# Vibrations in Electric Motors - MpCCI FSIMapper Case Study

Motors with MagNetElectromagnetic forces in motors excite structural vibrations. They lead to material failure and to noise in the surrounding area.

To predict vibrations in early development phases, FSIMapper, a translation tool from Fraunhofer SCAI, provides the possibility to transfer the electromagnetic forces to structural NVH analyses.

In this case study we consider a 4-pole-24-slots electric motor, which is modeled in MagNet by a quarter section. The rotor rotates with a frequency of 30 Hz and the coils exhibit an odd parity. We are interested in the vibrational behavior of the full stator.

EM and CSM usually have incompatible mesh discretization and even non-matching geometry details. FSIMapper can handle such non-matching model definitions.

Vibrational analyses such as frequency response or acoustic simulations are performed in frequency domain. The excitation is given as complex data over a frequency range.

FSIMapper provides the possibility to process transient MagNet results by Fourier transformation in order to create the corresponding loading for vibrational analyses.

The following excerpts are from the "Vibrations in Electric Motors" case study by Fraunhofer SCAI. The original case study can be found on their website at http://www.scai.fraunhofer.de/.

### METHODS and RESULTS

## Motivation and Problem Description

For this purpose MagNet performs a transient simulation and the results are exported into a VTK-file. FSIMapper maps the data to the target MSC.Nastran mesh and processes the data by Fourier transformation. In this way the loading for a vibrational or acoustic analysis is created.

As result FSIMapper creates an ASCII file which comprises the electromagnetic loading for a frequency response analysis in MSC.Nastran bulk data syntax. It is used in the target simulation.

## MagNet Simulation

The MagNet model is simulated in the following way:

- Transient 3D with Motion
- ¼ turn using 180 time steps
- Constant time step (necessary for Fourier transformation)

The electromagnetic forces are available for each time step as surface force density (SFD).

## MagNet Export

The surface force density (SFD) is exported by the MagNet Exporter for MpCCI

- Select the component Stator from MagNet's object tree
- Open the exporter by Extensions->Exporter for MpCCI
- put in the time span for a ¼ turn

## MSC.Nastran Target Mesh File

The CSM mesh models the full stator by first order hexa and penta elements.

## Mapping Surface Definition

For the mapping process, elements are created on the stator's surface. It is necessary that the surface elements use the same nodes as the volume mesh.

## MpCCI FSIMapper

FSIMapper is an easy to use tool, which is available as GUI and in batch mode. The GUI is subdivided into different panels where the mapping configuration is applied.

Source (left column)

- MagNet as source simulation code
- file location of the exported SFD-Stator.vtk which contains the SFD
- unit system used in the VTK-file: m-kg-s
- SFD as force quantity

Target (right column)

- MSC.Nastran as target simulation code
- file location of the MSC.Nastran mesh stator_surface.bdf
- mapping surface
- unit system used in the mesh file: mm-t-s

**Cyclic Symmetry Transformation**

Because of the periodicity of the source model, a cyclic symmetric transformation has to be applied to the mesh and the quantity. In the Transformation panel, all relevant information is given to create the corresponding full model.

**Fourier Transformation**

To convert the transient electromagnetic forces to frequency domain, as it is presumed by frequency response analyses, check Apply Fourier Transformation in the Result panel.

## Mapping Result

Pressing the Map button starts the mapping. The quarter section of the stator surface is revolved in order to create the full model.

## MSC.Nastran surface mesh

The SFD of all 180 time steps is mapped to the MSC.Nastran surface mesh. The MpCCI Visualizer shows the mapping quality for each time step.

## Fourier Transformation of the Transient Forces

The Fourier transformation of the transient forces is done for all surface nodes of the target mesh.

With 180 time steps the transformation results in 91 frequency components, including 0Hz which corresponds to the mean value comprised in the transient nodal force.

The force excitations (described as complex data) can be visualized for each frequency component as corresponding transient fluctuation.

## Target Simulation

The mapping surface elements have to be excluded from the simulation since they would provide additional stiffness. The definition of the frequency response analysis includes the FSIMapper output file.

For each node a frequency dependent complex displacement vector is calculated. Using the inverse Fourier transformation (iFFT), these data can be transferred back to the time domain.

## Deformation of the Structure

The displacement calculated at 0Hz represents the mean deformation of the structure. At 120Hz the structural response (displacement) is the highest. The following frequencies play a decreasing role for the total vibrational response.

The frequency spectrum of stress oscillation amplitudes can be used for fatigue analyses.

Also, the acoustic response can be calculated when modeling the surrounding air.