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


General introduction

The major problem which all mechanical systems are facing today is vibration. Research is always going on to reducing the vibration of a system using different damping methods. After the emergence of smart materials, researchers found smarter way of reducing the vibrations that is called as active vibration control using magnetostrictive materials.

Smart materials produce response to signals such as temperature, voltage, pressure, magnetic fields and so on. These materials have the ability to transform one type of energy into another and therefore use of these materials improves the overall performance of a device.

Below is a list of some types of smart materials:
- Magneto rheological fluids
- Shape memory alloys
- Electrostrictive materials
- Piezoelectric materials
- Magnetostrictive materials 

Magnetostriction is the change in shape of materials under the influence of an external magnetic field. Causes of magnetostriction are changes of length due to rotation of small magnetic domains. This rotation and re-orientation causes internal strains in the structure.
The strains in the structure lead to stretching, in the case of positive magnetostriction, of the material in the direction of the magnetic field. During this stretching process, the cross section is reduced in a way that the volume is kept nearly constant. The size of the volume change is so small that it can be neglected under normal operating conditions.

Applying a stronger field leads to stronger and more definite reorientation of more and more domains in the direction of magnetic field.
When all the magnetic domains have become aligned with the magnetic field the saturation point has been achieved.

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.  

The coupling between the two physics is done by transferring the  magnetic force, exerted on the rectangular workpiece, to the mechanical solver.

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.
 

3D model of magnetostriction of a ferromagnetic rectangular workpiece

Figure 1 - 3D model of magnetostriction of a ferromagnetic rectangular workpiece

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).

BH curve of silicon steel (RM50)                                             Figure 2 - BH curve of silicon steel (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)
 

Fixed constraint applied on the model edges

                                 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.
 

Meshed model
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.

Magnetic flux plot

Figure 5 - Magnetic flux plot

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

Current density plot

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.

Resultant displacement plot

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 behavior of realistic material properties like magnetic materials with nonlinear permeability, under various operating conditions.

Reference

[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