Handbook of Lubrication part 2 ppsx

between the static and dynamic coefficient of friction for avoiding squeal or vibrations from brakes and clutches. 3. Quality control components that require constant friction. Two examples may be cited, but there are many more: a. In knitting and weaving of textile products, the tightness of weave must be controlled and reproducible to produce uniform fabric. b. Sheet metal rolling mills require a well-controlled coefficient of friction in order to maintain uniformity of thickness, width, and surface finish of the sheet and, in some instances, minimize cracking of the edges of the sheet. 4. Low friction components that are expected to operate at maximum efficiency while a normal force is transmitted. Examples are gears in watches and other machines where limited driving power may be available or minimum power consumption is desired, bearings in motors, engines and gyroscopes where minimum losses are desired, and precision guides in machinery in which high friction may produce distortion. SURFACE CHARACTERISTICS AND STATIC CONTACT AREA Frequently the coefficient of friction is more dependent upon surface properties and surface finish than on substrate properties. Substrate properties, however, influence both the surface finish achieved in processing and the kinetics of adsorption of chemical species. Surface Structure and Finish With the exception of surfaces that solidify from the liquid (either in air, in vacuum, or in contact with a mold), most technological surfaces are formed by a cutting operation. Coarse cutting is done with a cutting tool in a lathe, drill press, milling machine, etc. Finer cutting is done with abrasives by grinding, honing, lapping, etc. Cutting is simply localized fracture. Each individual microfracture joins another and/or extends into the substrate. The orientation of surface facets and the direction taken by subsurface cracks are often dependent upon the structure of the material. Seriousness of a substrate crack will probably depend upon the toughness of the material. For example, in cast irons and notably in white cast iron, machining often forms cracks that extend into the substrate and in fact may loosen some grains from the matrix. In more ductile materials, the cracks that extend into the substrate are less likely to be harmful and yet they may constitute a stress concentration from which fatigue cracks may emanate. Cracks may also become corrosion cells. Many surfaces are formed by ductile fracture mechanisms with a high amount of plastic strain and residual stress remaining in the surface. All of these conditions may influence the coefficient of friction either from the beginning of sliding or as a result of surface alteration during sliding. Adsorption on Surfaces Material cutting operations expose atoms or molecules, formerly in the substrate, to the environment around the material. Oxygen in the air is very reactive with most metals and is usually the first to adsorb and form oxides on metal surfaces. After oxides of between 20 Å to 100 Å thick form, the rate of oxidation diminishes and other gases adsorb. In air, for example, a significant amount of water vapor adsorbs on oxides and on other materials such as gold and plastic which do not oxidize quickly. The adsorbed gases can be the same thickness as the oxide film. Adsorption occurs very quickly. Pure oxygen gas at atmospheric pressure produces a 50% coverage by adsorption in about 1.75 × 10 −9 sec. The influence of all surface films on friction is not always the same. It might be expected 32 CRC Handbook of Lubrication Copyright © 1983 CRC Press LLC that adsorbed water would act as a liquid lubricant, and that some oxides or hydroxides might act as solid lubricants. On the other hand, some oxides such as aluminum oxide (A1 2 O 3 ) are abrasive and under some conditions greatly increase friction. Estimating Contact Area Explanations of friction are based upon the detailed nature of contact between two bodies. Historically the measurement of real contact area was attempted in order to decide between the two major theories of friction outlined below. The methods used include electrical resistance, heat transfer, total internal reflectance of an optical element pressed against a metal surface, phase contrast microscopy, ultrasonic transmission, election emission phe- nomena, computer simulation, large-scale surface model studies, and analytical methods based on the mechanics of solids. Most methods are unsatisfactory in that either the obser- vations are not made in real time, or the method is incapable of distinguishing between many small points of contact vs. few large regions. Results from all methods, however, produce the same conclusion: the contact area increases with normal load and when a friction force is applied. An adequate description of the behavior of asperities may be gained by a simple analytical model. Representation as a sphere is reasonable since most asperities are reasonably rounded rather than sharp or jagged. For the simplified case of a sphere pressed against a flat surface, the radius of contact, a, may be calculated as follows: 6 where N is the normal load, r is the radius of the sphere, v is Poisson’s ratio, E is