Simcenter STAR-CCM+ Integration of the Bertotti Loss model into Simcenter STAR-CCM+

Simcenter STAR-CCM+


Losses in electrical machines play an important role in limiting their efficiency. The iron losses in the magnetic parts of the machine are also known as core losses or magnetic losses. They are caused by the changing magnetic field in the cores of the stator or rotor machine. The iron loss models in Simcenter STAR-CCM+ are based on the Steinmetz equation. In addition to the various extensions of the Steinmetz equation, there is another type of iron loss equation that divides the iron losses into different physically based parts. This type of model includes the Bertotti loss model, which introduces an additional loss term to take into account the excess losses as a function of flux density and frequency.



Losses in electrical machines play a major role in limiting their efficiency. In general, the losses in electrical machines can be separated into mechanical losses, winding losses, and iron losses [1].


Workflows and examples for analysis of lots of aspects of electric machines can be found here:


Iron Losses

The iron losses in the magnetic parts of the machine are also referred to as core losses or magnetic losses. They are caused by the changing magnetic field in the stator or rotor core of the machine. In the case of conductive ferromagnetic materials, the iron losses are often divided into hysteresis losses and eddy current losses. The former describe the losses that are attributable to the hysteresis properties of the magnetic material. If a magnetic material is first slowly magnetised with an increasing magnetic field H and then demagnetised with an opposing magnetic field, the magnetisation curve does not describe the same path back. Instead, a hysteresis curve is created. The area enclosed by this hysteresis curve is equal to the specific energy (Ws/m3) for each cycle and is therefore proportional to the iron losses [1]. 

BH hysteresis curve of a ferromagnetic material at 10 Hz and 200 Hz.

Eddy currents are created by the induced voltages in the conducting magnetic materials due to the changing magnetic flux, leading to dynamic iron losses. These eddy currents counteract the variations (time and direction) of the magnetic fields. They lead to a broadening of the hysteresis curve and thus increase the magnetic coercivity Hc [1].

Iron Losses - Influencing Factors



Iron Losses - Calculation Models

The first group includes iron loss models based directly on the original Steinmetz equation. In the second group, the models attempt to break down the total iron losses into several terms based on the influence of physical variables (frequency dependence, alternating and rotational flux density behavior, harmonic analysis, etc.). The final group is mathematical hysteresis loss models. These models attempt to describe the hysteresis behavior of magnetic materials mathematically or empirically. The iron losses are then determined by the enclosed area of ​​the modeled dynamic hysteresis curves [1].

Iron Losses - Bertotti Loss Model

In addition to the various extensions of the Steinmetz equation, another type of iron loss equations divides the iron losses into different physically based parts, it is called the Bertotti Loss model. Another additional loss term pexc to account for the excessive losses as a function of flux density and frequency is introduced [1]. It divides the iron loss formula pFe into three terms: the static hysteresis losses physt, the dynamic eddy current losses pec and the excess losses pexc:


Bertotti developed a theory that led to a statistical model for calculating the iron losses by introducing so-called magnetic objects, which led to a physical description and function of the loss factor Cexc in relation to the active magnetic objects and the domain wall motion.


S is the cross-sectional area of ​​the laminating sample, G≈0.136 is a dimensionless coefficient of eddy current damping and σ is the electrical conductivity of the laminating sheets. V0 characterizes the statistical distribution of the local coercive fields and takes the grain size into account [2].
In recent studies it has been observed that the hysteresis losses of high-alloy silicon-iron laminations and other alloys do not really fit the first term in pFe in terms of the flux density squared dependence. This introduces a further adaptation coefficient α, which is usually between 1.6 and 2.2 for ferromagnetic materials and alloys. The inclusion of this factor leads to the following equation, which is now also commonly used in the post-processing calculations of finite element software, either with α = 2 [3] or a variable α [4], [5]:


It has to be noted that the presented loss separation approaches does not hold if the skin effect is not negligible [6]. A study on the properties of the coefficients from Bertotti’s statistical model is presented in [7].

Note: At low frequencies, the hysteresis terms are dominant, as expected. Frequency is a recurring difficult box. An article that should get this question out of the way for Steinmetz losses can be found here: Example: Template-based tightly coupled electro-thermal induction machine design.

