scholarly journals A phase-plane analysis of localized frictional waves

2017 ◽  
Vol 473 (2203) ◽  
pp. 20160606 ◽  
Author(s):  
T. Putelat ◽  
J. H. P. Dawes ◽  
A. R. Champneys
Keyword(s):  
Travelling Waves ◽  
Ground Surface ◽  
State Diagram ◽  
Friction Model ◽  
Phase Plane Analysis ◽  
Thin Elastic Plate ◽  
Stick Slip ◽  
State Laws ◽  
Friction Law ◽  
Numerical Bifurcation

Sliding frictional interfaces at a range of length scales are observed to generate travelling waves; these are considered relevant, for example, to both earthquake ground surface movements and the performance of mechanical brakes and dampers. We propose an explanation of the origins of these waves through the study of an idealized mechanical model: a thin elastic plate subject to uniform shear stress held in frictional contact with a rigid flat surface. We construct a nonlinear wave equation for the deformation of the plate, and couple it to a spinodal rate-and-state friction law which leads to a mathematically well-posed problem that is capable of capturing many effects not accessible in a Coulomb friction model. Our model sustains a rich variety of solutions, including periodic stick–slip wave trains, isolated slip and stick pulses, and detachment and attachment fronts. Analytical and numerical bifurcation analysis is used to show how these states are organized in a two-parameter state diagram. We discuss briefly the possible physical interpretation of each of these states, and remark also that our spinodal friction law, though more complicated than other classical rate-and-state laws, is required in order to capture the full richness of wave types.

Modeling and simulation of dynamics of a planar-motion rigid body with friction and surface contact

2017 ◽  
Vol 31 (16-19) ◽  
pp. 1744021 ◽  
Author(s):  
Xiaojun Wang ◽  
Jing Lv
Keyword(s):  
Rigid Body ◽  
Frictional Contact ◽  
Lagrange Equation ◽  
Linear Complementarity ◽  
Friction Model ◽  
Contact Forces ◽  
Planar Motion ◽  
Stick Slip ◽  
Normal Contact ◽  
Friction Law

The modeling and numerical method for the dynamics of a planar-motion rigid body with frictional contact between plane surfaces were presented based on the theory of contact mechanics and the algorithm of linear complementarity problem (LCP). The Coulomb’s dry friction model is adopted as the friction law, and the normal contact forces are expressed as functions of the local deformations and their speeds in contact bodies. The dynamic equations of the rigid body are obtained by the Lagrange equation. The transition problem of stick-slip motions between contact surfaces is formulated and solved as LCP through establishing the complementary conditions of the friction law. Finally, a numerical example is presented as an example to show the application.

Modeling of Piezo-Actuated Stick-Slip Micro-Drives: An Overview

2012 ◽  
Vol 81 ◽  
pp. 39-48 ◽  
Author(s):  
Ha Xuan Nguyen ◽  
Christoph Edeler ◽  
Sergej Fatikow
Keyword(s):  
Mechanical Model ◽  
Integrated Model ◽  
Friction Model ◽  
Fundamental Importance ◽  
Future Research ◽  
Stick Slip ◽  
Research Activities ◽  
Model Combining ◽  
Friction Models

This paper gives an overview about problems of modeling of piezo-actuated stick-slip micro-drives. It has been found that existing prototypes of such devices have been investigated empirically. There is only few research dealing with the theory behind this kind of drives. By analyzing the current research activities in this field, it is believed that the model of the drive depends strongly on the friction models, but in most cases neglecting any influences of the guilding system.These analyses are of fundamental importance for an integrated model combining friction model and mechanical model offering promising possibilities for future research.

Stick-Slip Compensation of Micro-Positioning Using Elastic-Plastic Static Friction Model

2008 ◽  
Vol 47-50 ◽  
pp. 246-249
Author(s):  
Min Gyu Jang ◽  
Chul Hee Lee ◽  
Seung Bok Choi
Keyword(s):  
Static Friction ◽  
Friction Model ◽  
Smart Structure ◽  
Asperity Contact ◽  
Stick Slip ◽  
Elastic Plastic ◽  
Highly Nonlinear ◽  
Bridge Type ◽  
Structural Parts ◽  
Rough Surface Contact

In this paper, a stick-slip compensation for the micro-positioning is presented using the statistical rough surface contact model. As for the micro-positioning structure, PZT (lead(Pb) zirconia(Zr) Titanate(Ti)) actuator is used to drive the load for precise positioning with its high resolution incorporating with the PID (Proportional Integral Derivative) control algorithm. Since the stick-slip characteristics for the micro structures are highly nonlinear and complicated, it is necessary to incorporate more detailed stick-slip model for the applications involving the high precision motion control. Thus, the elastic-plastic static friction model is used for the stick-slip compensation considering the elastic-plastic asperity contact in the rough surfaces statistically. Mathematical model of the system for the positioning apparatus was derived from the dynamic behaviors of structural parts. Since the conventional piezoelectric actuator generates the short stroke, a bridge-type flexural hinge mechanism is introduced to amplify the linear motion range. Using the proposed smart structure, simulations under the representative positioning motion were conducted to demonstrate the micro-positioning under the stick-slip friction.

scholarly journals Time Delay and Feedback Control of an Inverted Pendulum With Stick Slip Friction

2007 ◽  
Author(s):  
Sue Ann Campbell ◽  
Stephanie Crawford ◽  
Kirsten Morris
Keyword(s):  
Time Delay ◽  
Basin Of Attraction ◽  
Critical Time ◽  
Viscous Friction ◽  
Experimental System ◽  
Friction Model ◽  
Stable Equilibrium Point ◽  
Feedback Controllers ◽  
Stick Slip ◽  
The Basin Of Attraction

We consider an experimental system consisting of a pendulum, which is free to rotate 360 degrees, attached to a cart which can move in one dimension. There is stick slip friction between the cart and the track on which it moves. Using two different models for this friction we design feedback controllers to stabilize the pendulum in the upright position. We show that controllers based on either friction model give better performance than one based on a simple viscous friction model. We then study the effect of time delay in this controller, by calculating the critical time delay where the system loses stability and comparing the calculated value with experimental data. Both models lead to controllers with similar robustness with respect to delay. Using numerical simulations, we show that the effective critical time delay of the experiment is much less than the calculated theoretical value because the basin of attraction of the stable equilibrium point is very small.

