Underplatform Dampers Research Articles

A Static/Dynamic Coupled Harmonic Balance Method for Dry Friction Systems Containing Rigid Body Modes

Abstract A harmonic balance method for under-constrained dry friction systems containing rigid body modes (HBM-RBM) is proposed. This method aims to overcome the encountered obstacle when applying the harmonic balance method to turbine blades damped by underplatform dampers. The inspiration for HBM-RBM comes from the free interface modal synthesis method. The key innovation involves deriving the elastic inversion of the singular stiffness matrix through the elimination of rigid body modes. In this way, the general HBM framework can be adopted, and the frequency response of under-constrained dry friction systems can be solved in a static/dynamic coupled manner. The accuracy and efficiency are both verified on a lumped parameter model and a finite element model of turbines with UPDs from a real gas turbine. A comparative study between the HBM-RBM and the commonly adopted way of imposing artificial grounding springs (HBM-AGS) is conducted. Results demonstrate that the HBM-RBM holds a significant advantage over HBM-AGS, as it eliminates the need for artificial grounding springs (AGS) and avoids the necessity for numerous trial cases to determine AGS stiffness.

Modeling method and dynamic analysis of blade with double friction damping structure considering time-varying pressure distribution

A modeling and analytical method considering contact interface pressure characteristics is presented in this paper. Firstly, a high-fidelity model of a blade with a double friction damping structure is established by solid element, and a three-dimensional friction contact element is used to describe the nonlinear friction interface between the blade contact interfaces. Then, the static pressure distribution characteristics of the contact interface of the blade are obtained through the experimental device of the blade with double friction damping structure, and the accuracy of the pressure characteristics is verified. Based on the static pressure distribution, the time-varying dynamic pressure formula of blade contact interface is derived. The influence of the pressure distribution on the contact characteristics of the contact interface is analyzed and applied to the dynamic calculation of the rotating blade. The influence of different parameters on the blade dynamics is obtained. And the optimum mass ratio of the under-platform damper is obtained by simulating the operation condition of the aero engine blade acceleration process.

Numerical and Experimental Study on Dummy Blade with Underplatform Damper

To confirm the variation in damping ratio offered by dry friction dampers against structural vibration stress, this study developed a blade vibration response test system for capturing damping characteristic curves through both frequency sweep excitation and damping-freevibration methods. The damping-free vibration method demonstrates high efficiency, allowing for the acquisition of a complete damping ratio characteristic curve in a single experiment. Experimental findings indicate that the two contact surfaces on the triangular prism damper produce distinct damping effects, closely aligning with the predicted damping characteristic curves. The peak damping ratio was found to be independent of the centrifugal load of the damper; dampers with varying contact areas produce approximately similar damping characteristics; and the damping effect shows a positive correlation with the root extension length.

Experimental Research Into Aeroelastic Phenomena in Turbine Rotor Blades Inside ARIAS EU Project

Abstract This paper describes an aeroelastic experimental campaign on a low-pressure turbine-bladed rotor in a rotating wind tunnel that took place as a part of the Advanced Research Into Aeromechanical Solutions (ARIAS) EU project. The campaign can be considered a continuation of the free-flutter test that was performed as part of the FUTURE EU project, where the saturation of asynchronous vibrations due to dry friction was characterized. This new campaign studied new aspects of the physics behind saturated flutter, including the non-linear interaction between synchronous excitation and asynchronous vibration, the effectiveness of different mistuning patterns to suppress flutter, and the viability of under-platform dampers as a technology to control the amplitude of asynchronous vibrations. Furthermore, the campaign explored various operation conditions for the turbine rotor, including near-stall. In general, there was a good agreement between the theoretical predictions regarding all these different aspects of turbine flutter and the test results.

Multi-source uncertainty propagation and sensitivity analysis of turbine blades with underplatform dampers

