The Influence of a Variable Normal Load on the Forced Vibration of a Frictionally Damped Structure

1986 ◽  
Vol 108 (2) ◽  
pp. 300-305 ◽  
Author(s):  
C.-H. Menq ◽  
J. H. Griffin ◽  
J. Bielak
Keyword(s):  
Turbine Blade ◽  
Friction Force ◽  
Normal Load ◽  
Maximum Amplitude ◽  
Dynamic Coupling ◽  
Stick Slip ◽  
Study Results ◽  
Long Time ◽  
Response Increase ◽  
Lift Off

An approximate procedure is developed for calculating the steady-state response of frictionally damped structures for which the normal load across the friction interface consists of a constant force and a force that varies linearly with the vibratory displacement. Such situations occur quite frequently in practice, as, for example; in the case of shrouded fan blades or in certain types of turbine-blade friction dampers. Depending on the magnitudes of the constant and the variable normal loads, the friction element will either stick, slip, or lift off at various intervals during a cycle of oscillation. The various possibilities are considered in the present study. Results from the approximate method are compared with “long-time” solutions obtained from a conventional transient analysis of the problem in order to assess the accuracy of the proposed procedure. As an application, the new method is then used to study the influence of the dynamic coupling on the optimization of the friction force in turbine blade dampers. Results show that the optimum friction force and the maximum amplitude of the response increase with dynamic coupling.

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.

Friction-Induced Vibration Due to Mode-Coupling and Intermittent Contact Loss

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Alborz Niknam ◽  
Kambiz Farhang
Keyword(s):  
Friction Force ◽  
Mode Coupling ◽  
Degrees Of Freedom ◽  
Normal Load ◽  
Contact Stiffness ◽  
Relative Mass ◽  
Mass Motion ◽  
Stick Slip ◽  
Single Mass ◽  
Intermittent Contact

A two degrees-of-freedom (2DOFs) single mass-on-belt model is employed to study friction-induced instability due to mode-coupling. Three springs, one representing contact stiffness, the second providing lateral stiffness, and the third providing coupling between tangential and vertical directions, are employed. In the model, mass contact and separation are permitted. Therefore, nonlinearity stems from discontinuity due to dependence of friction force on relative mass-belt velocity and separation of mass-belt contact during oscillation. Eigenvalue analysis is carried out to determine the onset of instability. Within the unstable region, four possible phases that include slip, stick, separation, and overshoot are found as possible modes of oscillation. Piecewise analytical solution is found for each phase of mass motion. Then, numerical analyses are used to investigate the effect of three parameters related to belt velocity, friction coefficient, and normal load on the mass response. It is found that the mass will always experience stick-slip, separation, or both. When separation occurs, mass can overtake the belt causing additional nonlinearity due to friction force reversal. For a given coefficient of friction, the minimum normal load to prevent separation is found proportional to the belt velocity.

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.

Experimental Study of Static Friction in a Spherical Elastic-Plastic Contact

2008 ◽  
Author(s):  
Andrey Ovcharenko ◽  
Gregory Halperin ◽  
Izhak Etsion
Keyword(s):  
Friction Force ◽  
Normal Load ◽  
Static Friction ◽  
Tangential Displacement ◽  
Accurate Identification ◽  
Elastic Plastic ◽  
Static Friction Coefficient ◽  
Wide Range ◽  
Material Good ◽  
Contact Diameter

The elastic-plastic contact between a deformable sphere and a rigid flat during pre-sliding is studied experimentally. Measurements of friction force and contact area are done in real time along with an accurate identification of the instant of sliding inception. The static friction force and relative tangential displacement are investigated over a wide range of normal preloads for several sphere materials and diameters. It is found that at low normal loads the static friction coefficient depends on the normal load in breach of the classical laws of friction. The pre-sliding displacement is found to be less than 5 percent of the contact diameter, and the interface mean shear stress at sliding inception is found to be slightly below the shear strength of the sphere material. Good correlation is found between the present experimental results and a recent theoretical model in the elastic-plastic regime of deformation.

