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How Lubricants Behave in EHL Contacts
The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.
555
How Lubricants Behave in EHL Contacts B. Jacobson
SKF Engineering & Research Centre B.V. Postbus 2350, 3430 DT Nieuwegein, The Netherlands When more and more realistic models for the lubricant rheology in heavily loaded rough EHL contacts are used, some new insight is gained. For a long time it was assumed that if the calculated oil film thickness was larger than a few times the R, value of the surfaces, the lubrication could be expected to be successful. There was never any explanation why the highest tops in the surface structure did not break through the oil film despite the fact that they were higher than the oil film thickness. In some applications in the early ~ O ’ S ,where squeeze motion and sliding motion were superimposed on the rolling motion of an EHL contact, the old rule of thumb suddenly no longer worked. The oil film thickness to roughness ratio had to be larger than expected to avoid smearing damage which was caused by direct metallic interaction through the oil film. The surfaces behaved as if they were rougher when sliding was superimposed. In modem very smooth bearings, the opposite is clearly seen. The calculated mean oil film thickness needed to separate the bearing surfaces is much smaller than the composite surface roughness of the surfaces. This leads to the conclusion that the surface structure is to a higher or lower degree elastically deformed by the pressure variations in the oil film and thus that the lubricant rheology and shear stress will determine the behaviour of the asperities and whether the lubrication is successful or not.
1
INTRODUCTION
Different mathematical models for the lubricant behaviour in bearings have been proposed in order to explain why lubricant films can decrease the friction and wear of lubricated surfaces. The first mathematical model, proposed by Newton [ I ] in 1686, had a linear relationship between shear stress and shear rate, and the ratio was called the viscosity of the liquid. This model worked extremely well for lightly-loaded lubricated contacts such as journal bearings, and was already being used successfully in 1883 by Petrov [2] for the prediction of bearing friction. The Newtonian lubricant model also predicted the pressure build-up and the oil film thickness-load-speed relationships in a correct way. When Martin 131 published his calculation of the oil film thickness between gear teeth in 1916, his results predicted such a thin film that it was clear that the gears would not be able to work without wear having the roughness they had. In 1941, Meldahl [4] included the elastic deformationscaused by the oil film
pressure in the calculation model, but still the predicted film thickness was too low compared to engineering surface roughnesses to explain successful lubrication. When in 1949 Ertel [5] and Grubin [6] also included the pressure-viscosity effect on the oil film thickness, the calculated film thickness in a smooth elastohydrodynamic contact became about as large as the mean surface roughness heights. Later, this led engineers to use theoretical calculations of oil film thicknesses for smooth surfaces, also when predicting the lubrication of rough surfaces. The standard assumption was that the calculated oil film thickness had to be larger than a few times the R, value of the surfaces (Hamrock and Dowson [7] and Harris [8]) to make the lubrication successful. No detailed explanation was given of the phenomenon of full film lubrication (no metallic contact through the oil film) despite the fact that the highest peaks in the roughness distribution were often many times higher than the thickness of the lubricant film.
556 Already in 1958-59 F.W. Smith [9] had found that a Newtonian lubricant model could not describe the traction forces measured in combined rolling and sliding motion for heavily-loaded contacts. His measurements showed that the Newtonian model could only describe the tractional behaviour at very low sliding speeds, and when the sliding speed increased the shear stress reached a maximum and could even fall at higher sliding speeds. He concluded that lubricants had a shear strength which gave the maximum shear stress possible to transmit through the oil film. The concept of a limited shear strength and solid-like behaviour was used by Jacobson ( 101in 1970 in his calculation of oil film thickness for a point contact, see Figure 1. In the figure the oil film thickness and pressure distribution are shown and the region with solidified oil is indicated by a broken line in the pressure distribution. In the same report, shear strength measurementsfor oils solidified under pressure were recorded using the high pressure chamber shown in Figure 2. Later, measurements at higher pressures and temperatures (111, made in a new high pressure chamber, see Figure 3, revealed that the shear strength increased linearly with an increase in pressure: also, the pressure increase needed to retain the oil in the solid state at a higher temperature exactly matched the compression of the oil with the thermal expansion due to the increase in tempenture. The oil converted to a solid at a constant density, indpendent of temperature.