Underplatform dampers (UPDs) mitigate turbine blade vibrations in aeroengines through friction dissipation generated by the contact interface. However, in UPD design, uncertainties are often overlooked, including manufacturing discrepancies, excitation forces, and wear factors, leading to suboptimal predictions of structural dynamic responses. This study presents a dynamic model for the blade-UPD system with cyclic symmetric attributes, which simulates uncertainties using statistical methods. An efficient algorithm using adaptive techniques is proposed to construct polynomial chaos expansions (PCE) for precise and efficient uncertainty quantification (UQ) in turbine blades with UPDs. Further, the influence of single/multiple parameter uncertainties on the dynamic characteristics of the blade-UPD is explored. Sobol' indices are then employed to assess the sensitivity of uncertain factors to the vibration reduction properties of UPDs. The findings suggest that the new approach, which offers precise UQ at minimal computational cost, outperforms traditional methods like Ordinary Least Squares (OLS) and Sparse Least Angle Regression (LARS). Observations reveal a significant impact of parameter uncertainties on blade-UPD dynamic responses, which manifest as "resonance bands" and "frequency shifts" in some cases. Sensitivity analysis indicates noticeable variations in Sobol' indices for each uncertainty parameter as the excitation frequency changes. Specifically, the uncertainty in the friction coefficient demonstrates pronounced sensitivity to amplitude when slip occurs at the contact interface. Furthermore, the observed "drop" phenomenon in Sobol' indices is explained.

Insight into the influence of frictional heat on the modal characteristics and interface temperature of frictionally damped turbine blades

The reciprocating relative motions of friction pairs introduce nonlinearities into the host structure, while also generating frictional heat, leading to a noticeable temperature rise at the contact interface. Consequently, the contact mechanics properties are not invariant but highly dependent on temperature. To elucidate the thermo-mechanical interaction mechanism in dry friction systems, we propose a novel multi-physical nonlinear modal analysis method called Thermo-Mechanical damped Nonlinear Normal Mode (TM-dNNM). This numerical method enables the determination of nonlinear modal characteristics considering thermo-mechanical coupling and the prediction of detailed temperature distribution on contact interface. The efficiency and convergence of the TM-dNNM are ensured through three key techniques: multi-physics reduced order modeling, analytical Jacobian matrix, and scaling adjustment. We apply the proposed numerical method to a typical turbine blade with a flat underplatform damper for engineering purposes. Results indicate that frictional heat significantly affects the nonlinear modal characteristics, exhibiting complex behavior such as softening/stiffening reversal and resonance amplitude backtracking. Neglecting the thermo-mechanical coupling can lead to a deviation of more than 13 Hz in the predicted modal frequency and an overestimation of the modal damping ratio by a factor of three. Interface temperature rises considerably at higher vibration levels, with the hotspot located near the lower left corner of the contact surface, where the average temperature exceeds 1180 ℃, approaching the melting point. By employing the TM-dNNM, designers can predict critical resonance amplitudes and identify potential local hotspots, thus helping prevent excessive temperature at the interface of frictionally damped turbine blades.

Design theory for vibration characterisation experiments on real turbine blades with underplatform damper

One of the main causes of turbine rotor blade failures is high-frequency fatigue caused by blade resonance, and the vibration of turbine blades can be effectively suppressed through the reasonable design of dry friction damping structure. In order to understand the vibration characteristics of the blade-disc system and to check whether the damping effect meets the technical specifications, it is necessary to design and carry out dry friction damping blade vibration characteristics experiment. This paper takes a certain type of underplatform damped turbine blade in production as an example, and briefly describes the design idea and design process of such blade vibration characteristic experiments under the premise of the experiment blade structure, material and other physical parameters.

Convergence-free mapping of non-linear damper-blade performance

In the bladed disks of turbomachinery, the problem arises of finding a damping device that reduces as much as possible the amplitude of the alternating stresses produced by the forced vibrations excited by the gas flow. Dry friction solid underplatform dampers are an established solution.The shape and size of the damper, in association with those of the platform, neck and airfoil, determine the non-linear response curves having as parameter the intensity of external excitation, here synthetically represented by a “proof” excitation force. Of greatest importance are the combinations (frequency, excitation force) that realise the maximum amplitude of forced oscillation (measured, for example, at the blade tip) and the maximum value of the amplitude of the variable stress produced by the vibrations at a critical point of the blade. Since the design of the damper-blade coupling is High-Cycle Fatigue driven, this stress amplitude is taken as a reference and related to the value of the excitation force. This can finally take the well-known form of the damper performance curve.Especially in the case of parametric explorations concerning shape, size and contact parameters, the current approach to this non-linear response problem, based on iterative convergence, is numerically prohibitive unless one uses special search techniques, such as the surrogate models of various types that are favoured today.An alternative computational process is presented here, that of integrating PCR (Platform Centred Reduction) with a new approach called Amplitude Layered (excitation) Force Mapping. This process reduces the amount of computation by up to three orders of magnitude compared to standard techniques and is a winning alternative to surrogate models.

