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).

Multiple Reflow Influence over the FeCoCrAlTiCuNiMo Coating Obtained by Plasma Metallization on its Wear Resistance under Dry Friction

2021 ◽  
Vol 410 ◽  
pp. 475-481
Author(s):  
Anvar M. Kadyrmetov ◽  
Dmitri A. Popov ◽  
Yevgeny V. Snyatkov
Keyword(s):  
Wear Resistance ◽  
Dry Friction ◽  
Sliding Friction ◽  
Plasma Jet ◽  
Dry Sliding ◽  
Research Results ◽  
Open Atmosphere ◽  
Multicomponent Coating ◽  
Dry Sliding Friction

The article presents the research results of the plasma jet multiple reflow effect over the multicomponent coating FeCoCrAlTiCuNiMo, obtained by plasma metallization in an open atmosphere, on its wear resistance under dry sliding friction. The research results indirectly confirm the influence of the coating entropy over the wear resistance increasing along of the reflow number growth.

Improvement of Wear Resistance of UHMWPE by Adding Solid Lubricating Fillers

2016 ◽  
Vol 712 ◽  
pp. 155-160 ◽  
Author(s):  
Sergey V. Panin ◽  
Lyudmila А. Kornienko ◽  
Vladislav O. Alexenko ◽  
Larisa R. Ivanova
Keyword(s):  
Wear Resistance ◽  
Dry Friction ◽  
Sliding Friction ◽  
Weight Fraction ◽  
Dry Sliding ◽  
Polyethylene Matrix ◽  
Permolecular Structure ◽  
Uhmwpe Composites ◽  
Ultra High Molecular Weight ◽  
Tribotechnical Characteristics

For estimating effectiveness of adding solid fillers for composites with ultra-high molecular weight polyethylene matrix tribotechnical characteristics of UHMWPE mixture with graphite, molybdenum disulfide and polytetrafluoroethylene were investigated under dry friction, boundary lubrication and abrasion. The optimum filler weight fraction was determined in terms of increasing wear resistance. Permolecular structure and surface topography of wear tracks for UHMWPE composites with different weight fraction of the fillers was studied. The mechanisms of wear of polymeric composites “UHMWPE-graphite”, “UHMWPE-PTFE” and “UHMWPE-MoS2” under dry sliding friction and abrasive wear are discussed.

Newton, Isaac (1642–1727)

2018 ◽  
Author(s):  
William L. Harper ◽  
George E. Smith
Keyword(s):  
Natural Philosophy ◽  
Spherical Shape ◽  
Rigid Bodies ◽  
Newtonian Mechanics ◽  
Important Work ◽  
Sharp Distinction ◽  
Halley's Comet ◽  
Action At A Distance ◽  
Contact Mechanism ◽  
Mathematics And Physics

Newton is best known for having invented the calculus and formulated the theory of universal gravity – the latter in his Principia, the single most important work in the transformation of natural philosophy into modern physical science. Yet he also made major discoveries in optics, and put no less effort into alchemy and theology than into mathematics and physics. Throughout his career, Newton maintained a sharp distinction between conjectural hypotheses and experimentally established results. This distinction was central to his claim that the method by which conclusions about forces were inferred from phenomena in the Principia made it ’possible to argue more securely concerning the physical species, physical causes, and physical proportions of these forces’. The law of universal gravity that he argued for in this way nevertheless provoked strong opposition, especially from such leading figures on the Continent as Huygens and Leibniz: they protested that Newton was invoking an occult power of action-at-a-distance insofar as he was offering no contact mechanism by means of which forces of gravity could act. This opposition led him to a tighter, more emphatic presentation of his methodology in the second edition of the Principia, published twenty-six years after the first. The opposition to the theory of gravity faded during the fifty to seventy-five years after his death as it fulfilled its promise on such issues as the non-spherical shape of the earth, the precession of the equinoxes, comet trajectories (including the return of ’Halley’s Comet’ in 1758), the vagaries of lunar motion and other deviations from Keplerian motion. During this period the point mass mechanics of the Principia was extended to rigid bodies and fluids by such figures as Euler, forming what we know as ’Newtonian’ mechanics.

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.

Numerical Modeling of Friction-Induced Vibrations and Dynamic Instabilities

1994 ◽  
Vol 47 (7) ◽  
pp. 255-274 ◽  
Author(s):  
W. W. Tworzydlo ◽  
E. B. Becker ◽  
J. T. Oden
Keyword(s):  
Numerical Study ◽  
Normal Modes ◽  
Friction Model ◽  
Rigid Bodies ◽  
Stick Slip ◽  
Quantitative Correlation ◽  
Frictional System ◽  
Pin On Disk ◽  
Stick Slip Motion ◽  
Slip Motion

A numerical study of dynamic instabilities and vibrations of mechanical systems with friction is presented. Of particular interest are friction-induced vibrations, self-excited oscillations and stick-slip motion. A typical pin-on-disk apparatus is modeled as the assembly of rigid bodies with elastic connections. An extended version of the Oden-Martins friction model is used to represent properties of the interface. The mechanical model of the frictional system is the basis for numerical analysis of dynamic instabilities caused by friction and of self-excited oscillations. Coupling between rotational and normal modes is the primary mechanism of resulting self-excited oscillations. These oscillations combine with high-frequency stick-slip motion to produce a significant reduction of the apparent kinetic coefficient of friction. As a particular study model, a pin-on-disk experimental setup has been selected. A good qualitative and quantitative correlation of numerical and experimental results is observed.

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.

Mechanics in the Eighteenth Century

2017 ◽  
Author(s):  
Sandro Caparrini ◽  
Craig Fraser
Keyword(s):  
Eighteenth Century ◽  
Celestial Mechanics ◽  
Natural Philosophy ◽  
Mathematical Physics ◽  
Rigid Bodies ◽  
Mechanics Of Fluids ◽  
Elastic Bodies ◽  
Modern Period ◽  
Mathematical Investigation ◽  
Statics And Dynamics

This article focuses on mechanics in the eighteenth century. The publication in 1687 of Isaac Newton’s Mathematical Principles of Natural Philosophy has long been regarded as the event that ushered in the modern period in mathematical physics. The success and scope of the Principia heralded the arrival of mechanics as the model for the mathematical investigation of nature. This subject would be at the cutting edge of science for the next two centuries. This article first provides an overview of the fundamental principles and theorems of mechanics, including the principles of inertia and relativity, before discussing the dynamics of rigid bodies. It also considers the formulation of mechanics by Jean-Baptiste le Rond d’Alembert and Joseph-Louis Lagrange, the statics and dynamics of elastic bodies, and the mechanics of fluids. Finally, it describes major developments in celestial mechanics.

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