twenty-five years of tribology

Tribology International Vol. 28, No. 1, pp. 23-27, 1995 Copyright 0 1995 Elsevier Science Ltd

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Twenty-five years of tribology

W. Hirst

This is a personal story about a problem in tribology. It is not a balanced review, and the references given relate only to investigations which impinge directly on my own.

Early days

I studied friction, lubrication and wear for 20 years and then I became a tribologist, for the next 25 years. I began as a research student under Philip Bowden before the war and in 1947 joined the new A.E.I. fundamental laboratory at Aldermaston Court, Berk- shire. The head was Dr T.E. Allibone who asked me to build up a research team to work on surface contact with the ultimate aim of benefiting the manufacturing side of A.E.I. With one exception, Norman Welsh who was a metallurgist, we, i.e. Jack Archard, Jim Crook, John Lancaster, John Halliday, myself and, later, Gerald Hamilton, were all physicists. The essence of our contribution was that we introduced the tools of the physicist, his measurement techniques, methods of surface examination and so on into this branch of mechanical engineering. Eventually we were able to simulate many types of sliding, rolling or mixed systems embracing the speeds, loadings and geometrical features of industrial conditions. By using new methods of instrumentation, we were able to perform experiments in the domain of engineering without unduly lowering the standards of a physics laboratory. We worked on theoretical and experimental aspects of impact, friction, contact resistance, wear, fretting corrosion, and boundary and elastohydrodynamic lubrication.

A.E.I. became less profitable after 1955 and in 1963 its Aldermaston laboratory was closed, A.E.I. itself being taken over a few years later. I moved to Reading University as did Gerry Hamilton and we brought a great deal of the apparatus of our former laboratory with us. Jack Archard went to Leicester, also taking apparatus with him. John Lancaster joined the R.A.E. Farnborough. The remaining three moved away from tribology, one becoming a director of research in industry, the other two eventually becoming professors. I was fortunate to have led a team of such high calibre and it had been a very stimulating time.

Reading and elastohydrodynamic lubrication

In Reading, I was again the founder member of a new department. Apart from Agriculture, Reading

Whitchurch, Hampshire, RG28 7NF, UK

had little applied science; it did not, as now, have engineering courses or even one in applied physics. For a while, Gerry and I spent most of our time setting up new courses, but after a few months we began to think about research again. The work in A.E.I. had thrown up many problems, one of the most interesting concerning elastohydrodynamic lubrication. Jim Crook1-4 had made the first reliable measurements of the film thickness and traction whilst Geoffrey Archard (N.B. not Jack), Frank Gair and I5 had been working out the theory. Dowson and Higginson beat us to it on the theoretical side by a few months. The two theoretical sets of values for the oil film thickness were in general agreement with one another and with Crook’s measured values. The measured variation of the film thickness with speed differed somewhat from the theoretical variation but at that early stage of the subject it was not of major significance.* In contrast, Crook’s measurements of the traction were very odd: the magnitude of the traction decreased quite rapidly with rolling speed. The new theories did not predict this.

A problem

Crook had attempted to explain the variation of the traction with rolling speed by treating it as an example of viscoelastic behaviour. However, to do so, the value of the elastic modulus which was necessary had to be orders of magnitude smaller than those obtained by other methods. Moreover, the value varied greatly with the applied pressure. There were too many questions to be answered before the hypothesis could be accepted as true.

It occurred to me that there are more ways than one of subjecting oil to a sudden high pressure. Had the oil exhibited viscoelastic behaviour in Crook’s disk

*It is fascinating to look back to those times. In the decades before Crook made his measurements, there had been a number of theories of gear lubrication giving results ranging over orders of magnitude. There was also some uncertainiy about the method of deriving the film thickness from his experimental results. Crook thought it unrealistic to hope to attain great numerical accuracy; if the absolute values were correct to 20 or 30%, that would be good enough; it would be a waste of time to apply finicky corrections. His method was actually much better than he realized.

