On the non-uniqueness of friction forces and the systematic computation of dynamic response boundaries for turbine bladed disks with contacts

Turbine bladed disks with friction contacts may have a large scattering of dynamic response amplitudes in laboratory conditions even for two consecutive tests. The non-repeatability of experimental studies might directly be related to a physical phenomenon associated with an uncertainty in contact forces. This observation has also been computationally shown in many studies with non-unique contact forces and multiple responses obtained for the same set of inputs. This study presents a numerical aspect and a deeper insight for understanding the variability observed in the periodic vibration analysis of turbine bladed disks with friction damping. A novel method based on an optimization algorithm is proposed to systematically detect the nonlinear dynamic response boundaries. The main idea of the developed approach is to minimize the system loss factor which ultimately determines the damping ability of the structure. In the meanwhile, algebraic set of dynamic balance equations are simultaneously imposed as the nonlinear constraints to be satisfied. In this way, two cases with the minimum values of the positive and negative loss factor determine the upper and the lower boundaries, respectively. The method is validated and demonstrated on a realistic turbine bladed disk with friction interfaces on the shrouds and on the blade-disk interface. Several case studies are performed on different cases by using the state of the art 2D friction model with varying normal load. The results show that the limits of the variability range can be successfully captured by utilizing the offered optimization algorithm. The great contribution of the study is also discussed with some accompanying numerical drawbacks.