Nonlinear Damper-Blade Coupling Calculations Reduced to Essentials

Abstract

To improve the numerical efficiency of the nonlinear calculations required for the dynamic response of damped turbine blades, the authors recently introduced the platform centered reduction (PCR) method which represents the platform as a rigid body subject to a single moment representing the effect of forces from adjacent dampers. The concept of a” basic cycle” is now introduced to simplify—without introducing additional approximations—the functional relationship between the moment on the platform due to the frictional forces and its angle of rotation, both of which are calculated around an axis parallel to the main axis of neck bending. It is shown that, for the first bending mode of vibration, this function completely characterizes the damper-platform assembly, such that for rotation values greater than the” base cycle,” the values of the real and imaginary components of the damper-platform flexural stiffness are obtained a priori, without having to repeat the contact cycle calculations at each amplitude change. The advantage of this approach for numerical calculations and the convenience of having a model focused on the essential aspects of the engineering problem of best coupling between damper and blade are demonstrated. Also, considering the improvements introduced, the” designer's diagram,” already proposed by these authors, is revised. The advantage lies in representing the essential, yet adequate approximation in the relationship between the maximum alternating bending stress due to vibration and the values of the excitation force on the airfoil, values each associated with a corresponding “oscillation amplitude/resonance frequency” pair.