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Twenty-five years of tribology: W. Hirst

machine it would also do so in other conditions. I had been joined by this time by an old acquaintance, Mr R. Caesar, a very capable toolmaker from the former A.E.I. laboratory. He made a long linear air bearing on which M.J. Booth, a research student, mounted a Hopkinson pressure bar. With its aid we were able to subject a film of oil to an impulsive high pressure of a magnitude comparable to those in the disk machine and to derive the values of the instantaneous viscosity of the oil throughout the duration of the impact7. Typical mineral oils showed no sign of viscoelastic behaviour, the behaviour being completely explicable on the assumption that the viscosity depended on pressure and temperature in the manner observed using more conventional types of viscometer. Later, using polymer solutions in the same apparatus, another student, M.G. Lewis, and I* did observe an elastic rebound, but this was found to be due to the normal compressional or bulk modulus of the fluid. In the mid 1960s we appointed an assistant, S.L. (Stuart) Moore, who later obtained a PhD degree. Both he and Gerry Hamilton were first-class exper- imenters and they set out to measure elastohydrodynamic pressure distributions experimentally. Although the results of the early theories had ranged widely, this did not mean that all of the theories had necessarily been wrong. Once the full theory had been developed, it became apparent that the work of two Russian scientists, though more limited in scope, had brought out some of the main features of this form of lubrication. Both Grubin and Petrusevich had con- cluded that the film thickness in the region of high pressure would be approximately constant and almost independent of the magnitude of the pressure. Grubin’s theory9, despite some simplifying assumptions, gave a good approximation to the measured value of the oil film thickness. Petrusevichl” obtained solutions for three different speeds which simultaneously satisfied the governing elastic and hydrodynamics equations. The main features were that the film in the highly loaded zone is nearly parallel and that the pressure distribution is nearly Hertzian. But, near the outlet there was a local constriction in the film and, most striking of all, a very high localized pressure maximum near to it. This is commonly known as the Petrusevich ‘spike’ or the Petrusevich pressure peak. These were the features that Gerry and Stuart were looking for. The pressure was measured by a technique due to Kannel et aZ.‘l in which a small manganin resistance gauge was deposited on the surface of one of the disks. Gerry and Stuart improved on this technique by combining the pressure gauge with a capacity gauge, thereby obtaining synchronized measurements of both the pressure distribution and the shape of the oil film. They observed the peak and the constriction. Neither feature was quite so striking as the theory had predicted, but both were most definitely there12. In 1969, I had the great pleasure of meeting Dr Petrusevich in London and of asking him whether he had had ever seen his ‘spike’. He had not. That afternoon I drove him and Professor Kragelski to see one (after phoning Stuart Moore to warn him we would be coming). That day, Murphy’s law did not

operate - Stuart showed us the apparatus running; the pressure distribution with its ‘spike’ and the shape of the oil film with its constriction were clearly visible on the cathode ray tube. Petrusevich was overjoyed; he hadn’t seen this before: some of his colleagues had doubted his results and he had had to come all the way to Reading in England to see his own ‘spike’. Next time I met him I was given a bottle of vodka.

Non-Newtonian behaviour

In the late 1960s two graduates, David Adams and Tony Moore, from the Chemistry department joined me as research students; they wanted to work on applied problems rather than continue as pure chemists. David was set to work to look at film thickness and traction in a disk machine covering a more extended range than Crook had done. Dyson et al. l3 had recently measured the film thickness over a wide range of speed and had shown that there is excellent agreement with theory at low speeds but at higher speeds the experimental values fell below the theoretical values. The small discrepancy between Crook’s results and theory had occurred because he had happened to work in the border region. David confirmed Dyson et al.‘s13 observations in respect of the film thickness and he also found, as Crook had done, that the traction and the associated viscosity fell markedly with the rolling speed. However, this time we had Hamilton and (Stuart) Moore’s measured pressure distributions for some of the same conditions. These also changed with speed but not in the manner predicted by theory; the maximum pressures fell when the speed increased. Comparison between the viscosities and the pressures showed that the enhancement of the viscosity by the applied pressure had been quite normal. The fall in the traction with rolling speed was not due to an anomalous response of the viscosity to pressure; it was the change in the pressure itself that needed to be explained14.

