New Modeling Combining Kinematic and Stiffness Nonlinearity in Under Platform Dampers

2021 ◽  
Author(s):  
Ryuichi Umehara ◽  
Sotaro Takei ◽  
Tomohiro Akaki ◽  
Hiroki Kitada
Keyword(s):  
Friction Coefficient ◽  
Gas Turbines ◽  
Normal Load ◽  
Contact Stiffness ◽  
Turbine Blades ◽  
Frequency Variation ◽  
Friction Damper ◽  
Nonlinear Characteristics ◽  
Friction Dampers ◽  
Geometric Nonlinear

Abstract Turbine blades are used under increasingly severe conditions in order to increase the thermal efficiency of the gas turbines in operation. Friction dampers are often used to reduce the vibration of the blade and improve the plant reliability. Under platform dampers designed to generate friction between platforms and dampers have been widely adopted in gas turbines as one of the friction dampers. It is important to predict the vibration characteristics of such damper blades analytically during the design phase, and many analysis methods have been proposed vigorously. However, the phenomenon of the friction damper is not fully understood because of its complicated behavior due to nonlinearity such as contact and sliding. One of them is the variability of frequency generated in the under platform dampers. Recently, it has been reported on the variability of frequency in the mock-up blade test greatly under small excitation force, due to variability of contact surfaces. As different approach, mechanism of the variability of frequency is explained even if each damper pin has the same dimensions and characteristics of stiffness each other under the range of small vibration without slipped phenomena. In this paper, the phenomenon of this frequency variation is shown based on two physical phenomena. First, it shows the geometric nonlinear characteristics in which the normal load changes by the friction coefficient of the pin and the pin angle. Second, it shows the stiffness nonlinear characteristics in which the contact stiffness changes with the normal load of the pin. Based on the new proposed modeling of combining the geometric nonlinear characteristics and nonlinear stiffness characteristics, the phenomenon is shown in which the relative displacement of the pin changes the load and contact stiffness, and the frequency changes. It also shows that the maximum normal load before sliding is different depending on the friction coefficient and the pin angle, and that when the friction coefficient is large and the damper angle is large, the change in contact stiffness due to the normal load is large and the variability of frequency is large.

Estimation of Contact Stiffness and its Role in the Design of a Friction Damper

2001 ◽  
Author(s):  
J. Szwedowicz ◽  
M. Kissel ◽  
B. Ravindra ◽  
R. Kellerer
Keyword(s):  
Finite Element ◽  
Friction Coefficient ◽  
Contact Stiffness ◽  
Contact Problems ◽  
Analytical Models ◽  
Rational Approach ◽  
Friction Damper ◽  
Friction Dampers ◽  
Performance Curves ◽  
Damper Design

The use of under-platform friction dampers is a common practice for the elimination of high cycle fatigue failures of turbomachinery blading. Damper performance curves and damper optimization curves are used for the design of friction dampers. It is establishedAAfrom the previous work that apart from damper mass, the contact stiffness between damper and the blade platform is an important parameter in achieving a good damper design. Several methods for the estimation of damper stiffness have been proposed in the literature. Some of them include: 1. Curve fitting approach to a measured frequency response function, 2. Compliance measurement, 3. Measurement of hysteresis loop etc. However, it is not possible to carry out extensive sets of experiments to observe the influence of various parameters on the contact stiffness. Numerical and/or analytical models for contact stiffness evaluation are the present needs for a damper designer. This paper addresses a detailed investigation of the contact stiffness computation. Finite element modeling of the damper and the platform is carried out to study the effect of various parameters such as friction coefficient, centrifugal load, material properties etc. on the contact stiffness. The role of surface roughness and wear are neglected in the present analysis. The reliability of the applied finite element meshes is verified by simulating Hertz’s contact problems. The parametric study indicates that the contact stiffness builds up with increase in friction coefficient, centrifugal force and elastic modulus of the damper material. The results received from a pilot experiment are also presented for further evaluation of the computed results. Finally, a very good agreement between the numerical and experimental performance curves (resonance response amplitude of the blade versus excitation amplitude for the constant damper mass; Cameron et. al, 1987) of the blade with the damper is found for the tangential contact stiffness obtained from the finite element calculation. The present work extends the quest for a rational approach to damper design.

