3-D 10-Node
Electromagnetic Solid
SOLID237 Element Description
SOLID237 is a 3-D 10-node, element capable of modeling electromagnetic fields. The element has magnetic and electric degrees of freedom. Magnetic degrees of freedom are based on the edge-flux formulation.
The edge-flux (AZ) degrees of freedoms are the line integrals of the magnetic vector potential along the element edges. They are defined at the midside nodes only and there are no magnetic degrees of freedom associated with the corner nodes. The edge-flux formulation uses tree gauging (see the GAUGE command) to produce a unique solution.
In an electromagnetic analysis, the electric degree of freedom is the electric potential (VOLT) defined at each node. The element also has an option to perform an electromagnetic analysis with time-integrated electric potential.
In a stranded coil analysis, the electric degrees of freedom are the voltage drop across the coil (VOLT) and the electromotive force (EMF). In a coil region, all the VOLT and EMF degrees of freedom must be coupled using the CP command. The element has the option to perform a stranded coil analysis with time-integrated voltage drop or time-integrated electromotive force.
The element is applicable to 3-D static, time-harmonic and time-transient electromagnetic analyses. The magnetic analysis option typically is used to model air, iron, nonferrous materials and permanent magnets. The analysis is driven by the current density applied as an element body load.
The electromagnetic analysis option is suitable for modeling solid (massive) conductors. The solid (massive) conductor may be voltage- or current-driven, as well as circuit-fed. The electromagnetic analysis has the option to suppress the eddy current effect in time-varying analyses to model stranded conductors. The Hall effect can be taken into account in a static or transient electromagnetic analysis. The velocity effects can be taken into account in a static, time-harmonic or time-transient electromagnetic analysis.
The stranded coil analysis option is suitable for modeling a stranded winding with a prescribed current flow direction vector. The stranded coil may be voltage- or current-driven, as well as circuit-fed.
The following command macros can be used with SOLID237 for solution postprocessing: EMAGERR, EMFT, MMF, POWERH. See Electric and Magnetic Macros in the Low-Frequency Electromagnetic Analysis Guide for more details.
The element has nonlinear magnetic capability for modeling B-H curves or permanent magnet demagnetization curves for static and time-transient analyses. See SOLID237 in the Mechanical APDL Theory Reference for more details about this element.
SOLID237 Input Data
The geometry, node locations, and the coordinate system for this element are shown in Figure 237.1: SOLID237 Geometry. The element is defined by 10 node points and the material properties.
The type of units (MKS or user defined) is specified through the EMUNIT command. EMUNIT also determines the value of MUZRO and EPZRO. The EMUNIT defaults are MKS units and MUZRO = 4π10-7 Henry/meter and EPZRO = 8.854 x 10-12 Farad/meter. In addition to MUZRO and EPZRO, orthotropic relative permeability and permittivity is available and is specified through the MURX, MURY, and MURZ and PERX, PERY, PERZ material options, respectively. Orthotropic resistivity is specified through RSVX, RSVY, and RSVZ material property labels. MGXX, MGYY, and MGZZ represent vector components of the coercive force for permanent magnet materials. The magnitude of the coercive force is the square root of the sum of the squares of the components. The direction of polarization is determined by the components MGXX, MGYY, and MGZZ. Permanent magnet polarization directions correspond to the element coordinate directions. The element coordinate system orientation is as described in Coordinate Systems. Nonlinear magnetic B-H properties are entered with the TB command. Nonlinear orthotropic magnetic properties can be specified with a combination of a B-H curve and linear relative permeability. The B-H curve is used in each element coordinate direction where a zero value of relative permeability is specified. Only one B-H curve may be specified per material. In an electromagnetic analysis, the Hall coefficient is specified through the RH material option.
Nodal loads are defined with the D and F commands. For edge-based analyses, the edge-flux constraint is applied to the node using the D command with Lab = AZ. Flux-parallel boundary conditions are prescribed by setting AZ to zero. No AZ constraint is required to set flux-normal boundary conditions. The DFLX command can be used to impose a uniform magnetic flux on the selected nodes.
