Underplatform Dampers Research Articles

Topology optimisation of friction under-platform dampers using moving morphable components and the efficient global optimization algorithm

Under-platform dampers (UPDs) are traditionally used in aircraft engines to reduce the risk of high cycle fatigue. By introducing friction in the system, vibrations at resonance are damped. However, UDPs are also the source of nonlinear behaviours making the analysis and the design of such components complex. The shape of such friction dampers has a substantial impact on the damping performances, and topology optimisation is seldomly utilised—particularly for nonlinear structures. In the present work, we present a numerical approach to optimise the topology of friction dampers in order to minimise the vibration amplitude at a resonance peak. The proposed approach is based on the moving morphable components framework to parametrise the damper topology, and the efficient global optimisation algorithm is employed for the optimisation. The results demonstrate the relevance of such an approach for the optimisation of nonlinear vibrations in the presence of friction. New efficient damper geometries are identified in a few iterations of the algorithm, illustrating the efficiency of the approach. Results show that the most efficient geometry divides the vibration amplitude at resonance by 3, corresponds to a lower mass (80%) and a smaller frequency shift compared to the non-optimised case. More generally, the different geometries are analysed and tools for clustering are proposed. Different clusters are identified and compared. Thus, more general conclusions can be obtained. More specifically, the most efficient geometries correspond to geometries that reduce the mass of the damper and increase the length of the contact surface. Physically, it corresponds to a reduction of the initial normal contact pressure, which implies that the contact points enter stick/slip earlier, bringing more damping. The results show how topology optimisation can be employed for nonlinear vibrations to identify efficient layouts for components.

Nonlinear dynamic analysis of three-dimensional bladed-disks with frictional contact interfaces based on cyclic reduction strategies

In bladed disks, friction nonlinearities occurring within the contact between the blades and disk or between the blades and underplatform dampers are used to decrease the vibratory energy of the system and extend its lifespan. Modeling these nonlinearities and simulating their effects correctly are challenging: complex nonlinear phenomena such as stick, slip and separation may occur in the contact zones. Efficient numerical methods must be used to compute the dynamics of the system in a reasonable amount of time. This paper proposes a reduction strategy to tackle large cyclically symmetric finite-element models undergoing static preload from centrifugal effects and strong nonlinearities (friction and separation). It combines the nonlinear identification of the possible interacting nodal diameters with a linear component mode synthesis procedure. Its potential and performances are assessed through comparisons with some state-of-the-art methods. Complex and realistic nonlinear finite-element models of bladed disks with underplatform dampers and dovetail or fir-tree blade roots are used. The Dynamic Lagrangian Frequency Time algorithm is employed to capture the nonlinear effects. Using the proposed reduction method, the effect of underplatform dampers on bladed disk contact occurrence and damping efficiency is investigated.

Impact of Mistuned Underplatform Dampers on the Nonlinear Vibration of Bladed Disks

Abstract Before the final experimental validation and certification of a turbo-engine, designers perform a numerical simulation of its vibratory properties, among other things, in order to estimate its lifespan and adjust the design in an optimization process. One possible practical solution to decrease the vibratory response is to add underplatform dampers to the system. These components dissipate energy by friction and are widely employed in turbomachinery. However, a specific underplatform damper is usually efficient only for a specific mode. The purpose of this work is to investigate the possibility of adding different kinds of underplatform dampers to the cyclic structure in order to decrease the vibratory energy over a larger panel of modes. Different methods exist to determine the vibrations of nonlinear cyclic symmetric systems, but creating a robust methodology to account for the additional effect of mistuning remains a big challenge in the community. In this paper, the structure is mistuned through the friction coefficient of the dampers and not by altering its geometry, as is usually done in the literature. First, assuming a cyclic symmetric structure, the performance of the dampers is assessed for specific modes. Then, employing a method recently developed, the efficiency of an intentional mistuning pattern of underplatform dampers is studied and an optimal pattern proposed.

Verification of a Mathematical Model of a Dry Friction Damper for a GTE Blade

This paper presents the verification of the mathematical model utilized to calculate the damping capacity of a dry friction damper. The mathematical model is based on determining natural frequencies and mode shapes, as well as relative characteristics of the friction energy losses. To estimate the applicability of the mathematical model to full-scale assemblies of a gas-turbine engine, the model was verified by the results of the experiment. The experiment was carried out in a laboratory where the damping capacity of the gas-turbine engine blade with a model under-platform damper was examined at constrained and damped oscillations. During the experiment multiple materials of contact pair were examined to determine how microslip affects the damping capacity. Based on the results of comparing calculations with the experiment, by selecting the dry friction coefficient, a good convergence on the oscillation decrement and natural frequency was achieved. The conducted research has shown that the mathematical model provides reliable results with Coulomb friction and can consider microslip effects on the damper capacity.

