On comparing behavior and performance of Underplatform Dampers according to shape.
Abstract
This paper is the completion of a previous work in which an algorithm was developed for direct calculation of the hysteresis cycle of Underplatform Dampers (UDs) used for vibration damping of turbine blades.
While the previous paper examined the scalability of a given damper shape as a function of its size, platform size and contact parameters, this paper instead shows how the method can be used to evaluate the advantages and disadvantages of different damper shapes.
Only the asymmetric contact damper is studied, in its simplest version with three pad-located contacts, and its merits are discussed in comparison with the wedge or cottage-roof type dampers, whose crucial difficulties are pointed out.
A family of five dampers obtained by distortion of an isosceles damper of 60° vertex aperture is studied as an example of application of the method. A criterion is defined for positioning the single contact to avoid lifting when the coefficient of friction is maximum at =0.7, then performance is studied for two values in the range expected for normal operation, =0.5 and =0.3.
For each of the five dampers, the different problems that arise in calculating the hysteresis cycle at the onset of the total full-slip, called Base-Cycle, are examined, first on the damper in terms of the “force Base-Cycle,” otherwise known as the “equilibrium trace diagram,” then of the “moment Base-Cycle” on the platform.
The “moment Base-Cycle” is employed in the context of the Platform Centered Reduction (PCR) technique, and diagrams of the real and imaginary components of the complex moment-rotation stiffness of the platform representing the mutual damper-platform actions are defined.
Finally, the values of the energies dissipated on the contact pads of the dampers are determined, the sum of which is checked against the total energy dissipated by the moment of the contact forces acting on the platform, consistent with the Platform Centered Reduction.
The parameters and diagrams that characterize the shape of a damper, regardless of its subsequent coupling with a specific turbine blade, are useful tools for characterizing its performance with greater insight than can be obtained from the usual purely numerical approach.