Surface Instabilities in Linear Orthotropic Half-Spaces With a Frictional Interface

2011 ◽  
Vol 78 (4) ◽  
Author(s):  
M. A. Agwa ◽  
A. Pinto da Costa
Keyword(s):  
Boundary Conditions ◽  
Plane Strain ◽  
Coefficient Of Friction ◽  
Isotropic Case ◽  
Flutter Instability ◽  
The Coefficient Of Friction ◽  
Frictional Interface ◽  
Rigid Plane ◽  
Plane Oscillations ◽  
Plane Strain Case

This paper studies the friction induced vibrations that may develop in the neighborhood of steady sliding states of elastic orthotropic half-spaces compressed against a rigid plane moving tangentially with a prescribed speed. These vibrations may lead to flutter instability associated to a surfacelike oscillation. The system of dynamic differential equations and boundary conditions that governs the small plane oscillations of the half-space about the steady sliding state is established. The general form of the surface solutions to the plane strain case is given. The way how the coefficient of friction varies with changes in some of the system’s parameters is investigated. It is shown that for certain combinations of material data, low coefficients of friction are found for surface flutter instability (lower than in the isotropic case).

Stresses Due to Tangential and Normal Loads on an Elastic Solid With Application to Some Contact Stress Problems

1953 ◽  
Vol 20 (2) ◽  
pp. 157-166
Author(s):  
J. O. Smith ◽  
Chang Keng Liu
Keyword(s):  
Plane Strain ◽  
Coefficient Of Friction ◽  
Contact Area ◽  
Normal Load ◽  
Elastic Solid ◽  
Real Variable ◽  
The Body ◽  
Shearing Stress ◽  
Tangential Load ◽  
The Coefficient Of Friction

Abstract The results of two-dimensional approach using real variable method to Hertz’s problem of contact of elastic bodies are presented. Both normal and tangential loads are assumed to be distributed in Hertzian fashion over the area of contact. The magnitude of the intensity of the tangential load is assumed to be linearly proportional to that of the normal load when sliding motion of the body is impending. The stresses in the elastic body due to the application of these loads on its boundary are presented in closed form for both plane-stress and plane-strain cases. A numerical value of f = 1/3 is assumed for the linear proportionality (coefficient of friction) between the tangential and normal loads in order that the distribution of stresses may be illustrated. The significance of the stress distribution, across the contact area and in the body, is also discussed. It is shown that when the combination of loads considered in the paper are applied at the contact area of bodies in contact the maximum shearing stress may be at the surface instead of beneath the surface. For example, for plane strain, if the coefficient of friction is f = 1/3, the maximum shearing stress is at the surface and is 43 per cent larger than the maximum shearing stress, which would be below the surface, that occurs when the normal force acts alone. The effect of range of normal stress and of shearing stress on the plane of maximum shear and on the plane of maximum octahedral shear on failure by progressive fracture (fatigue) is discussed.

Effect of surface structure, composition and texture on friction under boundary conditions

1952 ◽  
Vol 212 (1111) ◽  
pp. 508-512
Keyword(s):  
Oxide Film ◽  
Boundary Conditions ◽  
Coefficient Of Friction ◽  
Substrate Material ◽  
Pure Aluminium ◽  
Surface Layers ◽  
The Coefficient Of Friction ◽  
The Difference ◽  
Frictional Behaviour ◽  
Effect Of Surface

The coefficient of friction of surfaces lubricated under boundary conditions may be profoundly affected by such factors as the degree of working of the substrate material, the nature of the oxide film and the degree of roughness of the surface. Experiments are described wherein the frictional behaviour of surfaces of stainless steel specimens prepared in various ways was compared. The worked surface layers in these particular experiments appear to increase the value of the coefficient of friction, but the effect of surface texture is of predominant importance. The effect of different oxide films is best illustrated by reference to pure aluminium, the surface of which has been oxidized under different environmental conditions. The constitution of the oxide film formed is modified with a consequent effect on boundary friction. When the friction of rough and smooth surfaces is compared, the difference in behaviour appears to be qualitative rather than quantitative.