Experimental Investigation of the Dynamic Response of a Flat Blade with Dual Dry Friction Dampers

One test rig comprising two blades and dual under-platform dampers (UPDs) was built to enhance the understanding of the dynamic response behavior of blades with dual UPDs. A turnbuckle was applied to enable the smooth and uninterrupted linear adjustment of the normal load on the dual UPDs. Non-contact vibration-response measurements were achieved through eddy-current displacement sensors. Contact excitation was employed using an electromagnetic exciter to determine the magnitude of the excitation load, which was measured using a force sensor mounted on the excitation rod. A feedback system was established to maintain a constant magnitude of the excitation force throughout the excitation process. The chosen experimental variables include the normal load, the amplitude of the excitation force, the effective contact area, and the position of the damper action. The frequency response function of the blade under various experimental parameters was obtained through frequency sweeping under sinusoidal excitation. The influence of each parameter on the dynamic characteristics of blades was studied. The results demonstrate that the double-layer damping system offers distinct advantages over its single-layer counterpart. The upper damping has a wider frequency-adjustment range and a lower resonance amplitude and takes a larger share of the damping efficiency.

Transient Resonance Passage of a Mistuned Bladed Disk with and without Underplatform Dampers

In this work, the vibration response of an academic free-standing turbine blisk is analyzed in regard to transient resonance passages. Measurement data are recorded using strain gauges and tip timing to evaluate the blades first bending mode both linearly and with two different types of underplatform dampers. These results are validated against steady-state responses and show good agreement with each other. To examine the effects of a transient resonance passage, response functions of each blade are evaluated both with and without the underplatform dampers. It is shown that friction damping is able to inhibit any appearance of a transient ring-down. Additionally, a multi-mass oscillator model with frictional contacts is analyzed, which qualitatively exhibits the same dynamics as the measurements. Due to geometric mistuning, all blades exhibit different vibration responses. This can lead to a transient amplitude amplification, which is observed on several blades. Analogously, this phenomenon can be mitigated by friction damping.

Study on the Forced Torsional Vibration Response of Multiple Rotating Blades with Underplatform Dampers

Underplatform dampers (UPDs), a type of dry friction damper, are commonly used for vibration reduction of turbine blades. This study investigated the effect of UPDs on the forced torsional vibration response of turbine blades within a multi-blade system. Pre-stressed finite element modal analysis and the harmonic balance method were combined to calculate the forced torsional vibration responses of a system with and without UPDs. The experiments were then carried out on a rotating multi-blade system with and without UPDs, with a focus on the effect of mass stacking on damping performance. The results showed that the installation of underplatform dampers could increase the frequency corresponding to the maximum response of the blade torsional vibration and cause multiple peaks that varied in the vibration response based on the mass of the UPDs. With an appropriate normal force, the underplatform dampers could effectively reduce the blade torsional vibration by 68.9%. However, excessive normal force of UPDs could lead to multiple large vibration peaks, which should be avoided in engineering practice. Additionally, the numerical results for the forced torsional vibration response of the rotating multi-blade system with UPDs were relatively close to the experimental results, indicating that the calculation method could be effectively applied to the nonlinear prediction of forced vibrations of rotating blades with dampers.

Experimental and Computational Study of a Rotating Bladed Disk with Under-Platform Dampers

There has been an extensive amount of work developing reduced-order models (ROMs) for bladed disks using single-sector models and a cyclic analysis. Several ROMs currently exist to accurately model a bladed disk with under-platform dampers. To better predict the complex nonlinear response of a system with under-platform dampers, this work demonstrates how two linear models can determine bounds for the nonlinear response. The two cases explored are where the under-platform damper is completely stuck and also where the damper slides without friction. This work utilizes the component mode mistuning method to model small mistuning and a parametric ROM method to capture changes in properties due to rotational speed effects. Previously, these ROM methodologies have modeled freestanding bladed disk systems. To evaluate the ROM in predicting the bounds, blade tip amplitudes from the models are compared with high-speed rotating experiments conducted in a large, evacuated vacuum tank. The experimental data were collected during testing using strain gauges and laser blade tip timing probes. The blade amplitudes of the tip timing data, strain gauge data, and computational simulations are compared to determine the effectiveness of the simplified linear analysis in bounding the nonlinear response of the physical system.

Vibration analysis characteristics of a pre-twisted tenon jointed blade with under-platform dampers in a thermal environment

This study proposes a method to study blades with multiple friction interfaces, to reveal the coupling effect of multi-interface blades on nonlinear vibrations. The dynamics of a pre-twisted tenon jointed blade with under-platform dampers in a thermal environment is modeled, considering the combined effects of thermal effects and nonlinear loads. Subsequently, a friction model of the tenon and under-platform dampers contact interface is developed. While studying the coupling effect of multiple friction interface, the effects of natural frequency, temperature, rotational speed and pre-twisted angle on blade vibration characteristics and nonlinear characteristics are analyzed.

