Engineering Tribology Episode 2 Part 6 ppt

350 ENGINEERING TRIBOLOGY temperature [56] and this characteristic cannot be neglected in any model of EHL with sliding present. EHL Between Meshing Gear Wheels From the view point of practical engineering an important EHL contact takes place between the lubricated teeth of opposing gears. As is the case with rolling bearings, it is essential to maintain an adequate EHL film thickness to prevent wear and pitting of the gear teeth. The same fundamental equations for EHL film thickness described for a simple Hertzian contact also apply for gears. However, before applying the formulae for contact parameters and minimum film thickness it is necessary to define reduced radius of curvature, contact load and surface velocity for a specific gear. The contact geometry is illustrated in Figure 7.42. ω A ω B ω a ω B ω A ψ ψ O B O A C 1 P S C C 2 R B R A R A sinψ + S R B sinψ − S Locus of contact Pitch circle Base circle Base circle Pitch circle W W h B h A FIGURE 7.42 Contact geometry of meshing involute gear teeth. The surface contact velocity is expressed as: U = U A + U B 2 = ω A R A sinψ+ω B R B sinψ 2 where: R A , R B are the pitch circle radii of the driver and follower respectively [m]; ψ is the pressure angle (acute angle between contact normal and the common tangent to the pitch circles); ω A , ω B are the angular velocities of the driver and follower respectively [rad/s]. Since: R A R B = ω B ω A Then the contact surface velocity is: TEAM LRN ELASTOHYDRODYNAMIC LUBRICATION 351 U = ω A R A sinψ = ω B R B sinψ (7.53) Assuming that the total load is carried by one tooth only then, from Figure 7.42, the contact load in terms of the torque exerted is given by: W = T B h B = T B R B cosψ (7.54) where: W is the total load on the tooth [N]; h B is the distance from the centre of the follower to interception of the locus of the contact with its base circle, i.e. h B = R B cosψ [m]; T B is the torque exerted on the follower [Nm]. The torque exerted on the driver and the follower expressed in terms of the transmitted power is calculated from: T A = H ω A = 9.55 H N A T B = H ω B = 9.55 H N B where: N A , N B are the rotational speeds of the driver and follower respectively [rps]; H is the transmitted power [kW]. Substituting into (7.54) yields the contact load. The minimum and central EHL film thicknesses can then be calculated from formulae (7.26) and (7.27). The line from ‘C 1 ’ to ‘C 2 ’ (Figure 7.42) is the locus of the contact and it can be seen that the distance ‘S’ between the gear teeth contact and the pitch line is continuously changing with the contact position during the meshing cycle of the gears. It is thus possible to model any specific contact position on the tooth surface of an involute gear by two rotating circular discs of radii (R A sinΨ + S) and (R B sin Ψ - S) as shown in Figure 7.42. This idea is applied in a testing apparatus generally known as a ‘twin disc’ or ‘two disc‘ machine shown schematically in Figure 7.43. Since the gear tooth contact is closely simulated by the two rotating discs, these machines are widely used to model gear lubrication and wear and in selecting lubricants or materials for gears. It is much cheaper and more convenient experimentally to use metal discs instead of actual gears for friction and wear testing. The wear testing virtually ensures the destruction of the test specimens and it is far easier to inspect and analyse a worn disc surface than the recessed surface of a gear wheel. It may also be apparent that the fixed dimensions of the discs only allow modelling of one particular position in the contact cycle. Of particular importance to friction and wear studies is the increasing amount of sliding as the contact between opposing gear teeth moves away from the line of shaft centres. The radii of curvature also vary with position of gear teeth so that the ‘two-disc’ test rig is not entirely