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.

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.

scholarly journals Friction Damper Optimisation: Simulation of Rainbow Tests

1999 ◽  
Author(s):  
Kenan Y. Sanliturk ◽  
David J. Ewins ◽  
Robert Elliott ◽  
Jeff S. Green
Keyword(s):  
Harmonic Balance Method ◽  
Lumped Parameter Model ◽  
Friction Damper ◽  
Blade Vibration ◽  
Friction Dampers ◽  
Lumped Parameter ◽  
Engine Order ◽  
Resonance Response ◽  
Theoretical Predictions ◽  
Different Characteristics

Friction dampers have been used to reduce turbine blade vibration levels for a considerable period of time. However, optimal design of these dampers has been quite difficult due both to a lack of adequate theoretical predictions and to difficulties in conducting reliable experiments. One of the difficulties of damper weight optimisation via the experimental route has been the inevitable effects of mistuning. Also, conducting separate experiments for different damper weights involves excessive cost. Therefore, current practice in the turbomachinery industry has been to conduct so-called ‘rainbow tests’ where friction dampers with different weights are placed between blades with a predefined configuration. However, it has been observed that some rainbow test results have been difficult to interpret and have been inconclusive for determining the optimum damper weight for a given bladed-disc assembly. A new method of analysis — a combination of Harmonic Balance Method and structural modification approaches — is presented in this paper for the analysis of structures with friction interfaces and the method is applied to search for qualitative answers about the so-called ‘rainbow tests’ in turbomachinery applications. A simple lumped-parameter model of a bladed-disc model was used and different damper weights were modelled using friction elements with different characteristics. Resonance response levels were obtained for bladed discs with various numbers of blades under various engine-order excitations. It was found that rainbow tests, where friction dampers with different weights are used on the same bladed-disc assembly, can be used to find the optimum damper weight if the mode of vibration concerned has weak blade-to-blade coupling (the case where the disc is almost rigid and blades vibrate almost independently from each other). Otherwise, it is very difficult to draw any reliable conclusion from such expensive experiments.

scholarly journals A review of friction damping modeling and testing

2019 ◽  
Vol 90 (1) ◽  
pp. 107-126 ◽  
Author(s):  
Louis Gagnon ◽  
Marco Morandini ◽  
Gian Luca Ghiringhelli
Keyword(s):  
Internal State ◽  
Experimental Testing ◽  
Analytical Models ◽  
Friction Damper ◽  
Friction Damping ◽  
Friction Dampers ◽  
Modeling Approaches ◽  
Planar Surfaces ◽  
Wide Range ◽  
Friction Models

Abstract This survey provides an insight into the modeling and testing of uniaxial friction dampers. The focus is on attenuating the linear relative movement along planar surfaces for frequencies between 10 Hz and 1 kHz. An overview of the different approaches seen in the literature concerning friction damping is provided. Examples and evaluation of such dampers excited over a wide range of frequencies are presented. The information required to develop models of friction dampers is covered. To that end, different modeling approaches are presented for dry friction. Dynamic friction models with an internal state are covered, and their advantages are described. Other modeling approaches are reported for complete systems with friction dampers. Both numerical and analytical models are covered. Experimental configurations from a selection of authors are also included. Finally, a series of suggestions for the numerical modeling and experimental testing of a friction damper are given.

Steady Compressible Flow through a Single Row of Radial Holes in the Wall of a Pipeline

1970 ◽  
Vol 12 (4) ◽  
pp. 248-258 ◽  
Author(s):  
G. H. Trengrouse
Keyword(s):  
Discharge Coefficient ◽  
Pressure Change ◽  
Single Row ◽  
One Dimensional ◽  
Discharge Coefficients ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Flow Through ◽  
Flow Theories ◽  
Good Agreement

Measured values of discharge coefficient for air flow through a single row of radial holes in the wall of a pipeline are reported, together with the values of pipe Mach numbers in the immediate vicinity of the holes. A wide range of pressure and area ratios are considered, the flow through the holes being either into or out of the pipe. It is shown that the effects on the measured values of both the pressure level at discharge from the holes and the air temperature are negligible. The agreement between the pressure change in the pipeline due to the holes, obtained experimentally, and that predicted by simple, one-dimensional flow theories is generally unsatisfactory. However, theoretical predictions of the jet efflux angles based on two-dimensional, incompressible, non-viscous flow arguments are in good agreement with those measured, but discrepancies do arise in the prediction of discharge coefficients.

