# Article: JMAG A to Z

## Issue 8 Understanding Conditions from A to Z

### Overview

In this issue's A to Z, I will present conditions used for linking JMAG magnetic field analysis with other kinds of analysis, and also with other software. I will also present conditions for easily managing complex modeling and analysis properties that govern general analysis settings.

### Linking

JMAG-Designer has functions for thermal and structural analysis in addition to magnetic field analysis. It is particularly robust for linking with structural and thermal analysis software such as Abaqus and Virtual.Lab, and also with the HILS ECU evaluation system (Fig. 1). Here, I will introduce necessary functions for linked analysis with these, and also for coupled analysis within JMAG.

Fig. 1 JMAG and surrounding software

(HILS is a company name. Only software titles relevant are included here)

#### Partial Model

This condition is for accurately transferring the temperature distribution to a magnetic field analysis when making a partial thermal analysis model with periodicity or symmetry for coupled thermal and magnetic field analysis.

It is possible to use a partial model when a model has periodicity or symmetry by simplifying the thermal structure. However, a full model may be necessary for magnetic field analysis depending on the core geometry or the relationship between the number of poles and number of slots in a rotating machine (Fig. 2). In such cases, this condition can be used to accurately transfer the temperatures generated in the thermal analysis to the magnetic field analysis.

Fig. 2 Transferring temperatures from thermal analysis to magnetic field analysis

#### External Circuit Link

This condition is set when linking JMAG and SILS software.

Electric machine drive is becoming increasingly complex, and in order to predict machine performance, the link between electromagnetic field analysis and drive circuits cannot be broken. In such cases, it is effective to analyze the drive circuit with MATLAB/Simulink or PSIM and do electromagnetic field analysis in JMAG.

For the External Circuit Link condition, choose the terminals you want to display in the external circuit simulator (Simulink, PSIM, etc.) (Fig. 3). As examples, you might think of the torque used for control in an external circuit and the electric potential, etc. for drive in JMAG. Linked analysis is achieved by connecting the connection terminals that appear from JMAG's block with another block in the external circuit simulator.

I would also like you to know about the further evolution of this condition in the JMAG-RT system for faster linked analysis. This is recommended when linking with SILS, MILS, and HILS systems. Settings are done via the JMAG-RT Library Manager.

Here is one example use. Line-start is one startup method for induction motors. It is often seen as a problem for the startup current to grow too large, but it is not possible to estimate it with electromagnetic field analysis alone due to the complexity of the drive circuit. With this condition, it becomes possible to link MATLAB/Simulink and JMAG (Fig. 4.) to evaluate the current (Fig. 5).

Fig. 3 External Circuit Link condition panel

Fig. 4 MATLAB/Simulink setting diagram

Fig. 5 Induction motor startup current evaluation

#### Frozen Permeability

This makes it possible to use past JMAG electromagnetic field analysis results to identify material properties in subsequent electromagnetic field analyses. For example, it is used in cases like the following:

- To separate a rotating machine's torque into magnet torque and reluctance torque.
- To precisely calculate the dynamic inductance with DC superposed in a reactor, etc.

Here I will discuss separating a rotating machine's torque. First, a normal electromagnetic field analysis is run on the rotating machine (hereafter called Analysis A). Next, an analysis is run of the magnetomotive force for the magnets only (hereafter called Analysis B). Frozen Permeability is set in Analysis B, with the results file from Analysis A specified. This way, material operating points from Analysis A are used in Analysis B.

If the results obtained from Analysis B are defined as the magnet torque, the reluctance torque is obtained by subtracting Analysis B's torque from Analysis A's (Fig. 6). An exact torque separation is difficult, but the torque can be separated here by assuming that the operating point does not change.

Fig. 6 Torque separation results for a rotating machine

#### Stress Distribution

This condition is used to display the deterioration of magnetic properties in magnetic steel sheet caused by stress.

Magnetic steel sheet's magnetic properties are known to deteriorate due to stress. This leads to concerns about increased loss. With JMAG's Stress Distribution condition, it is possible to set the stress for each part and replicate the materials' deterioration. For coupled magnetic field - structural analysis, the stress distribution obtained in the structural analysis can also be represented in the magnetic field analysis.