Analysis of Ultralong Friction Pile Based on Gradient Dependent Nonlocal Friction Model

2014 ◽  
Vol 638-640 ◽  
pp. 380-383
Author(s):  
Xiao Yan Luo ◽  
Wei Ping Liu
Keyword(s):  
Frictional Resistance ◽  
Friction Model ◽  
Gradient Theory ◽  
Friction Mechanism ◽  
New Model ◽  
Friction Law ◽  
Nonlocal Friction ◽  
Set Up ◽  
Friction Pile ◽  
Geotechnical Problems

Based on the gradient theory, the gradient dependent nonlocal friction model is established. It is a new model which can describe the nonlocal friction effect. Based on Mindlin’s solution of displacement, an elastic solution of the lateral frictional resistance for ultralong friction pile is derived. The ultralong friction pile is analyzed by using the gradient dependent nonlocal friction model. Compared with the solution to the local friction law, the results shows that nonlocal friction law is feasible and reliable. The study is helpful for understanding the friction mechanism in geotechnical problems. It is a good attempt to set up the more actual and more accurate friction model.

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.

Simulacija i odstranjivanje stick-slip efekta servosistema sprovodnog aparata hidraulične turbine

2021 ◽  
Vol 23 (1) ◽  
pp. 37-41
Author(s):  
Darko Babunski ◽  
◽  
Emil Zaev ◽  
Atanasko Tuneski ◽  
Laze Trajkovski ◽  
...  
Keyword(s):  
Hydraulic Cylinder ◽  
Friction Model ◽  
Slip Effect ◽  
Hydraulic Systems ◽  
Hydraulic Actuator ◽  
Stick Slip ◽  
Hydro Turbine ◽  
Servo Mechanism ◽  
The Mathematical Model ◽  
Slip Phenomenon

Friction is a repeatable and undesirable problem in hydraulic systems where always has to be a tendency for its removal. In this paper, the friction model is presented through which the most accurate results are achieved and the way of friction compensation, approached trough technique presented with the mathematical model of a hydraulic cylinder of a hydro turbine wicket gate controlled by a servomechanism. Mathematical modelling of a servo mechanism and hydraulic actuator, and also the simulation of hydraulic cylinder as a part of a hydro turbine wicket gate hydraulic system where the stick-slip phenomenon is present between the system components that are in contact is presented. Applied results in this paper and the theory behind them precisely demonstrate under what circumstances the stick-slip phenomenon appears in such a system. The stick-slip effect is simulated using Simulink and Hopsan software and the analysis of the results are given in this paper. Removal of the stick-slip effect is presented with the design of a cascade control implemented to control the behaviour of the system and remove the appearance of a jerking motion.

A Novel Trans-Scale Precision Positioning Stage Based on the Stick-Slip Effect

2012 ◽  
Vol 2 (2) ◽  
pp. 1-14 ◽  
Author(s):  
Bowen Zhong ◽  
Liguo Chen ◽  
Zhenhua Wang ◽  
Lining Sun
Keyword(s):  
Friction Model ◽  
Slip Effect ◽  
Precision Positioning ◽  
Stick Slip ◽  
Kinematics Model ◽  
Lugre Friction Model ◽  
Positioning Stage ◽  
Simulation Results ◽  
Relationship Of ◽  
The Relationship

This article focuses on developing a novel trans-scale precision positioning stage based on the stick-slip effect. The stick-slip effect is introduced and the rigid kinematics model of the stick-slip driving is established. The forward and return displacement equations of each step of the stick-slip driving are deduced. The relationship of return displacement and the acceleration produced by friction are obtained according to displacement equations. Combining with LuGre friction model, the flexible dynamics model of the stick-slip driving is established and simulated by using Simulink software. Simulation results show that the backward displacement will reduce with the acceleration of the slider produced by dynamic friction force, the rigid kinematics model is also verified by simulation results which are explained in further detail in the article.

A Stick-Slip Interactions Model of Soft-Solid Frictional Contacts

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Hongbiao Xiang ◽  
Mitja Trkov ◽  
Kaiyan Yu ◽  
Jingang Yi
Keyword(s):  
Network Structure ◽  
Systems Design ◽  
Friction Model ◽  
Dynamic Friction ◽  
Interaction Patterns ◽  
Contact Interactions ◽  
Solid Contact ◽  
Mechatronic Systems ◽  
Stick Slip ◽  
Frictional Contacts

Modeling of the soft-solid frictional interactions plays an important role in many robotic and mechatronic systems design. We present a new model that characterizes the two-dimensional (2D) soft-solid contact interactions. The new computational approach integrates the LuGre dynamic friction model with the beam network structure of the soft-solid contact. The LuGre dynamic friction model uses the bristle deformation to capture the friction characteristics and dynamics, while the beam network structure represents the elastic contact interactions. We also present a model simplification to facilitate analysis of model properties. The model prediction and validation results are demonstrated with the experiments. The experimental results confirm the effectiveness of the modeling development. We further use the model to compute the influence of the normal load and sliding velocity on the stick-slip interaction patterns and properties. These results explain and provide analytical foundation for the reported experiments in the literature.

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