2
ROUGH SURFACES
As the mean lubricant film thickness in a rough, lubricated EHL contact seems mainly to be determined by the inlet zone, except for contacts at high sliding speeds when the lubricant is in a glassy state, the calculated film thickness could predict lubrication behaviour quite well for typical engineering surfaces in beatings and gears, despite the fact that the roughness peaks ought to have penetrated the oil film if their form was maintained in the EHL contact. The first indications that the simple EHL theory for smooth surfaces could not fully predict the behaviour of rough surfaces were noticed about 20 years ago when lubricated surfaces in combined rolling and sliding needed a thicker calculated oil film than predicted for pure rolling, in order not to damage the surfaces. It
could also be seen on gears where some running in took place. The simple EHL theory failed to provide an adequate description of solid contact through the oil film. As the elastohydrodynamic calculations assumed linear Newtonian behaviour [I] for the lubricant, one possible way to explain the oil film collapse was by assuming the lubricant to be no longer Newtonian. If the oil was non-Newtonian, an increase in shear strain rate would no longer give a shear stress increase proportional to the shear strain rate increase. This permitted enhanced pressure flow peqendicular to the relative sliding velocity of the bearing surfaces compared to that expected for the Newtonian case. Indeed, if this side flow was large enough, the whole macro-Hertzian contact would collapse within the contact time. For shorter times, it was still possible for an individual, compressed asperity to re-emerge from the surface. It was only necessary that, by virtue of a slightly higher pressure compared to the surrounding ambient level, the side flow was sufficient to empty the micro-contact. As the local asperity pressure fluctuations are functions of the heights and slopes of the asperities, the film collapse is governed by these as well as by the surface velocities. The steeper the pressure fluctuation, the faster the collapse of the oil film under the asperity, Asperities with low slopes will be elastically flattened by the pressure variations in the oil film while sharp and steep asperities will maintain their form until they touch the opposite surface, see Figure 4. Asperities with intermediate slopes will be elastically flattened at the inlet of the EHL contact but will slowly re-emerge into the oil film due to the elastic spring-back of the asperity, see Figure 5. Depending on how fast the asperities reemerge compared with the time available for the transport through the contact (typically lC3 to lo4 s), the asperities can touch through the oil film at the outlet or not. This phenomenon was experimentally shown by superimposing a sliding speed on normal squeeze motion between a polished steel ball and a flat lubricated surface using the test rig shown in Figure 6 (111. Oil film breakthrough was indicated by electric contact between the balls and the plate. Polished surfaces (R, = 0.008 pm) needed only 5 cSt viscosity to avoid metallic contact during the
557 impact time when the sliding speed was zero. A sliding speed of 0.14 m/s made it necessary to increase the viscosity to 26 cSt in order to avoid metal to metal contact. For a rough surface, R, = 0.18 pm, in contact with the polished ball, the viscosity needed to be much higher, 68 cSt at pure impact and between 7000 and 16300 cSt for a total sliding distance of 29 pm during the impact time. It was thus necessary to have a viscosity more than 100 times higher to keep the surfaces sepmted by an oil film when a sliding distance of 2.5 percent of the Hertzian contact width took place during impact. That sliding distance is of the m e order as the surface roughness wave length. The non-Newtonian behaviour of the lubricant allowed oil film breakthrough which could not be predicted by a Newtonian lubricant model.
