Wear, 38 (1976) 153 - 163 0 Elsevier Sequoia S. A., Lausanne - Printed in

A FINAL YEAR. UNDERGRADUATE TRIBOLOGY”

J. SCHWARZENBACH and D. DOWSON

153 the Netherlands

LECTURE COURSE ON

Institute of Tribology, Department of Mechanical Engineering, The University of Leeds, Leeds, LS2 9JT (Gt. Britain)

(Received October 9, 1975)

Summary

An outline syllabus is presented for an integrated lecture course on tribology appropriate for the final year of an undergraduate honours degree scheme. It is suggested that in a course of about 24 lectures the subject can be treated in adequate breadth and depth to provide an understanding of tribology useful to the professional engineer, and to form a foundation for further study and reading. The educational merit of such a course is believed to be much greater than just the transmission of tribological information to the student, in that it illustrates important characteristics of many techno- logical disciplines. It demonstrates amongst other things that not all theory is rigid and well proven, that sometimes gross assumptions must be made to permit any mathematical analysis to be carried out, that many unpredictable and varied factors affect component life, and that the understanding of a subject is continually being improved by research.

Introduction

Tribology, as a word, dates back just less than 10 years to the latter half of the sixties but there is evidence that aspects of the subject were being employed by man at least 5000 years ago. Bearings and lubrication were used for drills, wheeled vehicles, transport of heavy carvings etc., but the earliest evidence of any theoretical understanding is in the notes of Leonardo da Vinci around the end of the 15th century. Certain of the basic principles of tribology have long been taught at undergraduate level in mechanical engi- neering, engineering science and similar degree schemes, but the subject is essentially interdisciplinary and extends also into other areas such as chem- istry, physics and metallurgy. The material which has been taught has tended to be scattered throughout the traditional engineering courses such as fluid mechanics, dynamics, strength of materials, engineering materials and engi- neering design. Many advantages can be seen in attempting to present the fundamentals of tribology in a unified manner, particularly since certain -~

*Paper presented at the 3rd International Tribology Conference, “Tribology for the Eighties”, Paisley, September 22 - 25, 1975.

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aspects such as contact conditions in dry and lubricated sliding do not fit neatly into the traditional courses. This indeed was one of the recommenda- tions of the Jost report, namely that “consideration should be given to the presentation of the subject in a manner designed to reflect its coherent nature, its multi-disciplinary approach, and its wide significance in engineering prac- tice”.

The authors have been presenting such a unified course to the final year students on the Mechanical Engineering Honours BSc. Course at Leeds Uni- versity since 1969, having previously taught certain aspects within the fluid mechanics and the dynamics courses. It is felt to be a very worthwhile course which offers many advantages, and which appears to be enjoyed by the stu- dents as well as the lecturers. This paper presents a skeleton syllabus and comments on aspects which can most usefully be highlighted in th+. presenta- tion of the various topics, in the belief that such a course, continually updated to mirror advances made in tribology and with the order of topics adjusted to fit best with other lecture courses, is well worth recommending for students elsewhere now and into the eighties.

Duration and timing

Academic schemes of study vary considerably with regard to the total number of hours made available for lectures, practical work and tutorial work, to the breadth of subject material covered, and to the extent to which courses are compulsory or available as options. The number of hours which might be made available for a lecture course on tribology can thus vary widely. Courses are commonly presented at the rate of one lecture per week for a full session, or perhaps two lectures per week for a half-session, giving a total of some 24 lectures of 50 min duration. It is the experience of the authors that within such a time period a very useful and interesting course can be presented with the aim of imparting to the student an awareness of the fundamentals of tribology. In polytechnics it is not uncommon to find a more generous alloca- tion of time for any given course, and any increase would be a valuable bonus.

Many of the areas of tribology are inherently descriptive in nature, and unless dealt with at quite an advanced level the mathematics is relatively straightforward. Furthermore, with a constraint of about 24 lectures to cover the subject there is insufficient time to get too deeply involved in theoretical analysis, even where this is now well established. This, together with the fact that there is no great dependence on material taught in other engineering courses, suggests that it is feasible to present a basic course in tribology within any year of an undergraduate course. There seems very little reason, however, to mount such a course at first year level where there is normally severe pressure from other material, although certain topics would probably be introduced as parts of other courses - notably rolling contact and plain bearings are very relevant in a descriptive way to a design course. Although the course could be presented at second year level it is felt that it is most valuable if pitched at final year level. The main section of this paper therefore outlines

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a suggested syllabus for a 24 lecture final year course on tribology, and highlights the facets which are felt to be most worthwhile and the advantages which accrue.

