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Research Papers: Tribochemistry & Tribofilms

# A Mathematical Model for the Mixed Lubrication of Non-Conformable Contacts With Asperity Friction, Plastic Deformation, Flash Temperature, and Tribo-Chemistry

[+] Author and Article Information
L. Chang

Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802;
With High-Tech Innovations,
National Chung Cheng University,
Ming-Hsiung, Chia-Yi 621, Taiwan

Yeau-Ren Jeng

With High-Tech Innovations,
National Chung Cheng University,
Ming-Hsiung, Chia-Yi 621, Taiwan

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received May 31, 2013; final manuscript received January 15, 2014; published online February 24, 2014. Assoc. Editor: Robert L. Jackson.

J. Tribol 136(2), 022301 (Feb 24, 2014) (9 pages) Paper No: TRIB-13-1113; doi: 10.1115/1.4026589 History: Received May 31, 2013; Revised January 15, 2014

## Abstract

A mathematical model is presented in this paper for rolling-sliding contacts operating in a mixed regime of elastohydrodynamic lubrication and boundary lubrication. The model is based on the framework of Johnson et al. (1972, “A Simple Theory of Asperity Contacts in Elastohydrodynamic Lubrication,” Wear, 19, pp. 91–108). It incorporates into this framework a number of important asperity-level variables including asperity friction, friction-induced plastic flow, flash temperature, and boundary-film tribo-chemistry. The model yields a number of variables useful for the assessment of the state of the mixed lubrication. They include the load sharing between fluid and asperities, area of asperity contacts, and fraction area of asperity contacts undergoing plastic flow along with experimentally measurable variables such as the traction coefficient, friction power intensity, and temperature of the overall contact. The model is limited to mixed-lubrication problems in which the load is mainly carried by the fluid pressure and the total area of asperity contacts is a small percentage of the Hertz area. Further development is possible to formulate a model into a wider mixed-lubrication regime using some modeling concepts developed in this paper in conjunction with other modeling techniques.

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## Figures

Fig. 1

Schematic of the equivalent-surface contact model (the mean height of the peaks is the reference plane with which the heights of the asperities are defined)

Fig. 2

Effects of the reaction film parameters on the predicted performance of the mixed lubrication

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