satisfactory and another model gear apparatus such as the ‘Ryder gear tester’ may be necessary for some studies. A recently developed test- apparatus where two contacting discs are supplied with additional movement of their corresponding shafts allows a much closer, more realistic simulation of the entire gear tooth contact cycle [68]. TEAM LRN 352 ENGINEERING TRIBOLOGY ω A ω B R B sinψ − S W R A sinψ + S W FIGURE 7.43 Schematic diagram of a ‘two disc‘ machine used to simulate rolling/sliding contact in meshing gears, i.e.: for S = 0 pure rolling and for S ≠ 0 rolling/sliding in EHL contact; S is the distance between the pitch line and the gear teeth contact [m]. 7.8 SUMMARY A fundamental lubrication mechanism involved in highly loaded concentrated contacts was discussed in this chapter. The remarkable efficiency of elastohydrodynamic lubrication in preventing solid to solid contact even under extreme contact stresses prevents the rapid destruction of many basic mechanical components such as rolling bearings or gears. EHL is, however, mostly confined to mineral or synthetic oils since it is essential that the lubricant is piezo-viscous. The mechanism of EHL involves a rapid change in the lubricant from a nearly ideal liquid state outside of the contact to an extremely viscous or semi-solid state within the contact. This transformation allows the lubricant to be drawn into the contact by viscous drag while generating sufficient contact stress within the contact to separate the opposing surfaces. If a simple solid, i.e. a fine powder, is supplied instead, there is no viscous drag to entrain the powder and consequently only poor lubrication results. A non-piezo- viscous lubricant simply does not achieve the required high viscosity within the contact necessary for the formation of the lubricating film. The formulae for the calculation of the EHL film thickness are relatively simple and are based on load, velocity, dimensions and elastic modulus of the contacting materials. As well as providing lubrication of concentrated contacts, the EHL mechanism can be used to generate traction, i.e. where frictional forces enable power transmission. A unique combination of high tractive force with minimal wear, reduced noise levels, infinitely variable output speed and an almost constant torque over the speed range can be obtained by this means. REFERENCES 1 A.N. Grubin, Fundamentals of the Hydrodynamic Theory of Lubrication of Heavily Loaded Cylindrical Surfaces, in Investigation of the Contact Machine Components, Kh.F. Ketova, ed. Translation of Russian Book No. 30, Central Scientific Institute for Technology and Mechanical Engineering, Moscow, 1949. 2 H.M. Martin, Lubrication of Gear Teeth, Engineering, London, Vol. 102, 1916, pp. 119-121. 3 D. Dowson and G.R. Higginson, Elastohydrodynamic Lubrication, Pergamon Press, Oxford, 1977. 4 A.W. Crook, Elastohydrodynamic Lubrication of Rollers, Nature, Vol. 190, 1961, pp. 1182. 5 A. Cameron and R. Gohar, Optical Measurement of Oil Film Thickness under Elasto-hydrodynamic Lubrication, Nature, Vol. 200, 1963, pp. 458-459. TEAM LRN ELASTOHYDRODYNAMIC LUBRICATION 353 6 H. Hertz, Uber die Beruhrung Fester Elastischer Korper, (On the Contact of Elastic Solids), J. Reine und Angewandte Mathematik, Vol. 92, 1881, pp. 156-171. 7 B.J. Hamrock and D. Dowson, Ball Bearing Lubrication, The Elastohydrodynamics of Elliptical Contacts, John Willey & Sons, 1981. 8 H. Hertz, Miscellaneous Papers by H. Hertz, Jones & Schott (eds), Macmillan, London, 1986. 9 K.L. Johnson, Contact Mechanics, Cambridge University Press, 1985. 10 B.J. Hamrock and W.J. Anderson, Analysis of an Arched Outer-Race Ball Bearing Considering Centrifugal Forces, Transactions ASME, Journal of Lubrication Technology, Vol. 95, 1973, pp. 265-276. 11 R. Gohar, Elastohydrodynamics, Ellis Horwood Limited, 1988. 