Suggested syllabus

The basic topics can be arranged in a number of logical ways, the order of presentation sometimes being strongly influenced by the desire to present material which can be made use of in other courses, particularly design, as early as possible. Outlined below is a syllabus which has been found by the authors to give a well-balanced and logically sequenced course.

(a) Introduction and history 1 lecture (b) Surface contact, dry friction and wear 4 lectures (c) Lubrication regimes, bearing selection 2 lectures (d) Boundary lubrication, lubricant properties 2 lectures (e) Bearing materials, dry bearings 2 lectures (f) Rolling element bearings 2 lectures (g) Reynolds’ equation 2 lectures (h) Self-acting thrust and journal bearings 4 lectures (i) Externally pressurized bearings 2 lectures (j) EHL and gears 1 lecture (k) Examples and discussion session 2 lectures

Total 24 lectures

Space limitations do not allow detailed listing of the suggested contents of the material for each topic, but key points are discussed and observations made about what can most usefully be brought out in the presentation of each topic.

Introduction and history Students could be told that the aim of the course is to present a picture

of what happens when two contacting surfaces move relative to one another, what factors influence the friction and wear between the surfaces, how fric- tion and wear can be reduced or eliminated by the use of a lubricant, what the mechanisms of lubrication are, and how significant such tribological considerations are in engineering practice. Physical descriptions could be accompanied by theoretical analysis to show how widely the accuracy and complexity of the analysis can vary, what simplifying assumptions must be made and what experimental work is feasible for verification. It is helpful to demonstrate the antiquity of the subject by giving an illustrated historical survey of the practice of tribology, and to outline the main stages of the theoretical development to show how much in the past has been done on a trial and error basis. The historical material, in which undergraduates show considerable interest, can alternatively be very effectively presented as the last lecture of the course.

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Surface contact, dry friction and wear This first part of the course can usefully start with a discussion of the

topography of the surfaces of components produced by conventional manu- facturing techniques, outlining considerations of asperity height distributions and slopes and radii of asperity peaks on what are nominally smooth surfaces. The student can then easily be led to visualize that when two such surfaces come into contact under a normal load the contact’will be limited to a finite number of mating asperities, that stresses even with modest loads will be extremely high, and hence that plastic flow will occur allowing more asper- ities to meet until the real area of contact becomes sufficient to support the load. This leads on to the concept of cold welding at the resulting junctions, and to Bowden and Tabor’s theory of friction and its explanation of the basic laws of friction. A brief discussion of some other theories of friction helps to show the student that analysis is not always clear-cut and unchallenged. Consideration can then be given to the more gross effect of ploughing action, and to the concept of junction growth during sliding. The latter is presented to explain in part why actual coefficients of friction are greater than the value of about l/6 which would be expected from the basic theory, and the effect of surface contamination is shown to be significant in limiting the rise in the value of the friction coefficient and avoiding seizure. Dry contact can be concluded by discussing the different wear mechanisms, the rather limited analysis that is possible, and the difficulty of predicting wear and hence of designing for wear. With emphasis on wear as one of the most im- portant and yet least understood aspects of tribology, the increasing interest in “life” and “reliability” of components can be discussed in relation to the evolving nature of engineering education.

Lubrication regimes and bearing selection A lubricant can be presented as any substance which can be introduced

between sliding or rolling surfaces to reduce friction and wear and hence give smooth running and long life. The main modes of lubrication can be categor- ized in terms of the ratio of the meanfilm thickness to the sum of the surface roughness values, and the general nature of each mode can be described -- boundary lubrication where there remains appreciable contact between the mating surfaces, fluid film lubrication (hydrodynamic, hydrostatic, EHL) where the surfaces are completely separated by lubricant, and mixed lubrica- tion as the transition region between these. The background to the compila- tion of the Institute of Mechanical Engineers bearing selection charts, with their plots of log W versus log N for the different types of bearing, can be outlined preparatory to illustration of their use as a guide to the type of bearing likely to be most suitable in a given design situation, Mention can be made of the availability of standardized design procedures for many types of bearing.

