Platform centered reduction: A process capturing the essentials for blade-damper coupled optimization

The purpose of this document is to continue along the line of research of the authors in the direction of developing an attractive tool for designers in the initial design phase of the damping of the turbomachinery blades. In particular, in order to guide their initial choice of a dry friction underplatform damper in the most appropriate way. 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 modelled with Euler beam finite elements so to speed up the updating of its dimensions during the optimisation process; - the contact forces exerted by the dampers on the two sides of the blade platform are represented by the resultant forces and moments applied to a reference point on the platform, associated to its displacements and rotations; - as an improvement to the model proposed in the paper presented at Turbo Expo 2019, the airfoil is now obtained from a full 3D FE model after a component mode synthesis reduction; this choice is justified by the facts that the airfoil is by large the item with most complex shape and that during the coupled optimization of the damper the airfoil is considered to be of fixed shape. It is shown that the 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 domains of optimal matching between the damper and the blade is 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. At the same time, it allows an assessment of the interplay between blade parameters and damper parameters in determining the modal features and the damping capabilities. It is shown how different matching solutions may be identified depending on the expected forcing level on the blade.