coefficient of friction usually accompanied by a severe rearrangement of surface material with little loss of material. In most other sliding pairs there is no connection between the coefficient of friction and wear rate. Static and Kinetic Friction The force required to begin sliding is usually greater than the force required to sustain sliding. For dry surfaces the reason for the starting (or static) coefficient of friction being larger than the sliding (or kinetic) coefficient of friction may most simply be explained in terms of the adhesion of asperities. It is often found that the static coefficient of friction increases with time of standing. This suggests diffusion bonding of the points of contact which progresses with time. Sustained sliding could be viewed as providing a very short standing time of one asperity upon another. This should also produce a decrease in the coefficient of friction as the sliding speed increases, which is found in many systems. When a hard sphere slides on some plastics, the frictional behavior is such as to require a new definition of static friction. For example, for a sphere of steel sliding on Nylon 6-6 the coefficient of friction at 60°C varies with sliding speed as shown in Figure 6. The “static” coefficient of friction is lower than that at v 2 . Most observers would, however, measure the value of µ at v 2 as the static value of µ. The reason is that v 1 in the present example is imperceptibly slow. The coefficient of friction at the start of visible sliding at v 2 is higher than at v 3 . In this case it may be useful to define the starting coefficient of friction as that at v 2 and the static coefficient of friction as that at or below v 1 . In lubricated systems the starting friction is often higher than the kinetic friction. When the surfaces slide, lubricant is dragged into the contact region and separates the surfaces. This will initially lower the coefficient of friction, but at a still higher sliding speed there is a viscous drag which again causes an increase in coefficient of friction as shown in Figure 9. This McKee-Petroff curve is typical for a shaft rotated in a sleeve bearing. The abscissa 42CRC Handbook of Lubrication FIGURE 9.Coefficient of friction pattern for a typical lubricated contact. Z is lubricant vis- cosity, N′ shaft speed, and P the unit load transferred radially by the shaft to the bearing. Copyright © 1983 CRC Press LLC is given in units of ZN′/P where Z is the viscosity of the lubricant, N′ is the shaft rotating speed, and P is the load transferred radially from the shaft to the bearing. ROLLING FRICTION The force required to initiate rolling motion may be larger than the force to maintain motion if the contacting surfaces are very rough. Sustained rolling motion requires very little force, usually about 0.01 times that for unlubricated sliding. There are at least three causes for rolling resistance. The first arises from the strains within each of the solid bodies in the region of contact. During rolling a point in each body passes through complex strain cycles; since energy is lost during a cycle of strain in all materials, energy must be supplied to sustain rolling. The second reason for rolling friction is due to differences in distortion of the contacting bodies. This can be seen by pressing the eraser of a pencil into the palm of the hand. During indentation the skin of the hand stretches, in the contact region as well as outside of it, more than the eraser increases in size. Thus, there is relative slip between the eraser and the hand. The same occurs between a ball and flat surfaces and the net effect is that energy is expended in rolling. The effect of the micro-slip can be decreased by lubrication. A third reason for rolling friction may be that the rolling bodies are not moving in the direction of the applied force. A misaligned roller slides axially to some extent and a poorly guided ball spins about the contact region. Again, lubrication will reduce the energy loss due to slip. Frictional resistance of ball and roller bearing assemblies is usually much greater than the rolling resistance of simple rolling elements because of the cages, grooves, and shoulders intended to control the travel of the balls or rollers. Tapping and Jiggling to Reduce Friction One of the practices in the use of instruments is to tap and/or jiggle to obtain accurate readings. There are two separate effects. One effect is achieved by