Realistic and efficient finite element simulation of hysteresis effects in magnetic devices

Hysteresis phenomena not only influence the distribution of a magnetic field and the energy losses in a magnetic system, but also the waveforms of linked electric quantities. This means that in order to accurately predict the performance of many electrical devices it is necessary to include such effects – often not an easy task. Opera’s (De-) Magnetization and Hysteresis module holds the answer.

Background

Many devices operational characteristics are strongly affected by the hysteretic properties of magnetic materials used in their construction or on which they operate. These include electromechanical equipment (linear and rotating actuators, motors, generators, electromagnetic braking systems), scientific and medical devices (bending, focussing and wiggler magnets), power conversion systems (transformers and reactors), de-perming systems for naval vessels etc…

Whilst many designers realize the importance of trying to minimize the effects of hysteresis in their designs, few have the tools necessary to understand precisely how magnetic material hysteresis will affect their device performance and how to make improvements.

Figure 1: Hysteresic B-H material data for 0.5 mm laminated Silicon Steel (FeSi 3% wt)

Figure 1: Hysteresic B-H material data for 0.5 mm laminated Silicon Steel (FeSi 3% wt)

Science

All ferromagnetic material shows some level of magnetic hysteresis; simply described it is the dependence of the current magnetization of a system on both its past and present operation.

In hard magnetic materials significant amounts of energy can be stored in the magnetization of the material which in turn requires large amounts of energy to displace/remove. In soft magnetic materials less energy is required to overcome the stored energy. However, the process is not perfectly elastic and hence there is necessity for work to be done which manifests itself as lost energy through vibration/heat. This not only effects the efficiency of devices that make use of such materials but also the distribution and transient response of fields in the material to the way in which it is driven.

Typically efforts to incorporate hysteresis effects in computational models of devices result in both significant computational overheads that can make computation impractical, that require measurements of material properties that are infeasible for the majority of systems or both.

For more information surrounding this topic please refer to our Institute of Physics webinar: Advanced modelling of magnetic materials using Opera FEA software.

Opera

The vector based hysteresis material model which is available to use with any of the transient field solution modules within the Opera Simulation Software suite and was developed under the UK government Technology Strategy Board “Advanced Electrical Machines through Materials” project in collaboration with TRW Conekt[1]. It is a trajectory method whose path is determined by interpolation from the actual measured magnetic induction, and applied field characteristics of the major loop. The turning points of the trajectory are used to predict the behaviour of arbitrary minor hysteresis loops, providing a good approximation of true physical behaviour without requiring extensive computation, and additionally making only realistic demands for materials data. The model accurately predicts the stored magnetic and dissipated energy at all times during the simulation and not solely after the completion of a closed hysteresis loop.

Simple Example: Dual Solenoid Valve (Axisymmetric)

The geometry (Figure 2) consists of two solenoids driven by a switched rectified sinusoidal voltage supply (Figure 3) that produce the fields used to move a valve plunger freely along the z-axis repeatedly between fully open and fully closed positions.

Figure 2: Dual Solenoid Valve (Axisymmetric Geometry on z axis)

Figure 2: Dual Solenoid Valve (Axisymmetric Geometry on z axis)

Figure 3: Solenoid Valve Circuit

Figure 3: Solenoid Valve Circuit

Figure 4: Response of valve to switch on of solenoid (with and without hysteresis effects)

Figure 4: Response of valve to switch on of solenoid (with and without hysteresis effects)

Comparison of the plunger position with time for a situation in which there is a hysteretic and an-hysteretic material used in the plunger (Figure 4) highlights the stored energy in the system. It takes ~1.5 ms of additional time to fully open the plunger due to the remanence which equates to ~15% less time in the open state (and hence the amount of fluid able to propagate through the valve is also modified). For a precision device this is clearly something that needs to be accounted for.

Additionally an extra 4.4 J of energy is used per cycle in overcoming the energy stored in the system.

Validation Example: TEAM Problem 32

The purpose of the TEAM problems is to provide benchmarking tools for the characterization/validation of computational procedures and tools that are used in magnetic field analysis packages (such as the Opera Simulation Software Suite) through providing of relevant measurement data for comparison.

Here we look specifically at one of the four cases (#2) provided within TEAM Problem 32; Validation of Magnetic Field Analysis with Vector Hysteresis.

The problem comprises a 3-leg transformer core with two drive coils (one on each of the outer core legs) and a series of pick-up coils (designed to pick up separately the x and y components of the field in the core) distributed in regions of interest (Figure 5). The steel used in its construction is 0.5mm laminated Silicon steel (FeSi 3% wt) regularly used in the construction of rotating machines.

Figure 5: Device schematic highlighting pick-up coils[1],

Figure 5: Device schematic highlighting pick-up coils[1],

In Case 2 the two main coils are driven with identical voltage waveforms that consist of a 10 Hz fundamental and 5thharmonic component with an approximately 8 degree phase shift between the two harmonics (Figure 6).

Figure 6: Drive source for measurements and simulations

Figure 6: Drive source for measurements and simulations

Comparison between the currents observed in the windings in the simulation with and without the hysteresis material model with the currents observed during measurement is shown in Figure 7.

Figure 7: Comparison of Current (A) for hysteretic and anhysteretic simulations with measurement

Figure 7: Comparison of Current (A) for hysteretic and anhysteretic simulations with measurement

Clearly the currents are modified by the inclusion of hysteresis effects and are in agreement with measurement. This can be understood by review of the magnetization in the sample (Figure 8).

Figure 8: Comparison of simulated hysteretic and anhysteretic B-H path for pick-up coil C6

Figure 8: Comparison of simulated hysteretic and anhysteretic B-H path for pick-up coil C6

The magnitude of the B field at C6 for the hysteretic and anhysteretic simulation data is compared with the measured data in figure 9.

Figure 9: Comparison of measured B-Field with hysteretic and anhysteretic simulations.

Figure 9: Comparison of measured B-Field with hysteretic and anhysteretic simulations.

The magnitude of the peak of the B-Field is ~20% different in this instance due to the inclusion of hysteresis effects in the simulations. The magnitude of the higher harmonics are also significantly reduced in the fields produced and would hence not be transmitted to a secondary set of phases, if this were actually being used as a three phase transformer. Additionally there is a phase shift of ~10 degrees between the hysteretic and anhysteretic data which emphasises the requirement for the inclusion of these effects if predictive design of a devices performance is to be achieved.

Conclusions

Whilst techniques exist to accurately calculate the additional losses in a magnetic device caused by hysteresis effects little has been done to account for the energy stored in magnetic materials and the effects on device performance. In both of the above examples the hysteretic behaviour of the materials involved has translated to a significant change to the magnetic properties of the device in question, not only by reducing the efficiency of the device but also by modifying its transient response to an input. Clearly as the material used in the TEAM Problem is one commonly used in the construction of rotating electrical machines it is necessary to account for the changes in transient response of a system to hysteresis effects in order to optimize the performance of devices for real-world applications.