Influence of Inclination Angle and Machining Direction on Friction and Transfer Layer Formation

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Pradeep L. Menezes ◽  
Kishore ◽  
Satish V. Kailas ◽  
Michael R. Lovell
Keyword(s):  
Plane Strain ◽  
Coefficient Of Friction ◽  
Inclination Angle ◽  
Sliding Contact ◽  
Steel Plates ◽  
Layer Formation ◽  
Transfer Layer ◽  
Stick Slip ◽  
The Coefficient Of Friction ◽  
Slip Phenomenon

In the present investigation, unidirectional grinding marks were created on a set of steel plates. Sliding experiments were then conducted with the prepared steel plates using Al–Mg alloy pins and an inclined pin-on-plate sliding tester. The goals of the experiments were to ascertain the influence of inclination angle and grinding mark direction on friction and transfer layer formation during sliding contact. The inclination angle of the plate was held at 0.2 deg, 0.6 deg, 1 deg, 1.4 deg, 1.8 deg, 2.2 deg, and 2.6 deg in the tests. The pins were slid both perpendicular and parallel to the grinding marks direction. The experiments were conducted under both dry and lubricated conditions on each plate in an ambient environment. Results showed that the coefficient of friction and the formation of transfer layer depend on the grinding marks direction and inclination angle of the hard surfaces. For a given inclination angle, under both dry and lubricated conditions, the coefficient of friction and transfer layer formation were found to be greater when the pins slid perpendicular to the unidirectional grinding marks than when the pins slid parallel to the grinding marks. In addition, a stick-slip phenomenon was observed under lubricated conditions at the highest inclination angle for sliding perpendicular to the grinding marks direction. This phenomenon could be attributed to the extent of plane strain conditions taking place at the asperity level during sliding.

Disturbance at a Frictional Interface Caused by a Plane Elastic Pulse

1982 ◽  
Vol 49 (2) ◽  
pp. 361-365 ◽  
Author(s):  
Maria Comninou ◽  
J. R. Barber ◽  
John Dundurs
Keyword(s):  
Closed Form ◽  
Coefficient Of Friction ◽  
Graphical Representation ◽  
Critical Value ◽  
Elastic Solids ◽  
Supersonic Speed ◽  
The Coefficient Of Friction ◽  
Frictional Interface

We consider a plane pulse striking the frictional interface between two elastic solids which are held together by compressive applied tractions and sheared. The pulse causes a disturbance involving separation or slip between the bodies, which propagates along the interface at supersonic speed. The extent of these zones is determined using a convenient graphical representation and the interface tractions are given in closed form. It is found that the results change qualitatively when the coefficient of friction exceeds a critical value.

The Full Journal Bearing

1949 ◽  
Vol 161 (1) ◽  
pp. 59-72 ◽  
Author(s):  
A. Cameron ◽  
W. L. Wood
Keyword(s):  
Boundary Conditions ◽  
Coefficient Of Friction ◽  
Journal Bearing ◽  
Complete Solution ◽  
Radial Clearance ◽  
Eccentricity Ratio ◽  
Relaxation Methods ◽  
The Coefficient Of Friction ◽  
Final Answer ◽  
Detailed Application

The basic mathematics of the full journal bearing have been known since 1904 when Sommerfeld‡ made the complete solution, for the infinite journal, of Reynolds theory of 1886. The detailed application of the theory has not been possible owing to the uncertainty in the choice of boundary conditions. In this paper the Reynolds condition that p = 0 at θ = 0 and p = ∂ p/∂θ = 0 at θ = π + α is shown to follow for the infinite bearing from a consideration of continuity of flow and, equally important, from the shaft stability condition, first put forward by Swift in 1933. It is claimed that this is the final answer to the question of correct boundary conditions. The Reynolds equation for the infinitely wide bearing was solved using these conditions. Assuming the viscosity is constant all round the bearing, the coefficient of friction-load criterion curve has the same slope as experimentally determined curves. The Mathematics Division, N.P.L., computed, by Southwell's relaxation methods (1946), the figures for finite bearings of diameter length ratios of 4, 2, and 1. The theoretical figures for eccentricity ratio-load criterion are satisfactorily compared with some of Nücker's experimental results, and the coefficient of friction, load criterion, figures explain the apparent intercept found by McKee and McKee. A diagram is given allowing the eccentricity ratio c, to be obtained from the load criterion for any bearing of diameter/length ratio from 0 to 4, and this enables the minimum film thickness, which equals (1 — c) x radial clearance, to be calculated.

Dynamic Surface Solutions in Linear Elasticity and Viscoelasticity With Frictional Boundary Conditions

1995 ◽  
Vol 117 (4) ◽  
pp. 445-451 ◽  
Author(s):  
J. A. C. Martins ◽  
J. Guimara˜es ◽  
L. O. Faria
Keyword(s):  
Boundary Conditions ◽  
Viscous Dissipation ◽  
Deformable Body ◽  
The Body ◽  
Dynamic Surface ◽  
Linear Elastic ◽  
Finite Dimensional ◽  
Rigid Plane ◽  
Short Time ◽  
Plane Oscillations

