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Part III - Fully flooded results'. Reine Angew. Cambridge University Press Petrusevich A. Izv, Akad. The former has more significance but the latter may be useful in estimates of traction, Figure 4A. If the centres of curvature of the cylinders are on opposite sides of the contact point both radii will be positive, if not one will be negative.

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The determination of the approach of remote points on the solids is more complex for line contacts than point contacts. If the centres of curvature of the ellipsoids in one plane are on opposite sides then both radii in that plane will be positive, if not one will be negative. NOTE the principal radii of curvature of each contacting ellipsoids are here taken to be in the same two planes for cases where the principal planes of one solid do not coincide with those of the other see ESDU Design Item Lond, A , 1 , p Childs Department of Mechanical Engineering, University of Leeds, Leeds LS2 9JT Abstract This chapter reviews by the development of friction mechanism maps the responses of sliding surfaces to friction and wear in the absence of hydrodynamic lubrication.

It initially considers the classical views of adhesive and abrasive friction before discussing in more detail the variety of plastic contact flows that can occur, depending on surface roughness slope and interfacial adhesion. It then considers the conditions that result in elastic contact. Mechanisms of friction and wear in the different regimes of surface stressing are described.

This occurs when the lubricant film thickness becomes less than the heights of the surface roughness, perhaps because of slow or zero motion between the surfaces, too heavy a load or because of loss of fluid viscosity at high temperatures. Friction and wear rates invariably rise, sometimes with immediate catastrophic consequences. The mechanisms and magnitudes of friction and wear in the absence of fluid lubrication depend on the surfaces' mechanical properties: their elastic moduli and hardness and for ceramics also their brittle properties and the shear strength of any remaining surface films; on the surface roughness: the important quantity is the surface asperity slope; and on their chemical reactivity with the surrounding atmosphere: commonly wear occurs not by the removal of material with the composition of the bulk but by removal of surface reaction films.

The lecture will consider the influence of these on friction and wear both to form a view as to what might be minimum magnitudes of friction and wear in the absence of fluid lubrication, and to establish design requirements such as surface finish for avoiding early failures. The chapter is divided into four parts. A closer consideration is then given to the ways in which plastic contacts can flow, in order to distinguish between benign, surface smoothing or wave, flows and conditions of prow or chip formation that lead to rapid failure.

It is now recognised that run-in surface contacts are not plastic but elastic: the third section will establish the conditions for elastic contact and represent these in a friction mechanism 52 map. Finally the range of wear mechanisms that accompany the different friction mechanisms is explored. Adhesive and deformation or ploughing or abrasive friction Bearing surfaces are usually loaded so lightly that even in the absence of fluid films they touch over only a small fraction of their apparent contact area.

The interface at the real contacts can be inclined to the sliding direction. Figure 1 illustrates an artificially simple example in which the roughness of the upper surface is imagined to be a collection of wedges of constant slope 0 and the interface normal stresses p and tangential stresses s are the same on each contact and only act on the leading face of each. Both s and p contribute to the reaction against the friction force F and the normal load W.

Two special cases are particularly simple to consider. They both are in accord with Amonton's Laws that state that friction coefficient is independent of load and apparent area of contact.

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Figure 1 A sliding contact between two surfaces 53 2. Adhesive friction and junction growth. At the time that equation 2 was developed it was assumed that real areas of contact between metals would be plastically stressed. The interaction between s and p was used to explain the high sliding friction coefficients, 1. The key point was noted that the area of a plastically loaded junction would grow if a friction force were added to it. By analogy with the combined loading and shear of a block between two parallel platens, figure 2a, for which p and s can be related by the Tresca yield criterion equation 4a, p and s acting on an adhesive friction junction, figure 2b, may be assumed to be related by an equation of the form of 4b, where a and p are assumed to be constants, and k is the shear yield stress of the plastically loaded material.

Ploughing friction and geometry. In the absence of adhesion, the prediction of equation 3 for ploughing friction varies slightly with the details of the assumed shape of the contact. Figure 3 shows a cone scratching a metal flat. If the contact pressure is assumed uniform over the interface and the interface is assumed to be just the area of intersection between the indenter and the flat i.

