On Constitutive Relations for Friction From Thermodynamics and Dynamics

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Michael D. Bryant
Keyword(s):  
Friction Coefficient ◽  
Entropy Production ◽  
Internal Energy ◽  
Coefficient Of Friction ◽  
Slip Velocity ◽  
Constitutive Relations ◽  
Thermodynamic Quantities ◽  
Stick Slip ◽  
Friction Forces ◽  
Kinetic Coefficients

Constitutive and dynamic relations for friction coefficient are presented. A first thrust combines the laws of thermodynamics to relate heat, energy, matter, entropy, and work of forces. The equation sums multiple terms—each with a differential of a variable multiplied by a coefficient—to zero. Thermodynamic considerations suggest that two variables, internal energy and entropy production, must depend on the others. Linear independence of differentials renders equations that yield thermodynamic quantities, properties, and forces as functions of internal energy and entropy production. When applied to a tribocontrol volume, constitutive laws for normal and friction forces, and coefficient of friction are derived and specialized for static and kinetic coefficients of friction. A second thrust formulates dynamics of sliding, with friction coefficient and slip velocity as state variables. Differential equations derived via Newton's laws for velocity and the degradation entropy generation (DEG) theorem for friction coefficient model changes to the sliding interface induced by friction dissipation. The solution suggests that the transition from static to kinetic coefficient of friction with respect to slip velocity for lubricant starved sliding is a property of the motion dynamics of sliding interacting with the dynamics of change of the surface morphology. Finally, sliding with stick-slip was simulated to compare this model to others.

Hydrodynamic Model for Cold Strip Rolling

1967 ◽  
Vol 182 (1) ◽  
pp. 153-162 ◽  
Author(s):  
D. S. Bedi ◽  
M. J. Hillier
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Entropy Production ◽  
Coefficient Of Friction ◽  
Hydrodynamic Model ◽  
Reynolds Equation ◽  
Viscous Friction ◽  
Strip Rolling ◽  
Roll Pressure ◽  
Cold Strip Rolling

The theory of rolling is modified to allow calculation of a hydrodynamic film thickness and viscous friction coefficient using Reynolds equation for the lubricant. Calculations are made for the case where the fluid film covers the arc of contact. The film thickness is assumed uniform and is determined by the principle of minimum rate of entropy production. It is shown that the apparent coefficient of friction varies significantly over the arc of contact. At small reductions the roll load tends to decrease with speed of rolling, while at high reductions the load tends to increase. The point of maximum roll pressure does not coincide with the neutral plane; and under certain rolling conditions there may be no maximum in the pressure over the arc of contact.

Lateral Friction Behavior of a Thin, Tensioned Tape Wrapped Over a Grooved Roller: Experiments and Theory

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Hankang Yang ◽  
Johan B. C. Engelen ◽  
Walter Häberle ◽  
Mark A. Lantz ◽  
Sinan Müftü
Keyword(s):  
Friction Coefficient ◽  
Axial Direction ◽  
Friction Behavior ◽  
Stick Slip ◽  
Friction Forces ◽  
Lateral Dynamics ◽  
Lateral Tape Motion ◽  
Complex Interactions ◽  
Recording Tape ◽  
Effective Friction

Effects of friction forces on the lateral dynamics of a magnetic recording tape, wrapped around a grooved roller are investigated experimentally and theoretically. Tape is modeled as a viscoelastic, tensioned beam subjected to belt-wrap pressure and friction forces. Including the effects of stick and slip and velocity dependence of the friction force render the tape's equation of motion nonlinear. In the experiments, tape was wrapped under tension around a grooved roller in a customized tape path. The tape running speed along the axial direction was set to zero, thus only the lateral effects were studied. The grooved roller was attached to an actuator, which moved the roller across the tape. Tests were performed in slow and fast actuation modes. The slow mode was used to identify an effective static, or breakaway, friction coefficient. In the fast mode, the roller was actuated with a 50 Hz sinusoid. The same effective friction coefficient was deduced from the fast actuation mode tests. This test mode also revealed a periodic stick–slip phenomenon. The stick-to-slip and slip-to-stick transitions occurred when the tape vibration speed matched the roller actuation speed. Both experiments and theory show that upon slip, tape vibrates primarily at its natural frequency, and vibrations are attenuated relatively fast due to frictional and internal damping. This work also shows that an effective friction coefficient can be described that captures the complex interactions in lateral tape motion (LTM) over a grooved roller.

