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Measurement of Elastohydrodynamic Film Formation in Rolling Contacts at Very High Pressures
Lubricants and Lubrication / 1995 Elsevier Science B.V.
D. Dowson et al. (Editors)
497
MEASUREMENT OF ELASTOHYDRODYNAMICFiLM FORMATION IN ROLLING CONTACTS AT VERY HIGH PRESSURES By M Smeeth, P M Cann and H A Spikes Tribology Section. ImperialCollege. London SW7 2BX A modified optical interferarnetry technique was used to measure the EHD central f i thickness of two oils up to pressures of 3.6 GPa. In order to generate such pressures a tungsten carbide ball was loaded against a hardened steel disc with a sapphire window insert. The results showed that the film thickness genenued was slightly lower than that predicted by the Dowson-Hamrock quation and the load exponent lay between that
predicted by Dowson-Hamrock and recent high pnssure computed solutions 1. INTRODUCTION
It has now become routine practice in the analysis of lubricated systems to estimate elastohydrodynamic film formation using regression equations. These regression equations are normally generated from results acquired by computationally solving, simultaneously. Reynold's equation, and the influence of pressure on both elastic deformation and lubricant viscosity. These equations have also been extensively confirmed by experimental measurement of film thickness, mainly using optical techniques. One limitation of past work, both computational and experimental, is that little of it has looked at very high contact pressures. Computationally it is quite difficult to obtain solutions of the EHD problem at high pressure, especially in 2-D systems, since it is difficult to obtain solution convergence of the very non-linear equations involved. Experimentally. the main technique employed to accurately measure film thickness is optical interferometry which uses a steel ball on a glass or sapphire disc. Because of the danger of damaging such materials,most optical work has tended to be confmed to pressures below 1.5 GPa. This is below the pressures found in many rolling element bearing and gear contacts which are often between 2 and 3.5 GPa.
In the current work a modified interferometric approach has been employed to enable low cost film thickness measurements to be taken at high pressures. These measurements are then compared to existing regression equations.
2. BACKGROUND It is of considerable importance to be able to calculate both minimum and central film thickness in high pressure, elastohydrodynamic contacts as found in cams, rolling element bearings and gears. The central film thickness plays an important role in determining the rheological response and
temperature rise of the lubricant in the contact and thus the frictional losses. The minimum film thickness. in combination with the surface roughness of the two contacting solids. provides an indication of the likely extent of solid-solid contact and can be used in the prediction of rolling contact fatigue life (I), scuffing (2) and wear rate (3). The first useful elastohydrodynamic film thickness equation was developed by Ertel and Grubin in 1945 (4). This was a expression for the central film thickness in a 1-Dline contact and was derived by an ingenious, semi-analytical approach. Ertel realised that the film thickness generated in an elastohydrodynamic contact is dependent almost solely upon the rheological response of the lubricant in the inlet of the contact where the two surfaces converge and hardly at all upon its behaviour in the central zone. He was thus able to decouple the inlet from the flat central region of the contact and solve only for the hydrodynamic behaviour of the lubricant in the f o m a , assuming a constant film thickness and Hertzian pressure distribution in the latter. Despite this simplification,Ertel and Grubin's solution proved to be remarkably accurate in predicting film thickness and showed that central film thickness depends strongly upon entrainment speed and viscosity, quite strongly on lubricant pressure viscosity coefficient and contact geometry but only very weakly on the applied load and the elastic moduli of the solids in contact These dependencies can be understood by appreciating that the film thickness results only from the behaviour of the lubricant in the inlet The extent to which lubricant is entrained thus depends upon the inlet shape of the two surfaces and the effective viscosity of the lubricant in the inlet region. The former will depend upon the radii of curvature of the two solids but not significanlly upon the applied load or stiffness of the surfaces which will change the overall contact area but not markedly alter the inlet shape. The lubricant behaviour in the inlet will depend upon both upon the viscosity of the lubricant at atmospheric pressure and also, since the pressures in the inlet are
498 high enough to signifsandy influence the Viscosity of the lubricant,its pressure viscosity coefficient. The availability of high speed computers in the 1960s made possible the accurate solution, f a of the 1-D line and then the 2-D elliptical contact elastohydrodynamic problem. These broadly confirmed the form of Ertel-Grubin's original quation but showed that there was a region of minimum film thickness at the sides and rear of the contact where the film thickness was typically only 75% of the central value. At the present time the most widely used expressions for elliptical contact are those due to Dowson and Hammck (5): Central film thickness.
