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This paper describes a theoretical model for analyzing the dynamic characteristics of wedge-shaped underplatform dampers for turbine blades, with the objective that this model can be used to minimize the need for conducting expensive experiments for optimizing such dampers. The theoretical model presented in the paper has several distinct features to achieve this objective including: (i) it makes use of experimentally measured contact characteristics (hysteresis loops) for description of the basic contact behavior of a given material combination with representative surface finish, (ii) the damper motion between the blade platform locations is determined according to the motion of the platforms, (iii) three-dimensional damper motion is included in the model, and (iv) normal load variation across the contact surfaces during vibration is included, thereby accommodating contact opening and closing during vibration. A dedicated nonlinear vibration analysis program has been developed for this study and predictions have been verified against experimental data obtained from two test rigs. Two cantilever beams were used to simulate turbine blades with real underplatform dampers in the first experiment. The second experiment comprised real turbine blades with real underplatform damper. Correlation of the predictions and the experimental results revealed that the analysis can predict (i) the optimum damping condition, (ii) the amount of response reduction, and (iii) the natural frequency shift caused by friction dampers, all with acceptable accuracy. It has also been shown that the most commonly used underplatform dampers in practice are prone to rolling motion, an effect which reduces the damping in certain modes of vibration usually described as the lower nodal diameter bladed-disk modes.

Although considerable effort has been devoted to the formulation of predictive models of friction damper behavior in turbomachinery applications, especially for turbine blades, the problem is far from being solved due to the complex nonlinear behavior of the contact surfaces. This paper primarily focuses on analytical and numerical aspects of the problem and addresses the problem in the frequency domain while exploring the viability of equivalent time-domain alternatives. The distinct features of this work are: (i) the modelling of nonlinear friction damper behavior as an equivalent amplitude-dependent complex stiffness via a first-order harmonic balance method (HBM), (ii) the use of sine sweep excitation in time-marching analysis, (iii) the application of the methodology to numerical test cases, including an idealised 3D turbine blade model with several friction dampers, (iv) the verification of the numerical findings using experimental data, and (v) a detailed assessment of the suitability of HBM for the analysis of structures with friction dampers.