Pierrick Jean

Structural multi-modal damping by optimizing shunted piezoelectric transducers

The capacity of different auto-supplied devices using shunted piezoelectric circuits are studied here to improve structural damping by avoiding implementation of complex and heavy control devices. The presented technique uses a dedicated numerical piezo-mechanical model combining both mechanical and electrical coupling parameters. An original methodology are also introduced for optimizing the parameters of electrical shunt circuits connected to piezoelectric elements and also structural locations of these integrated transducers. The results, experimentally validated (on beams and a plate), demonstrate that vibrations can be significantly reduced when shunted piezoelectric devices are mounted on a real structure. Finally, the proposed methodology is used for optimizing shape and location of the shunted piezoelectric patches to damp several modes of a plate.

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.

Dual Time Stepping Algorithms With the High Order Harmonic Balance Method for Contact Interfaces With Fretting-Wear

Contact interfaces with dry friction are frequently used in turbomachinery. Dry friction damping produced by the sliding surfaces of these interfaces reduces the amplitude of bladed-disk vibration. The relative displacements at these interfaces lead to fretting-wear which reduces the average life expectancy of the structure. Frequency response functions are calculated numerically by using the multi-harmonic balance method (mHBM). The dynamic Lagrangian frequency-time method is used to calculate contact forces in the frequency domain. A new strategy for solving nonlinear systems based on dual time stepping is applied. This method is faster than using Newton solvers. It was used successfully for solving Nonlinear CFD equations in the frequency domain. This new approach allows identifying the steady state of worn systems by integrating wear rate equations a on dual time scale. The dual time equations are integrated by an implicit scheme. Of the different orders tested, the first order scheme provided the best results.

Nonlinear dynamics of a bladed dual-shaft

In the industrial context of performance improvement of dual-shaft aircraft engines, experimental results demonstrate how important it is to consider the influence of the dynamics of the high pressure (HP) shaft on the response of the bladed disk located on the low pressure (LP) shaft. Indeed, this coupling seems to play an important role in the design purposes in rotating machinery industry as it can have a significant impact on the dynamic behaviour of turbomachines. The model developed here consists of a HP shaft and a LP bladed shaft connected by an intershaft bearing. Nonlinear features of this intershaft bearing require the development of specific nonlinear algorithms. Thus, this paper aims at coupling the two modelling levels in order to grasp the nonlinear vibratory phenomena of a bladed dual-shaft under unbalances.

Turbomachinery blades damping thanks to optimized shunted piezoelectric circuits

Dynamics of gas-turbine blades are particularly aero-elastic coupling sensitive. These aerodynamic limits can be pushed away by adding extra damping to the structure in order to reach even better compressor performance. However nowadays design and manufacturing techniques in aero-mechanics are achieving their maximum of state-of-the-art. As in many fields active control would solve easily this kind of instability. But the diffculty remains in the needed energy supply for actuators whereas these components are aimed to be bonded on rotating structures. The capacity of different auto-supplied devices using shunted piezoelectric circuits had been studied here to prevent turbomachine bladed from fluttering. Before realizing the study on complex turbomachine geometries, the presented technique uses a numerical development thanks to a 1D Euler-Bernoulli beam model combining both mechanical and electrical coupling parameters. A second development thanks to a 3D model had been made using a commercial tool, Comsol software. These approximate models are used to optimize electrically the shunted piezoelectric element and its localization. The results, verified experimentally, let suppose that vibrations can be reduced signiffcantly when shunted piezoelectric circuits are mounted on a real structure.

On Forced Response of a Rotating Integrally Bladed Disk: Predictions and Experiments

An experimental setup is described which permits to rotate a bladed disk in vacuum and to measure its dynamic response to excitations provided by some embedded piezoelectric actuators. A particular spatial placement of actuators associated with phase-shifting electronic circuits is set for simulating travelling wave excitations with respect to the rotating frame. The system is demonstrated on an actual high-pressure compressor (HCP) integrally bladed disk. The dynamic response of the blisk is analyzed experimentally and results are correlated with those obtained from a simplified finite elements model taking into account Coriolis effect. The paper focuses on the influence of the latter which is most of the time neglected and its implication on the forced response levels is studied into two situations without or with mistuning.