Given the shape of the oil film and the pressure distribution it is also possible to derive the viscosity by means of the Reynolds’ equation. Hamilton and Moore’s experimental results were examined in this way. They showed, despite the above, that there is an anomalous response of the viscosity to pressure; it is found where the pressure gradients, and therefore the shear stresses, are high, not where the pressures alone are high. It occurs first in the outlet zone where the shear stresses, due to the pressure peak, are the greatest of all and also in the inlet zone if the shear stress is big enough. The extremely steep gradients near the pressure peak which are predicted by E.H.L. theory arise because the theory assumes that oils behave in Newtonian fashion no matter how great the shear stress. The more gradual fall off observed experimentally by Hamilton and Moore shows that they do not do so. There is clearly a limit to the range of shear stress in which fluids can behave as Newtonian fluids. Meanwhile Tony Moore had been looking at the relation between traction and shear stress in elastohydrodynamic lubrication and had shown the effect directly.

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Viscoelasticity

In the range of conditions explored by Crook and by Adams, the viscoelastic model, which had at first seemed to offer an explanation of the variation of the traction with the rolling speed, was therefore invalid. Viscoelastic behaviour in oils can, however, be observed in the elastohydrodynamic regime but only at much higher pressures. Johnson and Cameron15, in Cambridge, measured the tractions at very low sliding speeds under isothermal conditions and found a striking change in the shear behaviour above 100000 lbf/in2 (0.67 GPa), the highest pressure used by Crook. Johnson and Roberts16 in an ingenious experiment subsequently showed that at these pressures the oil behaves as an elastic solid when the shear stress is small. The change from viscous to elastic behaviour occurs when the apparent viscosity reaches about 10’ Pa s. There is an elastic limit and, at higher shear stress, the shear increases rapidly with relatively little increase in the stress.

Eyring type fluids

Crook built his disk machine in the mid 1950s so that when Tony Moore began to measure traction we had had many years of experience with them and had refined the experimental techniques considerably. As is well known, when the disks are caused to slip, the traction is initially proportional to the slip; later it increases less rapidly, reaches a maximum and then falls away. Crook calculated the temperature rises in the oil film and attributed these effects to viscous heating. Tony Moore, with his much more sensitive apparatus, found however that the departure from linearity begins before viscous heating becomes significant. The essence of his work was the finding that there is a critical stress above which an oil no longer behaves as a Newtonian fluid17. A theoretical model which behaves similarly is Eyring’s energy barrier model. Eyring’” supposed that each molecule in a fluid is surrounded by a barrier which has to be surmounted before it can move from its position to an adjacent site. Molecules with sufficient thermal energy of agitation are able to do so and, when shear stress is applied, more will move in the direction aided by the stress than against it. Eyring developed his theory in some detail in terms of molecular structure. Tony looked to see whether there were any obvious conflicts between the more detailed model and his experimental results; there were none. This, of course, did not establish the validity of the model in detail, but at least no reason had appeared why the energy barrier model should not be adopted as a working hypothesis.

From then on, we kept in close contact with K.L. Johnson in Cambridge. Our next move was to build a new disk machine capable of working at pressures up to 2.5 GPa. Such a machine has to be heavily built and it is not easy to achieve the requisite sensitivity. But we managed to do so and made a comprehensive series of experiments analogous to those made previously at lower pressure. Two mineral oils were examined, and over the range 0.7-2.5 GPa both behaved as elastic solids with a well defined elastic


