Modeling of Friction Contact and Its Application to the Design of Shroud Contact

Designers of aircraft engines frequently employ shrouds in turbine design. In this paper, a variable normal load friction force model is proposed to investigate the influence of shroud-like contact kinematics on the forced response of frictionally constrained turbine blades. Analytical criteria are formulated to predict the transitions between slick, slip, and separation of the interface so as to assess the induced friction forces. When considering cyclic loading, the induced friction forces are combined with the variable normal load so as to determine the effective stiffness and damping of the friction joint over a cycle of motion. The harmonic balance method is then used to impose the effective stiffness and damping of the friction joint on the linear structure. The solution procedure for the nonlinear response nf a two-degree-of-freedom oscillator is demonstrated. As an application, this procedure is used to study the coupling effect of two constrained forces, friction force and variable normal load, on the optimization of the shroud contact design.

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Characterization of Contact Kinematics and Application to the Design of Wedge Dampers in Turbomachinery Blading: Part 1—Stick-Slip Contact Kinematics

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.2818138 ◽

1998 ◽

Vol 120 (2) ◽

pp. 410-417 ◽

Cited By ~ 48

Author(s):

B. D. Yang ◽

C. H. Menq

Keyword(s):

Friction Force ◽

Harmonic Balance Method ◽

Forced Response ◽

Operating Conditions ◽

Force Model ◽

Blade Vibration ◽

Stick Slip ◽

Friction Forces ◽

Contact Kinematics ◽

Stiffness And Damping

Friction dampers are often used in turbine design to attenuate blade vibration to acceptable levels so as to prolong blades’ service life. A wedge damper, also called a self-centering, blade-to-blade damper, can provide more design flexibility to meet various needs in different operating conditions when compared with conventional platform dampers. However, direct coupling of the two inclined friction interfaces of the wedge damper often leads to very complex contact kinematics. In Part I of this two-part paper, a dual-interface friction force model is proposed to investigate the coupling contact kinematics. The key issue of the model formulation is to derive analytical criteria for the stick-slip transitions that can be used to precisely simulate the complex stick-slip motion and, thus, the induced friction force as well. When considering cyclic loading, the induced periodic friction forces can be obtained to determine the effective stiffness and damping of the interfaces over a cycle of motion. In Part II of this paper, the estimated stiffness and damping are then incorporated with the harmonic balance method to predict the forced response of a blade constrained by wedge dampers.

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Characterization of Contact Kinematics and Application to the Design of Wedge Dampers in Turbomachinery Blading: Part I — Stick-Slip Contact Kinematics

Volume 4: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education; IGTI Scholar Award ◽

10.1115/97-gt-019 ◽

1997 ◽

Cited By ~ 3

Author(s):

B. D. Yang ◽

C. H. Menq

Keyword(s):

Friction Force ◽

Harmonic Balance Method ◽

Forced Response ◽

Operating Conditions ◽

Force Model ◽

Blade Vibration ◽

Stick Slip ◽

Friction Forces ◽

Contact Kinematics ◽

Stiffness And Damping

Friction dampers are often used in turbine design to attenuate blade vibration to acceptable levels so as to prolong blades’ service life. A wedge damper, also called a self-centering blade-to-blade damper, can provide more design flexibility to meet various needs in different operating conditions when compared with conventional platform dampers. However, direct coupling of the two inclined friction interfaces of the wedge damper often leads to very complex contact kinematics. In Part I of this two-part paper, a dual-interface friction force model is proposed to investigate the coupling contact kinematics. The key issue of the model formulation is to derive analytical criteria for the stick-slip transitions that can be used to precisely simulate the complex stick-slip motion and, thus, the induced friction force as well. When considering cyclic loading, the induced periodic friction forces can be obtained to determine the effective stiffness and damping of the interfaces over a cycle of motion. In Part II of this paper, the estimated stiffness and damping are then incorporated with the harmonic balance method to predict the forced response of a blade constrained by wedge dampers.

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Forced Response of Shrouded Blades With Intermittent Dry Friction Force

Volume 5: Structures and Dynamics, Parts A and B ◽

10.1115/gt2008-51041 ◽

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.

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Characterization of Contact Kinematics and Application to the Design of Wedge Dampers in Turbomachinery Blading: Part II — Prediction of Forced Response and Experimental Verification

Volume 4: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education; IGTI Scholar Award ◽

10.1115/97-gt-020 ◽

1997 ◽

Cited By ~ 1

Author(s):

B. D. Yang ◽

C. H. Menq

Keyword(s):

Harmonic Balance Method ◽

Linear Structure ◽

Forced Response ◽

Force Model ◽

Algebraic Equations ◽

Test Beam ◽

Friction Forces ◽

External Forces ◽

Stiffness And Damping ◽

Dual Interface

In the second part of this paper, the application of the proposed dual-interface model to the prediction of the forced response of a blade constrained by wedge dampers will be presented. When considering cyclic loading, the induced friction forces and contact normal loads are combined so as to determine the effective stiffness and damping of the friction interfaces over a cycle of motion. The harmonic balance method is then used to impose the approximate stiffness and damping of the friction interfaces to a linear structure model of the blade. This approach results in a set of nonlinear algebraic equations that can be solved to yield the forced response of the blade excited by harmonic external forces. The predicted forced response can then be used to optimize a given damper design, namely to determine the dynamic weight at which the maximum reduction of resonant response is obtained. In order to illustrate the capacity of the proposed method and to examine its accuracy, the forced response of a test beam is examined. The prediction is also compared with the results of lab tests to validate the proposed dual-interface friction force model.

