New material property B(Stress)

Introduction

In version 2022.3, Flux can now model the dependency between the B(H) constitutive relation of an electrical steel and a mechanical constraint through a new magneto-mechanical material property B(Stress). This new feature is particularly useful for users interested in modeling the modification of the magnetic properties of materials due to the fabrication process (e.g. punching of laminated steel sheets), which impacts the performance of electrical machines.

This new model allows considering the influence of an equivalent mechanical stress on the B(H) magnetic behavior of a steel sheet. In other words, the new B(Stress) property is coupled to the B(H) property of the material and allows Flux to account for plastic or elastic deformation effects that modify the magnetic behavior that would be verified in an unconstrained sample of the material. The modified B(H) curves are computed automatically by Flux and used in the FEM computations. Figure 1 shows the computed B(H) curves that result from different values of mechanical stress for an electrical steel sheet (FeSi alloy):

Figure 1. Example of modified B(H) curves of a FeSi steel sheet that are automatically computed by Flux, in accordance with the coupled B(Stress) property for different mechanical constraint values.

Utilisation outline

This new magneto-mechanical model is available only in Flux 2D, both for Transient Magnetic and Magneto-static applications.

To use it, the user must create a material containing definitions for the following two properties:

the new B(Stress) magneto-mechanical property, given by the saturation magnetostriction constant of the material;
a B(H) magnetic property of subtype isotropic analytic saturation + knee adjustment (arctg, 3 coef.).

Then, the material must be assigned to a Laminated magnetic non-conducting region. In the region description dialog box, the user must then enable the new option Mechanical stress dependence and choose between two options:

Uniform over the whole region: useful for describing a region subjected to a uniformly distributed mechanical constraint
Exponential decay towards region center: useful for describing a mechanical stress distribution that is restricted to the region boundaries, as in the case of steel sheets that were cut through punching.

In both cases, the user must also provide the equivalent uniaxial stress representing the constraint in MPa. Option Exponential decay towards region center also requires informing a distance in millimeters, that caracterizes the exponential decay of the mechanical constraint from the region boundary.

The complete and detailed procedure is presented in the corresponding new chapter of the user guide.

Application example

Let's consider a Permanent Magnet Synchronous Machine (PMSM) modeled with Flux 2D and use it as an example to investigate the effect of punching on iron losses computations. Let's also consider the two approaches described in the previous section for the description of the required Laminated magnetic non-conducting region when applied to this specific machine:

Approach based on the constraint Uniform over the whole region: the stator of the PMSM is split in two separate regions. The first is a narrow band corresponding to the edges of the stator and has been damaged by the punching process. The second represents the innermost parts of the stator that have not been damaged through punching.
Approach based on the Exponential decay towards region center of the constraint: the stator is represented by a single region. The compressive mechanical stress is set to its maximum value on the boundary nodes and it exponentially decays as the nodes are located inside the region. This approach assumes that the width of the damaged zone along the boundaries is small when compared to the stator dimensions.

Figure 2. The geometry of the stator and the adopted meshes for each approach. The mesh used together with the approach based on uniform stress values applied to two regions is shown in (a). The mesh used together with the approach based on the application of a decaying mechanical stress towards the center of the unique region used is displayed in (b).

Several computations were performed with the compressive mechanical stress going from 0 to -210 MPa and with both approaches: in the case of uniform stress a damaged zone width of 0.25 mm has been used, while in the case of exponential decaying stress, the decay rate has been fixed at 0.08 mm, so that 95% of the mechanical stress is applied on the three-times (0.24 mm) width external band. The total Bertotti iron losses were evaluated while in post-processing, after resolution of a Transient Magnetic scenario. A comparison of the total iron losses obtained for each value of mechanical stress is summarized in Figure 3 below:

Figure 3. The iron losses dissipated in the stator as a function of the mechanical stress. The blue line corresponds to the approach based on a stator split in two parts: a boundary region with an active magneto-mechanical property and an inner region without the mechanical stress dependency. The orange line, on the other hand, corresponds to the approach in which the stress decays exponentially from the boundaries towards the center of a single region.

The magnetic flux density distribution may be visualized through an isovalue plot in the stator, as shown in the Figure 4 below. In this figure we can clearly see the impact of the punching process and of the mechanical stress on the stator teeth boundaries. The intensity of the magnetic flux density in a narrow region along the perimeter of a tooth is visibly lower when compared to its innermost parts.

Figure 4. Distribution of the magnetic flux density in the bulk of the stator. Results obtained with approach based on the application of mechanical stress of -60 MPa decaying from the boundaries towards the region center.

The weakening of the magnetic flux density along the boundaries is a consequence of the localized degradation of the magnetic permeability resulting from punching during the fabrication of the stator, as shown in Figure 1.