As in any other type of analysis, for harmonic magnetic analyses you create a physics environment, build a model, assign attributes to model regions, mesh the model, apply boundary conditions and loads, obtain a solution, and then review the results. Most of the procedures for conducting a 2D harmonic magnetic analysis are identical or similar to the procedures for performing 2D static analyses. This topic discusses the tasks specific to harmonic analysis.
A 2D harmonic magnetic analysis uses the same procedures to set GUI preferences, the analysis title, element types and KEYOPT options, element coordinate systems, real constants, and a system of units. 2D Static Magnetic Analysis describes these procedures.
When specifying material properties, in general use the same methods discussed in 2D Static Magnetic Analysis; that is, where possible, use existing material property definitions from the material library or that other users at your site have developed.
The next few topics provide some guidelines for setting up physics regions for your model, including an illustrated discussion of terminal conditions you can model within a simulated physical region.
The program offers several options to handle terminal conditions on conductors. These options offer enormous flexibility in modeling, for example, stranded and massive conductors, short circuit and open circuit conditions, and circuit-fed devices. To model each of these entities, you perform these tasks:
Add extra degrees of freedom (DOFs) to the conducting region.
Assign required real constants, material properties, and special treatments to the DOFs. Element types and options, material properties, real constants and element coordinate systems are defined as "attributes" of the solid model; you assign them using the AATT and VATT commands or equivalent GUI paths.
Conductors modeled with only the AZ DOF simulate short-circuit conditions, due to the absence of electric scalar potential which implies zero voltage drop along the length of the conductor.
PLANE233 always behaves as a stranded conductor (no eddy current effects are modeled) in a harmonic or transient analysis when the element does not have the VOLT degree of freedom (KEYOPT(1) = 0).
The AZ-VOLT option allows you to model massive conductors with various terminal conditions by including an electric potential in the overall electric field calculation:
E = δA/δt -
V
The program replaces V with ν = 
Vdt
(time-integrated potential), allowing additional flexibility for considering
open circuit conditions, current-fed massive conductors, and multiple conductors
with end connections, by allowing control over the electric field (VOLT).
The potential ν has units of volt-seconds and uses the VOLT degree of freedom. In a planar or axisymmetric analysis, ν is constant over the conductor cross-section (that is, the voltage drop is in the out-of-plane direction only). To enforce this requirement, you must couple nodes in each conducting region using one of the following:
The coupling essentially reduces the unknowns to a single potential drop unknown in the conducting region.
By default, the meaning of the VOLT degree of freedom for PLANE233 is electric potential. To do an electromagnetic analysis with time-integrated electric potential as the VOLT degree of freedom, use KEYOPT(2) = 2.
Mechanical APDL offers several options you can use to handle terminal conditions on conductors in 2D magnetic analyses. Figure 3.1: Physical Region With Optional Terminal Conditions for Conductors pictures a physical region for a 2D magnetic analysis and the conditions (options) that can exist within it.
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| Short circuit conductor | DOFs: AZ Material Properties: MUr, (MURX), rho (RSVX) Eddy currents flow in a closed loop; there is no voltage drop due to a short-circuit condition. |
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| Open circuit conductor | DOFs: AZ, VOLT Material Properties: mur (MURX), rho (RSVX) Special characteristics: Couple VOLT DOF |
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No net current flows in an open circuit conductor. The axisymmetric case simulates a conductor with a finite cut (slit). | |
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| Current-fed massive conductor | DOFs: AZ, VOLT Material Properties: MUr (MURX), rho (RSVX) Special characteristics: Couple VOLT DOF in region; apply total current (F,,AMPS command) to single node Assumes a short-circuit condition with a net current flow from a current source generator. Net current is unaffected by surroundings. |
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| Multiple massive conductors terminated by a common ground plane | DOFs: AZ, VOLT Material Properties: MUr (MURX), rho (RSVX) Special characteristics: Couple VOLT DOF of all conductor regions into a single coupled node set. |
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Used to simulate devices such as squirrel cage rotors where end effects can be ignored. | |
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| Current-fed stranded coil | DOF: AZ Material properties: MUr (MURX) Special characteristics: No eddy currents; can apply source current density (JS ) using BFE,,JS command (or alternatively using the BFL or BFA command and transferring the load to the finite element model by using the BFTRAN or SBCTRAN command) |
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Assumes a stranded insulated coil producing a constant AC current, unaffected by surrounding conditions. Current density can be calculated from the number of coil turns, the current per turn, and the cross-section area of the coil. | |
| Laminated iron | DOF: AZ Material Properties: MUr (MURX) or B-H curve Simulating permeable regions where eddy currents can be neglected. Requires only the AZ DOF. |
| Air | DOF: AZ Material Properties: MUr (MURX = I) |
| Moving conductor (velocity effects) | Model velocity effects from conductors moving at constant velocity using PLANE233 elements. For more information about moving conductors, see the sections on velocity effects in this chapter and 2D Static Magnetic Analysis. |
You can solve electromagnetic fields for special cases of moving bodies under the influence of an AC excitation. Velocity effects are valid for static, harmonic, and transient analyses. 2D Static Magnetic Analysis discusses applications and limitations for motion analysis.
The procedure for solving a 2D harmonic analysis with a moving conductor is identical to that for a static analysis in terms of element KEYOPT options and body loads (PLANE233). Applied velocities are constant and do not vary sinusoidally (as do the coil or field excitation) in a harmonic analysis.
The magnetic Reynolds number characterizes the velocity effect and numerical stability of the problem. The equation used to produce this number is shown below:
Mre = μ νd/ρ
In the above equation, μ is permeability, ρ is resistivity, ν 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. In addition to a field solution, the motion solution includes currents in the conductor due to motion.