The Material Library in TRAFOLO provides properties for both electromagnetic and thermal analysis. It includes a wide range of material data sourced from various databases. The software regularly updates the material library.
Global Materials – These are shared across all simulation cases and users (if multiple users share the same TRAFOLO installation). Materials shown in bold are the default ones provided with the software and cannot be modified. User-added materials, not in bold, can be edited. By default, global materials are stored in: C:\Users\%username%\AppData\Roaming\Trafolo\materials.
Local Materials – Add all the materials required for a specific simulation to Local Materials. These will appear in the Default Material section and the Assembly tab. They are only available for the specific simulation case and are stored in the case folder.
Default Materials – You can optionally assign default materials here, which will automatically be applied to corresponding components in the Assembly tab. The default material can be overridden later within the Assembly tab if needed.
Copy – Duplicates materials between the Global and Local databases. To copy, select the material and click the Copy button.
- Right arrow – copies material from the Global to the Local database.
- Left arrow – moves material from the Local to the Global database.
Add New Material
Material property editor
Material type – The software uses different numerical methods and parameters depending on the material type to calculate losses and responses to electromagnetic fields. For instance, core materials require core loss data, whereas general materials might have a temperature coefficient for electrical conductivity.
Core Material Type – This field is only visible when selecting a Core material type. Different core materials, such as laminated electrical steel and ferrites, require specific material properties. They utilize distinct numerical models to calculate losses and their response to magnetic fields.
Laminate Stack Conductivity – This field is available only for Laminated Core materials and is used to adjust the permeability of laminated materials at high frequencies. It requires setting the electrical conductivity for the lamination material. The temperature dependency of conductivity is not considered.
Laminate Thickness – This field is visible exclusively for Laminated Core materials and requires lamination thickness as an input. It works in conjunction with the Laminate Stack Conductivity.
Temperature coefficient – α is temperature-dependent electrical conductivity approximated as linear dependence:
σ = σ0 / (1 + α (T – T0) )
where σ0 is electrical conductivity at 20 °C, T is solution temperature, and T0 is the constant temperature at 20 °C.
IMPORTANT: In TRAFOLO, electromagnetic and heat transfer simulations are weakly coupled. This means the initial electromagnetic simulation uses the Initial Temperature provided by the user to account for temperature-dependent material properties. To incorporate the calculated temperature into the electromagnetic simulation, set the Temperature Iterations parameter to a value greater than 1.
Relative Permeability – Core materials require a constant relative permeability or a B-H hysteresis curve. B-H hysteresis curves are stored in separate files with two columns, one representing magnetic field flux in [T] and another representing magnetic field strength in [A/m].
Core materials require either a constant relative permeability or a B-H hysteresis curve.
IMPORTANT:
- We advise using constant permeability whenever the effective permeability of the core changes slightly throughout the operational range.
- The use of B-H curve makes the numerical problem non-linear and requires more iterations to converge.
These B-H hysteresis curves are stored in separate files, with one column representing the magnetic field flux in [T] and the other representing the magnetic field strength in [A/m].
B-H Tab and Incremental permeability
One of the primary benefits of the 3D Finite Element Method (FEM) is its ability to account for the material’s response to a magnetic field across the entire core volume. A hysteresis loop typically defines this response, which retains information about the material’s magnetic history and how the field has changed over time.
However, for 3D simulations, using hysteresis loops requires complex numerical techniques (such as the Jiles-Atherton model).
In ElmerFEM, as in most other FEM solvers, a simplified model is commonly used – a B-H curve that neglects coercivity and retentivity. This simplification focuses on the relationship between magnetic flux density (B) and magnetic field strength (H), but it does not store the material’s magnetic history, meaning hysteresis losses cannot be directly derived from the B-H curve in the simulation. Those losses are computed separately during a post-processing step.
Moreover, many material manufacturers either do not provide or are unaware of the B-H correlation for their materials. Additionally, measured data may contain outliers, leading to simulation convergence issues. For more details, check out our LinkedIn article discussing common B-H curve issues in FEM simulations: Fixing B-H Curve in FEM Simulations.
Incremental relative permeability with outlier points
Importing data
To import B-H data (for H-B, the process is identical) into your core material, follow these steps:
- Ensure your B-H data file contains two columns separated by a delimiter (e.g., comma, space, tab, or semicolon).
- Click the “Import” button and navigate to the location where your B-H data file is saved. The software will read the data from the file and populate the B-H curve for the selected material.
TRAFOLO supports most text file formats (CSV, txt, etc.). If you get an error during import, save the file in a different format or try a different delimiter.
B-H data format – two columns separated by a delimiter
Algorithms to modify and extrapolate the B-H curve
TRAFOLO provides simple algorithms that improve B-H data. For example, to remove outlier points, it takes B-H data and derives Incremental permeability:
µi = dB / dH
Then, outlier points can be identified according to such conditions
- it cannot be smaller than 1
- sudden ups or downs
- incremental permeability in the saturation region should strive to 1
Additionally, you can smoothen the curve and extrapolate values into the saturation region. Users can choose to use the original or modified version of the B-H curve.
