### Objectives

This article shows how to use MANATEE software dedicated to the fast electromagnetic and NVH simulation of electrical machines to calculate the **effect of eccentricities on noise and vibrations due to electromagnetic excitations**.

### Principle

MANATEE can simulate both** static and dynamic eccentricities, as well as radial and axial eccentricities**. Static eccentricity is known to change magnetic force wavenumbers (sidebands +/-1), while dynamic eccentricity changes both magnetic force wavenumbers and excitation frequencies. Therefore a 10% dynamic eccentricity is always worse compared to a 10% static eccentricity in terms of acoustic noise and vibration levels. Dynamic eccentricity can change the frequency content of vibration and sound spectra, contrary to static eccentricity.

Eccentricity modelling is available for all electromagnetic models of MANATEE based on multi-slice techniques. However, due to large computing time required by electromagnetic finite element model, it is recommended to use the permeance/mmf (PMMF) analytical electromagnetic model , where the first order harmonics due to eccentricities are accounted for in the electromagnetic field distribution.

Note that both **static and dynamic eccentricity effects on noise and vibrations** due to magnetic forces can be simulated at the same time, and that the simulation of eccentricities does not increase the calculation time in PMMF, contrary to a finite element method approach.

A more complete example is available in the SCIM tutorial.

### GUI implementation

In the GUI, all eccentricities are defined in the Fault panel. TBC

### Scripting implementation

The permeance/mmf analytical electromagnetic model is activated using

`Input.Simu.type_Bmodel=0`

##### Static radial eccentricity

To define a static eccentricity (10% of mechanical airgap width in this example), one must set (in the project file):

`Input.Simu.sta_ecc_rate=0.1;`

##### Dynamic radial eccentricity

Similarly one can introduce 15% dynamic eccentricity (relative to the mechanical airgap width) by setting:

`Input.Simu.dyn_ecc_rate=0.15; `

##### Axial eccentricity

The degrees of static and dynamic axial eccentricities are defined respectively with

`Input.Simu.Ksta=0`

Input.Simu.Kdyn=0

The airgap is assumed to vary linearly along the axial length of the machine. A factor Kdyn or Ksta=2 models symmetrical eccentricity (maximum eccentricity at DE and NDE) while Kdyn or Ksta=1 models asymmetrical eccentricity (maximum eccentricity at DE, no eccentricity at NDE).

### Plot commands

One can check that the static eccentricity is correctly taken into account by plotting the permeance function per unit area along the airgap (plot_Per_space), which is roughly given by the inverse of the airgap width:

For dynamic eccentricities, both the permeance variations with space and time should be affected (plot_Per_time)

### Validation cases

EM_SCIM_NL_013 favorably compares FEMM and permeance/mmf model when introducing static eccentricity on a squirrel cage induction machine.

### See also

An uneven airgap (non circular stator or rotor bore radius) can also be simulated in MANATEE.