Session: 28-07 Dynamic Response of Bladed Disks

Paper Number: 123245

123245 - The Impact of Different Equilibrium Hypothesis on the Non-Linear Response of Bladed Disks 

Friction damping devices are widely used in bladed disks to mitigate blades’ vibration amplitude. Such devices introduce localized nonlinearities, whose modelling requires nonlinear solution techniques.

One of the fastest and most reliable solution methods is the Harmonic Balance Method (HBM), which operates in the frequency domain by approximating periodic quantities into a finite series of Fourier coefficients. In the literature two different implementations of the HBM are available for the solution of the forced response of friction damped bladed disks.

The most consolidated approach, largely applied in the industry, is the so called uncoupled approach, where the 0^th order harmonic is solved in advance to determine the static equilibrium condition. The static contact forces, obtained as a result of the static analysis are then used as input parameters to determine the dynamic equilibrium by means of the other harmonics.

On the contrary, the coupled approach, where the static and dynamic equilibria are determined simultaneously, is widely used in the academia, since it represents a more accurate model of reality, although characterized by larger calculation times.

A common issue of both approaches, in case of friction damped systems, is the uncertainty in the value of the tangential contact forces, when the Coulomb friction model is used. Multiple equilibrium conditions are possible and, under certain circumstances, they can result in multiple vibration levels.

The engineering interest is in the computation of maximum and minimum vibration levels (response boundaries), nevertheless, although the existence of multiple solutions is well documented for both approaches, a comparison between the response boundaries obtained by the coupled and by the uncoupled approaches has never been performed.

In this paper, the response boundaries of a closed blade array with interposed underplatform dampers are computed. An optimization algorithm originally developed for the coupled approach is extended to the uncoupled approach allowing for a systematic comparison of the response boundaries.

To the best of the authors knowledge this paper represents the first attempt to extend the calculation of the response boundaries to bladed disks models with multiple blades and underplatform dampers, neglecting cyclic symmetry boundary conditions. Due to the large computation times associated with optimization algorithms, a lumped parameter model is used, nevertheless the main findings of the paper can be considered general.

Presenting Author: Gianmarco Zara Politecnico di Torino

Presenting Author Biography: Mr. Gianmarco Zara is a PhD student from Politecnico di Torino. His work is mostly invested in bladed disks' dynamics and friction damping.

Authors:

Gianmarco Zara Politecnico di Torino
Teresa Maria Berruti Politecnico di Torino
Stefano Zucca Politecnico di Torino