I am using two ball bearings from SKF Stuck (W 603 and W 618). But I do not know their damping coefficients and I do not want to bother testing the bearings to find their damping coefficient. An approximate answer would be sufficient.
For what it is worth. The values mentioned are a bit higher than the Steel material damping, 5E-4 to 5E-5. Sounds reasonable to me as there should be a bit of friction, relaxation and some sound radiation in there as well.
What are you really meaning by "damping" for a moving component like a (ball?) bearing?
In its nominal function of supporting a rotating part, the bearing degrades some energy from the rotation but it is efficiency, not damping. When the rotor is stopped and the machine subject to vibration or shocks, yes the bearing introduces some damping between the stator movement and the shaft movement, and this is a non-linear phenomenon involving primarily the lubricant properties hence the temperature. The 5e-3 value proposed above is realistic for very low vibration levels (and warm temperatures) but damping might become far more important at high level when friction occurs between balls and inner/outer shafts! If you want to assess the damping provided by the bearings to the vibrations while rotating, it turns to an extremely complex problem involving the respective structural dynamics of foundation, stator and rotor...
(And if you would use fluid bearings, its another story too...)
Sorry, but the art of vibration control is complex!!!
As stated by Mr Garnier, damping can be many things and a bearing to some degree is nonlinear - it has to be as it is a moving object and hence, cannot have time invariant properties..
True, then again, as our understanding on the concept of damping is rather poor, it almost always boils down to one of cheating with simplified models of the loss mechanisms and this still is when considering things to be linear.
That said, I believe the question was asked when modelling a bearing as a complex spring element, i.e. an element such as Kcplx = K*(1 +j*eta), where eta is the structural loss factor. This model, albeit much simpler than reality and probably not usable for all bearings or a bearing in all situations, suffice for practical analysis in many situations, e.g. rotor dynamics and similar.
Again, the model can be criticized for missing simple things like physical distance as a mathematical spring is a zero length element, etc. Within the bounds of usability for the task in hand, it can still provide usable analysis. The trick lies in knowing how far a simplified description can be pushed before its trustworthiness breaks down.
For those interested, some ramblings of mine on the topic of damping is found here. https://qringtech.com/2014/06/22/designed-damping-types-mechanisms-application-limitation/
Some thoughts on simulation, test, quality assurance and optimization are provided here. https://qringtech.com/learnmore/why-simulate-measure-correlate-automate/