A coupled electromagnetic–thermomechanical approach for the modeling of electric motors

Future developments of lighter, more compact and powerful motors – driven by environmental and sustainability considerations in the transportation industry – involve higher stresses, currents and electromagnetic fields. Strong couplings between mechanical, thermal and electromagnetic effects will consequently arise and a consistent multiphysics modeling approach is required for the motors’ design. Typical simulations – the bulk of which are presented in the electrical engineering literature – involve a stepwise process, where the resolution of Maxwell's equations provides the Lorentz and magnetic forces which are subsequently used as the external body forces for the resolution of Newton's equations of motion. The work presented here proposes a multiphysics setting for the equations governing electric motors. Using the direct approach of continuum mechanics, a general framework that couples the electromagnetic, thermal and mechanical fields is derived using the basic principles of thermodynamics. Particular attention is paid to the derivation of the coupled constitutive equations for isotropic materials under small strain but arbitrary magnetization. Due to the complex geometry of a typical electric motor, numerical solutions of the governing equations are in order. To gain insight, the theory is hereby applied to obtain the analytical solution of an idealized asynchronous motor for which we calculate the electric current, magnetic, stress and temperature fields as a function of the applied current and slip parameter. The different components of the stress tensor and body force vector are compared to their purely mechanical counterparts due to inertia, quantifying the significant influence of electromagnetic phenomena.