The Elastic Field for Spherical Hertzian Contact Including Sliding Friction for Transverse Isotropy

1992 ◽  
Vol 114 (3) ◽  
pp. 606-611 ◽  
Author(s):  
M. T. Hanson
Keyword(s):  
Coulomb Friction ◽  
Sliding Friction ◽  
Contact Region ◽  
Transverse Isotropy ◽  
Elastic Field ◽  
Hertzian Contact ◽  
Elementary Functions ◽  
Elastic Bodies ◽  
Title Problem ◽  
Equivalent Expressions

This paper gives closed-form expressions in terms of elementary functions for the title problem of spherical Hertzian contact of elastic bodies possessing transverse isotropy. Traction in the contact region is also included in the form of Coulomb friction; thus the shear stress is proportional to the contact pressure. The present expressions derived here by integration of the point force Green’s functions are simpler and easier to apply than equivalent expressions which have previously been given.

The Elastic Field for Conical Indentation Including Sliding Friction for Transverse Isotropy

1992 ◽  
Vol 59 (2S) ◽  
pp. S123-S130 ◽  
Author(s):  
M. T. Hanson
Keyword(s):  
Shear Stress ◽  
Coulomb Friction ◽  
Sliding Friction ◽  
Contact Region ◽  
Transverse Isotropy ◽  
Elastic Field ◽  
Elementary Functions ◽  
Elastic Bodies ◽  
Title Problem ◽  
Conical Indentation

This paper gives closed-form expressions in terms of elementary functions for the title problem of conical indentation of elastic bodies possessing transverse isotropy. Traction in the contact region is also included in the form of Coulomb friction; thus, the shear stress is taken proportional to the contact pressure. The present expressions are derived here by integration of the point force Green’s functions.

The Elastic Field for Spherical Hertzian Contact of Isotropic Bodies Revisited: Some Alternative Expressions

1993 ◽  
Vol 115 (2) ◽  
pp. 327-332 ◽  
Author(s):  
M. T. Hanson ◽  
T. Johnson
Keyword(s):  
Coulomb Friction ◽  
Contact Region ◽  
Complete Solution ◽  
Elastic Field ◽  
Hertzian Contact ◽  
Hertz Contact ◽  
Elementary Functions ◽  
Present Solution ◽  
Coulomb Friction Law ◽  
Isotropic Bodies

Closed-form expressions in terms of elementary functions are derived for the elastic field resulting from spherical Hertz contact of isotropic bodies. Shear traction is also included using a Coulomb friction law; thus the shear stress in the contact region is equal to the contact pressure multiplied by a friction coefficient. This paper provides alternative expressions to those recently given by Hamilton (1983) and Sackfield and Hills (1983a). Two methods are outlined for obtaining the present solution and the complete solution for displacements and stresses are given for both normal and tangential loading in terms of just two distorted length parameters. The elastic field is written in a complex notation allowing the expressions to be put in a compact form. This also allows the expressions for sliding in two directions to be written as simply as for sliding in one direction.

The Elastic Potentials for Coplanar Interaction Between an Infinitesimal Prismatic Dislocation Loop and a Circular Crack for Transverse Isotropy

1992 ◽  
Vol 59 (2S) ◽  
pp. S72-S78 ◽  
Author(s):  
M. T. Hanson
Keyword(s):  
Isotropic Material ◽  
Transverse Isotropy ◽  
Circular Crack ◽  
Transversely Isotropic ◽  
Internal Crack ◽  
Elementary Functions ◽  
Elastic Potentials ◽  
Title Problem ◽  
Dislocation Crack ◽  
In The Beginning

This paper gives a closed-form evaluation in terms of elementary functions for the title problem of coplanar dislocation—crack interaction. The two cases of an external and internal crack are considered and the potential for each is found for an isotropic material. The similarity between isotropy and transverse isotropy is discussed in the beginning sections and is used to write the corresponding potential for a transversely isotropic material from the isotropic result.

Effect of Sliding Friction on Contact Stresses for Multi-Layered Elastic Bodies With Rough Surfaces

1997 ◽  
Vol 119 (3) ◽  
pp. 476-480 ◽  
Author(s):  
K. Mao ◽  
T. Bell ◽  
Y. Sun
Keyword(s):  
Sliding Friction ◽  
Rough Surfaces ◽  
Numerical Technique ◽  
Contact Region ◽  
Rolling Contact Fatigue ◽  
Contact Fatigue ◽  
Rolling Contact ◽  
Near Surface ◽  
Elastic Bodies ◽  
Contact Fatigue Life

The stress distributions associated with frictionless and smooth surfaces in contact are rarely experienced in practice. Factors such as layers, friction, surface roughness, lubricant films, and third body particulate are known to influence the state of stress and the resulting rolling contact fatigue life. A numerical technique for evaluating the subsurface stresses arising from the two-dimensional sliding contact of two elastic bodies with real rough surfaces has been developed, where an elastic body contacts with a multi-layer surface under both normal and tangential forces. The presence of friction and asperities within the contact region causes a large, highly stress region exposed to the surface. The significance of these near-surface stresses is related to modes of surface distress leading to surface eventual failure (Mao et al., 1997).