Young’s modulus, and subscripts 1 and 2 refer to the two materials if the sphere and flat plate are of different materials. The pressure distribution over the area of contact is semielliptical. The average pressure is P m = N/πa 2 and the maximum pressure q o at the center of contact is 3/2 P m . Thus, q o = (3/2) N/πa 2 . Other equations are available that give the stress state of all points in the substrate 6 and may be used to calculate the limits of elastic behavior. A principle of plasticity is that plastic flow will occur whenever the difference between the largest and smallest stresses in per- pendicular directions at a point is equal to the yield strength of the material. As normal load increases, the conditions for plastic flow first occur directly under the center of the ball at a depth of 0.5a and plastic yielding will occur when P m = 1.1 Y, where Y equals the tensile yield strength of the material. Experimental work has shown that continued loading of the ball produces a progressively larger plastically deformed region. 1 The mean contact pressure increases and finally ap- proaches 2.8 Y. Other experimental work on practical surfaces indicates that very many asperities are in the advanced state of plastic flow. 7 From this we may estimate the real area of contact, A, between nominally flat surfaces touching each other at asperities is approx- imately equal to N/3Y. For a metal with a yield strength Y = 15,000 psi, a 1-in. (2.5-cm) cube pressed with a load N as shown in the table below produces a real contact area A r , Volume II 33 The above paragraph implies that contact area increases linearly with applied load. Re- Copyright © 1983 CRC Press LLC Table 1 COEFFICIENT OF ADHESION FOR VARIOUS METALS search suggests that real contact area between nominally flat surfaces increases more neary as the 0.8 power of applied load. 7 Adhesion and Peeling In the above model of the elastic sphere pressing against an elastic flat plate, the radius and area of contact increase as the normal load increases. As a matter of practical experience, the area of contact also returns to 0 (point contact) as the load is decreased. From such observations it is easy to assert that there is no adhesion between surfaces. This at least has been the argument against adhesion being operative in friction. On the other hand, measurable adhesion does occur during contact between two surfaces that were vigorously cleaned in a high vacuum, which makes a total denial of adhesion untenable. The influence of a cycle of loading and unloading of a sphere on a flat plate with and without adhesion may be seen in the illustration of a rubber ball pressed against a rigid flat surface. As each increment of load is added, a ring of larger diameter of contact forms between the ball and flat plate. The reverse occurs upon progressive removal of the load. If the flat surface were covered with a tacky substance, the increment of added load would produce increasing contact area as before, but upon decrease in load the outer ring of contact will not readily separate. A state of tension will exist across the adhesive bond. As the next increment of load reduction occurs, the second ring inward experiences higher tensile stress, etc. Finally, the normal load N may be completely removed but the ball still remains in contact with the flat surface. The stress state over the contact region is one of tension at the outer edges of contact and compression in the middle of contact to achieve static equilibrium. The compression force constitutes a recovery force and its origin is in the elastic strain field “stored” in the rubber ball. At the outer edges of contact where the stresses are highest, there is also a sharp crack or stress concentration. Thus, the conditions are right for “peeling” or continuous fracture of adhesive bonds at the outer edge of contact. With visco-elastic materials the fracture would be time-dependent but with metals the fracture would occur progressively as the load decreases. The bonds of a ductile material do not fracture as readily as those of a brittle material, thus leaving a residual contact region. A force, – N, required to separate a sphere from a flat plate once N is removed, divided by N may be called the coefficient of adhesion A, with A = | – N/N|. Absolute values for various metals are shown in Table 1. 34 CRC Handbook of Lubrication Copyright © 1983 CRC Press LLC MECHANISMS OF SLIDING FRICTION Recent Understanding Research in the last 50 years has focused on whether friction is due to adhesion or the interlocking of asperities. The interlocking theory views surfaces as being composed of relatively rigid asperities which must follow complex paths to move around or over each other. The adhesion theory assumes that two contacting surfaces will bond or weld together and the resulting bonds must be broken for sliding to occur. There are now two convincing arguments against the interlocking theory. First is the observation that monomolecular films of lubricants decrease the friction of the sliding pair by a factor of five or more while having a negligible effect on the size and shape of asperities. The second argument stems from the statement in the ‘interlocking theory’ that the coefficient