For massive conductors (KEYOPT(1) = 1), Lab = VOLT is valid with the D command and VALUE defines the electric potential. Note that electric potential is time-integrated if KEYOPT(2) = 2. With the F command, Lab = AMPS and VALUE corresponds to the total current.
For stranded coils (KEYOPT(1) = 2), Lab = VOLT is valid with the D command and VALUE defines the voltage drop across the coil. The D command with Lab = EMF can
be used to apply constraints on the electromotive force. Note that
voltage drop and the electromotive force are time-integrated if KEYOPT(2)
= 2. The total current through the coil can be applied with the F command using Lab = AMPS.
The temperature (for material property evaluation only) body loads may be input based on their value at the element's nodes or as a single element value [BF, BFE]. In general, unspecified nodal values of temperatures default to the uniform value specified with the BFUNIF or TUNIF commands.
For modeling stranded conductors KEYOPT(1) = 0, source current density may be applied to an area or volume [BFE or BFV] or input as an element value [BFE]. The vector components of the current density are with respect to the element coordinate system. See "SOLID237 Assumptions and Restrictions" for a description of the solenoidal condition.
A summary of the element input is given in "SOLID237 Input Summary". A general description of element input is given in Element Input.
SOLID237 Input Summary
- Nodes
I, J, K, L, M, N, O, P, Q, R
- Degrees of Freedom
See KEYOPT(1)
- Real Constants
There are no real constants for KEYOPT(1) = 0 or 1.
The following are the real constants for KEYOPT(1) = 2:
SC, NC, VC, TX, TY, TZ R, SYM See Table 237.1: SOLID 237 Real Constants for more information.
- Material Properties
MP command: MURX, MURY, MURZ, MGXX, MGYY, MGZZ
RSVX, RSVY, RSVZ, RH, PERX, PERY, PERZ (see "SOLID237 Assumptions and Restrictions")
EMUNIT command: EPZRO, MUZERO
- Surface Loads
None
- Body Loads
- Temperature --
T(I), T(J), ..., T(P), T(Q), T(R)
- Source Current Density (valid for KEYOPT(1) = 0 only)
JSX(I), JSY(I), JSZ(I), PHASE(I),
JSX(J), JSY(J), JSZ(J), PHASE(J),
...
JSX(P), JSY(P), JSZ(P), PHASE(P),
JSX(Q), JSY(Q), JSZ(Q), PHASE(Q),
JSX(R), JSY(R), JSZ(R), PHASE(R)
Velocity (valid for KEYOPT(1) = 1 only) --
VELOX(I), VELOY(I), VELOZ(I), OMEGAX(I), OMEGAY(I), OMEGAZ(I)
VELOX(J), VELOY(J), VELOZ(J), OMEGAX(J), OMEGAY(J), OMEGAZ(J)
...
VELOX(P), VELOY(P), VELOZ(P), OMEGAX(P), OMEGAY(P), OMEGAZ(P)
VELOX(Q), VELOY(Q), VELOZ(Q), OMEGAX(Q), OMEGAY(Q), OMEGAZ(Q)
VELOX(R), VELOY(R), VELOZ(R), OMEGAX(R), OMEGAY(R), OMEGAZ(R)
- Special Features
- KEYOPT(1)
Element capability and degrees of freedom:
- 0 --
Magnetic:
AZ
- 1 --
Electromagnetic:
AZ, VOLT
- 2 --
Stranded coil:
AZ, VOLT, EMF
- KEYOPT(2)
Coupling method between magnetic and electric degrees of freedom (KEYOPT(1) = 1 or 2); also defines the meaning of the VOLT and EMF degrees of freedom for KEYOPT(1) = 1 or 2:
- 0 --
Strong (matrix) coupling. Produces an unsymmetric matrix. In a linear analysis, a coupled response is achieved after one iteration. Applicable to all analysis types
- 1 --
Weak (load vector). Produces a symmetric matrix and requires at least two iterations to achieve a coupled response. Applicable to static and transient analyses only. (see "SOLID237 Assumptions and Restrictions")
- 2 --
Strong (matrix) coupling with time-integrated electric potential (VOLT) for KEYOPT(1) = 1 (electromagnetic analysis). Produces a symmetric matrix.
