The Stick-Slip Motion of a Chaplygin Sleigh With a Piecewise Smooth Nonholonomic Constraint

2015 ◽  
Author(s):  
Vitaliy Fedonyuk ◽  
Phanindra Tallapragada
Keyword(s):  
Numerical Simulations ◽  
Nonholonomic Constraint ◽  
Nonholonomic Constraints ◽  
Piecewise Smooth ◽  
Chaplygin Sleigh ◽  
Stick Slip ◽  
Stick Slip Motion ◽  
Smooth Dynamics ◽  
Slip Motion

The Chaplygin sleigh is a canonical problem of mechanical systems with nonholonomic constraints, which arises due to the role of friction. The motion of the cart has often been studied under the assumption that the magnitude of friction is as high as necessary to prevent slipping. We relax this assumption by setting a maximum finite value to the friction. The Chaplygin sleigh is then under a piecewise smooth nonholonomic constraint and transitions between ‘slip’ and ‘stick’ modes. We investigate these transitions and the resulting non smooth dynamics of the system. Further more the piecewise smooth constraint offers the possibility of controlling the speed of the sleigh and we investigate this with numerical simulations.

Stick–Slip Motion of the Chaplygin Sleigh With a Piecewise-Smooth Nonholonomic Constraint

2017 ◽  
Vol 12 (3) ◽  
Author(s):  
Vitaliy Fedonyuk ◽  
Phanindra Tallapragada
Keyword(s):  
Nonholonomic Constraint ◽  
Nonholonomic Constraints ◽  
Piecewise Smooth ◽  
Nonsmooth Dynamics ◽  
Chaplygin Sleigh ◽  
Stick Slip ◽  
Velocity Decay ◽  
Asymptotic Speed ◽  
Asymptotic Motion ◽  
Stick Slip Motion

The Chaplygin sleigh is a canonical problem of mechanical systems with nonholonomic constraints. Such constraints often arise due to the role of a no-slip requirement imposed by friction. In the case of the Chaplygin sleigh, it is well known that its asymptotic motion is that of pure translation along a straight line. Any perturbations in angular velocity decay and result in an increase in asymptotic speed of the sleigh. Such motion of the sleigh is under the assumption that the magnitude of friction is as high as necessary to prevent slipping. We relax this assumption by setting a maximum value to the friction. The Chaplygin sleigh is then under a piecewise-smooth nonholonomic constraint and transitions between “slip” and “stick” modes. We investigate these transitions and the resulting nonsmooth dynamics of the system. We show that the reduced state space of the system can be partitioned into sets of distinct dynamics and that the stick–slip transitions can be explained in terms of transitions of the state of the system between these sets.

Studies on Friction and Formation of Transfer Layer in HCP Metals

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Pradeep L. Menezes ◽  
Kishore ◽  
Satish V. Kailas ◽  
Michael R. Lovell
Keyword(s):  
Surface Texture ◽  
Steel Plates ◽  
Ambient Conditions ◽  
Transfer Layer ◽  
Stick Slip ◽  
The Coefficient Of Friction ◽  
Hcp Materials ◽  
Stick Slip Motion ◽  
Slip Motion

Surface texture plays an important role in the frictional behavior and transfer layer formation of contacting surfaces. In the present investigation, basic experiments were conducted using an inclined pin-on-plate sliding apparatus to better understand the role of surface texture on the coefficient of friction and the formation of a transfer layer. In the experiments, soft HCP materials such as pure Mg and pure Zn were used for the pins and a hardened 080 M40 steel was used for the plate. Two surface parameters of the steel plates—roughness and texture—were varied in tests that were conducted at a sliding speed of 2 mm/s in ambient conditions under both dry and lubricated conditions. The morphologies of the worn surfaces of the pins and the formation of the transfer layer on the counter surfaces were observed using a scanning electron microscope. In the experiments, the occurrence of stick-slip motion, the formation of a transfer layer, and the value of friction were recorded. With respect to the friction, both adhesion and plowing components were analyzed. Based on the experimental results, the effect of surface texture on the friction was attributed to differences in the amount of plowing. Both the plowing component of friction and the amplitude of stick-slip motion were determined to increase surface textures that promote plane strain conditions and decrease the textures that favor plane stress conditions.

