Hysteresis modeling in Simcenter MAGNET™ software allows engineers and scientists to model a real-world scenario incorporating the effects of iron losses into the simulation of low-frequency electromagnetic devices. Accurately representing a ferromagnetic material by the full BH loop instead of the SV BH curve affects the local quantities, i.e., the magnetic field distributions. As a result, the device operating point and other global quantities such as input power, torque/force, etc. also change and this can be critical for multi-objective device optimization to find the best design. The incorporation of hysteresis is also a crucial step towards accurate modeling of these materials in multiphysics simulations of electromagnetic devices in the Simcenter© environment, where the magnetic properties of these materials are also affected by mechanical stresses and high temperatures.
Introduction
The finite element (FE) method is widely used in the commercial computer-aided design (CAD) software industry to analyze and design low-frequency electromagnetic devices such as actuators, motors, and transformers. Maxwell's equations are discretized to calculate magnetic fields in complex geometries, which would otherwise not be possible to simulate. Advanced numerical techniques have been developed to improve the accuracy of solutions for better prediction of the performance of these electromagnetic devices. However, field solutions will not be accurate if the magnetic properties of the ferromagnetic materials, from which these devices are manufactured, are not properly modeled in CAD simulations.
In commercial software the magnetic properties of ferromagnetic materials are typically modeled by a single-valued nonlinear magnetization (SV) curve (known as the BH curve, an example is shown in Figure 1) for several reasons, including numerical stability, limited computational resources available and the lack of material data. Such an approximation leads to simulations without magnetic losses, which means that the overall results, for example the motor torque, do not include any magnetic (iron) losses. These are subsequently calculated in a post-processing phase, often with empirical loss formulas developed at the beginning of the 20th century. The following equation (1) represents the energy balance in this scenario.
The terms Eohmic and EStoredMag in (1) represent the ohmic loss (I²R) and the magnetic energy stored in the material, respectively. It is important to note that there is no iron loss term in (1), indicating that the SV simulations do not incorporate iron loss in the field solutions.
Figure 1: Single-value BH curve of 35WW300 non-oriented electrical steel.
Incorporating hysteresis
In reality, ferromagnetic materials do not exhibit a single-valued BH curve, but a BH loop (like the one shown in figure 2). Energy is dissipated within the material in the form of heat when the intensity of the applied magnetic field H changes. The loss resulting from this is called hysteresis loss. The inclusion of hysteresis in the FE simulation modifies the energy balance equation (1) as shown below.
The term E hys in (2) represents both the hysteresis loss and the magnetic energy stored in the ferromagnetic material. For this reason, the stored magnetic energy and coenergy tab in Simcenter MAGNET is disabled for hysteresis simulations. This is demonstrated in detail in the Single Sheet Tester (SST) sample example in the next section.
Figure 2: 35WW300 Non-Oriented Electrical Steel BH Loop
Despite the advent of powerful computers and advanced numerical techniques, the inclusion of hysteresis in commercial software remains a rare practice. Although academic research has produced many hysteresis models, such as the Jiles-Atherton⁽¹⁾ and Preisach⁽²⁾ models, commercial FE software companies have generally not adopted them to accurately represent the magnetic behavior of ferromagnetic materials in electromagnetic simulation. modern. devices, e.g. actuators, magnetic storage and recording devices, power transformers, variable speed electric motors, etc. Now that simulation times have been reduced (as a result of faster processors), computationally expensive hysteresis models can be employed on a large scale in complex geometries of these devices.
Simcenter MAGNET from Siemens Digital Industries Software is a general-purpose 2D/3D electromagnetic field simulation software used for virtual prototyping of simple to complex electromagnetic and electromechanical devices. Using Simcenter MAGNET , engineers and scientists can design motors, sensors, transformers, actuators, solenoids or any component with permanent magnets or coils, saving time and money.