Bouncing on thin air: how squeeze forces in the air film during non-wetting droplet bouncing lead to momentum transfer and dissipation

2015 ◽  
Vol 776 ◽  
pp. 531-567 ◽  
Author(s):  
Jolet de Ruiter ◽  
Rudy Lagraauw ◽  
Frieder Mugele ◽  
Dirk van den Ende
Keyword(s):  
Oscillation Mode ◽  
Interference Microscopy ◽  
Droplet Motion ◽  
Solid Substrates ◽  
Long Time ◽  
Lift Off ◽  
Continuous Presence ◽  
Air Film ◽  
Single Oscillation

Millimetre-sized droplets are able to bounce multiple times on flat solid substrates irrespective of their wettability, provided that a micrometre-thick air layer is sustained below the droplet, limiting $\mathit{We}$ to ${\lesssim}4$. We study the energy conversion during a bounce series by analysing the droplet motion and its shape (decomposed into eigenmodes). Internal modes are excited during the bounce, yet the viscous dissipation associated with the in-flight oscillations accounts for less than 20 % of the total energy loss. This suggests a significant contribution from the bouncing process itself, despite the continuous presence of a lubricating air film below the droplet. To study the role of this air film we visualize it using reflection interference microscopy. We quantify its thickness (typically a few micrometres) with sub-millisecond time resolution and ${\sim}30~\text{nm}$ height resolution. Our measurements reveal strong asymmetry in the air film shape between the spreading and receding phases of the bouncing process. This asymmetry is crucial for effective momentum reversal of the droplet: lubrication theory shows that the dissipative force is repulsive throughout each bounce, even near lift-off, which leads to a high restitution coefficient. After multiple bounces the droplet eventually hovers on the air film, while continuously experiencing a lift force to sustain its weight. Only after a long time does the droplet finally wet the substrate. The observed bounce mechanism can be described with a single oscillation mode model that successfully captures the asymmetry of the air film evolution.

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

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

<p>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: <em>recurrent movement</em> resembling stick-slip motion similar to predicted by [2] and <em>sub-frictional movement</em>. 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.</p><p>[1] Bafekrpour,<strong> </strong>E., A.V. Dyskin, E. Pasternak, A. Molotnikov and Y. Estrin (2015), Internally architectured materials with directionally asymmetric friction. <em>Scientific Reports</em>, 5, Article 10732.</p><p>[2] Pasternak, E. A.V. Dyskin and I. Karachevtseva, 2020. Oscillations in sliding with dry friction. Friction reduction by imposing synchronised normal load oscillations. <em>International Journal of Engineering Science</em>, 154, 103313.</p><p><strong>Acknowledgement</strong>. AVD and EP acknowledge support from the Australian Research Council through project DP190103260.</p>

scholarly journals Experimental Study on the Transition between Static and Kinetic Frictions of Steel/Shale Pairs

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Qin Lian ◽  
Chunxu Yang ◽  
Jifei Cao
Keyword(s):  
Friction Coefficient ◽  
Normal Load ◽  
Critical Distance ◽  
Dynamic Friction ◽  
Stick Slip ◽  
Dynamic Friction Coefficient ◽  
The Coefficient Of Friction ◽  
The Difference ◽  
Stick Slip Motion ◽  
Insight Into

The transition between static and kinetic frictions of steel/shale pairs has been studied. It was found that the coefficient of friction decreased exponentially from static to dynamic friction coefficient with increasing sliding displacement. The difference between static and dynamic friction coefficients and the critical distance Dc under the dry friction condition is much larger than that under the lubricated condition. The transition from static to dynamic friction coefficient is greatly affected by the normal load, quiescent time, and sliding velocity, especially the lubricating condition. Maintaining continuous lubrication of the contact area by the lubricant is crucial to reduce or eliminate the stick-slip motion. The results provide an insight into the transition from static to dynamic friction of steel/shale pairs.

scholarly journals The Secure Anonymised Information Linkage databank Dementia e-cohort (SAIL-DeC)