limit19. The transition from viscous to elastic behaviour took place over a relatively narrow range of pressure and above the elastic limit the shear increased much faster than the shear stress. Johnson and Tevaarwerk” then devised a new fluid model, substituting a non- linear viscous fluid of the Eyring type for the Newtonian fluid in the Maxwell model of viscoelasticity. The behaviour of the new model showed all the main characteristics observed in practice. An experimental problem was to find a good method of measuring the elastic modulus of the oil. The difficulty is that the oil film is so thin in comparison with the size of the disks that the elastic deflection of the disks themselves may be as much or more than that in the oil film. Johnson calculated the deformation in the disks but with only partial success. Tony Moore and I mitigated the effect experimentally by working with disks of tungsten carbide. We examined many liquids*l in a search for better traction fluids but found nothing which suggested that it might be possible to produce a traction fluid substantially better than those already available.

Two final investigations

I retired formally from Reading University at the end of 1980 and by that time many of the problems of elastohydrodynamic lubrication had been solved. So far as I was concerned there were two remaining ones. The theory of E.H.L. needed to be reworked for a non-Newtonian liquid and a simple method was needed for calculating the shape of the traction curve given the fundamental properties of an oil, i.e. its viscosity and pressure coefficient of viscosity, its thermal conductivity and the limiting Newtonian stress. John Rich- mond had recently joined me and I asked him to tackle the second problem. In engineering practice the elastic region is usually of secondary importance because the slip is so small, sometimes less than in the rollers themselves. The slip in the non-linear viscous region, more particularly, the value of the maximum traction, and the slip at which it occurs, is usually of much greater interest. To calculate the traction curve in this region, the elastic properties are not needed, the liquid properties alone being sufficient. The calculations are relatively simple, but to be useful the data employed have to be reliable. The derivation of the limiting Newtonian stress can be quite difficult, especially at high pressure, because the elastic region, the non-linear isothermal region and the thermal region are not separate and distinct but merge into each other. Unless a detailed analysis of all three regions is made it is not possible to derive the limiting Newtonian stress with adequate accuracyZ2. However, while the derivation of the correct values of the Newtonian limit may present the research worker with problems, the important practical point is that once obtained, it is then quite simple to use them to calculate the relevant part of the traction curve. Another difficulty was the dearth of information about the thermal properties of oils at high pressure. When the usual values measured at atmospheric pressure were used, the calculated traction curves in the thermal region fell away more rapidly than the measured curves. John made an associated investi-

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gation to measure the thermal conductivity at high pressure, finding it to be about twice that at atmospheric pressure. When these values were used, the calculated and the measured curves agreed to within experimental error (Fig 1).

The Reading work on E.H.L., taken together with Johnson’s work, had covered many of the more important experimental aspects of the subject. The remaining task was to work out the theory of E.H.L. by a non-Newtonian lubricant. In 1978 I was approached by a Miss Avril Dance who told me she was interested in the studentships then being offered by the Science Research Council to enable mathematics students to work on suitable problems in engineering, the supervision being shared jointly by the Departments of Engineering and of Mathematics; would I accept her as a research student? I did.

I asked her to rework the theory of E.H.L. using the method I had devised 20 years previously with Frank Gair and Geoffrey Archard. In those days, the A.E.I. computer was located in Manchester and we had had to communicate with it by post via the A.E.I. (Manchester) librarian. It was a slow method, results being returned by post ten days or so later. It was out of the question to explore variations in our method of calculation and we were only able to obtain solutions for heavily loaded systems at slow speeds. With the more accessible computers in Reading I wanted to try again, to remove the restrictions in our earlier method and in particular to obtain a set of solutions for an Eyring type non-Newtonian lubricant. Between us and aided by the supervision of Avril Dance by Professor Hunt in the Mathematics Department we succeeded23.

She obtained quite a comprehensive series of results, beginning by extending tke earlier sets of results obtained by Dowson and Hrgginson, and by Archard, Gair and myself. She found that on a non-dimensional plot of load against speed (the parameters g, and g4 of Johnson24) solutions which have the pressure peak in the same position fall on a straight line. This was true of the distributions obtained for incompressible Newtonian liquids (Fig 2), for compressible Newtonian liquids and for compressible Eyring type fluids also.

