VM207

VM207
Stranded Coil Excited by External Circuit

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
Element Type(s):
2D 8-Node Electromagnetic Solid Elements (PLANE233)
2D Infinite Solid Elements (INFIN110)
Electric Circuit Elements (CIRCU124)
Input Listing:vm207.dat

Test Case

A stranded coil with 500 turns and a fill factor of 0.9 is connected to an external circuit consisting of an independent voltage source and a 2 ohm resistor. A static analysis is run with a 12 volt DC excitation to determine the coil resistance and inductance. A transient analysis is run to calculate the coil current response to a step 12 volt excitation.

Figure 324: Stranded Coil Problem Sketch

Stranded Coil Problem Sketch

Material PropertiesGeometric PropertiesLoading
Rext = 2 Ω
µr = 1.0 (coil)
µr = 1.0 (air)
ρ = 3.04878 x 10-8 ohm-m (coil)
n = 500 turns
s = 0.02 m
r = 3(s)/2 m
FC = 0.9 Fill factor
Vo = 12 volts (static)
Vo|t = 0+ = 12 volts (static)

Analysis Assumptions and Modeling Notes

The problem is similar to VM206 except the coil is excited by an external circuit using the general circuit element. In the circuit, the coil is modeled by a stranded coil circuit component that shares a common node with the coil in the finite element model. The finite element model provides to the circuit the necessary coil resistance and inductance to characterize the stranded coil circuit impedance. The nodes in the coil region are coupled in the EMF and VOLT degrees of freedom so that a single voltage drop (EMF) and coil current (CURR) are calculated.

A static analysis is run to obtain the coil resistance and inductance so that an analytical solution of the transient response can be calculated and compared to the solution results. A transient solution to a step voltage excitation is run for 0.01 seconds. The calculated coil current is compared to the solution current. The coil current response is plotted versus time.

Results Comparison

 TargetMechanical APDLRatio
Static Analysis Inductance, Henry 0.01274 0.01273 1.00
Transient Analysis Current, Amps 1.985 2.00300 1.01

Figure 325: Current vs. Time

Current vs. Time