2019 ◽  
Vol 4 (3) ◽  
Author(s):  
Christian Schnier ◽  
Tim Wilkinson ◽  
Chris Orton ◽  
Laura North ◽  
Ryan Rochford ◽  
...  
Keyword(s):  
Additional Data ◽  
Diagnostic Code ◽  
Inclusion Criteria ◽  
Study Results ◽  
Dementia Research ◽  
Long Time ◽  
Study Designs ◽  
Time Information ◽  
Dementia Subtype

Introduction Dementia Platform UK (DPUK) brings together over 50 different dementia-related cohorts. Most studies have restricted follow-up times and all are based on information from people who volunteer time and data for research. Participants are therefore often not representative of the 'wider population' and generalization of results is complicated. The Secure Anonymised Information Linkage databank (SAIL) holds long-time information on every person in Wales registered with the national health service, so generalization of study results is easier; however, data management and analysis of SAIL data is not trivial. We used data from SAIL to construct an easily accessible, well described dementia e-cohort. Methods With some age restrictions, all Welsh residents for whom primary care data were available were included. Within SAIL, a table was created holding demographic information for every participant including follow-up times and several dementia indicators. Using validated diagnostic code lists, this table was linked to information on every dementia-related diagnostic event and several covariates and co-morbidites. SAIL-DeC can be modified according to varying study designs using annotated SQL-based scripts. Information on SAIL-DeC can easily be updated and linked to additional data on the SAIL database. Interactive visualisations effectively summarise cohort characteristics, aiding researchers to quickly determine cohort eligibility for dementia studies. Results From 4.4 million participants in SAIL, 1.2 million met the cohort inclusion criteria, resulting in 18.8 million person-years of follow-up. Of these, 129,650 (10%) developed all-cause dementia during follow-up, with 77,978 (60%) having dementia subtype codes. Seventy-nine percent of participants who developed dementia died during follow-up. Median survival was 12.3 years for participants diagnosed with dementia when aged 50-60, 6.8 years when aged 60-70, 4.2 years when aged 70-80 and 2.4 years when aged 80-90. Conclusions We have created a generalisable, national dementia e-cohort, aimed at facilitating epidemiological dementia research.

Numerical Analysis on the Leading Edge Film Cooling of Bifurcation Holes for Gas Turbine Blade

2021 ◽  
Author(s):  
Zhonghao Tang ◽  
Gongnan Xie ◽  
Honglin Li ◽  
Wenjing Gao ◽  
Chunlong Tan ◽  
...  
Keyword(s):  
Turbine Blade ◽  
Film Cooling ◽  
Turbulence Models ◽  
Leading Edge ◽  
Spanwise Direction ◽  
Cooling Effectiveness ◽  
Film Cooling Effectiveness ◽  
Blowing Ratio ◽  
Cylindrical Holes ◽  
Lift Off

Abstract Film cooling performance of the cylindrical film holes and the bifurcated film holes on the leading edge model of the turbine blade are investigated in this paper. The suitability of different turbulence models to predict local and average film cooling effectiveness is validated by comparing with available experimental results. Three rows of holes are arranged in a semi-cylindrical model to simulate the leading edge of the turbine blade. Four different film cooling structures (including a cylindrical film holes and other three different bifurcated film holes) and four different blowing ratios are studied in detail. The results show that the film jets lift off gradually in the leading edge area as the blowing ratio increases. And the trajectory of the film jets gradually deviate from the mainstream direction to the spanwise direction. The cylindrical film holes and vertical bifurcated film holes have better film cooling effectiveness at low blowing ratio while the other two transverse bifurcated film holes have better film cooling effectiveness at high blowing ratio. And the film cooling effectiveness of the transverse bifurcated film holes increase with the increasing the blowing ratio. Additionally, the advantage of transverse bifurcated holes in film cooling effectiveness is more obvious in the downstream region relative to the cylindrical holes. The Area-Average film cooling effectiveness of transverse bifurcated film holes is 38% higher than that of cylindrical holes when blowing ratio is 2.

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