Minimum f i m thickness.
where U is the mean entrainment speed of the two surfaces, TO the dynamic viscosity of the lubricant at atmospheric pressure, a the pressure viscosity coefficient of the lubricant, E the reduced elastic modulus of the two surfaces, R the reduced radius in the direction of entrainment, W the applied load and k' and k are geometric parameters describing the ellipticity of the contact. A major problem encountered in the numerical solution of the elastohydrodynamic problem is to obtain convergent solutions at high load. There are two main reasons for this. Firstly elastic deformation of the contacting solids is very great at high pressures, far larger than separating elastohydrodynamic film thickness. This means that very accurate pressure and consequent deformation profiles are needed. Secondly the exponential dependence of lubricant viscosity on pressure makes the hydrodynamic quation of fluid flow in the contact highly non-linear. The combination of these two factors meant that. until quite recently, most numerical elastohydrodynamic solutions were confined to relatively low contact pressures, below 2 GPa. In the last few years however, improved numerical techniques have
enabled both line and point contact elastohydrodynamic problems to be solved up to pressures greater than 4 GPa (6)(7). A number of different methods have been employed to experimentally measure film thickness and thus verify Ertel-Grubin's o r subsequent elastohydrodynamic film thickness equations. These include capacitance (8) and x-ray techniques (9). However by far the most widely used and accurate method has been optical interferometry (10). This has the advantage of yielding a map of film thickness over the contact area and can thus yield unambiguous central and minimum film thiclolesseS. The f a comprehensive test of the point contact elastohydrodynamicfilm thickness equation using optical interfemmetry was published Gohar in 197 1 (11). Gohar used a ball on flat geometry with a series of d i f f m t materials, including perspex, steel and tungsten carbide to cover a wide range of contact conditions. When this study was made, the point cOntaCt elastohydrodynamiccontact problem had not been solved, so no reliable film thickness regression equation existed. However Gohar showed that existing approximate solutions were reasonably well obeyed ova a wide range of speed, load and elastic modulus. Since this early date many different workers have made experimental measurements of film thickness using optical interferometry and compared these with theory. Typical examples are to be found in references (12)-(14). The three main nondimensional parameters in the film thickness equation have been examined, as well as the influence of ellipticity (13) and the effect of slide roll ratio (14). Although a large number of film thickness studies have been carried out, most of these have centred on a mid-range of conditions of speed and load, although some work has been carried out at very high speeds up to 20 m/s (15). Two mgions which have only been very cursorily explored are very low speeds and very high applied loads or contact pressures. The reason for lack of work at very slow speeds is that such conditions result in very low film thicknesses and it is difficult to measure such thin films. Recently a new technique of optical interferometry has been developed which makes it possible to study the low speedflow film thickness range (16). The reason for the paucity of experimental film thicknesses at high applied loads or contact pressures is more mundane. Optical interferometry generally employs glass or sapphire 8s one of the contacting solids. With glass, the elastic modulus is too low to attain high pressures at realistic applied loads. With sapphire the elastic modulus is quite high but even so, high pressures
499 can only be attained by applied loads of several hundred Newtons. In practice, most researchers have been unwilling to subject expensive sapphire discs to such loads. This means that most optical elastohydrodynamic film thickness studies have One exception is the taken place below 1.5 .a"' early work of Gohar who used a tungsten carbide ball loaded against a circumferentially supported sapphire disc and measured film thicknesses at pressures up to 3.5 GPa (1 1). These measurements showed close agreement with existing approximate point contact film thicloless equations although only one lubricant was tested. Gentle also used a tungsten carbide ball against a sapphire disc to look at pressures up to 2 GPa and showed that the variation of film thickness with load was approximately in accord with EHD point contact theory (17). No attempt was made, however, to directly compare film thickness with theory. The current situation is thus that regression equations are mutinely used for calculating film thicknesses under high pressure conditions where these equations have not yet been properly tested. The aims of the research described in this paper were therefore to make elastohydrodynamic film thickness measurements in rolling contact at high pressures and to test the validity of the existing regression equation under these conditions.
3. EXPERIMENTAL TECHNIQUE
To obtain high contact pressures. a 19 mm diameter tungsten carbide ball was loaded against a sapphire flat. Table 1 lists the typical contact pressures obtainable in such a conjunction. The elastic modulus of the tungsten carbide ball was taken as 630 GPa and that of the sapphire, 400 GPa. The lauer value was confiied by direct measurement of the contact diameter of a statically loaded contact.