A Resonance Tracking Algorithm for the Prediction of Turbine Forced Response With Friction Dampers

2000 ◽  
Author(s):  
C. Bréard ◽  
J. S. Green ◽  
M. Vahdati ◽  
M. Imregun
Keyword(s):  
Rotor Blade ◽  
Turbine Blades ◽  
Turbine Rotor ◽  
Forced Response ◽  
Rotor Blades ◽  
Test Case ◽  
Friction Damper ◽  
Blade Vibration ◽  
Frequency Shifts ◽  
Friction Dampers

This paper presents an iterative method for determining the resonant speed shift when non-linear friction dampers are included in turbine blade roots. Such a need arises when conducting response calculations for turbine blades where the unsteady aerodynamic excitation must be computed at the exact resonant speed of interest. The inclusion of friction dampers is known to raise the resonant frequencies by up to 20% from the standard assembly frequencies. The iterative procedure uses a viscous, time-accurate flow representation for determining the aerodynamic forcing, a look-up table for evaluating the aerodynamic boundary conditions at any speed, and a time-domain friction damping module for resonance tracking. The methodology was applied to an HP turbine rotor test case where the resonances of interest were due to the 1T and 2F blade modes under 40 engine-order excitation. The forced response computations were conducted using a multi-stage approach in order to avoid errors associated with “linking” single stage computations since the spacing between the two bladerows was relatively small. Three friction damper elements were used for each rotor blade. To improve the computational efficiency, the number of rotor blades was decreased by 2 to 90 in order to obtain a stator/rotor blade ratio of 4/9. However, the blade geometry was skewed in order to match the capacity (mass flow rate) of the components and the condition being analysed. Frequency shifts of 3.2% and 20.0% were predicted for the 1T/40EO and 2F/40EO resonances in about 3 iterations. The predicted frequency shifts and the dynamic behaviour of the friction dampers were found to be within the expected range. Furthermore, the measured and predicted blade vibration amplitudes showed a good agreement, indicating that the methodology can be applied to industrial problems.

A Contact Model for Nonlinear Forced Response Prediction of Turbine Blades: Calculation Techniques and Experimental Comparison

2008 ◽  
Author(s):  
Christian M. Firrone ◽  
Marco Allara ◽  
Muzio M. Gola
Keyword(s):  
Normal Load ◽  
Contact Stiffness ◽  
Turbine Blades ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Contact Forces ◽  
Contact Model ◽  
Experimental Comparison ◽  
Normal Contact ◽  
Contact Models

Dry friction damping produced by sliding surfaces is commonly used to reduce vibration amplitude of blade arrays in turbo-machinery. The dynamic behavior of turbine components is significantly affected by the forces acting at their contact interfaces. In order to perform accurate dynamic analysis of these components, contact models must be included in the numerical solvers. This paper presents a novel approach to compute the contact stiffness of cylindrical contacts, analytical and based on the continuous contact mechanics. This is done in order to overcome the known difficulties in simultaneously adjusting the values of both tangential and normal contact stiffness experimentally. Monotonic loading curves and hysteresis cycles of contact forces vs. relative displacement are evaluated as a function of the main contact parameters (i.e. the contact geometry, the material properties and the contact normal load). The new contact model is compared with other contact models already presented in literature in order to show advantages and limitations. The contact model is integrated in a numerical solver, based on the Harmonic Balance Method (HBM), for the calculation of the forced response of turbine components with friction contacts, in particular underplatform dampers. Results from the nonlinear numerical simulations are compared with those from validation experiments.

Harmonic Balance Vibration Analysis of Turbine Blades With Friction Dampers

1997 ◽  
Vol 119 (1) ◽  
pp. 96-103 ◽  
Author(s):  
K. Y. Sanliturk ◽  
M. Imregun ◽  
D. J. Ewins
Keyword(s):  
Harmonic Balance ◽  
Turbine Blades ◽  
Numerical Test ◽  
Harmonic Balance Method ◽  
Nonlinear Behavior ◽  
Friction Damper ◽  
Friction Dampers ◽  
Equivalent Time ◽  
Time Marching ◽  
Detailed Assessment

Although considerable effort has been devoted to the formulation of predictive models of friction damper behavior in turbomachinery applications, especially for turbine blades, the problem is far from being solved due to the complex nonlinear behavior of the contact surfaces. This paper primarily focuses on analytical and numerical aspects of the problem and addresses the problem in the frequency domain while exploring the viability of equivalent time-domain alternatives. The distinct features of this work are: (i) the modelling of nonlinear friction damper behavior as an equivalent amplitude-dependent complex stiffness via a first-order harmonic balance method (HBM), (ii) the use of sine sweep excitation in time-marching analysis, (iii) the application of the methodology to numerical test cases, including an idealised 3D turbine blade model with several friction dampers, (iv) the verification of the numerical findings using experimental data, and (v) a detailed assessment of the suitability of HBM for the analysis of structures with friction dampers.

