The Finite Element Software suite Opera-3d offers the perfect tools for modelling transient phenomena in electromagnetic systems, and Cobham are diligent in verifying accuracy against industry-standard benchmarks. Advanced time-stepping controls and selective use of hexahedral elements are the key to the accurate simulation of the complex fields generated in this benchmark known as TEAM Problem 24.
The local field distribution is evaluated by measuring the flux in the rotor teeth and the airgap flux density during the transient analysis. The calculation of the overall energy in the device is assessed by way of the torque measured at the shaft.
Accurate representation of induced eddy currents plays a crucial role in the simulation of problems that include time-transient fields. The way in which these currents distribute in the modeled device, along with the fields they produce, is of great importance to the correct simulation of transient problems. The thermal effects associated with eddy current losses are also of particular interest for a wide range of applications.
Modelling of eddy current skin effect is one of the major challenges due to its localized nature. A combination of hexahedral mesh elements and mesh layering is used by Opera in order to accurately capture these effects.
Validation example: TEAM Problem 24
Problem 24 is an electromagnetic benchmark proposed by the International Compumag Society and is a part of the Testing Electromagnetic Analysis Methods (T.E.A.M)  benchmarks, which cover a wide range of electromagnetic devices and phenomena.
The device used is a simplified topology of a Switched Reluctance Motor (SRM) with one pair of stator and rotor teeth. Unlike a real SRM, however, the stator and rotor are not laminated – allowing substantial eddy currents to be induced. The axial length of the machine is relatively short compared with the overall diameter, which makes end–effects significant and a 3D simulation mandatory. A pair of coils is wound around the stator poles and the rotor is locked at a position of partial misalignment with the stator poles. This increases the local magnetic saturation at the tip of the teeth and makes the overall distribution of the field in the machine (especially near the gap) more difficult to predict and compute.
The coils are powered with a step voltage and a series of measurements are performed in order to evaluate the response of the device. Values of current, flux in the rotor teeth, flux density at a certain point in the airgap and torque are all measured during the transient and are the basis for the evaluation of the simulation model.
The effects of including eddy currents
For the purpose of this case study, the benchmark has been run with and without electrical conductivity in the back iron in order to demonstrate the importance of correct representation of eddy current on the accuracy of the results.
The distribution of the eddy currents in the modelled device can be seen in Figures 2 and 3. The inductance of the system is modified by these currents, leading to a significant difference in the transient results obtained. In order to capture these effects accurately, a combination of advanced time-stepping method, hexahedral mesh elements and mesh layering is used.
The effects of modelling eddy currents on the flux through the stator tooth can be seen in Figure 4. Although both models converge to the same steady-state value, the difference in the rise time of the flux can be clearly seen.
For the case when eddy currents are not included, the flux in the device reaches its maximum value at the same time as the drive current, at t=0.1s. However, for the case when eddy currents effects are included, the response of the flux in the device is delayed, reaching its maximum value around 0.08s later. This is because the eddy currents flow so that oppose the change in flux linking the coil.
A similar effect can be seen in Figures 5 and 6 where the results for the flux density in the airgap and the torque production respectively are compared for both cases. The results that include eddy currents are in good agreement with the measured results made available for this benchmark.
A full description of the modelling and analysis of the TEAM 24 benchmark using the Finite Element Software Opera, is available at TEAM 24 – Nonlinear time transient rotational test rig. This includes the use of the advanced time-stepping available in Opera as well as considerations for correctly capturing the skin effects produced by the eddy currents.
 N. Allen and D. Rodger. “Description of team workshop problem 24: Nonlinear time transient rotational test rig” TEAM 24