Nonlinear dynamics of turbine bladed disk with friction dampers: Experiment and simulation

Accurately predicting the nonlinear dynamic response of aero-engine components is critical, as excessive vibration amplitudes can considerably reduce the operational lifespan. This paper compares experimental and numerical nonlinear dynamic responses of an industrial aero-engine, specifically focusing on the first stage turbine bladed disk with under-platform dampers (UPDs). The friction forces between UPDs and blades result in a strongly nonlinear dynamic response, influenced by stick, slip and separation contact states at the interfaces. These contact states, and the resulting global dynamic responses, are predicted with an advanced industrial modelling approach for nonlinear dynamics. The predictions are compared, updated and validated against measurement data from an operational engine test. Results highlight the importance to validate models against industrial data and show that realistic contact pressure distributions are required for increased prediction reliability. The novelty of this work includes (1) the use of unique industrial experimental data from a fully operational aero-engine, (2) the observation, at the end of engine testing, of real contact conditions in blade/UPD interfaces, (3) detailed modelling of these contact conditions with high-fidelity finite element representations in nonlinear dynamic solvers. Based on this unique industrial validation work, guidelines are proposed to improve the state-of-the-art modelling of nonlinear dynamics in structures with friction contacts.

A general geometrical theory of turbine blade underplatform asymmetric dampers

This paper presents a general geometric theory of in-plane motion of underplatform dampers as a function of blade neck deflection and the resulting platform kinematics. In-plane treatment is compatible with Mode 1 blade vibration, in which the rigid-body platform rotation associated with pure neck bending largely predominates over other rotations. The method applies when the amplitude of platform vibrational rotation reaches at least (or is greater than) the minimum value required to have, at both ends of the forward and reverse half-cycles, the onset of full slip in the last contact element still in stick.In this context, the first objective of this paper is to present a general geometric theory for damper kinematics and damper-platform forces, for both the In-Phase and Out-of-Phase blade vibrations and is then developed in detail for the In-Phase case. The concept of equivalent virtual parallel geometry is introduced, which transforms a case with nonnegligible inclination between adjacent blades into one, more tractable, valid for a very large (ideally infinite) number of blades. The equations are developed for the In-Phase case according to a formulation whose structure is particularly suited to highlighting the properties of the system, thus facilitating both its solution and interpretation.The second objective is to employ the equations in a piecewise linear algorithm to pre-compute a cycle as a sequence of a few finite linear sections in the number, per half-cycle, of Jenkins-type contact elements, so as to avoid both the time-step integration of the damper cycle used in the HBM-AFT approach and its repetition at each iteration of the solving system.The concept of a force Base-Cycle is introduced for the contact forces, unique for a given damper shape and its set of contact parameters, along with a moment Base-Cycle for the platform-damper system, an in-plane moment on the platform, generated by the contact forces, function of platform rotation.It is shown that such Base Cycles uniquely characterize a damper shape so that, once produced for a convenient Reference Case, they can be scaled linearly without recalculation according to size, radial force, platform proportions, and proportional variation of contact stiffness.To better illustrate the procedure, a practical example is developed in parallel with the theory, concluding with indications on how the moment Base-Cycle can be used in a reduced version of the Platform Centered Reduction, proposed in recent papers, meant to be a utility tool to support the initial damper design phase.

The Influence of Interface Roughness on the Vibration Reduction Characteristics of an Under-Platform Damper

Analysis of the vibration reduction characteristics of shock absorbers is crucial for engines. In this study, the fractal theory was applied to the contact surface of an under-platform damper (UPD), and the influence of the excitation force in the same and opposite directions on the roughness of the contact surface was studied. First, based on fractal geometry theory (FGT), the roughness characterization method of a UPD contact surface was proposed. Then, the friction mechanical model of the rough contact surface was established by combining it with a 3D contact mechanical model. Furthermore, a finite element dynamic model of a blade with a UPD structure was set up. Next, the harmonic balance method was used to calculate the nonlinear response characteristics of a blade under different levels of contact surface roughness. Finally, the influence of the contact surface roughness on the vibration reduction ability of a UPD under different excitation modes was analyzed. According to the simulation results, as the contact surface became rougher, the vibration suppression ability of the UPD on the blade became stronger and stronger. With the change in the centrifugal force of the UPD and the amplitude of the same/reverse excitation force, the influencing law of the contact surface roughness on the vibration suppression ability of the UPD remained unchanged, indicating that the rougher the contact surface roughness, the better the vibration suppression effect.

