Modeling Underplatform Dampers for Turbine Blades: a Refined Approach in the Frequency Domain.

Friction damping is one of the most exploited systems of passive control of the vibration of mechanical systems. In order to mitigate vibration of turbine blades, friction dampers are commonly included in the bladed disk design. A common type of blade-to-blade friction dampers are the so-called underplatform dampers (UPDs); these are metal devices placed under the blade platforms and held in contact with them by the centrifugal force acting during rotation. The effectiveness of UPDs to dissipate energy by friction and reduce vibration amplitude depends mostly on the damper geometry and material and on the static loads pressing the damper against the blade platforms. The common procedure used to estimate the static loads acting on UPDs consists in decoupling the static and the dynamic balance of the damper. A preliminary static analysis of the contact is performed in order to compute the static pressure distribution over the damper/blade interfaces, assuming that it does not change when vibration occurs. In this paper a coupled approach is proposed. The static and the dynamic displacements of blade and UPD are coupled together during the forced response calculation. Both the primary structure (the bladed disk) and the secondary structure (the damper) are modeled by finite elements and linked together by contact elements, allowing for stick, slip and lift off states, placed between each pair of contact nodes, by using a refined version of the state-of-the-art friction contact model. In order to model accurately the blade/damper contact with a large number of contact nodes without increasing proportionally the size of the set of nonlinear equations to be solved, damper and blade dynamics are modeled by linear superposition of a truncated series of normal modes. The proposed method is applied to a bladed disk under cyclic symmetric boundary conditions in order to show the capabilities of the method compared to the classical decoupled approaches.