The Elastic Field Resulting From Elliptical Hertzian Contact of Transversely Isotropic Bodies: Closed-Form Solutions for Normal and Shear Loading

1997 ◽  
Vol 64 (3) ◽  
pp. 457-465 ◽  
Author(s):  
M. T. Hanson ◽  
I. W. Puja
Keyword(s):  
Closed Form ◽  
Half Space ◽  
Elastic Field ◽  
Transversely Isotropic ◽  
Normal Pressure ◽  
Shear Loading ◽  
Potential Functions ◽  
Hertzian Contact ◽  
Elementary Functions ◽  
Shear Traction

This analysis presents the elastic field in a half-space caused by an ellipsoidal variation of normal traction on the surface. Coulomb friction is assumed and thus the shear traction on the surface is taken as a friction coefficient multiplied by the normal pressure. Hence the shear traction is also of an ellipsoidal variation. The half-space is transversely isotropic, where the planes of isotropy are parallel to the surface. A potential function method is used where the elastic field is written in three harmonic functions. The known point force potential functions are utilized to find the solution for ellipsoidal loading by quadrature. The integrals for the derivatives of the potential functions resulting from ellipsoidal loading are evaluated in terms of elementary functions and incomplete elliptic integrals of the first and second kinds. The elastic field is given in closed-form expressions for both normal and shear loading.

Motion of a Ball in a Ball Bearing

1973 ◽  
Vol 95 (1) ◽  
pp. 263-268
Author(s):  
H. Portig ◽  
H. G. Rylander
Keyword(s):  
Deformation Theory ◽  
Coulomb Friction ◽  
Ball Bearing ◽  
Digital Simulation ◽  
Equations Of Motion ◽  
Unsteady Motion ◽  
Hertzian Contact ◽  
Contact Deformation ◽  
Normal Forces ◽  
Simulation Language

A method is developed which allows the digital simulation of the unsteady motion of a single ball constrained only by two moving bearing races. Any desired motion of the races can be simulated. Normal forces acting on the ball are calculated by Hertzian contact deformation theory. If there is slippage between ball and races, Coulomb friction is assumed to occur. Solutions to the differential equations of motion were obtained on a computer with the digital simulation language MIMIC. The phenomenon of ball control as well as the behavior of the ball as it reached a controlled state from rest were observed. This analysis can produce more realistic results than methods that assume that the ball is controlled at all times, especially when the races are radially or angularly displaced with respect to each other.

Coulomb Friction, Plasticity, and Limit Loads

1954 ◽  
Vol 21 (1) ◽  
pp. 71-74
Author(s):  
D. C. Drucker
Keyword(s):  
Plastic Deformation ◽  
Coulomb Friction ◽  
Limit Theorems ◽  
Sliding Friction ◽  
Cohesionless Soil ◽  
Limit Loads ◽  
Perfectly Plastic

Abstract Additional attention is given to the somewhat subtle but extremely important difference between Coulomb friction and the apparently corresponding resistance to plastic deformation. It is shown that the limit theorems previously proved for assemblages of perfectly plastic bodies do not always apply when there is finite sliding friction. Theorems are developed which relate the limit loads with finite Coulomb friction to the extreme cases of zero friction and of complete attachment, and also to the case where the frictional interfaces are “cemented” together with a cohesionless soil.

scholarly journals Ternary Logic of Motion to Resolve Kinematic Frictional Paradoxes

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 620 ◽  
Author(s):  
Michael Nosonovsky ◽  
Alexander D. Breki
Keyword(s):  
Dry Friction ◽  
Sliding Friction ◽  
Rigid Bodies ◽  
Newtonian Mechanics ◽  
Stability Criteria ◽  
Ternary Logic ◽  
Elastic Bodies ◽  
Logic Approach ◽  
Frictional System ◽  
Painlevé Paradoxes

Paradoxes of dry friction were discovered by Painlevé in 1895 and caused a controversy on whether the Coulomb–Amontons laws of dry friction are compatible with the Newtonian mechanics of the rigid bodies. Various resolutions of the paradoxes have been suggested including the abandonment of the model of rigid bodies and modifications of the law of friction. For compliant (elastic) bodies, the Painlevé paradoxes may correspond to the friction-induced instabilities. Here we investigate another possibility to resolve the paradoxes: the introduction of the three-value logic. We interpret the three states of a frictional system as either rest-motion-paradox or as rest-stable motion-unstable motion depending on whether a rigid or compliant system is investigated. We further relate the ternary logic approach with the entropic stability criteria for a frictional system and with the study of ultraslow sliding friction (intermediate between the rest and motion or between stick and slip).

Sliding Contact Between Dissimilar Elastic Bodies

1988 ◽  
Vol 110 (4) ◽  
pp. 592-596 ◽  
Author(s):  
A. Sackfield ◽  
D. A. Hills
Keyword(s):  
Elastic Constants ◽  
Carrying Capacity ◽  
Sliding Contact ◽  
Hertzian Contact ◽  
Load Carrying Capacity ◽  
Two Dimensional ◽  
Careful Choice ◽  
Elastic Bodies ◽  
Load Carrying ◽  
Two Bodies

An analysis is presented of the stresses induced by sliding between two bodies having different elastic constants. It is assumed that the bodies are plane (i.e., two dimensional), are symmetrical with respect to a line perpendicular to the plane of contact, and are smooth and continuous. It is shown that a careful choice of profile leads to a better load carrying capacity than for a Hertzian contact, but that the severity of the stresses induced is greater than for uncoupled sliding, i.e., where the bodies have similar elastic constants.

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