Abstract
One of the main tasks in the design of turbomachines like turbines, compressors, and fans is to increase the reliability and efficiency of the arrangement. Failures due to blade cracks are still a problem and have to be minimized with respect to costs and safety aspects. To reduce the maximum stresses, the blades can be coupled via friction damping devices such as underplatform dampers that are pressed onto the blade platforms by centrifugal forces. In this work, a method will be presented to optimize two different types of underplatform dampers in bladed disk applications with respect to a maximum damping effect. In practice, underplatform dampers with various geometric properties—cylindrical and wedge-shaped—are commonly used and lead to different contact conditions. A discretization of the contact areas between the blade platforms and the dampers is applied to be able to investigate nearly arbitrary contact geometries and spatial blade vibrations. The functionality of the two mentioned damper types has been studied in detail under different working conditions of the assembly. The advantages and disadvantages of both damper types are pointed out and strategies are presented to improve the damper design. In this context, the influence of mistuning effects is discussed in terms of statistical mistuning of the blades’ natural frequencies due to manufacturing tolerances as well as systematical mistuning due to a deliberate slight variation of the blade masses or geometries.
Highlights
One of the main tasks in the design of turbomachines like turbines, compressors, and fans is to increase the reliability and efficiency of the arrangement
To reduce the maximum stresses, the blades can be coupled via friction damping devices such as underplatform dampers that are pressed onto the blade platforms by centrifugal forces
The influence of mistuning effects is discussed in terms of statistical mistuning of the blades’ natural frequencies due to manufacturing tolerances as well as systematical mistuning due to a deliberate slight variation of the blade masses or geometries
Summary
Modal Description of the Linear Structures The dynamic behavior of an individual blade of an assembly can be described after discretization by means of the ordinary differential equation of the entire system with a large number of DOF will lead to an enormous computational effort, especially in the case of a mistuned system. In order to develop a fast algorithm with the objective of improving the damper design, the nonlinear periodic contact forces are developed in a Fourier series that is truncated after the fundamental harmonic, where the Fourier coefficients are a function of the amplitude of the relative displacements between the contacting bodies. The angular excitation frequency E is defined by the angular rotational speed of the assembly R and the engine order EO by denotes the diagonalized dynamic stiffness matrix, containing the natural angular frequencies ω0 j and the modal damping ratios D j of the nm considered vibration modes of the blade; qis the vector of modal amplitudes, i is the imaginary unit, and (ˆ) indicates complex quantities. In the case of spatial vibrations, three translational and three rotational relative displacements have to be determined for the left and right contact points, respectively. From the contact forces F C and the relative displacements wfrom Equation (6), a nonlinear diagonalized contact stiffness matrix is generated:
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