This paper presents a study on the dynamic stability of the steady frictional sliding of a linear elastic or viscoelastic half-space compressed against a rigid plane which moves with a prescribed nonvanishing tangential speed. The system of differential equations and boundary conditions that govern the small plane oscillations of the body about the steady-sliding state of deformation is established. It is shown that for large coefficient of friction and large Poisson’s ratio the steady-sliding of the elastic body is dynamically unstable. This instability manifests itself by growing surface oscillations which necessarily propagate from front to rear and which in a short time lead to situations of loss of contact or stick. Similarly to what has been found with various finite dimensional frictional systems, these flutter type surface instabilities result from the intrinsic nonsymmetry of dry friction contact laws. The effect of viscous dissipation within the deformable body is also assessed: when viscous dissipation is present larger coefficients of friction are required for the occurrence of surface solutions propagating and growing from front to rear.

scholarly journals Effects of velocity-slip and viscosity variation on journal bearings

2004 ◽  
Vol 46 (1) ◽  
pp. 143-155 ◽  
Author(s):  
R. Raghavendra Rao ◽  
K. R. Prasad
Keyword(s):  
Boundary Conditions ◽  
Coefficient Of Friction ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Velocity Slip ◽  
Journal Bearings ◽  
Viscous Layer ◽  
The Coefficient Of Friction ◽  
Viscosity Variation

AbstractA generalised form of the Reynolds equation for two symmetrical surfaces is derived by considering slip at the bearing surfaces. This equation is then used to study the effects of velocity-slip for the lubrication of journal bearings using half-Sommerfeld boundary conditions. Expressions for pressure and load capacity and the coefficient of friction are obtained and numerically analysed for various parameters. It is found that the load capacity decreases with slip. This is unfavourable for lubrication. The coefficient of friction decreases with a high viscous layer and increases with slip.

Experimental Investigation of aluminum doping crumb rubber/epoxy composite in reciprocating motion

2015 ◽  
Vol 3 ◽  
pp. 1
Author(s):  
Goutam Chandra Karar ◽  
Nipu Modak
Keyword(s):  
Experimental Investigation ◽  
Coefficient Of Friction ◽  
Epoxy Composite ◽  
Normal Load ◽  
Crumb Rubber ◽  
The Other ◽  
Reciprocating Motion ◽  
Molding Process ◽  
Friction Tester ◽  
The Coefficient Of Friction

The experimental investigation of reciprocating motion between the aluminum doped crumb rubber /epoxy composite and the steel ball has been carried out under Reciprocating Friction Tester, TR-282 to study the wear and coefficient of frictions using different normal loads (0.4Kg, 0.7Kgand1Kg), differentfrequencies (10Hz, 25Hz and 40Hz).The wear is a function of normal load, reciprocating frequency, reciprocating duration and the composition of the material. The percentage of aluminum presents in the composite changesbut the other components remain the same.The four types of composites are fabricated by compression molding process having 0%, 10%, 20% and 30% Al. The effect of different parameters such as normal load, reciprocating frequency and percentage of aluminum has been studied. It is observed that the wear and coefficient of friction is influenced by the parameters. The tendency of wear goes on decreasing with the increase of normal load and it is minimum for a composite having 10%aluminum at a normal load of 0.7Kg and then goes on increasing at higher loads for all types of composite due to the adhesive nature of the composite. The coefficient of friction goes on decreasing with increasing normal loads due to the formation of thin film as an effect of heat generation with normal load.

scholarly journals Holographic anisotropic model for light quarks with confinement-deconfinement phase transition

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Irina Ya. Aref’eva ◽  
Kristina Rannu ◽  
Pavel Slepov
Keyword(s):  
Phase Transition ◽  
Boundary Conditions ◽  
Chemical Potential ◽  
String Tension ◽  
Isotropic Case ◽  
Holographic Model ◽  
Anisotropic Model ◽  
Dilaton Field ◽  
Cornell Potential ◽  
Qcd Phase Diagram

Abstract We present a five-dimensional anisotropic holographic model for light quarks supported by Einstein-dilaton-two-Maxwell action. This model generalizing isotropic holographic model with light quarks is characterized by a Van der Waals-like phase transition between small and large black holes. We compare the location of the phase transition for Wilson loops with the positions of the phase transition related to the background instability and describe the QCD phase diagram in the thermodynamic plane — temperature T and chemical potential μ. The Cornell potential behavior in this anisotropic model is also studied. The asymptotics of the Cornell potential at large distances strongly depend on the parameter of anisotropy and orientation. There is also a nontrivial dependence of the Cornell potential on the boundary conditions of the dilaton field and parameter of anisotropy. With the help of the boundary conditions for the dilaton field one fits the results of the lattice calculations for the string tension as a function of temperature in isotropic case and then generalize to the anisotropic one.

Sign in / Sign up

Export Citation Format

Share Document