A method to minimize the effort for damper-blade matching demonstrated on two blade sizes

A method called PCR (Platform Centered Reduction) is designed to more effectively perform complex iterative and nonlinear calculations required for the dynamic response of turbine blades damped by dry friction contacts between rigid dampers and airfoil-to-neck platform. The key feature of PCR is to represent all nonlinear forces on the blade platform by means of only six degrees of freedom at a point located within the platform volume, regardless of the number of damper-platform contact elements. Despite reducing the effort and computational time by more than one order of magnitude, the method proves to be fully accurate by a check against the corresponding nonlinear Finite Elements (FE) calculation. It is also shown that the limit exciting force, indicating the upper capability to dampen vibrations, can be calculated with a simple linear modal analysis. In order to search for the best blade-damper match, the preferred graph represents relevant bending stresses on the airfoil against excitation forces. A detailed application of the method concerns two significantly different blade sizes, by varying parameters such as neck length and damper centrifugal force. Finally, it is emphasized that a final check by a complete FE analysis is still possible as a purely linear solution fed by sets of contact forces previously determined through the PCR at any desired frequency and excitation.