If you are running Mechanical APDL via the GUI, the first thing you should do after the GUI becomes active is choose menu path Main Menu> Preferences. Then, on the dialog box that appears, select Magnetic-Nodal from the list of magnetic analysis types. Because the GUI filters the elements available to you based on the preference you choose, you must set preferences before doing anything else, and you must specify Magnetic-Nodal to ensure that you can use the elements needed for 2D static analysis.

Give your analysis a title that reflects the problem being analyzed, such as "2D solenoid actuator static analysis." Be sure to choose a unique title to distinguish this analysis problem from others that may use similar model geometry or physics. To assign a title, use either of the following:

The tasks you perform to choose element types are the same for a static magnetic analysis as they are for other analysis types, and the Basic Analysis Guide explains these procedures at length.

Element types establish the physics of the problem domain. Depending on the nature of the problem, you may need to define several element types to model the different physics regions in the model. For example, a permeable iron region may require one element type, and a stranded coil may require a different element type. The element types you choose and their options (KEYOPTS, discussed next) must be compatible with the nature of the domain to be solved. Once you have specified element types and options, you can assign them to different regions of the model.

The tables and figures below show you regions that can exist within a 2D model. Details on specifying material properties and real constants noted in the tables and figures follow in the next few sections.

Current-fed stranded coil	DOF: AZ Material Properties: MUr (MURX) Special characteristics: Apply source current density, JS (using BFE,,JS command)
Assumes a stranded insulated coil producing a constant DC current, unaffected by surrounding conditions. You can calculate current density from the number of coil turns, the current per turn, and the cross-section area of the coil.

Voltage-fed stranded coil	DOFs: AZ, VOLT, EMF (with PLANE233) Material Properties: MUr (MURX), rho (RSVX) Real constants: SC, NC, RAD, TZ, R, SYM Special characteristics: Couple CURR DOFs in region.
Applied voltage is unaffected by surroundings. For more details about voltage source modeling, see 2D Stranded Coil Analysis.

Moving conducting bodies	DOFs: AZ (with PLANE233) Material Properties: MUr (MURX), or B-H curve (TB command), rho (RSVX) Real constants: None Special characteristics: Apply velocities VELOX, VELOY, OMEGAZ via BF,,VELO command
Moving body must not undergo spatial change in the "material". See Step 1d for more details.

Dissimilar mesh interface	DOFs: AZ Contact elements: TARGE169, CONTA172, CONTA175 CONTA17x KEYOPTS: KEYOPT(1)=7 (AZ), KEYOPT(2)=2 (MPC approach), KEYOPT(4) = 1 or 2 (n/a for CONTA175), KEYOPT(12)=5

Use PLANE13 or PLANE233 elements to represent all interior regions of your model magnetic (permeable) regions, current-conducting regions, permanent (that is, magnet) regions, and air (free space), etc.

To model an unbounded problem domain, use of INFIN110, the four- or eight-node boundary element, is recommended. INFIN110 can model the far-field decay in the magnetic field and will give better results than an assumed flux-parallel or flux-normal boundary condition.

Most element types have additional options known as KEYOPTS, which you use to modify element characteristics. For example, element PLANE233 has the following KEYOPTS:

Each element type uses different KEYOPTS, and the characteristics that KEYOPTS define vary from one element to another. KEYOPT(1) controls the use of additional degrees of freedom. These additional DOFs are used to model different physics in the electromagnetic domain (for example, a stranded conductor, a massive conductor, a circuit-coupled conductor, etc.). To see which KEYOPTS and KEYOPT settings apply to a particular element, see its description in the Element Reference.

To specify KEYOPT settings, use one of the following:

If you have laminated materials or permanent magnets aligned in an arbitrary manner, you need to specify the element coordinate system or systems to be used. The Global Cartesian coordinate system is the default. After defining element types and options, you can specify a different coordinate system by specifying its origin location and orientation angles. To do so, use either of the following:

The coordinate system types available are Cartesian, cylindrical (circular or elliptical), spherical (or spheroidal), and toroidal. Once you have defined one or more element coordinate systems, you can set a pointer that identifies the coordinate system to be assigned to subsequently defined elements (area and volume elements only). Set the pointer using one of the following:

Element real constants are miscellaneous properties that depend on the element type. You specify real constants using the R family of commands (R, RMODIF, etc.) and their equivalent GUI paths. In electromagnetics, you use real constants to define stranded coil geometry and winding characteristics, or to describe velocity effects. Observe two rules when defining real constants:

See Getting Started in the Basic Analysis Guide for more information about defining real constants.