A linear differential formulation of friction forces for adaptive estimator algorithms

Robotica ◽  
2001 ◽  
Vol 19 (4) ◽  
pp. 407-421 ◽  
Author(s):  
C. J. Tsaprounis ◽  
N. A. Aspragathos
Keyword(s):  
Differential Equation ◽  
Friction Coefficient ◽  
Control Systems ◽  
Friction Model ◽  
Model Parameters ◽  
Coefficient Function ◽  
Stick Slip ◽  
Friction Forces ◽  
Differential Formulation ◽  
Linear Differential

In this paper a new approach for the formulation of the friction forces velocity function is introduced. The scope of this formulation is to facilitate the implementation of control laws for systems where friction forces appear. The friction model includes the exponential decay part, the Coulomb and viscous friction. The introduced formulation is based on the observation that the friction coefficient function of velocity can be presented as the solution of a linear differential equation. Due to this linearity, the parameters of the derived differential equation can be estimated easily by an adaptive system. The estimation of these parameters is equivalent to the estimation of the friction coefficient in the full range of operational velocities. This knowledge gives to the designed control systems the potential to avoid successfully the stick-slip phenomenon.A control law for one D.O.F. system, where friction appears, is designed in order to prove the applicability of the proposed formulation of the friction model in control systems. A MRAC adaptive algorithm estimates the differential friction model parameters, using the measured friction force, while a sliding controller adjusts the motion of the mechanical system. The proposed friction model can be used in any control system where friction forces have to be compensated. The linear form of the model is suitable for common adaptive estimators. Therefore, the proposed structure is suitable for robotic applications, such as assembly, deburring, etc.

Steady Sliding of Two Elastic Half-Spaces With Friction Reduction due to Interface Stick-Slip

1998 ◽  
Vol 65 (2) ◽  
pp. 470-475 ◽  
Author(s):  
G. G. Adams
Keyword(s):  
Friction Coefficient ◽  
Coefficient Of Friction ◽  
Dynamic Instability ◽  
Steady Motion ◽  
Friction Reduction ◽  
Stick Slip ◽  
Interface Friction ◽  
Stick Slip Motion ◽  
Frictional Slip ◽  
Slip Motion

The sliding of two perfectly flat elastic half-spaces with a constant interfacial coefficient of friction is investigated. Previous work has demonstrated that this configuration is dynamically unstable due to the destabilization of frictional slip waves. It was speculated that this dynamic instability could lead to stick-slip motion at the sliding interface. It is shown here that stick-slip motion at the interface can exist with a speed-independent interface coefficient of friction. Steady motion persists sufficiently far from the interface and thus gives the impression of uniform sliding. This type of stick-slip motion is due to interfacial slip waves and allows the bodies to slide with an apparent coefficient of friction which is less than the interface coefficient of friction. Furthermore it is shown that the apparent friction coefficient decreases with increasing speed even if the interface friction coefficient is speed-independent. Finally, it is shown that the presence of slip waves may make it possible for two frictional bodies to slide without a resisting shear stress and without any interface separation. No distinction is made between static and kinetic friction.

scholarly journals Effect of Stick - Slip Phenomena between Human Skin and UHMW Polyethylene

2021 ◽  
Vol 29 (3) ◽  
Author(s):  
Emad Kamil Hussein ◽  
Kussay Ahmed Subhi ◽  
Tayser Sumer Gaaz
Keyword(s):  
Friction Coefficient ◽  
Human Skin ◽  
Coefficient Of Friction ◽  
Normal Load ◽  
Static Friction ◽  
Time Interval ◽  
Dynamic Friction ◽  
Sliding Velocity ◽  
Stick Slip ◽  
The Coefficient Of Friction

The present paper investigates experimentally effect of applied load and different velocity on the coefficient of friction between two interacting surfaces (human skin and Ultra-high-molecular-weight polyethylene (UHMW- polyethylene) at static and dynamic friction. It is possible to conclude specific point based on the above practical part and frictional analysis of this investigation as the most important mechanical phenomenon was creep has been observed a stick time interval where the static friction force is significantly increased during this stroke. The analytical model for stick-slip of skin and UHMWPE is proposed. The difference between static and kinetic friction defines the amplitude of stick-slip phenomena. The contact pressure, the sliding velocity, and rigidity of system determine the stability conditions of the movement between skin and UHMWPE. Experiments were carried out by developing a device (friction measurement). Variations of friction coefficient during the time at different normal load 4.6 and 9.2 N and low sliding velocity 4, 5, 6 and 7 mm/min were experimentally investigated. The results showed that the friction coefficient varied with the normal load and low sliding velocity. At static friction, the coefficient of friction decreased when the time increases, whereas, at dynamic friction, the coefficient of friction decreased when the time increased at normal load 4.6 and 9.2 N.

