Denis Laxalde

Qualitative analysis of forced response of blisks with friction ring dampers

A damping strategy for blisks (integrally bladed disks) of turbomachinery involving a friction ring is investigated. These rings, located in grooves underside the wheel of the blisks, are held in contact by centrifugal loads and the energy is dissipated when relative motions between the ring and the disk occur. A representative lumped parameter model of the system is introduced and the steady-state nonlinear response is derived using a multi-harmonic balance method combined with an AFT procedure where the friction force is calculated in the time domain. Numerical simulations are presented for several damper characteristics and several excitation configurations. From these results, the performance of this damping strategy is discussed and some design guidelines are given.

Forced Response Analysis of Integrally Bladed Disks With Friction Ring Dampers

This paper investigates a damping strategy for integrally bladed disks (blisks) based on the use of friction rings. The steady-state forced response of the blisk with friction rings is derived using the so-called dynamic Lagrangian frequency-time method adapted to cyclic structures with rotating excitations. In addition, an original approach for optimal determination of the number of Fourier harmonics is proposed. In numerical applications, a representative compressor blisk featuring several rings is considered. Each substructure is modeled using finite-elements and a reduced-order modeling technique is used for the blisk. The efficiency of this damping technology is investigated, and friction dissipation phenomena are interpreted with respect to frequency responses. It is shown that the friction damping effectiveness depends mainly on the level of dynamic coupling between blades and disk, and on whether the dynamics features significant alternating stick/slip phases. Through parameter studies, design guidelines are also proposed.

Dynamics of Multistage Bladed Disks Systems

This paper presents a new and original method for dynamical analysis of multistage cyclic structures such as turbomachinery compressors or turbines. Each stage is modeled cyclically by its elementary sector and the interstage coupling is achieved through a cyclic recombination of the interface degrees of freedom. This method is quite simple to set up; it allows us to handle the finite element models of each stages sector directly and, as in classical cyclic symmetry analysis, to study the nodal diameter problems separately. The method is first validated on a simple case study which shows good agreements with a complete 360 deg reference calculation. An industrial example involving two HP compressor stages is then presented. Then the forced response application is presented in which synchronous engine order type excitations are considered.

Dynamics of a linear oscillator connected to a small strongly non-linear hysteretic absorber

The present investigation deals with the dynamics of a two-degrees-of-freedom system which consists of a main linear oscillator and a strongly nonlinear absorber with small mass. The nonlinear oscillator has a softening hysteretic characteristic represented by a Bouc-Wen model. The periodic solutions of this system are studied and their calculation is performed through an averaging procedure. The study of nonlinear modes and their stability shows, under specific conditions, the existence of localization which is responsible for a passive irreversible energy transfer from the linear oscillator to the nonlinear one. The dissipative effect of the nonlinearity appears to play an important role in the energy transfer phenomenon and some design criteria can be drawn regarding this parameter among others to optimize this energy transfer. The free transient response is investigated and it is shown that the energy transfer appears when the energy input is sufficient in accordance with the predictions from the nonlinear modes. Finally, the steady-state forced response of the system is investigated. When the input of energy is sufficient, the resonant response (close to nonlinear modes) experiences localization of the vibrations in the nonlinear absorber and jump phenomena.

Mistuning Identification and Model Updating of an Industrial Blisk

The results of a complete study of mistuning identification on an industrial blisk are presented. The identification method used here is based on a model-updating technique of a reduced order. This reduced-order model is built using component mode synthesis, and mistuning is introduced as perturbations of the cantilevered-blade modes. The measured modal data are extracted from global measurements of the blisks forced response. As we use a single point excitation, this measurement procedure allows the acquisition of all the modes of a given family with a quite simple experimental set-up. A selection of the best identified modal data is finally performed. During the mistuning identification procedure, these measured data are regularized using an eigenvector assignment technique which reduces the influence of eventual measurement errors. An inverse problem, based on the perturbed (mistuned) modal equation, is defined with measured modes as input and mistuning parameters as unknown. Then, the reduced-order model is updated with the identified mistuning, we first perform a correlation on modal responses (using eigenfrequency deviation criteria and MACs). Finally, correlation results on forced responses are presented and discussed.