Numerical and Experimental Damping Assessment of a Thin-Walled Friction Damper in the Rotating Set-Up With High Pressure Turbine Blades

2006 ◽  
Author(s):  
J. Szwedowicz ◽  
C. Gibert ◽  
T. P. Sommer ◽  
R. Kellerer
Keyword(s):  
High Pressure ◽  
Contact Stiffness ◽  
Turbine Blades ◽  
Mode Shapes ◽  
Friction Damper ◽  
High Pressure Turbine ◽  
Friction Forces ◽  
Normal Contact ◽  
Contact Behaviour ◽  
Thin Walled

Under-platform friction dampers are preferably solutions for minimizing vibrations of rotating turbine blades. Solid dampers, characterized by their compact dimensions, are frequently used in real applications and often appear in patents in different forms. A different type of the friction damper is a thin-walled structure, which has larger dimensions and smaller contact stresses on a wider contact area in relation to the solid damper. The damping performance of a thin-walled damper, mounted under the platforms of two rotating, freestanding high pressure turbine blades is investigated numerically and experimentally in this paper. The tangential and normal contact stiffness, that are crucial parameters in optimal design of each friction damper, are determined from three-dimensional finite element (FE) computations of the contact behaviour of the thin-walled damper on the platform including friction and centrifugal effects. The computed contact stiffness values are applied to non-linear dynamic simulations of the analysed blades with the friction damper of a specified mass. These numerical analyses are performed in the modal frequency domain with a code, which is based on the Harmonic Balance Method (HBM) for the complex linearisation of friction forces. The blade vibrations are characterised by a set of the lowest FE mode shapes of one freestanding blade without damper. The dynamic results of the calculated blades with the damper are in good agreement with the measured data of the real mistuned system. In the analysed excitation range, the numerical performance curve of the thin-walled damper is obtained within the scatter band of the experimental results. For the known friction coefficients and available FE and HBM tools, the described numerical process confirms its usability in the design of under-platform dampers.

Dynamic Behavior of Spherical Friction Dampers and Its Implication to Damper Contact Stiffness

2006 ◽  
Vol 129 (2) ◽  
pp. 511-521 ◽  
Author(s):  
K-H. Koh ◽  
J. H. Griffin
Keyword(s):  
Contact Stiffness ◽  
Friction Damper ◽  
Test Fixture ◽  
Friction Dampers ◽  
Vibratory Response ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Vibrating Systems ◽  
Good Agreement ◽  
Mindlin’S Theory

A model that predicts the quasi-static behavior of a friction damper that has spherical contacts was developed using Mindlin’s theory. The model was integrated into a dynamic analysis that predicts the vibratory response of frictionally damped blades. The analytical approach was corroborated through a set of benchmark experiments using a blades/damper test fixture. There was good agreement between the theoretical predictions of amplitude and the values that were measured experimentally over a wide range of test conditions. It is concluded that it is possible to predict the vibratory response of frictionally damped vibrating systems using continuum mechanics, provided that the contact geometry is clearly defined and the local nonlinear contact is correctly taken into account.

Forced Response of Shrouded Blades With Intermittent Dry Friction Force

2008 ◽  
Author(s):  
Weiwei Gu ◽  
Zili Xu ◽  
Lv Qiang
Keyword(s):  
Friction Coefficient ◽  
Friction Force ◽  
Normal Load ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Gap Size ◽  
Algebraic Equations ◽  
Friction Damper ◽  
Friction Forces ◽  
Contact Points

The gap friction damper model is presented in this paper, which is employed to simulate the friction forces at the contact points of the shroud interface. Using the harmonic balance method (HBM), the friction force can be approximated by a series of harmonic functions. The governing differential equations of blade motion are transformed into a set of nonlinear algebraic equations, which can be solved iteratively to yield the steady-state response. The results show that the forced response is attenuated due to the additional damping introduced by frictional slip. The predicted results agree well with those of the Runge-Kutta method. In addition, the effect of parameters of damping structures such as the gap size, friction coefficient and normal load on the forced response of blades were studied. The results show that increasing the damper gap size causes a increase in resonant response. However, the increment isn’t obvious. In addition, an increase in friction coefficient or normal load decreases the forced response of blade.