scholarly journals Method for determining the coefficient of friction between fence and scraped object in equilibrium of the friction force

2018 ◽  
Vol 19 (6) ◽  
pp. 790-794
Author(s):  
Mirosław Wolski ◽  
Tomasz Piątkowski ◽  
Przemysław Osowski
Keyword(s):  
Friction Coefficient ◽  
Friction Force ◽  
Coefficient Of Friction ◽  
Conveyor Belt ◽  
Determination Method ◽  
Friction Forces ◽  
The Coefficient Of Friction

In this paper presents friction coefficient determination method between scraped object's material and fence material, determined directly on the conveyor belt, which then is introduced in the FEM program (LSDyna) for simulation of the scraping process in the automated sorting plant. In this case, the necessity of using an additional laboratory stand to determine the coefficient of friction is omitted. Due to the existing balance of friction forces, the model of the phenomenon can be treated as static, therefore the measurement is very simple and does not depend on time.

scholarly journals EXPERIMENTAL RESEARCH REGARDING THE INFLUENCE OF THE FRICTION FORCE FROM LINEAR ROLLING GUIDEWAYS ON THE POSITIONING PRECISION OF KINEMATIC FEED CHAINS USED ON CNC MACHINE TOOLS

2017 ◽  
Vol 20 (1) ◽  
Author(s):  
MARIAN FUNARU ◽  
GHEORGHE STAN
Keyword(s):  
Friction Coefficient ◽  
Machine Tools ◽  
High Speed ◽  
Negative Impact ◽  
Cnc Machine Tools ◽  
Cnc Machine ◽  
Stick Slip ◽  
Friction Forces ◽  
Positioning Precision ◽  
Stick Slip Motion

<p>Friction represents one of the major sources of disturbing forces which affect the functioning of the kinematic feed chains from CNC machine tools. Its influence reflects on the positioning precision values, having a negative impact on the table movement and leading to stationary errors, stick-slip motion and trajectory errors. The present paper presents an experimental analysis regarding the influence of the friction forces which appear in the linear rolling guideways on the positioning precision of kinematic feed chains. The rolling guideways present the advantages of a good behavior in terms of axis stability at low speeds and also for achieving high positioning speeds. Concerning the friction coefficient values, rolling and hydrostatic guideways are most suitable for the construction of high speed and high precision kinematic feed chains; in these cases, the friction coefficient has small values, which maintain quasi-constant against the feed rate. </p>

Motion of masses with asymmetric and symmetric friction. Application to fault sliding

2021 ◽  
Author(s):  
Rui Xiang Wong ◽  
Elena Pasternak ◽  
Arcady Dyskin
Keyword(s):  
Frictional Force ◽  
Normal Load ◽  
Power Spectra ◽  
Inertial Force ◽  
Friction Reduction ◽  
Relative Mass ◽  
Hydraulic Fractures ◽  
Driving Frequency ◽  
Stick Slip ◽  
Friction Forces