Strong (matrix) coupling with time-integrated voltage drop (VOLT) and time-integrated electromotive force (EMF) for KEYOPT(1) = 2 (stranded coil analysis). Produces a symmetric matrix if the coil symmetry factor is 1; produces a nonsymmetric matrix if the coil symmetry factor is greater than 1.
In a linear analysis, a coupled response is achieved after one iteration. Applicable to harmonic and transient analyses only.
- KEYOPT(5)
Eddy currents or velocity effects in electromagnetic (KEYOPT(1) =1) analyses:
- 0 --
Active
- 1 --
Eddy currents are suppressed in harmonic or transient analyses
- 2 --
Velocity effects are suppressed
- 3 --
Eddy currents and velocity effects are suppressed
- KEYOPT(7)
Electromagnetic force output:
- 0 --
At each element node (corner and midside)
- 1 --
At element corner nodes only (midside nodes forces are condensed to the corner nodes)
- KEYOPT(8)
Electromagnetic force calculation:
- 0 --
Maxwell
- 1 --
Lorentz
Table 237.1: SOLID 237 Real Constants
| No. | Name | Description | Default | Definition |
|---|---|---|---|---|
| 1 | SC | Coil cross-sectional area | none | True physical cross-section of the coil regardless of symmetry modeling considerations. It includes the cross-sectional area of the wire and the non-conducting material filling the space between the winding. |
| 2 | NC | Number of coil turns | 1 | Total number of winding turns in a coil regardless of any symmetry modeling considerations. |
| 3 | VC | Coil volume | none | True physical volume of the coil regardless of symmetry modeling considerations. It includes the volume occupied by the wire and the non-conducting material filling the space between the winding. |
| 4 | TX | Coil winding X-directional cosine | 0 | The coil direction vector T = {TX, TY, TZ}T is a unit vector tangent to the coil winding. It designates the current flow direction. |
| 5 | TY | Coil winding Y-directional cosine | 1 | |
| 6 | TZ | Coil winding Z-directional cosine | 0 | |
| 7 | R | Coil resistance | none | Total coil DC resistance regardless of any symmetry modeling considerations. |
| 8 | SYM | Coil symmetry factor | 1 | Ratio of the true physical volume of the coil (real constant VC) to the modeled coil volume. The input should be greater or equal to 1. |
SOLID237 Output Data
The solution output associated with the element is in two forms:
Nodal degrees of freedom included in the overall nodal solution
Additional element output as shown in Table 237.2: SOLID237 Element Output Definitions
The element output directions are parallel to the element coordinate system. A general description of solution output is given in Solution Output. See the Basic Analysis Guide for ways to view results.
The Element Output Definitions table uses the following notation:
A colon (:) in the Name column indicates that the item can be accessed by the Component Name method (ETABLE, ESOL). The O column indicates the availability of the items in the file Jobname.OUT. The R column indicates the availability of the items in the results file.
In either the O or R columns, “Y” indicates that the item is always available, a number refers to a table footnote that describes when the item is conditionally available, and “-” indicates that the item is not available.
Table 237.2: SOLID237 Element Output Definitions
| Name | Definition | O | R |
|---|---|---|---|
| EL | Element Number | - | Y |
| NODES | Nodes - I, J,…, P, Q, R | - | Y |
| MAT | Material number | - | Y |
| VOLU: | Volume | - | Y |
| XC, YC, ZC | Location where results are reported | - | 2 |
| TEMP | Input temperatures T(I), T(J), ..., T(P), T(Q), T(R) | - | Y |
| LOC | Output location (X, Y, Z) | - | - |
| B: X, Y, Z, SUM | Magnetic flux density components and vector magnitude | - | 1 |
| H: X, Y, Z, SUM | Magnetic field intensity components and vector magnitude | - | 1 |
| EF: X, Y, Z, SUM | Electric field intensity components and magnitude [7] | - | 1 |
| JC: X, Y, Z, SUM | Nodal conduction current density components and magnitude [7] | - | 1 |
| FMAG: X, Y, Z, SUM | Electromagnetic force components and magnitude [3] | - | 1 |
| JT: X, Y, Z, SUM | Element conduction current density components (in the global Cartesian coordinate system) and vector magnitude [6] | - | 1 |
| JS: X, Y, Z, SUM | Element current density components (in the global Cartesian coordinate system) and vector magnitude [4] [6] | - | 1 |
| JHEAT: | Joule heat generation rate per unit volume [3] [5] [6] | - | 1 |
| SENE or MENE: | Magnetic energy [3] | - | 1 |
| COEN | Magnetic co-energy [3] | - | 1 |
| AENE | Apparent magnetic energy [3] | - | 1 |
| IENE | Incremental magnetic energy [3] | - | 1 |
The solution value is output only if calculated (based upon input data). The element solution is at the centroid.