Hertz Pressure (GPa) 27 50 100 150 200 250 300 400
1.63 2.0 2.51 2.87 3.17 3.41 3.67 4.0
The use of an entire sapphire disc was judged to be prohibitively expensive since such a disc would need to have both high radius, to permit rolling measurements at reasonably high speeds, and to be thick enough to withstand high loads. As an alternative. a 25 mm diameter, 3 mm thickness sapphire window was inserted in a hardened steel disc (VPN 68) and the two ground flush. The sapphire window was then coated with a thin. semireflective layer of chromium. The test equipment is shown schematicallyin figure 1. MICROSCOPE
fr'""'
CARRIAGE
BAu
Figure 1. Schematicdrawing of test equipment. The tungsten carbide ball was rotated on a shaft against the underside of the steel disc, to drive the latter in nominally pure rolling. The disc was loaded down against the ball using weights aaached to a lever arm to produce high contact loads. Clearly in this arrangement, the ball rolls only intermittently over the sapphire window, so that provision has to be made to measure the film thickness optically during this period. To accomplish this, a spectrometer/frame grabber system was employed. White light was shone into the contact and the reflected light was passed, using a beam splitter, into a spectrometer which dispersed in into ils component wavelengths. The resultant spectral intensity curve was detected by a TV camera and captured by a frame grabbex during the passage of the ball over the sapphire window. A microcomputer then calculated the wavelength of maximum constructive interference and thus the oil film thickness. The method is similar to that previously employed for measuring very thin films (16) but wilhout a spacer layer and is considerably more accurate that relying upon the visual identification of fringes. as is done in conventional optical Interferometry. In each test, the equipment was cleaned thoroughly using toluene, followed by acetone, and a small amount of lubricant then applied to the rotating ball surface. Film thicknesses were then measured as a
500 function of rolling speed ova several optical orders. All tests were conducted at mom temperature and temperature measured close to the contact inlet using a thermocouple. The test lubricants employed and their properties are listed in table 2.
P -I+--
po
0.58~
1+1.68p
where p is the pressure in GPa. equation was produced, and is thus wholly valid only for mineral oils. However it is likely to yield a quite adequate approximation for this study, since the influence of pressure on r e k t i v e index is, in fact, quite small.
The latter Viscosity (Mas) 0.381 0.824
HVI-60
PAO-40
Pressure viscosity coefficient (GPa-l)
4. RESULTS
21.7 15.6
The technique of optical interferometry yields the optical film thickness in a contact. This must be divided by the refractive index of the film to give the m e film thickness. It is therefore neceSSary to know the refractive index of the lubricant at the very high pressure in the contact. In the current study, the refractive index of each lubricant at atmospheric pressure was measured using an Abbe refractometer. From this, the refractive index at high pressure was estimated from the h e n t z Lorenz relationship (18)
[-k)i =k
Figures 2 and 3 show the variation of film thickness with load for the two lubricants. This data is for a speed of O.llm/s for the HVI-60 and 0.278mls for the POA-40. Also shown is the theoretical film thickness variation calculated using equation (1).
(3) 10
100
1000
Load (N)
where n is the rehctive index, p the density of the fluid and k a constant The constant can be determined from the atmospheric pressure refractive index, no and density po to give:
Figure 2.Load against film thickness for HVI-60
where.
€
1000
G
100 10
Evaluation of equation 4 requires a knowledge of the effect of pressure on lubricant density. This was available from Dowson and Higginson's empirical formula, equation 5, (19):
100
Load (N)
1000
Figure 3 Load against film thickness for POA40
50 1
Table 3. Gradient of measured film thickness against load.
I
HVI-60
-0.0814
I
POA4O
-0.090
1
5. DISCUSSION
The results show quite good agreement with the Dowson and Hamrock central film thickness equation, both in terms of absolute film thickness determination and in tenns of the dependence of film thickness on applied load. The measured film thickness is up to 10% lower than the predicted. The agreement is closer at low loads than high
reflective coating on the disc. This was a disappointment since, although useful results could still be obtained, it meant that the system was not such a robust and reliable tool as had originally been intended. It would be very difficult 10 match the elastic modulus of sapphire with that of any practical disc material. A better solution might be to use a very thin and thus low cost sapphire flat supported entirely on a steel disc with a small hole drilled in the steel to fonn a window. This would avoid the problem of edge effects whilst retaining the original concept of a low cost approach to routine, high pressure film thickness measurements. 6. CONCLUSIONS
A study has been made of the EHD film-forming properties of two lubricants in high pressure. rolling
loads.
COntaCt.
Dowson and Hamrock predict a load exponent of -0.067.However, a recent point contact solution at high contact loads has suggested that under these conditions the central film thickness should vary with load raised to the power -0.1 1 (7). The results of the current study lie between these two values. It is not possible. given the accuracy of the current measurements and the small dependence of film thickness on load. to unambiguously determine which of the two is most accurate.
The results show good agreement with the theoretical Dowson and Hamrock central film thickness equation and other recent regression equations computed at higher pressure. The fact that high pressure has little effect of f i l m thickness is probably indicative of the fact that central EHD film formation is determined almost entirely by the behaviour of the lubricant in the inlet. where the pressures are relatively low and the pressureviscosity coefficient reasonably constant over the pressure range. In such a case, Grubin's original approach is essentially valid and the influence of pressure on viscosity is effectively taken account of using a single alpha-valueof the lubricant.
