# Article: JMAG A to Z

## Issue 10 Structural Analysis from A to Z

In this series, I would like to introduce "Things that we should know" in JMAG, as well as some advantageous applications.

### Overview

Many JMAG users probably wouldn't have a clear idea of what to do if told to carry out a JMAG structural analysis. Many use JMAG for evaluation of electromagnetic phenomena, but when it comes to structural analysis many confine themselves to only limited uses, such as vibration phenomena. JMAG undoubtedly handles electromagnetic phenomena well, but we'd like to propose linking with heat transfer analysis or structural analysis as expanded functions to heighten analysis precision of those phenomenon. On the other hand, if the phenomena are simple, it's easy to do a good enough evaluation of physical phenomena using just heat transfer analysis or structural analysis.

This issue of A to Z will focus on how to handle particular types of phenomena using JMAG's structural analysis, as well as introduce material properties and various types of conditions so we can get you acquainted with structural analysis.

### Analysis model dimension

Geometries handled can be either 2D or 3D analysis. If you've modeled a 2D sketch thin sheet on your JMAG geometry editor, it can be used as a 2D analysis model. Fig. 1 shows a 2D thin sheet eigenmode example. If you've modeled a solid thin sheet on your JMAG geometry editor, it can be used as a 3D analysis model. Fig. 2 shows a 3D thin sheet eigenmode example. If using a 3D analysis, it's possible to evaluate the vertical distortion in the sheet.

Fig. 1 Thin sheet eigenmode example (2D analysis)

Fig. 2 Thin sheet eigenmode example (3D analysis)

### Setting the Analysis Type and Study

JMAG's structural analysis handles three types of analyses: static, eigenmode and frequency response analysis. Right click the JMAG-Designer Project Manager, select the type of analysis for the structural analysis and create the applicable study.

With structural analysis, it's possible to look for displacement or stress distribution if force is applied to a particular component. A featured phenomenon looks at handling analysis of stress distribution from centrifugal force, distortion through heat expansion, or press fit analysis if using a 2D model.

Under an eigenmode analysis, you can calculate how a particular component may distort based on its geometry, materials or constraining conditions (Fig. 3). Before analyzing vibration caused by such factors as electromagnetic force, it's possible to gain an idea of properties within the product that are susceptible to particular distortions.

Using a frequency response analysis, you can analyze vibration or sound pressure when an excitation force such as electromagnetic force operates on a particular component. Balancing frequency of the excitation force and eigenmode can cause generation of significant vibration or sound pressure.

Caution must be paid under structural analysis to mesh dependency. If using hexahedral elements, even the default first-order element enables analysis precision to be obtained. However, when using a tetrahedral element such as automatic mesh generation, select a secondary element from [Properties] in [Study]

The eigenmode and frequency response analyses will analyze objects in an eigenmode, so specify the desired eigenvalue starting frequency and eigenvalue. Calculate only the specified number in the lowest order mode of frequency higher than the starting frequency.

When evaluating vibration or sound pressure, specify a frequency and conduct a frequency response analysis. Calculate the size of vibrations from the relationship between the excitation force of the specified frequency component and the eigenmode. Defining a modal damping can specify the extent of effects a frequency's excitation force will have on frequencies around it. If the modal damping is 1, only frequencies matching the eigenmode will be defined as contributing to vibration. If the modal damping is 0, it will be an inappropriate setting as the excitation force of a particular frequency component will be seen as contributing to all eigenmodes.

Fig. 3 Eigenmode example

### Material Properties

Material properties used in structural analysis are density (g/cm^{3}), Young's Modulus (MPa), Shear Modulus (MPa) and Poisson's Ratio. With isotropic material, Young's Modulus, Shear Modulus and Poisson's Ratio establish the relationship in Formula (1). Consequently, setting just two objects that are not isotropic materials will suffice. Normally, you would set Young's Modulus and Poisson's Ratio (Fig. 4).

(1)

However, G is Shear Modulus, E is Young's Modulus and y is Poisson's Ratio.

Structural analysis can also handle thermal expansion phenomena based on temperature distribution. When handling this phenomena, specify the thermal expansion coefficient (1/deg C) and reference temperature (1/deg C), which will form the base (Fig. 1). Displacement will increase as the temperature rises.

When handling anisotropic materials, two setting methods are possible: One setting Young's Modulus for each direction and the other using matrix specifications. For the thermal coefficient, set for each direction. Piezoelectric analysis is possible for anisotropic materials. Set the piezoelectric constant and permittivity. Set the Permittivity in the [Electric Properties] tab.

Fig. 4 Mechanical properties tab in the Materials Editor dialog box

### Constraint Conditions

Structural analysis requires identification of an object to be fixed. Two situations significantly effect analysis results. These are specifying the place forming the standard for displacement and the second is being able to accurately simulate the constrained state on actual machinery. We'll now describe each of the constraint conditions.

#### Constraint

Can be used with all analysis types. Settings can be made to constrain movement of a specified place so that it will not morph in a particular direction. Settings are possible for all parts, part surfaces, edges and vertex. For example, if the analysis target is completely fixed to the floor, set the constraint conditions to constrain all directions (Fig. 5, left). If the model is a partial model, set the cross-section to normal constraint (Fig. 5, right).

