Claude Gibert

Numerical and Experimental Study of Friction Damping in Blade Attachments of Rotating Bladed Disks

In order to mitigate high cycle fatigue risks in bladed disks, the prediction of the vibration levels early in the design process is important. Therefore, the different sources of damping need to be modeled accurately. In this paper the impact of friction in blade attachments on forced response is investigated both numerically and experimentally. An efficient multiharmonic balance method is proposed in order to compute the forced response of bladed disks with contact and friction nonlinearities in blade roots. For experimental validation purposes, a rotating bladed disk was tested in a vacuum chamber, with excitation being provided by piezoelectric actuators. A model of the rig was built and numerical results were obtained with a normal load dependent coefficient of friction and a constant material damping ratio. Nonlinear behavior observed experimentally at resonances was well reproduced and an acceptable correlation was found with experimental resonant frequencies, amplitudes, and amount of damping throughout the spinning speed and excitation level range. The proposed numerical method can therefore serve to enhance the prediction of the alternating stresses in bladed disk assemblies.

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

Chebyshev Polynomials Fits for Efficient Analysis of Finite Length Squeeze Film Damped Rotors

The nonlinear behavior of the hydrodynamic forces generated by squeeze film dampers makes dynamical analyses of rotor-bearing systems incorporating such devices a complex and often long task. When steady-state orbits are to be sought, approximate methods (e.g., harmonic balance method, trigonometric collocation method) can be used in order to save computation cost. However, numerical integration in the time domain cannot be avoided if one wishes to calculate transient responses, or to carry out more meticulous analyses concerning the effects of the damper nonlinear nature on the motion of the system. For finite length squeeze film dampers, neither the short nor the long bearing approximations can be suitably applied, and the fluid pressure field has to be estimated numerically, thus rendering rotordynamics predictions even longer and, for engineering purposes computationally prohibitive. To surmount this problem, the present paper proposes a straightforward procedure to derive polynomial expressions for the squeeze film damper (SFD) forces, for given damper geometry and boundary conditions. This is achieved by applying Chebyshev orthogonal polynomial fits over force data generated by numerically solving the two-dimensional pressure field governing equation. For both transient and steady-state calculations, the use of the SFD forces polynomial expressions is seen to be very efficient and precise.

Experimental Analysis of Dynamic Interaction Between a Centrifugal Compressor and Its Casing

In turbomachinery, one way to improve aerodynamic performance and reduce fuel consumption consists of minimizing the clearance between rotor and casing. Yet, the probability of contact is increased and this may lead in some specific conditions to a large and even unstable excitation on the impeller and stator. To achieve better understanding of the dynamic behavior occurring during the blade-to-casing contact, many numerical studies have been conducted but only a few experiments have been reported in the literature thus far. The interaction experiment reported in this paper involves a low-pressure, rotating centrifugal compressor and its casing tested in a vacuum chamber. Contact is initiated by introducing a gap near zero, and certain events with significant dynamic levels are observed during the run-up. Measurements are performed using strain gauges on both the rotating and stationary parts and a scanning laser Doppler vibrometer on the stator. This research focuses on an analysis of the recorded data. Time series data are also analyzed by means of standard signal processing and a full spectrum analysis in order to identify the direction of traveling wave propagation on the two structures as well as nodal diameters and frequencies. The dynamic response of structures is accompanied by variations in other physical parameters such as temperature, static deformed shapes, speed, and torque. A wearing pattern is evaluated following the contact experiments. The spectral content of response is dominated by frequency modes excited by rotating speed harmonics as well as by sidebands due to inherent system nonlinearity.

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

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.