tapping the face of a meter or gage, which may cause the sliding surfaces in the gage to separate momentarily, reducing friction resistance to zero. The sliding surfaces (shafts in bearings, or racks on gears) will advance some distance before contact between the surfaces is reestablished. Continued tapping will allow the surfaces to progress until the force to move the gage parts is reduced to zero. Jiggling is best described by using the example of a shaft advanced axially through an O-ring. Such motion requires the application of a force to overcome friction. Rotation of the shaft also requires overcoming friction, but rotation reduces the force required to effect axial motion. In lubricated systems the mechanism may involve the formation of a thick fluid film between the shaft and the O-ring. In a dry system an explanation may be given in terms of components of forces. Frictional resistance force usually acts in the exact opposite direction as the direction of relative motion between sliding surfaces. If the shaft is rotated at a moderate rate, there will be very little frictional resistance to slow axial motion. In some apparatus the shaft is rotated in an oscillatory manner to avoid difficulties due to anisotropic (grooved) frictional behavior. Such oscillatory rotation may be referred to as jiggling, fiddling, or coaxing. STICK-SLIP MOTION Principles of Stick-Slip Some sliding systems vibrate. Vibration can be a mere annoyance such as the squeal of automobile brakes or door hinges. Other vibrations serve to notify of abnormal conditions, Volume II 43 Copyright © 1983 CRC Press LLC such as in the squeal of automobile tires and unlubricated electric motors. In other instances, vibration may compromise the function of a machine. In machine tools, surface finish and shape of final parts are affected by the vibration of tool carriers. 13 Vibration of sliding systems is usually described as stick-slip, frictional vibration, or frictional oscillation. In the simple model of Figure 10, an object of weight Wis connected to a prime mover by a spring. As the prime mover moves at constant speed in the direction shown, the spring stretches until it applies a force to Wthat will initiate sliding. If the coefficient of friction remains constant after sliding begins, the weight Wwill advance at the same speed as the prime mover. If on the other hand, the coefficient of friction decreases after sliding begins, less force will be required to sustain sliding than the spring force. Weight Wwill, therefore, accelerate, shortening the spring, and finally overshooting the equilibrium position. The spring then exerts a force less than that required to sustain sliding so the weight decelerates and may even stop. After deceleration, its velocity is lower than before and the coefficient of friction may increase. To meet the increased force required to sustain or reinitiate sliding, the spring must stretch. This produces a never ending cycle with the weight advancing by a series of fast and slow segments of motion. An experimental trace of the force exerted by the spring will show interesting differences depending upon the speed of the prime mover as shown in Figure 11. The upper trace for slow velocity shows true stick-slip as the force drops to nearly zero as the object comes to a standstill and the prime mover then advances to stretch the spring once more. In the second trace where the velocity is moderately high, force variations are smaller and the weight oscillates between two limiting sliding speeds in frictional oscillation. In the simplest approach, where the coefficient of friction between the sliding object and the table is taken to be µ k when sliding occurs and µ s to start sliding, and where µ s > µ k , motion of the weight would follow simple laws of dynamics. Thus, one could reasonably expect that the frequency of frictional oscillations would be low at low speeds of the prime mover, with a large weight, and with a flexible or compliant spring. The frictional oscillations would diminish at high speeds of the prime mover, with small weights and with stiff springs, producing the lower trace of Figure 11. It is of great commercial interest to design sliding systems to eliminate or minimize vibration. In general, the larger the difference (µ s – µ k ), the more likely a system will oscillate. The transition from µ s to µ k is influenced by the surface finish of the sliding parts and by the physical and chemical nature of the lubricant. In general, µ k rises as velocity decreases, as lubricant viscosity increases, as chemical reactivity of lubricant with surfaces increases, and as surface finish decreases. 