3
SMOOTH SURFACES ASPERITY LUBRICATION
AND
In recent years the opposite effect has also been seen. For extremely smooth surfaces the asperity pressure gradients are not able to displace the lubricant sideways and cause an oil film collapse at the asperity level so that the lubricated contact behaves as if it was mathematically smooth [12]. This leads to oil film collapse only at very high sliding speeds and high loads when the whole Hertzian contact collapses. Depending on how far up on the shear stress-shear strain rate curve the lubricant stress point is situated, different behaviour will be experienced by the asperities. If the lubricant stress is far below its local shear strength, an increase of the shear rate will increase the shear stress and thereby build up steeper local pressure gradients. This leads to build-up of steep pressure spikes, both in pure rolling situations and in combined rolling and sliding. These pressure spikes above the high points of the surface structure flatten the surfaces locally and give them a lower effective roughness. This is probably one of the main reasons why well run-in surfaces can work without metallic contact through the oil film, even when the asperity heights are considerably larger than the calculated mean oil film thickness. The rule of thumb for choice of oil film thickness compared to the composite surface roughness of the lubricated surfaces can thus be explained if the roughness is about halved inside the
EHL contacts for good surfaces compared to the roughness outside the contact. The smoother the mating surfaces, the more important this phenomenon because both the local pressure gradients and the heights of the local pressure spikes go down. The decrease in the local pressure gradients decreases the risk of pushing out the oil from under the asperities for any given shear strength of the oil. At the m e time the lower asperity pressures will maintain the lubricant in the Newtonian state at the asperity tops and thus allow some sliding speed between the surfaces before the stress in the oil reaches the shear strength and gives the oil a much smaller effective shear strength in a direction perpendicular to the sliding direction. and thus can be pushed out from the asperity contact. The higher the sliding speed and the higher the local viscosity at the asperity tops, the further into the non-Newtonian behaviour regime the lubricant will come, and the earlier the asperity tops will break through the oil film.
4
CONCLUSIONS
The above leads to the conclusion that rough surfaces lubricated with oils having a high a-value (pressure viscosity coefficient) need a much thicker mean oil film compared to the surface roughness than smooth surfaces lubricated with low a-value I ubricants. Thus, the ratio between the mean oil film thickness and the surface roughness height needed for good lubrication steeply decreases when surfaces get smoother and the lubricants remain Newtonian in the EHL contact.
REFERENCES 1. 2.
3.
Newton, I. (1686), "Philosophiae Natumles Principia Mathematica". Imprimature S . Pepys, Reg. Soc. Praeses. 5 Julii, Londini. Petrov, N.P. (1883), "Friction in Machines and the Effect of the Lubricant", Inzh. Zh., St. Peterb.: 1.71-140; 2.227-279; 3.377-436; 4. 535-564. Martin, H.M.(1916), "Lubrication of Gear Teeth", Engineering (London), 102, 199.
558 4.
5.
6.
7.
Meldahl, A. (194I), "Contribution to Theory of Lubrication of Gears and of Stressing of Lubricated Flanks of Gear Teeth", Brown Boveri Rev., Vol. 28,No. 11, pp. 374-382. Ertel, A.M., "Hydrodynamic Lubrication Based on New Principles", Akad. Nauk SSSR, hikdnaya Malhematica i Mechanika, 3,2,4152. Grubin, A.N. and Vinogmdova, I.E. (1949), "Fundamentals of the Hydrodynamic Theory of Lubrication of Heavily Loaded Cylindrical Surfaces", Investigation of the Contact Machine Components, Kh. F. Ketova, ed.. Translation of Russian bdok No. 30,Central Scientific Institute for Technology and Mechanical Engineering, Chapter 2. Hamrock, BJ. and Dowson, D. (1977). "Isothermal Elastohydrodynamic Lubrication of Point Contacts: Part 111- Fully Flooded Results", J. Lubr. Technology, Vol. 99,No. 2,264-276.
Figure 1
8.
Harris, T.A. (1991). "Rolling Bearing Analysis", Third Edition, John Wiley & Sons, Inc. 9. Smith, F.W. (1958-59)."Lubricant Behimiour in Concentrated Contact Systems - The Castor Oil-Steel System", Wear, Vol. 2, 250-263. 10. Jacobson, Bo (1970), "On the Lubrication of Heavily Loaded Spherical Surfaces Considering Surface Deformations and Solidification of the Lubricant". Acta Polytechnica Scandinavica, Mech. Eng. Series No. 54,Stockholm. 11. Jacobson, Bo (1991). "Rheology and Elastohydrodynamic Lubrication", Tribology Series 19,Elsevier. 12. Cann, P. et al. (1994), "The Lambda Ratio A Critical Reexamination", Wear, 175, 177188.
Theoretical height function and pressure field The broken line surrounds the solidified region.
559
Figure 2
Photograph of the fust high pressure chamber.
Figure 3
Photograph of the second high pressure chamber.
-
560
EHk contact
Mo
micro-EHL
Figure 4
EHL contact with asperities of different slope.
Figure 5
Asperities flattened and reemerging during the transport through the contact.
56 1
View A-A Figure 6
Drawing of the test apparatus.
