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TEAM Problem 7: Eddy Currents in a Plate Compared with Measurements

TRAFOLO computes the eddy currents of TEAM Problem 7, the Compumag benchmark of an aluminium plate with a hole under a coil, within 1.6 to 6.5 % of the measurement on 14 of its 16 measured curves, at 50 and 200 Hz.

  • Result: Bz above the plate 2.5 to 5.4 %, Jy on both plate faces 1.6 to 6.5 % (mean difference in % of each curve's largest measured value). Two curves are left out and three printing errors of the published tables are corrected, see Reference data.
  • Source: TEAM Problem 7 description, Compumag Society; K. Fujiwara, T. Nakata, "Results for benchmark problem 7 (asymmetrical conductor with a hole)", COMPEL 9(3), 1990, pp. 137–154, doi:10.1108/eb010071.
TEAM Problem 7 in TRAFOLO at 50 Hz, the coil above the aluminium plate with the hole, current density per element
TEAM Problem 7 in TRAFOLO at 50 Hz: the coil above the plate, current density J per element.

Case

TEAM Problem 7 to scale, top view and section through line A1-B1, with the plate, the hole, the coil and the four measurement lines
TEAM Problem 7 to scale, TEAM axes: top view and the section through line A1–B1. Dashed: the measurement lines.
Part Material in the model Size [mm] Position [mm]
Plate Aluminum: σ = 3.526 × 10⁷ S/m, μr = 1, temperature coefficient 0 294 × 294 × 19 x, y = 0–294, z = 0–19
Hole, through the plate – 108 × 108 x, y = 18–126
Coil Copper, Stranded & Litz outside 200 × 200 (corner radius 50), inside 150 × 150 (radius 25), 100 high x = 94–294, y = 0–200, z = 49–149
  • Excitation: 2742 ampere-turns peak at 50 and 200 Hz. Skin depth in the plate: 12.0 mm at 50 Hz, 6.0 mm at 200 Hz.
  • Measured: Bz at z = 34 mm on lines A1–B1 (y = 72 mm) and A2–B2 (y = 144 mm); Jy on the top face (A3–B3, z = 19 mm) and on the bottom face (A4–B4, z = 0) at y = 72 mm. Points every 18 mm from x = 0 to 288 mm, at ωt = 0° and 90°.
  • Air box: −500 to 650 mm on every axis.

Reference data

The published tables (problem7.pdf, p. 14) carry three printing errors, corrected here:

  1. The two Jy tables are printed under swapped headings: table (b) belongs to the top face and table (a) to the bottom face, as the 1990 results paper plots them.
  2. In all four Jy tables the ωt = 0° and 90° columns are interchanged, with their signs reversed; the 1990 paper's own figures plot the measured points this way.
  3. On the bottom face at 50 Hz the values belong one measurement position further along the line; printed as they are, they sit one position off the results of all 25 codes of the 1990 benchmark.

Two measured curves are left out: Bz at 200 Hz and ωt = 90° on A1–B1 and A2–B2. This out-of-phase field is at most 5 G. Independent published FEM results agree with TRAFOLO there, and the measured curves would mean that the plate loss hardly grows from 50 to 200 Hz. The corrected values are attached.

TEAM07_reference_data_co…

Results

Bz along lines A1-B1 and A2-B2 at 50 and 200 Hz, measured and TRAFOLO, both phases, the two left-out curves in grey
Bz above the plate on lines A1–B1 (top) and A2–B2 (bottom), 50 Hz (left) and 200 Hz (right). Grey: left out.
Jy along lines A3-B3 on the top face and A4-B4 on the bottom face at 50 and 200 Hz, corrected measurement and TRAFOLO
Jy on the top face (A3–B3) and the bottom face (A4–B4), 50 Hz (left) and 200 Hz (right); no metal at x = 18–126 mm.
Mean difference, run R2 [%] 50 Hz, ωt = 0° 50 Hz, ωt = 90° 200 Hz, ωt = 0° 200 Hz, ωt = 90°
Bz above the plate, A1–B1 3.3 2.5 3.5 left out
Bz above the plate, A2–B2 4.5 2.8 5.4 left out
Jy on the top face, A3–B3 2.0 3.4 1.7 6.5
Jy on the bottom face, A4–B4 1.8 3.2 1.6 4.6

Difference: TRAFOLO minus measured, in % of the largest measured value on the same curve, so that values near a zero crossing do not inflate it.

Eddy current density per element on the top face of the plate at 50 and 200 Hz, seen from above
Current density J per element on the top face at 50 Hz (left) and 200 Hz (right), seen from above in the model axes.

The eddy currents circle under the coil and crowd along the hole edge and the plate edges, where the Jy lines cross them. At 200 Hz they are stronger and kept closer to the surface.

TRAFOLO model

The TEAM7 template that ships with TRAFOLO, with the hole at its published position, in TRAFOLO 1.66.1beta. The template's y axis points up: template (x, y, z) = TEAM (x, z, y).

TEAM07_plate_template_ax…

Tab Setting
Setup DOMAIN TYPE Full: the plate has no symmetry plane. ELECTROMAGNETICS Inductance.
Other The plate, imported from TEAM07_plate_template_axes.step (attached).
Materials Plate: Aluminum (σ = 3.526 × 10⁷ S/m, temperature coefficient 0). Coil: Copper.
Coil Stranded & Litz, Turns per solid 2742, Closed coil.
ElMag Coil on the primary, current excitation.
Waveform Inductance Sweep, SWEEP BY Frequency: 50 and 200 Hz, primary 0.70711 A rms.
Mesh Plate Max Element Edge Size 2 mm (a third of the 200 Hz skin depth), coil 4 mm, Growth Rate 0.3; 1 084 071 elements.
Solve 16 cores, Solver Preset Normal: both frequencies in about 20 minutes.

The fields are read at the measured points: ωt = 0° is the real part of the complex field, ωt = 90° the negative imaginary part. Jy at the hole edges (x = 18 and 126 mm) is read 0.1 mm inside the metal.

Checks

  • Mesh: refining the plate from 6 to 3 to 2 mm takes Bz on A1–B1 at 50 Hz from 7.3 to 4.3 to 3.3 %. With the 3 mm plate, 350 000 elements, both frequencies solve in about 4 minutes on 16 cores.
  • Air box: doubling it shifts Bz by about 0.5 % on average and by 3 % at most.
All runs
Run Plate / coil mesh [mm] Growth Rate Air box [mm] Elements Mesh / solve time [s] Bz A1–B1 mean, 50 / 200 Hz [%] Note
R0 6 / 6.25 0.5 −500…650 134 228 78 / 264 7.3 / 7.8 First run
R1 3 / 6.25 0.3 −500…650 346 418 175 / 260 4.3 / 4.3 Mesh check
R2 2 / 4 0.3 −500…650 1 084 071 534 / 1155 3.3 / 3.5 Reference run
R3 3 / 6.25 0.3 −1000…1150 348 450 75 / 180 4.1 / 4.4 Air box doubled

Each run solves 50 and 200 Hz on 16 cores.

Limits

  • Values per element: B and J are constant inside each element, so a single point value moves with the mesh by up to 10 %, while the mean along a line converges.
  • Hole edges (x = 18 and 126 mm on the Jy lines) are corners: the values there are read 0.1 mm inside the metal.
  • Two curves left out: Bz at 200 Hz and ωt = 90°, see Reference data.