# 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.

### Tasks

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

### Hints

- Use the provided templates
`coil_transient.xml`

,`mat.xml`

and`HW5_template.ipynb`

. - Adapt the Trelis input
`geometry.jou`

. - Use the static simulation to check the prescribed current and boundary conditions.
- Use a time resolution of 20 steps per period.
- Pole force can be neglected.

### 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**.