555
How Lubricants Behave in EHL Contacts B. Jacobson
SKF Engineering & Research Centre B.V. Postbus 2350, 3430 DT Nieuwegein, The Netherlands When more and more realistic models for the lubricant rheology in heavily loaded rough EHL contacts are used, some new insight is gained. For a long time it was assumed that if the calculated oil film thickness was larger than a few times the R, value of the surfaces, the lubrication could be expected to be successful. There was never any explanation why the highest tops in the surface structure did not break through the oil film despite the fact that they were higher than the oil film thickness. In some applications in the early ~ O ’ S ,where squeeze motion and sliding motion were superimposed on the rolling motion of an EHL contact, the old rule of thumb suddenly no longer worked. The oil film thickness to roughness ratio had to be larger than expected to avoid smearing damage which was caused by direct metallic interaction through the oil film. The surfaces behaved as if they were rougher when sliding was superimposed. In modem very smooth bearings, the opposite is clearly seen. The calculated mean oil film thickness needed to separate the bearing surfaces is much smaller than the composite surface roughness of the surfaces. This leads to the conclusion that the surface structure is to a higher or lower degree elastically deformed by the pressure variations in the oil film and thus that the lubricant rheology and shear stress will determine the behaviour of the asperities and whether the lubrication is successful or not.
1
INTRODUCTION
Different mathematical models for the lubricant behaviour in bearings have been proposed in order to explain why lubricant films can decrease the friction and wear of lubricated surfaces. The first mathematical model, proposed by Newton [ I ] in 1686, had a linear relationship between shear stress and shear rate, and the ratio was called the viscosity of the liquid. This model worked extremely well for lightly-loaded lubricated contacts such as journal bearings, and was already being used successfully in 1883 by Petrov [2] for the prediction of bearing friction. The Newtonian lubricant model also predicted the pressure build-up and the oil film thickness-load-speed relationships in a correct way. When Martin 131 published his calculation of the oil film thickness between gear teeth in 1916, his results predicted such a thin film that it was clear that the gears would not be able to work without wear having the roughness they had. In 1941, Meldahl [4] included the elastic deformationscaused by the oil film
pressure in the calculation model, but still the predicted film thickness was too low compared to engineering surface roughnesses to explain successful lubrication. When in 1949 Ertel [5] and Grubin [6] also included the pressure-viscosity effect on the oil film thickness, the calculated film thickness in a smooth elastohydrodynamic contact became about as large as the mean surface roughness heights. Later, this led engineers to use theoretical calculations of oil film thicknesses for smooth surfaces, also when predicting the lubrication of rough surfaces. The standard assumption was that the calculated oil film thickness had to be larger than a few times the R, value of the surfaces (Hamrock and Dowson [7] and Harris [8]) to make the lubrication successful. No detailed explanation was given of the phenomenon of full film lubrication (no metallic contact through the oil film) despite the fact that the highest peaks in the roughness distribution were often many times higher than the thickness of the lubricant film.
556 Already in 1958-59 F.W. Smith [9] had found that a Newtonian lubricant model could not describe the traction forces measured in combined rolling and sliding motion for heavily-loaded contacts. His measurements showed that the Newtonian model could only describe the tractional behaviour at very low sliding speeds, and when the sliding speed increased the shear stress reached a maximum and could even fall at higher sliding speeds. He concluded that lubricants had a shear strength which gave the maximum shear stress possible to transmit through the oil film. The concept of a limited shear strength and solid-like behaviour was used by Jacobson ( 101in 1970 in his calculation of oil film thickness for a point contact, see Figure 1. In the figure the oil film thickness and pressure distribution are shown and the region with solidified oil is indicated by a broken line in the pressure distribution. In the same report, shear strength measurementsfor oils solidified under pressure were recorded using the high pressure chamber shown in Figure 2. Later, measurements at higher pressures and temperatures (111, made in a new high pressure chamber, see Figure 3, revealed that the shear strength increased linearly with an increase in pressure: also, the pressure increase needed to retain the oil in the solid state at a higher temperature exactly matched the compression of the oil with the thermal expansion due to the increase in tempenture. The oil converted to a solid at a constant density, indpendent of temperature.