Platform-Centered Reduction: A Process Capturing the Essentials for Blade-Damper Coupled Optimization

Abstract The purpose of this paper is to develop an attractive tool for designers in the initial design phase of the damping of turbomachinery blades through dry friction underplatform dampers. The paper shows how, to this purpose, certain reasonable simplifications are introduced in the procedure and in the model, leaving the customary full high fidelity computations to the final design verification analysis. The key simplifications here considered are: the blade neck is modeled with Euler beam finite elements (FE) to speed up the updating of its dimensions during the optimization process; the contact forces exerted by the dampers on the blade platform are represented by the resultant forces and moments applied to a reference point on the platform, associated with its displacements and rotations; the airfoil, which is not modified during the coupled optimization of the damper, is obtained from a full three-dimensional (3D) FE model after a component mode synthesis (CMS) reduction. It is shown that the here proposed process captures the essentials of the nonlinear dynamics of the blade-damper problem without sacrificing in any way the accuracy of the results. This hybrid model is then employed in the process where the optimal match domains between the damper and the blade are searched for, by exploring the influence of blade neck thickness (flexibility) and damper mass. Such a purposely simplified process allows a clear identification of relationships between relevant blade features and response with a focus on fatigue life.

Propagation of friction parameter uncertainties in the nonlinear dynamic response of turbine blades with underplatform dampers

Underplatform dampers are widely used in turbomachinery to mitigate structural vibrations by means of friction dissipation at the interfaces. The modelling of such friction dissipation is challenging because of the high variability observed in experimental measurements of contact parameters. Although this variability is not commonly accounted for in state-of-the-art numerical solvers, probabilistic approaches can be implemented to include it in dynamics simulations in order to significantly improve the estimation of the damper performance. The aim of this work is to obtain uncertainty bands in the dynamic response of turbine blades equipped with dampers by including the variability observed in interfacial contact parameters. This variability is experimentally quantified from a friction rig and used to generate uncertainty bands by combining a deterministic state-of-the-art numerical solver with stochastic Polynomial Chaos Expansion (PCE) models. The bands thus obtained are validated against experimental data from an underplatform damper test rig. In addition, the PCEs are also employed to perform a variance-based global sensitivity analysis to quantify the influence of contact parameters on the variation in the nonlinear dynamic response via Sobol indices. The analysis highlights that the influence of each contact parameter in vibration amplitude strongly varies over the frequency range, and that Sobol indices can be effectively used to analyse uncertainties associated to structures with friction interfaces providing valuable insights into the physics of such complex nonlinear systems.

Experimental and Numerical Assessment of Mistuning Effects on Vibratory Response of a Bladed Disk With Underplatform Dampers

Abstract This paper presents experimental and numerical investigation of mistuned forced responses of an integrally bladed disk with full set of underplatform dampers (UPDs). This research aims at providing: 1. An experimental benchmark for nonlinear dynamics of a mistuned bladed disks with UPDs. 2. A numerical model that can account for features of a mistuned forced response level. Accordingly, a detailed experimental campaign is conducted on a static test rig called Octopus. This rig is specifically designed to investigate the dynamics of a full-scale integrally bladed disk (blisk) with UPDs in a noncontact manner so that the dynamic response of the system is not modified. The effect of mistuning on experimental forced response levels is assessed and a linearized model is proposed to predict the modulation of frequency response functions (FRFs) due to the frequency splitting. In the development of the model, the mistuning pattern identified from the linear blisk without UPDs is used and it is assumed that adding the dampers does not change the structural mistuning of the blisk. In this study, the fundamental mistuning model identification (FMM ID) was employed to identify the mistuning pattern of the blisk. It is shown that the proposed model successfully predicts the modulation of linear mistuned FRFs. The linearized model is also able to predict the modulation of nonlinear mistuned FRFs in stick condition (when nonlinear friction damping is negligible) with a good accuracy validating this assumption that adding the dampers does not change the mistuning pattern.

