Underplatform Dampers Research Articles

A method for detection and characterisation of structural non-linearities using the Hilbert transform and neural networks

This paper presents a method for detection and characterisation of structural non-linearities from a single frequency response function using the Hilbert transform in the frequency domain and artificial neural networks. A frequency response function is described based on its Hilbert transform using several common and newly introduced scalar parameters, termed non-linearity indexes, to create training data of the artificial neural network. This network is subsequently used to detect the existence of non-linearity and classify its type. The theoretical background of the method is given and its usage is demonstrated on different numerical test cases created by single degree of freedom non-linear systems and a lumped parameter multi degree of freedom system with a geometric non-linearity. The method is also applied to several experimentally measured frequency response functions obtained from a cantilever beam with a clearance non-linearity and an under-platform damper experimental rig with a complex friction contact interface. It is shown that the method is a fast and noise-robust means of detecting and characterising non-linear behaviour from a single frequency response function.

On the relevance of a microslip contact model for under-platform dampers

A crucial part of building reliable models for the design of under-platform dampers for turbine blades resides in the appropriate description of the contact conditions, both in the normal and in the tangential direction.The aim of this paper is to determine to what extent microslip due to the combined non-linearities along the normal and the tangent of non-conforming contact surfaces influences the damper behavior. The ultimate goal is to determine whether introducing these features in the contact model would improve the performance of numerical routines used at the blade-damper design stage. In order to explore this problem, a purposely developed contact model is tuned on a single-contact test and then included in the numerical model of a curved-flat damper to simulate its cylindrical interface. The damper numerical routine is then validated against the results from an experimental device purposely developed to test the dynamics of a damper loaded between moving platforms.It is shown that the validated numerical routine featuring the newly introduced contact model predicts, in comparison with the standard contact model (where partial slip and normal approach non-linearity are not considered), a lower dissipated energy by an amount that would not be justifiable to neglect.

Optimal normal load variation in wedge-shaped Coulomb dampers

Wedge-shaped frictional dampers are widely used in civil, mechanical and aeronautical engineering with the purpose to limit and damp vibrations, increase component fatigue life, or resist seismic loads. The wedge shape induces normal load variations which complicates the analysis. Here, we study a model which can be considered a generalization of the Griffin model, originally devised for underplatform dampers in turbine blade attachments. The model has a mass element (the body whose vibrations are to be damped) linked to the wall by means of a spring and to a massless Coulomb damper via a “contact stiffness". In Griffin’s work the normal load acting on the Coulomb damper was kept constant. We introduce cyclic amplitude of the normal load, and phase shift between tangential and normal load. It is found that the optimization curves maintain the minimum for the mean normal load expected by Griffin’s model. However, a lower vibration amplitude is found for in-phase loading with respect to the constant load, over the entire frequency range. When the “contact stiffness" is higher than the structure stiffness (as it is generally expected), the maximum vibration decrement for in-phase loading is around 40%.

Latest investigations on underplatform damper inner mechanics

Underplatform dampers (UPDs) are widely used as a source of friction damping and are frequentlyincorporated into compressors and turbines for both aircraft and power-plant applications to mitigate the effectsof resonant vibrations on fatigue failure. Due to the nonlinear nature of dry friction, in general dynamic analysisof structures constrained through frictional contacts is difficult, direct time integration with commercial finiteelement codes may not be a suitable choice given the large computation times. For this reason, ad hoc numericalcodes have been developed in the frequency domain. Some authors prefer a separate routine in order to computecontact forces as a function of input displacements, others include the damper in the FE model of the bladedarray. All numerical models, however, require knowledge or information of contact -friction parameters, whichare established either through direct frictional measurements, done with the help of single contact testarrangements, or by fine tuning the parameters in the numerical model and comparing the experimental responseof damped blade against its computed response. The standard approach is to fine-tune and experimentallyvalidate the UPDs models by comparing measured and calculated vibration response of blade pairs. To ourknowledge, nobody has ever attempted to directly measure the forces transmitted between the platforms throughthe damper and the relative damper-platform movement.In the light of recent results from direct measurements on dampers it is evident that a dedicated routinefor the damper mechanics is an effective tool to capture those finer details which are essential to an appropriatedescription of damper behaviour. This was made possible by the successful effort of the present authors toaccurately measure the forces transmitted between the platforms through the damper, to connect them with therelative platforms movement and to use the findings for the validation of the numerical model. The crosscomparisonbetween numerical and experimental results allows to gain a clear understanding of all contactevents (stick, slip, lift) which take place during the cycle, and on how they influence the damping performance.

