Simulating Conductors for Inductance/Resistance Measurements in Maxwell ANSYS

1. Maxwell ANSYS Tutorial for Simulating Conductors for Inductance/Resistance MeasurementsIncludes Analysis of Mesh Setup for ANSYS Adaptive Solutions Quillen Blalock Master’s Candidate for Dr. CostinettApril 2019

2. Tutorial Guide • Simulate electrical conductors (like inductors) to evaluate electrical properties across frequencies such as: • Inductance • Resistance (DC and AC) • Magnetic Field • Current Distribution Please see the additional resources from Maxwell for more information • “(Rc)” – means “Right Click” • “(Lc)” – means “Left Click”

3. Maxwell ANSYS • Open Maxwell ANSYS and create a new project. • (Rc) on the newly created project and (Lc) on “Insert” • (Lc) on “Insert Maxwell 3D Design” • (Rc) on “Maxwell3DDesign#” and (Lc) “Solution Type” • Choose “Eddy Current” under the Magnetostatic Options

4. How to Setup ANSYS Maxwell • Modeler (Lc) – Import (Lc) • Choose design to upload • Choose .stpfile • May upload additional unnecessary “Lines” – can delete • (Rc) on object (shown highlighted in blue below) • (Lc) properties • Choose “Copper” for material • (Lc) Draw – Box • Create a box surrounding object. Will become the vacuum • Needs to sufficiently cover object. After drawing, may need to double click on “create box” (shown highlighted in grey below) and adjust “Position” value to have vacuum surround box • Material automatically “vacuum”

5. How to Setup ANSYS Maxwell Another way to do step 4: Click on the “red box” as shown above. “Pad all directions similarly” and choose a value like “300”

6. How to Setup ANSYS Maxwell • (Lc) object (shown below highlighted in blue in picture top right) • Under “Modeler,” select (Lc) “Surface,” then select “Section…” • Choose a plane like “XY” • Screen will look like bottom right picture • (Lc) On created section of object (shown highlighted in blue bottom right)

7. How to Setup ANSYS Maxwell • Go to “Modeler” – Boolean – “Separate Bodies” • Choose one section to have your excitation • Can delete the rest of the sections if you’d like • (Lc) chosen section (shown highlighted in blue bottom right) • Assign Excitation • Current • Input desired current value Note: depending on your geometry, it may not be not continuous (I.E. the solid is not enclosed. For example, a conductive rod with a top and bottom that do not connect). You can manually click on an outer face to assign an entry excitation and another face for the exit excitation. The entry should have a positive current and the exit a negative current. BUT the vacuum boundary must be “plush” with both excitation faces!

8. How to Setup ANSYS Maxwell • Once an excitation is specified, in the project manager window, (Rc) on the Parameters option, (Lc) on Assign, and choose matrix • Check the box to include the current excitation • The last step is creating a “Solution” under Analysis. Once created, you will (Rc) on the solution name and (Lc) ”Analyze” But this solution setup is complicated to create, and the next slides address what is happening.

9. Next Steps • Now, before we can continue, let’s examine how the adaption solver of Maxwell ANSYS works. • Essentially, ANSYS will recreate your model into a number of tetrahedra. Each tetrahedra is solved in terms of the Maxwell equations, and the solutions are summed together to evaluation the whole of the model. • The system of the tetrahedra is referred to as the “Mesh” of the model. A finer mesh contains high accuracy, but also takes more time to solve.

