VM206

VM206
Stranded Coil with Voltage Excitation

Overview

Reference:W. B. Boast, Principles of Electric and Magnetic Fields, Harper & Brothers, New York, NY, 1948, pg. 247, eq. 12.18.
Analysis Type(s):Static, Harmonic
Element Type(s):
2D 8-Node Electromagnetic Solid Elements (PLANE233)
2D Infinite Solid Elements (INFIN110)
Input Listing:

vm206.dat

VM206 requires a supplemental .cdb input file which is too long to include full input listings. This file must be downloaded and placed in your working directory for the test case to run properly. Additionally, the geometry and mesh should be regenerated.

Download link: MAPDL Test Case Files for 2024 R2

vm206.cdb

Test Case

A stranded coil with 500 turns is modeled in free space. A static analysis with a 12 volt DC excitation is run first to calculate the coil resistance and inductance. A 1/4 symmetry model is constructed. An AC (harmonic) analysis is run to simulate an RL circuit response with an applied excitation of 12 volts at 60 Hz. The complex coil current is calculated.

Figure 323: Stranded Coil Problem Sketch

Stranded Coil Problem Sketch

Material PropertiesGeometric PropertiesLoading
µr = 1.0 (coil)
µr = 1.0 (air)
ρ = 3 x 10-8 ohm-m (coil)
n = 500 turns
s = 0.02 (coil winding width and depth) m
r = (3 x s )/2 m
Vo = 12 volts (static)
V = Vo cos ωt (harmonic)
where:
Vo = 12 volts
ω = 60 Hz

Analysis Assumptions and Modeling Notes

Due to symmetry only 1/4 of the problem domain is required. The open boundary is modeled with infinite elements to accurately represent the decaying field. The infinite element region is set to a width of 6s, doubling the original problem domain of 6s for optimal performance.

The coil is characterized through the real constant table. A direct voltage load is applied to the coil region. Nodes in the coil region are coupled in the VOLT degree of freedom to solve for a single valued coil current (per turn).

The real and imaginary current are extracted from the AC solution.

Results Comparison

 TargetMechanical APDLRatio
Static Analysis Coil current, Amps3.39500 3.395591.00
Harmonic Analysis Real solution, Amps 1.19200 1.193741.00
 Imag solution, Amps -1.62100 -1.621241.00