Figure 1 – NSTX Upper Umbrella Assembly Upgrade Design: Version 4

Figure 2 – Single Segment 3-Strap Assembly Solid Model: Version 4

Figure 3 – ANSYS Multiphysics Analysis Block Diagram

Figure 4 – Single Segment 3-Strap Assembly FEA Model: Mesh

Figure 5 – Single Segment 3-Strap Assembly Electric Model Results: Voltage

Fig. 6 – Single Segment 3-Strap Assembly Electric Model Results: Current Density

Figure 7 – Single Segment 3-Strap Assembly Electric Model Results: Joule Heat

Fig. 8 – Single Segment 3-Strap Assembly Thermal Model Results: Temperature

Study: Determine Current Best-Practice to Perform Magnetostatic Analysis in ANSYS 12.0 WorkBench

• New SOLID236/237 magnetic analysis elements – Have both Magnetic Vector Potential (MVP) and Line Edge method capability.

Replaces SOLID97 and SOLID117.– Compatible with WB generated Electric, Thermal, and Static Structural analyses

meshes.

• No 3D MVP or Line Edge contact elements– Requires conformal mesh with shared nodes across the joints, which makes

modeling assemblies including frictional and pressure-dependent electric and thermal contact impossible, or

– Non-conformal/ dissimilar mesh, with duplicate nodes across the joint. Magnetic coupling using CPINTF command requires nearly-matched meshing, which is difficult to achieve in a large assembly.

• Above problems are greatly reduced if modeling the air enclosure, and modeling the magnetic coupling across the joints, are not necessary

– May be valid for materials with a relative magnetic permeablity = 1.– Goal: Prove with a comparison study.

Outer-most Lamination Arch Segment with Air Enclosure: Solid Model

Merged Volumes

B = 1 T

I = 4074 A

Air

Outer-most Lamination Arch Segment with Air Enclosure: Mesh

Conformal Mesh:

Nodes shared at Interface(perfect magnetic coupling)

Arch Segment w/ Air Magnetostatic Model Results: Current Density (A/m^2)

Arch Segment w/ Air Magnetostatic Model Results: Joule Heat

SOLID236:LINE EDGE METHOD

Arch Segment w/ Air Magnetostatic Model Results: Magnetic Flux (Metal +Air)

Arch Segment w/ Air Magnetostatic Model Results: Magnetic Flux (Metal Only)

Arch Segment w/ Air Magnetostatic Model Results: Current Density

Arch Segment w/ Air Magnetostatic Model Results: Lorentz Forces (N)

Arch Segment w/ Air Magnetostatic Model Results: Magnetic Flux (Metal Only)

Arch Segment w/ Air Magnetostatic Model Results: Lorentz Forces (N)

Arch Segment w/ Air Static Structural Model Results: von Mises Stress (Pa)

SOLID186

Stress and reaction force results closely agree with hand-calculated values.

SOLID236LINE EDGE METHOD

Arch Segment _No Air - Magnetostatic Model Results: Magnetic Flux (Tesla)

Arch Segment _No Air - Magnetostatic Model Results: Current Density (A/m^2)

Arch Segment _No Air - Magnetostatic Model Results: Lorentz forces (N)

Arch Segment _No Air - Magnetostatic Model Results: Magnetic Flux (Tesla)

Arch Segment _No Air - Magnetostatic Model Results: Lorentz Forces (N)

SOLID186

Stress and reaction force results closely agree with hand-calculated values.

Arch Segment _ No Air - Static Structural Model Results: von Mises Stress (Pa)

Arch _ No Air - Static Structural WB Model Results: von Mises Stress (psi)

Total Reaction Force:

ANSYS = 262.5 lbfMathCAD = 262.6 lbf

Hoop Stress:

ANSYS = 729.9 psiMathCAD = 729.3 psi

Arch _ No Air_Neg Az - Magnetostatic Model Results: Magnetic Flux (Tesla)

Arch _ No Air_Neg Az - Magnetostatic Model Results: Lorentz Forces (N)

Arch _ NoAir_NegAz - Static Structural WB Model Results: von Mises Stress (psi)

Arch _NoAir_.3Ty+(-1)Tz - Magnetostatic Model Results: Magnetic Flux (Tesla)IsoView

Arch _NoAir_.3Ty+(-1)Tz - Magnetostatic Model Results: Magnetic Flux (Tesla)Side View

Arch _NoAir_.3Ty+(-1)Tz - Magnetostatic Model Results: Lorentz Forces (N)

Arch _NoAir_.3Ty+(-1)Tz – Static Structural Model Results: von Mises Stress (psi)Iso View

Arch _NoAir_.3Ty+(-1)Tz – Static Structural Model Results: von Mises Stress (psi)Side View

Conclusions

• SOLID236 results using line edge method closely agree with hand-calculated classic solution values. – SOLID117 results are not valid

• No difference between results with air enclosure modeled and without. – Modeling without air enclosure is valid only for cases where all materials

have a relative magnetic permeability = 1, and where magnetic coupling across the joint is not required (static analysis, no eddy current calculation).

• Unlike MVP method, negative values of Az are allowed– Combined Fields: Az input as a vector with magnitude and direction

• Use WPRO to rotate WP so that Z-direction is aligned with Az direction, then use CSWP to define coordinate system aligned with WP

• Apply Az = resultant, magnitude of vector • Must change to metric units in WB prior to SOLVE so that the

Lorentz forces in newtons from Magnetostatic analysis scale correctly. – Can switch back to english units after solution.

Single Lamination Bolted Assembly - Magnetostatic Model: Mesh

Single Lamination_.3Ty+(-1)Tz - Magnetostatic Results: Magnetic Flux (Tesla)

Single Lamination_.3Ty+(-1)Tz - Magnetostatic Results: Current Density (A/m^2)

Single Lamination_.3Ty+(-1)Tz - Magnetostatic Results: Lorentz Forces (N)

Single Lamination_.3Ty+(-1)Tz - Magnetostatic Results: Magnetic Flux (Tesla)

Single Lamination_.3Ty+(-1)Tz - Magnetostatic Results: Current Density (A/m^2)

Single Lamination_.3Ty+(-1)Tz - Magnetostatic Results: Lorentz Forces (N)