13 In machine design it may be possible to stiffen the connection between the prime mover and sliding object, to reduce the weight of the sliding object, or to provide a thick fluid film. An additional design consideration is that frictional oscillation can produce pitching and yawing motion of the moving element if the driving force is applied at a different plane 44CRC Handbook of Lubrication FIGURE 10.Simplified model of vibrating sliding system. Copyright © 1983 CRC Press LLC Table 2 COEFFICIENTS OF STATIC AND SLIDING FRICTION 46 CRC Handbook of Lubrication Copyright © 1983 CRC Press LLC Table 2 (continued) COEFFICIENTS OFSTATIC AND SLIDING FRICTION Note:Reference letters indicate the lubricant used; numbers in parentheses give sources (see References). Key to Lubricants Used: a = oleic acidm = turbine oil (medium mineral) b = Atlantic spindle oil (light mineral)n = olive oil c = castor oilp = palmitic acid d = lard oilq = ricinoleic acid e = Atlantic spindle oil plus 2% oleic acidr = dry soap f = medium mineral oils = lard g = medium mineral oil plus 1 / 2 %oleic acidt = water h = stearic acidu = rape oil i = grease (zinc oxide base)v = 3-in-1 oil j = graphitew = octyl alcohol k = turbine oil plus 1% graphitex = triolein l = turbine oil plus 1% stearic acidy = 1%lauric acid in paraffin oil REFERENCES (1) Campbell Trans. ASME,1939: (2) Clarke, Lincoln, and Sterrett Proc. API,1935; (3) Beare and Bowden Phil. Trans. Roy. Soc.,1935; (4) Dokos, Trans. ASME,1946; (5) Boyd and Robertson, Trans. ASME,1945; (6) Sachs, zeit. f. angew. Math,undMech.,1924; (7) Honda and Yama la, Jour. I. ofM,1925; (8) Tomlinson, Phil. Mag., 1929; (9) Morin, Acad. Roy. desSciences,1838; (10) Claypoole, Trans. ASME,1943; (11) Tabor, Jour. Applied Phys.,1945; (12) Eyssen, General Discussion on Lubrication, ASME,1937; (13) Brazier and Holland-Bowyer, General Discussion on Lubrication, ASME,1937; (14) Burwell, Jour. SAE,1942; (15) Stanton, “Friction”, Longmans; (16) Ernst and Merchant, Conference on Friction and Surface Finish, M.I.T., 1940; (17) Gongwer, Conference on Friction and Surface Finish, M.I.T., 1940; (18) Hardy and Bircumshaw, Proc. Roy. Soc.,1925; (19) Hardy and Hardy, Phil. Mag.,1919; (20) Bowden and Young, Proc. Roy. Soc.,1951; (21) Hardy and Doubleday, Proc. Roy. Soc.,1923; (22) Bowden and Tabor, “The Friction and Lubrication of Solids”, Oxford; (23) Shooter, Research,4, 1951. From StandardHandbookforMechanicalEngineers,7th ed., Baumeister, T., Ed.,McGraw-Hill, New York, 1967. With permission. about 20% of the midpoint value, averaging must be done with caution. Trace averaging can be aided by using a parallel plate (noncontacting) viscous damper to diminish oscillations during tests, as shown in Figure 10. Volume II 47 Copyright © 1983 CRC Press LLC TABLES OFCOEFFICIENTOFFRICTION The coefficient of friction is not an intrinsic property of a material or combinations of materials. Rather the coefficient of friction varies with changes in humidity, gas pressure, temperature, sliding speed, and contact pressure. It is different for each lubricant, for each surface quality, and for each shape of contact region. Furthermore, it changes with time of rubbing, and with different duty cycles. Very few materials and combinations have been tested over a wide range of more than three or four variables, and then they are usually tested in laboratories using simple geometries. Thus, it is rarely realistic to use a general table of values of coefficient of friction as a source of design data. Information such as that in Table 2 may provide guidelines, 14 but where a significant investment will be made or high reliability must be achieved, the friction should be measured using a prototype device under design conditions. REFERENCES 1.Bowden, F. E. and Tabor, D.,The Friction and Lubrication of Solids, Oxford University Press, Vols. I and II, London. 1954 and 1964. 2.Buckley, D. H.,Surface Effects in Adhesion, Wear and Lubrication, Elsevier, Amsterdam, 1981. 3.Barwell, F. T.,Bearing Systems: Principles and Practice, Oxford University Press, London, 1979. 4.Ling, F. F., Klaus, E. E., and Fein, R. S., Eds.,Boundary Lubrication. An Appraisal of World Literature, American Society of Mechanical Engineers. New York, 1969. 