A Historical Review on Dry Friction and Stick-Slip Phenomena

1998 ◽  
Vol 51 (5) ◽  
pp. 321-341 ◽  
Author(s):  
Brian Feeny ◽  
Arde´shir Guran ◽  
Nikolaus Hinrichs ◽  
Karl Popp
Keyword(s):  
Dry Friction ◽  
Historical Review ◽  
Review Article ◽  
Stick Slip ◽  
Daily Lives ◽  
Friction Forces ◽  
Sliding Surfaces ◽  
Highly Nonlinear ◽  
History Of ◽  
Friction Oscillators

This article gives a historical overview of structural and mechanical systems with friction. Friction forces between sliding surfaces arise due to complex mechanisms and lead to mathematical models which are highly nonlinear, discontinuous and nonsmooth. Humankind has a long history of magnificent usage of friction in machines, buildings and transportation. Regardless, our state of knowledge of the friction-influenced dynamics occurring in such systems as well as in our daily lives was, until recently, rather primitive. To represent our understanding of friction in nonlinear dynamics, we first trace examples from the earliest prehistoric technologies and the formulation of dissipation laws in mechanics. The work culminates with examples of friction oscillators and stick-slip. This review article contains 304 references.

scholarly journals Micro-Slip as a Loss of Determinacy in Dry-Friction Oscillators

2019 ◽  
Vol 29 (06) ◽  
pp. 1930015 ◽  
Author(s):  
S. Webber ◽  
M. R. Jeffrey
Keyword(s):  
Differential Equations ◽  
Dry Friction ◽  
Dynamical Theory ◽  
Stick Slip ◽  
Friction Forces ◽  
Mechanical Oscillators ◽  
The Stability ◽  
Stick Slip Motion ◽  
Friction Oscillators ◽  
Slip Motion

Dry-friction contacts in mechanical oscillators can be modeled using nonsmooth differential equations, and recent advances in dynamical theory are providing new insights into the stability and uniqueness of such oscillators. A classic model is that of spring-coupled masses undergoing stick-slip motion on a rough surface. Here, we present a phenomenon in which multiple masses transition from stick to slip almost simultaneously, but suffer a brief loss of determinacy in the process. The system evolution becomes many-valued, but quickly collapses back down to an infinitesimal set of outcomes, a sort of “micro-indeterminacy”. Though fleeting, the loss of determinacy means masses may each undergo different microscopic sequences of slipping events, before all masses ultimately slip. The microscopic loss of determinacy is visible in local changes in friction forces, and in creating a bistability of global stick-slip oscillations. If friction forces are coupled between the oscillators then the effect is more severe, as solutions are compressed instead onto two (or more) macroscopically different outcomes.

Analysis of Beam-Like Structures With Displacement-Dependent Friction Forces: Part I — Single-Degree-of-Freedom Model

1995 ◽  
Author(s):  
Wayne E. Whiteman ◽  
Aldo A. Ferri
Keyword(s):  
Dry Friction ◽  
Damping Ratio ◽  
Strong Dependence ◽  
Time Integration ◽  
Single Mode ◽  
Stick Slip ◽  
Friction Forces ◽  
Equivalent Damping ◽  
Damping Characteristics ◽  
Parameter Values

Abstract The dynamic behavior of a beam-like structure undergoing transverse vibration and subjected to a displacement-dependent dry friction force is examined. In Part I, the beam is modeled by a single mode while Part II considers multi-mode representations. The displacement dependence in each case is caused by a ramp configuration that allows the normal force across the sliding interface to increase linearly with slip displacement. The system is studied first by using first-order harmonic balance and then by using a time integration method. The stick-slip behavior of the system is also studied. Even though the only source of damping is dry friction, the system is seen to exhibit “viscous-like” damping characteristics. A strong dependence of the equivalent natural frequency and damping ratio on the displacement amplitude is an interesting result. It is shown that for a given set of parameter values, an optimal ramp angle exists that maximizes the equivalent damping ratio. The appearance of two dynamic response solutions at certain system and forcing parameter values is also seen. Results suggest that the overall characteristics of mechanical systems may be improved by properly configuring frictional interfaces to allow normal forces to vary with displacement.