Your model may have any or all of the following material regions: air, (free-space) permeable materials, current-conducting regions, and permanent magnets. Each type of material region has certain required material properties.

The material library contains definitions of several materials with magnetic properties. Instead of defining material properties from scratch, you can read these material properties into the database and, if necessary, modify them to match the materials in your analysis problem more closely.

Materials with magnetic properties defined in the material library are as follows:

The copper property presents temperature-dependent resistivity and relative permeability. All other properties are B-H curves.

The property definitions in the material library specify properties "typical" for the materials listed. Mechanical APDL has extrapolated these properties to cover high saturation conditions. Your actual material values may differ from those supplied; therefore, you may need to modify the material library files you use.

 

2.3.1.6.2. Additional Guidelines for Defining Regional Material Properties and Real Constants

The next few paragraphs provide some guidelines for setting up physics regions for your model. In addition, you may want to consult 2D Harmonic Magnetic (AC) Analysis; it pictures and describes the regions that can exist within a 2D model.

For air regions:

Specify a relative permeability of 1.0. To do so, use one of the following:

Command(s): MP,MURX

GUI: Main Menu> Preprocessor> Material Props> Material Models> Electromagnetics> Relative Permeability> Constant

For permeable material regions:

For linear magnetic material, you can specify relative permeability values MURX, MURY, and MURZ using the MP command. To specify a linear isotropic material, you only need to specify MURX. MURY and MURZ default to MURX. Free-space permeability MUZRO is set by the EMUNIT command. Ignoring permanent magnet effects, the B-H equations for linear magnetic materials are:

Bx = (MUZRO) (MURX) (Hx)

By = (MUZRO) (MURY) (Hy)

Bz = (MUZRO) (MURZ) (Hz)

For nonlinear soft magnetic material, specify the B-H curve by reading from a material library or by creating your own B-H curve:

Command(s): MPREAD,filename, ...

GUI: Main Menu> Preprocessor> Material Props> Material Library> Import Library

Command(s): TB, TBPT

GUI: Main Menu> Preprocessor> Material Props> Material Models> Electromagnetics> BH Curve

If you specify a B-H curve, it should meet the following requirements for the material to be represented accurately:

• The B values must be unique for each H value, and must start at the origin and monotonically increase with H, as shown in Figure 2.1: B-H and Reluctivity vs. B Squared Curves(a). By default, the B-H curve will pass through the origin (that is, the 0.0 point is not to be explicitly defined). You can verify this by plotting B versus H using one of the methods shown below. (For more information, see the Element Reference.)

  Command(s): TBPLOT

  GUI: Main Menu> Preprocessor> Material Props> Material Models> Electromagnetics> BH Curve

• The ν-B² curve that Mechanical APDL calculates internally (where ν is the reluctivity) should be smooth and continuous. You can verify this by plotting ν versus B² using the TBPLOT command. (See Figure 2.1: B-H and Reluctivity vs. B Squared Curves(b).)

• The B-H curve should cover the complete operating range of the material. If a point beyond the end of the curve is required, the B-H curve is extrapolated with a slope equal to the free-space permeability. You can view values in the extrapolated region by adjusting the X-axis range. To do so, use one of the following together with the TBPLOT command:

  Command(s): /XRANGE

  GUI: Utility Menu> PlotCtrls> Style> Graphs

Figure 2.1: B-H and Reluctivity vs. B Squared Curves

If a nonlinear B-H curve is specified without any relative permeability values, the B-H equations are:

Bx = F(|H|) / (|H|) (Hx)

By = F(|H|) / (|H|) (Hy)

Bz = F(|H|) / (|H|) (Hz)

where:

|H| = {(Hx)2 + (Hy)2 + (Hz)2}1/2

If a nonlinear B-H curve and relative permeability (MURX label) are specified for the same material, the relative permeability will be used.