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

Test-Model Correlation of Dry-Friction Damping Phenomena in Aero-Engines

In order to control the risk of high cycle fatigue of bladed disks, it is important to predict precisely the vibration levels and to design damping solutions to attenuate them. Therefore, Snecma has made some efforts in the last years in order to characterize better the damping in aero-engines. Among the various damping sources, friction damping is particularly difficult to model due to its non-linear behaviour [1]. For that purpose, two methods based on multi-harmonic balance strategy have been especially developed for Snecma, dedicated to the study of the non-linear forced response of bladed disks. The first one enables to model the bladed disk equipped with dry-friction dampers [2], and the second one takes into account intrinsic friction located in disk-blade interface [3]. To validate both models experimentally, a test campaign has been carried out in a vacuum chamber on a rotating bladed disk excited by piezoelectric actuators. The blade shanks have been softened in order to increase friction effects. Experimental results show a regular and reproducible behaviour of the non-linear forced response, over various rotation speed and excitation levels. The contributions of friction dampers and friction in blade attachment have been decoupled thanks to glue applied in the blade root. Both friction phenomena that were observed experimentally at resonance of the blade first bending mode have been reproduced numerically. After updating modeling parameters, an acceptable correlation was found on resonance frequencies, amplitudes and damping levels over the full experimental setup range, which validates these numerical tools for their use in design process.© 2008 ASME

Calibrated Non Linear Dissipative Model of Fan Bladed Disk

The results of non linear modeling of mechanical damped behavior of fan bladed disk are presented in the paper. A combined test/modeling strategy dedicated to the prediction of behavior of bladed disk in all operating flight range is proposed. The proposed methodology is applied on 2 configurations: firstly, on a well known fan stage (wide chord titanium blade with curvilinear attachment) and secondly, on a new one based on woven composite technology. This strategy needs to perform efficient and precise modal tests able to measure as well as possible the damping parameters. The test procedure is set up after trying of different test configurations: the robustness/repeatability of measure is verified and the scatter is quantified. A non linear tool (Snecma in-house code) is used to predict the behavior of the test configuration and allows the identification of damping parameters. These damping parameters are then used to assess the dissipative behavior in operating conditions. This tool is based on DLFT method derived from classical harmonic balance method and allows fast calculations of NL responses. The results presented illustrate the quality of tests measurement and the validity of the non linear model used to predict the characterized physics. The calibration is based on the damping parameters updated on a wide test configurations.Copyright

Dynamic Analysis of Fretting-Wear in Joint Interface by a Multiscale Harmonic Balance Method Coupled With Explicit or Implicit Integration Schemes

Assembled bladed disks have many contact interfaces (blade-disk joint, blade shrouds, friction damper, etc). Because of relative displacements at these interfaces, fretting-wear can occur, which shortens the life expectancy of the structure. Moreover, vibrations that occur in bladed-disks can increase this fretting-wear phenomenon. Two previous papers in Turboexpo have introduced a numerical method based on the Dynamical Lagrangian Frequency Time algorithm (DLFT) to calculate worn geometry, especially wear of bladed-disks’ dovetail roots. Numerical investigations have illustrated the performances of this method and shown the coupling between dynamical and tribological phenomena. The basic idea of the DLFT-with-wear method is to separate time in two scales, slow scale for tribological phenomena and fast scale for dynamics. In the present paper, implicit and explicit integration schemes on the slow time scale are compared. An ad hoc prediction-correction method is used in both methods to accelerate the convergence of the non-linear solver. Numerical experiments on bladed-disk show that the implicit scheme is more appropriate to deal with fretting-wear under dynamical loading.Copyright