Jean-Pierre Lombard

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 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

Reduction of Multistage Disk Models: Application to an Industrial Rotor

The present study deals with the reduction of models of multistage bladed disk assemblies. The proposed method relies on the substructuring of the rotor into sectors. The bladed disks are coupled by intermediate rings, which remove the problem of incompatible meshes. The sectors are represented by superelements whose kinematic subspaces are spanned by a set of cyclic modeshapes and a set of normal modes when their left and right interfaces are fixed. The first step is to compute the cyclic modeshapes that are defined on the full rotor by enforcing the uncoupling of the spatial Fourier harmonics. This leads to a family of subproblems parametrized by the harmonic coefficient, similar to the classical approach used to deal with tuned bladed disks. The subsequent reduction process leads to compact reduced models whose accuracy has been extensively tested on simple but realistic academic models. The proposed methodology was then applied to an industrial rotor to conduct an analysis at a wider scale. This case was also the occasion to point out the fact that the assembly of individual disk models into a rotor model is really straightforward and provides an efficient tool to observe and predict coupled phenomena.

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

Turbine Mistuned Forced Response Prediction: Comparison With Experimental Results

It is currently a major challenge for aeroengines manufacturer to be able to predict early in the design process the dynamic response of bladed disk. To guaranty a good accuracy of prediction, it is necessary to define properly the excitation (unsteady aerodynamics) and to take into account some phenomenon such as mistuning. This paper proposes an application of Snecma prediction method for mistune forced response on an experimental test case. The method used is a component modes synthesis method similar to the one proposed by Castanier and Pierre in 1997 [1] and validated against experiment in [2]. Some improvement have been performed to take into account more accurately the centrifugal forces effects in the projection basis and to couple the method with unsteady Computational Fluids Dynamic (CFD) codes. It is now possible to use this method in an industrial process. The method is applied to a HP turbine representative case, for which experimental results are available. These experimental results have been obtained in a European Community funded project dedicated to forced response study [3]. Mistuning effects have been measured. Moreover, a full characterization, of unsteady aerodynamics, aeroelastic and structural dynamics aspects have been performed. The results obtained with the proposed method are then compared to the experimental one. This application shows the consistency of the method and its efficiency.Copyright

Reduction of Multi-Stage Disk Models: Application to an Industrial Rotor

The present study deals with the reduction of multi-stage bladed disk assemblies. The guidelines of the proposed method which uses rotor cyclic modeshapes in conjunction with blade-dominated modes to account for the kinematics of each bladed sector of each disk are first recalled. This leads to compact reduced models whose accuracy has been extensively tested on simple but realistic academic models. In the second part of this paper, the proposed methodology is applied to an industrial rotor provided by Snecma to conduct an analysis at a wider scale.Copyright

Mistuning Phenomena on Bladed Disk: Industrial Methods and Applications

This paper deals with the methods used at Snecma (SAFRAN Group) to simulate the real mistuned dynamic behavior of bladed disks. Many applications of the method on industrial cases are also presented. The dissymmetry of a real bladed disk, which is mainly generated by small deviations in its geometry, leads to different dynamic impedances of the blades. These variations in impedance cause significant amplification of the forced response of the bladed disk. We propose to focus on industrial methods that can be used to simulate the mistuned dynamic behavior of a bladed disk in the case of small “frequency mistuning” or of greater “large mistuning”. This method, based on the modal synthesis technique (Benfield and Hruda family), can be classified as a “first generation method”. The first originality of this method consists in taking into account major mistuning, such as that induced by an FOD event. A second innovation concerns the use of these methods to assess in probabilistic terms the correction factor to apply to the maximum dynamic level measured during engine certification tests. The first part of the paper relates to the proposed method and its validation for large-scale “shape” mistuning on an academic test case. In the second section, we present a number of industrial applications: • An application of “geometric mistuning” is presented on a bladed disk after an FOD event. The same kind of analysis as previously described is carried out and the numerical results are commented. • The mistuning analyses are carried out on an industrial blisk with a local defect. The sensitivity of the response amplification factor is calculated versus the mistuning rate using a probabilistic approach. • Another application of the mistuning strategy is discussed: it concerns the use of the mistuning method to specify the correction factor of partial dynamic strain gauge measurements in order to assess the maximum level of a bladed disk. • The last application is dedicated to the simulation of intentional mistuning to increase the aeroelastic stability of an industrial test case.Copyright

Forced Response Prediction: Methodology for the Design of HP Compressors Bladed Disks

This paper presents a general approach related to bladed disk forced response prediction and a typical way to use it in the design process. Firstly, a good confidence level in prediction tools must be reached. The first application is a highly instrumented HP compressor blisk representative of a real engine environment. Simulation of forced response is compared to measurements in order to check the accuracy of prediction. For this test case, the results obtained are in very good agreement with measurements. The good quality of prediction is due to the complete characterization performed on the test case: all the influent parameters were identified before testing. But during the design process, many important parameters are unknown and this level of accuracy can not be obtained. Nevertheless, forced response prediction in the early design process can provide interesting information even if uncertainties are high for some parameters. As an illustration, a second application is proposed, based on the design experience of a new HP compressor of a known engine family. Some forced response predictions were performed during development and compared afterwards with measurements obtained during engine testing. This analysis has permitted to confirm some technical choices and to assess the High Cycle Fatigue risk associated to this new engine configuration.Copyright

Study of component mode synthesis methods in a rotor-stator interaction case

The study of rotor-stator interactions between blade-tips and outer casings through direct contact in modern turbomachines is very time-consuming if the classical finite element method is used. In order to improve the knowledge over these interaction phenomena, faster methods have to be applied. The construction of reduced-order models using component mode synthesis methods generally allows for dramatic increase in computational efficiency. Two of these methods, namely a fixed interface method and a free interface methods are considered in an original manner to reduce the size of a realistic two-dimensional model. They are then compared in a very specific contact case-study. The equations of motion are solved using an explicit time integration scheme with the Lagrange multiplier method where friction is accounted for. The primary goal of the present study is to investigate the general behavior of such approaches in the presence of contact nonlinearities. It will be shown that in our contact case, a good accuracy can be obtained from a reduced models with very limited number of modes.