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

Author(s):  
B. D. Yang ◽  
C. H. Menq

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.

1998 ◽  
Vol 120 (2) ◽  
pp. 410-417 ◽  
Author(s):  
B. D. Yang ◽  
C. H. Menq

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.


1997 ◽  
Vol 119 (4) ◽  
pp. 958-963 ◽  
Author(s):  
B.-D. Yang ◽  
C.-H. Menq

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.


Author(s):  
Been-Der Yang ◽  
Chia-Hsiang Menq

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.


Author(s):  
B. D. Yang ◽  
C. H. Menq

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.


1998 ◽  
Vol 120 (2) ◽  
pp. 418-423 ◽  
Author(s):  
B. D. Yang ◽  
C. H. Menq

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.


Author(s):  
Shangguan Bo ◽  
Zili Xu ◽  
Qilin Wu ◽  
XianDing Zhou ◽  
ShouHong Cao

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.


Author(s):  
Weiwei Gu ◽  
Zili Xu ◽  
Lv Qiang

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.


Author(s):  
David Hemberger ◽  
Roberto De Santis ◽  
Dietmar Filsinger

As a means of meeting ever increasing emissions and fuel economy demands car manufacturers are using aggressive engine downsizing. To maintain the power output of the engine turbocharging is typically used. Compared to Mono scroll turbines, with a multi-entry system the individual volute sizing can be better matched to the single mass flow pulse from the engine cylinders. The exhaust pulse energy can be better utilised by the turbocharger turbine improving turbocharger response. Additionally the interaction of the engine exhaust pulses can be better avoided, improving the scavenging of the engine. Besides the thermodynamic advantages, the multi-entry turbine represents a challenge to the structural dynamic design of the turbine. A higher number of turbine wheel resonance points can be expected during operation. In addition, the increased use of exhaust pulse energy leads to a distinct accentuation of the blade vibration excitation. Using validated engine models, the interaction of the multi-entry turbine with the engine has been analyzed and various operating points, which may be critical for the blade vibration excitation, have been classified. These operating points deliver the input variables for unsteady computational flow dynamics (CFD) analyses. From these calculations unsteady blade forces were derived providing the necessary boundary conditions for the structural dynamic analyses by spatially and temporally high-resolved absolute pressures on the turbine surface. Goal of the investigation is to identify critical operating conditions. Important is also to investigate the effect of a scroll connection valve on blade excitation. The investigations utilize validated tools that were introduced and successfully applied to several turbine types in a series of publications over recent years. It can be stated that the engine operating condition and the admission type significantly influence the forced response reaction of the blade to the different excitation orders (EO). In case of equal admission even (or multiples of two) EOs generate the largest dynamic blade stress as can be expected due to the two turbine inlet segments. This reaction also increases with the engine speed. In the case of unequal admission, the odd EOs produce the largest forced response reaction. The maximum dynamic blade stress occurs in the region where the scroll connection is just closed. Above all, the scroll connection valve influences the Beta value and thus the basic behavior — unequal or equal admission. It has been possible to reconstruct the forced response behavior of the turbine blade within an engine combustion cycle. For the first time it could be shown for a double scroll application that there is a significant dynamic blade stress change dependent on the engine crankshaft angle. Certainly, due to the inertia of the mass and damping (mass, structure, flow), the blade will not exactly follow the predicted course. However, it is clear that the transient processes within an engine combustion cycle will affect the dynamic blade stress. This applies to the turbine wheels investigated in the work at hand with low damping, high eigenfrequencies and the considered internal combustion engines — as they are typically used in the passenger car sector.


Author(s):  
Henric Larsson ◽  
Kambiz Farhang

Abstract The paper presents a lumped parameter model of multiple disks in frictional contact. The contact elastic and dissipative characteristics are represented by equivalent stiffness and damping parameters in the axial as well as the torsional directions. The formulation accounts for the coupling betwen the axial and angular motions by viewing the contact normal force to be the result of axial behavior of the system. The frictional contact of two disks in contact is modeled in two dynamic states (i.e. sticking and slipping state) having individual lumped parameter models and the conditions that control the switching between the two states are established. The friction forces are represented by assuming the coefficient of friction to be a function of the sliding velocity, varying exponentially from its static value at zero relative velocity to its kinetic value at high velocities. A computer simulation of an eight-rotor disk assembly is presented. The torsional vibration characteristics and how it is liked to the axial modes of vibration is analyzed. The vibration characteristics in the transient, steady-state and stick-slip region is compared. In the stick-slip region, the angular velocity of the interfaces in frictional contact is depicted and the sticking and slipping states are defined. It is shown that the duration of slip is approximately constant and the duration of stick increases almost exponentially until a final sticking is achieved.


1993 ◽  
Author(s):  
Kenan Y. Sanliturk ◽  
Mehmet Imregun ◽  
David J. Ewins

The effects of random stiffness and damping variations on damped natural frequencies and response levels of turbomachinery blades are investigated by employing probabilistic approach using a single-degree-of-freedom (SDOF) model. An important feature of this study is the determination of the cumulative probability distributions for damped natural frequencies and receptance frequency response functions without having to compute their probability density distributions since it is shown that those of stiffness and damping can be used directly. The advantage of this approach is not only in the simplicity of problem formulation but also in the substantial reduction of computational requirements. Furthermore, results suggest that both stiffness and damping properties should be considered as random parameters in statistical analyses of forced response.


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