This can also be used while linking with other software. For example, in the example below, stress distribution results obtained in Abaqus are represented in JMAG for an iron loss calculation (Fig. 7).

Fig. 7 Iron loss calculation accounting for stress (linked to Abaqus)

#### Displacement

Magnetic circuits also change when a geometry is changed. The Displacement condition is for carrying out linked analyses in JMAG and Abaqus that take geometry changes into account.

For example, when a billet is subjected to compression, it is squashed and its geometry changes as seen below. Its magnetic properties may also deteriorate due to a rise in temperature. Magnetic field analysis considering these factors can be done by using this condition (Fig. 8).

The Displacement function can also be used for coupled magnetic field - structural analysis within JMAG.

Fig. 8 JMAG-Abaqus linked analysis using the Displacement condition

#### Reusing Demagnetization

Magnets that have already undergone irreversible demagnetization may be used in subsequent analyses. When using magnets that have already been used without being remagnetized, such as when reusing the rotor of a rotating machine, etc., there may be concerns about the effects of demagnetization caused during earlier operation. In JMAG, a 2-stage analysis can be done for a performance estimate in these cases.

In the example below, the first stage is an analysis of the rotating machine during operation. In the second stage analysis, the results from the first stage are set in the Reusing Demagnetization condition to express the demagnetized state.

The reduction in torque during reuse, due to the effects of irreversible demagnetization caused by the heat generated in the first stage, is estimated using analysis (Fig. 9).

Fig. 9 Torque reduction from irreversible demagnetization

### Modeling

There are probably many who think that complicated settings are needed to do high-precision analysis of complex phenomena. But with JMAG, complex analysis can be easily achieved through some tricks in the modeling process. I will now introduce some conditions that will allow you to use these tricks.

#### External Field

This condition is used for analysis of objects inside a uniform magnetic field. Normally, in order to produce a magnetic field in space, it is necessary to produce magnetomotive force by creating a coil as a finite element model and setting a Current condition, or by linking to a circuit. By using this condition, a uniform magnetic field can be generated without modeling a coil, therefore reducing modeling time.

For example, this is an effective function for evaluating the performance of a shield placed in a uniform magnetic field as shown in Fig. 10. It can be seen that in this model, the magnetic flux density in the area around the shield is high in the red boxes and low near the blue boxes. Shields are usually made of thin parts, and because JMAG also has functions for automatically creating a thin shell mesh, using these together is convenient.

Fig. 10 Magnetic flux density distribution around a shield

#### Gap

This condition is for setting very thin magnetic air gaps without generating a mesh.

For example, when a core is constructed with multiple core divisions, thin air gaps are created between them. Because air gaps cause strong magnetic resistance, it is preferable to generate a mesh for them in order to be sure of accurate analysis. However, the number of mesh elements will become much greater if the mesh is created for the thin air gaps, and more calculation time will be required. The ICCG convergence may also deteriorate due to the mesh becoming too thin.

With this function, this magnetic resistance can be expressed without the need to generate a mesh in the thin air gaps.

In the graph below, this condition is used to evaluate coil magnetic flux while varying the gap width of a reactor's center gap from 0.1 mm to 2 mm without generating a mesh (Fig. 11). Magnetic flux evaluation is made easy by using Case Control in JMAG-Designer.

Fig. 11 Relationship between gap width and magnetic flux

#### Insulation

Similar to the Gap condition, this condition is for expressing electric insulation without modeling the air gaps built into cores or magnets.

For example, magnets are sometimes divided to reduce eddy currents, but it can require a lot of work to create another model every time the number of divisions is changed if mesh is generated in the gaps.

The electric insulation can be modeled simply by setting this condition to the division faces or by checking the Insulation check box for the part. Precise evaluation of eddy currents is done easily without the need to change the mesh (Fig. 12).

Fig. 12 Evaluation of eddy current reduction due to magnet division

#### Section

This function makes it possible to automatically extract a 2D cross-section from a 3D model for analysis.

2D analysis is considered to provide adequate precision when the shaft length is long compared to the radius. For example, looking at a rotating machine's torque history, there is only a difference of a few percent between 3D and 2D analysis (Fig. 13). Analysis could be done by first obtaining a rough estimation in 2D analysis and then running 3D analysis when seeking more detailed precision. If this were the case, it would be a lot of work to make a separate model just for 2D analysis, but a 2D model can be automatically output from a 3D solid model using JMAG's Section condition (Fig. 14). The analysis could be done immediately without the need to set materials, conditions, etc. again.

