### Definition

In structural dynamics, **damping** is a general term to name all physical phenomena dissipating vibrational energy. Viscous damping describes the energy loss arising from specific forces which are proportional and contrary to velocity displacement. One can show that the maximum dynamic displacement of a linear mass-spring system at resonance is proportional to

`U_{max}=\frac{1}{2 \xi} `

**The larger is the damping, the lower is the vibration and resulting noise.** When relating damping to acoustic noise one can show that the variation of the sound pressure level in dB is given by

`\Delta L_{w}=-20 \log(\frac{ \xi_{2}}{ \xi_{1}}) `

Therefore doubling the damping gives 6 dB noise reduction. Increasing damping from 0.5% to 2% gives 12 dB noise reduction.

**Modal damping** describes damping of a specific structural mode. Each structural mode has a particular modal shape which dissipates vibrational energy differently.

### Application to e-NVH

In electrical machines, several **sources of damping ** occur:

- structural or hysteresis material damping (e.g. due to resin impregnation, insulation varnish on copper coils)
- dry or solid friction Coulomb damping (e.g. friction between lamination sheets, friction between copper strands)
- viscous damping (e.g. electromagnetic damping)

Electromagnetic damping can be neglected and **most of the damping comes from the winding of the stator**. Outer rotor with permanent magnets have no winding and their modal damping is therefore much smaller, which also explains why outrunner motors can be particularly noisy.

**Damping cannot be calculated theoretically**, and damping has a high influence on maximum vibration and noise levels. Damping is therefore a major source of uncertainty when calculating electromagnetically-excited noise and vibrations. As damping mainly depends on winding impregnation, damping depends on the winding type (e.g. preformed or random wires), insulation type and impregnation type (e.g. dry, VPI, potting), as well as resin curing cycle and operating temperature. It is therefore highly recommended to measure the modal damping of the electric machine along its dedicated manufacturing process to be able to improve NVH simulation accuracy. EOMYS can assist measure experimental damping using specialized e-NVH tests.

Based on EOMYS experience, **modal damping can vary from 0.5% to 4%}. An average value of 2% is recommended in e-NVH simulation with MANATEE software.**

### Application to MANATEE

In MANATEE software damping can be imposed as a constant damping value, or enforced as modal damping for each structural mode of the stator or rotor. This way, the results of an experimental modal analysis can be used in the simulation.

When using a constant modal damping of 1% for all structural modes, the accuracy of noise and vibration levels at resonance might vary of +/- 6 dB compared to measurements. This is not linked to MANATEE software but to any NVH simulation model that is not fit with experiments. However, this uncertainty on the absolute vibration levels does not prevent to have reliable results when comparing in relative values the electromagnetically-excited noise and vibration levels of two electrical machines in MANATEE.