# Numerical Modeling

Various complex field problems (e.g. magnetostatics, electrostatics, acoustics, heat transport, structural mechanics) can be solved numerically using the finite element method (FEM).

In electromagnetics, the aim is to solve the Maxwell equations. To do this, the geometry of a field problem is split into discrete area elements (for 2D problems) or volume elements (for 3D problems). This discretization converts the differential equation into a system of algebraic, linear equations. Solving the linear system of equations provides the required field sizes in the discrete points. The finite element method is widely used in various areas of research and development both in science and industry. FEM allows various field problems to be solved and coupled, such as electrical, magnetic, thermal and mechanical parameters.

Thus, magnetic field problems are solved at the institute which release heat energy due to losses. By solving the heat transport problem, the effects of temperature on material properties of the magnetic field problem are determined (e.g. change in the coercive field strength of a permanent magnet).

At IEW, numerical modelling is used both for electrical machines and for contactless energy transmission. As a tool for 2D problems SmartFEM and FEMM, for 2D/3D problems COMSOL Multiphysics is used. COMSOL allows a deep insight into the equation to be solved and the mathematical procedure of the solver.

## Electrical Machines

The simulation of an electric machine is primarily a magnetic field problem. At the Institute of Electrical Energy Conversion, electrical machines are simulated using numerical modelling and optimized by the use of optimization methods. Due to the experience at the institute and the early exchange with manufacturers, simulated and measured values are a good match.

Both nonlinear and anisotropic materials are modeled. Figure 1 shows the magnetic flux density over a pole pair of a transverse flux machine. Red arrows show the direction of the magnetic field and black arrows the direction of the impressed current.

## Contactless Energy Transmission

The main focuses of numerical simulation in contactless energy transmission are the determination of the coupling factor between different coil pairs, the comparison of different coil geometries and the analysis of flux and shielding. In particular, losses in the various components can be detected by the analysis. This includes, for example, foreign objects inserted between the coils. In most cases, the simulation consists of a pure magnetic field problem.

COMSOL integrates electrical circuits to simulate complete systems. In addition to the calculation of the magnetic field problem, it is also possible to determine the thermal losses in the same simulation model. This is currently particularly important for transcutaneous systems in medical technology.