Orthotropic material relative permeability may be assigned using the MURX, MURY, and MURZ labels on the MP command. A B-H curve may be used in conjunction with relative permeability to model nonlinear effects along any one of the three orthogonal axes (such as for laminated iron material). To invoke the usage of a B-H curve along one of the axes, set the relative permeability for that axis explicitly to zero. For example, assume a B-H curve is defined for material number 2. You want to have the curve active along the Y-axis, while assigning the X and Z axes a relative permeability of 1000. Your input would be:

mp,murx,2,1000
mp,mury,2,0! read B-H curve for material 2
mp,murz,2,1000

If a B-H curve is specified along with zero permeability in two directions and a non-zero permeability in one direction, the B-H curve will be applied to the two axes with zero permeability. For example, if MURX and MURY are zero and MURZ is non-zero, the B-H equations are:

Bx = F(|H|) / (|H|) (Hx)

By = F(|H|) / (|H|) (Hy)

Bz = (MUZRO) (MURZ) (Hz)

where:

|H| = {(Hx)2 + (Hy)2 + (Hz)2}1/2

If a nonlinear B-H curve is specified with a thermal coefficient C1 (TBOPT = TCF on the TB,BH command), then the material pearmeability is calculated as:

μh = (μh,ref)*(C1)+(MUZRO)*(1-C1)

where μ_h,ref = F(|H|) / (|H|) is the reference permeability calculated from the specified B-H curve. The thermal coefficient is calculated from the specified thermal coefficient data table for a given element temperature value. Among 2D elements, only PLANE223 and PLANE233 support the TBOPT = TCF option.

To define the thermal coefficient data table, use the TBTEMP command, or the TBFIELD,TEMP command, along with the TBDATA command. For field variable data definition and calculation, see TBFIELD and Understanding Field Variables in the Material Reference.

A source conductor is a conductor connected to an external current "generator" that supplies a constant current. Specify resistivity if you wish to have the program calculate Joule heating losses. Resistivity may be isotropic or orthotropic. To specify resistivity, use one of the following:

In a static analysis, resistivity is used only for loss calculations.

For a moving conductor analysis (velocity effects), specify isotropic resistivity (using the command or GUI path shown above).

You can solve electromagnetic fields for special cases of moving bodies. Valid special cases are those in which the moving body presents itself as a homogeneous moving body for which the moving "material" undergoes no spatial change. Figure 2.2: Applicable Configurations for Considering Velocity Effects of Moving Bodies shows two valid cases:

Figure 2.2: Applicable Configurations for Considering Velocity Effects of Moving Bodies

An invalid case would be a "slotted" rotor rotating at constant speed. In this case, the slots in the motor present a discontinuity in material as the body rotates. Another invalid case would be a translating conductor of finite width moving in a magnetic field. Typical valid applications are solid rotor induction machines, linear induction machines, and eddy-current braking systems.

A static analysis requires input to specify the translational velocity or the rotational speed of the conductor. With PLANE233, specify the following nodal velocities (BF,,VELO):

Velocity effects can be suppressed (KEYOPT(5) = 2) if they are undesirable in the electromagnetic elements adjacent to the domain with a specified velocity.

Accuracy of analysis results for electromagnetic problems with moving bodies depends on the mesh refinement, permeability, conductivity, and velocity. A magnetic Reynolds number is defined to characterize the problem:

Mre = μvd/ρ

In the equation above, μ is permeability, ρ is resistivity, v is velocity, and d is characteristic length (in the directional motion) within a finite element of the conducting body. The magnetic Reynolds number is meaningful only in a static or transient analysis.

The motion formulation is valid and accurate for relatively small values of the Reynolds number, typically on the order of 1.0. Accuracy for higher Reynolds number values will vary from problem to problem. The magnetic Reynolds number is calculated and available in the postprocessor for viewing. In addition to a field solution, the motion solution includes currents in the conductor due to motion. This is available in the postprocessor.

Requirements are the normal demagnetization B-H curve (or relative permeability, if linear) and components of the magnetic coercive force vector (values MGXX, MGYY, or MGZZ for either of the following):

The demagnetization B-H curve, which normally lies in the second quadrant, must be defined in the first quadrant. To do this, you need to add a constant "shift" to all H values, as shown in Figure 2.3: Actual and Mechanical APDL (Shifted) Demagnetization Curves. The shift, given by:

represents the magnitude of the coercive force. The coercive force components are used to align the magnetization axis of the magnet with the element coordinate system.

Figure 2.3: Actual and Mechanical APDL (Shifted) Demagnetization Curves

The example below shows a bar magnet that lies along an axis 30^o to the global X-Y plane. The elements in the magnet are to be assigned to a local element coordinate system whose X-axis is aligned with the polarization direction. The example also shows the magnet's demagnetization characteristics and the corresponding material property input.