of friction is related to the steepness of asperities, implying that the force to slide a body up an inclined plane has the horizontal component F. Since with continued motion the force, F, must be constantly applied, one would suppose that the upper body continues to rise and would soon be separated some distance from the lower body! The adhesion theory has been criticized for two reasons. One is based on the belief that adhesion is a force measured normal to surfaces whereas friction is a force measured parallel to the surfaces. The second criticism arises from the common experience that surfaces are readily separated after sliding ceases, requiring no force to separate as would be required with adhesive bonding. The modern view is that friction is primarily due to adhesion but an adhesion that is limited by the oxides and adsorbed gases found on all surfaces during sliding and destroyed by peeling when load is removed. In some instances of very rough surfaces where some of the roughness may be due to carbide particles, there may be a second component of friction due to asperity collision. Laws of Friction The earliest law of friction is due to Leonardo DeVinci (1452 to 1519). 8 He observed that F is proportional to N, where F is the force to initiate sliding and N is the normal force holding the surfaces together. Amontons (1663 to 1705), a French architect-engineer, in 1699 reported to the French Academy that he found F is roughly equal to N/3 and F is independent of the size of the sliding body. The specimens tested were copper, iron, lead, and wood in various combinations, and in each experiment the surfaces were coated with pork fat (suet). Amontons saw the cause of friction as the collision of surface irregularities. Coulomb (1736 to 1806), a French physicist-engineer, supported Amontons in stating that friction is due to the interlocking of asperities. He discounted adhesion (cohesion) as a source of friction because friction was usually found to be independent of (apparent) area of contact. While Coulomb was in error in his explanation of friction and he did not improve on the findings of Amontons, yet today “dry friction” is almost universally known as “Coulomb friction”. This is taken to mean simple friction, invariant with load, speed, temperature, starting rate, etc. The investigators most commonly associated with the adhesion theory of friction are Bowden and Tabor. 1 An early model from this school began with the idea that the force of friction is the product of A r , the summation of the microscopic areas of contact, and the shear strength, S s , of the bond in that region; i.e., F = A r S s . To complete the model, the load, N, was thought to be borne by the tips of asperities, altogether comprising a total area of contact, A r , multiplied by the average pressure of contact, N = A r P f , where P f is the average pressure of contact on the asperities. Altogether, the coefficient of friction is taken as Volume II 35 Copyright © 1983 CRC Press LLC S s is usually approximately Y/2 where Y is the yield strength of the material in tension. P f is usually no more than 3Y. Thus, the ratio S s /P f is about 1/6, which is not far from 0.2, a value often found in practice for “clean” metals in air. Using the best estimates for A r and S s , however, the closest estimate of friction is only 1/10 of the measured values. Estimation of the real area of contact is generally considered the most difficult problem in this model. From 1938 when the above model was proposed, there have been many developments in technology, particularly in the use of vacuum equipment. In vacuum, the coefficient of friction is often seen to exceed 0.2 by a large margin and sometimes approaches 40. To explain such values and other anomalies in friction, Tabor developed a new model based on principles of biaxial stresses in metals and its influence on plastic strain of the metals. 9 Conceptually, the model of the sphere on the flat plate can be applied here. As load on the sphere increases, its contact area with the flat plate increases and the stresses pass from the elastic to the plastic regime. In the elastic regime, a superimposed shear stress on the sphere would produce an elastic shear strain in the sphere and the contact area between the sphere and flat plate would not be affected. In the plastic range, however, after a normal load is applied that produces plastic flow, a horizontal force producing a shear stress in the sphere would produce a new increment of strain in the direction of the resultant of the initial normal force and the applied shear force. Thus, the shear force causes a further normal strain in asperities with the effect of increasing the area of contact. If adhesion increases in proportion to the area of contact, the area of contact will grow in proportion to the average shear stress that can be sustained or developed at the interface between the sphere and the flat plate. The final form of the model is expressed as, where k = S i /S s , and S i is the shear strength of the interface between the sphere and the flat plate. If k = 1 in this model, µ = ∞. This corresponds to a clean surface achieved in a high vacuum. In this state, contact area increases indefinitely