Topological Optimization of Under-Platform Dampers With Moving Morphable Components and Global Optimization Algorithm for Nonlinear Frequency Response

Abstract To limit the risk of high cycle fatigue, underplatform dampers (UDPs) are traditionally used in aircraft engines to control the level of vibration. Many studies demonstrate the impact of the geometry of the damper on its efficiency, thus the consideration of topological optimization (TO) to find the best layout of the damper seems natural. Because of the nonlinear behavior of the structure due to the friction contact interface, classical methods of TO are not usable. This study proposes to optimize the layout of an UDP to reduce the level of nonlinear vibrations computed with the multiharmonic balance method (MHBM). The approach of TO employed is based on the moving morphable components (MMC) framework together with the Kriging and the efficient global optimization algorithm to solve the optimization problem. The results show that the level of vibration of the structure can be reduced to 30% and allow for the identification of different efficient geometries.

On the Efficiency of a Conical Underplatform Damper for Turbines

Abstract Underplatform dampers (UPDs) are commonly used in aircraft engines to limit the risk of high-cycle fatigue of turbine blades. The latter is located in a groove between two consecutive blades. The dry friction contact interface between the damper and the blades dissipates energy and so reduces the vibration amplitudes. Two common geometries of dampers are used nowadays, namely wedge and cylindrical dampers, but their efficiency is limited when the blades have an in-phase motion (or a motion close to it), since the damper tends to have a pure rolling motion. The objective of this study is to analyze a new damper geometry, based on a conical shape, which prevents from this pure rolling motion of the damper and ensures a high kinematic slip. The objective of this study is to demonstrate the damping efficiency of this geometry. Hence, in a first part, the kinematic slip is approximated with analytical considerations. Then, a nonlinear dynamic analysis is performed, and the damping efficiency of this new geometry is compared to the wedge and the cylindrical geometries. The results demonstrate that the conical damper has a high damping capacity and is more efficient and more robust than the two others.

Contact nonlinear analysis for the under-platform dampers of blade based on a frictional energy dissipation model

The under-platform dampers of blade in an aero-engine can reduce the vibration through friction energy dissipation, which is generally regarded as a kind of foundation vibration model subjected to fluctuant pressure. The possible unstable air-flow and complex changes in aero-engine’s speed at service result in the consequence that the tangential pressure originated from blade vibration as well as the centrifugal force applied on the foundation vibration model appear fluctuating. These fluctuant parameters are often assumed in the sinusoidal form. Meanwhile, the frequency ratio and phase difference between them also change during the operation process. To explore the effects of the changes in frictional energy dissipation and nonlinear contact response, a differential equation for a frictional energy model with the vibrational foundation is deduced and proposed in this paper. The equation integrates the complex condition of friction into a simple differential form, through which the hysteresis characteristic for different frequency ratios and phase differences are calculated precisely and efficiently. Additionally, the amplitude-frequency characteristics of the relative displacement between the contact surfaces of the proposed model are further investigated. This study can provide a reference for dynamic tribology design of the under-platform damper for engineering.

Modeling Complex Contact Conditions and Their Effect on Blade Dynamics

Abstract Dry friction devices such as underplatform dampers are commonly included in turbine bladed disks designs to mitigate structural vibrations and avoid high cycle fatigue failures. The design of frictionally damped bladed disks requires adequate models to represent the friction contact. A widely used approach connects contact node pairs with normal and tangential springs and a Coulomb friction law. This simple model architecture is effective in capturing the softening behavior typically observed on frictionally damped structures subjected to increasing forcing levels. An unexpected hardening behavior was observed on the frequency response functions (FRFs) of a two-blades-plus-damper system tested by the authors in a controlled laboratory environment. The reason behind this unexpected behavior will be carefully analyzed and linked to the damper kinematics and to the dependence of contact elasticity on the contact pressure. The inadequacy of contact models with constant spring values will be discussed and alternatives will be proposed. The importance of being able to represent complex contact conditions in order to effectively predict the system dynamics is shown here using a laboratory demonstrator; however, its implications are relevant to any other case where large contact pressure variations are to be expected. The nonlinear steady-state simulations of the blades-plus-damper system will be carried out using an in-house code exploiting the multiharmonic balance method in combination with the alternating frequency time method.