scholarly journals Gas Turbine Blade Damper Optimization Methodology

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
R. K. Giridhar ◽  
P. V. Ramaiah ◽  
G. Krishnaiah ◽  
S. G. Barad
Keyword(s):  
Gas Turbines ◽  
Normal Load ◽  
Phase 1 ◽  
Second Phase ◽  
Friction Damper ◽  
Friction Damping ◽  
Engine Order ◽  
Optimization Methodology ◽  
Model Tuning ◽  
Two Phases

The friction damping concept is widely used to reduce resonance stresses in gas turbines. A friction damper has been designed for high pressure turbine stage of a turbojet engine. The objective of this work is to find out effectiveness of the damper while minimizing resonant stresses for sixth and ninth engine order excitation of first flexure mode. This paper presents a methodology that combines three essential phases of friction damping optimization in turbo-machinery. The first phase is to develop an analytical model of blade damper system. The second phase is experimentation and model tuning necessary for response studies while the third phase is evaluating damper performance. The reduced model of blade is developed corresponding to the mode under investigation incorporating the friction damper then the simulations were carried out to arrive at an optimum design point of the damper. Bench tests were carried out in two phases. Phase-1 deals with characterization of the blade dynamically and the phase-2 deals with finding optimal normal load at which the blade resonating response is minimal for a given excitation. The test results are discussed, and are corroborated with simulated results, are in good agreement.

Nonlinear Vibration by Asynchronous Excitation Force in Friction Damper of Turbine Blade

2020 ◽  
Author(s):  
Ryuichi Umehara ◽  
Haruko Shiraishi ◽  
Naoki Onozato ◽  
Tetsuya Shimmyo
Keyword(s):  
Nonlinear Vibration ◽  
Turbine Blade ◽  
Gas Turbines ◽  
Turbine Blades ◽  
Harmonic Balance Method ◽  
Time History ◽  
Harmonic Excitation ◽  
Friction Damper ◽  
Excitation Force ◽  
Force Components

Abstract Turbine blades are now being used under increasingly severe conditions in order to increase the thermal efficiency of gas turbines. Friction dampers are often used to reduce the vibration of the blade and improve the plant reliability. This is a general study dealing with resonance passing where the natural frequency of the turbine blade coincides with the frequency of specific harmonic excitation forces while increasing the turbine rotation speed. Asynchronous components of excitation forces are also considered in addition to the synchronous components caused by specific harmonic excitation forces. In this study, a new method for predicting the characteristics of nonlinear vibration under excitation force including both synchronous and asynchronous force components is developed. In order to investigate the effect of additional asynchronous loading, time history response analyses considering nonlinear vibration using simulated turbine blades were conducted. Results showed that friction damper slip can be induced by the presence of the additional asynchronous excitation force components even for low values of synchronous excitation force. It is shown that it is possible to use a calibration factor to predict vibration characteristics considering friction slipping by estimating the ratio of the total excitation force to the single harmonic excitation force. To verify the effect of asynchronous excitation force and the validity of the proposed correction method, verification tests were conducted experimentally. The experimental results show that friction slipping occurred under small harmonic excitation force when there was asynchronous excitation force and show good agreement with the numerical results. Moreover, the validity of the proposed method which corrects the dynamic characteristics obtained using of the first order harmonic balance method is confirmed.

Dynamic Behavior of Spherical Friction Dampers and Its Implication to Damper Contact Stiffness

2006 ◽  
Author(s):  
K.-H. Koh ◽  
J. H. Griffin
Keyword(s):  
Contact Stiffness ◽  
Friction Damper ◽  
Test Fixture ◽  
Friction Dampers ◽  
Vibratory Response ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Vibrating Systems ◽  
Good Agreement ◽  
Mindlin’S Theory

A model that predicts the quasi-static behavior of a friction damper that has spherical contacts was developed using Mindlin’s theory. The model was integrated into a dynamic analysis that predicts the vibratory response of frictionally damped blades. The analytical approach was corroborated through a set of benchmark experiments using a blades/damper test fixture. There was good agreement between the theoretical predictions of amplitude and the values that were measured experimentally over a wide range of test conditions. It is concluded that it is possible to predict the vibratory response of frictionally damped vibrating systems using continuum mechanics, provided that the contact geometry is clearly defined and the local nonlinear contact is correctly taken into account.

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