Experimental and Numerical Investigations of Friction Rings Damping of Blisks

The use of friction ring dampers for integrally bladed disks (blisks) is investigated numerically and experimentally in this paper. A test rig was developed and consists in an industrial HP compressor blisk rotating inside a vacuum chamber. Excitation is produced through piezoelectric actuators and measured data are obtained from strain gauges. Non-linear resonance curves obtained by stepped sine tests are studied. Interesting phenomena on the behaviour of this damping technology are obtained experimentally. Parametric studies on the influence of the rotation speed or of the excitation level are also presented. A non-linear modal identification method is used in order to extract the modal parameters from the resonance curves. Then a comparison of these experimental results to the results of numerical simulations is proposed. The numerical methods is based on a frequency domain formulation of the system’s dynamics; a non-linear modal approach is used. The correlation between the experiments and the predicted results are in quite good agreement given the complexity and the variability of the system and phenomena.Copyright

Non-Linear Modal Analysis for Bladed Disks With Friction Contact Interfaces

A method for non-linear modal analysis of mechanical sys- tems with contact and friction interfaces is proposed. It is based on a frequency domain formulation of the dynamical systems equations of motion. The dissipative aspects of these non- linearities result in complex eigensolutions and the modal pa- rameters (natural frequency and modal damping) can be obtained without any assumptions on the external excitation. The gener- ality of this approach makes it possible to address any kind of periodic regimes, in free and forced response. In particular, sta- bility analysis in flutter applications can be performed. Applications for the design of friction ring dampers for blisks and for the dynamical simulation of bladed disk with dove- tail attachment are proposed. Finally, we propose a study of dy- namical behaviour coupling with the calculation of fretting-wear at the interfaces based on non-linear modal characterization.

Dynamics of Multi-Stage Bladed Disks Systems

This paper presents a new and original method for dynamical analysis of multi-stage cyclic structures such as turbomachinery compressors or turbines. Each stage is modeled cyclically by its elementary sector and the inter-stage coupling is achieved through a cyclic recombination of the interface degrees of freedom. This method is quite simple to set-up; it allows to handle the finite element models of each stage’s sector directly and, as in classical cyclic symmetry analysis, to study the nodal diameter problems separately. The method is first validated on a simple case study which shows good agreements with a complete 360° reference calculation. An industrial example involving two HP compressor stages is then presented. Then the forced response application is presented in which synchronous of engine order type excitations are considered.Copyright

Vibration Control for Integrally Bladed Disks Using Friction Ring Dampers

A damping strategy for integrally bladed disks (blisks) is discussed in this paper; this involves the use of friction rings located underside the wheel of bladed disks. The forced response of the blisk with friction rings is derived in the frequency domain using a frequency domain approach known as Dynamic Lagrangian Frequency-Time method. The blisk is modeled using a reduced-order model and the rings are modeled using beam elements. The results of some numerical simulations and parametric studies are presented. The range of application of this damping device is discussed. Parametric studies are presented and allow to understand the dissipation phenomena. Finally some design and optimization guidelines are given.Copyright

Non-Linear Vibrations of Multi-Stage Bladed Disks Systems With Friction Ring Dampers

In this paper, we study the non-linear dynamics of a multi-stage system of turbomachinery bladed disks with friction dampers. We focus on the quasi-periodic forced response of this system under multi-frequency rotating excitations. The system’s equations of the motion are expressed in the multi-frequency domain using a multi-frequency harmonic balance method in combination a multi-stage cyclic symmetry reduction. A Dynamic Lagrangian formulation in alternating frequency/time domains is also used for the calculation of the contact and friction forces. In applications we consider a system of two HP compressor stages of integrally bladed disks with friction ring dampers.© 2007 ASME