This article focuses on applying a new advanced feature of Simcenter MAGNET , which allows users to incorporate hysteresis into field solutions using the Jiles-Atherton (Hys) hysteresis vector model ⁽³⁾. The feature can be enabled when the simulation is solved using the Transient Solver in 2D (with and without movement).
Application examples
In this section, we will discuss the effects of incorporating hysteresis on local magnetic fields and iron losses and global results such as currents, voltages, force/torque, and transients for a wide range of electromagnetic devices. Comparison with the conventional SV model will also be presented.
1. The Single Sheet Tester (SST) ⁽⁴⁾
The magnetic properties of steels are measured in the laboratory using steel strips (dimension: 30 mm x 250 mm x 0.35 mm) in magnetic testers, for example, a single sheet tester (SST), an Epstein structure, etc. the unique SST sample itself. The Simcenter MAGNET model of the SST sample is shown in figure 3 (a). An excitation coil surrounds the sample and the voltage on the coil can be adjusted to obtain the desired flux density B in the sample.
Figure 3: Simulation model of a single strip of 35WW300 unoriented electrical steel (a) Solid view, uniform B-field calculated using single-value (SV) model (b) and hysteresis (Hys) model (c) a 15 milliseconds (peak sinusoidal excitation).
The model is solved using the SV and Hys models for the non-oriented electrical steel 35WW300. B-field plots using both models are shown in Figures 3(b) and (c) at t = 15 ms. In the case of the SV model, iron losses are calculated in the post-processing stage using the empirical loss formula in Simcenter MAGNET , presented below.
Where Khys , α and Keddy are the material loss coefficients that are identified using the user-supplied power loss curves. When using the Hys model, the hysteresis loss term in (3) i.e. KhysƒBᵃ is replaced by (4) which calculates the area of the BH loop.
The calculated coil currents corresponding to Bmax = 1.13 T in the sample using the two models are shown in figure 4 (a). A comparison of the measured and calculated (using the Hys model) BH loops is presented in figure 4 (b) to reflect the accuracy of the Hys model. A sinusoidal voltage of different amplitudes was applied to calculate the iron loss at different induction levels using the SV and Hys models, and the results are shown in Figure 5.
Figure 4: (a) Coil current calculated using SV and Hys models at Bmax = 1.13 T (b) BH loops calculated and measured at Bmax = 1.13 T
Figure 5: Iron losses measured and calculated using the SV and Hys models. The frequency is 50 Hz.
The stored magnetic energies calculated by Simcenter MAGNET for the SST sample using the SV and Hys models are shown in figure 6. As explained previously, the hysteresis loss calculation using the Hys model also includes the stored magnetic energy, which continues to accumulate over time. over time. For this reason, the magnetic energy stored in the Simcenter MAGNET is disabled for the Hys case. However, hysteresis loss is not incorporated into field solutions when using the SV model, and the stored magnetic energy can be calculated directly from the SV curve.
Figure 6: Stored magnetic energy. In the case of the Hys model, it represents the energy being dissipated as hysteresis loss that continues to increase over time.
Table 1 shows the power balance using both models for a complete excitation cycle. It can be seen that the time-averaged stored magnetic energy is zero for the SV case. However, time-averaged stored magnetic energy (hysteresis loss) is part of the power balance equation. The small difference that arises in both cases is due to numerical integration error and can be ignored.
Table 1 – Power balance (one excitation cycle, frequency = 50 Hz)
Model Used | SV | Hys |
Average Input Power (IV) (W) | 9.7 x 10⁻⁷ | 0.148719 |
Average Stored Magnetic Energy (W) | 0 | 0.148756 |
Average Ohmic Loss (W) | 3.21 x 10⁻⁷ | 2.48 x 10⁻⁷ |
Difference | 6.39 x 10⁻⁷ | 3.21 x 10⁻⁵ |
2. Team Problem 32⁽⁵⁾
The test bench is a three-member ferromagnetic core, as shown in figure 7 (a). The core is made of five laminations of 3.2 wt% Fe-Si, 0.48 mm thick, with conductivity σ = 1.78 MS/m and mass density δ = 7650 kg/m³. Two 90-turn windings are placed on the outer members; the DC resistance of each winding is 0.32 ohms. These windings can be connected in series or powered by two independently controlled voltage sources.
