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

1998 ◽  
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.

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

1999 ◽  
Vol 121 (3) ◽  
pp. 523-529 ◽  
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.

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

1997 ◽  
Vol 119 (4) ◽  
pp. 958-963 ◽  
Author(s):  
B.-D. Yang ◽  
C.-H. Menq
Keyword(s):  
Friction Force ◽  
Normal Load ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Effective Stiffness ◽  
Force Model ◽  
Stick Slip ◽  
Friction Forces ◽  
Friction Joint ◽  
Stiffness And Damping

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 shroudlike contact kinematics on the forced response of frictionally constrained turbine blades. Analytical criteria are formulated to predict the transitions between stick, 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 of 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.

Research on Stiffness and Damping Characteristics of Fixed Oily Porous Materials Joint Interface

2011 ◽  
Vol 422 ◽  
pp. 575-579
Author(s):  
Chong Nian Qu ◽  
Liang Sheng Wu ◽  
Jian Feng Ma ◽  
Yi Chuan Xiao
Keyword(s):  
Porous Material ◽  
Porous Materials ◽  
Parallel Plate ◽  
Joint Interface ◽  
Force Model ◽  
Equivalent Stiffness ◽  
Contact State ◽  
Damping Characteristics ◽  
Stiffness And Damping ◽  
Damping Model

In this document, using the anti-squeezed force model in the narrow parallel plate when fluid is squeezed, the equivalent stiffness and damping model is derived. It is further verified that it can increase the stiffness and damping while there are oil between the joint interfaces theoretically. Because the contact state of oily porous material can divide into liquid and solid parts, the document supposes that it is correct and effective to think the stiffness and damping of the two parts as shunt connection.

scholarly journals Modeling of Friction Contact and its Application to the Design of Shroud Contact

1996 ◽  
Author(s):  
Been-Der Yang ◽  
Chia-Hsiang Menq
Keyword(s):  
Friction Force ◽  
Normal Load ◽  
Turbine Blades ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Effective Stiffness ◽  
Force Model ◽  
Friction Forces ◽  
Friction Joint ◽  
Stiffness And Damping

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.

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

1998 ◽  
Vol 120 (2) ◽  
pp. 410-417 ◽  
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.

Nonlinear Dynamics of Shrouded Turbine Blade System with Impact and Friction

2014 ◽  
Vol 706 ◽  
pp. 81-92 ◽  
Author(s):  
B. Santhosh ◽  
S. Narayanan ◽  
C. Padmanabhan
Keyword(s):  
Frequency Response ◽  
Turbine Blade ◽  
Dry Friction ◽  
Normal Load ◽  
Harmonic Balance Method ◽  
Tangential Direction ◽  
Stick Slip ◽  
Variable Friction ◽  
Blade System ◽  
Constant Normal Load

Dry friction dampers are passive devices used to reduce the resonant vibration amplitudes in turbine bladed systems. In shrouded turbine blade systems, in addition to the stick- slip motion induced by dry friction during the contact state in the tangential direction, the interface also undergoes intermittent separation in the normal direction. The problem can thus be treated as a combination of impact and friction. In this work, the dynamics of dry friction damped oscillators which are representative models of dry friction damped bladed system is investigated. A one dimensional contact model which is capable of modeling the interface under constant and variable normal load is used. The steady state periodic solutions are obtained by multi - harmonic balance method (MHBM). Frequency response plots are generated for different values of normal load using the arc length continuation procedure. The MHBM solutions are validated using numerical integration. A single degree of freedom (dof) model under constant normal load with constant and variable friction coefficients, a dry friction damped two dof system under constant normal load and a two dof system under variable normal load are investigated. In the presence of variable normal load, the system shows multivalued frequency response and jump phenomenon. The optimal value of the normal load which gives minimum resonant response is also obtained.

scholarly journals Vibrational Interaction of Two Rotors with Friction Coupling

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
H. Larsson ◽  
K. Farhang
Keyword(s):  
Lumped Parameter Model ◽  
Equivalent Stiffness ◽  
Stick Slip ◽  
Lumped Parameter ◽  
Disk Friction ◽  
Axial Behavior ◽  
Stiffness And Damping Coefficient ◽  
Stiffness And Damping ◽  
Two Parameter ◽  
Very High

