Stick-slip vibrations of a self-excited SD oscillator with Coulomb friction

2020 ◽  
Vol 102 (3) ◽  
pp. 1419-1435 ◽  
Author(s):  
Zhixin Li ◽  
Qingjie Cao ◽  
Zairan Nie
Keyword(s):  
Coulomb Friction ◽  
Stick Slip ◽  
Sd Oscillator

Threshold of Multiple Stick-Slip Chaos for an Archetypal Self-Excited SD Oscillator Driven by Moving Belt Friction

2017 ◽  
Vol 27 (01) ◽  
pp. 1750009 ◽  
Author(s):  
Z. X. Li ◽  
Q. J. Cao ◽  
A. Léger
Keyword(s):  
Multiple Solutions ◽  
Coulomb Friction ◽  
Homoclinic Orbits ◽  
The Self ◽  
External Excitation ◽  
Stick Slip ◽  
Sd Oscillator ◽  
Excited System ◽  
Analytical Expressions ◽  
Natural Characteristics

In this paper, we investigate the multiple stick-slip chaotic motion of an archetypal self-excited smooth and discontinuous (SD) oscillator driven by moving belt friction, which is constructed with the SD oscillator and the classical moving belt. The friction force between the mass and the belt is modeled as a Coulomb friction for this system. The energy introduction or dissipation during the slip and stick modes in the system is analyzed. The analytical expressions of homoclinic orbits of the unperturbed SD oscillator are derived by using a special coordinate transformation without any pronominal truncation to retain the natural characteristics, which allows us to utilize the Melnikov’s method to obtain the chaotic thresholds of the self-excited SD oscillator in the presence of the damping and external excitation. Numerical simulations are carried out to demonstrate the multiple stick-slip dynamics of the system, which show the efficiency of the prediction for stick-slip chaos of the perturbed self-excited system. The results presented herein this paper demonstrate the complicated dynamics of stick-slip periodic solutions, multiple stick-slip chaotic solutions and also coexistence of multiple solutions for the perturbed self-excited SD oscillator.

Asperity Spring Friction Model With Application to Belt-Drives

2003 ◽  
Author(s):  
Tamer M. Wasfy
Keyword(s):  
Finite Element ◽  
Coulomb Friction ◽  
Friction Model ◽  
Belt Drive ◽  
Finite Element Code ◽  
Time Step ◽  
Stick Slip ◽  
Normal Contact ◽  
Belt Drives ◽  
Coulomb Friction Model

An asperity spring friction model that uses a variable anchor point spring along with a velocity dependent force is presented. The model is incorporated in an explicit timeintegration finite element code. The friction model is used along with a penalty-based normal contact model to simulate the dynamic response of a two-pulley belt-drive system. It is shown that the present friction model accurately captures the stick-slip behavior between the belt and the pulleys using a much larger time-step than a pure velocity-dependent approximate Coulomb friction model.

Variational Formulation for Frictional Interface Dynamics

2012 ◽  
Author(s):  
Timothy Truster ◽  
Arif Masud ◽  
Lawrence A. Bergman
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Coulomb Friction ◽  
Bolted Joints ◽  
Lap Joint ◽  
Stick Slip ◽  
Element Simulation ◽  
Friction Models ◽  
Frictional Interface ◽  
Current Emphasis

The dynamic response of component bolted joints often plays a significant role in the overall behavior of a structural system. Accurate finite element simulation of these problems requires proper treatment of the interface conditions. We present a formulation carefully suited to these problems that incorporates discontinuous Galerkin (DG) treatment locally at the interface. The present work is an extension of our previous investigations of friction models within a finite element method for quasi-static problems. The current emphasis is on the treatment of the inertial term and ensuring that artificial resonance is not induced by the discrete interface. The weak imposition of continuity constraints allows the stick-slip behavior at the jointed surface to proceed smoothly, reducing the numerical instability compared to node-to-node contact techniques. As a model problem, we simulate the dynamic response of a lap joint subjected to an impulse axial force assuming Coulomb friction at the interface.

Global convergence for two-pulse rest-to-rest learning for single-degree-of-freedom systems with stick-slip Coulomb friction

Robotica ◽  
2006 ◽  
Vol 25 (3) ◽  
pp. 307-313
Author(s):  
Brian J. Driessen ◽  
Nader Sadegh
Keyword(s):  
Global Convergence ◽  
Coefficient Of Friction ◽  
Coulomb Friction ◽  
Sliding Friction ◽  
Input Pulse ◽  
Iterative Learning ◽  
Degree Of Freedom ◽  
Stick Slip ◽  
Single Degree Of Freedom ◽  
Single Degree

SUMMARYIn this paper, we consider the problem of rest-to-rest maneu-ver learning, via iterative learning control (ILC), for single-degree-of-freedom systems with stick-slip Coulomb friction and input bounds. The static coefficient of friction is allowed to be as large as three times the kinetic coefficient of friction. The input is restricted to be a two-pulse one. The desired input's first pulse magnitude is required to be five times the largest possible kinetic (sliding) friction force. The theory therefore allows the stiction force to be as large as the desired second input pulse. Under these conditions, we prove global convergence of a simple iterative learning controller. To the best of our knowledge, such a global-convergence proof has not been presented previously in the literature for the rest-to-rest problem with stick-slip Coulomb friction.

