How to simulate an uneven airgap?

Objectives

This article shows how to use MANATEE software specialized in noise calculation of electric motors to calculate the effect of uneven airgap on noise and vibrations due to electromagnetic excitations.

Principle

The non-circularity of stator and rotor laminations can be due to:

• weldings deformation
• segmentation effect -
• deformation during transportation-
• effect of weight
• manufacturing tolerances

The non-circularity of the laminations modulate magnetic forces and therefore significantly change the vibration and acoustic behaviour of the machine under Maxwell forces. Stator non circular bore radius only introduces new magnetic force wavenumbers (it represents a generalization of static eccentricity) while rotor non circular bore radius introduces both new magnetic force wavenumbers and frequencies (it represents a generalization of dynamic eccentricity). Rotor asymmetry can change the frequency content of vibration and sound spectra, contrary to stator asymmetry.

Both effects can be studied in MANATEE using the permeance / mmf electromagnetic model. Two types of uneven airgap shapes can be defined in MANATEE:

• periodic change of the lamination shape (“flower-shape”)
• user-defined shape

GUI implementation

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

Scripting implementation

To study the effect of a periodic change of the lamination shape (“flower-shape”), you have to set the following Input (in the project file):

```Input.Simu.type_rotor_deflection = 1;  %flower shape abs(cos) Input.Simu.Nsegs = 6;                %number of maximum Input.Simu.deflection_rates=0.2;  %nominal airgap deviation```

This indicates that a 6 segment or 6 weldings stator is considered with +/- 20% deflection from the nominal airgap. The last parameter ensure that the stator periodic deflections due to segmentations and weldings are taken into account in the model.

To model an elliptical shape of the stator bore radius (variation of +/-10% of the nominal 2mm airgap in the following example) one can define the following user defined shape:

```Input.Simu.type_stator_deflection = 3; %user defined vector Input.Simu.deflection_rates=(10/100)*2e-3*cos(2*linspace(0,2*pi,200);```

Plot commands

The shape of the airgap can be checked with the command plot_airgap_shape :

Airgap shape
plot_airgap_shape

A display amplification factor is used to plot the non-circularities in the structure Plot, you can change it by directly specifying

`Input.Plot.disp_ampfactor=100`

TBC