FEMM Manual - Finite Element Method Magnetics

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Figure 2.7: Nodal Property dialog. The next selection is the BC Type drop list. This specifies the boundary condition type. Currently, <strong>FEMM</strong> supports the following types of boundaries: • Prescribed A With this type of boundary condition, the vector potential, A, is prescribed along a given boundary. This boundary condition can be used to prescribe the flux passing normal to a boundary, since the normal flux is equal to the tangential derivative of A along the boundary. The form for A along the boundary is specified via the parameters A0, A1, A2 and φ in the Prescribed A parameters box. If the problem is planar, the parameters correspond to the formula: A = (A0 + A1x+A2y)e jφ (2.2) If the problem type is axisymmetric, the parameters correspond to: A = (A0 + A1r+ A2z)e jφ (2.3) • Small Skin Depth This boundary condition denotes an interface with a material subject to eddy currents at high enough frequencies such that the skin depth in the material is very small. A good discussion of the derivation of this type of boundary condition is contained in [2]. The result is a Robin boundary condition with complex coefficients of the form: ∂A ∂n + � 1+ j 24 δ � A = 0 (2.4)
Figure 2.8: Boundary Property dialog. where the n denotes the direction of the outward normal to the boundary and δ denotes the skin depth of the material at the frequency of interest. The skin depth, δ is defined as: � 2 δ = (2.5) ωµrµoσ where µr and σ are the relative permeability and conductivity of the thin skin depth eddy current material. These parameters are defined by specifying µ and σ in the Small skin depth parameters box in the dialog. At zero frequency, this boundary condition degenerates to ∂A/∂n = 0 (because skin depth goes to infinity). • Mixed This denotes a boundary condition of the form: � 1 � ∂A ∂n + coA+c1 = 0 (2.6) µrµo The parameters for this class of boundary condition are specified in the Mixed BC parameters box in the dialog. By the choice of coefficients, this boundary condition can either be a Robin or a Neumann boundary condition. There are two main uses of this boundary condition: 1. By carefully selecting the c0 coefficient and specifying c1 = 0, this boundary condition can be applied to the outer boundary of your geometry to approximate an upbounded solution region. For more information on open boundary problems, refer to Appendix A.3. 25
Page 1 and 2: Finite Element Method Magnetics Ver
Page 3 and 4: 2.3.10 Line Integrals . . . . . . .
Page 5 and 6: 3.7.8 View Commands . . . . . . . .
Page 7 and 8: The purpose of this document is to
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: yet been defined. Pushing the Add P
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
Page 57 and 58: some types of integrals; however, s
Page 59 and 60: dF = 1 (D(E · n)+E (D · n) −(D
Page 61 and 62: The second edit box is the Solver P
Page 63 and 64: Figure 2.41: Boundary Property dial
Page 65 and 66: Figure 2.43: Materials Library dial
Page 67 and 68: 2.7 Heat Flow Postprocessor The the
Page 69 and 70: Figure 2.49: When in doubt plots an
Page 71 and 72: 2.8.1 Problem Definition Figure 2.5
Page 73 and 74: 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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