Analysis of Stick-Slip Motion by the Rate-Dependent Friction Model

2008 ◽  
Vol 33-37 ◽  
pp. 867-874 ◽  
Author(s):  
S. Ozaki ◽  
Koichi Hashiguchi ◽  
D.H. Chen
Keyword(s):  
Numerical Experiments ◽  
Friction Model ◽  
Dimensional Model ◽  
Mass System ◽  
Stick Slip ◽  
One Dimensional ◽  
Rate Dependent ◽  
The One ◽  
Stick Slip Motion ◽  
Slip Motion

In this study, the rate-dependent subloading-friction model, which can rationally describe the reciprocal transition of static-kinetic frictions by the unified formulation, is proposed. Then, the one-dimensional model of spring-mass system is implemented by incorporating the present friction model, and is applied to simulations of stick-slip motion. Further, we verified the validity of the present approach for the stick-slip motion by numerical experiments under various dynamic conditions.

Numerical Modeling of Friction-Induced Vibrations and Dynamic Instabilities

1994 ◽  
Vol 47 (7) ◽  
pp. 255-274 ◽  
Author(s):  
W. W. Tworzydlo ◽  
E. B. Becker ◽  
J. T. Oden
Keyword(s):  
Numerical Study ◽  
Normal Modes ◽  
Friction Model ◽  
Rigid Bodies ◽  
Stick Slip ◽  
Quantitative Correlation ◽  
Frictional System ◽  
Pin On Disk ◽  
Stick Slip Motion ◽  
Slip Motion

A numerical study of dynamic instabilities and vibrations of mechanical systems with friction is presented. Of particular interest are friction-induced vibrations, self-excited oscillations and stick-slip motion. A typical pin-on-disk apparatus is modeled as the assembly of rigid bodies with elastic connections. An extended version of the Oden-Martins friction model is used to represent properties of the interface. The mechanical model of the frictional system is the basis for numerical analysis of dynamic instabilities caused by friction and of self-excited oscillations. Coupling between rotational and normal modes is the primary mechanism of resulting self-excited oscillations. These oscillations combine with high-frequency stick-slip motion to produce a significant reduction of the apparent kinetic coefficient of friction. As a particular study model, a pin-on-disk experimental setup has been selected. A good qualitative and quantitative correlation of numerical and experimental results is observed.

scholarly journals Kompiuterinis biojutiklių su perforuota ir selektyvia membrana modeliavimas vienmačiu keturių sluoksnių modeliu

2009 ◽  
Vol 50 ◽  
pp. 328-333
Author(s):  
Karolis Petrauskas
Keyword(s):  
Numerical Experiments ◽  
Enzymatic Reaction ◽  
Diffusion Reaction ◽  
Homogeneous Layer ◽  
Dimensional Model ◽  
One Dimensional ◽  
Proposed Model ◽  
The One ◽  
Menten Kinetic ◽  
Reaction Equations

Straipsnyje pateikiamas vienmatis biojutiklio su perforuota ir selektyvia membrana modelis. Šis modelis sudarytas pakeičiant perforuotą membraną dviem homogeniškais sluoksniais atitinkamai membranos dalims, kur skylutės yra užpildytos fermento ir kur fermento nėra. Pasiūlytas modelis buvo ištirtas vykdant skaitinius eksperimentus, kad būtų nustatytos sąlygos, kuriomis jis gali būti taikomas tiksliam biojutiklio veiksmo modeliavimui. Šio modelio tikslumas buvo vertinamas lyginant juo gaunamus rezultatus su dvimačio modelio rezultatais. Pasiūlyto modelio rezultatai taip pat buvo palyginti su vienmačio modelio, kuriame perforuota membrana pakeičiama vienu homogenišku sluoksniu, rezultatais. Biojutiklis buvo modeliuojamas reakcijos-difuzijos lygtimis su netiesiniu nariu, aprašančiu fermentinės reakcijos Michaelio–Menteno kinetiką. Modelio lygčių sistema buvo sprendžiama skaitiškai, naudojant baigtinių skirtumų metodą.Computer-Aided Modeling of a Biosensor with Selective and Perforated Membranes Using a Four-Layered One-Dimensional ModelKarolis Petrauskas SummaryThis article presents a one-dimensional model for a biosensor with perforated and selective membranes. This model is constructed by replacing the perforated membrane with two homogeneous layers. These layers are used to model parts of the perforated membrane, where holes are fi lled with an enzyme and where is no enzyme in the holes, separately. The proposed model was investigated by performing numerical experiments in order to determine conditions, under which the proposed model can be used to simulate an operation of a biosensor with an outer perforated membrane precisely. A preciseness of the model was measured by comparing its results with results of the corresponding two-dimensional model. Beside the measurement of the preciseness, results of the proposed model were compared to the results of the one-dimensional model, constructed by replacing the perforated membrane with one homogeneous layer. A biosensor was modeled using diffusion-reaction equations with a nonlinear member representing the Michaelis-Menten kinetic of an enzymatic reaction. These equations were solved numerically, using the method of fi nite differences.: 18px;"> 