A direct experimental–numerical method for investigations of a laboratory under-platform damper behavior

Under-platform dampers are commonly adopted in order to mitigate resonant vibration of turbine blades. The need for reliable models for the design of under-platform dampers has led to a considerable amount of technical literature on under-platform damper modeling in the last three decades.Although much effort has been devoted to the under-platform damper modeling in order to avail of a predictive tool for new damper designs, experimental validation of the modeling is still necessary. This is due to the complexity caused by the interaction of the contacts at the two damper-platform interfaces with the additional complication of the variablity of physical contact parameters (in particularly friction) and their nonlinearity. The traditional experimental configuration for evaluating under-platform damper behavior is measuring the blade tip response by incorporating the damper between two adjacent blades (representing a cyclic segment of the bladed disk) under controlled excitation. The effectiveness of the damper is revealed by the difference in blade tip response depending on whether the damper is applied or not. With this approach one cannot investigate the damper behavior directly and no measurements of the contact parameters can be undertake. Consequently, tentative values for the contact parameters are assigned from previous experience and then case-by-case finely tuned until the numerical predictions are consistent with the experimental evidence. In this method the physical determination of the contact parameters is obtained using test rigs designed to produce single contact tests which simulate the local damper-platfom contact geometry. However, the significant limitation of single contact test results is that they do not reveal the dependence of contact parameters on the real damper contact conditions. The method proposed in this paper overcomes this problem.In this new approach a purposely developed test rig allows the in-plane forces transferred through the damper between the two simulated platforms to be measured, while at the same time monitoring in-plane relative displacements of the platforms. The in-plane damper kinematics are reconstructed from the experimental data using the contact constraints and two damper motion measurements, one translational and one rotational. The measurement procedures provide reliable results, which allow very fine details of contact kinematics to be revealed. It is demonstrated that the highly satisfactory performance of the test rig and the related procedures allows fine tuning of the contact parameters (local friction coefficients and contact stiffness), which can be safely fed into a direct time integration numerical model.The numerical model is, in turn, cross-checked against the experimental results, and then used to acquire deeper understanding of the damper behavior (e.g. contact state, slipping and sticking displacement at all contact points), giving an insight into those features which the measurements alone are not capable of producing. The numerical model of the system is based on one key assumption: the contact model does not take into account the microslip effect that exists in the experiments.Although there is room for improvement of both experimental configuration and numerical modeling, which future work will consider, the results obtained with this approach demonstrate that the optimization of dampers can be less a matter of trial and error development and more a matter of knowledge of damper dynamics.

Modeling and Validation of the Nonlinear Dynamic Behavior of Bolted Flange Joints

Linear dynamic finite element analysis can be considered very reliable today for the design of aircraft engine components. Unfortunately, when these individual components are built into assemblies, the level of confidence in the results is reduced since the joints in the real structure introduce nonlinearity that cannot be reproduced with a linear model. Certain types of nonlinear joints in an aircraft engine, such as underplatform dampers and blade roots, have been investigated in great detail in the past, and their design and impact on the dynamic response of the engine is now well understood. With this increased confidence in the nonlinear analysis, the focus of research now moves towards other joint types of the engine that must be included in an analysis to allow an accurate prediction of the engine behavior. One such joint is the bolted flange, which is present in many forms on an aircraft engine. Its main use is the connection of different casing components to provide the structural support and gas tightness to the engine. This flange type is known to have a strong influence on the dynamics of the engine carcase. A detailed understanding of the nonlinear mechanisms at the contact is required to generate reliable models and this has been achieved through a combination of an existing nonlinear analysis capability and an experimental technique to accurately measure the nonlinear damping behavior of the flange. Initial results showed that the model could reproduce the correct characteristics of flange behavior, but the quantitative comparison was poor. From further experimental and analytical investigations it was identified that the quality of the flange model is critically dependent on two aspects: the steady stress/load distribution across the joint and the number and distribution of nonlinear elements. An improved modeling approach was developed that led to a good correlation with the experimental results and a good understanding of the underlying nonlinear mechanisms at the flange interface.

