The advent of the industrialization era raised the interest in friction, in order either to increase its effects in some processes (braking, rail-wheel tire adherence), or to reduce them between the moving parts of machines. Mostly considered as a plague in machine operation, friction has important, beneficial effects: For instance, no vehicle on the road could move without friction and even human or animal walking should be impossible without it. Friction also enabled man to generate fire, the first step toward civilization. In some way, we can postulate that life depends on friction. However, from the engineer's point of view, avoiding friction is much more difficult than generating it, such that what we generally call lubrication has especially attracted the attention of the research workers during the last decades.

The relatively slow advance of lubrication science (the name Tribology appears only in 1966) is due to different causes. First of all, the theoretical and numerical analysis of dissipative processes belongs to the most difficult areas of the applied sciences. A second reason is the complex, interdisciplinary content of lubrication, such that a wide collaboration of scholars with different backgrounds is necessary in order to take important steps forward. Surprisingly, the multitude of applications has also delayed the development of Tribology as a science. The various industrial requirements in this field lead to the gathering of a great amount of empirical data and design recommendations, which were considered as being satisfactory for a certain time interval. However, the creation of high performance machines operating under special conditions has triggered the present explosive development of Tribology as an independent science.

We are now facing new problems, where Tribology has important involvements. The increasing scarcity of natural energy resources, as the result of increasing energy demands, has enhanced the need of reducing the energy losses caused by friction. Therefore, the scientific bases of Tribology have been enlarged and developed to a very high degree in both theoretical and experimental investigation, in order to reduce the power losses in the moving parts of machines. For the mathematical analysis of lubricating films, numerical solutions of complicated systems of simultaneous differential equations are possible at the present time by using computers, such that Tribology has now reached the age of maturity. Therefrom raises the question of what are the goals and what is still to be prospected in the field of friction, lubrication and wear ?

There is a kind of cycle to be observed in applied research work in physical sciences which includes the observation of a new phenomenon, followed by the elaboration of a schematic model, then the mathematical treatise which yields further discussions and generalizations and, finally, the comparison with experiments. The above succession is somewhat idealized, since the progress of an investigation is not even, in most cases, with respect to all the mentioned phases. Each step taken in one direction challenges the other aspects such that progress is attained by successive advances and setbacks of different elements of the research. A striking example is offered by the diverse branches of Tribology. A huge amount of information regarding the wear of materials was gathered through very complex and ingenious experiments, but poorly supported by mathematical analysis. There are good reasons for this, but the fact remains and in a certain measure limits our knowledge in this domain. On the other hand, fluid film lubrication had from the beginning the benefit of results  2  provided by Continuum Mechanics. As a consequence,, one was able in early times to predict with remarkable accuracy the performance of viscous lubricating films. SupPorted by computers, Fluid Mechanics and Rheology now yield answers to the most complicated problems regarding hydrodynamic, rheodynamic and elastohydrodynamic lubrication. It took months of hard work for Michell to provide the first numerical data for slider lubrication with side leakage; the same problem may now be solved in a few minutes.

Unfortunately, it appears more and more clearly that some assumptions and simplifications do not match the high accuracy of numerical calculations which, at the present time, are ahead of the physical models of lubrication. Although opinions may differ, it is undeniable that some of the concepts used have become obsolete and there is a need for reconsidering them in the light of present applications and computational methods. It is not my intention to present a criticism of Tribology and it should be a very presumptuous attitude in trying to do so. However, since the daily work has revealed to myself, and perhaps to others too, some weaknesses of our basic ideas, I should like to share some personal thoughts.

The usual Hydrodynamic Theory of Lubrication assumes that the solid surfaces are smooth, the surface curvature is negligible, there is a perfect alignment of journal and bearing axes and inertia forces are negligible. Although many papers have been written in order to show the limits of these simplifications or to replace them by more realistic assumptions, they are currently used when other aspects of lubrication are analyzed. In gas lubrication or wherever high Reynolds numbers are reached or special geometries (discontinuous surfaces, step bearings, etc.) are used, inertia forces may be important not only with regard to bearing performance, but also with respect to the stability and to the stiffness of the system. Inertia becomes significant for Stokes roughness problems when the height of the asperities is of the same order as the film thickness. Under these conditions, the velocity components normal to the solid surfaces are no longer negligible and the Reynolds pressure equation is not applicable.

Boundary conditions for pressure and temperature are often a matter of controversy. Pressure conditions for lubricated areas with open boundaries (slider bearings, par tial journal bearings) are obvious if inlet phenomena are neglected, but for full journal bearings the inlet and outlet regions of the pressure zone need special attention. There is a general consent that Reynolds (or Swift-Stieber) exit conditions are valid and continuity or energy related arguments are invoked to support them. A closer look, however, raises serious doubts. Extensive local pressure measurements in this region show a negative slope of the curve at the point where the pressure reaches the ambient value. Besides, a misfit between the accepted phenomenology and the mathematical analysis takes place. After the point of minimum pressure the ambient one is supposed to exist, while the formulae yield increasing superambient pressures. There is no mathematical or physical argument to reject this region of superatmospheriz pressure; as a consequence, with the Reynolds exit condition the pressure function becomes multivalued. This remark holds for the unidimensional flow, such that no side flow effects can be considered to support the assumption that a constant pressure should immediately follow the minimum. Moreover, we are confronted with a similar problem at the inlet of the load carrying zone, where a discontinuity of the pressure gradient is generally accepted. At this point continuity is also violated, however this situation is always forgotten. On the other hand, in short bearing theory only Sommerfeld (GUmbel) or half-Sommerfeld boundary conditions may be used. The fact that a simple inlet condition, associated to the Reynolds exit condition "work" together for high speed bearings may be a pragmatic consideration, but barely a satisfactory one from the physico-mathematical point of view.

