Force Product Criteria of Sliding Motions in a Forced Linear Oscillator Including Dry Friction

2005 ◽  
Author(s):  
Albert C. J. Luo ◽  
Brandon C. Gegg
Keyword(s):  
Numerical Simulations ◽  
Dry Friction ◽  
Linear Oscillator ◽  
Analytical Prediction

In this paper, the switching conditions for sliding motions in a periodically, forced linear oscillator with dry friction are obtained analytically. The generic mappings for the friction-induced oscillator are introduced. From the generic mappings, the corresponding criteria for the sliding motions are presented through the force product conditions. The analytical prediction of the onset and vanishing of the sliding motions is illustrated. Finally, numerical simulations of sliding motions are carried out to verify the analytical prediction.

The Stick Motion of a Harmonically Excited, Friction-Induced Oscillator on a Sinusoidally Traveling Surface

2006 ◽  
Author(s):  
Albert C. J. Luo ◽  
Brandon C. Gegg ◽  
Steve S. Suh
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Dry Friction ◽  
The Other ◽  
Linear Oscillator ◽  
Analytical Prediction ◽  
Nonlinear Friction ◽  
Friction Forces

In this paper, the methodology is presented through investigation of a periodically, forced linear oscillator with dry friction, resting on a traveling surface varying with time. The switching conditions for stick motions in non-smooth dynamical systems are obtained. From defined generic mappings, the corresponding criteria for the stick motions are presented through the force product conditions. The analytical prediction of the onset and vanishing of the stick motions is illustrated. Finally, numerical simulations of stick motions are carried out to verify the analytical prediction. The achieved force criteria can be applied to the other dynamical systems with nonlinear friction forces possessing a CO - discontinuity.

Analysis of Motion of the Impact-Dry-Friction Pair of Bodies and its Application to the Investigation of the Impact Dampers Dynamics

1999 ◽  
Author(s):  
František Peterka
Keyword(s):  
Analytical Solution ◽  
Numerical Simulations ◽  
Mechanical System ◽  
Relative Motion ◽  
Dry Friction ◽  
Friction Pair ◽  
Strong Nonlinearity ◽  
Friction Forces ◽  
The Impact ◽  
Analysis Of Motion

Abstract The motion with impacts and dry friction forces appears in some mechanical systems as mechanisms with clearances, (e.g., in gearings, pins, slots, guides, valve gears etc.), impact dampers, relays, forming and mailing machines, power pics etc. Such mechanisms include one or more pairs of impacting bodies, which introduce the strong nonlinearity into the system motion. The motion of the general pair of bodies with the both-sides impacts and dry friction forces is assumed (Fig.1). It can be the part of a more complex chain of masses in the mechanical system. Dead zones in the relative motion of bodies can be caused by assumed nonlinearities. The mathematical conditions controlling the numerical simulations or analytical solution of the motion are introduced. The application of this method is explained by the study of the influence of dry friction force on amplitude-frequency characteristics of four types of dynamical and impact dampers with optimised parameters.

Hysteretic effects of dry friction: modelling and experimental studies

2007 ◽  
Vol 366 (1866) ◽  
pp. 747-765 ◽  
Author(s):  
Jerzy Wojewoda ◽  
Andrzej Stefański ◽  
Marian Wiercigroch ◽  
Tomasz Kapitaniak
Keyword(s):  
Numerical Simulations ◽  
Dry Friction ◽  
Experimental Studies ◽  
Friction Model ◽  
Hysteretic Effect ◽  
Motion Characteristic ◽  
Friction Models ◽  
Theoretical Analyses ◽  
Friction Modelling

In this paper, the phenomena of hysteretic behaviour of friction force observed during experiments are discussed. On the basis of experimental and theoretical analyses, we argue that such behaviour can be considered as a representation of the system dynamics. According to this approach, a classification of friction models, with respect to their sensitivity on the system motion characteristic, is introduced. General friction modelling of the phenomena accompanying dry friction and a simple yet effective approach to capture the hysteretic effect are proposed. Finally, the experimental results are compared with the numerical simulations for the proposed friction model.

A General Model for Two-Point Contact Dry-Friction Whip and Whirl

2012 ◽  
Author(s):  
Jason C. Wilkes
Keyword(s):  
Numerical Simulations ◽  
Analytical Model ◽  
General Model ◽  
Dry Friction ◽  
Point Contact ◽  
Current Work ◽  
Equipment Failure ◽  
Air Bearings ◽  
Single Location ◽  
Arbitrary Phase

Numerous papers have investigated the behavior of dry-friction whip and whirl; most of them consider contact between a rotor and stator at a single location. For rotors running on multiple magnetic bearings, air bearings, or bushings, equipment failure may result in rub at more than one location. For these cases, it is important to have an analytical model that characterizes possible regions of two-point contact dry-friction whip and whirl. Until a recent publication by Childs and Kumar in 2011, there were no attempts to analytically describe the behavior of dry-friction whip and whirl at more than one location. In their work, they assume that forces at the two rotor/stator contacts are either in-phase, or out-of phase. The current work presents a method that is more general, allowing for an arbitrary phase between contact locations. In theory this method can be applied to more than two contact locations; however, a two-point contact example case is developed and compared to numerical simulations in the current work.

