Finite Element Method Magnetics

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Figure A.2: Magnet as an equivalent current sheet.point of view, the demagnetization curve is what occurs when different amounts of magnetomotiveforce are applied to a long magnet, acting in the direction opposing the field of the magnet. Whenenough MMF is applied so that the field is exactly cancelled out, the applied MMF must be exactlythe same as the MMF that is driving the magnet. The B-H profile that is traversed on the way tothe B = 0 point is just the B-H curve of the material inside the magnet.Using these insights, the permanent magnet can be modeled. The coercivity (denoted H c )ofthe magnet is the absolute value of the MMF that it takes to bring the the field in the magnet tozero. This value (in units of Amps/Meter) is entered in the H_c box in the Block Property dialog(see Figure 2.9). If the magnet material is nonlinear, the appropriate values to enter in the B-H datadialog can be obtained by shifting the curve to the right by exactly H c , so that the B = 0 point linesup with the origin. For example, the shifted demagnetization curve corresponding to Alnico 5 ispictured in Figure A.3. If the demagnetization curve is straight enough to be considered linear, onecan obtain the appropriate permeability by taking the slope of the demagnetization curve.Strong rare-earth materials at room temperature have a very linear demagnetization curve. Usually,a linear model is sufficient for these materials. In addition, these materials have a relative permeabilityvery close to 1. The modeling of these materials can be simplified (while only incurringsmall errors) by assuming that the permeability is exactly 1. Then, if you know the energy productof the magnet material in units of MGOe (the unit in which the energy product is almost alwaysgiven), the appropriate H c can be determined via (A.1).H c = 5(105 ) √ E(A.1)πwhere E is the energy product in MGOe and the resulting H c is in units of A/m (e.g. 40 MGOe≈ 10 6 A/m).With alnico magnets, great care must be taken in interpreting the finite element results. Unlikerare-earth magnets, these magnets exhibit a great degree of hysteresis when they are demagnetized.That is, when the flux density is pushed below the “knee” in the demagnetization curve, theflux level does not recover to the previous magnitude when the opposing MMF is removed. Thishysteresis is illustrated in Figure A.4. This sort of demagntization and recoil can occur when the102
Figure A.3: Shifting the B-H curve of a permanent magnetFigure A.4: Recoil in partially demagnetized Alnico 5.103
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Chapter 1IntroductionFEMM is a suit
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where J src represents the applied
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1.4 Finite Element AnalysisFigure 1
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2.2.2 Keyboard and Mouse CommandsAl
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ActionLeft Button ClickRight Button
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2.2.6 Problem DefinitionThe definit
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een defined. Pushing the Add Proper
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Figure 2.8: Boundary Property dialo
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Figure 2.9: Block Property dialog.r
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Figure 2.11: Sample B-H curve plot.
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Associated with the lamination thic
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Figure 2.14: Circuit Property dialo
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2.3 Magnetics PostprocessorThe the
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Figure 2.19: Graph Mode toolbar but
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In all of these plots, the directio
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• A This integral, the evaluation
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To compute the force on a region or
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Figure 2.23: Properly defined conto
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• ToolBar Use this toggle to hide
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Point Mode KeysKey FunctionSpace Ed
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point, is the “snap to grid” bu
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Lastly, there is an optional Commen
Page 52 and 53: Figure 2.32: Boundary Property dial
Page 54 and 55: Figure 2.34: Materials Library dial
Page 56 and 57: 2.5.1 Postprocessor modesSimilar to
Page 58 and 59: 2.5.6 Density PlotDensity plots are
Page 60 and 61: In certain cases, the quantity to b
Page 62 and 63: Weighted Stress Tensor Volume Integ
Page 64 and 65: Probably the easiest way to get gra
Page 66 and 67: • pause() Waits for the ok button
Page 68 and 69: • mi setarcsegmentprop(maxsegdeg,
Page 70 and 71: 3.3.7 Zoom Commands• mi zoomnatur
Page 72 and 73: - For a “Strategic dual image”
Page 74: 3.3.10 Miscellaneous• mi savebitm
Page 78 and 79: 3.4.2 Selection Commands• mo sete
Page 80 and 81: - upper_A Upper limit for A contour
Page 82 and 83: • ei setblockprop("blockname", au
Page 84 and 85: • ei movetranslate(dx,dy,(editact
Page 86 and 87: • ei deleteconductor("conductorna
Page 88 and 89: 3.6.1 Data Extraction Commands• e
Page 90 and 91: • eo addcontour(x,y) Adds a conto
Page 92 and 93: 3.6.5 Miscellaneous• eo close() c
Page 94 and 95: nection and manually transferring i
Page 96 and 97: Chapter 6Numerical MethodsFor those
Page 98 and 99: its Gauss Point). One desires a con
Page 100 and 101: [15] Q. Chen and A. Konrad, “A re
Page 104 and 105: magnets are being handled prior to
Page 106 and 107: Figure A.6: Equivalent circuit for
Page 108 and 109: One could think of this solution as
Page 110 and 111: A quick note on computational effic
Page 112 and 113: Figure A.8: Example input geometry.
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Finite Element Method Magnetics

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