The fact that these results and the high and low pressure solutions agree so well suggest that the inlet behaviour in EHD confacts is in accord with Grubin's original concept
To deviate significantly from the theoretical quation. one of Grubin's assumptions would have to break down at high pressure. The most likely would be either the lubricant not obeying a simple pressure-viscosity relationship in the inlet or the pressure in the inlet causing a significant change in the inlet geometry due to elastic deformation. In practice, because inlet pressures are still quite low even at high loads. the assumptions appear to be correct In this work, the aim was to produce a low cost, robust method of measuring elastohydrodynamic film thicknesses in a rolling contact at very high pressures. However, considerable experimental problems were experienced using a sapphire window mounted in a steel disc. Because the steel disc and the sapphire had different elastic moduli, the ball elastically penetrated the two surfaces to different deplhs. This meant that the ball encountered a step when rolling born steel on to the sapphire, which resulted in some damage to the edge of the sapphire window. Consequently fragments of sapphire then damaged the semi-
It is worth noting that, whilst for central film thickness, recent high pressure EHD computation has broadly confirmed earlier low pressure work, both indicating that film thickness depends only very weakly upon applied load, this is not the case for minimum film thickness. Here, the low contact load, Dowson and Hamrock equation predicts a load exponent of -0.073but recent high pressure studies suggest that, whilst this is the case for low pressures, the exponent increases with pressure to approach the elastic-isoviscous value of -0.21 when the pressure is increased to 3.5 GPa. This is an important possibility which has not been tested experimentally and will be the subject of a following study. REFERENCES I.
Life Adjrrslmeni Faclorsfor Ball and Roller Bearings, An Engineering Guide Sponsored by the Rolling-Elements Committee. The Lubrication Div. of the ASME 1971.
502
2. Dyson, A. 'The Failure of Elastohydrodynamic Lubrication of Circumferentially Ground Discs", Proc. Inst. Mech. Engnrs., lea. 52/76,(1976). 3.
Sastry, V.R.K., Sethuramiah,A. and Singh, B.V. "A Study of Wear under Partial EHD Conditions" PKC 1 lth Leeds-Lyon Symposium on Tribology, Mixed Lubrication and Lubricated Wear, Leeds, 1984,ed, D Dowson, Publ. Butterworths, 1985.
4. Grubin, A.N. and Vinogradava, I.E. Central Scientific Research Institute for Technology and Mechanical Engineering, 1949. D.S.1.R BookNo. 30,MOSCOW, Trans. No. 337. 5. Ball Bearing Lubrication: The Elastohydrodynam'csof Elliptical Contacts,Hamrock, B.T. and Dowson, D., publ. J. Wiley & Sons, New York, 1981 6. Kweh, C.C., Evans, H.P. and Snide, R.W. "ElastohydrodynamicLubrication of Heavily Loaded Circular Contacts" Roc. I Mech E. 203,p~ 133-148,(1989). 7. Venner C.H. "Multilevel Solution of the EHL Line and Point Contact Problems" PhD Thesis, Twente University, January 1991. 8. Archard, JF. and Kirk, M.T. "Lubrication at Point Contacts", Proc. Roy. Soc.Lond. ,4261,p 532,(1961). 9. Sibley,L.B. andOrcutt,F.K., "ElastohydrodynamicLubrication of Rolling Contact Surfaces", ASLE Trans. 4,p 234. (1961) 10. Gohar, R. and Cameron, A. "The Mapping of Elastohydrodynamic Contacts." ASLE T h s . 1Q.pp 215-225,(1967)..
11. Gohar, R. "Oil Film Thickness and Rolling Friction in Elastohydrodynamic Point Contact", Trans ASME J. Lub. Tech. B,pp 371-382,(1971). 12. Wedeven, L.D. "Optical Measurements in Elastohydrodynamic Rolling Contact Bearings, PhD Thesis, University of London, June 1971. 13. Koye, K.A. and Winer, W.O. "An Experimental Evaluaton of the Dowson and Hamrock Minimum Film Thickness Equation for Fully Flooded EHD Point Contacts." ASME J Lub. Tech.m, pp284294,(1981). 14. Johnston, GJ. "A Study of Lubricating Films Generated by Organo-Phosphorus Antiwear Additives", PhD Thesis, University of ondon. 1990.
15. Dickenson, PJ. "Polymer Modified Oils in Elastohydrodynamic Lubrication." PhD 'Ihesis, University of London, June 1982.
16. Johnston, GJ., Wayte, R. and Spikes, H.A. The Measurementand Study of Very Thin Lubricant Films in Concentrated Contacts." . (1991). Trib. Trans. 34,p ~ 187-94, 17. Gentle, CR. and Cameron, A "Optical Elastohydrodynamics at Extreme Pressures." Nature 246, pp. 478-479, (1973). 18. Textbook of Physical Chemistry, S Glasstone, publ. Macmillan, London, 1948. 19. Dowson, D. and Higginson, GR. "New Roller Bearing Lubrication Formula", p158 (1961). Engineering. Lond.