A GLOBAL PERIOD-1 MOTION OF A PERIODICALLY EXCITED, PIECEWISE-LINEAR SYSTEM

2005 ◽  
Vol 15 (06) ◽  
pp. 1945-1957 ◽  
Author(s):  
SANTHOSH MENON ◽  
ALBERT C. J. LUO
Keyword(s):  
Linear System ◽  
Numerical Simulations ◽  
Piecewise Linear ◽  
Dynamical Behavior ◽  
Analytical Prediction ◽  
Algebraic Equations ◽  
Piecewise Linear System ◽  
Nonlinear Algebraic Equations ◽  
The Stability ◽  
Nonsmooth Dynamical Systems

The period-1 motion of a piecewise-linear system under a periodic excitation is predicted analytically through the Poincaré mapping and the corresponding mapping sections formed by the switch planes pertaining to the two constraints. The mapping relationship generates a set of nonlinear algebraic equations from which the period-1 motion is determined analytically. The stability and bifurcation of the period-1 motion are determined, and numerical simulations are carried out for confirmation of the analytical prediction of period-1 motion. An unsymmetrical stable period-1 motion is observed. This investigation helps us understand the dynamical behavior of period-1 motion in the piecewise-linear system and more efficiently obtain other periodic motions and chaos through numerical simulations. The similar methodology presented in this paper can be used for other nonsmooth dynamical systems.

Periodic Motions in a Periodically Forced Oscillator Moving on the Oscillating Belt With Dry Friction

2005 ◽  
Author(s):  
Albert C. J. Luo ◽  
Brandon C. Gegg
Keyword(s):  
Relative Motion ◽  
Efficient Method ◽  
Periodic Motion ◽  
Dry Friction ◽  
Displacement Velocity ◽  
Eigenvalue Analysis ◽  
Analytical Prediction ◽  
Periodic Motions ◽  
Mapping Structures ◽  
Forced Oscillator

In this paper, periodic motion in an oscillator moving on a periodically vibrating belt with dry-friction is investigated. The conditions of stick and non-stick motions for such an oscillator are obtained in the relative motion frame, and the grazing and stick (or sliding) bifurcations are presented as well. The periodic motions are predicted analytically and numerically, and the analytical prediction is based on the appropriate mapping structures. The eigenvalue analysis of such periodic motions is carried out. The periodic motions are illustrated through the displacement, velocity and force responses in the absolute and relative frames. This investigation provides an efficient method to predict periodic motions of such an oscillator involving dry-friction. The significance of this investigation lies in controlling motion of such friction-induced oscillator in industry.

The Estimation of Viscous and Coulomb Damping in Harmonically Excited Oscillators

1999 ◽  
Author(s):  
J.-W. Liang ◽  
B. F. Feeny
Keyword(s):  
Free Vibration ◽  
Numerical Simulations ◽  
Dry Friction ◽  
Mechanical Vibration ◽  
Degree Of Freedom ◽  
Identification Algorithm ◽  
Single Degree Of Freedom ◽  
Coulomb Damping ◽  
Single Degree

Abstract This paper proposes a simple identification algorithm for estimating both viscous and dry friction in harmonically forced single-degree-of-freedom mechanical vibration systems. The method is especially suitable for the identification of systems for which the traditional free-vibration scheme is difficult to implement. Numerical simulations are included to show the effectiveness of the proposed algorithm. A numerical perturbation study is also included for insight on the robustness of the algorithm.

On the Mechanism of Stick and Non-Stick, Periodic Motions in a Forced Linear Oscillator Including Dry Friction

2004 ◽  
Author(s):  
Albert C. J. Luo ◽  
Brandon C. Gegg
Keyword(s):  
Dry Friction ◽  
Local Stability ◽  
Displacement Velocity ◽  
Linear Oscillator ◽  
Periodic Motions ◽  
Friction Forces ◽  
Stability And Bifurcation ◽  
Mapping Structures ◽  
Linear Friction ◽  
Friction Oscillator

In this paper, the dynamics mechanism of stick and non-stick motion for a dry-friction oscillator is discussed. From the theory of Luo in 2004, the conditions for stick and non-stick motions are achieved. The stick and non-stick periodic motions are predicted analytically through the appropriate mapping structures. The local stability and bifurcation for such periodic motions are obtained. The stick motions are illustrated through the displacement, velocity and force responses. This investigation provides a better understanding of stick and nonstick motions of the linear oscillator with dry-friction. The methodology presented in this paper is applicable to oscillators with non-linear friction forces.

scholarly journals Analytical prediction of stick-slip chaos in a double self-excited Duffing-type oscillator

2006 ◽  
Vol 2006 ◽  
pp. 1-79 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Mariusz Holicke
Keyword(s):  
Numerical Simulations ◽  
Analytical Prediction ◽  
Stick Slip ◽  
Homoclinic Bifurcations

We have analytically predicted homoclinic bifurcations in a class of double self-excited Duffing-type oscillators using the Melnikov-Gruendler approach. Both stick-slip and smooth chaotic behaviors predicted analytically have been confirmed by numerical simulations.

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