Modelling and Analysis of Frictional Phenomena in Dynamical Systems

2001 ◽  
Author(s):  
Roman Bogacz ◽  
Boguslaw Ryczek
Keyword(s):  
Computer Simulation ◽  
Dynamical Systems ◽  
Dry Friction ◽  
Friction Model ◽  
Harmonic Vibration ◽  
Stick Slip ◽  
Kinematic Excitation ◽  
Vibrating System ◽  
Viscoelastic Element ◽  
Excitation Conditions

Abstract The paper deals with investigation of a self-excited vibrating system with dry friction. The system is composed of a mass connected by viscoelastic element with the referring frame and interacting with a moving belt by means of dry friction. An experimentally identified, multi-parametric dry friction model for the pair composed of soft and hard elements like steel-polyester pair, describing both the case of stick-slip and quasi-harmonic vibration, has been applied. Additionally, the system is influenced by external, two-frequency kinematic excitation. The results of computer simulation for different excitation conditions is submitted in the present paper.

scholarly journals Cluster synchronization of dry friction oscillators

2018 ◽  
Vol 148 ◽  
pp. 10004
Author(s):  
Michał Marszal ◽  
Andrzej Stefański
Keyword(s):  
Dry Friction ◽  
Numerical Study ◽  
Excitation Frequency ◽  
Friction Model ◽  
Cluster Synchronization ◽  
Stick Slip ◽  
Closed Ring ◽  
Mass Spring ◽  
Friction Oscillators ◽  
Two Parameter

Synchronization is a well known phenomenon in non-linear dynamics and is treated as correlation in time of at least two different processes. In scope of this article, we focus on complete and cluster synchronization in the systems of coupled dry friction oscillators, coupled by linear springs. The building block of the system is the classic stick-slip oscillator, which consists of mass, spring and belt-mass friction interface. The Stribeck friction itself is modelled using Stribeck friction model with exponential non-linearity. The oscillators in the systems are connected in nearest neighbour fashion, both in open and closed ring topology. We perform a numerical study of the properties of the dynamics of the systems in question, in two-parameter space (coupling coefficient vs. angular excitation frequency) and explore the possible configurations of cluster synchronization.

Discontinuous Bifurcations in Stick-Slip Mechanical Systems

2001 ◽  
Author(s):  
Ugo Galvanetto
Keyword(s):  
Dynamical Systems ◽  
Dry Friction ◽  
Scientific Literature ◽  
Mechanical Systems ◽  
Stick Slip ◽  
Floquet Multipliers ◽  
Discontinuous Bifurcations ◽  
Active Research ◽  
Grazing Bifurcations

Abstract Non-smooth dynamical systems exhibit continuous and discontinuous bifurcations. Continuous bifurcations are well understood and described in many textbooks, whereas discontinuous bifurcations are still the object of active research. Grazing bifurcations, C-bifurcations and other types of bifurcations characterised by jumps of the relevant Floquet multipliers have been described in the scientific literature. This paper deals with two discontinuous bifurcations found in mechanical systems affected by dry friction.

scholarly journals Mathematical model for two-dimensional dry friction modified by dither

2016 ◽  
Vol 22 (10) ◽  
pp. 1936-1949 ◽  
Author(s):  
Adam Wijata ◽  
Jan Awrejcewicz ◽  
Jan Matej ◽  
Michał Makowski
Keyword(s):  
Mathematical Model ◽  
Dry Friction ◽  
Slip Velocity ◽  
Dimensional Space ◽  
Friction Model ◽  
Polar Coordinates ◽  
Two Dimensional ◽  
Friction Anisotropy ◽  
Stick Slip ◽  
Integrator Model

A new dynamic two-dimensional friction model is developed that is based on the bristle theory. Actually, it is the Reset Integrator Model converted into a two-dimensional space. Usually, two-dimensional friction models are in fact one-dimensional models that are rotated into a slip velocity direction. However, this common approach cannot be applied to the bristle model. That is why the idea of a two-dimensional bristle is presented. The bristle’s deformation is described using polar coordinates. The carried-out numerical simulation of a planar oscillator has proved that the new model correctly captures the mechanism of smoothing dry friction by dither applied in both a perpendicular and co-linear way regarding body velocity. Furthermore, the introduced mathematical model captures two-dimensional stick-slip behaviour. Cartesian slip velocity components are the only inputs to the model. In addition, our proposed model allows one to describe friction anisotropy using bristle parameters. The paper contains the results of an experimental verification of the new friction model, conducted with a special laboratory rig employed to investigate a two-dimensional motion in the presence of dither as well as to validate our numerical results.