Use Cubic Spline Interpolation – By default, linear interpolation is used to fill in the gaps between sparse data points in the B-H curve. This option enables higher-order interpolation that smooths out the curve, making it easier for nonlinear solvers to converge faster in some cases.
Core loss
Core losses are calculated during the postprocessing stage using magnetic flux values and frequencies (for harmonic cases) or time derivatives of the magnetic flux (for transient cases).
Kh – This coefficient is often associated with the hysteresis component of core loss.
Ke – This coefficient is often associated with the eddy (Joule) component of core loss.
IMPORTANT: While it may seem logical in theory to separate core losses into hysteresis, eddy, and excess mechanisms, in practice, when fitting manufacturer core loss data, the coefficients are highly dependent on the range of data used. In some cases, the best fit for core loss data may result in negative coefficients, which is not physically accurate. In TRAFOLO, we use limiters during data fitting to prevent this issue. Additionally, several important factors, such as core shape, which becomes critical at higher frequencies, are often missing from core loss data.
Getting coefficient for Steinmetz Equation
Material manufacturers typically provide core loss data as P(f, B) or P(B, f) tables, where f – frequency and B – magnetic flux density.
Core loss data and curves obtained by fitted Steinmetz coefficients
Importing data
TRAFOLO can read core loss data tables in .csv format and extract information. To import:
- Prepare your core loss data table in most text file formats (CSV, txt, etc.), with columns and rows defined by frequency in Hz and magnetic flux density in teslas (T). TRAFOLO can identify transposed data and correct its orientation if needed.
- In the Core Loss Data Table section, click the “Import” button and browse to the location where your core loss data table file is saved. Select the file and confirm your selection.
- TRAFOLO will read the data and identify the frequency and magnetic flux density values.
In the Core Loss tab, you can ensure that the imported data is represented well with 4 fitted coefficients.
Core loss data stored as a CSV file
Fitting data to Steinmetz equation
TRAFOLO fits data on Steinmetz + Eddy Equation (SE+Eddy)
P = Kh fm Bn + Ke (f B)2
where four coefficients that are obtained for every material are
- Kh – the coefficient is related to the hysteresis part of the total core loss.
- m – exponent for frequency, typically around 1.
- n – exponent for magnetic flux density, typically around 2.
- Ke – the coefficient is related to the eddy current part of the total core loss.
The additional Ke coefficient improves the representation of data across the entire frequency and magnetic flux range. Still, users can disable this fourth coefficient and revert to the traditional Steinmetz notation.
IMPORTANT: It’s crucial to ensure that the coefficients accurately reflect the core loss data. The Core Loss tab in the material editor lets you review and compare charts for losses obtained from fitted coefficients and compare them with original data. If the coefficients do not adequately represent the core loss data, it’s likely that four coefficients are not sufficient to represent the entire data. In such cases, consider splitting the dataset into smaller frequency ranges for better accuracy.
Core loss data spanning a wide frequency range was fitted using the 4-coefficient Steinmetz + Eddy equation. While the fitted coefficients align well with the original data at high frequencies, there is a significant discrepancy at low frequencies and high magnetic flux amplitudes.
Core loss computation
For harmonic simulations, the Steinmetz + Eddy equation is applied during the processing step to calculate losses at all frequencies independently, then sum them together (superposition principle). This assumes that losses at different frequencies are independent. However, due to the nonlinear nature of the B-H curve and the dependence of core losses on magnetic flux and frequency, this assumption is an approximation that can sometimes lead to significant errors. We recommend validating core losses with transient simulations, especially when core losses are critical.
In transient simulations, the Generalized Steinmetz Equation (GSE) is used after each iteration to compute core losses at every time step. The losses are then averaged over one or more complete periods. The GSE model uses the same fitted coefficients as the Steinmetz + Eddy model applied in harmonic simulations.
IMPORTANT: If the core’s electrical conductivity (a parameter in all core material types except laminated cores) is greater than zero, the total core losses shown in the results will also include Joule losses (resistive losses) caused by eddy currents in the core. These losses are influenced by the core’s shape and typically become more significant at very high frequencies.
Heat Transfer
Density – This parameter is used to convert core losses between W/m³ and W/kg and plays a role in modeling transient heat transfer, where it contributes to thermal mass (related to heat absorption). For steady-state thermal simulations, this parameter does not affect the results.
Heat Conductivity – One of the most critical parameters in thermal simulations, it determines how heat is transferred within the component. Since thermal conductivity can vary by more than three orders of magnitude between different materials (e.g., 400 for copper and about 0.2 for epoxy resin), it is particularly essential to account for thermal conductivity in dielectric materials. Additionally, thermal conductivity can be anisotropic, meaning it varies by direction. This value is a scalar for homogeneous materials, while for non-homogeneous materials (e.g., laminated cores), it can be expressed as a vector (kx, ky, kz).
Heat Capacity – Similar to density, this parameter contributes to thermal mass and is crucial in transient thermal simulations.