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Characterization of Contact Kinematics and Application to the Design of Wedge Dampers in Turbomachinery Blading: Part 2—Prediction of Forced Response and Experimental Verification

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.2818139 ◽

1998 ◽

Vol 120 (2) ◽

pp. 418-423 ◽

Cited By ~ 40

Author(s):

B. D. Yang ◽

C. H. Menq

Keyword(s):

Harmonic Balance Method ◽

Linear Structure ◽

Forced Response ◽

Force Model ◽

Algebraic Equations ◽

Test Beam ◽

Friction Forces ◽

External Forces ◽

Stiffness And Damping ◽

Dual Interface

In the second part of this paper, the application of the proposed dual-interface model to the prediction of the forced response of a blade constrained by wedge dampers will be presented. When considering cyclic loading, the induced friction forces and contact normal loads are combined so as to determine the effective stiffness and damping of the friction interfaces over a cycle of motion. The harmonic balance method is then used to impose the approximate stiffness and damping of the friction interfaces to a linear structure model of the blade. This approach results in a set of nonlinear algebraic equations that can be solved to yield the forced response of the blade excited by harmonic external forces. The predicted forced response can then be used to optimize a given damper design, namely to determine the dynamic weight at which the maximum reduction of resonant response is obtained. In order to illustrate the capacity of the proposed method and to examine its accuracy, the forced response of a test beam is examined. The prediction is also compared with the results of lab tests to validate the proposed dual-interface friction force model.

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Forced Response Prediction of Blades With Loosely Assembled Dovetail Attachment by HBM

Volume 6: Structures and Dynamics, Parts A and B ◽

10.1115/gt2009-59778 ◽

2009 ◽

Author(s):

Shangguan Bo ◽

Zili Xu ◽

Qilin Wu ◽

XianDing Zhou ◽

ShouHong Cao

Keyword(s):

Friction Force ◽

Centrifugal Force ◽

Dry Friction ◽

Harmonic Balance ◽

Harmonic Balance Method ◽

Forced Response ◽

Balance Method ◽

Force Model ◽

Equivalent Stiffness ◽

Equivalent Damping

To understand the mechanism of interfacial damping of axial loosely assembled dovetail to suppress blade vibration, a dry friction force model is presented by the Coulomb friction law and the macroslip model, and the mathematical expression of the friction force is derived. The nonlinear friction force is linearized as an equivalent stiffness and an equivalent damping through the one-term harmonic balance method. The effect of centrifugal force on the equivalent stiffness and the equivalent damping is studied. The forced response of one simplified blade with loosely assembled dovetail attachment is predicted by the harmonic balance method, in which the blade is described by the lumped mass and spring model, and the friction contact joints is simplified as a ideal friction damper. The results show that the equivalent stiffness of loosely assembled dovetail attachment increases with blade centrifugal force, gradually reaches a certain value, and there exists the maximum value for the equivalent stiffness. The equivalent damping increases at the beginning and then decreases with blade centrifugal force increasing, there exists a maximum too. The resonant frequency of blade rises with blade centrifugal force, but it no longer increases when the centrifugal force exceed a certain value. There exists a special centrifugal force on which the effect of dry friction damping is the best.

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Prediction of Resonant Response of Shrouded Blades With 3D Shroud Constraint

Volume 5: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education ◽

10.1115/98-gt-485 ◽

1998 ◽

Cited By ~ 1

Author(s):

B. D. Yang ◽

J. J. Chen ◽

C. H. Menq

Keyword(s):

Relative Motion ◽

Normal Load ◽

Three Dimensional ◽

Force Model ◽

Resonant Response ◽

Equivalent Stiffness ◽

Stick Slip ◽

Contact Plane ◽

Blade System ◽

Stiffness And Damping

In this paper, the 3D shroud contact kinematics of a shrouded blade system is studied. The assumed blade motion has three components, namely axial, tangential, and radial components, which result in a three dimensional relative motion across the shroud interface. The resulting relative motion can be decomposed into two components. The first one is on the contact plane and can induce stick-slip friction. The other component is perpendicular to the contact plane and can cause variation of the contact normal load and, in extreme circumstances, separation of the two contacting surfaces. In order to estimate the equivalent stiffness and damping of the shroud contact an approach is proposed. In this approach, the in-plane slip motion is assumed to be elliptical and is decomposed into two linear motions along the principal major and minor axes of the ellipse. A variable normal load friction force model (Yang and Menq, 1996) is then applied separately to each individual linear motion, and the equivalent stiffness and damping of the shroud contact can be approximately estimated. With the estimated stiffness and damping, the developed shroud contact model is applied to the prediction of the resonant response of a shrouded blade system. The effects of two different shroud constraint conditions, namely 2D constraint and 3D constraint, on the resonant response of a shrouded blade system are compared and the results are discussed.

