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.

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.

Asymptotic Impact Control of Hydraulic Actuators With Friction

2004 ◽  
Author(s):  
P. Sekhavat ◽  
N. Sepehri ◽  
Q. Wu
Keyword(s):  
Steady State ◽  
Nonlinear Control ◽  
Dry Friction ◽  
Position Control ◽  
Past Research ◽  
Hydraulic Actuator ◽  
Stick Slip ◽  
Hydraulic Actuators ◽  
Control Scheme ◽  
Control Schemes

The focus of this work is stabilization of hydraulic actuators during the transition from free motion to constraint motion and regulating the intermediate impacts that could drive the system unstable. In our past research, we introduced Lyapunov-based nonlinear control schemes capable of fulfilling the above goal by resting the implement on the surface of the environment before starting the sustained-contact motion. The hydraulic actuator’s stick-slip friction effect was, however, either not included in the analysis or not compensated by the control action. In this paper, the application of our previously introduced friction compensating position control scheme is extended to impact regulation of a hydraulic actuator. Theoretical solution and stability analyses as well as actual experiments prove that such control scheme is also effective for asymptotic impact control (with no position steady-state error) of hydraulic actuators in the presence of actuator’s dry friction.

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.

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.

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.

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

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.

scholarly journals The Influence of Different Types of Nanofluid on Thermal and Fluid Flow Performance of Liquid Cold Plate

2018 ◽  
Vol 7 (4.35) ◽  
pp. 148 ◽  
Author(s):  
Nur Irmawati Om ◽  
Rozli Zulkifli ◽  
P. Gunnasegaran
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Steady State ◽  
Pressure Drop ◽  
Volume Fraction ◽  
Cold Plate ◽  
Governing Equations ◽  
Flow And Heat Transfer ◽  
Different Types ◽  
Volume Method

The influence of utilizing different nanofluids types on the liquid cold plate (LCP) is numerically investigated. The thermal and fluid flow performance of LCP is examined by using pure ethylene glycol (EG), Al2O3-EG and CuO-EG. The volume fraction of the nanoparticle for both nanofluid is 2%. The finite volume method (FVM) has been used to solved 3-D steady state, laminar flow and heat transfer governing equations. The presented results indicate that Al2O3-EG able to provide the lowest surface temperature of the heater block followed by CuO-EG and EG, respectively. It is also found that the pressure drop and friction factor are higher for Al2O3-EG and CuO-EG compared to the pure EG.

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