Fig. 5 Examples of complete constraint (left) and normal constraint (right)

#### Rigid Body

Can be used with all analysis types. All specified places have an unchanged relative position and move as one. Settings are possible for all parts, part surfaces, edges and vertex. Use a spring condition to combine the spaces between vertices when there are two or more vertices and they have a degree of freedom.

#### Displacement

Can be used with all analysis types. Calculate stress distribution by specifying the amount of change a specified place will undergo in a specified direction. Settings are possible for all parts, part surfaces, edges and vertex. Setting a phase in a frequency response analysis enables simulation of phase displacement where distortion occurs between places to be displaced.

#### Rotation Periodic Boundary

Can be used with all analysis types. Specify the model cross-section and periodic angle when the analysis target is a partial model. Narrowing the analysis scope cuts calculation time and the memory needed for calculation.

#### Notes for applying constraints

Setting the rotation periodic boundary conditions for geometries with geometric periodicity can narrow the scope of the model in an effective method of reducing analysis costs. Conversely, using an ill-planned partial model for a structural analysis also runs the risk of an evaluation overlooking an eigenmode generated using actual machinery. For example, think about half models and quarter models (Fig. 6). Periodic boundary conditions are set for both of these. But there are times when a quarter model cannot simulate an eigenmode a half model has simulated. Take note of the fixed state you're working with when setting the constraint conditions.

Fig. 6 Example of an eigenmode capable of simulating a quarter model (Two upper images)

Example of an eigenmode incapable of simulating a quarter model (Lower image)

### Load Conditions

Force exerted on the object will distort it. Set this force in the Load Conditions. We'll now describe each of the load conditions.

#### Concentrated Load

Useable in static and frequency response analyses. Simulates conditions where force is exerted on a particular point. The unit of measurement is N. In a frequency response analysis, you can also set the phase.

#### Pressure Load

Useable in static and frequency response analyses. Simulates contact pressure being applied to a particular surface. The unit of measurement is MPa. In a frequency response analysis, you can also set the phase.

#### Volume Load

Useable in static and frequency response analyses. Simulates a body force being applied to all parts. The unit of measurement is N. This can be used, for example, to see what happens when gravitational force or Lorentz force is exerted on all parts. In a frequency response analysis, you can also set the phase.

#### Acceleration Load

Can only be used in a static analysis. Simulates acceleration being applied to all parts. The unit of measurement is m/s^{2}. This can be used, for example, to specify gravitational acceleration when slackness is generated after exerting gravitational force on all parts (Fig. 7).

Fig. 7 A work piece slackened by gravitational acceleration

#### Centrifugal Force

Can only be used in a static analysis. This looks for the stress distribution generated within a part centrifugal force exerted on a part at high speed rotation. The unit is r/min. This is used, for example, with a peeling analysis of a magnet when surface permanent magnet (SPM) motors are at high speed rotation. Set conditions for the high speed rotation parts (Fig. 8).

Fig. 8 Distortion caused by centrifugal force (Left: Complete adhesion; Right: Partial peeling)

#### Electromagnetic Force

Useable in static and frequency response analyses. Analyze stress or distortion or conduct a vibration analysis based on the electromagnetic force sought in a magnetic field analysis (Fig. 9). Set for the parts.

Fig. 9 Example of extracting frequency components from electromagnetic force

#### Temperature Load

Can only be used in a static analysis. Calculate stress or displacement amount with a thermal expansion analysis based on a specified temperature or temperature distribution obtained from a thermal analysis (Fig. 10). Units of measurement include deg C. Set all parts, part surfaces, edges and vertex.

Fig. 10 Distortion caused by thermal expansion

#### Press Fit

Can only be used in a 2D static analysis. Selecting an edge between two objects and specifying the interference range enables calculation of stress distribution during a press fit (Fig. 11). Units for measurement include mm because it is the range of interference being specified.

Fig. 11 Principal stress distribution obtained from press fit analysis

### Spring-Mass

Gradually combining the space between two objects enables simplification of a particular part. Two functions are described below.

#### Spring

Can be used with all analysis types. Simulates gradual combination of two specified areas between vertices and joined by a spring. The unit of measurement is N/m. Used rigid body conditions if the relative position is completely fixed.

#### Concentrated Mass

Useable in eigenmode and frequency response analyses. Can be handled as a point mass without creating a detailed model of a part's geometry. The unit of measurement is g. The point mass and a modeled geometry and be joined by such items as spring conditions.

### Electric Potential Boundary

Analysis using piezoelectric materials is possible. Set the anisotropy material in Parts and specify the piezoelectric constant and permittivity. Setting electric potential conducts a piezoelectric analysis when a particular part comes into contact with an electrode. Consequently, this evaluates factors such as electric potential distribution or the state of distortion. Settings are possible for all parts, part surfaces, edges and vertex. The unit of measurement is V. The phase of electric potential distribution can be set in eigenmode and frequency response analyses.

### Output/Sound Pressure

When evaluating vibration in a frequency response analysis, it is also possible to evaluate the radiated sound spreading in the area after being generated by acceleration from the object surface. Two types of radiated sound evaluation plane can be used, spherical and cylindrical (Fig. 12).

Fig. 12 Example of sound pressure distribution (Left: No peeling on spacer; Right: Peeling on spacer)

### In Closing

In this edition I have talked about the conditions used in a structural analysis and described the meaning of its functions and how to use them. There's still so much more we want to tell you about conditions, so I plan to continue with my descriptions in the next edition, too.

(Hiroshi Hashimoto)