5.Peterson, M. B., Ed.,Wear Control Handbook, American Society of Mechanical Engineers, New York, 1980. 6.Timoshenko, S. and Goodier, J. N.,Theory of Elasticity, 2nd ed., McGraw-Hill, New York, 1951. 7.Greenwood, J. A. and Williamson, J. B. P.,Contact of nominally flat surfaces, Proc. R. Soc. (London), A295, 300, 1966. 8.Dowson, D.,An interesting account of the life and times of 23 prominent figures in the field of tribology, J. Lubr. Technol, 99, 382, 1977; J. Lubr. Technol, 100, 2, 1978. 9. Tabor, D., Junction growth in metallic friction, Proc. R. Soc., (London), A251, 378, 1959. 10. Benzing, R., Hopkins, V., Petronio, M., and Villforth, F., Jr., Friction and Wear Devices, 2nd ed., Americal Society of Lubrication Engineers, Park Ridge, III., 1976. 11. Ludema, K. C. and Tabor, D., The friction and visco-elastic properties of polymeric solids, Wear, 9, 329, 1966. 12. Yeager, R. W., Tire hydroplaning, in The Physics of Tire Traction, Hayes, D. F. and Browne, A. L., Eds., Plenum Press, New York, 1974, 25. 13. Kato, S., Yamaguchi, K., Malsubayashi, T., and Sato, N., Stick-Slip motion and characteristics of friction in machine tool slideway, Nagoya Univ. 27, 1, 1975. 14. Fuller, D. D., Friction, Marks’ Standard Handbook for Mechanical Engineers, 8th ed., Baumeister, T., Ed., McGraw-Hill, New York, 1978. 48 CRC Handbook of Lubrication Copyright © 1983 CRC Press LLC BOUNDARYLUBRICATION Richard S. Fein CHARACTERISTICS OF BOUNDARYLUBRICATION Boundary lubrication is defined by OECD as a condition of lubrication in which the friction and wear between two surfaces in relative motion are determined by the properties of the surfaces, and the properties of the lubricant other than bulk viscosity. Boundary lubrication also may be defined in terms of contrast with full-fluid film lubrication where load-bearing surfaces are completely separated and the load is supported entirely by pressure in the fluid film. Usually, boundary lubrication is associated with some load support by interaction of asperities on the bearing surfaces or of the surfaces with solid particles in the fluid. In the extreme, asperity and/or panicle interactions support all of the load and friction appears to be independent of bulk fluid viscosity. 1 Friction and WearPhenomena Friction and wear under boundary lubrication conditions often approximately obey rather simple “laws” over considerable ranges of operating and machine configuration conditions. For friction, the Amonton-Coulomb law states that the coefficient of friction, the ratio of the friction force to the load, is independent of load and of apparent area of contact. 1 For wear, the volume of material worn from a surface is proportional to the product of the load and sliding distance divided by the hardness of the material being worn. 2 The proportionality constant is the “wear coefficient”, k, (1) in which v is wear volume, H is hardness, Wis normal load, 1 is distance slid, d is depth of wear, Pis normal pressure, A w is area being worn, and Ais area of apparent load support. For surfaces which are not in continuous “contact” and the sliding and relative motion are parallel: (2) in which Lis face width of line contact, n is number of passes through load support area, U is sweep velocity through the area, and U s is sliding velocity. For the more general noncontinuous contact case, (3) in which c is width of load support area in the direction of motion and Pis the mean normal pressure. Since the wear coefficient, as shown in Table 1, ranges over at least a hundred- to million- fold range, it is convenient to transform it to the AntiWear Number (AWN) defined as (4) Volume II 49 Copyright © 1983 CRC Press LLC coefficient is relatively constant. Above 13.4 MJ for the straight mineral oil and 161 MJ for the mild EP oil, the rapid increase in wear corresponds to a wear coefficient about a hundred times greater than that at low load. Note that strong EP chemical additives increased the load-carrying capacity over 20-fold. Operating conditions that produce a transition are commonly expressed in terms of a “severity parameter”. Common parameters are load P, velocity V, PV, fPV, a measured temperature in the oil or machine, calculated conjunction temperature for the load support area, or the reciprocal of the fluid “film thickness parameter” (1/A). These measures all reflect mechanical or thermal stress. In addition, severity often seems to increase with decreased lubricant viscosity