Friction damping and forced-response of vibrating structures: An insight into model validation

Dry friction is widely incorporated in turbomachinery, in the form of under-platform dampers, to limit vibrations at resonance and reduce risks of high-cycle fatigue failures. Most of the test rigs that were used to investigate the behavior of under-platform dampers aim at evaluating the damper performance in terms of reduction of forced-response amplitude in blades. This approach could be insufficient to understand local nonlinearities in the contact and the influence of dampers on blade dynamics. A recently developed test rig provides the authors with an unprecedented set of information. It is capable to measure contact forces and relative displacements between dampers and blade in addition to the overall blade dynamic response. This controlled environment, together with an effective model of the blade/dampers system, is used to provide an insight into the subject of model validation. The presented experimental and numerical study of the damper is used to highlight the relevance of an accurate representation of the constraints induced by friction contacts and to discuss the adequacy of state-of-the-art contact models.

Robust design optimisation of underplatform dampers for turbine applications using a surrogate model

Underplatform dampers (UPD) represent an effective way to limit blade vibration in turbomachinery via frictional energy dissipation, leading to a wide range of applications. The design of an effective and reliable UPD is highly challenging, due to the inherently nonlinear nature of the contact forces, the associated computational cost for high fidelity simulation, and the manufacturing uncertainties in damper geometry. This paper presents a novel UPD optimisation approach that combines high-order, detailed nonlinear modelling of the damper interfaces with a surrogate model optimisation technique. The nonlinear dynamic behaviour of the UPD is predicted using the existing explicit damper model in combination with an ‘in-house’ multi-harmonic balance solvers, which enables capture of the damper kinematics and local contact conditions. A radial basis function based surrogate model will be used to address the computational requirement of the high fidelity simulations for alternative designs. The objective function takes into account the damping performance, resonance frequency stability and robustness due to possible uncertain variations of design parameters with manufacture tolerance. The feasibility of the proposed approach is demonstrated on a cottage roof UPD by comparing the proposed optimisation method with conventional parametric simulation method. A significantly improved solution with considerable reduction in computational effort is achieved by the current method.

The Effect of Surface Finish on the Proper Functioning of Underplatform Dampers

Abstract Underplatform dampers are used to limit the resonant vibration of turbine blades. In recent years, various strategies have been implemented to maximize their damping capability. Curved-flat dampers are preferred to ensure a predictable bilateral contact, while a pre-optimization procedure was developed to exclude all those cross-sectional shapes that will bring the damper to roll and thus limit the amount of dissipated energy. The pre-optimization bases its predictions on the assumption that the effective width of the flat contact interface corresponds to the nominal one. It is shown here that this hypothesis cannot be relied upon: the energy dissipated by two nominally identical dampers, machined according to the usual industrial standards, may differ by a factor up to three due to the morphology of the flat-to-flat contact interface. Five dampers have been tested on two dedicated test rigs, available in the AERMEC laboratory, specially designed to reveal the details of the damper behavior during operation. Their contact interfaces are scanned by means of a profilometer. In each case, the mechanics, the kinematics, and the effectiveness of the dampers in terms of cycle shape and dissipated energy are correlated to the morphology of the specific contact surface. To complete the picture, a state-of-the-art numerical simulation tool is used to show how this tribo-mechanic phenomenon, in turn, influences the damper effect on the dynamic response of the turbine.

Adaptive control of normal load at the friction interface of bladed disks using giant magnetostrictive material

A novel application of magnetostrictive actuators in underplatform dampers of bladed disks is proposed for adaptive control of the normal load at the friction interface to achieve the desired friction damping in the structure. Friction damping in a bladed disk depends on operating parameters, such as rotational speed, engine excitation order, nodal diameter normal contact load, and contact interface parameters, such as contact stiffness and friction coefficient. The operating parameters have a fixed value, whereas the contact interface parameters vary in an unpredictable way at an operating point. However, the ability to vary some of these parameters such as the normal contact load in a controlled manner is desirable to attain an optimum damping in the bladed disk at different operating conditions. Under the influence of an external magnetic field, magnetostrictive materials develop an internal strain that can be exploited to vary the normal contact load at the friction interface, which makes them a potentially good candidate for this application. A commercially available magnetostrictive alloy, Terfenol-D is considered in this analysis that is capable of providing magnetostrain up to 2 × 10-3 under prestress and a blocked force over 1500 N. A linearized model of the magnetostrictive material, which is accurate enough for a direct current application, is employed to compute the output force of the actuator. A nonlinear finite element contact analysis is performed to compute the normal contact load between the blade platform and the underplatform damper as a result of magnetostrictive actuation. The nonlinear contact analysis is performed for different actuator mounting configurations and the obtained results are discussed. The proposed solution is potentially applicable to adaptively control vibratory stresses in bladed disks and consequently to reduce failure due to high-cycle fatigue. Finally, the practical challenges in employing magnetostrictive actuators in underplatform dampers are discussed.