Numerical Analysis of Bladed Disk–Casing Contact With Friction and Wear

In order to increase the aerodynamic performances of their engines, aircraft engine manufacturers try to minimize the clearance between rotating and stationary parts in axial and centrifugal compressors. Consequently, the probability of contact increases, leading to undesirable phenomena caused by forced excitation of the natural modes, or by modal interaction. Due to the complexity of these phenomena, many numerical studies have been conducted to gain a better understanding of the physics associated with them, looking primarily at their respective influence on potential unstable behaviors. However, the influence of other physical phenomena, such as friction and wear, remains poorly understood. The aim of this work is to show some effects associated with friction and wear on the dynamic behavior resulting from blade-to-casing interaction.The numerical study reported here is based on a simplified finite element model of a rotating bladed disk and a flexible casing. The contact algorithm uses an explicit time marching scheme with the Lagrange multipliers method. Friction and wear are formulated using respectively Coulomb’s and Archard’s Laws. The rotational speed is set to critical speed giving rise to modal interaction between a backward mode of the casing and a counter-rotating mode of the bladed disk with one nodal diameter. Contact is initiated by a dynamic excitation of the stator.In the presence of friction, the system becomes unstable when a sideband of the excitation frequency coincides with a one nodal diameter mode of the bladed disk. The introduction of wear leads to a vibration reduction, while the abradable material is removed by the wear process. The number of wear lobes produced on the casing is related to the ratio between the vibration frequency of the blades and the rotating speed. The ratio obtained by means of the FE model corroborates experimental observations.Copyright

Numerical Analysis of Bladed Disk-Casing Contact With Friction and Wear

In order to increase the aerodynamic performances of their engines, aircraft engine manufacturers try to minimize the clearance between rotating and stationary parts in axial and centrifugal compressors. Consequently, the probability of contact increases, leading to undesirable phenomena caused by forced excitation of the natural modes, or by modal interaction. Due to the complexity of these phenomena, many numerical studies have been conducted to gain a better understanding of the physics associated with them, looking primarily at their respective influence on potential unstable behaviors. However, the influence of other physical phenomena, such as friction and wear, remains poorly understood. The aim of this work is to show some effects associated with friction and wear on the dynamic behavior resulting from blade-to-casing interaction.The numerical study reported here is based on a simplified finite element model of a rotating bladed disk and a flexible casing. The contact algorithm uses an explicit time marching scheme with the Lagrange multipliers method. Friction and wear are formulated using respectively Coulomb’s and Archard’s Laws. The rotational speed is set to critical speed giving rise to modal interaction between a backward mode of the casing and a counter-rotating mode of the bladed disk with one nodal diameter. Contact is initiated by a dynamic excitation of the stator.In the presence of friction, the system becomes unstable when a sideband of the excitation frequency coincides with a one nodal diameter mode of the bladed disk. The introduction of wear leads to a vibration reduction, while the abradable material is removed by the wear process. The number of wear lobes produced on the casing is related to the ratio between the vibration frequency of the blades and the rotating speed. The ratio obtained by means of the FE model corroborates experimental observations.Copyright

Experimental and Numerical Investigations on a Rotating Centrifugal Compressor

Controlling the dynamic behavior of turbomachines requires an experimental validation phase to ensure their safety. The application of two experimental techniques to measure the modal properties of a rotating centrifugal compressor impeller is described in this paper. The impeller was tested in a vacuum chamber with excitation provided by piezoelectric actuators mounted on the rear side of the impeller disk.The most common technique used to measure the dynamic behavior of a rotating structure is based on strain gauges and a telemetry system or a slip ring for signal transmission. Nevertheless, in some cases this method is an intrusive technique that could introduce damping and blade mistiming, and it can also be time consuming to prepare. Strain gauge measurement has been compared to measurements performed under the same conditions by Scanning Laser Doppler Vibrometer associated with a derotator optical system, which allows measurement at fixed points on a rotating part.This work focuses on the study of the dynamic behavior of a centrifugal compressor impeller in view to preparing stator contact interaction tests requiring precise characterization of frequencies and nodal diameters and of the influence of rotation speed and other possible parameters.The advantages and disadvantages of the two methods used have been assessed for this particular application. A correlation between the experiments and the numerical simulations using the finite element method is provided.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