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.

Modeling and Simulation of a Micro-Actuator with Long-Travel

2008 ◽  
Vol 392-394 ◽  
pp. 804-809
Author(s):  
W.R. Jiang ◽  
Ze Sheng Lu
Keyword(s):  
Mathematical Model ◽  
High Resolution ◽  
Transfer Function ◽  
Friction Model ◽  
Theory Analysis ◽  
Stick Slip ◽  
Micro Actuator ◽  
Transmission Part ◽  
Speed Change ◽  
Set Up

A microactuator with long-travel and high-resolution based on the principle of tribology is presented, which stroke is up to 300mm and displacement resolution is 0.01μm. It resolves the contradiction of large-stroke and high-resolution in macro/micro drive successfully. The dynamic model of the microactuator is set up. The theory analysis on the dynamic character of the system is carried out based on Karnopp “stick-slip” friction model. The physical and mathematical model of the drive part and transmission part are set up respectively by the method of modularization. The transfer function of the system is attained. The tacking simulation is carried out based on fuzzy control with speed change integral, the result is proved that error is 0.004μm.

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.

An AFM-Based Nanomanipulation Model Describing the Atomic Two Dimensional Stick-Slip Behavior

2007 ◽  
Author(s):  
Fakhreddine Landolsi ◽  
Fathi H. Ghorbel ◽  
James B. Dabney
Keyword(s):  
Friction Model ◽  
Modular Approach ◽  
Dynamic Friction ◽  
Asperity Contact ◽  
Two Dimensional ◽  
Stick Slip ◽  
Complex Interactions ◽  
Proposed Model ◽  
Lattice Periodicity ◽  
Afm Cantilever

A new AFM-based nanomanipulation model describing the relevant physics and dynamics at the nanoscale is presented. The nanomanipulation scheme consists of integrated subsystems that are identified in a modular approach. The model subsystems define the AFM cantilever-sample dynamics, the AFM tip-sample interactions, the contact mechanics and the friction between the sample and the substrate. The coupling between these different subsystems is emphasized. The main contribution of the proposed nanomanipulation model is the use of a new 2D dynamic friction model based on a generalized bristle interpretation of one asperity contact. The efficacy of the proposed model to reproduce experimental data is demonstrated via numerical simulations. In fact, the model is shown to describe the 2D stick-slip behavior with the substrate lattice periodicity. The proposed nanomanipulation model facilitates the improvement and extension of each subsystem to further take into account the complex interactions at the nanoscale.

scholarly journals Biojutiklių, modeliuojamų dvimatėje erdvėje, kompiuterinių modelių automatizuotas sudarymas

2008 ◽  
Vol 42 (43) ◽  
pp. 108-113
Author(s):  
Karolis Petrauskas ◽  
Romas Baronas
Keyword(s):  
Mathematical Model ◽  
Dimensional Space ◽  
Industrial Applications ◽  
Two Dimensional ◽  
Model Composition ◽  
Clinical Environment ◽  
Physical Experiments ◽  
Highly Sensitive ◽  
Target Analyte

Biojutikliai yra plačiai naudojami tirti medžiagų koncentracijai tirpaluose. Viena pagrindinių biojutiklio sudedamųjų dalių yra fermentas. Fermentai yra gana brangios medžiagos, dėl to ir vykdyti eksperimentus yra brangu. Kuriant naujus biojutiklius tenka atlikti daug eksperimentų. Kad būtų sumažintas reikiamų eksperimentų skaičius, taikomas kompiuterinis biojutiklių veiksmo modeliavimas. Dažniausiai konkrečios geometrijos biojutikliui kuriamas konkretus jo kompiuterinis modelis. Šiame straipsnyje pristatoma sistema, kuri gali prisitaikyti prie konkrečios geometrijos biojutiklio. Sistema gali būti taikoma biojutikliams, kurių veiksmas aprašomas matematiniais modeliais, formuluojamais dvimatėje stačiakampėje srityje. Konkretaus biojutiklio matematinio modelio sprendinys komponuojamas parenkant konkrečius algoritmus.Computer aided model composition for biosensors modelled in two-dimensional spaceKarolis Petrauskas, Romas Baronas SummaryBiosensors are analytical devices that use biological components, usually enzymes, which catalyse the interaction with a target analyte. Biosensors are widely used in clinical, environment and industrial applications for the determination of species concentrations. In some applications of biosensors, enzymes are very expensive and only available in very limited quantity. In design of novel highly sensitive biosensors a lot of experiments are required. Computer simulation of the biosensor action is an effective way to decrease a number of physical experiments. This paper presents a system adaptive to a concrete geometry of the biosensor. The system may be applied for biosensors, the action of which can be described by a mathematical model formulated in a two dimensional space. A simulator for a concrete biosensor is generated from the detailed description of the biosensor action.eight: 18px;"> 

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.