&lt;p&gt;This study analyses a situation when a geological fault contains a section of anisotropic gouge with inclined symmetry axes (e.g. inclined layering), Bafekrpour et al. [1]. Such gouge in a constrained environment induces, under compression, asymmetric friction (different friction forces resisting sliding in the opposite directions). The rest of the gouge produces conventional symmetric friction. A mass-spring model of the gouge with asymmetric and symmetric friction sections is proposed consisting of a mass with asymmetric friction connected through a spring to another mass with symmetric friction. These masses are set on a base subjected to vibration. A parametric analysis is performed on this system. Two distinct characteristic regimes were observed: &lt;em&gt;recurrent movement&lt;/em&gt; resembling stick-slip motion similar to predicted by [2] and &lt;em&gt;sub-frictional movement&lt;/em&gt;. Recurrent movement arises when the inertial force is sufficient to overcome frictional force of a block with symmetric friction. Sub-frictional movement occurs when the inertial force is not sufficient to overcome frictional force of an equivalent system with only symmetric friction. The sub-frictional movement is produced by the force in the connecting spring increased due to the movement of the asymmetric friction block in the direction characterised by low friction. We formulate the criterion at which sub-frictional movement occurs. The occurrence of sub-frictional depends upon the relative mass of the symmetric and asymmetric friction sections, as well as the amplitude and driving frequency of the excitation. Power spectra of the produced vibrations are determined for both regimes. The results can shed light on mechanisms of sliding over pre-existing discontinuities and their effect on seismic event generation and propagation of hydraulic fractures in the presence of discontinuities.&lt;/p&gt;&lt;p&gt;[1] Bafekrpour,&lt;strong&gt; &lt;/strong&gt;E., A.V. Dyskin, E. Pasternak, A. Molotnikov and Y. Estrin (2015), Internally architectured materials with directionally asymmetric friction. &lt;em&gt;Scientific Reports&lt;/em&gt;, 5, Article 10732.&lt;/p&gt;&lt;p&gt;[2] Pasternak, E. A.V. Dyskin and I. Karachevtseva, 2020. Oscillations in sliding with dry friction. Friction reduction by imposing synchronised normal load oscillations. &lt;em&gt;International Journal of Engineering Science&lt;/em&gt;, 154, 103313.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Acknowledgement&lt;/strong&gt;. AVD and EP acknowledge support from the Australian Research Council through project DP190103260.&lt;/p&gt;

Experimental study on the relationship between the friction coefficient and interference in locomotive axle press-fitting

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ting Wang ◽  
Hanfei Guo ◽  
Jianjun Qiao ◽  
Xiaoxue Liu ◽  
Zhixin Fan
Keyword(s):  
Friction Coefficient ◽  
Coefficient Of Friction ◽  
Friction Pair ◽  
Rolling Stock ◽  
Content Type ◽  
Press Fitting ◽  
The Press ◽  
The Coefficient Of Friction ◽  
The Relationship ◽  
Locomotive Wheels

PurposeTo address the lack of data in this field and determine the relationship between the coefficient of friction and the interference between locomotive wheels and axles, this study evaluates the theoretical relationship between the coefficient of friction and the interference under elastic deformation.Design/methodology/approachWhen using numerical analyses to study the mechanical state of the contacting components of the wheels and axle, the interference between the axle parts and the coefficient of friction between the axle parts are two important influencing factors. Currently, as the range of the coefficient of friction between the wheel and axle in interference remains unknown, it is generally considered that the coefficient of friction is only related to the materials of the friction pair; the relationship between the interference and the coefficient of friction is often neglected.FindingsA total of 520 press-fitting experiments were conducted for 130 sets of wheels and axles of the HXD2 locomotive with 4 types of interferences, in order to obtain the relationship between the coefficient of friction between the locomotive wheel and axle and the amount of interference. These results are expected to serve as a reference for selecting the coefficient of friction when designing axle structures with the rolling stock, research on the press-fitting process and evaluations of the fatigue life.Originality/valueThe study provides a basis for the selection of friction coefficient and interference amount in the design of locomotive wheels and axles.

Analysis of Beam-Like Structures With Displacement-Dependent Friction Forces: Part I — Single-Degree-of-Freedom Model

1995 ◽  
Author(s):  
Wayne E. Whiteman ◽  
Aldo A. Ferri
Keyword(s):  
Dry Friction ◽  
Damping Ratio ◽  
Strong Dependence ◽  
Time Integration ◽  
Single Mode ◽  
Stick Slip ◽  
Friction Forces ◽  
Equivalent Damping ◽  
Damping Characteristics ◽  
Parameter Values

Abstract The dynamic behavior of a beam-like structure undergoing transverse vibration and subjected to a displacement-dependent dry friction force is examined. In Part I, the beam is modeled by a single mode while Part II considers multi-mode representations. The displacement dependence in each case is caused by a ramp configuration that allows the normal force across the sliding interface to increase linearly with slip displacement. The system is studied first by using first-order harmonic balance and then by using a time integration method. The stick-slip behavior of the system is also studied. Even though the only source of damping is dry friction, the system is seen to exhibit “viscous-like” damping characteristics. A strong dependence of the equivalent natural frequency and damping ratio on the displacement amplitude is an interesting result. It is shown that for a given set of parameter values, an optimal ramp angle exists that maximizes the equivalent damping ratio. The appearance of two dynamic response solutions at certain system and forcing parameter values is also seen. Results suggest that the overall characteristics of mechanical systems may be improved by properly configuring frictional interfaces to allow normal forces to vary with displacement.

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