A random sampling strategy for tuning contact parameters of underplatform dampers

All numerical models of friction damped bladed arrays require knowledge of contact-friction parameters, which are established either through direct frictional measurements, done with the help of a separate single contact test arrangement, or by fine tuning the parameters in the numerical model of the real damping device and comparing the experimental response of a damped blade against its computed response. Recent results from direct measurements on underplatform dampers and the subsequent cross-comparison of experimental and numerical results have put into evidence several features which are usually neglected in FE models of damper-blade systems: – markedly different friction coefficients at different contact points; – friction coefficients evolving with time and cycle number towards a stable shape, in a systematic and repeatable manner with dramatic consequences on the shape of the hysteresis cycle and on dissipated energy; – particular cases where minimal variations in the friction coefficients lead to gross changes of the damper behavior; Identifying the contact parameters to assure the best match between model and experimental results becomes crucial to guarantee that the validated damper model will produce the correct cyclic forces on the blades during vibrational motion. While the tuning process described in the previous papers was a search based on the progressive refinement whose results depended on the operator’s ability to match different patterns of the model and experimental results, this paper dwells on a more objective and controllable method based on properly chosen indicators. The latter method is based on a sampling technique (Latin Hypercube) which produces a large number of solutions (in the present case 5000) on the basis of randomized extractions of contact parameters (in the present case 5) between given boundaries. An advantage of this method is a systematic exploration of the influence of each input contact parameter on the collection of output indicators, considered acceptable according to predetermined criteria. The main indicators suited for the purpose are three, i.e., the relative errors on the real and imaginary parts of the HBM complex spring equivalent to the hysteresis cycle and a measure of shape similarity between the experimental and simulated cycle. The paper shows the selection procedure which has been adopted to produce the final set of eligible solutions, which are further reduced by applying a secondary indicator based on the similarity of a kinematical parameter. In this paper this parameter is chosen to be a measure of the shape similarity of the damper rotationduring the hysteresis cycle.