Here we will only consider the case in which the two windings are excited by two independent sinusoidal sources with amplitude of 14.5 V, frequency of 10 Hz and phase differences of 90°. In this way, we will have a rotation of fields in the upper part of the central arm of the device (at point P in figure 7 (a)).
The Simcenter MAGNET model of the problem is shown in figure 7 (b). The simulation was run for 125 milliseconds (for 1.25 excitation periods with 40 points per period) using the SV and Hys models. Shaded plots for B-fields calculated at t = 75 ms using both models are shown in figure 8 (a) and (b), respectively. It can be seen that for the Hys case (shown in figure 8(b)), almost no streamlines are present in the rightmost limb, and the streamlines are closing at the corners of the same limb. Arrow plots for fields B and H are shown in Figures 9 and 10, respectively, to investigate this phenomenon. It can be seen that the H field varies between 0 A/m (outer corner) to almost 100 A/m (inner corners) in the rightmost member. In the SV case shown in figures 9 (a) and 10 (a), the sign of B changes with H, that is, the SV BH curve passes through the origin (H = 0, B = 0). However, in the Hys case, the ferromagnetic material has coercivity, and the reversal of B happens when H reaches coercivity, so the field nodes have different signs from B in the same corner, that is, although H does not change sign, B changes.
Figure 7: (a) Geometry of the 3-member transformer ⁽⁶⁾ (dimension in mm) (b) Simcenter MAGNET model.
Figure 8: Shaded field plot B at t = 75 ms calculated using the (a) SV, and the (b) Hys models.
Figure 9: B-field arrow plot at t = 75 ms calculated using the (a) SV, and the (b) Hys models.
Figure 10: Arrow plot of H field at t = 75 ms calculated using the (a) SV, and (b) Hys models.
The voltages and flux connections of both coils using both material models are shown in figure 11 (a) and (b), respectively. The phase difference in the Hys case is obvious due to the phase delay between fields B and H. The results for calculated and measured coil currents and magnetic flux densities at point P are shown in figure 12 (a) and (b) , respectively. The results for the first quarter of the excitations are not shown due to the initial magnetization curve. A good agreement is reached when using the Hys model, which is a good argument for its use in electromagnetic simulations.
Figure 11: (a) Voltages in two coils and (b) flux connections in two coils using the SV and Hys models.
Figure 12: (a) Calculated and measured coil currents, and (b) Flux densities Bx and By at point P.
3. An actuator:
In this example, a load-driven electromagnetic actuator is simulated using Transient 2D with motion solver in Simcenter MAGNET . The actuator simulation model is shown in Figure 13 (a). The coil in the actuator is driven by a capacitor charged to 12 V. A spring holds the plunger against the top stop. At time t = 0, a switch closes to connect the charged capacitor to the coil. Both the body and the plunger are made of M47 – 24 Ga steel.
The shaded plot for the B fields calculated at t = 26.9 ms for the SV and Hys models is shown in Figures 13 (b) and 13 (c), respectively. There's not much noticeable difference here. However, it is desired to accurately predict the position of the piston as a function of time. Figure 14 (a) illustrates the difference between the computed positions as a function of time using both models, and a lag can be observed between the SV case and the Hys case. This can be important for critical applications where precise position knowledge is desired. The coil currents calculated using both models are also shown in Figure 14(b).
Figure 13: (a) Simcenter MAGNET model of an actuator. Shaded B field and arrow plot at t = 26.9 ms calculated using the (b) SV, and the (c) Hys models.
Figure 14: (a) Actuator position and (b) Excitation coil current calculated using the SV and Hys models.
4. An induction machine [6]
A Simcenter MAGNET simulation of a voltage-driven induction motor is presented here. Test engine nominal specifications are given in table 2.
