TEAM 13: Three-dimensional nonlinear magnetostatic analysis

This benchmark problem verifies the case of a magnetostatic analysis with magnetic vector potential formulation to compute the magnetic field in two steel channels and a steel plate. It is part of the standard suite of problems designed for Testing Electromagnetic Analysis Methods (TEAM). The problem consists of two steel channels and a steel plate excited by a coil carrying direct current. The objective is to compute the magnetic field in the channels and the plate, taking into account the nonlinear magnetic material response of steel.

This page discusses:

ProductsAbaqus/Standard

Problem description

The plan and top views of the problem setup are shown in Figure 1 and Figure 2, respectively. They depict two U-shaped channels and a planar plate excited by a coil carrying direct current. The dimensions of various parts are marked in the figures. The rest of the parameters are as follows. Both the channels and plate are assumed to be made of steel. The nonlinear magnetic properties of the steel are specified as a B–H curve; the data are obtained from Figure 3 of Team Problem 13: 3-D Non-Linear Magnetostatic Model. The current in the coil is assumed to be either 1000 A-turns or 3000 A-turns. The medium surrounding the brick is assumed to have properties similar to that of a vacuum.

Model and boundary conditions

A magnetostatic analysis with magnetic vector potential formulation is performed. Due to the symmetry of the problem, it is sufficient to model only one-half of the problem domain. A homogeneous Neumann boundary condition is applied on the symmetry plane z=0 since the magnetic flux density on this plane is expected to be perpendicular to the plane due to symmetry. Homogeneous Dirichlet boundary conditions are assumed on the outer boundaries of the domain.

Results and discussion

Figure 3 shows plots of the average magnetic flux density in the steel plate and channels along the paths A–B, C–D, and E–F, as shown in Figure 1. For simplicity, three different plots are combined into one with the horizontal axis split into three segments, each representing the distance along the paths A–B, C–D, and E–F from the beginning of the path. The experimental results are presented together with the simulation results that are obtained using Abaqus/Standard for two different specifications of current; namely, 1000 A-turns and 3000 A-turns. The plots indicate that the agreement between simulation and experimental results is good. Figure 4 shows plots of the magnetic flux density in the air along the path 1–2, as shown in Figure 1, for two different specifications of current. Again, the simulation results compare very well with the experimental results.

Input files

team_13_half_d2_bias2.inp

Nonlinear magnetostatic analysis of a steel plate and two steel channels excited by a coil carrying direct current of 1000 A-turns.

team_13_half_d2_bias2_3000.inp

Nonlinear magnetostatic analysis of a steel plate and two steel channels excited by a coil carrying direct current of 3000 A-turns.

References

  1. Preis,  K., et.al., “Different Finite Element Formulations for 3D Magnetostatic Fields,” IEEE Transactions on Magnetics, vol. 28, pp. 1056–59, 1992.
  2. “Team Problem 13: 3-D Non-Linear Magnetostatic Model,” accessed December 19, 2012, http://www.compumag.org/jsite/images/stories/TEAM/problem13.pdf.

Figures

Figure 1. Plan view of the problem setup.

Figure 2. Top view of the problem setup.

Figure 3. Magnetic flux density along the plate and the channels.

Figure 4. Magnetic flux density in the air.