Coulomb Friction Limit Cycles in Elastic Positioning Systems

1999 ◽  
Vol 121 (2) ◽  
pp. 298-301 ◽  
Author(s):  
A. Bonsignore ◽  
G. Ferretti ◽  
G. Magnani
Keyword(s):  
Coulomb Friction ◽  
Closed Loop ◽  
Tracking Error ◽  
Pole Placement ◽  
Stick Slip ◽  
Positioning Systems ◽  
Relay Control ◽  
Pure Coulomb ◽  
Pole Placement Controller ◽  
Motor Velocity

The state space control of a positioning system affected by torsional elasticity at the gearbox is considered, using a motor position transducer only. An output feedback, pole placement controller is used, with an additional integral action on the tracking error to cancel it at steady state. Both experiments and simulations point out that large oscillations may appear for some sets of closed-loop poles which yields, in contrast to stick-slip cycles, instantaneous motor velocity reversals. It is shown that such oscillations are induced by “pure” Coulomb friction. The period of the oscillations is predicted precisely following the Tsypkin’s relay control theory and also by the approximate describing function method. The latter also allows understanding of how oscillations depend on observer and feedback control design and on plant parameters; thus we are able to derive guidelines for the design of an oscillation free closed-loop system.

scholarly journals Transitions and singularities during slip motion of rigid bodies

2018 ◽  
Vol 29 (5) ◽  
pp. 778-804 ◽  
Author(s):  
P. L. VÁRKONYI
Keyword(s):  
Coulomb Friction ◽  
Rigid Bodies ◽  
Two Dimensions ◽  
Multiple Point ◽  
Point Contacts ◽  
Stick Slip ◽  
Unilateral Contacts ◽  
Rigid Rod ◽  
Body Theory ◽  
Slip Motion

The dynamics of moving solids with unilateral contacts are often modelled by assuming rigidity, point contacts, and Coulomb friction. The canonical example of a rigid rod with one endpoint slipping in two dimensions along a fixed surface (sometimes referred to as Painlevé rod) has been investigated thoroughly by many authors. The generic transitions of that system include three classical transitions (slip-stick, slip reversal, and liftoff) as well as a singularity called dynamic jamming, i.e., convergence to a codimension 2 manifold in state space, where rigid body theory breaks down. The goal of this paper is to identify similar singularities arising in systems with multiple point contacts, and in a broader setting to make initial steps towards a comprehensive list of generic transitions from slip motion to other types of dynamics. We show that – in addition to the classical transitions – dynamic jamming remains a generic phenomenon. We also find new forms of singularity and solution indeterminacy, as well as generic routes from sliding to self-excited microscopic or macroscopic oscillations.

Finite Element Model of Schallamach Waves in Belt-Drives

2019 ◽  
Author(s):  
Mohammed Khattab ◽  
Tamer Wasfy
Keyword(s):  
Finite Element ◽  
Friction Coefficient ◽  
Finite Element Model ◽  
Wave Phenomenon ◽  
Coulomb Friction ◽  
Element Model ◽  
Belt Drive ◽  
High Fidelity ◽  
Stick Slip ◽  
Belt Drives

Abstract The objective of this study is to investigate if a high-fidelity finite element model can predict the Schallamach wave phenomenon in belt-drives. To this end a computational model which closely mimics a recently developed one-pulley experimental belt-drive apparatus, was created. The dynamic response predicted by the model is compared to the experiment results in order to demonstrate that the model can be used to predict the Schallamach wave phenomenon. Furthermore, the model is used to investigate the roles of Coulomb friction coefficient, adhesion, and torque direction on stick-slip instability effects.

scholarly journals Multi-dimensional semi-analytical model for axial stick–slip of a rod sliding on a surface with Coulomb friction

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401983153
Author(s):  
Sigve Hovda
Keyword(s):  
Constant Velocity ◽  
Coulomb Friction ◽  
Element Model ◽  
Oil Well ◽  
Stick Slip ◽  
Well Drilling ◽  
Lumped Element ◽  
Fundamental Understanding ◽  
Real Time Applications ◽  
Lumped Element Model

A multi-dimensional lumped element model of a long non-rotating rod that moves on a slick surface with both dynamic and static Coulomb friction is outlined. The rod is accelerated to a constant velocity, and the free end of the rod experiences the effect of stick and slip. This article describes a new modeling approach, where the model is able to switch between different linear semi-analytical sub-models, depending on how much of the rod is moving. Fundamental understanding of the stick–slip effect is revealed, and a potential shortcoming of the model is also discussed. The model is computationally effective and may be suitable for real-time applications in, for instance, oil-well drilling.

Sign in / Sign up

Export Citation Format

Share Document