/PREP7
HC=3000             ! Coercive force
BR=4000            ! Residual induction


THETA=30           ! Permanent magnet orientation
*AFUN,DEG          ! Angular parametric functions in degrees
MP,MGXX,2,HC! X component of coercive force

! B-H curve:
TB,BH,2               ! B-H curve for material 2
TBPT,DEFI,-3000+HC,0  ! Shifted B-H curve
TBPT,,-2800+HC,500    ! First field defaults to "DEFI"
TBPT,,-2550+HC,1000
TBPT,,-2250+HC,1500
TBPT,,-2000+HC,1800
TBPT,,-1800+HC,2000
TBPT,,-1350+HC,2500
TBPT,,-900+HC,3000
TBPT,,-425+HC,3500
TBPT,,0+HC,4000
TBPLOT,BH,2           ! Plot of B vs. H

Figure 2.4: B-H Curve for Bar Magnet Example shows the B-H curve for the permanent magnet as created in the first quadrant. For more information, read the descriptions of the *AFUN, MP, TB, and TBPLOT commands in the Command Reference.

Figure 2.4: B-H Curve for Bar Magnet Example

You can represent nonlinear orthotropic materials (laminated structures) by combining a single B-H curve with orthotropic relative permeability. The program will use the B-H curve in each element coordinate system direction where a zero specified value of relative permeability is assigned. (For related information, see the description of the ESYS command in the Command Reference.)

This specifies applied current to a source conductor. The units of JS are amperes/meter² in the MKS system. For a 2D analysis, only the Z component of JS is valid; a positive value indicates current flowing in the +Z direction in the planar case and the -Z (hoop) direction in the axisymmetric case.

Usually, you apply current density directly to the elements. You specify source current density in location number 3 (for the BFE command), using either of the following:

Refer to the Command Reference for further information.

Alternatively, you can also apply source current densities to areas of the solid model by using the BFA command. You can then transfer the specified source current densities from the solid model to the finite element model by using either the BFTRAN command or the SBCTRAN command.

Infinite surface flags are not actual loads, but they are used to indicate which surface of an infinite element faces toward the open (infinite) domain. Applying the INF label to an element face turns the flag on for that face.

Maxwell surface flags are not actual loads, but they are used to indicate on which element faces the magnetic force distribution is to be calculated. Applying the MXWF label to an element face turns the flag on for that face.

Typically, you turn the MXWF flag on for the surfaces of air elements adjacent to an air-iron interface. Forces are calculated at the air-iron interface (using the Maxwell stress tensor approach) and stored in the air elements. In POST1, you can review and sum the stored forces in each air element to get the total force acting on the body. You may, if you wish, then use these forces as loads in a structural analysis.

You can specify more than one component, but the components must not share adjacent air elements. (Sharing air elements is typical when a single element layer separates two components.)

Magnetic virtual displacement flags are not actual loads, but they are used to initiate the calculation of forces on a body in the model. The MVDI method provides an alternative to the Maxwell surface (MXWF) method. The program calculates the forces, using the virtual work approach, as it processes the solution.

To trigger the calculation, specify the MVDI flag value as 1.0 at all nodes in the region of interest and 0.0 (default setting) at all adjacent air nodes. Although you can enter MVDI values greater than 1.0, you should not normally do so. Forces will be calculated and stored in the air elements adjacent to the body.

The band of air elements surrounding the region of interest should be uniformly thick. In POST1, you can review and sum the stored forces in each air element to get the total force.

Figure 2.5: MVDI Specifications for Virtual Work Force Calculation

This infrequently used load type applies nodal current loads. To compute the current segment for an axisymmetric analysis, you must multiply the current at a node by 2 πr. Units for current segments are ampere-meters in the MKS system.

Current flows in the Z direction, consistent with the degree of freedom AZ. You can specify a known sheet current, for example, through current segments. Take care in distributing a current segment load along nodes. For a discussion of load distribution on nodes, see the Modeling and Meshing Guide.

The first step is to enter the SOLUTION processor. To do so, use either of the following:

To specify the analysis type, do either of the following:

If you want to restart a previous analysis (for example, to restart an unconverged solution or to specify additional excitation), issue the command ANTYPE,STATIC,REST. You can restart an analysis only if you previously completed a 2D static magnetic analysis, and the files Jobname.EMAT, Jobname.ESAV, and Jobname.DB from the previous run are available.

