Laurent Blanc

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.

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.

Dynamic Analysis of Fretting-Wear in Friction Contact Interfaces

Fretting wear is a very important phenomenon occurring in bladed disks. It causes the blades to be replaced in turbomachines during their life-cycle. Methods exist to predict fretting-wear in quasistatic analysis. However, they do not predict all the phenomena observed in blade attachments on real turbomachines. That is why this study assumes that dynamics plays a role in fretting-wear. This paper is devoted to the realistic modeling and calculation of fretting-wear and dynamical response of structures in unilateral contact with friction. Vibration and wear phenomena present very different scales both in time and space. Therefore the difficulty is in finding methods that enable one to solve the nonlinear problem with a good compromise between the approximations made about the dynamical aspects and those linked with fretting-wear issues. Here, phenomenological examples are studied. They involve a small number of degrees of freedom with a view to understanding the complex coupling between vibration and fretting-wear. This way, they will show the relative importance of parameters.

Modal Tests and Analysis of a Radial Impeller at Rest: Influence of Surrounding Air on Damping

HCF risk assessment for turbomachinery blades requires the prediction of vibratory levels, which in turn requires fine damping quantification. This issue is especially sensitive for structures with low structural damping such as monobloc centrifugal compressor disks (blisks). The material composing blisks and aero-dynamic flow both contribute to damping phenomena. A strategy for non-aerodynamic damping characterization is to perform experiments in vacuum.This paper focuses on the use of modal tests in vacuum to estimate material damping under non-rotating conditions. Experiments are performed on an isolated impeller manufactured from a single piece in a vacuum chamber at different air pressure levels ranging from 10 mbar to 1 bar. Strong dependency of damping ratios on pressure can be found on the first flexural mode, leading to two types of application.Firstly, measurements enable assessing the validity of extrapolations of non-aerodynamic damping from measurements sometimes performed under less thorough vacuum conditions. Basic fluid-structure interaction models are used to interpret and quantify the evolution of modal quantities when air is progressively removed. Secondly, vacuum measurements can give frequency response functions (FRFs) with much greater separation between resonance peaks. In this study, the damping ratio found in vacuum condition are 3% of these at ambient pressure corresponding to a magnitude 30dB higher at resonance peaks. This contrasts with in-air measurements on cyclic symmetry structures, like blisks, with high modal density that make the direct interpretation of FRFs and their modal analysis more difficult.Copyright

Vibratory Behavior Prediction of a Mistuned Clustered Stator Vane: Non-Intrusive Stochastic Methods

The role of stator vanes is to straighten the air flow on each stage of axial compressors. They are so subject to dynamically fluctuating high pressure loads. Furthermore, monobloc clustered designs have been developed to facilitate manufacturing process and reduce costs, but they result in loss of cyclic symmetry properties and very low structural damping. This makes it more difficult to predict vibratory behavior, when taking high modal density and extreme sensitivity to mistuning into account, and even more essential to ensure structural strength in the context of fatigue. In most cases, mistuning due to geometrical and material tolerances is unknown. Here, a non-intrusive spectral stochastic method has been developed to predict the vibratory behavior of a clustered stator vane in which the Young modulus of some blades is associated with a random variable representing the mistuning effect. This method is based on a stochastic modal analysis which consists in projecting eigenfrequencies and modes shapes on a polynomial chaos basis. Computation of spectral coefficients is performed through non intrusive ways — making the method applicable to any problem — as Smolyak projection or regression by least square method. These two methods are compared based on criteria of computations costs, accuracy, robustness and convergence. These methods have been tested on a simplified stator vane model - based on a 2D Euler-Bernoulli beams assembly. Regression method provides rather accurate results unlike Smolyak projection whatever the initial configurations of the problem. Computation costs are reasonable but could increase really fast according to polynomial degree and stochastic dimension. Thus, regression method is an accurate, robust and fast enough method to predict the vibratory behavior of a mistuned clustered stator vane.Copyright

Elements of Dynamic Characterization of a Bladed Disk by Using the Tip-Timing Method Under Vacuum Conditions

This article describes the process of identifying the dynamic properties of a blisk by noncontact measurements provided by the tip-timing method. Attention is focused on tip-timing measurements for mode identification in the presence of the Coriolis effect. Firstly, the standing wave response is studied by using tip-timing measurements that provide the amplitude and phase distributions of each blade over a fixed measurement period for identifying the number of nodal diameters of the mode. Secondly, the travelling wave response is identified, followed by the calculation of the frequency response of the blisk, in order to derive the damping ratios. As the mode considered is found in the domain of strong disk-to-blade coupling, it could be subject to the Coriolis effect. Blade tip-timing (BTT) measurements were used to reveal that the mode was split into forward and backward modes with respect to blisk rotation. All the results obtained after processing the tip-timing measurements are compared with data from the strain gauges with which only a few blades were equipped. The correlation of deformations measured by the strain gauges and blade tip tangential displacement obtained through tip-timing measurements is performed by using realistic finite element models of the blisk.© 2011 ASME

A Simplified Method for Predicting the Average Vibratory Response of Mistuned Clustered Stator Vanes

The role of stator vanes is to straighten the air flow on each stage of axial compressors. They are so subject to dynamically fluctuating high pressure loads. Furthermore, monobloc clustered designs have been developed to facilitate the manufacturing process and reduce costs, but they result in the loss of cyclic symmetry properties and very low structural damping. This makes it more difficult to predict vibratory behavior, when taking high modal density and extreme sensitivity to mistuning into account, end even more essential to ensure structural strength in the context of fatigue. In most cases, mistuning due to geometrical and material tolerances is unknown. Here, an analytical method has been developed to predict the average vibratory response of a clustered stator vane in which the Young modulus of certain blades is associated with a random variable mimicking the mistuning effect. This method is based on a linear approximation of the evolution of eigenfrequencies as a function of a random variables, as eigenvectors are almost constant, and a dynamic flexibility matrix reconstruction strategy. This method was tested on a simplified stator vane model based on a 2D Euler-Bernoulli beam lattice. The results are quite accurate when pressure is uniformly distributed on the “blades” and when the ferrule to blade stiffness ratio is high. This approach provides a simple model that can be used in the first stages of design as it allows fast simulation with a large number of random variables and with good approximation of the average vibratory response.© 2014 ASME

Stability Study of a Bladed Disk in Interaction With a Casing via a Labyrinth Seal

In this paper a simplified coupled model of a bladed disk and flexible stator developed in a rotating frame is introduced. The interaction between the rotating and stationary parts is adjusted using the gas flow in the straight-through labyrinth seal located on the tip of the blades. This is therefore an “aero elastic contact” problem. An energy-based method is used to express the equations of motion. The computation of eigenvalues provides the Campbell diagram and information on stability. A single-control-volume analysis is performed to predict the destabilizing force exerted by the labyrinth seal.In terms of strategy a simpler and efficient model with a rigid rotating shaft is compared with models found in the literature before the complete rotor-stator aero elastic contact study is presented. This is followed by a study of the interaction between the bladed disk with a labyrinth seal and the flexible stator.The model proposed provides a new approach to modelling rotor systems with labyrinth seals. The stator is then modelled as a flexible body and the rotor as a bladed disk. It is shown in the example described that the stability of the system depends on the rigid body movement of the stator and is independent of its nodal diameter modes.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