Forced Response Analysis of Shrouded Blades by an Alternating Frequency/Time Domain Method

2006 ◽  
Author(s):  
Shi Yajie ◽  
Hong Jie ◽  
Shan Yingchun ◽  
Zhu Zigen
Keyword(s):  
Relative Motion ◽  
Time Domain ◽  
Dry Friction ◽  
Nonlinear Response ◽  
Harmonic Component ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Response Analysis ◽  
Stick Slip ◽  
Moving Contact

In turbine jet engine, the rotating blades are subjected to cyclic loading, which makes the blades experience the so-called High Cycle Fatigue (HCF). Dry friction is often employed in turbine design to attenuate the blade vibration and increase aeroclastic stability of the turbine. The dry friction dampers are often classified into four types, i.e., blade-to-blade, blade-to-ground, shrouds, and wedge damper, respectively. Compared with the under-platform dampers, shrouds make fan behavior be significantly more complex. It is very difficult to model and predict the nonlinear response of shrouded blades. In the present study, an efficient approach to investigate the nonlinear response of the shrouded blades is suggested using an alternating frequency/time domain (AFT) method. On one hand, the friction force between shrouds is numerically solved in time-domain. The trajectory of relative motion of the moving contact point is traced, and the stick-slip-separation transition for 3-D relative motion of the shroud-contact interface is considered. On the other hand, the response of the shrouded blades is iteratively solved in frequency-domain using Harmonic Balance Method (HBM). In this approach, the influence of high frequency modes of blade, and the coupling of each harmonic component on damping behavior can be taken into account. As an application, the performance of shroud damper is systematically investigated using the AFT method. The influence of shroud-to-shroud preload and contact stiffness on the shroud damping potential is studied. Some valuable results are got to the design of the shroud contact.

scholarly journals Numerical and Experimental Investigations on a Friction Ring Damper for a Flywheel

2021 ◽  
Author(s):  
Xiaodong He ◽  
Zhiwei Zheng ◽  
Xiuchang Huang ◽  
Sen Wang ◽  
Xinsheng Wei ◽  
...  
Keyword(s):  
Vibration Amplitude ◽  
Damping Ratio ◽  
Nonlinear Dynamic Analysis ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Experimental Investigations ◽  
Response Analysis ◽  
Contact Interface ◽  
Friction Contact ◽  
Stick Slip

Abstract A damping strategy using a friction ring damper for an industrial flywheel was numerically and experimentally investigated. The friction ring damper, located on the arms of the flywheel, was experimentally found to effectively reduce the vibration amplitude of the flywheel. The vibration energy is dissipated when relative motions occur at the friction contact interfaces. Nonlinear dynamic analysis based on a lumped-parameter model of a flywheel equipped with a friction ring damper was conducted. A dimensionless parameter, κ, defined as the ratio of the critical friction force to the amplitude of harmonic force, was used to evaluate the damping performance. For several values of κ, steady-state responses under harmonic excitation and nonlinear modes were obtained using the harmonic balance method (HBM) combined with the alternating frequency–time domain method (AFT). The forced response analysis proved the existence of an optimal value of κ, which can minimize the vibration amplitude of the flywheel. The nonlinear modal analysis showed that all the damping ratio–frequency curves are completely coincident even for different κ, and the frequency corresponding to the maximum damping ratio is equal to the frequency at the intersection of the forced response curves under the fully slip and the fully stick states of the friction contact interface. By analyzing the behaviors of the friction contact interface, it is shown that the friction contact interface provides damping in the combined stick–slip state. The forced response under random excitation was calculated using the Runge–Kutta method and the friction interface behaviors were analyzed. Finally, spectral testing was conducted to verify the numerical results.