12 D.E. Brewe and B.J. Hamrock, Simplified Solution for Elliptical Contact Deformation Between Two Elastic Solids, Transactions ASME, Journal of Lubrication Technology, Vol. 99, 1977, pp. 485-487. 13 F.T. Barwell, Bearing Systems, Principles and Practice, Oxford University Press, 1979. 14 Engineering Sciences Data Unit, Stress and Strength Sub-Series, Contact Stresses, Vol. 9, No. 78035, 1985. 15 H. Christensen, The Oil Film in a Closing Gap, Proc. Roy. Soc., London, Series A, Vol. 266, 1962, pp. 312-328. 16 B.J. Hamrock and D. Dowson, Isothermal Elastohydrodynamic Lubrication of Point Contacts, Part III - Fully Flooded Results, Transactions ASME, Journal of Lubrication Technology, Vol. 99, 1977, pp. 264-276. 17 K.A. Kaye and W.O. Winer, An Experimental Evaluation of the Hamrock and Dowson Minimum Film Thickness Equation for Fully Flooded EHD Point Contact, Transactions ASME, Journal of Lubrication Technology, Vol. 103, 1981, pp. 284-294. 18 D. Dowson and A.V. Whitaker, A Numerical Procedure for the Solution of the Elastohydrodynamic Problems of Rolling and Sliding Contacts Lubricated by Newtonian Fluid, Proc. Inst. Mech. Engrs., London, Vol. 180, Pt. 3B, 1965-1966, pp. 57-71. 19 B.J. Hamrock and D. Dowson, Minimum Film Thickness in Elliptical Contacts for Different Regimes of Fluid- Film Lubrication, Proc. 5th Leeds-Lyon Symp. on Tribology, Elastohydrodynamics and Related Topics, editors: D. Dowson, C.M. Taylor, M. Godet and D. Berthe, Sept. 1978, Inst. Mech. Engrs. Publ., London, 1979, pp. 22-27. 20 A.W. Crook, The Lubrication of Rollers, Part I, Phil. Trans. Roy. Soc., London, Series A, Vol. 250, 1958, pp. 387-409. 21 A. Dyson, H. Naylor and A.R. Wilson, The Measurement of Oil Film Thickness in Elastohydrodynamic Contacts, Proc. Inst. Mech. Engrs., Vol. 180, Pt. 3B, 1965, pp. 119-134. 22 L.B. Sibley, J.C. Bell, F.K. Orcutt and C.M. Allen, A Study of the Influence of Lubricant Properties on the Performance of Aircraft Gas Engine Rolling Contact Bearings, WADD Technical Report, 1960, pp. 60-189. 23 L.B. Sibley and A.E. Austin, An X-Ray Method for Measuring Thin Lubricant Films Between Rollers, ISA Transactions, Vol. 3, 1962, pp. 237-243. 24 D.R. Meyer and C.C. Wilson, Measurement of Elastohydrodynamic Oil Film Thickness and Wear in Ball Bearings by the Strain Gage Method, Transactions ASME, Journal of Lubrication Technology, Vol. 93, 1971, pp. 224-230. 25 A.T. Kirk, Hydrodynamic Lubrication of Perspex, Nature, Vol. 194, 1962, pp. 965-966. 26 A. Cameron and R. Gohar, Theoretical and Experimental Studies of the Oil Film in Lubricated Point Contacts, Proc. Roy. Soc., London, Series A, Vol. 291, 1966, pp. 520-536. 27 N. Thorp and R. Gohar, Oil Film Thickness and Shape for Ball Sliding in a Grooved Raceway, Transactions ASME, Journal of Lubrication Technology, Vol. 94, 1972, pp. 199-210. 28 D. Dowson, Recent Developments in Studies of Fluid Film Lubrication, Proc. Int. Tribology Conference, Melbourne, The Institution of Engineers, Australia, National Conference Publication No. 87/18, December, 1987, pp. 353-359. 29 T.E. Tallian, On Competing Failure Modes in Rolling Contact, ASLE Transactions, Vol. 10, 1967, pp. 418-439. 30 K.L. Johnson, J.A. Greenwood and S.Y. Poon, A Simple Theory of Asperity Contact in Elastohydrodynamic Lubrication, Wear, Vol. 19, 1972, pp. 91-108. 31 J.A. Greenwood and J.B.P. Williamson, Contact of Nominally Flat Surfaces, Proc. Roy. Soc., London, Series A, Vol. 295, 1966, pp. 300-319. 32 T.E. Tallian and J.I. McCool, An Engineering Model of Spalling Fatigue Failure in Rolling Contact, II. The Surface Model, Wear, Vol. 17, 1971, pp. 447-461. TEAM LRN 354 ENGINEERING TRIBOLOGY 33 R.S. Sayles, G.M.S. deSilva, J.A. Leather, J.C. Anderson and P.B. Macpherson, Elastic Conformity in Hertzian Contacts, Tribology International, Vol. 14, 1981, pp. 315-322. 34 G.M.S. De Silva, J.A. Leather and R.S. Sayles, The Influence of Surface Topography on Lubricant Film Thickness in EHD Point Contact, Proc. 12th Leeds-Lyon Symp. on Tribology, Mechanisms and Surface Distress: Global Studies of Mechanisms and Local Analyses of Surface Distress Phenomena, editors: D. Dowson, C.M. Taylor, M. Godet and D. Berthe, Sept. 1985, Inst. Mech. Engrs. Publ., London, 1986, pp. 258-272. 