model that should be of course controlled. In this study, the authors apply an error estimator based on the verification of the constitutive relationship to compare the reduced model accuracy with the full model accuracy when POD is applied. This estimator is tested on an example of a permanent magnet synchronous machine.

Model Order Reduction Methods, like the Proper Orthogonal decomposition (POD), enable to reduce dramatically the size of a FE model. The price to pay is a loss of accuracy, compared to the original FE, model that should be controlled. In this communication, we apply an error estimator based on the verification of the constitutive relationship to compare the reduced model accuracy with the full model accuracy when the POD is applied. This estimator is evaluated on an example: a permanent magnet synchronous machine.