Nonlinear Numerical Prediction of Gas Foil Bearing Stability and Unbalanced Response

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Sébastien Le Lez ◽  
Mihaï Arghir ◽  
Jean Frêne
Keyword(s):  
Dry Friction ◽  
Stability Limit ◽  
Time Step ◽  
Structural Dynamic ◽  
Friction Forces ◽  
Foil Bearings ◽  
Mass Unbalance ◽  
Foil Bearing ◽  
Highly Nonlinear ◽  
The Stability

One of the main interests of gas foil bearings lies in their superior rotordynamic characteristics compared with conventional bearings. A numerical investigation on the stability limit and on the unbalanced response of foil bearings is presented in this paper. The main difficulty in modeling the dynamic behavior of such bearings comes from the dry friction that occurs within the foil structure. Indeed, dry friction is highly nonlinear and is strongly influenced by the dynamic amplitude of the pressure field. To deal with these nonlinearities, a structural dynamic model has been developed in a previous work. This model considers the entire corrugated foil and the interactions between the bumps by describing the foil bearing structure as a multiple degrees of freedom system. It allows the determination of the dynamic friction forces at the top and at the bottom of the bumps by simple integration of ordinary differential equations. The dynamic displacements of the entire corrugated sheet are then easily obtained at each time step. The coupling between this structural model and a gas bearing prediction code is presented in this paper and allows performing full nonlinear analyses of a complete foil bearing. The bearing stability is the first investigated problem. The results show that the structural deflection enhances the stability of compliant surface bearings compared with rigid ones. Moreover, when friction is introduced, a new level of stability is reached, revealing the importance of this dissipation mechanism. The second investigated problem is the unbalanced response of foil bearings. The shaft trajectories depict a nonlinear jump in the response of both rigid and foil bearings when the value of the unbalance increases. Again, it is evidenced that the foil bearing can support higher mass unbalance before this undesirable step occurs.

scholarly journals Cluster synchronization of dry friction oscillators

2018 ◽  
Vol 148 ◽  
pp. 10004
Author(s):  
Michał Marszal ◽  
Andrzej Stefański
Keyword(s):  
Dry Friction ◽  
Numerical Study ◽  
Excitation Frequency ◽  
Friction Model ◽  
Cluster Synchronization ◽  
Stick Slip ◽  
Closed Ring ◽  
Mass Spring ◽  
Friction Oscillators ◽  
Two Parameter

Synchronization is a well known phenomenon in non-linear dynamics and is treated as correlation in time of at least two different processes. In scope of this article, we focus on complete and cluster synchronization in the systems of coupled dry friction oscillators, coupled by linear springs. The building block of the system is the classic stick-slip oscillator, which consists of mass, spring and belt-mass friction interface. The Stribeck friction itself is modelled using Stribeck friction model with exponential non-linearity. The oscillators in the systems are connected in nearest neighbour fashion, both in open and closed ring topology. We perform a numerical study of the properties of the dynamics of the systems in question, in two-parameter space (coupling coefficient vs. angular excitation frequency) and explore the possible configurations of cluster synchronization.

scholarly journals SLIDING BIFURCATIONS: A NOVEL MECHANISM FOR THE SUDDEN ONSET OF CHAOS IN DRY FRICTION OSCILLATORS

2003 ◽  
Vol 13 (10) ◽  
pp. 2935-2948 ◽  
Author(s):  
M. DI BERNARDO ◽  
P. KOWALCZYK ◽  
A. NORDMARK
Keyword(s):  
Dry Friction ◽  
Sudden Onset ◽  
Stick Slip ◽  
Border Collision Bifurcations ◽  
Sliding Bifurcation ◽  
Nonsmooth Systems ◽  
Different Types ◽  
Nonsmooth Dynamical Systems ◽  
Sudden Jump ◽  
Friction Oscillators

Recent investigations of nonsmooth dynamical systems have resulted in the study of a class of novel bifurcations termed as sliding bifurcations. These bifurcations are a characteristic feature of so-called Filippov systems, that is, systems of ordinary differential equations (ODEs) with discontinuous right-hand sides. In this paper we show that sliding bifurcations also play an important role in organizing the dynamics of dry friction oscillators, which are a subclass of nonsmooth systems. After introducing the possible codimension-1 sliding bifurcations of limit cycles, we show that these bifurcations organize different types of "slip to stick-slip" transitions in dry friction oscillators. In particular, we show both numerically and analytically that a sliding bifurcation is an important mechanism causing the sudden jump to chaos previously unexplained in the literature on friction systems. To analyze such bifurcations we make use of a new analytical method based on the study of appropriate normal form maps describing sliding bifurcations. Also, we explain the circumstances under which the theory of so-called border-collision bifurcations can be used in order to explain the onset of complex behavior in stick-slip systems.

