Reliable material damping ratio determination in machine tool structures

The determination of material damping ratios in machine tools is afflicted with considerable uncertainties. For the estimation of damping ratios different methods are available, each with specific model assumptions and parameters. Depending on the experience already gained with one method, the quality of the resulting values therefore can vary considerably. This paper proposes the simultaneous application of two different calculation methods, namely the logarithmic decrement and the bandwidth method, to the same measured signal. Assuming a decaying, time-limited and very lightly damped response signal, both methods cannot be applied in their original form. Therefore a filter-based logarithmic decrement and a frequency resolution enhanced bandwidth method are used. To demonstrate the capability of the approach, both methods are applied to an analytical three-degree-of-freedom system derived from a measured structure. The damping ratios yielded by both methods deviate less than 1 % from the analytical value. Furthermore, in a real measurement with uncertain system properties and parameter choice, the combined use of both methods can be used to assess the uncertainty of the obtained values. The capability of the proposed method is demonstrated on the basis of the measurement of a small machine tool component.