# HW3: Magentic Mechanic

### Description

Consider an axi-symmetric model of a coil and a plate as depicted in the figure. The inner and outer radii of the coil, $r_1$ = 0.0025 m and $r_2$ = 0.0075 m. The length of the coil, $l_1$ = 0.008 m. The plate thickness and air gap is $l_2$ = 5 $\cdot 10^{-4}$ m respectively $l_3$ = 7.5 $\cdot 10^{-4}$ m. The point $C$ is located in the center of the coil, the point P in the middle of the plate at $z$ = 0.005 m. The plate is either made from iron or aluminum, with electric conductivity and linear magnetic permeability given in the mat.xml. The coil has 40 turns and is fed by a controlled current of $i$ = 10 kA.

1. Create a regular hexaedral mesh using Trelis. (1 Points)
2. Create input-xml files for the required CFS++ simulations. (1 Points)
3. Document your results by answering the questions below. (13 Points)

### Submission

Submit all your input files (*.jou, *.xml) as well as a concise PDF report of your results. Name the archive according to the format HWn_eNNNNNNN_Lastname.zip.

### Mesh Size

Estimate the skin depth for both materials. What element size do you suggest? Motivate your suggestion! (3 Points)

### Static Analysis

Compute the static solution of the coupled magnetic-mechanical problem.

• Plot the vector field of the magnetic flux density. (2 Points)
• Compare the cases for iron and aluminum plate. (2 Points)
• What is the difference? (3 Points)
• Are there displacements? Why / Why not? (3 Points)

### Transient Analysis

Set up a transient analysis with a sinusoidal coil current with a frequency of 100 Hz and solve the coupled magnetic-mechanical problem. Compute the solution for 4 periods of the coil current.

• Plot the time signal of the z-displacements of point $P$ for both plate-materials in one figure
• Plot the displacement of the plate (paraview warp by vector) for both plate-materials.
• Describe the time signals: Are there transient effects? What is the difference between the amplitudes with aluminum and iron plate and why is there a difference?

You can download the templates linked on this page individually by right click --> save target as. Alternativey, head over to the git repository and use the download button on the top right: Here is a direct link to the zip archive.