10. How Maxwell ANSYS Mesh Works Minimum Number of Passes – The minimum number of adaptive passes even if the conver­gence criteria are reaches • Maxwell uses “Adaptive Meshing” to achieve a solution based on user specifications • Adaptive meshing provides automated mesh refinement capability based on reported energy error in simulation • Maxwell re-computes the error, and the iterative process (solve — error analysis — adaptive refinement) repeats until the convergence criteria are satisfied or the maximum number of adaptive passes is completed. Refinement Per Pass – The percent you set for Refinement Per Pass determines how many tetrahedra are added at each iteration of the adaptive refinement process. The tetrahedra with the highest error are refined. Minimum Converged Passes – The minimum number of adaptive passes to continue after the convergence criteria are reached. Maximum number of mesh refinement cycles you would like Maxwell to perform. Percent Error Smaller values produce more accurate (but slower) solutions; larger values produce less accu­rate (but faster) solutions. At each step in the adaptive process, the energy and error energy are computed. The relative change between the previous matrix and the current matrix is then computed and reported as the matrix delta; the target matrix delta is the Percent Error. An adaptive solution is performed only at the specified solution frequency.

11. Mesh Refinement – Skin Depth • Computing Skin Depth • “Alternatively, do the following to calculate the skin depth based on the object's material per­meability and conductivity and the frequency at which the mesh is to be refined

12. Mesh Refinement – Skin Depth • When the mesh is generated, the refinement criteria you specified will be used. This operation will be approximately the same as having slabs of tetrahedra, but it is not guaranteed to prevent tetrahe­dra from crossing slab interfaces. Caution should be used with this mesh operation, as very thin lay­ers may cause a reduction in mesh quality or unnecessarily cause the generation of a very large mesh. Further regions refined under this operation and their close neighbors do not participate in solution adaptive refinement. This is another reason to use this seeding operation with caution. Number of Layers– Maxwell adds an equivalent number of mesh points to each layer. For example, if Maxwell adds 10 points to satisfy the Surface Triangle Length, it will add 10 points to each layer. Calculate Skin Depth– function to define skin depth at said frequency Surface Triangle LengthMaxwell maximum edge length of the surface mesh Number of Elements– To restrict the number of elements added during refinement on the faces

13. How Maxwell ANSYS Mesh Works

14. Convergence Statistics 100um thick Square Toroid (22.2mm side length): • Took 6 passes to complete starting with Initial Mesh • Only went through one pass after convergence reached in pass 6 • Used same solution setups as previous slide 1% error, 2 min passes, 1 min converge, 60 Hz Adaptive f, 6 passes complete, ended 0.92% error

15. What is Energy Error? • Maxwell generates a field solution using the specified mesh. • It then analyzes the accuracy of the solution by calculating an energy value based on the error in the solution. The exact mechanism for evaluating the error varies by solution type. For example, in magnetostatic it can use Curl H to find the current density and then subtract all input currents and other sources. For a perfect solution the result would be zero, for a real, finite mesh the result is some amount of residual current density. An energy value calculated from this residual current density is called the error energy. The “Energy Error %” is the error energy as a percentage of the total energy (calculated with the original sources). • If more than 1 pass has been completed, the software also calculates the change in total energy from the previous pass. The percentage difference is the “Delta Energy (%)”. Adaptive refine­ment continues until both the “Energy Error %” and the “Delta Energy (%)” are below the tar­get Percent Error specified by the user (or until it reaches the Maximum Number of Passes requested). • When the error targets are not satisfied the mesh is refined. This is generally done by subdivid­ing the elements with the highest error energy into smaller elements. • The user can optionally request to “Use Output Variable Convergence”. This is an additional stopping criterion. The Energy Error % and the Delta Energy must still be below the target Per­cent Error, but the software will also compute the specified Output Variable for each adaptive pass and will calculate the percentage change in that value for each pass after the first (this is the “Output Var. Delta (%)”). The solution will continue until the energy error criteria are met and the Output Var. Delta is below the target “Max. Delta Per Pass” specified by the user for output variable convergence (or until Maximum Number of Passes). • A small delta indicates that further mesh refinement will probably not change the solution.

