Difference between revisions of "Homework Assignment"

Revision as of 21:24, 14 February 2022

Aim of Assignment

Students will learn the basics of electromagnetic field calculations, their main steps, and gain practice in evaluating results and writing a Technical Report that meets international expectations.

Knowledge needed to solve the problem

• The main steps of the finite element method;
• Theoretical knowledge of the static magnetic field (for defining materials, for excitation);
• Knowledge of CAD system to create geometry;
• Download and install Ansys Electronics Desktop Student.

The Semester Assignment

The task consists of two parts, a basic task, with a faultless solution of up to 70%, and an extra task, with an additional maximum of 30%.

Deadline	-
Output Form:	PDF format. Color drawings should be made so that their contents are clear to the reader in black and white.
Language	English
Place of submission:	In Moodle system.
Late submission:	After every day started, a 5% deduction from the achieved result (i.e. after 5 days delay 100% can only be obtained up to 100% - 5x5% = 75%).
Evaluation:	0 - 48% - Insufficient [F] (1)
	50 - 59% - Sufficient [D] (2)
	60 - 70% Satisfactory [C] (3)
	71 - 84% Good [B] (4)
	85 - 100% - Very good [A] (5)
For the formal requirements, the requirements of CFD and mechanics are also valid here.

Part I of the Assignment - 80%

Calculating the resistance and the total loss of the shunt resistor by finite element method

The geometry and dimensions of the task.

The geometry dimensions for your task you can find in the following table: Semester Assigment.

This task is a DC current conduction problem. The solved equation is

[math]\nabla\cdot\sigma\nabla \varphi=0[/math]

with following boundary conditions

[math]\vec{J}\cdot\vec{n}=-J_{\text{n}}[/math] on [math]\Gamma_{\text{J}}[/math] (This is the input)

and

[math]\varphi=U_0 = \text{0 V}[/math] on [math]\Gamma_{\text{E}}[/math] (This is the output),

where [math]J_{\text{n}}[/math] is the current density calculated from the specified current excitation.

The task: determine the voltage drop, the resistance and the ohmic loss of the problem.
The voltage drop is the potential difference between the two terminals of the arrangement. You can determine resistance using Ohm's law:

[math]R = \frac{U}{I}[/math],

then the ohmic loss

[math]P = I^2\cdot R[/math]

where [math]U[/math] is the voltage drop, [math]I[/math] is the current and [math]R[/math] is the resistance.

Bulk conductivity of materials.

Material	Titanium	Copper	Aluminum	Copper-manganin alloy
[math]\sigma~[\text{MS/m}][/math]	1.82	58	38	20.833

Tasks

• Draw the geometry based on the specified dimensions.
• Define the problem based on the given material parameters and boundary conditions;
• Creating and specifying the task geometry in Ansys Electronics Desktop Student;
• Run the FEM simulation;

The parameters listed in the task can be calculated with the Maxwell 3D - DC Conduction solver and the Q3D Extractor - DC solver.

Figure 2. - Possible solution (Left - Maxwell 3D, Right - Q3D Extractor).

Results of the test example.

Quantities	Voltage drop [mV]	Resistance [[math]\text{n}\Omega[/math]]	Ohmic loss [W]
Maxwell 3D	10.9927	18.3211	6.5956
Q3D Extractor	10.9759	18.2931	6.5855

Part II of the Assignment - 20%

In the student version of Ansys EM, Icepak provides an opportunity to study the thermal phenomena of the task. Ansys Icepak is a general CFD solver with specific capabilities for testing the heating and cooling of electronic circuits (PCB / power module).

The task has a natural convection cooling. The excitation is the ohmic loss from the electromagnetic simulation.

Thermal properties of materials.

Material	Titanium	Copper	Aluminum	Copper-manganin alloy
[math]\rho~[\text{kg}/\text{m}^3][/math]	4500	8933	2689	8400
[math]c_{\text{P}}~[\text{J}/(\text{kg}\cdot\text{°C})][/math]	522	385	951	410
[math]\lambda~[\text{W}/(\text{m}\cdot\text{°C})][/math]	21	400	237.5	22

The table below shows the result of the thermal simulation.

Results of the test example.

Quantities	Max. temperature [°C]	Min. temperature [°C]	Max. velocity [m/s]
Maxwell 3D + Icepak	75.9284	71.3658	0.2881
Q3D Extractor + Icepak	75.8669	71.3002	0.2880

Here you can find the archive file of test example: Shunt Resistor.

References