Fig. 13 Torque history (comparison of 2D and 3D)

Fig. 14 Cross-section analysis settings

### Output

In addition to physical quantities such as torque and magnetic flux density, for which results are commonly evaluated, JMAG's magnetic field analysis can also output physical quantities with more specialized uses. Two of these physical quantities are presented below.

#### Magnetostriction

This is used for evaluating magnetic strain. Vibration caused by strain is particularly hard to ignore in large transformers, so it is helpful to be able to estimate it using analysis.

JMAG's Magnetostriction condition checks the magnetic field distribution obtained in magnetic field analysis against the magnetic flux density - strain properties, and converts it to magnetostriction. Vibration analysis is possible using this as the source of vibration (Fig. 15).

Fig. 15 Transformer using magnetostriction properties and magnetic flux density

#### Partial Inductance

This condition is used to output self- and mutual inductance generated in selected parts as a matrix model.

For example, inductance in the wiring seen in bus bars inside inverters, etc. varies widely depending on the geometry and spatial arrangements. Too large of an inductance can lead to surges during switching, so this must be improved.

However, actually measuring the inductance can only yield a value for the entire measurement target. This means that you cannot tell where in the wiring most of the inductance is. But by using this condition, you can see at a glance which areas to improve because the self- and mutual inductance is calculated in a matrix model for parts that have already been separated (Fig. 16).

In the example below, the surge voltage evaluated by the circuit simulator is reduced more than 10% by changing the geometry from the initial proposal based on examination of the inductance matrix of the bus bar parts (Fig. 17).

Fig. 16 Geometry improvement based on study of the inductance matrix

Fig. 17 Surge voltage reduction/

### Study Properties

Parameter tuning for time step settings, conversion, and iterative methods is done under Study Properties in JMAG-Designer.

#### Step

This contains settings for time steps. The number of steps, division method, end time, etc. are all set here.

#### Conversion

Periodic boundaries are often used in magnetic field analysis, and this converts those results to a full model for output. This is recommended because it allows results to be compared directly with actual measurements.

#### Circuit

This converts the parameters set to a circuit. It is effective when a partial model is being used.

With conversion, values such as vibration, resistance, and inductance for the power source specified in an analysis can be set to a full model.

#### Solver

This is where to handle: settings for Parallel Computing; Steady-State Approximate Transient Analysis that is run to make steadying faster in terms of time; and settings for Time Periodic Explicit Error Correction functions.

Under Parallel Computing, Shared Memory Multiprocessing (SMP) or Distributed Memory Multiprocessing (DMP) can be selected. Also, a GPU can be employed to increase speed.

Steady-State Approximate Transient Analysis is used when no delay is needed for starting up current, etc. generated by inductance effects in applications where there are no magnets (stationary devices, induction machines, etc.).

Time Periodic Explicit Error Correction is used for the same kinds of purposes, but can be used in PM motors, which have magnets (Fig. 18). It is also effective for rapid steadying of superimposed conditions such as switching transformers.

Fig. 18 SPM motor torque history

#### ICCG and Nonlinear

Iterative methods are used for solution-finding by JMAG solvers. Robust high-speed ICCG is used by the linear solver, and the Newton-Raphson method is used as a nonlinear iterative method. Convergence parameters for each of these are set here.

When convergence is slow in ICCG, setting the Acceleration Coefficient slightly higher may improve the convergence. Likewise, changing the default threshold value of nonlinear iterations from 1e-3 to around 1e-4 can help to increase precision when using nonlinear materials. There may not be many people who are even aware of these parameters, but I think it is a good idea to adjust parameters a little and see how sensitive calculation time and precision is to them, especially for those who are unsure whether their own analysis models are providing sufficiently fast and precise results.

### In Conclusion

Over the past two issues, we have presented a number of conditions used in magnetic field analysis in JMAG. I hope you have found some that you will be able to use in your own analyses. I also hope that you have gained more detailed knowledge of the conditions you already use on a regular basis.

JMAG's functions will continue to grow in the future. New conditions are often presented at our seminars and other events. It is our hope that you will be able to fully master all of these conditions.

(Kazuki Semba)