Effect of Sliding Friction on Contact Stresses in a Rectangle Compressed by Rigid Planes

1975 ◽  
Vol 42 (3) ◽  
pp. 656-662 ◽  
Author(s):  
S. N. Prasad ◽  
S. Dasgupta
Keyword(s):  
Aspect Ratio ◽  
Plane Strain ◽  
Integral Equations ◽  
Coefficient Of Friction ◽  
Contact Area ◽  
Sliding Friction ◽  
Practical Interest ◽  
Slip Zone ◽  
Surface Displacements ◽  
Frictional Coefficients

The plane-strain compression of an elastic rectangle by rigid, rough planes with finite coefficient of friction between the surfaces is considered. The contact area is divided into an inner adhesive region in which the surface displacements are known, surrounded by regions in which the friction is limiting and the displacement parallel to the interface is not known. The remaining set of parallel edges of the rectangle is free from tractions. The problem is formulated in terms of Papkovich-Fadle eigenfunctions which lead to the solution of a set of two integral equations of the second kind. Solution of the integral equations which satisfies the finiteness of stresses at the point which separates the adhesive from the slip zone, determines the extent of adhesion. This is found to be independent of the magnitude of load, but depends on the values of frictional coefficients, Poisson’s ratio and the aspect ratio. Numerical results of the quantities of practical interest are reported.

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.

scholarly journals Limiting shape of profile due to dual-mode fretting wear in contact with an elastomer

2015 ◽  
Vol 230 (9) ◽  
pp. 1417-1423 ◽  
Author(s):  
Xinyu Mao ◽  
Wei Liu ◽  
Yuanzhi Ni ◽  
Valentin L Popov
Keyword(s):  
Coefficient Of Friction ◽  
Contact Area ◽  
Constant Coefficient ◽  
Analytic Solutions ◽  
Slip Zone ◽  
Fretting Wear ◽  
Contact Interface ◽  
Dual Mode ◽  
Elastic Bodies ◽  
Initial Forms

We consider fretting wear due to superimposed normal and tangential oscillations of two contacting bodies, one of which is an elastomer with a linear rheology. Similarly to the contact of elastic bodies, at small oscillation amplitudes, the wear occurs only in a circular slip zone at the border of the contact area and the wear profile tends to a limiting form, in which no further wear occurs. It is shown that under assumption of a constant coefficient of friction at the contact interface, the limiting form of the wear profile does depend neither on the particular wear criterion nor on the rheology of the elastomer and can be calculated analytically in a general form. The general calculation procedure and explicit analytic solutions for two initial forms, parabolic and conical, are presented for various combinations of frequencies and phases of normal and tangential oscillations as well as for various linear rheologies of the elastomer.

Contact Mechanics of Soft Layer Artificial Hip Joints: Part 2: Application to Joint Design

1994 ◽  
Vol 208 (4) ◽  
pp. 206-215 ◽  
Author(s):  
J Q Yao ◽  
T V Parry ◽  
A Unsworth ◽  
J L Cunningham
Keyword(s):  
Shear Stress ◽  
Aspect Ratio ◽  
Coefficient Of Friction ◽  
Hip Joint ◽  
Contact Area ◽  
Hip Joints ◽  
Soft Layer ◽  
Physiological Loading ◽  
Artificial Hip ◽  
Artificial Hip Joints

In this paper, the general solutions previously obtained for the contact mechanics of a soft layer artificial hip joint have been applied to the design of such joints. In particular, simple power-law design formulae have been generated for the prediction of the contact radius and the maximum Tresca shear stress within the elastomeric layer, when the aspect ratio varied from 1 to 20 (which covered the entire range of the aspect ratio for soft layer artificial hip joints). The effects of the layer thickness, Young's modulus of the layer and the equivalent radius of the joint upon the contact area and the maximum Tresca shear stress have all been examined for physiological loading conditions which would be experienced by hip joint prostheses in the body. Furthermore, the shear strain field was calculated so that the level of strain expected for such joints under physiological loading conditions can be estimated. With these data, relevant fatigue tests can be devised to assess the long-term performance of any particular design of soft layer hip joint. Finally, the effect of the friction between articular surfaces upon the stress field within soft layers has been examined using a newly developed asymptotic analytical theory. It was shown that, for a low coefficient of friction, the maximum Tresca shear stress occurred at layer-substrate bonding interface. With an increase in the coefficient of friction, however, the maximum Tresca shear stress increased its magnitude and moved towards the centre of the contact area along the articular surface.

