ELEC-E8411 - Numerical Methods in Electromechanics
Assignment 1
Deadline: January 19th, 23:59
FEM Simulation of Levitation Melting
Introduction
Your task is to simulate a crude levitation melting device, as seen in the video
https://www.youtube.com/watch?v=VydPQuLyEns
The device consists of a doubly conical coil, fed by an AC current supply. Inside the coil is a
block of aluminum, being levitated and heated up by the induced eddy currents.
We recommend you do the simulations with FEMM software, freely available for Windows and
Linux computers at
http://www.femm.info/wiki/HomePage.
Mac users can pair up with Win/Linux users (recommended), or use the Comsol software
(available on Aalto computers; downloadable from download.aalto.fi)
The simulations can be done individually or in pairs. Everybody returns their own report.
The actual physical problem is simplified into the 2D geometry shown below.
The aluminum block is assumed to be a ball 1 cm in diameter, seen on the left side of the figure.
The coil is modelled by a single rectangular block of copper, fed by a current source. The
problem is assumed to be axially symmetric, with the symmetry line r = 0 being the blue line on
the left border of the figure.
Simulations
Workflow for the simulations is described below.
1. Open FEMM. Create a new magnetics problem (File – New).
2. Click on Problem. In the dialogue box that opens up, set the problem type to Axisymmetric, and
the supply frequency to 500 Hz.
3. Next, we will define the problem geometry. The desired end result is shown below for
reference, but we’ll go through the process in baby steps. The size of the box is 20 cm x 20 cm,
and the left side corresponds to r = 0 (remember we’re dealing with cylindrical coordinates
here).
The geometry is defined by first adding some nodes to the problem, and then connecting the
nodes with line segments.
First, select the node tool
New nodes can then be added either by clicking on the desired position, or by pressing Tab to
open up a dialogue box in which you can add the desired coordinates.
First, add four nodes at (0, 0), (0, 20), (20, 20) and (20, 0) (all units in centimeters) to define the
corners of the simulated domain.
Also, add two nodes at (0, 9) and (0, 11) for defining the aluminum ball.
Next, select the line tool to define some line segments.
Clicking two nodes in succession connects those nodes with a straight line segment. Do this for
all the nodes you have created, to generate the outer boundaries of your problem domain.
Then, select the arc segment tool on the right side of the line tool. This tool works like the line
tool, but generates curved lines rather than straight ones. Use this tool to create the one curved
boundary for the ball.
Finally, add the four nodes that define coil. Their positioning is not exact, but the end result
should be somewhat close to the picture. Connect these nodes with straight line segments.
4. Next, it is time to define the boundary conditions. Click on Properties – Boundary – Add
property to open up the dialog box
Select Prescribed A to define a homogeneous Dirichlet boundary.
Next, we have to assign this condition to the outer boundaries. This is done by selecting the line
segments that belong to the outer boundaries by right-clicking. (You can select several by
holding Ctrl). Once you have selected the segments, press Space to open up the Segment
Property dialog box
Select the Dirichlet boundary you have just defined, and press okay.
5. Next, we have to add some material properties to the problem, from Properties – Materials –
Add Property. Define the following materials:
a. Aluminum
b. Air
c. Copper
All these can be magnetically linear, but you’ll have to input the electrical conductivity for
copper and aluminum (Google is your friend here).
6. Finally, we’ll have to a circuit to the problem from Properties – Circuits – Add property. You will
have to specify the circuit current, but several hundred Amperes is a good starting point.
7. Now, it’s time to assign our newly-defined materials and circuits to the actual geometry. Select
the material label tool
and then click inside your coil to add a label there. Right-click to select the label, and press Space
to open up the dialog box
In the Block type drop-down menu you can assign the material; select the copper you’ve just
moments ago defined. In circuit drop-down menu lets you assign this block to the circuit you’ve
defined. You can also specify the number of turns, meaning the total current in the block is the
number of turns times the current defined for the circuit.
Similarly, add one material label inside the ball, and one somewhere in the air region. Assign the
materials aluminum and air, respectively. Obviously, these blocks don’t belong to any circuit.
8. Next, mesh the geometry, solve the problem, and enter the post-processing view by pressing the
corresponding buttons.
9. In the post-processing view, the flux lines should be shown by default (in case they aren’t, Click
View – Contour plot – Real component of A). Add also the flux density (amplitude) plot by
clicking View – Density plot. In the dialog window, select Flux Density (T) as the plotted value,
and remember to check the box Show Density Plot.
10. Next, compute the force acting on the ball. Select the post-processing line tool
and select the outer boundaries of the ball (by again clicking at the nodes in succession).
Compute the force by clicking Integrate – Force from Stress tensor.
11. Finally, compute some total losses. Select the block tool (on the right side of the line tool), and
click inside your coil to select it. Compute the total losses by clicking Integrate – Resistive losses.
Repeat the same for the aluminum ball.
Report
Write a report covering the following topics and questions.
1. What is the weight of the aluminum ball (yes, weight; in Newtons)?
2. A figure of your meshed geometry.
3. A figure of the flux lines and flux densities.
4. The computed force acting on the ball. Is it (=DC component of the force) enough to
levitate the ball? If not, you’ll have to increase either the current defined for the circuit,
or the number of turns in the coil. Remember to re-mesh and re-solve, before recomputing the force.
5. Once you get a force that can levitate the ball, compute the resistive losses in the ball
and in the coil.
6. A brief physical explanation about why the ball levitates (Hint: Lorentz force)
7. Do you think the losses in the ball are large enough to melt it? Why / why not?
The report is supposed to be a report, meaning you briefly introduce the problem,
methodology, and results. No need to write a full scientific article, but there should a nice flow
from section to section and paragraph to paragraph. A collection of figures and calculation
results thrown together is not enough.
Send your report as a pdf file to [email protected].