Nonlinear dynamics of mechanical system with external excitation

Open Physics ◽  
2005 ◽  
Vol 3 (1) ◽  
Author(s):  
Bogusław Ryczek
Keyword(s):  
Nonlinear Dynamics ◽  
Computer Simulation ◽  
Mechanical System ◽  
Dry Friction ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Friction Model ◽  
Lumped Mass ◽  
External Excitation ◽  
Transient Motion

AbstractThis paper attends to the problem of vibration of a self-excited mechanical system with a relatively complicated, history dependent dry friction model. The experimentally identified friction model allows description of various cases of stationary and transient motion. The system is composed of a lumped mass that interacts with a belt by means of dry friction. The system is additionally subjected to an external harmonic excitation through elastic element. The main objective of the experimental research has been focused on the analysis of the system behaviour for various values of the excitation frequency. This paper includes also computer simulation of the vibration of the considered system and comparison between the results of experimental and theoretical analysis. The comparison enables the assumed friction model for steel-polyester pair to be verified. It was another goal of the investigations.

Wavelet Analysis of Stick-Slip in an Oscillator With Dry Friction

1995 ◽  
Author(s):  
J. W. Liang ◽  
B. F. Feeny
Keyword(s):  
Wavelet Transform ◽  
Dry Friction ◽  
Low Frequency ◽  
Friction Model ◽  
Contour Plot ◽  
Dynamical Response ◽  
Friction Behavior ◽  
Stick Slip ◽  
Time Frequency ◽  
Coulomb Friction Model

Abstract The dynamic behavior of the transition between slipping and sticking motions of a mass-spring system with dry friction is studied numerically and experimentally. Three mathematical models of dry friction are incorporated in the forced oscillator’s equation of motion. The wavelet transform is used to analyze response signals for both high and low frequency contents. For the simulated dynamical response, the wavelet transform can efficiently depict the transition characteristics in the time/frequency domain. The signatures observed in wavelet contour plot are compared to experimental results to evaluate the mathematical friction models. The wavelet transform can also be used to detect the dynamics of the sensor. The low-frequency experimental friction behavior is somewhat like the Coulomb friction model and its smooth version.

scholarly journals A study on the vibration dissipation mechanism of the rotating blade with dovetail joint

2021 ◽  
pp. 146134842098533
Author(s):  
Chaofeng Li ◽  
Zengchuang Shen ◽  
Zilin Chen ◽  
Houxin She
Keyword(s):  
Dry Friction ◽  
Vibration Reduction ◽  
Friction Model ◽  
Rotating Speed ◽  
System Parameters ◽  
Tangential Stiffness ◽  
Damping Characteristics ◽  
Rotating Blade ◽  
Spatial Beam ◽  
Dissipation Mechanism

The vibration dissipation mechanism of the rotating blade with a dovetail joint is studied in this paper. Dry friction damping plays an indispensable role in the direction of vibration reduction. The vibration level is reduced by consuming the total energy of the turbine blade with the dry friction device on the blade-root in the paper. The mechanism of the vibration reduction is revealed by the variation of the friction force and the energy dissipation ratio of dry friction. In this paper, the flexible blade with a dovetail interface feature is discretized by using the spatial beam element based on the finite element theory. Then the classical Coulomb-spring friction model is introduced to obtain the dry friction model on the contact interfaces of the tenon-mortise structure. What is more, the effects of the system parameters (such as the rotating speed, the friction coefficient, the installation angle of the tenon) and the excitation level on blade damping characteristics are discussed, respectively. The results show that the variation of the system parameters leads to a significant change of damping characteristics of the blade. The variation of the tangential stiffness and the position of the external excitation will affect the nonlinear characteristics and vibration damping characteristics.

scholarly journals Asymmetric and chaotic responses of dry friction oscillators with different static and kinetic coefficients of friction

Meccanica ◽  
2021 ◽  
Author(s):  
Gábor Csernák ◽  
Gábor Licskó
Keyword(s):  
Dry Friction ◽  
Continuation Method ◽  
Friction Model ◽  
Lugre Friction Model ◽  
Kinetic Coefficients ◽  
Friction Oscillator ◽  
Lugre Friction ◽  
Friction Parameters ◽  
Two Parameter ◽  
Parameter Bifurcation

AbstractThe responses of a simple harmonically excited dry friction oscillator are analysed in the case when the coefficients of static and kinetic coefficients of friction are different. One- and two-parameter bifurcation curves are determined at suitable parameters by continuation method and the largest Lyapunov exponents of the obtained solutions are estimated. It is shown that chaotic solutions can occur in broad parameter domains—even at realistic friction parameters—that are tightly enclosed by well-defined two-parameter bifurcation curves. The performed analysis also reveals that chaotic trajectories are bifurcating from special asymmetric solutions. To check the robustness of the qualitative results, characteristic bifurcation branches of two slightly modified oscillators are also determined: one with a higher harmonic in the excitation, and another one where Coulomb friction is exchanged by a corresponding LuGre friction model. The qualitative agreement of the diagrams supports the validity of the results.

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.

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