An Analytical Thermodynamic Approach to Friction of Rubber on Ice

2012 ◽  
Vol 40 (2) ◽  
pp. 124-150
Author(s):  
Klaus Wiese ◽  
Thiemo M. Kessel ◽  
Reinhard Mundl ◽  
Burkhard Wies
Keyword(s):  
Coefficient Of Friction ◽  
Liquid Layer ◽  
Contact Area ◽  
Leading Edge ◽  
Viscous Friction ◽  
Analytical Approximation ◽  
Real Contact Area ◽  
Length Scales ◽  
Real Contact ◽  
Ice Surface

ABSTRACT The presented investigation is motivated by the need for performance improvement in winter tires, based on the idea of innovative “functional” surfaces. Current tread design features focus on macroscopic length scales. The potential of microscopic surface effects for friction on wintery roads has not been considered extensively yet. We limit our considerations to length scales for which rubber is rough, in contrast to a perfectly smooth ice surface. Therefore we assume that the only source of frictional forces is the viscosity of a sheared intermediate thin liquid layer of melted ice. Rubber hysteresis and adhesion effects are considered to be negligible. The height of the liquid layer is driven by an equilibrium between the heat built up by viscous friction, energy consumption for phase transition between ice and water, and heat flow into the cold underlying ice. In addition, the microscopic “squeeze-out” phenomena of melted water resulting from rubber asperities are also taken into consideration. The size and microscopic real contact area of these asperities are derived from roughness parameters of the free rubber surface using Greenwood-Williamson contact theory and compared with the measured real contact area. The derived one-dimensional differential equation for the height of an averaged liquid layer is solved for stationary sliding by a piecewise analytical approximation. The frictional shear forces are deduced and integrated over the whole macroscopic contact area to result in a global coefficient of friction. The boundary condition at the leading edge of the contact area is prescribed by the height of a “quasi-liquid layer,” which already exists on the “free” ice surface. It turns out that this approach meets the measured coefficient of friction in the laboratory. More precisely, the calculated dependencies of the friction coefficient on ice temperature, sliding speed, and contact pressure are confirmed by measurements of a simple rubber block sample on artificial ice in the laboratory.

scholarly journals Estimation of real contact area during sliding friction from interface temperature

AIP Advances ◽  
2016 ◽  
Vol 6 (6) ◽  
pp. 065227
Author(s):  
Sung Keun Chey ◽  
Pengyi Tian ◽  
Yu Tian
Keyword(s):  
Contact Area ◽  
Sliding Friction ◽  
Real Contact Area ◽  
Interface Temperature ◽  
Real Contact

Parameter Study of Offset Press Cylinder Based on Sliding Friction

2010 ◽  
Vol 174 ◽  
pp. 299-302 ◽  
Author(s):  
Hai Yan Zhang ◽  
He Ping Hou ◽  
Jun Feng Si ◽  
Xiao Yu Chen
Keyword(s):  
Contact Area ◽  
Sliding Friction ◽  
Accurate Determination ◽  
Rolling Process ◽  
Elastic Cylinder ◽  
Parameter Study ◽  
Cylinder Radius ◽  
Printing Quality ◽  
Dot Gain

In the contact area of offset, a relative slide occurs between the surface of plate cylinder and blanket cylinder, which changes the print image and influences the printing quality. The relative slide in the cylinders’ rolling process is investigated, and the determination rule of cylinders’ geometric parameters of offset press is proposed. The results show that the relative slide is minimization under the condition that the compression of elastic cylinder radius is 0.2 times bigger than that of rigid cylinder radius, and the deformation of print image and dot gain both are minimization. The results provide theoretical direction for accurate determination of cylinder radius of offset press.

scholarly journals Solid Lubrication by Multiwalled Carbon Nanotubes in Air and in Vacuum for Space and Aeronautics Applications

2005 ◽  
Author(s):  
K. Miyoshi ◽  
K. W. Street ◽  
R. L. Vander Wal ◽  
R. Andrews ◽  
David Jacques ◽  
...  
Keyword(s):  
Carbon Nanotubes ◽  
Multiwalled Carbon Nanotubes ◽  
Coefficient Of Friction ◽  
Sliding Friction ◽  
Solid Lubrication ◽  
Multiwalled Carbon ◽  
Solid Lubrication Friction ◽  
The Coefficient Of Friction ◽  
Dry Conditions ◽  
Steel Balls

To evaluate recently developed aligned multiwalled carbon nanotubes (MWNTs) and dispersed MWNTs for solid lubrication applications, unidirectional sliding friction experiments were conducted with 440C stainless steel balls and hemispherical alumina-yttria stabilized zirconia pins in sliding contact with the MWNTs deposited on quartz disks in air and in vacuum. The results indicate that MWNTs have superior solid lubrication friction properties and endurance lives in air and vacuum under dry conditions. The coefficient of friction of the dispersed MWNTs is close to 0.05 and 0.009 in air and in vacuum, respectively, showing good dry lubricating ability. The wear life of MWNTs exceeds 1 million passes in both air and vacuum showing good durability. In general, the low coefficient of friction can be attributed to the combination of the transferred, agglomerated patches of MWNTs on the counterpart ball or pin surfaces and the presence of tubular MWNTs at interfaces.

