Finite Element Method Magnetics

1 Finite Element Method MagneticsVersion s ManualOctober 25, 2015 David .. Partial Differential Equations .. Problems .. Magnetic Problems .. Problems .. Flow Problems .. Flow Problems .. Conditions .. and Electrostatic BCs .. Flow BCs .. Element Analysis .. 132 Interactive Import/Export .. Preprocessor .. Drawing Modes .. and Mouse Commands .. Manipulation .. Manipulation .. Definition .. of Properties .. Region .. Tasks .. Postprocessor .. modes .. and Grid Manipulation .. Commands .. Actions .. Useful View Commands .. Plot .. Plot .. Plots .. Plots.

2 Line Integrals .. Block Integrals .. Force/Torque Calculation .. Circuit Results .. Preprocessor .. Definition .. of Properties .. Tasks .. Postprocessor .. Plot .. Plot .. Plots .. Plots .. Integrals .. Integrals .. Calculation .. Results .. Flow Preprocessor .. Definition .. of Properties .. Tasks .. Flow Postprocessor .. Plot .. Plot .. Plots .. Plots .. Integrals .. Integrals .. Results .. Flow Preprocessor .. Definition .. of Properties .. Tasks .. Flow Postprocessor .. Plot .. Plot .. Plots .. Plots.

3 Integrals .. Integrals .. Results .. Exporting of Graphics .. 8133 Lua Lua scripting ? .. Lua Command Set .. Preprocessor Lua Command Set .. Add/Remove Commands .. Selection Commands .. Labeling Commands .. Commands .. Commands .. Commands .. Commands .. Commands .. Properties .. Miscellaneous .. Post Processor Command Set .. Extraction Commands .. Commands .. Commands .. Commands .. Preprocessor Lua Command Set .. Add/Remove Commands .. Selection Commands .. Labeling Commands .. Commands .. Commands .. Commands .. Commands .. Commands .. Properties.

4 Miscellaneous .. Post Processor Command Set .. Extraction Commands .. Commands .. Commands .. Commands .. Flow Preprocessor Lua Command Set .. Add/Remove Commands .. Selection Commands .. Labeling Commands .. Commands .. Commands .. Commands .. Commands .. Commands .. Properties .. Miscellaneous .. Flow Post Processor Command Set .. Extraction Commands .. Commands .. Commands .. Commands .. Flow Preprocessor Lua Command Set .. Add/Remove Commands .. Selection Commands .. Labeling Commands .. Commands .. Commands .. Commands .. Commands .. Commands .. Properties .. Miscellaneous.

5 Current Flow Post Processor Command Set .. Data Extraction Commands .. Selection Commands .. Zoom Commands .. View Commands .. Miscellaneous ..1394 Mathematica Interface1415 ActiveX Interface1436 Numerical Element Formulation .. Solvers .. Smoothing .. 145A Modeling Permanent Magnets .. Bulk Lamination Modeling .. Open Boundary Problems .. Truncation of Outer Boundaries .. Asymptotic Boundary Conditions .. Kelvin Transformation .. Nonlinear Time Harmonic Formulation .. 1605 Chapter 1 IntroductionFEMM is a suite of programs for solving low frequency electromagnetic problems on two-dimensionalplanar and axisymmetric domains.

6 The program currently addresses linear/nonlinear magneto-static problems, linear/nonlinear time harmonic magneticproblems, linear electrostatic problems,and steady-state heat flow is divided into three parts: Interactive shell ( ). This program is a Multiple Document Interface pre-processorand a post-processor for the various types of problems solved by FEMM. It contains a CAD-like interface for laying out the geometry of the problem to be solved and for defining ma-terial properties and boundary conditions. Autocad DXF files can be imported to facilitatethe analysis of existing geometries. Field solutions can bedisplayed in the form of contourand density plots. The program also allows the user to inspect the field at arbitrary points, aswell as evaluate a number of different integrals and plot various quantities of interest alonguser-defined contours.

7 Triangle breaks down the solution region into a large number of triangles,a vital part of the Finite Element process. This program was written by Jonathan Shewchukand is available at Solvers ( Magnetics ;belasolvfor electrostatics);hsolvfor heat flow prob-lems; andcsolvfor current flow Each solver takes a set of data files that describeproblem and solves the relevant partial differential equations to obtain values for the desiredfield throughout the solution Lua scripting language is integrated into the interactive shell. Unlike previous versions ofFEMM ( and lower), only one instance of Lua is running at any onetime. This singleinstance of Lua can both build and analyze a geometry and evaluate the post-processing results,simplifying the creation of various sorts of batch addition, all edit boxes in the user interface are parsed by Lua, allowing equations or mathe-matical expressions to be entered into any edit box in lieu ofa numerical value.

8 In any edit box inFEMM, a selected piece of text can be evaluated by Lua via a selection on the right mouse purpose of this document is to give a brief explanation ofthe kind of problems solved byFEMM and to provide a fairly detailed documentation of the programs OverviewThe goal of this section is to give the user a brief description of the problems that FEMM information is not really crucial if you are not particularly interested in the approach thatFEMM takes to formulating the problems. You can skip most ofOverview, but take a look atSection This section contains some important pointersabout assigning enough boundaryconditions to get a solvable familiarity with electromagnetism and Maxwell s equations is assumed, since a review ofthis material is beyond the scope of this manual.

9 However, the author has found several referencesthat have proved useful in understanding the derivation andsolution of Maxwell s equations invarious situations. A very good introductory-level text for magnetic and electrostatic problems isPlonus sApplied electromagnetics[1]. A good intermediate-level review of Maxwell s equations,as well as a useful analogy of magnetism to similar problems in other disciplines is containedin Hoole sComputer-aided analysis and design of electromagnetic devices[2]. For an advancedtreatment, the reader has no recourse but to refer to Jackson sClassical electrodynamics[3]. Forthermal problems, the author has found White sHeat and mass tranfer[4] and Haberman sEle-mentary applied partial differential equations[5] to be useful in understanding the derivation andsolution of steady-state temperature Relevant Partial Differential EquationsFEMM addresses some limiting cases of Maxwell s Magnetics problems addressedare those that can be consided as low frequency problems, in which displacment currents can beignored.

10 Displacement currents are typically relevant to Magnetics problems only at radio frequen-cies. In a similar vein, the electrostatics solver considers the converse case in which only the elec-tric field is considered and the magnetic field is neglected. FEMM also solves 2D/axysymmetricsteady-state heat conduction problems. This heat conduction problem is mathematically very sim-ilar to the solution of electrostatic Magnetostatic ProblemsMagnetostatic problems are problems in which the fields are time-invariant. In this case, thefieldintensity(H) andflux density(B) must obey: H=J( ) B=0( )subject to a constitutive relationship betweenBandHfor each material:B= H( )If a material is nonlinear ( iron or alnico magnets), the permeability, is actually afunction ofB: =BH(B)( )7 FEMM goes about finding a field that satisfies ( )-( ) via amagnetic vector potentialap-proach.