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

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.

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Stick-slip motion of turbine blade dampers

Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences ◽

10.1098/rsta.1992.0017 ◽

1992 ◽

Vol 338 (1651) ◽

pp. 503-517 ◽

Cited By ~ 38

Keyword(s):

Turbine Blade ◽

Dry Friction ◽

Sheet Steel ◽

Turbine Blades ◽

Design Parameters ◽

Stick Slip ◽

Stick Slip Motion ◽

Important Design ◽

Small Elements ◽

Slip Motion

Turbine blade dampers are small elements of a parabolic configuration usually fabricated from sheet steel. They are positioned loosely between the roots of turbine blades improving the damping of blade vibrations by generating dry friction from the relative motion of blades and damper. This paper presents a theoretical approach to these stick-slip vibrations and compares theory with measurements. Additionally, some design aspects of such dampers are discussed by considering the damping behaviour in relation to important design parameters.

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Stick–slip motion of solids with dry friction subject to random vibrations and an external field

Nonlinearity ◽

10.1088/0951-7715/24/2/001 ◽

2010 ◽

Vol 24 (2) ◽

pp. 351-372 ◽

Cited By ~ 34

Author(s):

A Baule ◽

H Touchette ◽

E G D Cohen

Keyword(s):

External Field ◽

Dry Friction ◽

Random Vibrations ◽

Stick Slip ◽

Stick Slip Motion ◽

Slip Motion

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The contact line of an evaporating droplet over a solid wedge and the pinned–unpinned transition

Journal of Fluid Mechanics ◽

10.1017/jfm.2016.68 ◽

2016 ◽

Vol 791 ◽

pp. 519-538 ◽

Cited By ~ 2

Author(s):

Seok Hyun Hong ◽

Marco A. Fontelos ◽

Hyung Ju Hwang

Keyword(s):

Differential Equation ◽

Contact Line ◽

Contact Angles ◽

Liquid Interface ◽

Stick Slip ◽

Small Perturbations ◽

Stability And Instability ◽

The Stability ◽

Stick Slip Motion ◽

Slip Motion

We compute the equilibrium contact angles for an evaporating droplet whose contact line lies over a solid wedge. The stability of the liquid interface is also considered and an integro-differential equation for small perturbations is deduced. The analysis of this equation yields criteria for stability and instability of the contact line, where the instability represents transition from the pinned to unpinned contact line representative of stick–slip motion.

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Effects of the Varying Normal Force on the Stick Slip Motion of Systems with Friction

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.479-481.1078 ◽

2012 ◽

Vol 479-481 ◽

pp. 1078-1083 ◽

Cited By ~ 1

Author(s):

Li Lan Liu

Keyword(s):

Normal Force ◽

Jacobian Matrix ◽

Mechanical Systems ◽

Structure Design ◽

Stick Slip ◽

Driven System ◽

Lugre Friction ◽

The Stability ◽

Stick Slip Motion ◽

Slip Motion

In most cases, the normal force applied to mechanical systems with friction is supposed to be constant for convenience. However, through experiments, normal vibration has been proved to have an effect on the stability of mechanical systems. Aiming at uncover the effects of the varying normal force on the stick slip motion, a belt driven system with LuGre friction is investigated. The driving velocity is considered as the critical parameter for stick slip occurrence. By means of the Jacobian matrix and the Taylor expansion, the critical driving velocity is achieved analytically as a function of frequency and acceleration of the varying normal force. In addition, the influence of the varying normal force on the size of limit cycles is also studied numerically. Results show that the variation of the applied normal force has an obviously effect on the stability of mechanical systems, and it should not be ignored in the structure design and the stability analysis for high precision mechanical systems.

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Two-dimensional stick-slip motion of Coulomb friction oscillators

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406215597954 ◽

2015 ◽

Vol 230 (14) ◽

pp. 2438-2448 ◽

Cited By ~ 3

Author(s):

M Fadaee ◽

SD Yu

Keyword(s):

Dry Friction ◽

Numerical Results ◽

Mathematical Programming Problem ◽

Two Dimensional ◽

State Equations ◽

Time Step ◽

Stick Slip ◽

Single Body ◽

Stick Slip Motion ◽

Slip Motion

Two-dimensional stick-slip motion of an oscillator subjected to dry friction is investigated in this paper. The equations of motion of the non-smooth system are discretized in the time domain by means of the implicit Bozzak-Newmark scheme. The system state equations in a time step are written in the incremental displacements to model the frictional constraints in accordance with Coulomb’s law. With the help of a coordinate transformation and introduction of paired non-negative and complementary variables, the non-smooth vibration problem is reduced to a mathematical programming problem for which a numerical solution can be obtained. Numerical results for a single body oscillator under a harmonic excitation are obtained using the proposed method and compared with those in the literature; excellent agreement is achieved. The proposed method is then applied to a general two-dimensional oscillator with stiffness and viscous coupling in addition to the frictional coupling. Experiments are conducted for free vibration of a single body vibration system subjected to two-dimensional dry friction. Good agreement between the measurements and numerical results obtained using the proposed scheme is observed.

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A Historical Review on Dry Friction and Stick-Slip Phenomena

Applied Mechanics Reviews ◽

10.1115/1.3099008 ◽

1998 ◽

Vol 51 (5) ◽

pp. 321-341 ◽

Cited By ~ 140

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.

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Bifurcation Analysis of Stick-Slip Motion of the Vibration-Driven System with Dry Friction

Mathematical Problems in Engineering ◽

10.1155/2018/2305187 ◽

2018 ◽

Vol 2018 ◽

pp. 1-10

Author(s):

Peng Li ◽

Ziwang Jiang

Keyword(s):

Dry Friction ◽

Numerical Continuation ◽

Internal Mass ◽

Stick Slip ◽

Sliding Bifurcation ◽

Directional Control ◽

Driven System ◽

Stick Slip Motion ◽

Two Parameter ◽

Slip Motion

This paper is concerned with the vibration-driven system which can move due to the periodic motion of the internal mass and the dry friction; the system can be modeled as Filippov system and has the property of stick-slip motion. Different periodic solutions of stick-slip motion can be analyzed through sliding bifurcation, two-parameter numerical continuation for sliding bifurcation is carried out to get the different bifurcation curves, and the bifurcation curves divide the parameters plane into different regions which stand for different stick-slip motion of the periodic solution. Furthermore, continuations with additional condition v=0 are carried out for the directional control of the vibration-driven system in one period; the curves divide the parameter plane into different progressions.

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