On Force Control of an Engine Order–Type Excitation Applied to a Bladed Disk With Underplatform Dampers

The paper presents an original multiple excitation system based on electromagnets with force control. The system is specifically designed in order to investigate the dynamics of bladed disks, since it mimics the excitation existing in a real engine. Moreover, the system is suitable for forced response tests of bladed disks with nonlinear dynamic response, like in the case of presence of friction contacts, since the amplitude of the exciting force is known with good precision. For this purpose, a device called force-measuring electromagnet (FMEM) was designed and employed during the system calibration. The excitation system is applied to the test rig Octopus, which includes underplatform dampers (UPDs). Tests were carried out under different excitation force amplitude values. The tests put in evidence the presence of mistuning and the UPDs' capability of attenuating the mistuning phenomena.

A Study of Nonlinear Vibrations in a Frictionally Damped Turbine Bladed Disk With Comprehensive Modeling of Aerodynamic Effects

A new effective method for comprehensive modeling of gas flow effects on vibration of nonlinear vibration of bladed disks has been developed for a case when the effect of the gas flow on the mode shapes is significant. The method separates completely the structural dynamics calculations from the significantly more computationally expensive computational fluid dynamics (CFD) calculations while providing the high accuracy of modeling for aerodynamic effects. A comprehensive analysis of the forced response using the new method has been performed for a realistic turbine bladed disk with root-disk joints, tip, and under-platform dampers. The full chain of aerodynamic and structural calculations are performed: (i) determination of boundary conditions for CFD, (ii) CFD analysis, (iii) calculation of the aerodynamic characteristics required by the new method, and (iv) nonlinear forced response analysis using the modal aerodynamic influence matrix (MAIM). The efficiency of the friction damping devices has been studied and compared for several resonance frequencies and engine orders. Advantages of the method for aerodynamic effect modeling have been demonstrated.

Measuring the performance of underplatform dampers for turbine blades by rotating laser Doppler Vibrometer

Underplatform friction dampers are commonly used to control the vibration level of turbine blades in order to prevent high-cycle fatigue failures. Experimental validation of highly non-linear response predictions obtained from FEM bladed disk models incorporating underplatform dampers models has proved to be very difficult so as the assessment of the performance of a chosen design. In this paper, the effect of wedge-shaped underplatform dampers on the dynamics of a simple bladed disk under rotating conditions is measured and the effect of the excitation level on the UPDs performances is investigated at different number of the engine order excitation nearby resonance frequencies of the 1st blade bending modes of the system. The measurements are performed with an improved configuration of a rotating test rig, designed with a non-contact magnetic excitation and a non-contact rotating SLDV measurement system.

Modeling underplatform dampers for turbine blades: a refined approach in the frequency domain

Friction damping is one of the most exploited systems of passive control of the vibration of mechanical systems. In order to mitigate vibration of turbine blades, friction dampers are commonly included in the bladed disk design. A common type of blade-to-blade friction dampers are the so-called underplatform dampers (UPDs); these are metal devices placed under the blade platforms and held in contact with them by the centrifugal force acting during rotation. The effectiveness of UPDs to dissipate energy by friction and reduce vibration amplitude depends mostly on the damper geometry and material and on the static loads pressing the damper against the blade platforms. The common procedure used to estimate the static loads acting on UPDs consists in decoupling the static and the dynamic balance of the damper. A preliminary static analysis of the contact is performed in order to compute the static pressure distribution over the damper/blade interfaces, assuming that it does not change when vibration occurs. In this paper a coupled approach is proposed. The static and the dynamic displacements of blade and UPD are coupled together during the forced response calculation. Both the primary structure (the bladed disk) and the secondary structure (the damper) are modeled by finite elements and linked together by contact elements, allowing for stick, slip and lift off states, placed between each pair of contact nodes, by using a refined version of the state-of-the-art friction contact model. In order to model accurately the blade/damper contact with a large number of contact nodes without increasing proportionally the size of the set of nonlinear equations to be solved, damper and blade dynamics are modeled by linear superposition of a truncated series of normal modes. The proposed method is applied to a bladed disk under cyclic symmetric boundary conditions in order to show the capabilities of the method compared to the classical decoupled approaches.

