Evaluation of the mechanical deformation in incompressible linear and nonlinear magnetic materials

General introduction

Vibration is the major problem facing almost of mechanical systems. Different damping methods are invented to reduce this harmful behavior.Among these, is using smart materials to decrease the amount of vibration such is the case in active vibration control which is based on magnetostrictive materials. Smart materials generate response to signals temperature, voltage, magnetic fiel, to name but a few.These materials such as magnetorheological fluids, shape memory alloys and magnetostrictive materials have the capability to transform one type of energy into another. Consequently, their use improves the overall performance of the device.

Magnetostriction is the phenomenon of changing the shape of materials due to the impact of an external magnetic field. Causes of magnetostriction are changes of length due to rotation of small magnetic domains. Internal strains in the structure are caused by this orientation and re-orientation. In the case of positive magnetostriction, strains in the structure lead to stretching of the material in the direction of the magnetic field. In the process of stretching, the cross section is reduced meanwhile the volume is kept almost constant. The detected volume change is too small that it could be neglected under normal operating conditions. When the magnetic field becomes more important, more domains will be aligned in the same direction of magnetic field. This process continues until reaching the saturation point when all magnetic domains become aligned with the magnetic field.

Multiphysics simulation using EMS for SOLIDWORKS

EMS ensures a Multi-physical simulation by the capability of coupling between Magneto- mechanical field. In this example, EMS helps to see the influence of a steady magnetic field on the geometry of a linear and a highly saturated magnetic material : Silicon steel RM50, under two different current densities, in two different regimes.  

Problem description

The magnetic system in question is presented in the figure below. It consists of two concentric wound coils fed by a constant current. The system includes, also, a rectangular test body surrounded by a ferromagnetic yoke.
 
The present model aims to find the mechanical deformation of the rectangular test body in the linear and saturation regimes of the ferromagnetic material that is assigned to the yoke and the test body. Two different current densities have been used to test deformation of the body.

Simulation Setup 

After creating a Magnetostatic Study coupled to Structural Analysis in EMS, four important steps shall always be followed:

1. Apply/Select the proper material for all solid bodies
2. Apply the necessary electromagnetic inputs
3. Apply the necessary structural inputs
4. Mesh the entire model
5. Run the solver.

Materials 

Below in table 1 are the properties of used materials. Electromagnetism equations are solved in complete solution domain. Stress analysis is done only in the rectangular workpiece.

 Table 1 -  Material properties

Material	Relative Permeability	Electrical Conductivity (Mho/m)	Elastic modulus (Pa)	Poisson's Ratio
Copper	1	5.9980e+07	Not required	Not required
Air	1	0	Not required	Not required
Silicon steel (RM50)	* 2175 (Linear case) * BH curve (nonlinear case)	2.1186e+06	2.035e+011	0.285

Figure 2 shows the BH curve of the Silicon steel material (RM50).

Electromagnetic inputs

In this study, Two wound coils are defined as the current source of the problem.

Table 2 - Coil information

	Number of turns	Wire diameter (mm)	Current amplitude (A)
Wound Coil 1	1	0.91168568 mm		47336.25 for case 1 473362.5 for case 2
Wound Coil 2	1	0.91168568 mm		4887.5  for case 1 48875   for case 2

Mechanical boundary conditions 

Fixed constraint on four edges of the rectangular workpiece (highlighted below in Figure 3)

                                 Figure 3 - Fixed constraint applied on the model edges

Meshing

Meshing is a very crucial step in the design analysis. EMS estimates a global element size for the model taking into consideration its volume, surface area, and other geometric details. The size of the generated mesh (number of nodes and elements) depends on the geometry and dimensions of the model, element size, mesh tolerance, and mesh control. In the early stages of design analysis where approximate results may suffice, you can specify a larger element size for a faster solution. For a more accurate solution, a smaller element size may be required.

Figure 4 - Meshed model

Magneto-mechanical results 

Figure 5 shows a 3D plot of magnetic flux in the whole magnetic system, when the test body and the yoke exhibit nonlinear permeabilities and are under the second applied current.

Figure 5 - Magnetic flux plot

Figure 6 presents current density distribution in the two coils, for the second treated case of current density.

Figure 6 - Current density plot

Figure 7 shows the mechanical deformation of the rectangular 3D test body under the second applied current density, when permeabilities of the yoke and the test body are nonlinear.

Figure 7 - Resultant displacement plot

Table 3 - Deflection of the workpiece under the two used current densities, using two different permeabilities

Current density	Linear     permeability	Nonlinear permeability
J=2.5e+06 A/m^2	0.98	0.88
J=25e+06 A/m^2	87.94	5.65

Conclusion

EMS offers the possibility to  study deformation of magnetic materials under the influence of a magnetic field, in both the linear and the saturation regimes. It is capable to simulate mechanical behaviour of realistic material properties like magnetic materials with nonlinear permeability, under various operating conditions.

References

[1]:Se-Hee Lee, Xiaowei He, Do Kyung Kim, Shihab Elborai, Hong-Soon Choi, II-Han Park and Markus Zhan.2005. Evaluation of the mechanical deformation in incompressible linear and nonlinear magnetic materials using various electromagnetic force density methods. Journal of applied physics. Volume 97, Issue 10.