Using several sources, analytic and semi-analytic solutions for frictional tractions of a lubricated line contact are presented in the appropriate non-dimensional form which is similar to that previously used by Moes for film thickness. A Newtonian lubricant with an exponential relationship between viscosity and pressure is assumed and, at this stage, the treatment is confined to fully flooded conditions. The components of frictional tractions arising from rolling (Poisseiulle) and sliding (Couette) flows are distinguished and sliding tractions in the outlet cavitated region are separated from those in the main pressure zone. Three main regimes of lubrication are studied: classical (isoviscous, undeformed), low elastic modulus (isoviscous, heavily deformed) and high elastic modulus (pressure dependent viscosity, heavily deformed). The results presented here provide a broad background of approximate results, covering a very wide range of conditions against which the results of more precise computer-based analyses can be judged. Thus the treatment reveals the existence of a range of conditions (typical of the lubrication of glassy polymers by hydrocarbon lubricants) which has been little studied and is, as yet, imperfectly understood.

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