Combined loading and shear of a a block, b a friction junction Figure 3. A cone scratching a flat surface W leads to equation 7a for the friction coefficient.

A similar calculation for a sphere ploughing a flat leads to equation 7b, where tan9 is the slope of the sphere at the edge of the contact. Adhesive and abrasive wear The adhesive and abrasive models of friction in figures 2 and 3 may be used to discuss wear 2,3. Equations 9 and 10 suggest that K has values, depending on 0, of the order 0.

Limitations of the initial concepts Equations 2 to 11 present the simplest description of friction and wear with any claim to reality. Yet as far as ploughing deformation is concerned they give no information about the flow pattern of material round the indenter, and a consideration of deformation combined with adhesive friction is avoided. It has nothing to say about the nature of interfacial rheology that controls s.

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Further by no means all metal sliding contacts are plastic: hard polished surfaces and many run-in surfaces suffer elastic or elasto-plastic deformation. Finally, as summarised in figure 4, equations 9 and 10 grossly overestimate measured wear rates 5. Further review of these topics is developed in the remainder of this lecture. The range of wear coefficients for wear modes in section 5 3.

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The surfaces can either become smoother and run-in or become rougher and fail. The purpose of this section is to establish what are the critical values of these variables and to give insight into the mechanisms of surface failure that can occur when they are exceeded, either because the as-formed surface is too rough or poorly lubricated or because the effective roughness is increased by the presence in the contract of trapped wear debris or hard particulate contamination.

Model experiments in which a metal is scratched by a hard cone or sphere 6,7 show that the metal can flow round the indentor as a wave, without any material removal, if the indentor is blunt and well lubricated. At the other extreme metal is removed as swarf or a chip. In between, initial sliding of the indentor results in displacement of a prow or wedge of metal that becomes trapped ahead of the indentor.

If that entrapment is stable further sliding occurs by wave flow round the wedge. Alternatively the wedge may be expelled from the contact. The formation process is then repeated. The conditions of slope and adhesion that lead to these flows may be studied for plane strain flows of ploughing by a wedge shaped asperity, for rigid plastic, non-workhardening metals, by means of slip-line field theory.

The results may then be compared with experiments on three-dimensional flows with real metals. Slip-line field theory may also be used to analyse junction growth more rigourously than in the discussion of the previous section. Essentials of slip-line field plasticity analysis The maximum shear stress in a plane strain flow of a non-hardening plastic material is everywhere k. Slip-line field theory provides a means of calculating the trajectories of the maximum shear stress the slip-lines and the variations of hydrostatic pressure throughout the plastic region.

The hydrostatic pressure variations are the starting point. Figure 5a shows slip lines a and P which at point 0 are inclined at to the cartesian axes x,y. Equations 14 themselves provide rules for obtaining the trajectories. Two common boundary conditions to determine the extent of the field and to give a starting point for pressure calculations are the rough surface and free surface conditions. Figure 5b shows slip lines intersecting, at an angle C, a rough surface on which the shear stress is s.

A more detailed account of the construction of slip-line fields, of the calculation of velocities in the fields and of force and velocity boundary conditions may be found in standard texts [8,9]. For the chip forming flow the sliding direction of the metal over the wedge is opposite to that of the wave flow. It may be surmised that these are the conditions that lead to prow or wedge formation.

Flowever the fields of figure 6 are not the only possible ones Surface plastic flow is highly non-unique. Further fields are shown in figure 8: more complex wave flows I , combined wave and wedge flows II , wedge flows III , combined wave and cutting flows IV and cutting flows with and without stagnant zones V and VI. Their range of validities are shown in figure 9a. These conclusions of plane strain plasticity theory are qualitatively supported by experiments on real surfaces In summary, to avoid any possibility of prow or chip formation surface finish and lubrication should satisfy equation Figure 8.

Junction growth The considerations of the previous section visually accord with abrasive conditions.