Next, you define which solver you want to use. You can specify any of these values:

To select an equation solver, use either of the following:

We recommend that you use the sparse solver for 2D or shell/beam models. However, the JCG or PCG solvers may be more useful for extremely large and bulky models. Models that are voltage-fed or that include velocity effects produce unsymmetric matrices and can use only the sparse solver, the JCG solver, or the ICCG solver. Circuit-fed models can use only the sparse solver.

Use the SAVE_DB button on the Toolbar to save a backup copy of the database. This enables you to retrieve your model should your computer fail while analysis is in progress. To retrieve a model, re-enter Mechanical APDL and use one of the following:

In this step, you specify magnetic solution options and initiate the solution. For a nonlinear analysis, use a two-step solution sequence:

You can specify the two-step solution sequence and initiate the solution using either of the following:

If you like, you can step manually through the two-step solution sequence. See Alternative Analysis Options and Solution Methods for the procedure to follow for manual solution.

As nonlinear electromagnetic analysis proceeds, the program computes convergence norms with corresponding convergence criteria each equilibrium iteration. Available in both batch and interactive sessions, the Graphical Solution Tracking (GST) feature displays the computed convergence norms and criteria while the solution is in process. By default, /GST is ON for interactive sessions and OFF for batch runs. To turn /GST on or off, use either of the following:

Figure 2.6: Convergence Norms Displayed by the Graphical Solution Tracking (GST) Feature below shows a typical GST display:

Figure 2.6: Convergence Norms Displayed by the Graphical Solution Tracking (GST) Feature

To leave the SOLUTION processor, use either of the following:

Calculating the differential inductance matrix and the total flux linkage in each coil requires assigning components to coil elements, defining nominal currents, and performing a nominal solution about an operating point using the sparse equation solver.

For a system of coils modeled with PLANE233, use linear perturbation analysis to calculate the self- and mutual differential inductances and the total flux linkage in each coil.

Additional data, specific to each element type, also is available. See the Element Reference for details.

You can review analysis results in POST1, the general postprocessor, by choosing either in the following:

The following section, "Reading In Results Data," discusses some typical postprocessing operations for a static magnetic analysis. For a complete description of all postprocessing functions, see the Basic Analysis Guide.

Flux lines show lines of constant AZ (or constant radius-times-AZ for axisymmetric problems). Display flux lines using either of the following:

You can contour almost any result item (including flux density, field intensity, and total current density (JTZ)) using the following commands or menu paths:

In PowerGraphics mode (default), you can visualize nodal averaged contour displays which account for material discontinuities. Should you need to activate PowerGraphics, use either /GRAPHICS,POWER or Utility Menu> PlotCtrls> Style> Hidden-Line Options.

Vector displays (not to be confused with vector mode) offer an effective way to view vector quantities such as B, H, and FMAG. For vector displays, use either of the following:

For vector listings, use either method shown below:

You can produce tabular listings of results data, either unsorted or sorted by node or by element. To sort data before listing it, use any of the following:

To produce tabular data listings, use any of the following:

Three types of magnetic forces are available when using PLANE13:

For information on calculating magnetic forces when using PLANE233, see Older vs. Current 2D Magnetic Element Technologies.

Lorentz, Maxwell and virtual work torque computations are available when using PLANE13:

For information on calculating magnetic torques when using PLANE233, see Older vs. Current 2D Magnetic Element Technologies.

For stranded coils with the voltage-fed or circuit-fed options, you can calculate the resistance and inductance of the coil. Each element stores values of resistance and inductance. Summing these values gives the total resistance and inductance of the modeled region of the conductor. To store and sum these values, select the conductor elements using the ETABLE,tablename,NMISC,n command or its equivalent menu path. (For the n value, use 8 for resistance and 9 for inductance.) Use the SSUM command or its menu path equivalent to sum the data.

You can calculate many other items of interest (such as global forces, torque, source input energy, inductance, flux linkages, and terminal voltage) from the data available in the database in postprocessing. The APDL command set supplies the following macros for these calculations:

For more discussion of these macros, see Electric and Magnetic Macros.

For information on the macros applicable to PLANE233, see the element's description in the Element Reference.