FEMM Manual - Finite Element Method Magnetics

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Chapter 1 Introduction FEMM is a suite of programs for solving low frequency electromagnetic problems on two-dimensional planar and axisymmetric domains. The program currently addresses linear/nonlinear magnetostatic problems, linear/nonlinear time harmonic magnetic problems, linear electrostatic problems, and steady-state heat flow problems. FEMM is divided into three parts: • Interactive shell (femm.exe). This program is a Multiple Document Interface pre-processor and a post-processor for the various types of problems solved by FEMM. It contains a CADlike interface for laying out the geometry of the problem to be solved and for defining material properties and boundary conditions. Autocad DXF files can be imported to facilitate the analysis of existing geometries. Field solutions can be displayed in the form of contour and density plots. The program also allows the user to inspect the field at arbitrary points, as well as evaluate a number of different integrals and plot various quantities of interest along user-defined contours. • triangle.exe. 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 Shewchuk and is available from his Carnegie-Mellon University web page at http://www.cs.cmu.edu/˜quake/triangl or from Netlib. • Solvers (fkern.exe for magnetics; belasolv for electrostatics); hsolv for heat flow problems; and csolv for current flow problems.. Each solver takes a set of data files that describe problem and solves the relevant partial differential equations to obtain values for the desired field throughout the solution domain. The Lua scripting language is integrated into the interactive shell. Unlike previous versions of FEMM (i.e. v3.4 and lower), only one instance of Lua is running at any one time. This single instance of Lua can both build and analyze a geometry and evaluate the post-processing results, simplifying the creation of various sorts of “batch” runs. In addition, all edit boxes in the user interface are parsed by Lua, allowing equations or mathematical expressions to be entered into any edit box in lieu of a numerical value. In any edit box in FEMM, a selected piece of text can be evaluated by Lua via a selection on the right mouse button menu. 6
The purpose of this document is to give a brief explanation of the kind of problems solved by FEMM and to provide a fairly detailed documentation of the programs’ use. 1.1 Overview The goal of this section is to give the user a brief description of the problems that FEMM solves. This information is not really crucial if you are not particularly interested in the approach that FEMM takes to formulating the problems. You can skip most of Overview, but take a look at Section 1.3. This section contains some important pointers about assigning enough boundary conditions to get a solvable problem. Some familiarity with electromagnetism and Maxwell’s equations is assumed, since a review of this material is beyond the scope of this manual. However, the author has found several references that have proved useful in understanding the derivation and solution of Maxwell’s equations in various situations. A very good introductory-level text for magnetic and electrostatic problems is Plonus’s Applied 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 contained in Hoole’s Computer-aided analysis and design of electromagnetic devices [2]. For an advanced treatment, the reader has no recourse but to refer to Jackson’s Classical electrodynamics [3]. For thermal problems, the author has found White’s Heat and mass tranfer [4] and Haberman’s Elementary applied partial differential equations [5] to be useful in understanding the derivation and solution of steady-state temperature problems. 1.2 Relevant Partial Differential Equations FEMM addresses some limiting cases of Maxwell’s equations. The magnetics problems addressed are those that can be consided as “low frequency problems,” in which displacment currents can be ignored. Displacement currents are typically relevant to magnetics problems only at radio frequencies. In a similar vein, the electrostatics solver considers the converse case in which only the electric field is considered and the magnetic field is neglected. FEMM also solves 2D/axysymmetric steady-state heat conduction problems. This heat conduction problem is mathematically very similar to the solution of electrostatic problems. 1.2.1 Magnetostatic Problems Magnetostatic problems are problems in which the fields are time-invariant. In this case, the field intensity (H) and flux density (B) must obey: ∇ × H = J (1.1) ∇ · B = 0 (1.2) subject to a constitutive relationship between B and H for each material: B = µH (1.3) 7
Page 1 and 2: Finite Element Method Magnetics Ver
Page 3 and 4: 2.3.10 Line Integrals . . . . . . .
Page 5: 3.7.8 View Commands . . . . . . . .
Page 9 and 10: and the constitutive relationship,
Page 11 and 12: − ∇ ·(k∇T) = q (1.24) FEMM s
Page 13 and 14: 1.3.2 Heat Flow BCs There are six t
Page 15 and 16: Chapter 2 Interactive Shell The FEM
Page 17 and 18: 2.2.2 Keyboard and Mouse Commands A
Page 19 and 20: Point Mode Action Function Left But
Page 21 and 22: 2.2.6 Problem Definition The defini
Page 23 and 24: yet been defined. Pushing the Add P
Page 25 and 26: Figure 2.8: Boundary Property dialo
Page 27 and 28: Figure 2.9: Block Property dialog.
Page 29 and 30: “B” (flux density) column as in
Page 31 and 32: constrained to run along a particul
Page 33 and 34: conductor of interest and achieve s
Page 35 and 36: as compared to a magnetostatic prob
Page 37 and 38: appears as a green line on the post
Page 39 and 40: Figure 2.21: X-Y Plot dialog. data
Page 41 and 42: • Force from stress tensor. This
Page 43 and 44: • Block cross-section area • To
Page 45 and 46: While an integration of (2.16) theo
Page 47 and 48: 2.4.1 Problem Definition Figure 2.2
Page 49 and 50: Figure 2.26: Property Definition di
Page 51 and 52: an unbounded solution region. For m
Page 53 and 54: For fixed voltages, one could alter
Page 55 and 56: 2.5.3 Vector Plots A good way of ge
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some types of integrals; however, s
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dF = 1 (D(E · n)+E (D · n) −(D
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The second edit box is the Solver P
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Figure 2.41: Boundary Property dial
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Figure 2.43: Materials Library dial
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2.7 Heat Flow Postprocessor The the
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Figure 2.49: When in doubt plots an
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2.8.1 Problem Definition Figure 2.5
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Figure 2.52: Property Definition di
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Materials Properties The Block Prop
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never have to call the mesher from
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• J.t Tangential current density
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2.10 Exporting of Graphics Figure 2
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• open("filename") Opens a docume
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- meshsize: size constraint on the
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- editaction 0 -nodes, 1 - lines (s
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- NStrands Number of strands in the
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The next parameter is the number of
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Type Definition 0 A · J 1 A 2 Magn
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• mo_getcircuitproperties("circui
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• mo_hidecontourplot() Hides the
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3.5.3 Object Labeling Commands •
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• mi createradius(x,y,r)turnsacor
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For an “Anti-Perodic” boundary
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• ei attachouterspace() marks all
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• eo getconductorproperties("cond
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If eo numcontours is -1 all paramet
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• hi setblockprop("blockname", au
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• hi movetranslate(dx,dy,(editact
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• hi deleteboundprop("boundpropna
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• hi detachouterspace() undefines
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• ho groupselectblock(n) Selects
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• ho maximize() maximizes the act
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automesh: 0 = mesher defers to the
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• ci seteditmode(editmode) Sets t
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e applied to the specified property
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3.10.1 Data Extraction Commands •
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graph, the command would be: co mak
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• co showdensityplot(legend,gscal
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Chapter 4 Mathematica Interface FEM
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Chapter 5 ActiveX Interface FEMM al
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preconditioner must also be stored.
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Bibliography [1] M. Plonus, Applied
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Appendix A Appendix A.1 Modeling Pe
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Figure A.3: Shifting the B-H curve
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Figure A.5: Equivalent circuit for
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non-laminated materials as well, si
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Figure A.7: Air-cored coil with “
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The next step is to transform (A.19
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Figure A.9: Solved problem. ear tim
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