. Two-dimensional modeling of an aircraft engine structural bladed disk-casing modal interaction. Journal of Sound and Vibration, Elsevier, 2009, 319 (1-2) In modern turbo machines such as aircraft jet engines, structural contacts between the casing and bladed disk may occur through a variety of mechanisms: coincidence of vibration modes, thermal deformation of the casing, rotor imbalance due to design uncertainties to name a few. These nonlinear interactions may result in severe damage to both structures and it is important to understand the physical circumstances under which they occur. In this study, we focus on a modal coincidence during which the vibrations of each structure take the form of a k-nodal diameter traveling wave characteristic of axi-symmetric geometries. A realistic two-dimensional model of the casing and bladed disk is introduced in order to predict the occurrence of this very specific interaction phenomenon versus the rotation speed of the engine. The equations of motion are solved using an explicit time integration scheme in conjunction with the Lagrange multiplier method where friction is accounted for. This model is validated from the comparison with an analytical solution. The numerical results show that the structures may experience different kinds of behaviors (namely damped, sustained and divergent motions) mainly depending on the rotational velocity of the bladed disk.

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 multiharmonic 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.

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 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.

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 degrees 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.

This paper deals with the characterization of the blade manufacturing geometric tolerances in order to get a given level of amplification in the forced response of a mistuned bladed-disk. The theory is based on the use of a nonparametric probabilistic model of blade random uncertainties. The dispersion parameters controlling the nonparametric model are estimated as a function of the geometric tolerances. The industrial application is devoted to the mistuning analysis of a 22 blades wide chord fan stage. Centrifugal stiffening due to rotational effects is also included. The results obtained validate the efficiency and the reliability of the method on three dimensional bladed disks.