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Prediction of Resonant Response of Shrouded Blades With Three-Dimensional Shroud Constraint

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.2818504 ◽

1999 ◽

Vol 121 (3) ◽

pp. 523-529 ◽

Cited By ~ 14

Author(s):

B. D. Yang ◽

J. J. Chen ◽

C. H. Menq

Keyword(s):

Relative Motion ◽

Normal Load ◽

Three Dimensional ◽

Force Model ◽

Resonant Response ◽

Equivalent Stiffness ◽

Stick Slip ◽

Contact Plane ◽

Blade System ◽

Stiffness And Damping

In this paper, the three-dimensional shroud contact kinematics of a shrouded blade system is studied. The assumed blade motion has three components, namely axial, tangential, and radial components, which result in a three dimensional relative motion across the shroud interface. The resulting relative motion can be decomposed into two components. The first one is on the contact plane and can induce stick-slip friction. The other component is perpendicular to the contact plane and can cause variation of the contact normal load and, in extreme circumstances, separation of the two contacting surfaces. In order to estimate the equivalent stiffness and damping of the shroud contact an approach is proposed. In this approach, the in-plane slip motion is assumed to be elliptical and is decomposed into two linear motions along the principal major and minor axes of the ellipse. A variable normal load friction force model (Yang and Menq, 1996) is then applied separately to each individual linear motion, and the equivalent stiffness and damping of the shroud contact can be approximately estimated. With the estimated stiffness and damping, the developed shroud contact model is applied to the prediction of the resonant response of a shrouded blade system. The effects of two different shroud constraint conditions, namely two-dimensional constraint and three-dimensional constraint, on the resonant response of a shrouded blade system are compared and the results are discussed.

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Motion of masses with asymmetric and symmetric friction. Application to fault sliding

10.5194/egusphere-egu21-3934 ◽

2021 ◽

Author(s):

Rui Xiang Wong ◽

Elena Pasternak ◽

Arcady Dyskin

Keyword(s):

Frictional Force ◽

Normal Load ◽

Power Spectra ◽

Inertial Force ◽

Friction Reduction ◽

Relative Mass ◽

Hydraulic Fractures ◽

Driving Frequency ◽

Stick Slip ◽

Friction Forces

This study analyses a situation when a geological fault contains a section of anisotropic gouge with inclined symmetry axes (e.g. inclined layering), Bafekrpour et al. [1]. Such gouge in a constrained environment induces, under compression, asymmetric friction (different friction forces resisting sliding in the opposite directions). The rest of the gouge produces conventional symmetric friction. A mass-spring model of the gouge with asymmetric and symmetric friction sections is proposed consisting of a mass with asymmetric friction connected through a spring to another mass with symmetric friction. These masses are set on a base subjected to vibration. A parametric analysis is performed on this system. Two distinct characteristic regimes were observed: recurrent movement resembling stick-slip motion similar to predicted by [2] and sub-frictional movement. Recurrent movement arises when the inertial force is sufficient to overcome frictional force of a block with symmetric friction. Sub-frictional movement occurs when the inertial force is not sufficient to overcome frictional force of an equivalent system with only symmetric friction. The sub-frictional movement is produced by the force in the connecting spring increased due to the movement of the asymmetric friction block in the direction characterised by low friction. We formulate the criterion at which sub-frictional movement occurs. The occurrence of sub-frictional depends upon the relative mass of the symmetric and asymmetric friction sections, as well as the amplitude and driving frequency of the excitation. Power spectra of the produced vibrations are determined for both regimes. The results can shed light on mechanisms of sliding over pre-existing discontinuities and their effect on seismic event generation and propagation of hydraulic fractures in the presence of discontinuities.[1] Bafekrpour, E., A.V. Dyskin, E. Pasternak, A. Molotnikov and Y. Estrin (2015), Internally architectured materials with directionally asymmetric friction. Scientific Reports, 5, Article 10732.[2] Pasternak, E. A.V. Dyskin and I. Karachevtseva, 2020. Oscillations in sliding with dry friction. Friction reduction by imposing synchronised normal load oscillations. International Journal of Engineering Science, 154, 103313.Acknowledgement. AVD and EP acknowledge support from the Australian Research Council through project DP190103260.

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