# Electromagnetic simulations

The way electric and magnetic fields interact in nature is utilized by many types of devices, from antennas to electric motors for example. Maxwell’s equations describe the behaviour of the fields and they can be solved using finite element analysis tools. Such simulations can be valuable because they can provide insight, or accurate specification and validation of a design. When optimizing a design, simulation is almost indispensable. DEMCON BuNova can provide the theoretical expertise and simulation skills that are necessary in electromagnetic engineering problems. Some obvious examples of systems for which this can be relevant are:

- Electrical machines
- Inductive, capacitive and resistive devices
- Magnetic shielding
- Magnetic circuits
- Superconductor systems

When setting up a simulation one has to be very careful that all significant physical phenomena are taken into account, but also that it is not overly complex. Therefore it is essential to have a good overview of all physical effects and their approximations in a simulation, and to be aware of their numerical implications. Often, engineers using FEM software spend only part of their time on simulations. As a result, building a simulation of a complex system can be quite challenging and time consuming, or even intractable. Also, the results can prove unreliable. We have years of experience, fully dedicated to building simulations and helping clients to solve their problems. That means we can deal with complex problems in an efficient and reliable manner.

# Multiphysics – Thermal

The most obvious multiphysics coupling involving electromagnetism is a coupling with heat transfer. In many cases heat transfer has the most dominant influence in determining the limits on operating conditions, for example the maximum current that can be sent through a coil. Related topics are for example:

- Induction heating
- Joule heating in resistive devices
- Thermal analysis of coils

When modelling induction heating for example, it is essential that radiative heat transfer is taken into account. In addition, there will be temperature dependent material properties, making this a strongly coupled, strongly non-linear problem. The same is true for resistive heaters used at high temperatures.

The picture on the left is of a resistive heater used in a pulsed laser deposition (PLD) device. Heat is generated by Joule heating in a heater element that is shielded from the environment with radiation shields. Radiation is the most important heat transfer mechanism in this system (high temperature and vacuum conditions). The technical challenge is to get the temperature in the wafer as homogeneous as possible and make the device work at very high temperatures.

Another example is the thermal analysis of a coil. In a coil there are many copper windings that conduct the heat very efficiently along their length direction. In the other directions the heat has to diffuse through the potting. Taking into account this anisotropic effect in the thermal problem is not entirely trivial. Combining this with the electromagnetic problem with a temperature dependent resistivity increases the complexity and again makes this a strongly coupled multiphysics problem. To the left is a picture of an actuator where this type of analysis was relevant.

Thermoelectric effects (Peltier, Seebeck and Thompson effect) are examples of more exotic multiphysics phenomena coupling electricity and heat transfer. The application of a thermocouple to measure temperatures is ubiquitous though. Simulating this effect can somtimes be important for the design of thermoelectric devices.

# Multiphysics – mechanical

The coupling of structural dynamics with electromagnetism via the Lorentz force is also quite common. This is generally relevant for electric motors and actuators. However, often a very simplified description of the dynamics suffices for such systems. For acoustic applications, a full description of the structural dynamics may be important.

When coupling to structural dynamics, a time dependent description is often inherent. Time dependent simulations of electric motors or generators can be challenging, especially in 3D. This is because the mesh consists of a moving and a stationary part. Between these parts, a mapping needs to take place. The implications of this mapping can be detrimental for the time dependent solver performance. A great deal of experience is required to deal with this problem.

Coupling with structural dynamics can occur via many other electromechanical effects. The Coulomb force (electrostatic) is relevant in microelectromechanical systems (MEMS) or certain acoustic transducers. Other effects are: electrostriction, magnetostriction, the piezoelectric effect and the piezoresistive effect. Of these, the piezoelectric effect is probably the most commonly utilized, for example in acoustic transducers.