Boundary lubrication and lubricant properties In dealing with this mode of lubrication where the lubricant films are

very thin and often of molecular proportions the various physical and chem-

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ical effects involved in the formation of surface layers can be outlined. The differences in effectiveness of physically adsorbed layers, chemically adsorbed layers and films formed by chemical reaction can be described and examples given of when and with what substances they are relevant. Boundary lubri- cants are thus seen as polar active compounds, and extreme pressure additives as materials which are reactive at high temperatures, where in both cases the surface layers continuously re-form as they are broken up during sliding. Referring back to the basic concept of adhesive friction the mechanism where- by these layers reduce friction and wear can be seen to be one of limiting the shear strength of the junctions and hence limiting the amount of junction growth. Lubricating oils are described as normally being a blend of mineral oil fractions with small proportions of other substances known as additives. The properties of oils of significance to the tribologist can then be defined, and the section concluded by reference to the structure of greases.

Bearing materials and dry bearings This is inherently descriptive. It can be pointed out that even with fluid

film lubricated bearings there can be surface contact under certain conditions, and that the bearing must be able to tolerate a certain amount of dirt conta- mination in the oil. Hence materials must be carefully chosen and consideration given to the combination of a steel shaft with an appropriate choice of lining,’ which can be one of a range of types of material between the very soft con- forming white metals and the very strong but non-conforming phosphor bronzes. There can also be discussion about suitable material combinations for cam and tappet, gear and other applications. A longer period of time can be spent on dry lubricants (graphite and MO&) and their principle of operation, on dry bearing materials (thermosetting compounds and the thermoplastics, especially nylon and PTFE) and on composite materials which combine the advantages of their constituent components. A suitable conclusion is to describe prelubricated bearings, and to give a range of applica- tions of these and dry bearings.

Rolling element bearings It is probable that the student will already be familiar with the different

types of rolling element bearing, with rolling bearing selection, and with mounting considerations. The object of these two lectures is to look at the tribological aspects - why there is frictional resistance in pure rolling, where friction arises in a rolling bearing, what considerations determine the static load capacity C,, listed in manufacturers’ catalogues and what happens if this is exceeded, what determines the dynamic load capacity C and the “life” of a rolling bearing, and what dictates the maximum permissible rotational speed. The modes of lubrication likely to be relevant in the different contact- ing regions of a bearing with oil or grease as the lubricant can be discussed, and conclusions drawn about lubrication requirements. This topic can be rounded off with a list of possible modes of failure and recommendations about action to be taken following a failure.

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Reynolds’ equation In turning to fluid film lubrication it seems worth stressing that one is

considering a regime where detailed theoretical analysis is feasible, where the assumptions which must be made are much more realistic than those required for analysis in the dry or boundary regime, and where equations can be set up in a straightforward manner. As a starting point the generalized Reynolds’ equation for viscous flow of fluid between two surfaces in relative motion can be derived, and it should be stressed that the equation is complex and can best be solved numerically by computer, and that for further analysis to be possible simplifying assumptions must be made. By making the appropriate assumptions the equation can then be simplified to the integrated Reynolds’ equation for two-dimensional steady state flow with an isoviscous incom- pressible fluid.

Self-acting thrust and journal bearing analysis The integrated Reynolds’ equation can now be solved to determine the

pressure profile for the specific geometries of thrust and journal bearings. For a thrust bearing it can be shown that if the surfaces are parallel the pressure in the film is constant and atmospheric, and the reasons why such bearings were nevertheless successfully used for decades in marine applica- tions are worthy of mention. The next logical step is to consider the plane inclined slider bearing, to derive pressure profile relationships for various angles of tilt, and hence to show that there is an optimum angle of tilt for maximum load capacity. How this is exploited in the pivoted pad bearing and why a fixed inclination thrust bearing is not desirable follow logically. Turning to the journal bearing case it could be pointed out that solution of the Reynolds’ equation is again possible analytically provided that a further approximation is made, namely that the bearing be considered to be either short or long relative to the shaft diameter. Time is unlikely to be sufficient to permit the derivation of both solutions and there seems little merit in attempting to do so; hence it appears best to choose the short bearing case and solve to determine the theoretical pressure profile, since it is the more representative of practical bearings and gives some indication of pressure variation in both the axial and circumferential directions. This can then be integrated to determine the load capacity and attitude angle using the Sommerfeld substitution, first assuming that the negative pressures predicted can exist and then introducing the half bearing solution in which it is as- sumed that cavitation occurs. To conclude, the available design procedures can be presented to show the student that he does not have to solve the Reynolds’ equation whenever he designs a bearing. The relationship between short and long bearing solutions together with full computer solutions of the Reynolds’ equation can be presented at this stage.

