The Piezo-Viscous Fluid, Rigid Solid Regime of Lubrication

Abstract

A general analysis of the lubrication of rigid-ellipsoidal solids by a piezo-viscous ,fluid is reported. S o h / ions based upon the Reynolds cavil d o n boundary condition are presented and details are given of the resulting pressure distrihutions and.film thickness prediclions.Four distinct forms qf the Juid film lubrication of a general curved solid near a plane have previously been noted and described as:Solutions already evist for the $rst three forms of lubrication for conjunctions formed between solids having curvatures in two principal directions, but the rigid-cariable viscosity regime has not previously been unalysed wi/hin the same general set of conditions.The results not only enable the j l m thickness between curved solids in nominal point contact to he predicted with reasonable confidence, hut they indicate quite clearly the dominant ph a1 effects guorrning the hydrodynamic performance of such conjunctions. NOTATION semi-axes of an ellipsoidal solid near dimensionless elasticity parameter for a plane line contact r / w 2 \ 1 / 2 w l dimensionless elasticitv uarameter for point contacts dimensionless viscosity parameter for dimensionless viscosity parameter for point contacts a (~' )~ j= = G u ( ; ) 3 1 film thickness minimum film thickness ellipticitv ratio for Hertzian contact zone pressure 1 reduced pressure principal radii of curvature of solid A in vicinity of closest approach principal radii of curvature of solid B in vicinity of closest approach entraining velocity [(uA + us)/2]surface velocities of solids A and B load per unit length on line contact load applied to point contact coordinates in plane of lubricating film (the x-axis represents the direction of motion). The M S was

Minimum Film Thicknesses in Lubricated Point Contacts Operating in the Elastic Piezoviscous Regime

“…The value of the coefficient D in equation (15) becomes increasingly large as a is increased and, well inside the elastic piezoviscous regime, dominates the pressure distribution. Under these conditions, P will be large inside the contact and the value of Q there will be close to 1.…”

“…The second is that the end region can be approximated by a short segment of a circle. The third is that the coefficient D in equations (15) is large. If the non-dimensional groups in equations (13) are examined, it may be seen that the first two conditions are satisfied if Z (Rk)' is sufficiently large.…”

Piezoviscous Effects in Nonconformal Contacts Lubricated Hydrodynamically

“…The more recent formula from the numerical solution by Dowson et al (1983) 1s (38) Figure 10 compares the minimum film thickness as obtained from Eqs. (37) and (38) with the present result for W = 0.6xlO" 7 or 0.9xlO~7 and a = 8 or 16.…”

“…In the p1ezov1scous-r1g1d regime of lubrication Marko and Clegg (1979) proposed a formula obtained by means of curve fitting Dowson and Whltaker's (1965) results for line contacts. For point contacts Hamrock and Dowson 4 (1978) proposed as an Interim measure that Blok's (1952) solution for line contacts be adjusted by applying the same "side-leakage factor" as that derived for the p1ezov1scous-elast1c condition.…”

A Novel Approach to the Description of Constitutive Relations

“…When one deals with a generalization of the Navier-Stokes fluid with a pressure dependent viscosity (usually referred to in the literature as a piezoviscous fluid), one cannot express the stress explicitly in terms of the velocity gradient, but one can express the velocity gradient as a non-linear function of the stress. Such fluids are special cases of the more general implicit fluid model and have been studied in detail in a variety of applications [see Dowson et al (1983); Tran and Suslov (2009);Saccomandi and Vergori (2010); Szeri (2011);Rajagopal et al (2012)]. …”