D. Dowson et al. (Editors)
497
MEASUREMENT OF ELASTOHYDRODYNAMICFiLM FORMATION IN ROLLING CONTACTS AT VERY HIGH PRESSURES By M Smeeth, P M Cann and H A Spikes Tribology Section. ImperialCollege. London SW7 2BX A modified optical interferarnetry technique was used to measure the EHD central f i thickness of two oils up to pressures of 3.6 GPa. In order to generate such pressures a tungsten carbide ball was loaded against a hardened steel disc with a sapphire window insert. The results showed that the film thickness genenued was slightly lower than that predicted by the Dowson-Hamrock quation and the load exponent lay between that
predicted by Dowson-Hamrock and recent high pnssure computed solutions 1. INTRODUCTION
It has now become routine practice in the analysis of lubricated systems to estimate elastohydrodynamic film formation using regression equations. These regression equations are normally generated from results acquired by computationally solving, simultaneously. Reynold's equation, and the influence of pressure on both elastic deformation and lubricant viscosity. These equations have also been extensively confirmed by experimental measurement of film thickness, mainly using optical techniques. One limitation of past work, both computational and experimental, is that little of it has looked at very high contact pressures. Computationally it is quite difficult to obtain solutions of the EHD problem at high pressure, especially in 2-D systems, since it is difficult to obtain solution convergence of the very non-linear equations involved. Experimentally. the main technique employed to accurately measure film thickness is optical interferometry which uses a steel ball on a glass or sapphire disc. Because of the danger of damaging such materials,most optical work has tended to be confmed to pressures below 1.5 GPa. This is below the pressures found in many rolling element bearing and gear contacts which are often between 2 and 3.5 GPa.
In the current work a modified interferometric approach has been employed to enable low cost film thickness measurements to be taken at high pressures. These measurements are then compared to existing regression equations.
2. BACKGROUND It is of considerable importance to be able to calculate both minimum and central film thickness in high pressure, elastohydrodynamic contacts as found in cams, rolling element bearings and gears. The central film thickness plays an important role in determining the rheological response and
temperature rise of the lubricant in the contact and thus the frictional losses. The minimum film thickness. in combination with the surface roughness of the two contacting solids. provides an indication of the likely extent of solid-solid contact and can be used in the prediction of rolling contact fatigue life (I), scuffing (2) and wear rate (3). The first useful elastohydrodynamic film thickness equation was developed by Ertel and Grubin in 1945 (4). This was a expression for the central film thickness in a 1-Dline contact and was derived by an ingenious, semi-analytical approach. Ertel realised that the film thickness generated in an elastohydrodynamic contact is dependent almost solely upon the rheological response of the lubricant in the inlet of the contact where the two surfaces converge and hardly at all upon its behaviour in the central zone. He was thus able to decouple the inlet from the flat central region of the contact and solve only for the hydrodynamic behaviour of the lubricant in the f o m a , assuming a constant film thickness and Hertzian pressure distribution in the latter. Despite this simplification,Ertel and Grubin's solution proved to be remarkably accurate in predicting film thickness and showed that central film thickness depends strongly upon entrainment speed and viscosity, quite strongly on lubricant pressure viscosity coefficient and contact geometry but only very weakly on the applied load and the elastic moduli of the solids in contact These dependencies can be understood by appreciating that the film thickness results only from the behaviour of the lubricant in the inlet The extent to which lubricant is entrained thus depends upon the inlet shape of the two surfaces and the effective viscosity of the lubricant in the inlet region. The former will depend upon the radii of curvature of the two solids but not significanlly upon the applied load or stiffness of the surfaces which will change the overall contact area but not markedly alter the inlet shape. The lubricant behaviour in the inlet will depend upon both upon the viscosity of the lubricant at atmospheric pressure and also, since the pressures in the inlet are
498 high enough to signifsandy influence the Viscosity of the lubricant,its pressure viscosity coefficient. The availability of high speed computers in the 1960s made possible the accurate solution, f a of the 1-D line and then the 2-D elliptical contact elastohydrodynamic problem. These broadly confirmed the form of Ertel-Grubin's original quation but showed that there was a region of minimum film thickness at the sides and rear of the contact where the film thickness was typically only 75% of the central value. At the present time the most widely used expressions for elliptical contact are those due to Dowson and Hammck (5): Central film thickness.