The complete Simcenter MAGNET model of the untilted motor is shown in figure 15. For simulation purposes, the quarterly model was solved for 25 power cycles (frequency = 50 Hz) using the 2D Transient solver with motion. Shaded plots for B fields calculated at t = 500 ms are shown in figure 16 for both the SV and Hys models. The difference in rotor position at 500 ms for both models can be noted.
Table 2 – Induction machine specifications
Rated power | 11 kW |
Rated Torque | 70 N.m |
Rated voltage | 400 Volts |
Frequency | 50 Hz |
Number of poles | 4 |
Number of Slots | 36 |
Number of rotor bars | 28 |
Slipping | ⁓ 1% |
Stator and rotor core | Aço M-19 29 Ga |
Figure 15: Simcenter MAGNET model 36-slot, 28-bar, 4-pole induction machine
Figure 16: Shaded plot of the B field at t = 500 ms calculated using the (a) SV), and the (b) Hys models.
The flow connections and currents of phase A are shown in figures 17 (a) and (b), respectively. It can be seen that there is a transient in the solution. The Hys model predicts higher overshoots in the current waveform, but the transients disappear more quickly than the SV model due to energy dissipation in the ferromagnetic material, changing the time constant of the system. This also implies that the steady state is reached earlier and hysteresis simulations can be performed for a smaller number of time steps in this case. An induction machine is a rotating transformer. Therefore, similar results can be expected in transformer simulations.
Figure 17: (a) Flux linkage and (b) A-phase phase current calculated using the SV and Hys models.
The speed and torque characteristics of the induction machine are shown in Figures 18 (a) and (b), respectively, and similar transient behavior is observed. There is no significant difference in the steady state values. Figure 19 presents the time-averaged power losses (hysteresis loss, eddy current loss and ohmic loss) in various parts of the machine calculated using the SV and Hys models. The hysteresis loss in the rotor is not presented here because the slip frequency, 0.5 Hz in this case, is very small, and obtaining the time-averaged hysteresis loss for a complete rotor frequency cycle in the Hys case will require many solution steps.
Figure 18: (a) Speed and (b) Torque calculated using the SV and Hys models.
Figure 19: Power loss in different parts of the machine calculated using the SV and Hys models.
5. A Surface Mounted Permanent Magnet Fractional Slotted Internal Rotor Machine⁽⁷⁾
This example illustrates the current-driven simulation of a surface-mounted permanent magnet (SMPM), lumped winding, fractional slot synchronous machine, which is used for traction applications. Engine specifications are shown in table 3.
Table 3 – SMPM machine specifications
Rated power | 30 kW |
Rated torque | 120 N.m |
Rated maximum current | 200 A |
Base speed | 2800 RPM |
Frequency | 233,33 Hz |
Number of poles | 10 |
Number of slots | 12 |
Stator and rotor material | Aço M-19 29 Ga |
The complete Simcenter MAGNET model of the SMPM synchronous machine is shown in figure 20 and was solved in the low speed (frequency = 50 Hz) high torque region for five power cycles using the 2D Transient with motion solver. Shaded plots for the B fields calculated at t = 0 ms using the SV and Hys models are shown in Figures 21 (a) and (b), respectively. It can be seen that the stator teeth are in deep saturation (around 2 T) in the SV case, which means that the extrapolation of the SV BH curve overestimates the field values.
Figure 20: Simcenter MAGNET model of a surface-mounted fractional PM slot machine with 12 slots and 10 poles.
Figure 21: Shaded plot of the B field at t = 0 ms calculated using the (a) SV, and (b) Hys models.
The A-phase flow connections and stresses calculated using the SV and Hys models are shown in Figures 22 (a) and (b), respectively. The flux bond in the Hys case is smaller than in the SV case, and the effects of the slots on voltage can be seen when using the Hys model. The torque calculated using both material models is shown in Figure 23. Since iron losses are incorporated into the field solution in the case of the Hys model, the resulting torque is smaller than that of the SV model. The iron losses calculated using both models are not very different and are shown in Figure 24.
