Date of Award

Fall 1995

Document Type


Degree Name

Doctor of Philosophy in Mechanical Engineering - (Ph.D.)


Mechanical Engineering

First Advisor

Avraham Harnoy

Second Advisor

Bernard Friedland

Third Advisor

Rong-Yaw Chen

Fourth Advisor

Roman Dubrovsky

Fifth Advisor

Zhiming Ji


The research reported in this dissertation is concerned with the development of friction models for lubricated contacts. A few analytical models have been developed to investigate the friction under dynamic velocity conditions. In this study, two different tribological situations such as conformal and non-conformal contacts have been chosen. Friction modeling covers boundary, mixed and full fluid film friction regions. A new theory based on the elastic properties of the surface materials, and fluid film properties of the lubricant at the contact has been developed to determine the dynamic friction in boundary, mixed and full hydrodynamic lubrication regions. In the full fluid film lubrication region, friction has been determined from the lubrication principles based on the tribological situation, i.e., hydrodynamic lubrication theory for a short journal bearing and elastohydrodynarnic lubrication theory for a line contact.

A conformal contact formed by a short journal bearing operating in the region where hydrodynamic lubrication theory is valid has been considered to develop a model. The model is simulated for unidirectional as well as bi-directional sinusoidal velocity oscillations for various frequencies. Simulation resulted in a phase lag in the fiction and hysteresis in ftiction versus velocity (f vs. U) curves. The results obtained for unidirectional velocity oscillations indicate qualitative agreement with experimental work on lubricated line contact by Hess and Soom (1990). Results for bi-directional oscillations also show phase lag in friction and similar hysteresis in f vs U curves. In addition to the hysteresis, results for the bi-directional velocity oscillations show a discontinuity in friction at velocity reversals. These results have been verified experimentally.

A special apparatus to measure the friction has been designed and built by using a sleeve bearing. Experiments have been conducted to measure friction under various velocity conditions, and the results have been used to determine the coefficients required to simulate the analytical model. The analytical model has been simulated for the above coefficients and the results have been compared with the friction measurements. The comparison shows similar hysteresis in f vs U curves for uni-directional and bi-directional velocity oscillations. However, the friction behavior of the apparatus during bi-directional oscillations differs in the magnitude of the discontinuity (step function) at velocity reversals.

The above analytical friction model developed for the hydrodynamic short journal bearing has been extended to investigate the effect of resisting forces on the dynamic friction behavior at low speed. Resistance forces include sliding friction as well as the presliding friction Dahl effect. The Dahl effect is due to elastic deformation of the compliance in the system before the force reaches the breakaway magnitude when sliding initiates. In this study, stiffness of the asperities as well as elastic support have been considered. Simulation results of the model for uni-directional velocity oscillations are in qualitative agreement with earlier experimental work. Simulation of the model for bi-directional velocity oscillations shows that the discontinuity at velocity reversals has been replaced by a line with slope. This work indicates that the stiffness, of the elastic compliance can play a significant role in replacing the discontinuity.

The above concepts of friction modeling has been extended for a non-conformal contact formed with a cylindrical surface sliding over a flat surface operating on elastohydrodynamic lubrication theory. In this model, elastohydrodynamic lubrication theory has been used to determine the friction in full fluid film region. Simulation results of this model for uni-directional as well as bi-directional sinusoidal velocity oscillations indicate a similar phase lag in the friction and hysteresis in f vs. U curves as observed in the earlier models.

Results of the present investigation indicate that the instantaneous friction is not only a function of the instantaneous velocity, but it is also a function of previous velocity or velocity history. These modelscan be improved with the aid of more experimental work. Also, these models can be extended for stick-slip analysis and for friction compensation