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.

Axial-Transverse Coupled Vibration Analysis of a Swinging Roller-Follower CAM Due to Flexible Follower Rod

In this paper, the equations of motion of a swinging roller-follower cam for rise-dwell-fall-dwell (RDFD) case are derived by applying Hamilton’s principle and the assumed mode method. The cycloidal displacement (sinusoidal acceleration) motion is used to describe the rise and the fall motions of the follower. The corresponding cam profile is determined using theory of envelopes. The follower rod is considered to be flexible and modeled as a Rayleigh beam including axial and transverse deflections. The roller rolls in the cam groove. The contact point between the cam and the roller is an unknown point though it is restrained in the cam groove. The contact point position depends not only on the rigid-body motions of the cam system but also the flexible vibrations of the follower rod. Two geometric constraints are formulated to restrict the roller motion and added to the Hamilton’s principle with Lagrange multipliers. The numerical integration method is applied to solve the non-linear differential-algebraic equations to obtain the vibration responses of the cam system. The numerical results for the studied cases show that the follower vibrates significantly especially for the case of high rotation speed of cam. The follower still vibrates during the dwell interval. The parameter effects including the cam rotation speed, the follower length and cross-sectional radius, and the total rise on the vibration behavior have been investigated.

Nonlinear Modal Analysis and Energy Localization in a Bladed Disk Assembly

The objective of this study is to carry out modal analysis of nonlinear periodic structures using nonlinear normal modes (NNMs). The NNMs are computed numerically with a method developed in [18] that is using a combination of two techniques: a shooting procedure and a method for the continuation of periodic motion. The proposed methodology is applied to a simplified model of a perfectly cyclic bladed disk assembly with 30 sectors. The analysis shows that the considered model structure features NNMs characterized by strong energy localization in a few sectors. This feature has no linear counterpart, and its occurrence is associated with the frequency-energy dependence of nonlinear oscillations.

A Time-Domain Fluid-Structure Interaction Analysis of Fan Blades

This paper presents aerodynamic and aeromechanical analyses for an entire row of fan blades (i.e. tens of blades with a finite aspect ratio) subject to a uniform incoming flow. In this regard, a new unsteady three-dimensional vortex lattice model has been developed for multiple blades in discrete time domain. Using the new model, the characteristics of the unsteady aerodynamic forces on vibrating blades, including their temporal development, are examined. Also, the new aerodynamic model is applied to examine the aeromechanical behavior of fan blades by using a standard eigenvalue analysis. For this analysis, the fan blades have been modeled as three-dimensional plates, and, increasing the number of blades (or solidity) is predicted to destabilize the fan blade row.

Forced Response Assessment Using Modal Force Based Indicator Functions

This paper will focus on core-compressor forced response with the aim to develop two design criteria, the so-called chordwise cumulative modal force and heightwise cumulative force, to assess the potential severity of the vibration levels from the correlation between the unsteady pressure distribution on the blade’s surface and the structural modeshape. It is also possible to rank various blade designs since the proposed criterion is sensitive to changes in both unsteady aerodynamic loads and the vibration modeshapes. The proposed methodology was applied to a typical core-compressor forced response case for which measured data were available. The Reynolds-averaged Navier-Stokes equations were used to represent the flow in a non-linear time-accurate fashion on unstructured meshes of mixed elements. The structural model was based on a standard finite element representation from which the vibration modes were extracted. The blade flexibility was included in the model by coupling the finite element model to the unsteady flow model in a time-accurate fashion. A series of numerical experiments were conducted by altering the stator wake and using the proposed indicator functions to minimize the rotor response levels. It was shown that a fourfold response reduction was possible for a certain mode with only a minor modification of the blade.

On the Use of Actively Controlled Auxiliary Bearings in Magnetic Bearing Systems

Auxiliary bearings are used to prevent rotor/stator contact in active magnetic bearing systems. They are sacrificial components providing a physical limit on the rotor displacement. During rotor/auxiliary bearing contact significant forces normal to the contact zone may occur. Furthermore, rotor slip and rub can lead to localized frictional heating. Linear control strategies may also become ineffective or induce instability due to changes in rotordynamic characteristics during contact periods. This work considers the concept of using actively controlled auxiliary bearings in magnetic bearing systems. Auxiliary bearing controller design is focused on attenuating bearing vibration resulting from contact and reducing the contact forces. Controller optimization is based on the H∞ norm with appropriate weighting functions applied to the error and control signals. The controller is assessed using a simulated rotor/magnetic bearing system. Comparison of the performance of an actively controlled auxiliary bearing is made with that of a resiliently mounted auxiliary bearing. Rotor drop tests, repeated contact tests, and sudden rotor unbalance resulting in trapped contact modes, are considered.

