Levitation with arbitrary motion

This gallery page shows the use of MagNet's Transient 3D with Motion solver. This solver, like the 2D version, can solve the equations of motion for an arbitrary number of degrees of freedom simultaneously.

Presented here is an aluminum plate that is 3 mm thick and positioned above two coils whose current is 180 degrees out of phase. Infolytica has already presented simulations of this device with motion along a single degree of freedom in these 2D and 3D simulations. The motion of the plate when the initial position is off center can be modeled using three degrees of freedom: translation along the x and y axes and rotation about the z-axis.

Results

The coils induce eddy currents in the plate resulting in a strong levitation force lifting the plate. The 180 degree phase difference between the inner and outer coils produces a restoring force that tends to return the plate to the centered position. Since the induced currents increase with the proximity of the plate to the coils, there is also a restoring torque that tends to keep the plate level when the plate is centered, although when the plate is off center this torque is not zero when the plate is level. The animations of the plate's position demonstrate the levitation force, restoring force and torque as a function of time, when starting from three different positions. The simulations end when the plate makes contact with the top plane of the driving coils.

Simulation A.
Initial position of plate: 1 cm from center.
Length: 0 to 90 ms.

Simulation B.
Initial position of plate: 3.2 cm from center.
Length: 0 to 291.5 ms.

Simulation C.
Initial position of plate: 6.7 cm from center.
Length: 0 to 157.5 ms.

Click image to see full size version

The device has mirror symmetry across the x-y plane so only half of the full model needs to be simulated -- this reduces the time required to solve the model. With MagNet's powerful and scriptable post-processing capabilities, it is easy to upgrade the partial solution to display the fields on the full model as shown here. An animation of the current density in Simulation B is shown below.

Click image to see full size version

MagNet's post processing tools report the forces and torques on all bodies present in a simulation. The graphs shown on the right are of the magnetic force and torque on the moving plate as a function of time in Simulation B.

Click image to see full size version

The graphs presented on the right report the x and y coordinates of the plate's center of gravity, as well as the angle of the plate from the horizontal for Simulation B. Note that for the most part, the time-averaged force and torque act to restore the plate to the center level position -- the exception is the torque when the plate is off-center.