Platform-Centered Reduction: A Process Capturing the Essentials for Blade-Damper Coupled Optimization

The purpose of this paper is to develop an attractive tool for designers in the initial design phase of the damping of turbomachinery blades through dry friction underplatform dampers. The paper shows how, to this purpose, certain reasonable simplifications are introduced in the procedure and in the model, leaving the customary full high fidelity computations to the final design verification analysis. The key simplifications here considered are: the blade neck is modeled with Euler beam finite elements (FE) to speed up the updating of its dimensions during the optimization process; the contact forces exerted by the dampers on the blade platform are represented by the resultant forces and moments applied to a reference point on the platform, associated with its displacements and rotations; the airfoil, which is not modified during the coupled optimization of the damper, is obtained from a full three-dimensional (3D) FE model after a component mode synthesis (CMS) reduction. It is shown that the here proposed process captures the essentials of the nonlinear dynamics of the blade-damper problem without sacrificing in any way the accuracy of the results. This hybrid model is then employed in the process where the optimal match domains between the damper and the blade are searched for, by exploring the influence of blade neck thickness (flexibility) and damper mass. Such a purposely simplified process allows a clear identification of relationships between relevant blade features and response with a focus on fatigue life.