6.6. 3D Stranded Coil Analysis

This section describes how to do a stranded coil analysis using the current technology 3D edge-based elements.

 

6.6.1. Elements Used in a 3D Edge-Based Stranded Coil Analysis

To do a stranded coil analysis, you need to use one of these elements:

  • SOLID236 20-node hexahedral solid, KEYOPT(1) = 2

  • SOLID237 10-node tetrahedral solid, KEYOPT(1) = 2

 

6.6.2. Performing a Stranded Coil Analysis

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

  1. Select SOLID236 or SOLID237 element type and set KEYOPT(1) = 2.

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

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

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

    • SC (R1) – 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 (R2) – Number of coil turns. This constant represents the total number of winding turns in a coil regardless of any symmetry modeling considerations. Default is 1 turn.

    • VC (R3) – Coil volume. This constant represents the true physical volume of the coil regardless of symmetry modeling considerations. It includes the volume occupied by the wire and the non-conducting material filling the space between the winding.

    • TX (R4) – Coil winding X-directional cosine. This constant represents the X-component of the coil direction vector T = {TX, TY, TZ}T, where T is a unit vector tangent to the coil winding that designates the current flow direction. Default TX is 0.

    • TY (R5) – Coil winding Y-directional cosine. This constant represents the Y-component of the unit coil direction vector T. Default TY is 1.

    • TZ (R6) – Coil winding Z-directional cosine. This constant represents the Z-component of the unit coil direction vector T. Default TZ is 0.

    • R (R7) – Coil resistance. This constant represents the total DC resistance of the coil 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 (R8) – Coil symmetry factor. This constant represents the ratio of the full symmetry coil volume (VC) to the modeled coil volume. The input should be greater or equal to 1.

    As an example, the figure below illustrates the application of these coil constants for a 90° arc of a stranded conductor. The figure depicts symmetry about a plane, for which only the top half needs to be modeled. To specify the current flow, you need to follow these steps:

    1. Specify a cylindrical element coordinate system using ESYS.

    2. Modify the elements to inherit the new ESYS attribute, using EMODIF.

    3. Set the current flow direction constants as {TX, TY, TZ}T = {0,1,0}T.

    Figure 6.3: Coil Constants for 1/8 Symmetry Sector of Circular Stranded Coil

    Coil Constants for 1/8 Symmetry Sector of Circular Stranded Coil

  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 (matrix) or weak (load vector) electromagnetic coupling. The strong coupling option (KEYOPT(2) = 0) produces an unsymmetric matrix. In a linear analysis, a strong 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' or time-integrated electric degrees of freedom (VOLT and EMF). The strong coupling option with 'true' voltage drop and back-EMF (KEYOPT(2) = 0) produces a nonsymmetric matrix. The strong coupling option with time-integrated voltage drop and time-integrated back-EMF (KEYOPT(2) = 2) produces a symmetric matrix provided the symmetry factor (SYM) is 1.

  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 KEYOPT(1) = 3, 4,or 9 through 12 of CIRCU124. Applicable when KEYOPT(2) is set to 0 or 1.

 

6.6.3. Reviewing Results from a 3D Stranded Coil Analysis

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

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

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

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

  • Element conduction current density JT or JS (X, Y, Z, SUM) at the element centroid [1]

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

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

  1. JT and JS 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 (VC) that includes the wire and the non-conducting material filling the space between the winding.