Prediction of periodic forced response of frictionally constrained turbine blades

In turbine engine design, friction dampers are often employed to attenuate the turbine blade vibration and at the same time to increase aeroelastic stability of the turbine blades. The periodic forced response of turbine blades with shroud contacts and wedge dampers are investigated in this research. During the engine operation, the turbine blades may bend and twist to cause the friction contacts to experience friction constraint. The resulting constraint force can add friction damping as well as nonlinear spring force to the bladed disk system. When subjecting to periodic excitation, a 3D shroud contact model and a dual-interface friction model are employed to simulate the hysteresis loops of the constrained forces at the contact points of turbine bladed with shroud contacts or wedge dampers. The constrained forces can be considered as feedback forces that influence the response of the friction contacts. By using the Multi-Harmonic Balance Method along with Fast Fourier Transform, the constrained force can be approximated by a series of harmonic functions and this approach results in a set of nonlinear algebraic equations, which can be solved iteratively to yield the periodic response of blades having 3D nonlinear shroud constraint or wedge dampers.; It is shown that the resonant frequency shifts due to the additional spring constant introduced by the frictional constraint, and forced response is damped due to the additional friction damping introduced by frictional slip. In addition, the intermittent interface separation can cause multi-valued response that leads to jump phenomena. The predicted results are also compared with those of the direct time integration method so as to validate the proposed method, and the effect of super-harmonic components on the forced response and jump phenomenon is examined. It is shown that super-harmonic components may induce significant changes of the frictional characteristics such as the transitions between stick, slip and separation, and may affect the prediction of forced response and jump phenomena. It is demonstrated that the Multi-Harmonic Balance Method can predict accurately and efficiently for the periodic forced response by including the super-harmonic components in the analysis.