35 N. Patir and H.S. Cheng, Effect of Surface Roughness Orientation on the Central Film Thickness in EHD Contacts, Proc. 5th Leeds-Lyon Symp. on Tribology, Elastohydrodynamics and Related Topics, editors: D. Dowson, C.M. Taylor, M. Godet and D. Berthe, Sept. 1978, Inst. Mech. Engrs. Publ., London, 1979, pp. 15-21. 36 H.S. Cheng, On Aspects of Microelastohydrodynamic Lubrication, Proc. 4th Leeds-Lyon Symp. on Tribology, Surface Roughness Effects in Lubrication, editors: D. Dowson, C.M. Taylor, M. Godet and D. Berthe, Sept. 1977, Inst. Mech. Engrs. Publ., London, 1978, pp. 71-79. 37 X. Ai and L. Zheng, A General Model for Microelastohydrodynamic Lubrication and its Full Numerical Solution, Transactions ASME, Journal of Tribology, Vol. 111, 1989, pp. 569-576. 38 P. Goglia, T.F. Conry and C. Cusano, The Effects of Surface Irregularities on the Elastohydrodynamic Lubrication of Sliding Line Contacts, Parts 1 and 2, Transactions ASME, Journal of Tribology, Vol. 106, 1984, Part 1, pp. 104-112, Part 2, pp. 113-119. 39 C.C. Kweh, H.P. Evans and R.W. Snidle, Micro-Elastohydrodynamic Lubrication of an Elliptical Contact With Transverse and 3-D Sinusoidal Roughness, Transactions ASME, Journal of Tribology, Vol. 111, 1989, pp. 577-584. 40 L. Chang and M.N. Webster, A Study of Elastohydrodynamic Lubrication of Rough Surfaces, Transactions ASME, Journal of Tribology, Vol. 113, 1991, pp. 110-115. 41 L.G. Houpert and B.J. Hamrock, EHD Lubrication Calculation Used as a Tool to Study Scuffing, Proc. 12th Leeds-Lyon Symp. on Tribology, Mechanisms and Surface Distress: Global Studies of Mechanisms and Local Analyses of Surface Distress Phenomena, editors: D. Dowson, C.M. Taylor, M. Godet and D. Berthe, Sept. 1985, Inst. Mech. Engrs. Publ., London, 1986, pp. 146-155. 42 K.P. Baglin, EHD Pressure Rippling in Cylinders Finished With a Circumferential Lay, Proc. Inst. Mech. Engrs, Vol. 200, 1986, pp. 335-347. 43 B. Michau, D. Berthe and M. Godet, Influence of Pressure Modulation in Line Hertzian Contact on the Internal Stress Field, Wear, Vol. 28, 1974, pp. 187-195. 44 J.F. Archard and R.A. Rowntree, The Temperature of Rubbing Bodies, Part 2, The Distribution of Temperature, Wear, Vol. 128, 1988, pp. 1-17. 45 F.P. Bowden and D. Tabor, Friction and Lubricating Wear of Solids, Part 1, Oxford: Clarendon Press, 1964. 46 H. Blok, Theoretical Study of Temperature Rise at Surfaces of Actual Contact Under Oiliness Lubricating Conditions, General Discussion on Lubrication, Inst. Mech. Engrs, London, Vol. 2, 1937, pp. 222-235. 47 J.C. Jaeger, Moving Sources of Heat and the Temperature at Sliding Contacts, Proc. Roy. Soc., N.S.W., Vol. 76, 1943, pp. 203-224. 48 J.F. Archard, The Temperature of Rubbing Surfaces, Wear, Vol. 2, 1958/59, pp. 438-455. 49 F.E. Kennedy, Thermal and Thermomechanical Effects in Dry Sliding, Wear, Vol. 100, 1984, pp. 453-476. 50 H. Blok, The Postulate About the Constancy of Scoring Temperature, Interdisciplinary Approach to Lubrication of Concentrated Contacts, P.M. Ku (ed.), Washington DC, Scientific and Technical Information Division, NASA, 1970, pp. 153-248. 51 T.A. Stolarski, Tribology in Machine Design, Heineman Newnes, 1990. 52 V.K. Ausherman, H.S. Nagaraj, D.M. Sanborn and W.O. Winer, Infrared Temperature Mapping in Elastohydrodynamic Lubrication, Transactions ASME, Journal of Lubrication Technology, Vol. 98, 1976, pp. 236-243. 53 V.W. King and J.L. Lauer, Temperature Gradients Through EHD Films and Molecular Alignment Evidenced by Infrared Spectroscopy, Transactions ASME, Journal of Lubrication Technology, Vol. 103, 1981, pp. 65-73. 