Aeroelastic Properties of Closely Spaced Modes for a Highly Loaded Transonic Fan

In the design of modern compressor blades of wide chord (low aspect ratio) type it is often hard to avoid having modes that are close to each other in frequency. Modes which are closely spaced can interact dynamically. Mistuning and localization of stresses are known problems with this. A potential problem with this is also the possibility of coalescence flutter of the modes. Even if the modes are frequency separated at zero rotational speed, the centrifugal stiffening may cause the modes to attract and even cross (or veer) at some rotational speed. In design, mode separation criteria are sometimes applied in order to minimize the risk of encountering unknown dynamic phenomena. This study is performed to better understand the dynamics of closely spaced modes with respect to risk for coalescence flutter. A reduced order aeroelastic system is then constructed that describes the interaction between the different modes. The aeroelastic couplings are then calculated for the 2 mode system. The method is general in terms of mode shapes and number of interacting modes. A parametrical study is performed in order to study how strongly the modes interact when the frequency separation is decreased and if there is a risk of destructive coalescence flutter. The investigation is performed on a high pressure ratio front stage fan blade. The tendency of the modes to interact depends on the strength of the coupling compared to the strength of the pure structural modes. The tendency towards instability was increased in cases where the stability margin was smaller of the single modes. The results can be considered to support a separation criterion of 2% for the lower. A re-evaluation should be considered if lighter blade material and increased loads are to be used.

Aerodynamic Asymmetry Analysis of Unsteady Flows in Turbomachinery

A nonlinear harmonic balance technique for the analysis of aerodynamic asymmetry of unsteady flows in turbomachinery is presented. The present method uses a mixed time-domain/frequency-domain approach that allows one to compute the unsteady aerodynamic response of turbomachinery blades to self-excited vibrations. Traditionally, researchers have investigated the unsteady response of a blade row with the assumption that all the blades in the row are identical. With this assumption the entire wheel can be modeled using complex periodic boundary conditions and a computational grid spanning a single blade passage. In this study, the steady/unsteady aerodynamic asymmetry is modeled using multiple passages. Specifically, the method has been applied to aerodynamically asymmetric flutter problems for a rotor with a symmetry group of two. The effect of geometric asymmetries on the unsteady aerodynamic response of a blade row is illustrated. For the cases investigated in this paper, the change in the diagonal terms (blade on itself) dominated the change in stability. Very little mode coupling effect caused by the off-diagonal terms was found.

Simulated Foreign Object Damage on Blade Aerofoils: Real Damage Investigation

During operating service, gas turbine aero-engines can ingest small hard particles which typically produce damage to the aerofoils. If the damage found is a tear or a perforation at the leading edge, it is known as a Foreign Object Damage or FOD and this leads to a reduction of the subsequent High-Cycle-Fatigue (HCF) strength. The objective of research work in this area is to assess the effect of FOD on the residual fatigue strength of compressor blades and to provide predictive tools for engineering judgment. The methodology followed is normally to carry out experimental simulation of FOD, followed by fatigue tests to assess subsequent performance. To date, research related to fatigue following FOD events has concentrated on HCF loading and the impact geometry is frequently that of a sphere against a flat surface or the edge of a blade-like specimen. Both of these aspects do not correspond to the worst cases of real FOD. Here it is intended to investigate the effect of a V-notch geometry, which is more representative of severe FOD found in service. Alongside this, numerical models can be used to simulate the damage and to evaluate the residual stress field. In addition analytical model are used to predict the residual fatigue strength. The current work explains the development of a new rig impact test and discusses the improvements necessary to obtain a sufficient repeatability of the impacts. From the experience gained with a gas gun, an alternative method using a pistol and a barrel, capable of achieving the necessary velocity of simulated FOD, was developed. The applied velocity was in the range of 250m/s to 300m/s and a technique to describe the impact is here discussed. Furthermore the introduction of a high speed camera has allowed to have a complete description of the impact scene and to better understand the impact. The impacted blades were measured and HCF tested. As a result, this has produced a large scatter in the residual fatigue strength. The current method to describe a notch using a 2D approach, which was applied to several geometries of notches, is here critically reviewed. The proposed method would incorporate a more sophisticated method, which reconstruct the real geometry using optical measurement. This latter measurement can fully describe the 3D geometry, showing particularly zones inside the notch where compressive residual might appears. Tears and shear of the material can also be described by applying this technique. The findings are compared with the residual HCF strength and the results are compared to special cases of HCF to justify the results out of theoretical prediction.

Topology-Optimized Intermediate Casing of Aero Engine and Comparative Evaluation of Titanium and Composite Architecture in Terms of Load Capacity and Weight Reduction

From Aero Engines of the future it is demanded to provide more power, while the fuel consumption and the mass should decrease. In order to reach the goal of an increasing specific power or a decreasing specific mass, respectively, structural optimization methods, like the topology optimization, find their way into the design process to a greater extent. Additionally one is going to consider more and more fiber reinforced composites as a substitute for titanium alloys in the “cold” structure of the engine. Composite materials offer significant advantages especially concerning the specific mass and the adjustability of their stiffness properties. Unfortunately it is very difficult to predict damage and fracture of such orthotropic materials. The presentation will show the results of a topology optimization of the titanium intermediate-casing of a Rolls-Royce aero engine. Further on the material of the casing will be substituted by a carbon fiber reinforced composite. The fiber orientations and layer thicknesses of the composite are optimized under certain strength constraints, which are described by a modern fracture plane based failure criterion (NASA LaRC04 criterion [6]). Such a failure criterion has a lot of advantages compared to classical ones like Tsai-Hill, Tsai-Wu, ..., which e.g. do not distinguish between fiber and inter-fiber fracture and are therefore not able to predict the type of inter-fiber fracture. Finally the results of the optimization with the current material titanium will be compared to the results of the composite-made intermediate casing in terms of their load capacity and weight.