Blades Forced Response Analysis With Friction Dampers

1998 ◽  
Vol 120 (2) ◽  
pp. 468-474 ◽  
Author(s):  
M. Berthillier ◽  
C. Dupont ◽  
R. Mondal ◽  
J. J. Barrau
Keyword(s):  
Time Domain ◽  
Dry Friction ◽  
Time Domain Analysis ◽  
Domain Analysis ◽  
Frequency Domain Analysis ◽  
Forced Response ◽  
Response Analysis ◽  
Friction Damper ◽  
Friction Dampers ◽  
Fan Blade

A multiharmonic frequency domain analysis combined with a Craig-Bampton component mode synthesis is presented to compute the dry friction damped forced response of blades. The accuracy of the analysis is established, for a cantilever beam with a dry friction damper attached, by comparison with experimental results and time domain analysis. The method has then been applied to a model fan blade damped by a blade to ground damper.

A New Method to Find the Forced Response of Nonlinear Systems with Dry Friction

2021 ◽  
Author(s):  
Gregory L. Altamirano ◽  
Meng-Hsuan Tien ◽  
Kiran D'Souza
Keyword(s):  
Dry Friction ◽  
Coulomb Friction ◽  
Nonlinear Response ◽  
Piecewise Linear ◽  
Time Integration ◽  
Nonlinear Behavior ◽  
Forced Response ◽  
New Method ◽  
Analysis Tools ◽  
Compatibility Constraint

Abstract Coulomb friction has an influence on the behavior of numerous mechanical systems. Coulomb friction systems or dry friction systems are nonlinear in nature. This nonlinear behavior requires complex and time demanding analysis tools to capture the dynamics of these systems. Recently, efforts have been made to develop efficient analysis tools able to approximate the forced response of systems with dry friction. The objective of this paper is to introduce a methodology that assists in these efforts. In this method, the piecewise-linear nonlinear response is separated into individual linear responses that are coupled together through compatibility constraint equations. The new method is demonstrated on a number of systems of varying complexity. The results obtained by the new method are validated through the comparison with results obtained by time integration. The computational savings of the new method is also discussed.

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.

Multi-Harmonic Analysis of Dry Friction Damped Systems Using an Incremental Harmonic Balance Method

1985 ◽  
Vol 52 (4) ◽  
pp. 958-964 ◽  
Author(s):  
C. Pierre ◽  
A. A. Ferri ◽  
E. H. Dowell
Keyword(s):  
Time Domain ◽  
Dry Friction ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Frequency Domain Analysis ◽  
Balance Method ◽  
Incremental Harmonic Balance Method ◽  
Incremental Harmonic Balance ◽  
The Time Domain ◽  
Damped Systems

A multi-harmonic, frequency domain analysis of dry friction damped systems is presented which uses an incremental harmonic balance method. When compared with time domain solution methods, it is found that the incremental harmonic balance method can yield very accurate results with some advantages over the time domain methods. Both one and two degree-of-freedom systems are studied.

Experimental Study of Dynamic Characteristics of Dry Friction Damping of Turbine Blade Steel

2013 ◽  
Vol 690-693 ◽  
pp. 1979-1982 ◽  
Author(s):  
Peng Fei Zhao ◽  
Qiang Zhang ◽  
Jun Wu ◽  
Di Zhang
Keyword(s):  
Dry Friction ◽  
Turbine Blades ◽  
Initial Pressure ◽  
Relative Displacement ◽  
Radius Of Curvature ◽  
Response Analysis ◽  
Friction Damper ◽  
Friction Damping ◽  
Stick Slip ◽  
Dry Friction Damping

For lot of structures, especially turbine blades, damper can dissipate the vibration energy by friction. Investigating the property of metal dry friction damping can give many usable data for response analysis of damping blade which is important in damped blade designs. The paper constructs an experimental rig and carries out experiment with pieces having radius of curvature 6mm, 12mm and 24mm. The relative displacement between contact surfaces and the friction force changed with time were obtained for different initial pressure and frequency of exciting force. Hysteresis curves of dry friction damper were derived. The variations of friction coefficient of stick-slip area, equivalent stiffness and equivalent damping were calculated based on experimental data.

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.

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