54 A.R. Wilson, An Experimental Thermal Correction for Predicted Oil Film Thickness in Elastohydrodynamic Contacts, Proc. 6th Leeds-Lyon Symp. on Tribology, Thermal Effects in Tribology, Sept. 1979, editors: D. Dowson, C.M. Taylor, M. Godet and D. Berthe, Inst. Mech. Engrs. Publ., London, 1980, pp. 179-190. 55 J.L. Tevaarwerk, Traction Calculations Using the Shear Plane Hypothesis, Proc. 6th Leeds-Lyon Symp. on Tribology, Thermal Effects in Tribology, Sept. 1979, editors: D. Dowson, C.M. Taylor, M. Godet and D. Berthe, Inst. Mech. Engrs. Publ., London, 1980, pp. 201-215. TEAM LRN ELASTOHYDRODYNAMIC LUBRICATION 355 56 H.A. Spikes and P.M. Cann, The Influence of Sliding Speed and Lubricant Shear Stress on EHD Contact Temperatures, Tribology Transactions, Vol. 33, 1990, pp. 355-362. 57 W.O. Winer and E.H. Kool, Simultaneous Temperature Mapping and Traction Measurements in EHD Contacts, Proc. 6th Leeds-Lyon Symp. on Tribology, Thermal Effects in Tribology, Sept. 1979, editors: D. Dowson, C.M. Taylor, M. Godet and D. Berthe, Inst. Mech. Engrs. Publ., London, 1980, pp. 191-200. 58 T.A. Dow and W. Kannel, Evaluation of Rolling/Sliding EHD Temperatures, Proc. 6th Leeds-Lyon Symp. on Tribology, Thermal Effects in Tribology, Sept. 1979, editors: D. Dowson, C.M. Taylor, M. Godet and D. Berthe, Inst. Mech. Engrs. Publ., London, 1980, pp. 228-240. 59 K.L. Johnson and J.A. Greenwood, Thermal Analysis of an Eyring Fluid in Elastohydrodynamic Traction, Wear, Vol. 61, 1980, pp. 353-374. 60 J.L. Lauer and Y-J. Ahn, Lubricants and Lubricant Additives Under Shear Studied Under Operating Conditions by Optical and Infra Red Spectroscopic Methods, Tribology Transactions, Vol. 31, 1988, pp. 120- 127. 61 P.M. Cann and H.A. Spikes, In Lubro Studies of Lubricants in EHD Contacts Using FITR Absorption Spectroscopy, Tribology Transactions, Vol. 34, 1991, pp. 248-256. 62 F.L. Snyder, J. L. Tevaarwerk and J. A. Schey, Effects of Oil Additives on Lubricant Film Thickness and Traction, SAE Tech. Paper No. 840263, 1984. 64 M. Alsaad, S. Bair, D.M. Sanborn and W.O. Winer, Glass Transitions in Lubricants: Its Relation to Elastohydrodynamic Lubrication (EHD), Transactions ASME, Journal of Lubrication Technology, Vol. 100, 1978, pp. 404-417. 63 S. Bair and W.O. Winer, Some Observations in High Pressure Rheology of Lubricants, Transactions ASME, Journal of Lubrication Technology, Vol. 104, 1982, pp. 357-364. 65 M. Kaneta, H. Nishikawa and K. Kameishi, Observation of Wall Slip in Elastohydrodynamic Lubrication, Transactions ASME, Journal of Tribology, Vol. 112, 1990, pp. 447-452. 66 K.L. Johnson and J.G. Higginson, A Non-Newtonian Effect of Sliding in Micro-EHL, Wear, Vol. 128, 1988, pp. 249-264. 67 K.L. Johnson and J.L. Tevaarwerk, Shear Behaviour of Elastohydrodynamic Oil Films, Proc. Roy. Soc., London, Series A, Vol. 356, 1977, pp. 215-236. 68 E. Van Damme, Surface Engineering, Gear Wear Simulations, Proc. International Tribology Conference, Melbourne, 1987, The Institution of Engineers, Australia, National Conference Publication No. 87/18, December, 1987, pp. 391-396. 69 C.A. Foord, W.C. Hammann and A. Cameron, Evaluation of Lubricants Using Optical Elastohydrodynamics, ASLE Transactions, Vol. 11, 1968, pp. 31-43. 70 P.L. Wong, P.Huang, W. Wang and Z. Zhang, Effect of Geometry Change of Rough Point Contact Due to Lubricated Sliding Wear on Lubrication, Tribology Letters, Vol. 5, 1998, pp. 265-274. 71 C. Bovington, Elastohydrodynamic Lubrication: a Lubricant Industry Perspective, Proc. Inst. Mech. Eng., Part J, Journal of Engineering Tribology, Vol. 213, 1999, pp. 417-426. TEAM LRN 356 ENGINEERING TRIBOLOGY TEAM LRN EXTREMEBOUNDARY 8 PRESSURE LUBRICATION AND 8.1 INTRODUCTION In many practical applications there are cases where the operating conditions are such that neither hydrodynamic nor EHL lubrication is effective. The question then is: how are the interacting machine components lubricated and what is the lubrication mechanism involved? The models of lubrication which are thought to operate under such conditions are discussed in this chapter. The traditional