Effects of Contact Interface Parameters on Vibration of Turbine Bladed Disks With Underplatform Dampers

The design of high cycle fatigue resistant bladed disks requires the ability to predict the expected damping of the structure in order to evaluate the dynamic behavior and ensure structural integrity. Highly sophisticated software codes are available today for this nonlinear analysis, but their correct use requires a good understanding of the correct model generation and the input parameters involved to ensure a reliable prediction of the blade behavior. The aim of the work described in this paper is to determine the suitability of current modeling approaches and to enhance the quality of the nonlinear modeling of turbine blades with underplatform dampers. This includes an investigation of a choice of the required input parameters, an evaluation of their best use in nonlinear friction analysis, and an assessment of the sensitivity of the response to variations in these parameters. Part of the problem is that the input parameters come with varying degrees of uncertainty because some are experimentally determined, others are derived from analysis, and a final set are often based on estimates from previous experience. In this investigation the model of a commercial turbine bladed disk with an underplatform damper is studied, and its first flap, first torsion, and first edgewise modes are considered for 6 EO and 36 EO excitation. The influence of different contact interface meshes on the results is investigated, together with several distributions of the static normal contact loads, to enhance the model setup and, hence, increase accuracy in the response predictions of the blade with an underplatform damper. A parametric analysis is carried out on the friction contact parameters and the correct setup of the nonlinear contact model to determine their influence on the dynamic response and to define the required accuracy of the input parameters.

An Electromagnetic System for the Non-Contact Excitation of Bladed Disks

In this paper a non-contact excitation system based on electromagnets is described. The system aims at exciting cyclically symmetric structures like bladed disks by generating typical engine order-like travelling wave excitations that bladed disks encounter during service. Detailed description of the analytical formulation for the electromagnets sizing, quality assessment and practical implications of the final assembly for the bladed disk excitation are addressed. In particular, the paper proposes an original method to setup the excitation system in order to perform step-sine controlled force measurements. This feature is necessary when non-linear forced response must be measured on bladed disks in order to characterize the dynamic behaviour at different level of excitation. Typical applications of the designed excitation system are two: the first is the study of the effect of a force pattern characterized by a particular engine order on the forced response of mistuned bladed disks, the second is the characterization of intentional non-linear damping source occurring, for instance, for friction phenomena in presence of shrouds or underplatform dampers.

A High-Accuracy Model Reduction for Analysis of Nonlinear Vibrations in Structures With Contact Interfaces

A highly accurate and computationally efficient method is proposed for reduced modeling of jointed structures in the frequency domain analysis of nonlinear steady-state forced response. The method has significant advantages comparing with the popular variety of mode synthesis methods or forced response matrix methods and can be easily implemented in the nonlinear forced response analysis using standard finite element codes. The superior qualities of the new method are demonstrated on a set of major problems of nonlinear forced response analysis of bladed disks with contact interfaces: (i) at blade roots, (ii) between interlock shrouds, and (iii) at underplatform dampers. The numerical properties of the method are thoroughly studied on a number of special test cases.

A Test Rig for Noncontact Traveling Wave Excitation of a Bladed Disk With Underplatform Dampers

This paper presents a static test rig called “Octopus” designed for the validation of numerical models aimed at calculating the nonlinear dynamic response of a bladed disk with underplatform dampers (UPDs). The test rig supports a bladed disk on a fixture and each UPD is pressed against the blade platforms by wires pulled by dead weights. Both excitation system and response measurement system are noncontacting. This paper features the design and the setup of the noncontacting excitation generated by electromagnets placed under each blade. A traveling wave excitation is generated according to a desired engine order by shifting the phase of the harmonic force of one electromagnet with respect to the contiguous exciters. Since the friction phenomenon generated by UPDs introduces nonlinearities on the forced response, the amplitude of the exciting force must be kept constant at a known value on every blade during step-sine test to calculate frequency response functions. The issue of the force control is therefore addressed since the performance of the electromagnet changes with frequency. The system calibration procedure and the estimated errors on the generated force are also presented. Examples of experimental tests that can be performed on a dummy integral bladed disk (blisk) mounted on the rig are described in the end.