Analysis on vibration reduction of a rotating dovetailed blade with underplatform damper and installation preload

The vibration reduction characteristics of the flexible blade with a dovetail joint and underplatform damper are studied in this paper. Considering the influence of the platform mass on the inherent characteristics of the blade, this paper regards the underplatform as a particle with mass. Moreover, two types of friction models are introduced on the contact interfaces of the blade. Meanwhile, the normal pressure of the contact interfaces will change with the rotating speed of the blade. Also, the dynamical equation for the rotating blade is established based on the finite element method. The nonlinear friction force on the contact interface is brought into the dynamical equation, and the vibration response of the blade is solved. The effects of the rotating speed, the initial preload, and the contact angle of the underplatform on the vibration reduction characteristic of the blade are investigated.

Measured and Simulated Forced Response of a Rotating Turbine Disk With Asymmetric and Cylindrical Underplatform Dampers

Abstract The dynamics of turbine blades with underplatform dampers (UPDs) is often experimentally explored by using small test rigs like two-blade models for cost and complexity reasons. In this paper, the dynamics of a large-scale academic turbine disk is measured on a special rotation test rig. Such measurements have rarely been published so far. The test rig supports speeds up to 3600 rpm and turbine disks up to a diameter of 1.2 m. The turbine disk is tested linearly as well as with asymmetric and cylindrical UPDs. The excitation forces and the excitation order are varied. The results prove the damper effectiveness by lowering resonance amplitudes. Additionally, the mistuning influence on the result depiction is discussed. The measurements are compared to simulations of the nonlinear frequency response functions (FRFs), showing good agreement.

Direct measurement of the damping and stiffening capabilities of cylindrical underplatform dampers

The paper focuses on the cylindrical underplatform damper, a friction damping device widely used in power generation turbines. The first goal of the paper is to estimate the stiffness and damping contribution of cylindrical dampers interposed between adjacent blades vibrating along a typical in-phase mode. For the first time, the damper characterization is performed through the direct measurement of contact forces and platform displacements.Measurements show that the damper does not introduce damping or stiffness if the two platforms, with which the damper is in contact, share the same angles (i.e. blade with symmetrical platform) and are vibrating in-phase. This is an adequate design choice if only the damper sealing function is required, while changes to the disk dynamics are not desired. The damper produces a small stiffening effect only if the two adjacent platforms have different angles. These findings are confirmed by an analytical derivation performed on the basis of a simple yet effective damper model.The damper numerical model requires parameters which may be calibrated, i.e. the cylinder-on-flat tangential contact stiffness. The second goal of the paper is to use the experimental evidence on contact forces and platform displacements to estimate these parameters for different centrifugal loads using a purposely developed technique. These values are compared with those obtained at an identically designed contact interface on a curved flat damper (i.e. cylindrical damper with a flattened side). The differences found in the calibration parameters show that the local stiffnesses depends not only on the local geometry of the contact but also on the damper kinematics.

Dynamics of a Turbine Blade with an Under-Platform Damper Considering the Bladed Disc’s Rotation

High-cycle fatigue (HCF) failure of the turbine blades of aero-engines caused by high vibrational stresses is one of the main causes of aero-engine incidents [...]

A novel test rig for friction parameters measurement on underplatform dampers

The focus of this paper is on the direct experimental investigation of underplatform dampers, friction damping devices used on turbine bladed disks to limit resonant vibrations. Given the nonlinear and highly complex nature of dry friction, model validation of bladed disks with underplatform dampers still relies heavily on experimental verification, which is typically performed using the Frequency Response Function.This paper is the authors’ most recent effort to increase the understanding of friction and damper mechanics by gathering experimental evidence directly at the blade platform/damper interface.A new test rig for frequencies and contact pressures in line with real working conditions has been developed. The geometry of the test rig and its technical features are described in detail in the paper. The dedicated experimental evidence thus obtained is used to estimate (not tune) contact parameters. The influence of frequency, centrifugal load and of the flat-on-flat contact interface morphology is highlighted. Results are compared with those gathered using similar dampers on a different test rig. Contact parameters are then be fed to a state-of-the-art numerical code for the prediction of the dynamic response of friction damped systems. The experimental-numerical comparison is used as validation and as a basis to investigate the simulation sensitivity to contact parameters variability.