16. Comparison of Solution Setup Results: 50μm Square Toroid – 22.1 mm side length Sim Time: 68 hours – 46 min Fine Mesh: 0.25mm Length, 0.65um Skin Depth Sim time: 15 hours Initial Mesh

17. Continue to analyze 50μm Square Toroid – 22.1 mm side length • Fine Mesh: 0.25mm Length, 0.65um Skin Depth • Computing Skin Depth to be ~ 66μm, specify that skin depth • 66μm (2 layers of elements) • 0.25 mm surface triangle length • Restrict number of elements to 1000 • On-Selection/Inside-Selection length = 0.25mm • Initial Mesh R Results for This. Sim Time: 68:46 hr Note that the Initial Mesh used 6.1% of the tetrahedra that was used in the “Finer Mesh” R Results for This. Sim Time: 1:08 hr

18. 50μm Square Toroid – 22.1 mm Side Length Continued

19. 50μm Square Toroid – 22.1 mm Side Length ContinuedCOMMENT ON RESULTS • If I am interested in a certain frequency (let’s say 1 MHz), I need to change the adaptive solution frequency to that specification. • Observe orange highlights • Though the Error Spec % was smaller (2% rather than 1% of the 60 Hz adaptive frequency solution), the AC characteristics reported a higher RAC for a solution that took the same amount of time (~1 hour) • More accurate solution (lower percent error) yields higher RAC. Leads me to believe that’s more accurate. • Specify higher Percent Error for quick simulations, but less for more accuracy • Restricting max elements helps solution speed, but for this geometry, it affects accuracy and # tetrahedral needed is much higher than 1000 (default) • Yellow Highlights – Increasing the refinement percentage per pass (# of tetrahedral increase) will lead to more accurate solution but take more time

20. We know DCR is Correct, But What about AC Resistance Accuracy of Maxwell ANSYS? Max Passes 6 Percent Error: 0.25% 30% Refinement per pass Min 2 passes Min 1 converged pass 1 MHz Adaptive Frequency Start Tetrahedra 4172 Final Tetradedra 15839 Energy Error Reported: 0.13% Time to sim: minutes • Resume looking at rectangular conductor • Width = 3.99 mm • Length = 5.625 mm • Thickness = 0.25 mm • Can observe DCR accurate based on theory and MATLAB estimates. What about ACR up to 1 MHz?

21. ACR Predictor by Alan Payne • AC resistance of rectangular conductors • Current Crowding • For a rectangular conductor the current concentrates at the edges and the corners at high frequencies. • Includes variation across frequency • Skin Effect • At high frequencies the current in a conductor tends to concentrate in a thin layer around its surface “Payne : Skin Effect, Proximity Effect and the Resistance of Circular and Rectangular Conductors”

22. Comparison of Maxwell ANSYS and Payne’s ACR • Payne’s ACR reports uncertainty of +/- 10% • Overall, (with exception of 100 kHz), this helps add credence to Maxwell ANSYS reporting accurate numbers as long as mesh and adaptive solution are setup correctly. • Of course, this is only for simplistic rectangular model conductors

23. So What Solution Setup Shall I Go With? • Adaptive Setup • Max Number of Passes: 10-12 • Percent Error: 0.25%-1% • Convergence • Refinement Per Pass: 30-35% • Minimum Number of Passes: 5 • Minimum Converged Passes: 2 • Solver • Adaptive Frequency: 1MHz (Or frequency you want) • Skin Depth Based Refinement (Mesh) • Calculate Skin Depth • 2-3 layers • 0.25mm-1mm surface triangle length • Element Length Based Refinement • Inside Selection • NA • On Selection • NA • This solution setup would often yield to solutions that require 5-20 hours of time to run • Solution time depends on • Number of Frequencies Analyzed • Accuracy of energy error specified • Number of passes required • Mesh Refinement done before adaptive solution • If using refinement, maybe use less passes? • Use this setup to get calculations • While this setup can work, you may need to modify this based on your needs

24. Additional Resource Video • https://www.youtube.com/watch?v=sAWL4W43Jks