# How to determine the damping coefficient?

For a project using rotating voice coils motor in order to balance a system I need to determine the damping coefficient of these voice coils in order to insert it in a ADAMS model and analyse its performances.

Starting with the oscillation data obtained during a physical test on a mock-up, I used the Matlab tool vibration data in order to find the damping ratio of these voices coils. To find this value the vibrationdata tool makes a FFT and then a "Half-Power Bandwidth Curve fit" method... At the end I got : damping ratio = 0.061, as well as the natural frequency $(f_n)$ 3.1Hz and the Q factor 5.8

As I was not sure about either to insert a damping coefficient or damping ratio value in my ADAMS model, I sent an email to MSC and they answered me "In Adams, bushing required the damping coefficient values, in the units as: - newton-sec/meter - newton-meter-sec/deg"

So, I have to calculate the damping_coefficient using the damping_ratio, natural frequency...

This is obtained using the expression : $$c = 2\,m\omega_n \times \text{(damping ratio)}$$ with $\omega_n = 2\pi f_n$

I get a certain value but I am totally not sure about the use of the mass $m$ in this expression as I want to get the damping coefficient of a rotating system... Can I directly replace this mass by the mass inertia coefficient around which the system rotate ($I_{yy}$ for example from the Matrix) ? Or what else should I do ? I would like to specify a damping coefficient in Translation in my ADAMS model...

On this awful drawing I just tried to sketch the two rotating voice coils in blacks with the magnets (right and left) rotating around the axis y... I would like to know what should I consider in term of mass or inertia to find the damping coefficient in the expression above.

• I am sorry you are still using ADAMS. – ja72 Jan 29 '16 at 15:32

You need to find the effective mass of a rotating rod at the point where the damping force is applied. This equals $$m_{eff} = \frac{I_{pivot}}{\ell^2}$$ where $I_{pivot}$ is the MMOI about the pivot, and $\ell$ is the distance where the force is applied to the pivot.