Influence of Third Element of TiNi Alloy on Tribological Behavior in Dry and Wet Conditions for Orthodontic Applications

2019 ◽  
Vol 803 ◽  
pp. 167-171
Author(s):  
Aphinan Phukaoluan ◽  
Anak Khantachawana ◽  
Pongpan Kaewtatip ◽  
Surachai Dechkunakorn
Keyword(s):  
Surface Roughness ◽  
Surface Area ◽  
Coefficient Of Friction ◽  
Sliding Friction ◽  
Tribological Behavior ◽  
Artificial Saliva ◽  
Tini Alloy ◽  
Oral Temperature ◽  
Wet Condition ◽  
Dry And Wet Conditions

The tribological behavior of Ti49.4Ni50.6, Ti49Ni46Cu5 and Ti50Ni47Co3 (at%) alloy in dry and wet conditions was studied. The alloy was prepared in a Vacuum Arc Re-melting (VAR), homogenized at 800°C for 3600 s and quenched in water. The phase transformation temperatures were measured by differential scanning calorimetry. Before a tribology test, it is necessary to determine surface roughness, because high surface roughness affects friction. The hardness behavior, based on the load over residual indent area, was determined by a Vickers hardness tester. The sliding friction tests were performed using a ball-on-disk tribometer in dry condition at room temperature and wet condition in artificial saliva (pH 5.35) at 37°C (Oral temperature). The results showed that transformation temperature (Af) lowered oral temperature (37°C), this was mainly attributed to the superelastic properties that can be taken into orthodontic applications. The studies showed significant influences in dry condition of coefficient of friction. Caused by the force between the ball and the disk, contact pressure of surface area effect in wear occurred. The debris could not be removed from the surface area tested. TiNiCu and TiNiCo generated significantly lower average coefficient of friction when tested under dry condition, which may have been due to the addition of Cu and Co. Wet condition decreased coefficient of friction more than dry condition, owing to the lubricating effects of artificial saliva.

scholarly journals Anisotropic Vibration Tactile Model and Human Factor Analysis for a Piezoelectric Tactile Feedback Device

Micromachines ◽  
2019 ◽  
Vol 10 (7) ◽  
pp. 448 ◽  
Author(s):  
Jichun Xing ◽  
Huajun Li ◽  
Dechun Liu
Keyword(s):  
Friction Coefficient ◽  
Coefficient Of Friction ◽  
Ciliary Body ◽  
Human Factor ◽  
Sliding Friction ◽  
Excitation Frequency ◽  
Tactile Feedback ◽  
Body Structure ◽  
Full Coverage ◽  
The Coefficient Of Friction

Tactile feedback technology has important development prospects in interactive technology. In order to enrich the tactile sense of haptic devices under simple control, a piezoelectric haptic feedback device is proposed. The piezoelectric tactile feedback device can realize tactile changes in different excitation voltage amplitudes, different excitation frequencies, and different directions through the ciliary body structure. The principle of the anisotropic vibration of the ciliary body structure was analyzed here, and a tactile model was established. The equivalent friction coefficient under full-coverage and local-coverage of the skin of the touch beam was deduced and solved. The effect of system parameters on the friction coefficient was analyzed. The results showed that in the full-coverage, the tactile effect is mainly affected by the proportion of the same directional ciliary bodies and the excitation frequency. The larger the proportion of the same direction ciliary body is, the smaller the coefficient of friction is. The larger the excitation frequency is, the greater the coefficient of friction is. In the local-coverage, the tactile effect is mainly affected by the touch position and voltage amplitude. When changing the touch pressure, it has a certain effect on the change of touch, but it is relatively weak. The experiment on the sliding friction of a cantilever touch beam and the experiment of human factor were conducted. The experimental results of the sliding friction experiment are basically consistent with the theoretical calculations. In the human factor experiment, the effects of haptic regulation are mainly affected by voltage or structure of the ciliary bodies.

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