Distributed-Parameters Base Modeling and Vibration Analysis of Microcantilevers Used in Atomic Force Microscopy

2009 ◽  
Author(s):  
A. A. Abouelsoud ◽  
J. Abdo Ahmed
Keyword(s):  
Limit Cycle ◽  
Time Derivative ◽  
Positive Definite Function ◽  
Friction Model ◽  
Sustained Oscillation ◽  
Definite Function ◽  
Stick Slip ◽  
Coulomb Friction Model ◽  
Stick Slip Motion ◽  
Slip Motion

Friction-induced self-sustained oscillation result in a very robust limit cycle that characterizes stick-slip motion. This motion should be avoided because it creates unwanted noise, diminishes accuracy, and increases wear. The stick-slip motion produced by a mass-spring-damper on a moving belt is analyzed using Lyapunov second method, which is based on constructing a positive definite function and checking the condition for which its time derivative is negative semi-definite. From this condition an estimate of the amplitude of the velocity of the limit cycle of the stick-slip motion is obtained. This estimate is found to be the zero of a certain function derived from the Coulomb friction model. An estimate of the amplitude of the displacement is also found. It is shown that the simulation results of the amplitude and the estimated amplitude are in a good match.

scholarly journals Experimental comparison of five friction models on the same test-bed of the micro stick-slip motion system

2015 ◽  
Vol 6 (1) ◽  
pp. 15-28 ◽  
Author(s):  
Y. F. Liu ◽  
J. Li ◽  
Z. M. Zhang ◽  
X. H. Hu ◽  
W. J. Zhang
Keyword(s):  
Friction Model ◽  
Test Bed ◽  
Lugre Model ◽  
Stick Slip ◽  
Motion System ◽  
Friction Models ◽  
Micro Motion ◽  
Coulomb Friction Model ◽  
Stick Slip Motion ◽  
Slip Motion

Abstract. The micro stick-slip motion systems, such as piezoelectric stick-slip actuators (PE-SSAs), can provide high resolution motions yet with a long motion range. In these systems, friction force plays an active role. Although numerous friction models have been developed for the control of micro motion systems, behaviors of these models in micro stick-slip motion systems are not well understood. This study (1) gives a survey of the basic friction models and (2) tests and compares 5 friction models in the literature, including Coulomb friction model, Stribeck friction model, Dahl model, LuGre model, and the elastoplastic friction model on the same test-bed (i.e. the PE-SSA system). The experiments and simulations were done and the reasons for the difference in the performance of these models were investigated. The study concluded that for the micro stick-slip motion system, (1) Stribeck model, Dahl model and LuGre model all work, but LuGre model has the best accuracy and (2) Coulomb friction model and the elastoplastic model does not work. The study provides contributions to motion control systems with friction, especially for micro stick-slip or step motion systems as well as general micro-motion systems.

Modelling Techniques in Applied Glaciology: Numerical Modelling of Avalanches

1983 ◽  
Vol 4 ◽  
pp. 297-297
Author(s):  
G. Brugnot
Keyword(s):  
Finite Difference Method ◽  
Transverse Velocity ◽  
Longitudinal Velocity ◽  
Momentum Conservation ◽  
Dimensional Model ◽  
One Dimensional ◽  
Modelling Techniques ◽  
Reference Grid ◽  
The One ◽  
Near Future

We consider the paper by Brugnot and Pochat (1981), which describes a one-dimensional model applied to a snow avalanche. The main advance made here is the introduction of the second dimension in the runout zone. Indeed, in the channelled course, we still use the one-dimensional model, but, when the avalanche spreads before stopping, we apply a (x, y) grid on the ground and six equations have to be solved: (1) for the avalanche body, one equation for continuity and two equations for momentum conservation, and (2) at the front, one equation for continuity and two equations for momentum conservation. We suppose the front to be a mobile jump, with longitudinal velocity varying more rapidly than transverse velocity.We solve these equations by a finite difference method. This involves many topological problems, due to the actual position of the front, which is defined by its intersection with the reference grid (SI, YJ). In the near future our two directions of research will be testing the code on actual avalanches and improving it by trying to make it cheaper without impairing its accuracy.

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