Force and Moment Measurements of Supercavitating Hydrofoils of Finite Span With Comparison to Theory

1975 ◽  
Vol 97 (4) ◽  
pp. 453-462
Author(s):  
P. Leehey ◽  
T. S. Stellinger
Keyword(s):  
Aspect Ratio ◽  
Asymptotic Expansions ◽  
Cavity Length ◽  
Large Aspect Ratio ◽  
Drag Coefficients ◽  
Finite Span ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Lift And Drag ◽  
Good Agreement

Measurements were made of lift, drag, and moment coefficients, and cavity length for aspect ratio 3 and 5 supercavitating hydrofoils of elliptical planform. These measurements are compared with theoretical predictions obtained from matching asymptotic expansions for large aspect ratio. Good agreement was obtained for lift and drag coefficients for angles of attack from 10 deg to 15 deg and for a wide range of cavity lengths. Theoretical moment coefficients were too large indicating the need for lifting surface corrections.

Stiffness and Bond Strength of Rubber-Filled Hinges

1993 ◽  
Vol 66 (5) ◽  
pp. 733-741 ◽  
Author(s):  
A. N. Gent ◽  
Y-W. Chang
Keyword(s):  
Finite Element Analysis ◽  
Bond Strength ◽  
Direct Analysis ◽  
Test Method ◽  
Bond Rupture ◽  
Experimental Measurements ◽  
Element Analysis ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Good Agreement

Abstract The stiffness of rubber-filled hinges for small rotations of the hinge plates has been determined by finite element analysis (FEA). The rubber is assumed to be linearly elastic and virtually incompressible, and the hinge is assumed to be long enough for the rubber to be in a state of plane strain, i.e., prevented from any displacement parallel to the hinge. Results have been obtained for hinges of a wide range of unstrained angle, ranging from 5° up to 360°. The calculated stiffnesses for long hinges vary by over four orders of magnitude over this range. For small angles, an approximate solution has been obtained by direct analysis—it is in good agreement with the FEA solution for hinge angles up to about 40°. Experimental measurements on several rubber-filled hinges are also reported. The measured rotational stiffnesses are in satisfactory agreement with theoretical predictions. Because a rubber-filled hinge constitutes a possible test method for bond strength, conditions are derived for bond rupture as a hinge is strained open.

Governing Equations of the Shear Angle Oscillation in Dynamic Orthogonal Cutting

1986 ◽  
Vol 108 (4) ◽  
pp. 280-287 ◽  
Author(s):  
D. William Wu
Keyword(s):  
Orthogonal Cutting ◽  
Shear Plane ◽  
Shear Angle ◽  
Governing Equations ◽  
Line Field ◽  
Angle Variation ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Transfer Behavior ◽  
Good Agreement

Chatter is a complex physical process in machining. One of the practical ways of modeling its transfer behavior is to derive the force functions theoretically from the substance of steady state cutting. This often requires a knowledge about the shear angle variation during the process. This paper presents a new method of modeling the angular oscillation in dynamic orthogonal cutting. The system governing equations were derived based on the work-hardening slip-line field theory in cutting mechanics by taking into account the changes of stress conditions on both the shear plane and the tool-chip interface. The result of a simulation study conducted for a wide range of cutting conditions has shown a very good agreement between the theoretical predictions and the existing experimental evidence.

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.

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.

Theoretical Dynamic Analysis of a Cantilever Beam Damped by a Dry Friction Damper

1995 ◽  
Author(s):  
I. Korkmaz ◽  
J. J. Barrau ◽  
M. Berthillier ◽  
S. Creze
Keyword(s):  
Dynamic Response ◽  
Cantilever Beam ◽  
Dry Friction ◽  
Coulomb Friction ◽  
Contact Stiffness ◽  
Temporal Integration ◽  
Element Model ◽  
Friction Damper ◽  
Coulomb Friction Law ◽  
Good Agreement

Abstract The dynamic behavior of a cantilever beam damped by dry friction has been studied The beam is represented partly by its effective modal parameters, obtained from a finite element model. The Coulomb friction law is used and a temporal integration of the dynamic response is performed. A detailed parametric study, highlighting the influence of the static and the dynamic friction coefficients, the viscous damping coefficient, the contact stiffness and the position of the damper along the span, on the dynamic response has been conducted. A better understanding of the damping mechanism by dry friction has been obtained. The numerical results have been compared to experimental results, and a good agreement was found. The results could be applied to a turbine blade with a blade to ground damper.

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