A lumped parameter model is presented for studying the dynamic interaction between two disks in relative rotational motion and in friction contact. The contact elastic and dissipative characteristics are represented by equivalent stiffness and damping coefficient in the axial as well as torsional direction. The formulation accounts for the coupling between the axial and angular motions by viewing the contact normal force a result of axial behavior of the system. The model is used to investigate stick-slip behavior of a two-disk friction system. In this effort the friction coefficient is represented as an exponentially decaying function of relative angular velocity, varying from its static value at zero relative velocity to its kinetic value at very high velocities. This investigation results in the establishment of critical curve defining two-parameter regions: one in which stick-slip occurs and that in which stick-slip does not occur. Moreover, the onset and termination of stick-slip, when it occurs, are related to the highest component frequency in the system. It is found that stick-slip starts at a period nearly equal to that of the highest component frequency and terminates at a period almost three times that of the highest component frequency.

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

1997 ◽  
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.

On the Tangential Displacement of a Surface Point Due to a Cuboid of Uniform Plastic Strain in a Half-Space

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
B. Fulleringer ◽  
D. Nélias
Keyword(s):  
Plastic Strain ◽  
Yield Stress ◽  
Half Space ◽  
Normal Load ◽  
Three Dimensional ◽  
Normal Displacement ◽  
Tangential Displacement ◽  
Surface Point ◽  
Stick Slip ◽  
Elastic Plastic

The elastic solution of a tangentially loaded contact is known as Cerruti’s solution. Since the contact surfaces could be easily discretized in small rectangles of uniform shear stress the elastic problem is usually numerically solved by summation of well known integral solution. For soft metallic materials, metals at high temperature, rough surfaces, or dry contacts with high friction coefficient, the yield stress within the material could be easily exceeded even at low normal load. This paper presents the effect of a cuboid of uniform plastic strain in a half-space on the tangential displacement of a surface point. The analytical solutions are first presented. All analytical expressions are then validated by comparison with the finite element method. It is found that the influence coefficients for tangential displacements are of the same order of magnitude as the ones describing the normal displacement (Jacq et al., 2002, “Development of a Three-Dimensional Semi-Analytical Elastic-Plastic Contact Code,” ASME J. Tribol., 124(4), pp. 653–667). This result is of great importance for frictional contact problem when coupling the normal and tangential behaviors in the elastic-plastic regime, such as stick-slip problems, and also for metals and alloys with low or moderate yield stress.

Molecular Dynamics Simulation of Rubbing Phenomena in Ultra-Precision Abrasive Machining

2010 ◽  
Vol 443 ◽  
pp. 417-422
Author(s):  
Jun Shimizu ◽  
Li Bo Zhou ◽  
Takeyuki Yamamoto ◽  
Han Huang
Keyword(s):  
Molecular Dynamics ◽  
Normal Load ◽  
Three Dimensional ◽  
Copper Surface ◽  
Atomic Scale ◽  
Dynamics Simulation ◽  
Abrasive Machining ◽  
Stick Slip ◽  
Abrasive Grain ◽  
The One

This study aims to clarify the friction and wear phenomena, which are of great importance in abrasive machining with atomic-scale material removal, such as polishing of magnetic disk substrates and CMP of semiconductor substrates. Various phenomena that occurred when a well-defined copper surface rubbed by an extremely fine rigid diamond abrasive, such asthe sliding without removal and the atomic-scale wear, were analyzed using a molecular dynamics model, in which the abrasive grain was connected to a three-dimensional spring and the holding rigidity of the abrasive grain was taken into account. A series of simulations using different indentation depths clarified that the one- or two-dimensional atomic-scale stick-slip phenomenon in proportion to the period of atomic arrays of workpiece surface occurred in the sliding processes without atomic removal. The results also demonstrated that the period and amplitude of the fundamental stick-slip wave varied when accompanied with atomic removal due to the increase in normal load.

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