A test rig for the full characterization of the dynamics of shrouded turbine blades

Highly stressed forced vibrations experienced by Low Pressure Turbine (LPT) blades during their operation can result in high cycle fatigue (HCF) which can ultimately lead to failure. To avoid this occurrence, the vibration amplitudes must be anticipated and reduced. This is generally done by employing friction damping devices like under-platform dampers, shrouds and snubbers. In case of blades with shrouds at their tips, the adjacent shrouded blades are coupled to each other and three-dimensional periodic shroud contact forces acting on shrouds significantly influence the vibration amplitudes as energy is dissipated due to friction. Hence, for the experimental validation of the numerical contact models that are used for the prediction of nonlinear forced response of shrouded blades, it is equally necessary to measure the contact forces acting at the shrouds. Moreover, present-day requirement of more accurate and detailed models requires thorough and comprehensive experimental validation calling for the measurement of three-dimensional shroud contact forces from purposely designed test rigs.This study presents the design, development and operation of an experimental test rig that allows full characterization of the dynamics of shrouded turbine blade, i.e., simultaneous measurement of three-dimensional shroud contact forces and shrouded blade forced response. The starting point was the design of the test rig components based on the design requirements. This is followed by the description of the major components of the proposed test rig i.e., the three-dimensional contact force measurement system and the torque screw mechanism. In the subsequent section, the details of the experimental setup to measure the forced response and three-dimensional shroud contact forces simultaneously are highlighted as the test campaign is performed for different normal preloads and excitation force levels. Consequently, the effects of the variation in the normal preload and excitation force on the measured response and shroud contact forces are discussed. Finally, it is shown how the results establish the efficacy of the proposed test rig in providing a comprehensive depiction of the dynamic response of the shrouded blade and 3D shroud contact forces that will result in more accurate and reliable experimental validation of numerical tools.

Effect of under-platform dampers on the forced vibration of high-speed rotating blades

Effect of under-platform dampers on the forced vibration of high-speed rotating blades

An experimental and computational comparison of the dynamic response variability in a turbine blade with under-platform dampers

In this paper, the nonlinear response variability in turbine bladed disks coupled with under-platform dampers (UPDs) is both numerically and experimentally investigated in detail. Non-uniqueness uncertainty of contact forces, which leads to different static force equilibria under the same nominal conditions, is shown as the main source of multiple responses. In the experiments, a previously designed test rig consisting of one blade and two UPDs is used to reveal the inherent kinematics of the friction force uncertainty. A large variability range is achieved in different tests while keeping all user-controlled inputs identical. On the computational side, the boundaries of the variability range are predicted by utilizing a recently developed numerical method. The loss factor of the system is exploited as an objective function to be minimized through an optimization algorithm. To compare the results, several cases with different excitation levels and pre-loads are studied. It is shown in most of the cases that the method is well-suited for the computation of nonlinear response boundaries. Experimentally measured variability range of the dynamic responses and contact forces is computationally obtained with a satisfactory level of accuracy. A slight deviation is also reported in few cases, particularly for highly nonlinear ones where the numerical model is not fully capable of replicating the non-ideal conditions achieved during the tests.

Forced Response Vibration Analysis of the Turbine Blade with Coupling between the Normal and Tangential Direction

This paper is about the nonlinear dynamic of turbine blades due to the friction between blades. This paper investigates the coupling effect in an experimental turbine blade model. In this contact model, coupling between friction in tangential and normal directions and energy dissipation in the lateral direction are considered simultaneously, which has not been considered elsewhere in the contact model of the turbine blade. The mathematical model of the blade under-platform damper model is derived, and to solve nonlinear equations, the multi-harmonic balance method is used. The contact force is calculated by the alternative frequency time-domain method in this solution method. To solve nonlinear derived algebraic equations, a continuation algorithm is applied. It is shown that considering the coupling phenomenon causes the results to be different from the situation in which this physical phenomenon is ignored. To validate the algorithm of the solution, numerical results of previous references in the turbine-blade field are regenerated. Experimental analysis on the under-platform damper and turbine blade model is done to investigate the coupling effect. It is shown that the contact model with consideration with coupling effect between tangential and normal direction can predict experimental results (amplitude and frequency of resonance) most of the other contact models used in the turbine field. To accurately determine the amplitude and frequency of resonance, it is necessary to consider the coupling effect.