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

1998 ◽  
Vol 120 (2) ◽  
pp. 418-423 ◽  
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.

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

1997 ◽  
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.

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.

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.

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.

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.

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

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.

Forced Response of Interlocked Vane Segments: Numerical Predictions and Experimental Results

2006 ◽  
Author(s):  
Stefano Zucca ◽  
Sergio Filippi ◽  
Fabio Droetti ◽  
Muzio M. Gola
Keyword(s):  
Tangential Force ◽  
Harmonic Balance Method ◽  
Outer Radius ◽  
Forced Response ◽  
Experimental Results ◽  
Numerical Code ◽  
Friction Forces ◽  
Normal Contact ◽  
Numerical Predictions ◽  
Local Compliance

Resonant vibrations affect fatigue life of vane segments. Friction damping is employed to reduce vibration amplitude. When vane segments are assembled, they are twisted so that lower platforms are in contact. The sum of displacements of the two ends of the lower platform after twisting is defined ‘interlocking’. Different ‘interlocking’ values correspond to different values of normal contact force. When interlocked vanes vibrate under external force excitation, energy is dissipated by friction forces at lower platform contacts providing damping to the system. The aim of this paper is the experimental validation of a numerical code for forced response calculation of interlocked vane segments. Since friction forces depend on relative displacements of bodies in contact, the system is nonlinear. System force response is computed by means of Harmonic Balance Method (HBM). Contact model implemented in the code is characterised by tangential and normal stiffness to take into account local compliance of the contact area. Gross slip occurs when the instantaneous ratio of tangential force to normal force is equal to the friction coefficient. Also effect of microslip is taken in account. The experimental set-up used to validate the code is made of a vane segment fixed at the outer radius to an aluminium frame and in contact with two supports at the inner radius. Comparison between the numerical predictions and experimental results is performed for different values of interlocking (i.e. force normal to the contact).

Forced Response of Bladed Disks in Cyclic Symmetry With Underplatform Dampers

2006 ◽  
Author(s):  
Stefano Zucca ◽  
Juan Borrajo ◽  
Muzio M. Gola
Keyword(s):  
Contact Stiffness ◽  
Harmonic Balance Method ◽  
Rigid Bodies ◽  
Forced Response ◽  
Numerical Code ◽  
Algebraic Equations ◽  
Bladed Disks ◽  
Disk Model ◽  
Normal Contact ◽  
Linear Algebraic Equations

In this paper a methodology for forced response calculation of bladed disks with underplatform dampers is described. The FE disk model, supposed to be cyclically symmetric, is reduced by means of Component Mode Synthesis and then DOFs lying at interfaces are further reduced by means of interface modes. Underplatform dampers are modeled as rigid bodies translating both in the radial and in the tangential direction of the engine. Contacts between blade platforms and damper are simulated by means of contact elements characterized by both tangential and normal contact stiffness, allowing partial separation of contact surfaces. Differential equilibrium equations are turned in non-linear algebraic equations by means of the Harmonic Balance Method (HBM). The methodology is implemented in a numerical code for forced response calculation of frictionally damped bladed disks. Numerical calculations are performed to evaluate the effectiveness of both the reduced order model and the underplatform model in simulating the dynamic behavior of bladed disks in presence of underplatform dampers.

scholarly journals Self-adaptive macroslip array for friction force prediction in contact interfaces with non-conforming meshes

2021 ◽  
Author(s):  
Giuseppe Battiato
Keyword(s):  
Harmonic Balance Method ◽  
Forced Response ◽  
Contact Forces ◽  
Friction Forces ◽  
Bladed Disk ◽  
Current State ◽  
Proposed Model ◽  
Conforming Meshes ◽  
Static Misalignment ◽  
Self Adaptive

AbstractThe steady-state nonlinear forced response (NFR) of finite element (FE) models with friction joints is usually computed in the frequency domain through the combination of node-to-node contact elements and the Harmonic Balance Method (HBM). In the current state of the art, rare are the cases where the friction forces are estimated for contact interfaces with non-conforming mesh grids. This need is nowadays taking place due to the improving capability of commercial FE software to manage any kind of boundary condition (i.e., either coupling or contact), without requiring coincident pairs of nodes at the joint interfaces. Such an advantage becomes a drawback when the analysts are requested to investigate the NFR of the assembly by using build-in codes, where the contact forces prediction usually requires node-to-node contact elements whose parameters (i.e., the contact stiffnesses and friction coefficients) can be easily identified by means of experiments. This paper addresses the mentioned limitation, and proposes a novel self-adaptive macroslip array (SAMA) model for the estimation of the nonlinear friction forces on FE contact interfaces with non-conforming meshes. The SAMA model consists on a set of node-to-node contact elements ordered in parallel, whose contact parameters and normal preloads are identified through a step-by-step self-adaptive weighting algorithm that depends on the topology of the meshes in contact. The goodness of the proposed model is assessed on the calculation of the NFR of a bladed disk with shroud contacts, under the hypotheses of cyclic symmetry and HBM. The nonlinear dynamic behavior of the bladed disk is evaluated in two different cases. First, in the case of lack of node-to-node congruence at the contact interface for the structure being in its undeformed configuration, and second, in the case of a relevant static misalignment of the contact interfaces due to the application of large static loads.

Sign in / Sign up

Export Citation Format

Share Document