Externally pressurized bearings This topic is conveniently introduced by citing the limitations of

hydrodynamic bearings and the general characteristics of EP bearings and

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then listing the types of bearing situation where the latter find application. For a circular thrust bearing it can be shown that the Reynolds’ equation can be applied but it should be pointed out that a simpler approach is to start from the Poiseuille equation, and expressions for pressure distribution, load capacity, frictional torque and power loss could be derived. This could be followed by a discussion of the question of stiffness and the need for compen- sation when the fluid source is at constant pressure, and the use of multi- pocket bearings to offer resistance to tilt. The topic can be concluded with a brief description of the differences &ich arise with rectangular and other shapes of plane bearing, with journal bearings, and with air bearings.

EHL and gears Most appropriate here is probably a descriptive approach highlighting

the fact that the equations are not very difficult to establish but that they are difficult to solve and require iterative calculations. Film thickness equa- tions could be quoted and the resultant geometry of the fluid film illustrated. This lecture and the subject material of the whole course can then be concluded by describing some of the many practical situations where EHL is the mode of lubrication. The important effect of film thickness upon the fatigue life of highly stressed components can be discussed at this stage and illustrations presented of practical gear and rolling element bearing situations which have benefited from research in the field of elastohydrodynamic lubrication.

Practical work

The time available in most courses for formal laboratory work is small, and at final year level there are frequently no set laboratory sessions. There would seem to be no strong case for standard experiments at this stage but instead use could be made of a number of simple demonstrations to illustrate the concepts. The scope for project work, whether experimental or numerical, is considerable. Throughout the course the relevance to practical engineering can be demonstrated by extensive use of slides and displays of hardware, illustrating both new and failed components.

Discussion

A course of the form described will give an adequate broad picture of the subject of tribology, and benefits markedly by being presented as a unified whole. In addition it fulfils an extremely useful function by illustrating to the student a number of important characteristics of many technological disciplines:

(a) it demonstrates that not all theory is rigid and well proven, and that sometimes gross assumptions must be made to obtain any equations;

(b) it provides a useful contrast between the analytically well-defined and relatively easily experimented fluid film situation and the much more difficult boundary lubrication end of the regime;

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(c) it highlights how many factors enter into the picture as far as life is concerned, and hence how difficult it is to design for life;

(d) it demonstrates the continual improvement in understanding of the subject resulting from research being currently carried out, and hence is as much a course for the eighties as for the present.

These wider aspects are much less readily appreciated at second year level, and it is for this reason rather than one of depth of treatment that the course is recommended as a final year course. .

The varied nature of the subject material makes it worth experimenting with different forms of assessment. The authors have been assessing by a 2 h terminal examination, half of the marks being assigned to 50 multiple choice questions, the remainder to two standard questions chosen from four which may be descriptive, analytical, numerical or a combination of these. The multiple choice questions are not easy to set in such a way that they unam- biguously test understanding rather than mere memory of factual details. They serve a very useful teaching function when the student is working through past papers as preparation for his own examination (see Appendices).

The authors have not recommended a single textbook for the course, since the subject matter has previously appeared in fragmented form in indi- vidual texts. Reference to papers and good texts covering individual topics has formed the necessary guidance for background reading. A number of textbooks on tribology are now being prepared and published, and it seems likely that the lecturer of the eighties will be in a more fortunate position than his present day counterparts. It is worth noting that the authors have found that summary sheets which outline the essential points of each group of lectures and list useful references are greatly appreciated by the students. They provide flexibility and are readily updated or modified to accord with teaching experience, and are relatively cheap.

The authors have found that the course has been very well received. The students find it interesting and a welcome contrast to the more highly ana- lytical type of course. The relevance of the subject to the engineer ismade very apparent, and few will complete their careers without meeting problems in tribology. The interdisciplinary nature of the subject provides great inter- est and a challenge to students and lecturers alike.

Appendix A

Typical multiple choice questions Students are instructed to select the most appropriate answer. A mark

is given for each correct answer.

Fifty questions with an allocated time of 1 h

1. The remarkable bearings built about 50 A. D. and mounted on the ships of Lake Nemi outside Rome were:

(A) early forms of tilting-pad bearings. (B) free wooden and metal rolling-element bearings.