grade, decreased speed, increased slide-roll ratio (U s /U), in- creased surface hardness, and increased asperity tip curvature (1/r). Run-In During initial sliding or rolling between a pair of surfaces, friction and wear coefficients as well as surface texture change towards a steady-state determined by operating conditions, the original surface configurations and textures, lubrication, and all other environmental and material parameters involved. Run-in is crucial since excessive friction and wear or cata- strophic surface damage are much more likely initially than after the surfaces have reached a steady state. Effective run-in involves alleviation by wear of misalignment and dimensional or other errors in geometry, and generates protective surface films that shear and wear sacrificially and prevent surface damaging transitions. Volume II 51 FIGURE 2. Effect of load on wear. FZG Gear Test A, 2175 pinion speed. (Redrawn from Nieman, G., Rettig. H., and Lechner, G., ASLE Trans., 4, 71, 1961.) FIGURE 1. Ironing of can wall in two-piece can manufacture. Copyright © 1983 CRC Press LLC During run-in, friction and wear coefficients often change approximately exponentially from beginning values f b and k b to steady-state values of f ss and k ss . Instantaneous values at any sliding distance, ᐉ,tend to follow the equations (5) and (6) Break-in sliding distance, ᐉ b typically may be in the order of a kilometer with an effective boundary lubricant, negligible load support by a fluid film, and negligible geometric errors in the sliding parts. This distance for the cylinder liner on a passenger car corresponds to the order of 1000 km of travel. For a typical spur gear at 30 Hz (1800 rpm) it corresponds to a day of operation. Any factor which increases operational severity generally decreases the break-in sliding distance. Usually, shortest run-ins involve operating conditions as near as is safely possible to a wear or surface damage transition. As a consequence, run-ins often use low viscosity oils at low speed and high load. Low speed has the dual effect of increasing severity by decreasing fluid film formation and of preventing catastrophic frictional heating if a friction transition is encountered. Common laboratory load-carrying and friction tests operate in the early stages of run-in and measure the rapidity of lubricant response to operational severity. By contrast, laboratory wear tests often are sufficiently long that steady-state conditions are approached. BOUNDARYLUBRICANTS Boundary films occur on almost all surfaces because they reduce the surface energy and are thus thermodynamically favored. Normally, air covers any surface with an oxidized layer plus adsorbed moisture and organic material. If surfaces slide while covered with a lubricant film, all elements in the lubricant appear in a chemically reacted boundary film along with the bearing material elements and atmospheric oxygen. Thicknesses of surface films may range from tenths of a nanometer (a few hundredths of a microinch) for single molecular layers of physically adsorbed gases to a few micrometers (several dozen mi- croinches) for thick chemically reacted boundary films from oils with EPadditives. Gases Inadvertent lubrication by air is the most common boundary lubrication. Among com- ponents listed in Table 2, oxygen and/or water vapor are necessary for satisfactory dry sliding of most metal surfaces. Without their adsorption and/or chemical reaction films, catastrophic levels of friction, wear, and surface damage usually occur. Hydrocarbons are also generally helpful. A gaseous component is capable of covering the surface with a monolayer in about 1/ (concentration, ppb) sec. Thus, oxygen alone could cover a clean surface in about 5 nsec (1/0.209 × 10 9 ppb), while sulfur dioxide alone would require about a second. Nitrogen mole- cules generally do not stick well to a clean surface. With clean air, the first molecular layer formed on a clean metal surface would be expected to have a composition approximating the distribution of the strongly adsorbing/reacting components. 52 CRC Handbook of Lubrication Copyright © 1983 CRC Press LLC [...]...54 CRC Handbook of Lubrication FIGURE 3 Effect of hydrocarbon type and viscosity on wear Fourball machine, 50-kg load, 3. 