Chaos and Force Fluctuations in Frictional Dynamics

1996 ◽  
Vol 464 ◽  
Author(s):  
M. G. Rozman ◽  
J. Klafter ◽  
M. Urbakh
Keyword(s):  
Chaotic Behavior ◽  
Power Spectra ◽  
Stick Slip ◽  
Liapunov Exponents ◽  
Force Fluctuations ◽  
Periodic Potentials ◽  
Wide Range ◽  
Stick Slip Motion ◽  
Slip Motion

ABSTRACTA model is presented of a particle that interacts with two periodic potentials, representing two confining plates, one of which is externally driven. The model leads to various behaviors in the motion of the top driven plate: stick-slip, intermittent regime, characterized by force fluctuations, and two types of sliding above a critical driving velocity vc. Similar behaviors are typical of a broad range of systems including thin sheared liquids. A detailed analysis of the different regimes displays a transition between the stick-slip and the kinetic regimes, ω−2 power spectra of the force over a wide range of velocities below vc, and a decrease of the force fluctuations that follows (vc – v)½ for v < vc. The velocity dependent Liapunov exponents demonstrate that the stick-slip motion is characterized by a chaotic behavior of the top plate and the embedded particle. An extension of the model to an embedded chain is introduced and preliminary results are presented and confronted with the single particle case. The role of the internal excitations of the chain in frictional dynamics is discussed.

scholarly journals Role of friction-induced torque in stick-slip motion

2010 ◽  
Vol 92 (5) ◽  
pp. 54001 ◽  
Author(s):  
J. Scheibert ◽  
D. K. Dysthe
Keyword(s):  
Stick Slip ◽  
Stick Slip Motion ◽  
Slip Motion

Dynamics of stick–slip motion, Whillans Ice Stream, Antarctica

2011 ◽  
Vol 305 (3-4) ◽  
pp. 283-289 ◽  
Author(s):  
J. Paul Winberry ◽  
Sridhar Anandakrishnan ◽  
Douglas A. Wiens ◽  
Richard B. Alley ◽  
Knut Christianson
Keyword(s):  
Stick Slip ◽  
Ice Stream ◽  
Whillans Ice Stream ◽  
Stick Slip Motion ◽  
Slip Motion

Dynamic simulation of stick–slip motion of a flexible solar array

2008 ◽  
Vol 16 (6) ◽  
pp. 724-735 ◽  
Author(s):  
Yasushi Kojima ◽  
Shigemune Taniwaki ◽  
Yoshiaki Okami
Keyword(s):  
Dynamic Simulation ◽  
Solar Array ◽  
Stick Slip ◽  
Stick Slip Motion ◽  
Slip Motion

scholarly journals Basal ice motion and deformation at the ice-sheet margin, West Greenland

2005 ◽  
Vol 42 ◽  
pp. 67-70 ◽  
Author(s):  
David M. Chandler ◽  
Richard I. Waller ◽  
William G. Adam
Keyword(s):  
Deformation Mode ◽  
Time Intervals ◽  
Stick Slip ◽  
Active Deformation ◽  
West Greenland ◽  
Shear Structures ◽  
Basal Ice ◽  
Ice Velocity ◽  
Stick Slip Motion ◽  
Slip Motion

AbstractMeasurements of basal ice deformation at the margin of Russell Glacier, West Greenland, have provided an opportunity to gain more insight into basal processes occurring near the margin. The basal ice layer comprises a debris-rich, heterogeneous stratified facies, overlain by a comparatively debris-poor dispersed facies. Ice velocities were obtained from anchors placed in both ice facies, at three sites under 5–15 m ice depth. Mean velocities ranged from 20 to 43 m a–1, and velocity gradients indicate high shear strain rates within the basal ice. Stick–slip motion and diurnal variations were observed during measurements at short (1–5 min) time intervals. Vertical gradients in horizontal ice velocity indicate two modes of deformation: (1) viscous deformation within the stratified ice facies, and (2) shear at the interface between the two basal ice facies. Deformation mode 1 may contribute to the folding and shear structures observed in the stratified facies. Deformation mode 2 may generate the stick–slip motion and be associated with the formation of debris bands. Active deformation close to the margin suggests that structures observed within the basal ice are only partially representative of processes occurring near the bed in areas away from the glacier margin.

Experimental Exploration of Schallamach Waves and Self-Excitation in a Belt-Drive System

2018 ◽  
Author(s):  
Yingdan Wu ◽  
Michael Varenberg ◽  
Michael J. Leamy
Keyword(s):  
Angular Velocity ◽  
Dynamic Behavior ◽  
Oscillation Amplitude ◽  
Operating Conditions ◽  
Drive System ◽  
Belt Drive ◽  
Stick Slip ◽  
Stick Slip Motion ◽  
System Inertia ◽  
Slip Motion

We study the dynamic behavior of a belt-drive system to explore the effect of operating conditions and system moment of inertia on the generation of waves of detachment (i.e., Schallamach waves) at the belt-pulley interface. A self-excitation phenomenon is reported in which frictional fluctuations serve as harmonic forcing of the pulley, leading to angular velocity oscillations which grow in time. This behavior depends strongly on operating conditions (torque transmitted and pulley speed) and system inertia, and differs between the driver and driven pulleys. A larger net torque applied to the pulley generally yields more remarkable stick-slip oscillations with higher amplitude and lower frequency. Higher driving speeds accelerate the occurrence of stick-slip motion, but have little influence on the oscillation amplitude. Contrary to our expectations, the introduction of flywheels to increase system inertia amplified the frictional disturbances, and hence the pulley oscillations. This does, however, suggest a way of facilitating their study, which may be useful in follow-on research.

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