name for this type of lubrication is ‘boundary lubrication’ or ‘boundary and extreme-pressure lubrication’. Neither of these terms describe accurately the processes at work since they were conceived long before any fundamental understanding of the mechanisms was available. Several specialized modes of lubrication such as adsorption, surface localized viscosity enhancement, amorphous layers and sacrificial films are commonly involved in this lubrication regime to ensure the smooth-functioning and reliability of machinery. The imprecise nature of present knowledge about these modes or mechanisms of lubrication contrasts with their practical importance. Many vital items of engineering equipment such as steel gears, piston-rings and metal-working tools depend on one or more of these lubrication modes to prevent severe wear or high coefficients of friction and seizure. Boundary and E.P. lubrication is a complex phenomenon. The lubrication mechanisms involved can be classified in terms of relative load capacity and limiting frictional temperature as shown in Table 8.1, and they will be described in this chapter. These lubrication mechanisms are usually controlled by additives present in the oil. Since the cost of a lubricant additive is usually negligible compared to the value of the mechanical equipment, the commercial benefits involved in this type of lubrication can be quite large. In general, boundary and E.P. lubrication involves the formation of low friction, protective layers on the wearing surfaces. One exception is when the surface-localized viscosity enhancement takes place. The occurrence of surface-localized viscosity enhancement, however, is extremely limited as is explained in the next section. The operating principle of the boundary lubrication regime can perhaps be best illustrated by considering the coefficient of friction. In simple terms the coefficient of friction ‘µ’ is defined as the ratio of frictional force ‘F’ and the load applied normal to the surface ‘W’, i.e.: µ = F/W (8.1) TEAM LRN 358 ENGINEERING TRIBOLOGY TABLE 8.1 Categories of boundary and E.P. lubrication. Temperature Load Lubrication mechanisms Low Low High High Medium High Viscosity enhancement close to contacting surface, not specific to lubricant. Friction minimization by coverage of contacting surfaces with adsorbed mono-molecular layers of surfactants. Irreversible formation of soap layers and other viscous materials on worn surface by chemical reaction between lubricant additives and metal surface. Surface-localized viscosity enhancement specific to lubricant additive and basestock. Formation of amorphous layers of finely divided debris from reaction between additives and substrate metal surface. Reaction between lubricant additives and metal surface. Formation of sacrificial films of inorganic material on the worn surface preventing metallic contact and severe wear. Since the contacting surfaces are covered by asperities, ‘dry’ contact is established between the individual asperities and the ‘true’ total contact area is the sum of the individual contact areas between the asperities. Assuming that the major component of the frictional force is due to adhesion between the asperities (other effects, e.g. ploughing, are negligible), then the expression for frictional force ‘F’ can be written as: F = A t τ where: F is the frictional force [N]; A t is the true contact area [m 2 ]; τ is the effective shear stress of the material [Pa]. Applied load can be expressed in terms of contact area, i.e.: W = A t p y where: p y is the plastic flow stress of the material (close in value to the indentation hardness) [Pa]. Substituting for ‘F’ and ‘W’ to (8.1) yields: µ = τ/p y (8.2) This simple model explains the rationale behind boundary lubrication. It can be seen from equation (8.2) that in order to obtain a low coefficient of friction, material of low shear strength and high hardness is required. These