### Static eccentricity

A new project is set-up in tuto_test_SCIM_09 by copy/paste tuto_test_SCIM_01.

The following parameters are modified for introducing 10% static eccentricity:

`Input.Simu.sta_ecc_rate=0.1;`

In the GUI, sta_ecc_rate is in the Fault group.

One can check that 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 :

The variable speed acoustic contour plot shows that some new resonance appear, for instant with the mode (3,0). The particularity of static eccentricity is to modulate all slotting exciting force wavenumbers by +/-1, so the second wavenumber force wave (r=2) that was responsible for the main resonance is now doubled with one excitation of wavenumber r=1 and one excitation of wavenumber r=3 with same excitation frequencies (plot_VS_ASPL_overall and plot_VS_ASPL_sonagram)

### Dynamic eccentricity

Similarly one can introduce 15% dynamic eccentricity (relative to the airgap width) by putting Input.Simu.dyn_ecc_rate=0.15; (In the GUI, dyn_ecc_rate is in the Fault group) This time, both the permeance variations with space and time should be affected (plot_Per_time)

The sound pressure level at variable speed is given by (plot_VS_ASPL_overall and plot_VS_ASPL_sonagram):

One can notice that similarly to static eccentricity case, the odd circumferential mode (3,0) is excited, leading to same acoustic pressure at resonance. However, the waterfall plot of the acoustic noise is a bit different, one can see that the excitation is wider in the frequency range.

This is because dynamic eccentricity not only modulates the existing force harmonics in space as for static eccentricity case, but also in time. This time modulation adds some sidebands at the magnetic force frequencies plus or minus the mechanical frequency. Close to the resonance with the (3,0) mode the fundamental is 150 Hz so the mechanical frequency is 50 Hz. To see the sidebands, the spectrum resolution should be therefore lower than 50 Hz. At nominal speed of 1200 rpm (60 Hz) the resolution is given in the text output (Spectrum time resolution df)

At 150 Hz it will become 20*150/60=50 Hz, so the resolution of the spectra at 150 Hz speed is too low to actually capture the time harmonics due to dynamic eccentricities. To compensate that one can simply increase the number of revolutions to **Input.Simu.Nrev = 2; **

Now the noise spectrogram becomes :

Two lines can be clearly distinguished. By zooming one can observe that one of them resonates with the (2,0) mode and that the other resonates with the (3,0) mode. The modal contribution due to eccentricity can also be checked with plot_VS_ASWL_modal_cont

One can clearly see that the eccentricity has introduced odd wavenumber force waves.

Note that both static and dynamic eccentricity effect 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, contrary to a finite element method approach.

### Diagonal or axial eccentricity

Axial variations of static and dynamic eccentricity can be included in MANATEE. The axial variation of eccentricity is assumed to be linear and is tuned with

`Input.Simu.Kdyn`

Input.Simu.Ksta

A new project is set-up in tuto_test_SCIM_31 by copy/paste tuto_test_SCIM_01. The following parameters are modified for introducing 10% static eccentricity:

`Input.Simu.sta_ecc_rate=0.1;`

A symmetrical diagonal eccentricity (null eccentricity in the middle of the lamination, maximal eccentricity at lamination extremities) is defined with

`Input.Simu.Ksta=2`

The global electromagnetic forces and moments experienced by the stator can be plot using plot_FxFy:

One can see that a static non zero bending moment MY tends to bring the stator closer to the rotor.