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Living Nano-Bearings Utilizing Matched Molecular Chemistry: 

An Alternative Approach to the Lubrication  Problem.
Submitted by Phil Rountree and Joe Luthern
When two surfaces rub together, progressive loss of material from the surfaces may occur. This loss of material, or wear, is accelerated by elevated temperatures and pressures such as those found in internal combustion machines, hypoid gears, transmissions, industrial machines, propulsion engines, wheel bearings, gears, turbines, cutting instruments, and other similar devices. Traditional lubricants operate by several methods. One method involves separation of moving parts by a film of viscous liquid. Under extreme operating conditions extreme pressure (EP) agents are utilized. Our unique approach is to dissolve small amounts of an electrophilic, highly polar material and a matched nucleophilic secondary highly polar material into a base oil, i.e., matched-molecular chemistry. Under catalytic action of surface interference energy, conjugate acid-base pairs are formed which have affinity for metallic surfaces. As a consequence the matched molecules are pulled into the boundary layer and form a coherent, cohesive, non-corrosive, boundary layer between working surfaces which significantly reduces friction and wear.
 
There are three main classifications involving wear. The first involves the appearance of a wear scar. Terms used to describe the scar include: pitted, spalled, scratched, polished, crazed, scuffed, fretted, and gouged. Another wear classification involves the physical mechanism that removes or causes damage to the working surfaces, terms utilized in this classification include abrasion, adhesion, oxidation, corrosion, and fatigue1. The third type of wear involves boundary and elastohydrodynamic lubrication2.
Addressing the phenomenon of adhesive wear, it is assumed that when two working surfaces make contact only a fraction of the “sea of electrons” defining the surface areas actually make contact. These contact areas will be referred to as junctions and at the junctions the two materials may form adhesive “bonds”. These bonds may be ion-dipole, dipole-dipole, induced dipole-dipole, or induced dipole-induced dipole interactions. At any rate the following is a mathematical model describing adhesive wear
The real area of contact between the working surfaces is given by:
Ar = nπd2/4 (1)
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where Ar = real surface area
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n= the number of junctions
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d = diameter of junctions
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Assuming that all junctions are plastically deformed Ar may also be given by the following relation:
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Ar = N/H (2)
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Where N = the normal force
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H = the penetration hardness of the softer of the two materials
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Combining equations (1) and (2) yields:
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N = 4N/πHd2 (3)
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The adhesive wear is influenced by the size of the contacting asperity as well as the load on the asperity. The criteria for adhesive wear may be calculated from the following model. If a circular asperity of diameter d forms a junction on a neighboring surface then the potential wear fragment is a hemispherical particle of diameter d. In order for adhesive wear to take place, the elastic energy stored in the volume of the potential fragment ,E’, must be equal to or greater than the energy associated with the new surface, Es.
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Assuming that the tip of the asperity has been plastically deformed, the stored elastic energy per unit volume is:
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E’ = σy/2E (4)
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Where = σy the yield point
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E = Young’s Modulus
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The volume of the hemispherical region is πd3/2E, the stored elastic energy in the potential fragment is:
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E’ = πd3σ2y/24E (5)
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Because two hemispherical surfaces are created when the fragment is formed and assuming that the material of the two working surfaces are the same:
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Es = πd2γ (6)
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where γ = the surface energy
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By allowing the equations (5) and (6) to be equal, one can calculate the minimum junction diameter required for the formation of an adhesive wear fragment, d’,:
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Let La = the load supported by an asperity
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Then
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La = πNd2/4 (8)
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Combining the two previous equations and making use of the following relations:
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σy = 3 x 10-3E (9)
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σy = N/3 (10)
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σy = No.333/β (11)
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where β is a constant for different classes of materials, it can be shown that the minimum asperity load for adhesive wear to take place in inversely proportional to the surface energy:
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La = 4.5 x 107β3/γ (12)
There are three general mechanisms for abrasive wear: two-body abrasion, three-body abrasion, and erosion. Filing, sanding, and grinding are all examples of two-body erosion. The equation for two and three-body abrasion wear can be derived by examining the wear created by a single abrasive grain4. The grain may be an asperity on the mating surface or a loose particle. The equation is based on the model in which a harder, conical shaped grain is pressed into a softer surface. As sliding occurs the grain produces a wear groove in the coating whose volume is the cross-sectional area of the indentation times the sliding distance.
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When traction or shear is applied to the interface between two working surfaces, let μ = the coefficient of friction and q(x) = the pressure distribution, μq(x) is traction across the contact.. For the case of a conforming contact, maximum shear stress, σmax, is approximately:
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σmax = q0(0.25 + μ2)1/2 (13)
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where q0is the maximum contact pressure. For the conforming case maximum shear stress is approximately μq0. For materials with μ > 0.3 the maximum shear stress occurs on the surface and for materials with μ < 0.3 this maximum occurs below the surface at a depth of 0.3r, where r is the radius of the apparent contact area.
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One outcome of the electrostatic attraction scenario between additive(s) and working surfaces is an increase in the traction coefficient, Ct. The coefficient of traction is given by the following formula:
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Ct = Ft/N (15)
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where:
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Ft = tangential force
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N = normal force
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When traction or shear is applied to the interface between two working surfaces, let μ = the coefficient of friction and q(x) = the pressure distribution, μq(x) is traction across the contact.. For the case of a conforming contact, maximum shear stress, σmax, is approximately:
􀂆
σmax = q0(0.25 + μ2)1/2 (13)
􀂆
where q0is the maximum contact pressure. For the conforming case maximum shear stress is approximately μq0. For materials with μ > 0.3 the maximum shear stress occurs on the surface and for materials with μ < 0.3 this maximum occurs below the surface at a depth of 0.3r, where r is the radius of the apparent contact area.
 



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