Abstract

This paper further refines the recently presented method called Platform Centered Reduction (PCR) and introduces a new element that increases its efficiency. To improve the numerical efficiency of the complex iterative and nonlinear calculations required for the dynamic response of nonlinearly damped turbine blades, the PCR method relies on the primary assumption of representing the platform as a rigid body. A secondary, but convenient, assumption is to represent the neck as a series of beams, while the airfoil model is obtained by reducing the FE model. A perfect match between the FE model and the PCR model requires some attention, detailed in the paper, in particular to the interfaces of the platform with the neck and the airfoil. Moreover, the value of the displacements due to neck bending at the contact points on the platform is evaluated in relation to those due to torsion, considering the real modal shapes of the blade. The first significant modes for the operation of the under-platform damper are studied. Finally, it is evaluated how many of the 6 DOFs of the rigid body platform model can be neglected in the analysis without loss of accuracy within the limits of the design engineering requirements. Once these aspects have been ascertained so as to guarantee the fidelity of the PCR model to reality, the concept of “base-cycle” is introduced for the diagram representing the moment on the platform due to friction against its angle of rotation, both calculated around an axis parallel to the main axis of neck bending. It is shown that this diagram completely characterizes the damper-platform assembly, so much so that for rotation values greater than that of the “base-cycle” the values of the real and imaginary (HBM) components of the damper-platform bending stiffness are obtained a priori and in an elementary manner, without having to repeat calculations of the contact cycle at each variation of amplitude. The extent of the advantage of such an approach for numerical calculations is shown, as well as the convenience of having a model more closely focused on the essential aspects of the engineering problem. Furthermore, in the light of the improvements introduced, its implications on the “designer’s diagram” showing the maximum bending stress on the airfoil against the excitation force at resonance are reviewed. Finally, the concept of the “GG design diagram”, a simplified construction of the “designer’s diagram”, is also reviewed and its effectiveness for the designer in determining the best damper-blade coupling for vibration damping is assessed.

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