2
ROUGH SURFACES
As the mean lubricant film thickness in a rough, lubricated EHL contact seems mainly to be determined by the inlet zone, except for contacts at high sliding speeds when the lubricant is in a glassy state, the calculated film thickness could predict lubrication behaviour quite well for typical engineering surfaces in beatings and gears, despite the fact that the roughness peaks ought to have penetrated the oil film if their form was maintained in the EHL contact. The first indications that the simple EHL theory for smooth surfaces could not fully predict the behaviour of rough surfaces were noticed about 20 years ago when lubricated surfaces in combined rolling and sliding needed a thicker calculated oil film than predicted for pure rolling, in order not to damage the surfaces. It
could also be seen on gears where some running in took place. The simple EHL theory failed to provide an adequate description of solid contact through the oil film. As the elastohydrodynamic calculations assumed linear Newtonian behaviour [I] for the lubricant, one possible way to explain the oil film collapse was by assuming the lubricant to be no longer Newtonian. If the oil was non-Newtonian, an increase in shear strain rate would no longer give a shear stress increase proportional to the shear strain rate increase. This permitted enhanced pressure flow peqendicular to the relative sliding velocity of the bearing surfaces compared to that expected for the Newtonian case. Indeed, if this side flow was large enough, the whole macro-Hertzian contact would collapse within the contact time. For shorter times, it was still possible for an individual, compressed asperity to re-emerge from the surface. It was only necessary that, by virtue of a slightly higher pressure compared to the surrounding ambient level, the side flow was sufficient to empty the micro-contact. As the local asperity pressure fluctuations are functions of the heights and slopes of the asperities, the film collapse is governed by these as well as by the surface velocities. The steeper the pressure fluctuation, the faster the collapse of the oil film under the asperity, Asperities with low slopes will be elastically flattened by the pressure variations in the oil film while sharp and steep asperities will maintain their form until they touch the opposite surface, see Figure 4. Asperities with intermediate slopes will be elastically flattened at the inlet of the EHL contact but will slowly re-emerge into the oil film due to the elastic spring-back of the asperity, see Figure 5. Depending on how fast the asperities reemerge compared with the time available for the transport through the contact (typically lC3 to lo4 s), the asperities can touch through the oil film at the outlet or not. This phenomenon was experimentally shown by superimposing a sliding speed on normal squeeze motion between a polished steel ball and a flat lubricated surface using the test rig shown in Figure 6 (111. Oil film breakthrough was indicated by electric contact between the balls and the plate. Polished surfaces (R, = 0.008 pm) needed only 5 cSt viscosity to avoid metallic contact during the
557 impact time when the sliding speed was zero. A sliding speed of 0.14 m/s made it necessary to increase the viscosity to 26 cSt in order to avoid metal to metal contact. For a rough surface, R, = 0.18 pm, in contact with the polished ball, the viscosity needed to be much higher, 68 cSt at pure impact and between 7000 and 16300 cSt for a total sliding distance of 29 pm during the impact time. It was thus necessary to have a viscosity more than 100 times higher to keep the surfaces sepmted by an oil film when a sliding distance of 2.5 percent of the Hertzian contact width took place during impact. That sliding distance is of the m e order as the surface roughness wave length. The non-Newtonian behaviour of the lubricant allowed oil film breakthrough which could not be predicted by a Newtonian lubricant model.