Oil supply conditions are customarily omitted at the inlet of the pressure zone. In the usual bearing calculations, we suppose that the exact amount of oil is supplied at the right place, which is rarely the case and often the bearing is either flooded or starved. Altogether, bearings operate for most of the time under conditions different from those accepted in calculations and design. Fortunately, lubrication processes are distinguished by the ability of self-adjustment of the moving parts in contact. Under external conditions (load, speed, temperature, etc.), the parameters such as eccentricity, clearance, thermal regime and even surface roughness automatically take the values required to ensure proper machine operation and only under very adverse conditions does failure occur. This permissiveness alleviates the responsibility of the designer, but does not constitute a valid excuse for our ignorance. Thus, the question is raised as to what extent the exact numerical solutions answer the real problems, or what should be done in order to take full advantage of mathematical analysis ? Actually, we have the potential of considering real or limit cases between which a bearing will operate, instead of simple, idealized conditions. In this scope, the above problems should be reanalyzed and refinements of the theory could be introduced.

Boundary conditions for temperature are subject to different assumptions and validated in particular cases. The often used assumption that there is no heat conduction in the lubricant along the free boundaries needs more attention. As an alternative, the hypothesis of a maximum temperature gradient normal to these boundaries may offer a better description of the thermal effects. The apparent mathematical incongruity raised by this condition is easely rejected when one considers the structure of the energy equation. Actually, the temperature field obtained with either of these conditions shows only slight differences, such that the problem is mainly of academic interest.

There remain other boundary conditions worthy of being reanalyzed. For instance, non slip conditions for velocity at the solid surfaces are not valid for porous bearings; also, under specific conditions, they are not valid for impermeable surfaces, due to the interaction of adsorbed layers with the bulk of lubricant.

Although being a part of an independent science, lubrication is not an absolutely independent process. It is conditioned by the kinematics and dynamics of the machine parts in contact and by the surrounding atmosphere. We agree that cryogenic or vacuum conditions may significantly influence lubrication, but impurities or high temperatures in gas and steam turbines using superheated steam are equally as important. Besides, thermal and elastic distortions modify the clearances and the geometry of the lubricating films. The elastic deflection of the shaft contributes to the non parallelism of the journal and bearing axes. This produces a nonsymmetrical pressure distribution along the bearing length and, occasionally leads to the failure of the hydrodynamic film at the bearing edges. The nature of the edge contact, either elastohydrodynamic, boundary or dry is still to be analyzed and varies from case to case. It appears then that for the same speed and load, bearings in different machines need to be designed in order to comply with specific conditions. Whenever possible, a simulation of the operational conditions in the laboratory is advisable. However, similitude criteria must be satisfied before transferring the experimental results to real operation.

Although rarely mentioned, bearing similitude is an important element to be considered in validating experimental data for practice. The problem includes numerous parameters as bearing geometry, size and lubricant properties; kinematic, dynamic, energetic and thermal considerations, flow quality (Reynolds and, at very high speeds, Mach number), load, friction and bearing materials. Actually, all similitude requiremnts are almost impossible to satisfy, unless the experiments are carried out on the real machine. In other cases, similitude conditions are partially fulfilled, in order to point on some particular aspects or to determine qualitative trends in lubrication processes.

The active agent, the lubricant itself, is often subject to misinterpretation. It is improper to use in our calculations the Newtonian viscosity as given by usual viscometric measurements, in order to represent fluids with complex theological behaviour, even in a limited range of shear rate values. Nevertheless, introducing the real shear properties may be a lengthy and tedious, but necessary process, for which computers can provide the solution.

For normal bearing calculation and design, methods of solving the direct problem are still to be found. The inverse problem is generally considered by assuming some data (journal diameter, length-width ratio, clearance, eccentricity) to obtain the load, the temperature, the friction, the flow rates, etc. From a designer's point of view, th last group, in many cases, contains the input elements of the problem. while the assumed magnitudes are to be calculated. Therefore, the calculation is an iterative process based on trial and error. In other situations, input elements are interchanged with output data and direct methods to solve the problem in diversified cases are not available.

The precedent considerations are not new or problems yet to be investigated. A large number of excellent papers are available on different subjects. However, it seems that we are still in a exploratory phase and many of the results already obtained are very little used. Therefore, I have tried to review some aspects in my very immediate domain of preoccupations this is not an exhaustive survey and many valuable additions may be introduced. It appears now that Tribology, as a self reliant science, raises new problems and yet unanswered questions. As for other branches of science, the wider becomes our knowledge, the larger appears to be our ignorance. Hence, a challenge faces the investigator, an incentive to reduce the existing gap, while knowing that absolute wisdom is not a human attribute. Science always offers a lesson of humbleness, when confronted with the work of nature.

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