2.4. 2D Stranded Coil Analysis

This section describes how to perform a 2D stranded coil analysis.

2.4.1. Performing a 2D Stranded Coil Analysis

To perform a stranded coil analysis using PLANE233, you need to do the following:

  1. Select PLANE233 element type and set KEYOPT(1) = 2.

  2. Specify magnetic properties using MP,MURX or TB,BH.

  3. Optionally, for a Joule heat calculation, you can specify isotropic electrical resistivity using MP,RSVX .

  4. Specify coil parameters using the element real constants on the R command:

    • THK (R1) – Out-of-plane thickness for the plane geometry (KEYOPT(3) = 0) and fraction of the 360° basis for the axisymmetric geometry (KEYOPT(3) = 1). For 2D planar problems, this constant represents the true length of the coil. Defaults to 1.

    • SC (R2) – Coil cross-sectional area. This constant represents the true physical cross-section of the coil regardless of symmetry modeling considerations. It includes the cross-sectional area of the wire and the non-conducting material filling the space between the winding.

    • NC (R3) – Number of coil turns. This constant represents the total number of winding turns in a coil regardless of any symmetry modeling considerations.

    • RAD (R4) – Mean radius of the coil. This constant applies to the axisymmetric geometry (KEYOPT(3) = 1) only. If the mean radius is not known, input VC/((2π)(SC)(THK)) , where VC is the full symmetry true physical volume of the coil. VC includes the volume occupied by the wire and the non-conducting material filling the space between the winding.

    • TZ (R5) – Current polarity. This constant assigns a direction to the current flow with respect to the Z-axis. It defaults to 1 for plane (KEYOPT(3) = 0) and to -1 for axisymmetric (KEYOPT(3) = 1) geometries.

    • R (R6) – Coil resistance. This constant represents the total coil DC resistance regardless of any symmetry modeling considerations. If the wire electrical resistivity ρ, total length L, and diameter D are available instead, the total coil DC resistance can be calculated as follows R = 4ρL/(πD2).

    • SYM (R7) – Coil symmetry factor. This constant represents the ratio of the full symmetry coil cross-sectional area (SC) to the modeled coil area. The input should be greater or equal to 1.

  5. Specify the analysis type. The stranded coil analysis can be static, transient, or harmonic.

    • If you perform a static analysis, you can use KEYOPT(2) to select a strong (using matrix terms) or weak (using the load vector) electromagnetic coupling. The strong coupling option (KEYOPT(2) = 0) produces an unsymmetric matrix and, in a linear analysis, a coupled response is achieved after one iteration. The weak coupling option (KEYOPT(2) = 1) produces a symmetric matrix and requires at least two iterations to achieve a coupled response.

    • If you perform a transient or harmonic analysis, you can use KEYOPT(2) to choose between strong coupling with 'true' voltage drop and back-EMF (VOLT and EMF) and strong coupling with time-integrated VOLT and EMF. The strong coupling option with 'true' VOLT and EMF (KEYOPT(2) = 0) produces an unsymmetric matrix. The strong coupling option with time-integrated VOLT and EMF (KEYOPT(2) = 2) produces a symmetric matrix (provided any stranded coil symmetry factor (SYM) is 1). In a linear analysis, a coupled response is achieved after one iteration.

  6. Couple VOLT and EMF degrees of freedom for each coil: CP,,VOLT and CP,,EMF.

  7. Apply magnetic and electric boundary conditions.

  8. Apply electric loading:

    • Nodal constraints for VOLT and EMF degrees-of-freedom: D,,VOLT and D,,EMF. Applicable when KEYOPT(2) is set to 0 or 1.

    • Nodal total electric current: F,,AMPS.

    • Voltage or current loading using CIRCU124 with KEYOPT(1) = 3,4,or 9 through 12. Applicable when KEYOPT(2) is set to 0 or 1.

2.4.2. Reviewing Results from a 2D Stranded Coil Analysis

In addition to the degrees of freedom results AZ, VOLT and EMF, the following derived data is available with the PLANE233 stranded-coil analysis:

  • Nodal magnetic flux density B (X, Y, SUM)

  • Nodal magnetic field intensity H (X, Y, SUM)

  • Nodal magnetic forces FMAG (X, Y, SUM)

  • Element conduction current density (JTZ or JSZ) at the element centroid [1]

  • Joule heat rate per unit volume (JHEAT) [2]

  • Element magnetic energy (SENE) (valid for linear materials only)

  1. JTZ and JSZ are the effective current densities as they are calculated based on the coil cross-sectional area (SC) that includes the wire and the non-conducting material filling the space between the winding.

  2. JHEAT represents the effective Joule heat generation rate per unit volume as it is calculated based on the modeled coil volume that includes the wire and the non-conducting material filling the space between the winding.