requirements are clearly incompatible. However, if a low shear-strength layer can be formed on a hard substrate then low coefficients of friction can be achieved. Thus, in general terms, the fundamental principles behind boundary and E.P. lubrication involve the formation of low shear-strength lubricating layers on hard substrates. It is evident that, since with most materials the ratio of ‘τ’ and ‘p y ’ does not vary greatly, changing the material type has little effect on friction. TEAM LRN BOUNDARY AND EXTREME PRESSURE LUBRICATION 359 8.2 LOW TEMPERATURE - LOW LOAD LUBRICATION MECHANISMS For a very large range of sliding speeds and loads, classical hydrodynamic lubrication prevails in a lubricated contact. As the sliding speed is reduced, hydrodynamic lubrication reaches its limit where the hydrodynamic film thickness declines until eventually the asperities of the opposing surfaces interact. This process was originally investigated by Stribeck and has already been discussed in Chapter 4. At low speeds, under certain conditions, contact between opposing surfaces can be prevented by the mechanism involving surface-localized viscosity enhancement. In other words, a thin layer of liquid with an anomalously high viscosity can form on the contacting surfaces. Hydrodynamic lubrication or quasi-hydrodynamic lubrication then persists to prevent solid contact and severe wear. In such cases linear molecules of a hydrocarbon align themselves normally to the contacting surfaces to form a lubricating, protective layer as shown in Figure 8.1. Since the molecules are polar the opposite ends are attracted to form pairs of molecules which are subsequently incorporated into the viscous surface layer. At the interface with the metallic substrate the attractive force of the free end of the molecules to the substrate is sufficient to firmly bond the entire layer. FIGURE 8.1 Low-temperature, low-load mechanism of lubrication [1]. It has been found that linear molecules are more effective than other hydrocarbons in preventing solid contact. The variation in film thickness between parallel discs as a function of the square root of squeeze time for paraffinic oil and cyclohexane is shown in Figure 8.2 [2]. According to the theory of hydrodynamic lubrication described in Chapter 4, there is a linear decline in film thickness with square root of squeeze time but as can be seen from Figure 8.2 this linearity is soon lost. The MS-20 oil contains paraffinic molecules which are approximately linear and this allows for the formation and persistence of a thicker film than for cyclohexane. Cyclohexane is a non-linear molecule which impedes the linear alignment of molecules and therefore the resulting film is less effective in preventing solid contact. The effectiveness of this mechanism of lubrication is limited to low temperatures and low loads. The data shown in Figure 8.2 was obtained at contact pressures of 0.4 [MPa], and further work revealed that at contact pressures beyond 2 [MPa] the residual film thickness is very small [2]. Since in many contacts pressures in the range of 1 [GPa] are quite common, the TEAM LRN [...]... LUBRICATION TABLE 8 .2 365 Frictional data for lauric acid lubricating metals of varying reactivity [15] Material Zinc Cadmium Copper Magnesium Platinum Nickel Aluminium Chromium Glass Silver Coefficient of friction at 20 °C Transition temperature [°C] % acid* reacting Type of sliding at 20 °C 0.04 0.05 0.08 0.08 0 .25 0 .28 0.30 0.34 0.3 − 0.4 0.55 94 103 97 80 20 20 20 20 20 20 10.0 9.3 4 .6 Trace 0.0 0.0... neglected by most researchers Time [h] Minimum film thickness [µm] 0.4 0 0 .25 0.5 1 1.5 2 2.5 Measured at a contact pressure of 0.4 MPa 0.3 0 .2 Paraffinic oil MS -20 0.1 Cyclohexane 0 0 10 20 30 40 50 60 70 80 90 100 t [s0.5] FIGURE 8 .2 8.3 Detection of permanent films formation as evidence of a surface-proximal layer of aligned molecules [2] LOW TEMPERATURE - HIGH LOAD LUBRICATION MECHANISMS The lubrication... to occur within the time available between successive sliding contacts This model is illustrated schematically in Figure 8 .20 TEAM LRN 3 72 ENGINEERING TRIBOLOGY µ 0.4 0.3 Lauric acid Myristic acid Palmitic acid 0 .2 Stearic acid Behenic acid 0.1 0.01 0. 