A View to the Energy Dissipation Mechanism of a Gas Foil Bearing’s Structure due to Dry Friction

2012 ◽  
Author(s):  
José A. Matute ◽  
Rafael O. Ruiz ◽  
Sergio E. Diaz
Keyword(s):  
Energy Dissipation ◽  
Dry Friction ◽  
Nonlinear Behavior ◽  
Excitation Amplitude ◽  
Equivalent Model ◽  
Stick Slip ◽  
Friction Forces ◽  
Energy Dissipation Mechanism ◽  
Variable Function ◽  
Dissipation Mechanism

The purpose of the present work consists on improving the understanding of the energy dissipation mechanism in the structure of a gas foil bearing. The analysis is based on an analytical model capable of predicting bumps deformation due to a load on the top coupled with dry friction forces at the top and bump ends. Models of mass-individual bump and mass-bump foil subject to a harmonic force are predicted numerically. The nonlinear behavior due to dry friction results in the possibility of stick-slip conditions over the surfaces in contact. The Variation of parameters such as excitation amplitude, mass magnitude, coefficient of friction, and bump geometry were considered. Equivalent dynamic coefficients of stiffness and damping are estimated through a least squares curve fitting, which constitutes a linearization of the system with dry friction. A computer program was developed in order to consider the effect of stick-slip. As a final product of this research the nonlinear model of the structure support was used to obtain a linear and simplified equivalent model. In most studied cases it is possible to represent the system with a linearized model of constant stiffness and viscous damping which is a variable function of the studied parameters and the frequency.

Stick-Slip Effect in a Vibration-Driven System With Dry Friction: Sliding Bifurcations and Optimization

2013 ◽  
Vol 81 (5) ◽  
Author(s):  
Hongbin Fang ◽  
Jian Xu
Keyword(s):  
Steady State ◽  
Bifurcation Diagram ◽  
Dry Friction ◽  
Classical Mechanics ◽  
System Optimization ◽  
Physical Parameters ◽  
Stick Slip ◽  
Friction Forces ◽  
Driven System ◽  
Different Types

Vibration-driven systems can move progressively in resistive media owing to periodic motions of internal masses. In consideration of the external dry friction forces, the system is piecewise smooth and has been shown to exhibit different types of stick-slip motions. In this paper, a vibration-driven system with Coulomb dry friction is investigated in terms of sliding bifurcation. A two-parameter bifurcation problem is theoretically analyzed and the corresponding bifurcation diagram is presented, where branches of the bifurcation are derived in view of classical mechanics. The results show that these sliding bifurcations organize different types of transitions between slip and sticking motions in this system. The bifurcation diagram and the predicted stick-slip transitions are verified through numerical simulations. Considering the effects of physical parameters on average steady-state velocity and utilizing the sticking feature of the system, optimization of the system is performed. Better performance of the system with no backward motion and higher average steady-state velocity can be achieved, based on the proposed optimization procedures.

Discriminant Analysis and its Applications in Epidemiology

1980 ◽  
Vol 19 (04) ◽  
pp. 220-226 ◽  
Author(s):  
P. A. Lachenbruch ◽  
W. R. Clarke
Keyword(s):  
Discriminant Analysis ◽  
Historical Review ◽  
Review Article ◽  
Logistic Discrimination

This review article discusses current use of discriminant analysis in epidemiology. Contents include historical review, simple extensions and generalizations, examples, evaluation of rules, logistic discrimination, and robustness.

Outbreak Of Nipah Encephalitis In Greater Faridpur District

1970 ◽  
Vol 5 (2) ◽  
pp. 63-65
Author(s):  
MY Ali ◽  
SA Fattah ◽  
MM Islam ◽  
MA Hossain ◽  
SY Ali
Keyword(s):  
Health Personnel ◽  
Viral Encephalitis ◽  
Review Article ◽  
Personal Protection ◽  
Emerging Infections ◽  
College Hospital ◽  
Personal Protection Equipment ◽  
Medical College ◽  
History Of ◽  
Deadly Disease

Nipah viral encephalitis is one of the fatal re-emerging infections especially in southeast Asia. After its outbreak in Malaysia and Singapore; repeated outbreaks occurred at western part of Bangladesh especially in Faridpur region. Besides, sporadic attacks appear to occur in the country throughout the year. Here two Nipah outbreaks in greater Faridpur district in 2003 and 2004 are described along with brief review on transmission of the virus. Where the history of illness among patients are very much in favour of man to man transmission. Moreover the death of an intern doctor from Nipah encephalitis who was involved in managing such patients in Faridpur Medical College Hospital strongly suggests man to man transmission of this virus. So, aim of this review article to make the health personnel and general people be aware about man to man transmission of virus, so that they can adapt personal protection equipment (PPE) for their protection against this deadly disease. DOI: 10.3329/fmcj.v5i2.6825Faridpur Med. Coll. J. 2010;5(2):63-65

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