The effect of underplatform dampers on the forced response of bladed disks by a coupled static/dynamic harmonic balance method

Friction contacts are often used in turbomachinery design as passive damping systems. In particular, underplatform dampers are mechanical devices used to decrease the vibration amplitudes of bladed disks. Numerical codes are used to optimize during designing the underplatform damper effectiveness in order to limit the resonant stress level of the blades. In such codes, the contact model plays the most relevant role in calculation of the dissipated energy at friction interfaces. One of the most important contact parameters to consider in order to calculate the forced response of blades assembly is the static normal load acting at the contact, since its value strongly affects the area of the hysteresis loop of the tangential force, and therefore the amount of dissipation. A common procedure to estimate the static normal loads acting on underplatform dampers consists in decoupling the static and the dynamic balance of the damper. A preliminary static analysis of the contact is performed in order to get the static contact/gap status to use in the calculation, assuming that it does not change when vibration occurs. In this paper, a novel approach is proposed. The static and the dynamic displacements of the system (bladed disk+underplatform dampers) are coupled together during the forced response calculation. Static loads acting at the contacts follow from static displacements and no preliminary static analysis of the system is necessary. The proposed method is applied to a numerical test case representing a simplified bladed disk with underplatform dampers. Results are compared with those obtained with the classical approach.

A test rig for the investigation of the dynamic response of a bladed disk with underplatform dampers

The paper presents the planning, structure and preliminary results of a new test rig for the validation of numerical models that calculate the dynamic response of bladed disks with underplatform dampers (UPDs).

Multiharmonic Forced Response Analysis of a Turbine Blading Coupled by Nonlinear Contact Forces

Abstract In turbomachinery applications, the rotating turbine blades are subjected to high static and dynamic loads. The static loads are due to centrifugal stresses and thermal strains whereas the dynamic loads are caused by the fluctuating gas forces resulting in high vibration amplitudes, which can lead to high cycle fatigue failures. Hence, one of the main tasks in the design of turbomachinery blading is the reduction in the blade vibration amplitudes to avoid high dynamic stresses. Thus, coupling devices like underplatform dampers and tip shrouds are applied to the blading to reduce the vibration amplitudes and, therefore, the dynamic stresses by introducing nonlinear contact forces to the system. In order to predict the resulting vibration amplitudes, a reduced order model of a shrouded turbine blading is presented including a contact model to determine the nonlinear contact forces. To compute the forced response, the resulting nonlinear equations of motion are solved in the frequency domain using the multiharmonic balance method because of the high computational efficiency of this approach. The transformation from the time domain into the frequency domain is done by applying Galerkin’s method in combination with a multiharmonic approximation function for the unknown vibration response. This results in an algebraic system of nonlinear equations in the frequency domain, which has to be solved iteratively in order to compute the vibration response. The presented methodology is applied to the calculation of the forced response of a nonlinear coupled turbine blading in the frequency domain.

Forced Response of Mistuned Bladed Disks in Gas Flow: A Comparative Study of Predictions and Full-Scale Experimental Results

An integrated experimental-numerical study of forced response for a mistuned bladed disk has been performed. A full chain for the predictive forced response analysis has been developed including data exchange between the computational fluid dynamics code and a code for the prediction of the nonlinear forced response for a bladed disk. The experimental measurements are performed at a full-scale single stage test rig with excitation by aerodynamic forces from gas flow. The numerical modeling approaches and the test rig setup are discussed. Comparison of experimentally measured and predicted values of blade resonance frequencies and response levels for a mistuned bladed disk without dampers is performed. A good correspondence between frequencies at which individual blades have maximum response levels is achieved. The effects of structural damping and underplatform damper parameters on amplitudes and resonance frequencies of the bladed disk are explored. It is shown that the underplatform damper significantly reduces scatters in values of the individual blade frequencies and maximum forced response levels.

Measurement of the kinematics of two underplatform dampers with different geometry and comparison with numerical simulation

Underplatform dampers are used as friction damping devices in order to reduce the amplitude of vibrations of blades in turbine rotors. In this paper a study was performed on the forced response of a mock up system which simulates the flexural behaviour of two turbine blades with an interposed underplatform damper. Two different geometries are tested for two different deflection shapes and the dynamic response of the whole system is explained with respect to the damper kinematics. The originality of the work consists in the measurement of the damper displacements by means of a laser Doppler vibrometers (LDV) equipment and in the comparison with the displacements obtained by numerical predictions of a numerical code used for damper design. The strong influence of the rotation of the underplatform damper on the dynamic response is analysed in particular for the in-phase vibration of the two dummy blades. Comparison between calculations and experiments shows that the damper model allows simulating the damper kinematics with good accuracy.

Underplatform dampers for turbine blades: The effect of damper static balance on the blade dynamics

In this paper, a novel method to compute the static balance of turbine blades with underplatform dampers is presented, focusing on the influence of the static loads on the system dynamics. The proposed method allows preventing the calculation of non-unique forced response levels of the blade, occurring when simplified hypotheses are applied to the damper static balance.