as a friction force is applied until the contact and adhesion area is very large. In this case, it may not be possible to separate the surfaces and this is defined as the state of seizure. Where some interruption of surface adhesion occurs, however, the value of S i is less than S s . The calculated values of µ for several conditions are shown in the table below. kµ 0.95 →1 0.8 0.45 0.6 0.25 0.1 0.03 The latest model of Tabor is not totally satisfying because of our inability to comprehend S i in realistic terms. It may be either an average shear strength over a contact region, or the fraction of surface over which very high adhesion occurs leaving other areas to have no adhesion. Other uncertainties in the model are due to the manner in which the plastic flow properties of materials were simplified, and it does not explain the effect of surface roughness in friction. On the other hand, the interlocking theory is not aided by the frequent observation that µ increases as surface finish decreases below a roughness of 10 µin. Neither of the Tabor models or the interlocking theory explain the influence of close lateral proximity of asperities which imposes a limit on the high value of µ. This is the case in metal working where there is high-contact pressure. 36 CRC Handbook of Lubrication Copyright © 1983 CRC Press LLC COEFFICIENT OF FRICTION Measurement of Friction Measurement of the coefficient of friction involves two quantities, namely F, the force required to initiate and/or sustain sliding, and N, the normal force holding two surfaces together. Some of the earliest measurements of the coefficient of friction were done by an arrangement of pulleys and weights as shown in Figure 1. Weight P s is applied to the pan until sliding begins and one obtains the static, or starting, coefficient of friction with µ s = P s /N. If the kinetic coefficient of friction µ k is desired, a weight is applied to the string and the slider is moved manually and released. If sliding is not sustained, more weight is applied to the string for a new trial until sustained sliding of uniform velocity is observed. In this case, the final weight P k is used to obtain µ k = P k /N. A second convenient system for measuring friction is the inclined plane shown in Figure 2. The measurement of the static coefficient of friction consists simply in increasing the angle of tilt of the plane to θ when the object begins to slide down the inclined plane. By simple trigonometric relations, F/N = W sin θ /W cos θ = tan θ = µ If the kinetic coefficient of friction is required, the plane is tilted and the slider is advanced manually. When an angle, θ, is found at which sustained sliding of uniform velocity occurs, tan θ is the kinetic coefficient of friction. As technology developed, it became possible to measure the coefficient of friction to a Volume II 37 FIGURE 1. String-pulley-weight measurement of coefficient of friction. FIGURE 2. Tilting plane measurement of coefficient of friction. Copyright © 1983 CRC Press LLC high accuracy under a wide range of conditions. Force measuring devices for this purpose range from the simple spring scale to devices that produce an electrical signal in proportion to an applied force. The principle of the instrumented devices is similar to the spring scale in measuring the elastic deflection of machine elements due to friction forces and normal forces on the sliding pair. The deflection can be measured by strain gages, capacitance sensors, inductance sensors, piezoelectric materials, optical interference, acoustic emission, moire fringes, light beam deflection, and several other methods. The most widely used because of its simplicity and reliability is the strain gage system. Just as there are many sensing systems available, there are also many designs of friction measuring devices. 10 The unit shown in Figure 3 is attractive because of its simplicity. It is attached to a prime mover which moves horizontally and may be adjusted vertically to load the pin against the flat. Strain gages are attached to horizontal flexible sections 1 and 2 to measure the normal force between the pin specimen and the flat plate. Strain gages attached to vertical flexible section 3 measure friction force by bending of the beam. Designs incorporating the principle of Figure 3 are usually favored in complex, automatically con- trolled machinery. The chief disadvantages of this design are (1) the skill required both to calibrate the instrument and to maintain it, and (2) the inevitable interaction or “cross talk” between the two force-measuring signals. Amore complex system which requires less skill to operate is shown in Figure 4. It is composed of two parts. Part Acan rotate about bearing G in a horizontal plane but is constrained by a wire between cantilevers x and y. Part B is attached to part Aby bearing H on a horizontal axis. Aslider test pin is inserted in body B. When the prime mover is moved vertically downward, the pin presses the flat plate tending to rotate body B in a clockwise direction which bends cantilever w. With strain gages attached to cantilever w, the vertical force on the pin may be measured. Motion of the prime mover to the left tends to rotate the pin about bearing G. Strain