Parametrising Temperature Dependent Properties in Thermal-Mechanical Analysis of Power Electronics Modules using Parametric Model Order Reduction

In this paper, a direct-coupled thermal-mechanical analysis of a Power Electronics Modules (PEM) using ANSYS-FEM (Finite Element Method) is integrated with a Parametric Model Order Reduction (pMOR) technique. Unlike most present studies on model order reduction, which perform the coupled thermal-mechanical analysis by sequential-coupled thermal-mechanical models, the direct-coupled thermal-mechanical approach deployed in this study solves the thermal and structural models simultaneously. Commonly, pMOR mainly focuses on parametrising model parameters (e.g., material properties, loads.) that are constants. In this investigation, a new approach to parametrise temperature-dependent properties using pMOR, such as the coefficient of thermal expansion (CTE) of the materials in PEM structures, has been demonstrated in the context of the reliability assessment of electronic modules. A two-dimensional finite element model of a PEM is developed and used to study the temperature-dependent CTE effects of the Aluminium (Al) alloy on the thermal-mechanical response of the system under thermal load. A Krylov subspace-based technique, PRIMA, has been used for the model order reduction and a linear approach of matrix interpolation for the parametrisation in the pMOR. The full-order state-space model has 30,612 degrees of freedom (DOFs), and the reduced model achieved by pMOR has just 8 DOFs. The simulation runs show that with this approach, a substantial reduction in computational time can be achieved, for this problem, by 81% between the full and the reduced order models. In modelling predictions, the pMOR-based solution has retained the accuracy of results. In this instance, the average difference in stress result, compared to the ANSYS-FEM model (FOM) solution, is only 0.43%.