Minimum f i m thickness.
where U is the mean entrainment speed of the two surfaces, TO the dynamic viscosity of the lubricant at atmospheric pressure, a the pressure viscosity coefficient of the lubricant, E the reduced elastic modulus of the two surfaces, R the reduced radius in the direction of entrainment, W the applied load and k' and k are geometric parameters describing the ellipticity of the contact. A major problem encountered in the numerical solution of the elastohydrodynamic problem is to obtain convergent solutions at high load. There are two main reasons for this. Firstly elastic deformation of the contacting solids is very great at high pressures, far larger than separating elastohydrodynamic film thickness. This means that very accurate pressure and consequent deformation profiles are needed. Secondly the exponential dependence of lubricant viscosity on pressure makes the hydrodynamic quation of fluid flow in the contact highly non-linear. The combination of these two factors meant that. until quite recently, most numerical elastohydrodynamic solutions were confined to relatively low contact pressures, below 2 GPa. In the last few years however, improved numerical techniques have
enabled both line and point contact elastohydrodynamic problems to be solved up to pressures greater than 4 GPa (6)(7). A number of different methods have been employed to experimentally measure film thickness and thus verify Ertel-Grubin's o r subsequent elastohydrodynamic film thickness equations. These include capacitance (8) and x-ray techniques (9). However by far the most widely used and accurate method has been optical interferometry (10). This has the advantage of yielding a map of film thickness over the contact area and can thus yield unambiguous central and minimum film thiclolesseS. The f a comprehensive test of the point contact elastohydrodynamicfilm thickness equation using optical interfemmetry was published Gohar in 197 1 (11). Gohar used a ball on flat geometry with a series of d i f f m t materials, including perspex, steel and tungsten carbide to cover a wide range of contact conditions. When this study was made, the point cOntaCt elastohydrodynamiccontact problem had not been solved, so no reliable film thickness regression equation existed. However Gohar showed that existing approximate solutions were reasonably well obeyed ova a wide range of speed, load and elastic modulus. Since this early date many different workers have made experimental measurements of film thickness using optical interferometry and compared these with theory. Typical examples are to be found in references (12)-(14). The three main nondimensional parameters in the film thickness equation have been examined, as well as the influence of ellipticity (13) and the effect of slide roll ratio (14). Although a large number of film thickness studies have been carried out, most of these have centred on a mid-range of conditions of speed and load, although some work has been carried out at very high speeds up to 20 m/s (15). Two mgions which have only been very cursorily explored are very low speeds and very high applied loads or contact pressures. The reason for lack of work at very slow speeds is that such conditions result in very low film thicknesses and it is difficult to measure such thin films. Recently a new technique of optical interferometry has been developed which makes it possible to study the low speedflow film thickness range (16). The reason for the paucity of experimental film thicknesses at high applied loads or contact pressures is more mundane. Optical interferometry generally employs glass or sapphire 8s one of the contacting solids. With glass, the elastic modulus is too low to attain high pressures at realistic applied loads. With sapphire the elastic modulus is quite high but even so, high pressures
499 can only be attained by applied loads of several hundred Newtons. In practice, most researchers have been unwilling to subject expensive sapphire discs to such loads. This means that most optical elastohydrodynamic film thickness studies have One exception is the taken place below 1.5 .a"' early work of Gohar who used a tungsten carbide ball loaded against a circumferentially supported sapphire disc and measured film thicknesses at pressures up to 3.5 GPa (1 1). These measurements showed close agreement with existing approximate point contact film thicloless equations although only one lubricant was tested. Gentle also used a tungsten carbide ball against a sapphire disc to look at pressures up to 2 GPa and showed that the variation of film thickness with load was approximately in accord with EHD point contact theory (17). No attempt was made, however, to directly compare film thickness with theory. The current situation is thus that regression equations are mutinely used for calculating film thicknesses under high pressure conditions where these equations have not yet been properly tested. The aims of the research described in this paper were therefore to make elastohydrodynamic film thickness measurements in rolling contact at high pressures and to test the validity of the existing regression equation under these conditions.
3. EXPERIMENTAL TECHNIQUE
To obtain high contact pressures. a 19 mm diameter tungsten carbide ball was loaded against a sapphire flat. Table 1 lists the typical contact pressures obtainable in such a conjunction. The elastic modulus of the tungsten carbide ball was taken as 630 GPa and that of the sapphire, 400 GPa. The lauer value was confiied by direct measurement of the contact diameter of a statically loaded contact.