5 mm/sec, 15 to 16 hr at 38 °C P, N, O, and A indicate paraffinic, naphthenic (i.e., cycloparaffinic), olefinic, and aromatic, respectively FIGURE 4 Example of chemical compounds used as boundary lubricant additives Figure 3 shows that aromatic and olefinic... in four-ball testing) Also, EP additives most often control wear and surface damage at loads above the lowest transition In many cases, this permits satisfactory performance of mechanisms such as gears above the transition Copyright © 19 83 CRC Press LLC 56 CRC Handbook of Lubrication for part of their life EP agents also commonly increase the severity of conditions required to produce failure by catastrophically... wear particle, is deformed plastically at the same time that confining bearing surfaces are being deformed plastically This extends the surface films on both the wear particle and the Copyright © 19 83 CRC Press LLC Volume II 63 Table 6 ELASTIC MODULI OF BEARING AND FILM-LIKE MATERIALS FIGURE 11 Cushioning of asperities carrying zones between interacting asperities If the film is liquid, the amount of. .. plasticlike behavior are strongly dependent on the viscosity of the material at normal temperatures and pressures and the variation of viscosity with temperature and pressure Thus, glass transition depends strongly on chemical composition Copyright © 19 83 CRC Press LLC Volume II FIGURE 9 sliding 61 Microchip wear particle from effective lubrication under lubrication situations For a plastic solid boundary film,... height a few orders of magnitude from approximately 10 nm (i.e., about 1/ 2 μin.) for the smoothest engineering surfaces Slopes on the sides of asperities range from the order of a degree upwards to 30 ° on roughly finished bearing surfaces When two bearing surfaces of the same material are brought together as illustrated in Figure 6, they initially “touch” at the highest asperities The size of the real contact... stresses on the substrate are thereby reduced Copyright © 19 83 CRC Press LLC 64 CRC Handbook of Lubrication Table 7 THERMAL CONDUCTIVITY OF STEEL AND FILM COMPONENTS Thermal Insulation Table 7 indicates that boundary films consisting of iron oxides and hydrocarbons should be thermal insulators compared to substrate bearing metals.6 With viscous heating of the hydrodynamic (or ehd) film, this insulation from... (or ehd) film thickness .12 Table 5 indicates that all but the thinnest boundary films should be capable of reducing friction of at least some ehd films The thickest boundary films may similarly affect friction of the thinnest hydrodynamic films Boundary films also appear capable of reducing friction due to shearing of micro-rhd films between asperities For this to occur, the part of the boundary film... probably partially explains why oiliness additives often enhance severe surface damage The effect is also a partial explanation of the beneficial effects of oiliness additives in metal processing where large surface extensions are necessary SELECTION OF BOUNDARY LUBRICANTS Need for a boundary lubricant may be indicated by any of the dimensionless factors listed in Table 8 The interaction factor,9 ,10 thermal... boundary lubricant film or a soft opposing surface When sliding occurs, the shear friction force depends on the shear resistance per unit area, S, of any “boundary film” in the real load-supporting area between asperities (10 ) Dividing by load, W, gives the shear contribution to the friction coefficient Note that this becomes independent of total load and apparent area of contact (11 ) Traditionally the boundary... early stage of deformation Friability can be caused by surface films which inhibit emergence of dislocations from the surface Oxide films cause embrittlement An active sulfur EP oil has similarily been shown to embrittle steel .11 Oxygen, water, and at least some EP additives likely reduce severe surface damage by making asperityto-asperity and asperity-to-particle welds friable.6 Copyright © 19 83 CRC Press . Morin, Acad. Roy. desSciences ,18 38 ; (10 ) Claypoole, Trans. ASME ,19 43; (11 ) Tabor, Jour. Applied Phys. ,19 45; (12 ) Eyssen, General Discussion on Lubrication, ASME ,19 37 ; ( 13 ) Brazier and Holland-Bowyer, General. M.I.T., 19 40; (18 ) Hardy and Bircumshaw, Proc. Roy. Soc. ,19 25; (19 ) Hardy and Hardy, Phil. Mag. ,19 19; (20) Bowden and Young, Proc. Roy. Soc. ,19 51; ( 21) Hardy and Doubleday, Proc. Roy. Soc. ,19 23; (22). plus 1% stearic acidy = 1% lauric acid in paraffin oil REFERENCES (1) Campbell Trans. ASME ,19 39 : (2) Clarke, Lincoln, and Sterrett Proc. API ,19 35 ; (3) Beare and Bowden Phil. Trans. Roy. Soc. ,19 35 ;