3
SMOOTH SURFACES ASPERITY LUBRICATION
AND
In recent years the opposite effect has also been seen. For extremely smooth surfaces the asperity pressure gradients are not able to displace the lubricant sideways and cause an oil film collapse at the asperity level so that the lubricated contact behaves as if it was mathematically smooth [12]. This leads to oil film collapse only at very high sliding speeds and high loads when the whole Hertzian contact collapses. Depending on how far up on the shear stress-shear strain rate curve the lubricant stress point is situated, different behaviour will be experienced by the asperities. If the lubricant stress is far below its local shear strength, an increase of the shear rate will increase the shear stress and thereby build up steeper local pressure gradients. This leads to build-up of steep pressure spikes, both in pure rolling situations and in combined rolling and sliding. These pressure spikes above the high points of the surface structure flatten the surfaces locally and give them a lower effective roughness. This is probably one of the main reasons why well run-in surfaces can work without metallic contact through the oil film, even when the asperity heights are considerably larger than the calculated mean oil film thickness. The rule of thumb for choice of oil film thickness compared to the composite surface roughness of the lubricated surfaces can thus be explained if the roughness is about halved inside the
EHL contacts for good surfaces compared to the roughness outside the contact. The smoother the mating surfaces, the more important this phenomenon because both the local pressure gradients and the heights of the local pressure spikes go down. The decrease in the local pressure gradients decreases the risk of pushing out the oil from under the asperities for any given shear strength of the oil. At the m e time the lower asperity pressures will maintain the lubricant in the Newtonian state at the asperity tops and thus allow some sliding speed between the surfaces before the stress in the oil reaches the shear strength and gives the oil a much smaller effective shear strength in a direction perpendicular to the sliding direction. and thus can be pushed out from the asperity contact. The higher the sliding speed and the higher the local viscosity at the asperity tops, the further into the non-Newtonian behaviour regime the lubricant will come, and the earlier the asperity tops will break through the oil film.
4
CONCLUSIONS
The above leads to the conclusion that rough surfaces lubricated with oils having a high a-value (pressure viscosity coefficient) need a much thicker mean oil film compared to the surface roughness than smooth surfaces lubricated with low a-value I ubricants. Thus, the ratio between the mean oil film thickness and the surface roughness height needed for good lubrication steeply decreases when surfaces get smoother and the lubricants remain Newtonian in the EHL contact.
REFERENCES 1. 2.
3.
Newton, I. (1686), "Philosophiae Natumles Principia Mathematica". Imprimature S . Pepys, Reg. Soc. Praeses. 5 Julii, Londini. Petrov, N.P. (1883), "Friction in Machines and the Effect of the Lubricant", Inzh. Zh., St. Peterb.: 1.71-140; 2.227-279; 3.377-436; 4. 535-564. Martin, H.M.(1916), "Lubrication of Gear Teeth", Engineering (London), 102, 199.
558 4.
5.
6.
7.
Meldahl, A. (194I), "Contribution to Theory of Lubrication of Gears and of Stressing of Lubricated Flanks of Gear Teeth", Brown Boveri Rev., Vol. 28,No. 11, pp. 374-382. Ertel, A.M., "Hydrodynamic Lubrication Based on New Principles", Akad. Nauk SSSR, hikdnaya Malhematica i Mechanika, 3,2,4152. Grubin, A.N. and Vinogmdova, I.E. (1949), "Fundamentals of the Hydrodynamic Theory of Lubrication of Heavily Loaded Cylindrical Surfaces", Investigation of the Contact Machine Components, Kh. F. Ketova, ed.. Translation of Russian bdok No. 30,Central Scientific Institute for Technology and Mechanical Engineering, Chapter 2. Hamrock, BJ. and Dowson, D. (1977). "Isothermal Elastohydrodynamic Lubrication of Point Contacts: Part 111- Fully Flooded Results", J. Lubr. Technology, Vol. 99,No. 2,264-276.
Figure 1
8.
Harris, T.A. (1991). "Rolling Bearing Analysis", Third Edition, John Wiley & Sons, Inc. 9. Smith, F.W. (1958-59)."Lubricant Behimiour in Concentrated Contact Systems - The Castor Oil-Steel System", Wear, Vol. 2, 250-263. 10. Jacobson, Bo (1970), "On the Lubrication of Heavily Loaded Spherical Surfaces Considering Surface Deformations and Solidification of the Lubricant". Acta Polytechnica Scandinavica, Mech. Eng. Series No. 54,Stockholm. 11. Jacobson, Bo (1991). "Rheology and Elastohydrodynamic Lubrication", Tribology Series 19,Elsevier. 12. Cann, P. et al. (1994), "The Lambda Ratio A Critical Reexamination", Wear, 175, 177188.
Theoretical height function and pressure field The broken line surrounds the solidified region.
559
Figure 2
Photograph of the fust high pressure chamber.
Figure 3
Photograph of the second high pressure chamber.
-
560
EHk contact
Mo
micro-EHL
Figure 4
EHL contact with asperities of different slope.
Figure 5
Asperities flattened and reemerging during the transport through the contact.
56 1
View A-A Figure 6
Drawing of the test apparatus.