Available only at centroid as a *GET item.
For a time-harmonic analysis, electromagnetic forces (FMAG), Joule losses (JHEAT) and stored energy (SENE, MENE) represent time-average values. These values are stored in both the real and imaginary data sets. In a linear perturbation analysis, only incremental and apparent energy values are time-averaged.
JS represents the sum of element conduction and displacement current densities.
Calculated Joule heat generation rate per unit volume (JHEAT) may be made available for a subsequent thermal analysis with companion elements [LDREAD].
For the stranded coil analysis option (KEYOPT(1) = 2), JT and JS are the effective current densities as they are calculated based on the coil cross-sectional (SC) that includes the wire and the non-conducting material filling the space between the winding. JHEAT represents the effective Joule heat generation rate per unit volume as it is calculated based on the modeled coil volume that includes the wire and the non-conducting material filling the space between the winding.
Not available with the stranded coil option (KEYOPT(1) = 2).
Table 237.3: SOLID237 Item and Sequence Numbers lists output available through the ETABLE command using the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide and The Item and Sequence Number Table in this reference for more information. The following notation is used in Table 236.3: SOLID236 Item and Sequence Numbers:
- Name
output quantity as defined in Table 237.2: SOLID237 Element Output Definitions
- Item
predetermined Item label for ETABLE command
- E
sequence number for single-valued or constant element data
SOLID237 Assumptions and Restrictions
The element must not have a zero volume or a zero length side. This occurs most frequently when the element is not numbered properly. Elements may be numbered either as shown in Figure 237.1: SOLID237 Geometry or in an opposite fashion.
Midside nodes may not be removed.
The magnetic analysis option (KEYOPT(1) = 0) requires the source current density specified with the BFE,,JS command to be solenoidal.
Permanent magnets are not permitted in a harmonic analysis.
It is not recommended to use the weak coupling option (KEYOPT(2) = 1) in a transient electromagnetic analysis with eddy currents or a transient stranded coil analysis because multiple iterations may be required to achieve convergence.
In a transient analysis, the
THETAintegration parameter defaults to the values shown in the following table. You can use the TINTP command to modify the default setting.Table 237.4: THETA Default Values
Analysis Type KEYOPT Values THETA Default Value Strongly coupled transient electromagnetic analysis with electric potential or stranded coil analysis with voltage drop (VOLT) KEYOPT(1) = 1 or 2 and KEYOPT(2) = 0 1.0 Strongly coupled transient electromagnetic analysis with time-integrated electric potential or stranded coil analysis with time-integrated voltage drop (VOLT) KEYOPT(1) = 1 or 2 and KEYOPT(2) = 2 0.5 The electrical permittivity material input (MP,PERX, also PERY, PERZ) is applicable to electromagnetic harmonic analyses (KEYOPT(1) = 1) only.
In a stranded coil (KEYOPT(1) = 2) domain, the winding direction vector T = {TX, TY, TZ}T must be specified in the element coordinate system and all VOLT and EMF degrees of freedom must be coupled (CP command).
This element may not be compatible with other elements having a VOLT degree of freedom. See Element Compatibility in the Low-Frequency Electromagnetic Analysis Guide) for more information. The electromagnetic analysis with time-integrated electric potential (KEYOPT(2) = 2) cannot be used with current-based circuit (e.g. CIRCU124) or low-frequency electric (e.g. SOLID232) elements.