Hertz Pressure (GPa) 27 50 100 150 200 250 300 400
1.63 2.0 2.51 2.87 3.17 3.41 3.67 4.0
The use of an entire sapphire disc was judged to be prohibitively expensive since such a disc would need to have both high radius, to permit rolling measurements at reasonably high speeds, and to be thick enough to withstand high loads. As an alternative. a 25 mm diameter, 3 mm thickness sapphire window was inserted in a hardened steel disc (VPN 68) and the two ground flush. The sapphire window was then coated with a thin. semireflective layer of chromium. The test equipment is shown schematicallyin figure 1. MICROSCOPE
fr'""'
CARRIAGE
BAu
Figure 1. Schematicdrawing of test equipment. The tungsten carbide ball was rotated on a shaft against the underside of the steel disc, to drive the latter in nominally pure rolling. The disc was loaded down against the ball using weights aaached to a lever arm to produce high contact loads. Clearly in this arrangement, the ball rolls only intermittently over the sapphire window, so that provision has to be made to measure the film thickness optically during this period. To accomplish this, a spectrometer/frame grabber system was employed. White light was shone into the contact and the reflected light was passed, using a beam splitter, into a spectrometer which dispersed in into ils component wavelengths. The resultant spectral intensity curve was detected by a TV camera and captured by a frame grabbex during the passage of the ball over the sapphire window. A microcomputer then calculated the wavelength of maximum constructive interference and thus the oil film thickness. The method is similar to that previously employed for measuring very thin films (16) but wilhout a spacer layer and is considerably more accurate that relying upon the visual identification of fringes. as is done in conventional optical Interferometry. In each test, the equipment was cleaned thoroughly using toluene, followed by acetone, and a small amount of lubricant then applied to the rotating ball surface. Film thicknesses were then measured as a
500 function of rolling speed ova several optical orders. All tests were conducted at mom temperature and temperature measured close to the contact inlet using a thermocouple. The test lubricants employed and their properties are listed in table 2.
P -I+--
po
0.58~
1+1.68p
where p is the pressure in GPa. equation was produced, and is thus wholly valid only for mineral oils. However it is likely to yield a quite adequate approximation for this study, since the influence of pressure on r e k t i v e index is, in fact, quite small.
The latter Viscosity (Mas) 0.381 0.824
HVI-60
PAO-40
Pressure viscosity coefficient (GPa-l)
4. RESULTS
21.7 15.6
The technique of optical interferometry yields the optical film thickness in a contact. This must be divided by the refractive index of the film to give the m e film thickness. It is therefore neceSSary to know the refractive index of the lubricant at the very high pressure in the contact. In the current study, the refractive index of each lubricant at atmospheric pressure was measured using an Abbe refractometer. From this, the refractive index at high pressure was estimated from the h e n t z Lorenz relationship (18)
[-k)i =k
Figures 2 and 3 show the variation of film thickness with load for the two lubricants. This data is for a speed of O.llm/s for the HVI-60 and 0.278mls for the POA-40. Also shown is the theoretical film thickness variation calculated using equation (1).
(3) 10
100
1000
Load (N)
where n is the rehctive index, p the density of the fluid and k a constant The constant can be determined from the atmospheric pressure refractive index, no and density po to give:
Figure 2.Load against film thickness for HVI-60
where.
€
1000
G
100 10
Evaluation of equation 4 requires a knowledge of the effect of pressure on lubricant density. This was available from Dowson and Higginson's empirical formula, equation 5, (19):
100
Load (N)
1000
Figure 3 Load against film thickness for POA40
50 1
Table 3. Gradient of measured film thickness against load.
I
HVI-60
-0.0814
I
POA4O
-0.090
1
5. DISCUSSION
The results show quite good agreement with the Dowson and Hamrock central film thickness equation, both in terms of absolute film thickness determination and in tenns of the dependence of film thickness on applied load. The measured film thickness is up to 10% lower than the predicted. The agreement is closer at low loads than high
reflective coating on the disc. This was a disappointment since, although useful results could still be obtained, it meant that the system was not such a robust and reliable tool as had originally been intended. It would be very difficult 10 match the elastic modulus of sapphire with that of any practical disc material. A better solution might be to use a very thin and thus low cost sapphire flat supported entirely on a steel disc with a small hole drilled in the steel to fonn a window. This would avoid the problem of edge effects whilst retaining the original concept of a low cost approach to routine, high pressure film thickness measurements. 6. CONCLUSIONS
A study has been made of the EHD film-forming properties of two lubricants in high pressure. rolling
loads.
COntaCt.
Dowson and Hamrock predict a load exponent of -0.067.However, a recent point contact solution at high contact loads has suggested that under these conditions the central film thickness should vary with load raised to the power -0.1 1 (7). The results of the current study lie between these two values. It is not possible. given the accuracy of the current measurements and the small dependence of film thickness on load. to unambiguously determine which of the two is most accurate.
The results show good agreement with the theoretical Dowson and Hamrock central film thickness equation and other recent regression equations computed at higher pressure. The fact that high pressure has little effect of f i l m thickness is probably indicative of the fact that central EHD film formation is determined almost entirely by the behaviour of the lubricant in the inlet. where the pressures are relatively low and the pressureviscosity coefficient reasonably constant over the pressure range. In such a case, Grubin's original approach is essentially valid and the influence of pressure on viscosity is effectively taken account of using a single alpha-valueof the lubricant.