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(C) trunnion-mounted wooden and metal rolling-element bearings.

(D) grease lubricated plain bronze journal bearings.

2. The surface quality R, of the rolling element8 in high quality ball and roll- ing element bearings is about:

(A) 5 X 10-8 m. (B) 15 X lo-* m. (C) 25 X 10-8 m. (D) 35 X 10e8 m.

3. Boundary lubricant additives are included in some spur gear lubricants to: (A) increase the elastohydrodynamic film thickness (B) increase the viscosity of the bulk lubricant. (C) reduce surface wear and assist running in. (D) improve the cooling properties of the lubricant.

4. Half of the bearing8 in any group of rolling contact bearings would be expected to last:

(A) 0.5 (B) 1 (C) 2 (D) 5 times the nominal life.

5. The upper limits of speed and load for which a hydrodynamic bearing is the most suitable type of thrust bearing are governed by:

(A) the temperature rise in the fluid. (B) the falling off of the load-speed curve. (C) the load capacity of the rolling bearing8 becoming greater. (D) mechanical strength.

6. If machine elements operate under conditions of mixed lubrication an increase in speed will cause the coefficient of friction to:

(A) increase. (B) remain constant. (C) initially increase and then decrease. (D) decrease.

7. Which of the following statements describes most closely the effect of the presence of dirt particles in an oil on a fluid film bearing life?

(A) The presence of dirt particles in a fluid film bearing causes failure. (B) Provided dirt particles are smaller than the radial clearance damage

is negligible. (C) A dispersant additive can be used to break up the dirt 80 that no

damage results. (D) Some dirt can be tolerated provided that one of the bearing materials

is Soft.

8. The force of friction F between two lubricated surfaces is recorded for various values of the normal load W, the sliding speed V and the viscosity n as shown in the table:

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J’(N) 80 40 40 80

W(N) 1000 500 500 1000 V(m s-l) 5 2 2 2 n(Ns me2) 0.05 0.05 0.10 0.05

What is the mode of lubrication? (A) boundary? (B) mixed? (C) elastohydrodynamic? (D) hydrodynamic?

9. According to the short bearing solution of Reynolds’ equation, the load capacity increases with length of bearing to the power n, where n is:

(A) 3. (B) 2. (C) 1.5. (D) 1.

10. In the (Archard) equation for adhesive wear the volume V of material lost is related to the total load W, the sliding distance x and the mean flow stressp, of the softer material by the relation

(A) V a p,x/W 03) Va PGW

(C) v a WX/P, (D) V 0: x/WP,

11. For a bearing with low sliding velocity running at high temperature graphite would be suitable as a bearing bush material up to a limit of about

(A) 1600 “C. (B) 600 “C. (C) 400 “C. (D) 250 “C.

12. For an externally pressurized bearing where the pocket pressure is constant, variation in film thickness under the land causes variation in:

(A) load capacity. (B) flow. (C) friction. (D) more than one of these.

Appendix B

Typical standard questions

Allocated time 30 min each

1. Write a short account of the adhesive wear mechanism and show that the volume V of material removed can be related to the applied load W, the sliding distance x and the hardness pm of the softer material by the equation

V= k Wx/3p,,,

where k is a dimensionless wear coefficient. Explain the physical significance of k and show that in the case of abrasive

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wear in which a hard conical asperity having sides of slope 8 to the mean surface plane ploughs through a softer material the equivalent wear coeffi- cient can be written in the form

k abrasive =LnB 71

2. Write an essay on the mechanism of boundary lubrication. Special mention should be made of the physical/chemical interactions involved between the lubricants (or additives) and the bearing solids. The essential features of boundary lubricants in each category of film strength should be noted, to- gether with reference to specific examples.

3. The pressure distribution in a plane inclined surface self-acting thrust bearing is given by the relationship

_ _h& 6(&--l) p -guI= (&+l) [

Z(l -5)

{Ki - (IFi - 1)F}2 1 Define clearly the symbols in this equation, sketch the form of the relation- ship, and discuss fully its significance.

Evaluate an expression for the load capacity in terms of 6; sketch the form of this relationship and outline its si~ific~ce.

4. Describe the main types of dry bearing material, giving in some detail the important characteristics and their effect on bearing performance. List briefly typical applications for the various types.