Implementation of the Bertotti equation into Simcenter STAR-CCM+

1. The Modified Steinmetz Monitors give us most of the parameters we need for the calculation of the Bertotti Loss: the Excitation Frequency and B Peak
The loss factors for the Eddy-Current Loss and the Hysteresis Loss of this Monitor are only valid for the Steinmetz models. The loss factors of the Bertotti model differ from them and have to be defined first.

2. Create parameters for the loss factor coefficients of the Bertotti model (at the end of the article you can find a description how to identify Bertotti loss coefficients with Simcenter SPEED):
3. Create a field function for the calculation of the Bertotti Losses taking the Bertotti equation with three terms the static hysteresis losses physt, the dynamic eddy current losses pec and the excess losses pexc (seperated in rotor/stator, radial/tangential):
e.g. the Bertotti_Rotor_Radial_SPEED field function looks like:
${Bertotti_Chyst_SPEED}*${Modified Steinmetz Rotor Excitation Frequency}*pow(${MagneticFluxDensityinRotor.RotorCyl[Radial]Peak},2)+
${Bertotti_Cec_SPEED}*pow(${Modified Steinmetz Rotor Excitation Frequency}*${MagneticFluxDensityinRotor.RotorCyl[Radial]Peak},2)+
${Bertotti_Cexc_SPEED}*pow(${Modified Steinmetz Rotor Excitation Frequency}*${MagneticFluxDensityinRotor.RotorCyl[Radial]Peak},1.5)

whereby ${Modified Steinmetz Rotor Excitation Frequency} and ${MagneticFluxDensityinRotor.RotorCyl[Radial]Peak} are taken from the Steinmetz monitor.

Example - WoundFieldExample_BertottiLoss.sim


In the figure you can see the the total loss of the Steinmetz model on the left and that of the Bertotti model on the right side.


Additional: Identify Bertotti loss coefficients with Simcenter SPEED

Using Simcenter SPEED, it is relatively easy to compare progression models and determine loss coefficients for different materials and frequencies. At the moment (11/2023) it is not possible to calculate the Bertotti loss coefficients with Simcenter E-Machine Design.

1. In Simcenter SPEED, navigate to the Steel database under Tools and then start the Database Editor:

Speed_Fig1.png   Speed_Fig2.png

2. Choose a material you want, view details via View and switch to the Losses tab. There you can display curves and compare them with other models of the same material or with other materials. Set the plot to Loss vs. frequency. If you select the checkbox at the bottom left Plot second set of losses, you can look at the curves resulting from the model for different frequencies and/or flux densities one after the other.

Speed_Fig3.png Speed_Fig4.png

3. When you now navigate to the Bertotti tab you can identify the loss coefficients of the respective model and use them to calculate the iron losses in Simcenter STAR-CCM+.


  4. Now you can compare the losses vs frequency of the respective models. In the following figure the losses of the Steinmetz (bold lines) vs. the Bertotti (thin lines) loss model are compared, whereas the overall loss of Bertotti is higher than that of the Steinmetz model. This graph confirms the comparison shown in rotor and stator loss distribution comparison.



[1] Andreas Krings, Iron Losses in Electrical Machines - Influence of Material Properties, Manufacturing Processes, and Inverter Operation, Sweden, Dissertation, 2014.
[2] G. Bertotti, G. Di Schino, A. Ferro Milone, and F. Fiorillo, “On the effect of grain size on magnetic losses of 3% non-oriented SiFe,” Le Journal de Physique Colloques, vol. 46, no. 6, p. 385, 1985.
[3] Flux 10 - 2D/3D Applications User’s Guide. Meylan, France: Cedrat Group, 2007.
[4] Estimating iron loss in opera-2d, in Opera-2d User Guide, Oxfordshire, UK: Cobham Technical Services, 2012.
[5] JMAG version 10 - User’s manual. Tokyo, Japan: JSOL Cooperation, 2010.
[6] G. Bertotti, “General properties of power losses in soft ferromagnetic materials,” IEEE Transactions on Magnetics, vol. 24, no. 1, pp. 621–630, 1988.
[7] W. A. Pluta, “Some properties of factors of specific total loss components in electrical steel,” IEEE Transactions on Magnetics, vol. 46, no. 2, pp. 322–325, 2010.

KB Article ID# KB000123175_EN_US



Associated Components

Simcenter STAR-CCM+