The fact that these results and the high and low pressure solutions agree so well suggest that the inlet behaviour in EHD confacts is in accord with Grubin's original concept
To deviate significantly from the theoretical quation. one of Grubin's assumptions would have to break down at high pressure. The most likely would be either the lubricant not obeying a simple pressure-viscosity relationship in the inlet or the pressure in the inlet causing a significant change in the inlet geometry due to elastic deformation. In practice, because inlet pressures are still quite low even at high loads. the assumptions appear to be correct In this work, the aim was to produce a low cost, robust method of measuring elastohydrodynamic film thicknesses in a rolling contact at very high pressures. However, considerable experimental problems were experienced using a sapphire window mounted in a steel disc. Because the steel disc and the sapphire had different elastic moduli, the ball elastically penetrated the two surfaces to different deplhs. This meant that the ball encountered a step when rolling born steel on to the sapphire, which resulted in some damage to the edge of the sapphire window. Consequently fragments of sapphire then damaged the semi-
It is worth noting that, whilst for central film thickness, recent high pressure EHD computation has broadly confirmed earlier low pressure work, both indicating that film thickness depends only very weakly upon applied load, this is not the case for minimum film thickness. Here, the low contact load, Dowson and Hamrock equation predicts a load exponent of -0.073but recent high pressure studies suggest that, whilst this is the case for low pressures, the exponent increases with pressure to approach the elastic-isoviscous value of -0.21 when the pressure is increased to 3.5 GPa. This is an important possibility which has not been tested experimentally and will be the subject of a following study. REFERENCES I.
Life Adjrrslmeni Faclorsfor Ball and Roller Bearings, An Engineering Guide Sponsored by the Rolling-Elements Committee. The Lubrication Div. of the ASME 1971.
502
2. Dyson, A. 'The Failure of Elastohydrodynamic Lubrication of Circumferentially Ground Discs", Proc. Inst. Mech. Engnrs., lea. 52/76,(1976). 3.
Sastry, V.R.K., Sethuramiah,A. and Singh, B.V. "A Study of Wear under Partial EHD Conditions" PKC 1 lth Leeds-Lyon Symposium on Tribology, Mixed Lubrication and Lubricated Wear, Leeds, 1984,ed, D Dowson, Publ. Butterworths, 1985.
4. Grubin, A.N. and Vinogradava, I.E. Central Scientific Research Institute for Technology and Mechanical Engineering, 1949. D.S.1.R BookNo. 30,MOSCOW, Trans. No. 337. 5. Ball Bearing Lubrication: The Elastohydrodynam'csof Elliptical Contacts,Hamrock, B.T. and Dowson, D., publ. J. Wiley & Sons, New York, 1981 6. Kweh, C.C., Evans, H.P. and Snide, R.W. "ElastohydrodynamicLubrication of Heavily Loaded Circular Contacts" Roc. I Mech E. 203,p~ 133-148,(1989). 7. Venner C.H. "Multilevel Solution of the EHL Line and Point Contact Problems" PhD Thesis, Twente University, January 1991. 8. Archard, JF. and Kirk, M.T. "Lubrication at Point Contacts", Proc. Roy. Soc.Lond. ,4261,p 532,(1961). 9. Sibley,L.B. andOrcutt,F.K., "ElastohydrodynamicLubrication of Rolling Contact Surfaces", ASLE Trans. 4,p 234. (1961) 10. Gohar, R. and Cameron, A. "The Mapping of Elastohydrodynamic Contacts." ASLE T h s . 1Q.pp 215-225,(1967)..
11. Gohar, R. "Oil Film Thickness and Rolling Friction in Elastohydrodynamic Point Contact", Trans ASME J. Lub. Tech. B,pp 371-382,(1971). 12. Wedeven, L.D. "Optical Measurements in Elastohydrodynamic Rolling Contact Bearings, PhD Thesis, University of London, June 1971. 13. Koye, K.A. and Winer, W.O. "An Experimental Evaluaton of the Dowson and Hamrock Minimum Film Thickness Equation for Fully Flooded EHD Point Contacts." ASME J Lub. Tech.m, pp284294,(1981). 14. Johnston, GJ. "A Study of Lubricating Films Generated by Organo-Phosphorus Antiwear Additives", PhD Thesis, University of ondon. 1990.
15. Dickenson, PJ. "Polymer Modified Oils in Elastohydrodynamic Lubrication." PhD 'Ihesis, University of London, June 1982.
16. Johnston, GJ., Wayte, R. and Spikes, H.A. The Measurementand Study of Very Thin Lubricant Films in Concentrated Contacts." . (1991). Trib. Trans. 34,p ~ 187-94, 17. Gentle, CR. and Cameron, A "Optical Elastohydrodynamics at Extreme Pressures." Nature 246, pp. 478-479, (1973). 18. Textbook of Physical Chemistry, S Glasstone, publ. Macmillan, London, 1948. 19. Dowson, D. and Higginson, GR. "New Roller Bearing Lubrication Formula", p158 (1961). Engineering. Lond.