Figure 22: (a) Flux connection and (b) Phase A phase voltage calculated using the SV and Hys models.
Figure 23: Torque calculated using the SV and Hys models.
Figure 24: Power losses in different parts of machines calculated using the SV and Hys models.
Timing performance
The temporal performance of the Hys model is important to users. A solution that takes a lot of calculation time is generally not desirable for design engineers. Therefore, the total simulation times for solving the examples mentioned above using both the SV model and the Hys model are shown in Table 4, and their relationship is plotted in Figure 25.
It is important to note that this graph provides an estimate of the temporal performance of the Hys model compared to the SV model and can vary greatly depending on the number of time steps per cycle, mesh density, polynomial order, etc. to collect the data provided in Table 4 are time steps per cycle = 100, polynomial order = 2, Newton tolerance = 1 percent. Reducing the Newton tolerance to very small values increases the number of nonlinear iterations, which significantly increases simulation times.
Table 4 – Relationship of simulation times for the SV and Hys models
Simulation model | Ratio (Thysteresis / Tsingle value) |
SST Sample | 2,56 |
TEAM 32 | 1,85 |
Actuator | 3,79 |
Induction machine | 2,94 |
Surface mounted permanent magnet (SMPM) Fractional slot internal rotor machine | 1,27 |
Figure 25: Temporal performance of the Hys model compared to the SV model.
When exploring the application of hysteresis modeling in Simcenter MAGNET™, it became evident how incorporating this feature is crucial for more accurate and realistic simulations of electromagnetic devices. The ability to capture nuances such as iron losses at low frequencies offers a more complete view of the behavior of these systems, directly impacting device design and optimization.
In this context, CAEXPERTS stands out as a strategic partner for companies seeking to improve their capabilities in computer simulation and advanced engineering. With an experienced and multidisciplinary team, CAEXPERTS is prepared to offer innovative solutions and boost the competitiveness of its customers.
If your company is looking to maximize product development efficiency, reduce operational costs and gain valuable insights through advanced simulations, CAEXPERTS is the ideal partner. Our experience ranges from projects and consultancy to studies focused on reducing costs and increasing operational reliability.
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Schedule a meeting with us to explore together how we can optimize your operations and reach new levels of engineering excellence. CAEXPERTS is ready to be your strategic partner in the search for innovation and efficiency. Get in touch now and take the next step towards success.
References
D. C. Jiles and D. L. Atherton. “Theory of ferromagnetic hysteresis”, J. Magn. Magn. Mater., vol. 61, no. 1–2, pp. 48–60, 1986.
F. Preisach. “Über die magnetische Nachwirkung”, Zeitschrift für Phys., vol. 94, no. 5–6, pp. 277–302, 1935.
A. J. Bergqvist. “A simple vector generalization of the Jiles-Atherton model of hysteresis”, IEEE Trans. Magn., vol. 32, no. 5 PART 1, pp. 4213–4215, 1996.
S. Hussain, Development of advanced material models for the simulation of low-frequency electromagnetic devices, Ph.D. Thesis, McGill University, Montreal, Canada, Feb. 2017.
O. Bottauscio, M. Chiampi, C. Ragusa, L. Rege, and M. Repetto. “Description of TEAM Problem: 32 A test case for validation of magnetic field analysis with vector hysteresis”, 2010. [Available online] www.compumag.org/jsite/images/stories/TEAM/problem32.pdf
S. Hussain, V. Ghorbanian, A. Benabou, S. Clénet, D. A. Lowther. “A study of the effects of temperature on magnetic and copper losses in electrical machines”, Proc. 2016 XXII Int. Conf. Elect. Mach., pp. 1277-1283, 2016.
T. Rahman, R. C. P. Silva, K. Humphries, M. H. Mohammadi, D. A. Lowther. “Design and optimization of fractional slot concentrated winding permanent magnet machines for class IV electric vehicles”, Proc. IEEE Transp. Electrific. Conf. Expo. (ITEC), June 2016.
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