02 0.05 0.1 0 .2 0.5 1 2 5 10 20 50 100 Concentration of additive [Moles/m3] FIGURE 8.19 Effect of solute fatty acid concentration on friction coefficients... friction [22 ] An adsorbate with its modified structure is shown in Figure 8.14 Much of the knowledge of adsorbate films is still provisional Although effective forms of adsorption are known, these can always be superseded by newly developed adsorbates a) b) Stearic acid α-Hydroxy palmitic acid CH3(CH2)16COOH CH3(CH2)13CHCOOH OH FIGURE 8.14 Diagram of a fatty acid (a) and a polymerized derivative (b) [22 ]... isostearic acid in paraffinic oil are shown [20 ] TEAM LRN BOUNDARY AND EXTREME PRESSURE LUBRICATION µ 1.0 0.9 0.8 0.7 0 .6 0.5 0.4 0.3 0 .2 0.1 0 367 Isostearic acid Stearic acid 0 0.01 0. 02 0.03 0.04 0.05 0. 06 0.07 Concentration [Moles/litre] FIGURE 8.11 Effect of varying concentrations of stearic and isostearic acid in paraffinic oil on the coefficient of friction [20 ] The difference between the molecular... seen from Figure 8 .22 that there is no gradual decline in film thickness to a zero value and there is no pre-indicator of film collapse These characteristics constitute a major limitation in the application of lubricated gears TEAM LRN 374 ENGINEERING TRIBOLOGY 0.3 Voltage drop across contact [V] Pitch line 0 .2 Scuffing Incipient Final 0.1 Base of gear teeth 0 0 0.1 0 .2 0.3 0.4 0.5 0 .6 0.7 0.8 0.9 1.0... chemisorption, which is in fact fundamental to lubrication [ 26 ,27 ] µ 0.9 0.8 0.7 0 .6 Surface previously abraded under water 0.5 Surface cut under lubricant Surface previously cut in air and wetted with water 0.4 0.3 0 .2 0.1 0 Mg Cd Zn Cu Fe Al Pt Ag Noble metals: no oxide film FIGURE 8.17 Friction data for metals with clean and oxidized surfaces [23 ] This indicates a fundamental weakness of adsorption... lubrication first postulated by Hardy and Doubleday [4,5] and later developed by Bowden and Tabor [6] The fatty acids are particularly effective because of their strong polarity, but other organic compounds such as alcohols and amines have sufficient polarity to be of practical use TEAM LRN 3 62 ENGINEERING TRIBOLOGY Intermolecular contact and load support Carboxyl group Fatty (i.e −COOH) acid Alkyl tail... molecular weight was raised [6] More importantly, there is a critical minimum chain length of fatty acids required in order to provide effective lubrication It was found that the minimum chain length for effective lubrication is n = 9 (pelargonic acid) [6] An increase in ‘n’ from 9 to 18 (stearic acid) raises the friction transition temperature TEAM LRN 366 ENGINEERING TRIBOLOGY by about 40°C Short... (lauric) lubricating platinum 0.3 C Copper laurate lubricating platinum D Fatty acid (lauric) lubricating copper 0 .2 0.1 0 0 100 20 0 Temperature [°C] FIGURE 8 .6 Effect of temperature on friction of platinum and copper surfaces lubricated by docosane and lauric acid [6] It can be seen from Figure 8 .6 that there is a sharp rise in friction at some ‘transition temperature’ which is about 45°C for the platinum . of Lubrication Technology, Vol. 93, 1971, pp. 22 4 -23 0. 25 A.T. Kirk, Hydrodynamic Lubrication of Perspex, Nature, Vol. 194, 19 62 , pp. 965 - 966 . 26 A. Cameron and R. Gohar, Theoretical and Experimental. ASME, Journal of Tribology, Vol. 1 12, 1990, pp. 447-4 52. 66 K.L. Johnson and J.G. Higginson, A Non-Newtonian Effect of Sliding in Micro-EHL, Wear, Vol. 128 , 1988, pp. 24 9 - 26 4. 67 K.L. Johnson. Engrs, London, Vol. 2, 1937, pp. 22 2 -23 5. 47 J.C. Jaeger, Moving Sources of Heat and the Temperature at Sliding Contacts, Proc. Roy. Soc., N.S.W., Vol. 76, 1943, pp. 20 3 -22 4. 48 J.F. Archard,