Investigation of Stick-Slip Severity in a Coupled Axial-Torsional Drillstring Dynamics Using a Two DOF Finite Element Model

2020 ◽  
Author(s):  
Ekaterina Wiktorski ◽  
Dan Sui
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Axial Velocity ◽  
Slip Surface ◽  
Rotational Velocity ◽  
Friction Model ◽  
Drilling Process ◽  
Two Dimensional ◽  
Stick Slip ◽  
Torsional Oscillations

Abstract Drilling industry focuses nowadays on process optimization and cost reduction. Unwanted events should be predicted and avoided to increase drilling efficiency, improve safety, and save costs. Development and application of mathematical models enable us to understand the dynamics of the drilling process, learn parameter interaction and regulate system behavior. It is also a way to reduce the risk of occurrence of such events or mitigate negative outcomes. Challenges in two-dimensional modeling of drillstring vibrations include: (1) correct and precise interpretation of coupled two-dimensional motion, (2) use of sub-models, as down-hole weight on bit (WOB) model, downhole torque on bit (TOB) model and friction model, and (3) proper definition of associated boundary conditions. In this paper, we propose a two-dimensional axial-torsional model that considers these criteria. We present a new way to calculate downhole WOB, which can be used as an alternative to a constant WOB value. Dynamic boundary conditions are introduced to represent the respective phases of stick-slip. The model is formulated using the finite element method and intended for vertical wells. The main goal for developing this model is evaluation of the effect of surface rotational and axial velocities on the downhole drill bit dynamics. A dimensionless parameter, stick-slip severity, is used to represent the intensity of torsional oscillations. The developed model is based on mathematical relations and defined boundary conditions, which describe the dynamics of drillstring during stick-slip events. The model allows to study the effect of up to twelve input parameters on stick-slip severity to determine a suitable range. Results presented in this paper show that axial velocity applied from the surface may cause initiation of stick-slip, which in turn provokes axial vibrations. Increase in surface axial velocity leads to higher amplitude of downhole torsional oscillations. To mitigate stick-slip, surface rotational velocity should be increased.

Two-dimensional stick-slip motion of Coulomb friction oscillators

2015 ◽  
Vol 230 (14) ◽  
pp. 2438-2448 ◽  
Author(s):  
M Fadaee ◽  
SD Yu
Keyword(s):  
Dry Friction ◽  
Numerical Results ◽  
Mathematical Programming Problem ◽  
Two Dimensional ◽  
State Equations ◽  
Time Step ◽  
Stick Slip ◽  
Single Body ◽  
Stick Slip Motion ◽  
Slip Motion

Two-dimensional stick-slip motion of an oscillator subjected to dry friction is investigated in this paper. The equations of motion of the non-smooth system are discretized in the time domain by means of the implicit Bozzak-Newmark scheme. The system state equations in a time step are written in the incremental displacements to model the frictional constraints in accordance with Coulomb’s law. With the help of a coordinate transformation and introduction of paired non-negative and complementary variables, the non-smooth vibration problem is reduced to a mathematical programming problem for which a numerical solution can be obtained. Numerical results for a single body oscillator under a harmonic excitation are obtained using the proposed method and compared with those in the literature; excellent agreement is achieved. The proposed method is then applied to a general two-dimensional oscillator with stiffness and viscous coupling in addition to the frictional coupling. Experiments are conducted for free vibration of a single body vibration system subjected to two-dimensional dry friction. Good agreement between the measurements and numerical results obtained using the proposed scheme is observed.

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.

Improved Dynamic Friction Models for Simulation of One-Dimensional and Two-Dimensional Stick-Slip Motion

2000 ◽  
Vol 123 (4) ◽  
pp. 661-669 ◽  
Author(s):  
Fitsum A. Tariku ◽  
Robert J. Rogers
Keyword(s):  
Mechanical Systems ◽  
Friction Model ◽  
Contact Forces ◽  
Force Balance ◽  
Two Dimensional ◽  
Lumped Mass ◽  
Stick Slip ◽  
Normal Contact ◽  
One Dimensional ◽  
Friction Models

In many mechanical systems, the tendency of sliding components to intermittently stick and slip leads to undesirable performance, vibration, and control behaviors. Computer simulations of mechanical systems with friction are difficult because of the strongly nonlinear behavior of the friction force near zero sliding velocity. In this paper, two improved friction models are proposed. One model is based on the force-balance method and the other model uses a spring-damper during sticking. The models are tested on hundreds of lumped mass-spring-damper systems with time-varying excitation and normal contact forces for both one-dimensional and two-dimensional stick-slip motions on a planar surface. Piece-wise continuous analytical solutions are compared with solutions using other published force-balance and spring-damper friction models. A method has been developed to set the size of the velocity window for Karnopp’s friction model. The extensive test results show that the new force-balance algorithm gives much lower sticking velocity errors compared to the original method and that the new spring-damper algorithm exhibits no spikes at the beginning of sticking. Weibull distributions of the sticking velocity errors enable maximum errors to be estimated a priori.

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