-i d

Fig 1 Predicted (solid line) and measured tractions at a mean pressure of 1.36 GPa plotted against shear rate

Fig 2 Lines of constant peak position (X--X--X) on the g2fg4 map

The calculations for non-Newtonian fluids introduce an additional parameter, the sheer stress parameter, g5 = o*-r,E’ where 01 is the pressure coefficient of viscosity and 7, is the characteristics shear stress. The most significant effects of the model (cf Figs 3 and 4) are (a) a reduction in the height of the peak accompanied by a large reduction in the pressure gradients in the outlet wing and (b) a shift in the position of the peak towards the inlet. As the

-I +l

Fig 3 Pressure distributions for an incompressible lubricant for g, = 16 and &2 = 0 (0), 1.71 (I), 2.4 (2), 4.31 (3), 8.13 (4), 11.3 (5), 14.2 (6), 18 (7), 22.6 (8)

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Fig 4 Pressure distributions for a non-Newtonian compressible fluid: (1) g, = 12, (2) g, = 15.8, (3) g4 = 20.8, (4) g, = 27.4, (5) g, = 33.7, (6) g, = 39.4

speed parameter is increased, the pressure distribution changes from the near Hertzian shape at low speeds to one which is almost triangular.

When Jim Crook made his measurements of the variation of traction with speed, I little thought his results would provide me, and a lot of other people too, with food for thought for the next 25 years.

References 1. Crook A.W. Phil. Trans. Roy. Sot. Lond. A 1958, 250, 387

2. Crook A.W. Phil. Trans. Roy. Sot. Lond. A 1961, 254, 223



5. Archard G.D. Gair F.C. and Hirst W. Proc. Roy. Sot. Lond. A 1961, 262, 51

6. Dowson D. and Higginson G.R.. Engineering 1961, 192, 158

7. Booth M.J. and Hirst W. Proc. Roy. Sac. Loud. A 1970, 316, 391

8. Hiti W. and Lewis M.G. Proc. Roy. Sot. Lond. A 1973, 334, 1

9. Grubin A.N. Book No 30. Central Scientific Research Institute for Technology and Mechanical Engineering, Moscow, 1949 (D.S.I.R. Translation)

10. Petrusevich, A. Izv. Akad. Nauk. SSSR. 1951. 2. 209 (D.S.1.R Translation no. 293)

11. Kannel J.W., Bell J.C. and Allen C.M. Am. Sot. Lub. Eng. 1964, 8, 423

12. Hamilton G.M. and Moore S.L. Proc. Roy. Sot. Lond. A 1971, 322, 313

13. Dyson A., Naylor H. and Wilson A.R. Proc. Instn Mech. Engrs 196.5

14. Adams D.R. and Hirst W. Proc. Roy. Sot. Lond. A 1973, 332. 505

15. Johnson K.L. and Cameron R. Proc. Instn. Mech. Engrs 1967, 182, pt. 1

16. Johnson K.L. and Roberts A.D. Proc. Roy. Sot. Lond. A 1974, 337. 217

17. Hirst W. and Moore A.J. Proc. Roy. Sot. Lond. A 1974, 337. 101

18. Eyring H. J. Chem. Phys. 1936. 4, 283

19. Hirst W. and Moore A.J. Proc. Roy. Sot. Lond. A 1975, 344, 403

20. Johnson K.L. and Tevaarwerk J.L. Proc. Roy. Sot. Lond. A 1977, 356, 215

21. Hirst W. and Moore A.J. Phil. Trans. Roy. Sot. Lond. A 1980, 298. 183

22. Hirst W. and Richmond J.W. Proc. Znstn. Mech. Engrs 1988, 202. c2

23. Dance AS. PhD Thesis, Reading University, 1981

24. Johnson K.L. J. Mech. Engng. Sci. 1970. 12, 9

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twenty-five years of tribology

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