3D Time-Harmonic Bath Plate

The model consists of a conducting plate with two holes symmetrically located at the center of the plate; it is referred to in the literature as the Bath Plate. A 400 Hz current-carrying coil is positioned above the plate. Taking into account the symmetry of the problem about the XZ and YZ planes, only one-quarter of the structure needs to be built and modeled. The model is shown below.

The plate is made of aluminum with a conductivity (s) of 0.3278 X 108. The exciting ampere-turns of the coil are 1260 AT at a frequency (f) of 400 Hz.

Skin Depth Calculation

The first step is always to calculate the skin depth (d) or the depth of penetration of the field for the conducting regions using the relation:

for the current problem, the skin depth must be calculated in the Aluminum plate at a frequency f = 400 Hz, m = mo = 4p X 10-7 H/m and s = 3.278 X 107 S/m. Thus d = 4.39 mm.

The height of the Aluminum plate H = 6.35mm. Since H/d = 6.35/4.39 = 1.44, the current problem must be treated with the AC magnetic analysis. Furthermore, remember that for the AC magnetic analysis the mesh must have at least two elements per skin depth in the conducting regions where an eddy current is expected to be induced. Given a ratio of H/d = 1.44, 3 to 4 mesh elements along the height of the Aluminum plate are sufficient.

Since the coil is stranded, it does not support eddy currents. Thus, the calculation of the skin depth in the coil is not needed.

EMS Results

• Real Part of the Magnetic Flux Density at wt=0

  

• Imaginary Part of Eddy Current Density in the Plate at wt = 0

  

• Power Loss Results