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Magneto-structural analysis of planar magnetic actuator Application



General Introduction

Magnetic levitation (maglev) is a method to suspend objects without any support or contact using magnetic field. The magnetic force created by Maglev is used to counteract the effects of gravitational force and any other accelerations. Magnetic levitation is exploited especially in maglev trains. It is used also in contactless melting, magnetic bearings and for product display purposes. Permanent magnets, electromagnets and superconductors all can be arranged together  to obtain  a successful levitation and a control of all 6 axes.

Moving planar actuators are showing promising performance, but they did not reach the required positioning accuracy. Accurate modeling of magnetic forces and actuator deflections present one of the greatest challenges. In this example, a planar magnetic actuator will be treated. It consists of a Halbach array of magnets mounted on an aluminum plate. The goal is to compute the magnetic forces acting on the plate.

Multiphysics simulation using EMS for SOLIDWORKS

EMS is capable of coupling Magnetic field and structural analysis. The mechanical structure on which the array of permanent magnets is mounted will deform due to magnetic fields and forces.


Planar actuator mounted on an aluminum carrier

Figure 1 - Planar actuator mounted on an aluminum carrier

Problem description

The magneto-structural system to be analyzed consists of a Halbach array (11x11) mounted on the conductive aluminum plate, as shown in figure 2. The main goal of this example is to examine the plate deflection.
All the dimensions are given in millimeters.


The-planar-actuator-model
          Figure 2 - The planar actuator  model


Coercivity direction (in blue arrows) of the magnets forming the Halbach array

Figure 3 - Coercivity direction (in blue arrows) of the magnets forming the Halbach array



Material properties

 
  Permeability Coercivity (A/m) Remanence(T)
NdFeB 1.04 948808.3 1.24
 

Meshing

High mesh quality is the key requirement for accuracy of the results. EMS offers flexible mesh control tools. You can readily refine mesh quality on faces, edges and bodies. In this model, a refined mesh is applied to the aluminum plate and the array of magnets to ensure accurate calculation of magnetic forces among them. Mechanical stress analysis is dependant on the accuracy of results obtained in the magnetic part of the problem.

You can see, in figure 4, the mesh used for the  current analysis.

The meshed model

Figure 4 -The meshed model

Magneto-structural Results

  • Magnetic flux density plot

Figure 5 presents the magnetic flux density plot in the analyzed planar actuator, created by the magnets . 

3D fringe plot of the magnetic flux density in the model

       Figure 5 - 3D fringe plot of the magnetic flux density in the model
  • Magnetic force density plot

Below (Figure 6) is a fringe  plot of the magnetic force density; it can be observed that maximum values of these forces are on the boundaries of the magnets, where the magnets are facing each other. 


 


Magnetic force density plot

Figure 6 - Magnetic force density plot

 

  • Displacement along the Z axis of the plate

The plate is bending towards its center under the influence of the magnetic forces acting on it. The magnitude of this deflection is significant.  EMS results correlate very well with experimental and numerical results given in [1].

 

  EMS Result The reference result
Deflection of the plate along Z axis (in m) 1.8e-04 2e-04
 
Table2 - Comparative table between EMS and the reference results



 
                    Figure 7. Displacement along the Z axis of the plate (the deformed shape)

                    Figure 7 - Displacement along the Z axis of the plate (the deformed shape)

 

Conclusion

This article shows the magneto-structural analysis of a Halbach array mounted on an aluminum plate. Mechanical results show that the plate deformation is significant and they agree well with the reference

References

[1] J. M. M. Rovers, J. W. Jansen, E. A. Lomonova and M.J.C. Ronde . Calculation of the static forces among the permanents magnets in a Halbach Array. IEEE Transactions on Magnetics, Volume 45,NO 10. October 2009: Netherlands.?