Robust design of turbine blades with friction contacts in the presence of multiple response levels

Dry friction damping is a widely used solution to mitigate vibrations of turbine blades. At design stage, the computation of the forced response of assemblies of bodies in contact (whose relative motion could result in dry friction damping) could give non-unique solutions due to the possibility of having different static equilibria. Infinite possible vibratory levels in a range are hence possible. A desirable condition for designers is to deal with systems whose response boundaries are not far from each other, i.e. with a low scatter in the response. For systems with multiple vibration levels, the notion of robustness (a robust system has a small response scatter, and viceversa), is particularly important. A robust design is hence needed for such assemblies. Once a design parameter is identified, two possible approaches are possible to accomplish this task. The so-called manual approach explores a certain number of values of the design parameter belonging to a certain interval, and chooses the most robust configuration among those calculated. This computation could result in a huge effort if the number of considered values of the design parameter is high. To overcome this issue, a second approach is here proposed. It is based on a Nested Optimization Algorithm (NOA), which consists in two levels of optimization in order to directly find the most robust configuration in the considered range for the design parameter. In this paper, NOA is applied to a particular test case consisting in a lumped-parameter system simulating three blades with two UPDs interposed among them. Such a system provides the necessary coupling between different contact interfaces necessary to obtain multiple response levels. In addition, it is useful to investigate the mutual interaction among different UPDs. Results of NOA are presented together with the results of the manual approach in order to give a validation of the double optimization. Dependence of the response scatter from the contact states of the interfaces is also investigated.