Underplatform Friction Dampers Research Articles

A novel method for predicting the response variability of friction-damped gas turbine blades

Predicting the response of gas turbine blades with underplatform friction dampers is challenging due to the combination of frictional nonlinearity and system uncertainty: a traditional Monte Carlo approach to predicting response distributions requires a large number of nonlinear simulations which is computationally expensive. This paper presents a new approach based on the principle of Maximum Entropy that provides an estimate of the response distribution that is approximately two orders of magnitude faster than Monte Carlo Harmonic Balance Method simulations. The premise is to include the concept of ‘computational uncertainty’: incorporating lack of knowledge of the solution as part of the uncertainty, on the basis that there are diminishing returns in computing precise solutions to an uncertain system. To achieve this, the method uses a describing function approximation of the friction-damped part of the system; chooses an ignorance prior probability density function for the complex value of the describing function based on Coulombs friction law; updates the distribution using an estimate of the mean solution, the admissible domain of solutions, and the principle of Maximum Entropy; then carries out a linear Monte Carlo simulation to estimate the response distribution. The approach is validated by comparison with HBM simulations and experimental tests, using an idealised academic system consisting of a periodic array of beams (with controllable uncertainty) coupled by single-point friction dampers. Comparisons with two- and eight-blade systems show generally good agreement. Predicting the response statistics of the maximum blade amplitude reveals specific well-understood circumstances when the method is less effective. Predictions of the overall blade response statistics agree with Monte Carlo HBM extremely well across a wide range of excitation amplitudes and uncertainty levels. Critically, experimental comparisons reveal the care that is needed in accurately characterising uncertainty in order to obtain agreement of response percentiles. The new method allowed fast iteration of uncertainty parameters and correlations to achieve good agreement, which would not have been possible using traditional methods.

Vibration analysis of beam structures with localized nonlinearities by a wave approach

This paper presents a general wave propagation approach for the vibration analysis of structures consisting of beam elements with localized nonlinearities. The scattering of a wave at a nonlinear discontinuity creates multi-harmonic waves. This forms the basis of the model formulation in which the displacement in each element composing the structure is defined as a sum of waves associated with the fundamental frequency and its harmonics. The coupling between separate elements is expressed using transmission coefficients function of the harmonic number and includes propagating and decaying near field waves whose amplitudes are the unknowns of the problem. With the use of harmonic balance, a characteristic algebraic equation of motion is derived. The general systematic methodology is demonstrated and detailed on beam-like systems with nonlinear boundaries for validation against a conventional finite element analysis. To illustrate the effectiveness of the approach on a more practical case, the method is also applied to a simplified model of a turbomachinery blade with underplatform friction dampers. The predictions of stick-slip effect and global nonlinear damping behavior made using the proposed approach are shown to be in excellent agreement with the results of numerical time integration with the advantage of reduced computational costs.

A substructure-based numerical technique and experimental analysis of turbine blades damping with underplatform friction dampers

Friction dampers are commonly used in jet and turboprop engines to decrease vibration stresses of turbine blades by means of irreversible conversion of mechanical energy into heat. Effectiveness of such an energy transfer depends on design, material and operational conditions of dampers. Optimization of dampers design is a complex task usually associated with analysis of nonlinear contact problems and complicated experimental verification. It is also coupled with high time costs causing the engineering task to be modified into a complex research problem. Although it is necessary to understand that numerical modeling of damping of turbine blades represents a task that need significant computational resources and precise experimental verification. So, it was decided to create a finite element-model for calculations of unsteady blade-damper interaction based on a substructure reduction method. The dummy blades and dampers were used to simplify the task.The presented technique is based on the finite-element method with a numerical model reduction by Craig–Bampton and Guyan algorithms. The model consisted of dummy blades pair with a wedged damper between the platforms. This technique allowed considering three-dimensional shapes of parts, non-linear contact forces, friction, various operational loads and conditions. The model was verified by experiments performed on a special test rig based on a vibration shaker and a 3D laser vibrometer. A relationship between oscillation amplitude of blades and a centrifugal load on the damper was obtained in the range of centrifugal loads 0…700 N. Also, the effect of friction coefficient µ in the range 0.2 … 0.8 on resonant blades amplitudes was investigated. An optimal operational range with maximum damper efficiency was defined. An effect of so-called anti-phase and in-phase modes of adjacent blades on damper efficiency was investigated.

Reliability optimization of friction-damped systems using nonlinear modes

A novel probabilistic approach for the design of mechanical structures with friction interfaces is proposed. The objective function is defined as the probability that a specified performance measure of the forced vibration response is achieved subject to parameter uncertainties. The practicability of the approach regarding the extensive amount of required design evaluations is strictly related to the computational efficiency of the nonlinear dynamic analysis. Therefore, it is proposed to employ a recently developed parametric reduced order model (ROM) based on nonlinear modes of vibration, which can facilitate a decrease of the computational burden by several orders of magnitude. The approach was applied to a rotationally periodic assembly of a bladed disk with underplatform friction dampers. The robustness of the optimum damper design was significantly improved compared to the deterministic approach, taking into account uncertainties in the friction coefficient, the excitation level and the linear damping. Moreover, a scale invariance for piecewise linear contact constraints is proven, which can be very useful for the reduction of the numerical effort for the analysis of such systems.

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.

Experimental and Numerical Investigation of Rotating Bladed Disk Forced Response Using Underplatform Friction Dampers

In this paper, we present a methodology and results from an experimental investigation of forced vibration response for a bladed disk with fitted underplatform “cottage-roof” friction dampers, together with the corresponding numerical predictions. A carefully designed and constructed rotating test rig is used to make precise measurements, which involve only the phenomena of interest. For this purpose, the measurement rig is operated under vacuum to eliminate aerodynamic effects on the rotating blisk and noncontact excitation and measurement techniques are employed so as not to modify the bladed disk dynamics. The experimental data measured are used for validation of multiharmonic balance-based prediction tools developed at the Imperial College. Predictions are carried out both with and without taking inherent mechanical mistuning into account, which is identified from measured data. Measured and predicted response curves are compared with each other and the degree of correlation is discussed.

Advanced Modeling of Underplatform Friction Dampers for Analysis of Bladed Disk Vibration

Advanced structural dynamic models for both wedge and split underplatform dampers have been developed. The new damper models take into account inertia forces and the effects of normal load variation on stick-slip transitions at the contact interfaces. The damper models are formulated for the general case of multiharmonic forced response analysis. An approach for using the new damper models in the dynamic analysis of large-scale finite element models of bladed disks is proposed and realized. Numerical investigations of bladed disks are performed to demonstrate the capabilities of the new models and an analysis of the influence of the damper parameters on the forced response of bladed disks is made.