In this thesis, an electromagnetic-thermal co-simulation algorithm is developed for the three-dimensional modeling of electric machines. To couple electromagnetic (EM) and heat transfer processes, the time-domain finite element method is employed for its capability of modeling complex geometries. Losses generated from EM fields lead to temperature increase, while the temperature change, in turn, modifies material properties and thus affects EM field distribution. An efficient and accurate EM-thermal scheme is proposed to fully couple these two phenomena.
Nonlinear magnetic problems arising from ferromagnetic materials are considered and solved by applying the Newton-Raphson method. For soft ferromagnetic materials, B-H curves are used to describe the permeability, and polynomial fitting is used to construct smooth curves from experimental data. To include the hysteresis phenomenon in hard ferromagnetic materials, the Jiles-Atherton (J-A) model is introduced to characterize the nonlinear property in which an ordinary differential equation (ODE) relates the magnetic flux density with its corresponding magnetic field. The classic Runge-Kutta method is adopted to accurately solve the ODE in the J-A model.
EM and thermal variations have different timescales and the heat transfer process is far slower than electromagnetic variations. To enhance the simulation efficiency, different time-step sizes are applied. After each thermal time step, the material properties are first updated based on the temperature distribution and the EM problem is solved for several periods. When marching into the next thermal time step, the heat source is extrapolated from the EM losses to obtain the updated values, and the thermal system is solved again until a steady state is reached. Various numerical examples are presented to validate the implementation and demonstrate the accuracy, efficiency, and applications of the proposed numerical algorithms