gages on cantilever x measure the force of friction of the pin against the flat plate. The design shown in Figure 4 avoids the interaction between force signals, which plagues the design of Figure 3. The two-part design also is nearly insensitive to the amount of extension of the pin specimen, which is convenient for setup. In addition, wire z in Figure 4 can be removed and the vertical loading on the pin can be conveniently effected by dead weights. The above designs are a few of many in use. Frequently, it is more convenient to use two flat surfaces, a shaft in a bearing, or three pins instead of one. 38CRC Handbook of Lubrication FIGURE 3.One-piece device for measuring pin-on-flat coefficient of friction. Strain gages on flexible sections 1 and 2 measure normal force; strain gage at 3 measures friction force by bending of the beam. Copyright © 1983 CRC Press LLC the temperature becomes high enough to increase the oxidation rate (which usually decreases µ). Increased temperature will lower the sliding speed at which surface melting occurs (see Figure 5) and increased temperature will shift the curve of coefficient of friction vs. slid- ingspeed to a higher sliding speed in many plastics (see Figure 6). Starting rate — Rapid starting from standstill is sometimes reported to produce a low initial coefficient of friction. In many such instances, the real coefficient of friction may be obscured by dynamic effects of the systems. Applied load orcontact pressure — In the few instances that the coefficient of friction is reported over a large range of applied load, three principles may be seen in Figure 8. 1 The first is that the coefficient of friction normally decreases as the applied load increases. For clean surfaces, as shown by curve ‘a’, values of µ in excess of 20 are reported at low load, decreasing to about 0.5 at high loads. An old theory suggests that the ultimate effect of increasing the contact pressure between clean surfaces is to effect adhesive bonding over 40CRC Handbook of Lubrication FIGURE 5.General effect of sliding speed on coefficient of friction for metals and other crystalline solids (e.g., ice). FIGURE 6.Influence of sliding speed on coefficient of friction of a steel sphere sliding on PTFE and Nylon 6-6. Copyright © 1983 CRC Press LLC 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 [...]... Proc Roy Soc., 1 925 ; (19) Hardy and Hardy, Phil Mag., 1919; (20 ) Bowden and Young, Proc Roy Soc., 1951; (21 ) Hardy and Doubleday, Proc Roy Soc., 1 923 ; (22 ) Bowden and Tabor, “The Friction and Lubrication of Solids”, Oxford; (23 ) Shooter, Research, 4, 1951 From Standard Handbook for Mechanical Engineers, 7th ed., Baumeister, T., Ed., McGraw-Hill, New York, 1967 With permission about 20 % of the midpoint... c d E′ AntiWear Number = —logl0k = logl0(1/k) Area of apparent load support Area of asperity load support Area being worn Surface profile correlation distance Width of load support area in direction of motion Depth of material worn from surface Relative effective elastic modulus, 2 E′1E 2/ (E′1 + E 2) Young modulus of elasticity/(1 — Poisson ratio )2 Plowing friction force, shear friction force Friction... 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... II 49 BOUNDARY LUBRICATION Richard S Fein CHARACTERISTICS OF BOUNDARY LUBRICATION 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... Press LLC 48 CRC Handbook of Lubrication TABLES OF COEFFICIENT OF FRICTION 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... root of sum of squares of the RMS roughness of the two surfaces) Shear stress Plasticity index REFERENCES 1 Bowden, F P and Tabor, D., The Friction and Lubrication of Solids, Oxford University Press, London, 1954 2 Archard, J F., Wear theory and mechanisms ASME Wear Control Handbook, Peterson, M, B and Winer, W O., American Society of Mechanical Engineers, New York, 1980 3 Fein, R S., Boundary lubrication, ... Elastohydrodynamic lubrication at point contacts, in Elastohydrodynamic Lubrication, Institute of Mechanical Engineers, London, 1965 and 1966, 47 10 Dowson, D., Elastohydrodynamic lubrication, in Interdisciplinary Approach to the Lubrication of Concentrated Contacts, NASA SP -23 7, Ku, P M., Ed., U.S Government Printing Office, Washington, D.C., 1970, 27 11 Fein, R S and Kreuz, K L., Discussion on boundary lubrication, ... independent of bulk fluid viscosity.1 Friction and Wear Phenomena 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. .. Printing Office, Washington, D.C., 1968, 358 12 Fein, R S., Friction effect resulting from thermal resistance of solid boundary lubricant, Lubr Eng., 27 , 190, 1971 13 Archard, J F., The temperature of rubbing surfaces, Wear, 2, 438, 1958-9 14 Peterson, M B and Winer, W O., Eds., ASME Wear Control Handbook, American Society of Mechanical Engineers, New York, 1980 15 Anon., Scoring Resistance of Bevel... 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 closer . 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. 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. Soc.,1 925 ; (19) Hardy and Hardy, Phil. Mag.,1919; (20 ) Bowden and Young, Proc. Roy. Soc.,1951; (21 ) Hardy and Doubleday, Proc. Roy. Soc.,1 923 ; (22 ) Bowden and Tabor, “The Friction and Lubrication of