Abstract
Simulating the dynamic behavior and determining equivalent material properties for anisotropic models, superelements or structures subjected to preloads or friction remains a challenging issue. Amongst other practical applications, modeling interactions between the steel sheets in industrial magnetic cores of electric motor stators is a complex task, as it requires anticipating behavioral heterogeneities in the structure, and possibly represents significantly costly operations for performing modal or dynamic response simulations. In this article, a method for identifying equivalent material properties to anisotropic structures is developed, which is able to take into account the influence of preloads and friction on the material properties, later used in structural dynamics simulations. The proposed approach can be used with superelements, converting stiffness matrices into elasticity matrices. The method is first applied to a triclinic model, and recreates its elasticity matrix with little derivation. Then, an equivalent linear material is computed for a continuous structure under preloading. Compared at low frequencies, the vibration behavior of the preloaded structure and its equivalent effective media are in good agreement. The operation is repeated with a laminated stack under preloading. Again, the dynamic behavior of the equivalent structure shows good accuracy compared to the initial preloaded stack. Finally, the magnetic core of an electric machine stator is modeled with equivalent anisotropic material properties, accounting for friction and preload in the yoke's and the teeth's steel sheets. The simulation of the structure's low-frequency radial vibration modes is satisfying, and shows improvement compared to orthotropic properties.
Highlights
For finite-element simulations, modelling heterogeneous structures strictly as they are in reality is sometimes both delicate and unrealistic if the heterogeneities are small or numerous: representing such models by equivalent homogeneous material properties may be a necessity in order to reduce the number of degrees of freedom in the models
Apart from the development itself, the main interest of this paper is to model multi-layered magnetic core bodies with representative homogeneous material properties that take into account the influence of preload and friction in the structure
Equivalent material properties The present analysis focuses on the interaction between the steel sheets and the possibility to take such effects into account in the equivalent material properties
Summary
For finite-element simulations, modelling heterogeneous structures strictly as they are in reality is sometimes both delicate and unrealistic if the heterogeneities are small or numerous: representing such models by equivalent homogeneous material properties may be a necessity in order to reduce the number of degrees of freedom in the models. There exist some cases in which equivalent isotropic or orthotropic materials are not accurate enough to recreate the behaviour of a given structure, with yet the same necessity of using representative elasticity matrices. In such a case, identifying elastic constants such as Young’s moduli, shear moduli or Poisson’s ratios is not possible in the case of anisotropic, or so-called “triclinic” structures, defined by 21 independent constants [3].
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