Handbook of Lubrication part 2 ppsx

2.5-cmcube pressed with a load N as shown in the table below produces a real contact area Ar, The above paragraph implies that contact area increases linearly with applied load... Re-sea

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 wherelimited driving power may be available or minimum power consumption is desired,bearings in motors, engines and gyroscopes where minimum losses are desired, andprecision guides in machinery in which high friction may produce distortion

SURFACE CHARACTERISTICS AND STATIC CONTACT AREAFrequently the coefficient of friction is more dependent upon surface properties and surfacefinish than on substrate properties Substrate properties, however, influence both the surfacefinish 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 Finercutting is done with abrasives by grinding, honing, lapping, etc

Cutting is simply localized fracture Each individual microfracture joins another and/orextends into the substrate The orientation of surface facets and the direction taken bysubsurface cracks are often dependent upon the structure of the material Seriousness of asubstrate crack will probably depend upon the toughness of the material For example, incast irons and notably in white cast iron, machining often forms cracks that extend into thesubstrate 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 mayconstitute a stress concentration from which fatigue cracks may emanate Cracks may alsobecome corrosion cells

Many surfaces are formed by ductile fracture mechanisms with a high amount of plasticstrain and residual stress remaining in the surface All of these conditions may influencethe coefficient of friction either from the beginning of sliding or as a result of surfacealteration during sliding

Adsorption on Surfaces

Material cutting operations expose atoms or molecules, formerly in the substrate, to theenvironment 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 materialssuch as gold and plastic which do not oxidize quickly The adsorbed gases can be the samethickness as the oxide film

Adsorption occurs very quickly Pure oxygen gas at atmospheric pressure produces a 50%coverage by adsorption in about 1.75 × 10−9sec

The influence of all surface films on friction is not always the same It might be expected

that adsorbed water would act as a liquid lubricant, and that some oxides or hydroxidesmight act as solid lubricants On the other hand, some oxides such as aluminum oxide(A12O3) 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 betweenthe two major theories of friction outlined below The methods used include electricalresistance, heat transfer, total internal reflectance of an optical element pressed against ametal surface, phase contrast microscopy, ultrasonic transmission, election emission phe-nomena, computer simulation, large-scale surface model studies, and analytical methodsbased 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 betweenmany 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 frictionforce is applied

An adequate description of the behavior of asperities may be gained by a simple analyticalmodel Representation as a sphere is reasonable since most asperities are reasonably roundedrather 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 Pm= N/πa2and the maximum pressure qo at the center of contact

is 3/2 Pm Thus, qo= (3/2) N/πa2

Other equations are available that give the stress state of all points in the substrate6andmay be used to calculate the limits of elastic behavior A principle of plasticity is that plasticflow 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 loadincreases, 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 Pm= 1.1 Y, where Y equals the tensileyield strength of the material

Experimental work has shown that continued loading of the ball produces a progressivelylarger 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 manyasperities are in the advanced state of plastic flow.7From this we may estimate the real area

of contact, A, between nominally flat surfaces touching each other at asperities is 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 Ar,

The above paragraph implies that contact area increases linearly with applied load

Re-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 radiusand 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 suchobservations it is easy to assert that there is no adhesion between surfaces This at least hasbeen the argument against adhesion being operative in friction On the other hand, measurableadhesion does occur during contact between two surfaces that were vigorously cleaned in ahigh 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 andwithout adhesion may be seen in the illustration of a rubber ball pressed against a rigid flatsurface As each increment of load is added, a ring of larger diameter of contact formsbetween 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 wouldproduce increasing contact area as before, but upon decrease in load the outer ring of contactwill not readily separate A state of tension will exist across the adhesive bond As the nextincrement 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 incontact with the flat surface The stress state over the contact region is one of tension at theouter 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 fracturewould be time-dependent but with metals the fracture would occur progressively as the loaddecreases The bonds of a ductile material do not fracture as readily as those of a brittlematerial, thus leaving a residual contact region A force, – N, required to separate a spherefrom 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

MECHANISMS OF SLIDING FRICTION

Recent Understanding

Research in the last 50 years has focused on whether friction is due to adhesion or theinterlocking of asperities The interlocking theory views surfaces as being composed ofrelatively rigid asperities which must follow complex paths to move around or over eachother The adhesion theory assumes that two contacting surfaces will bond or weld togetherand the resulting bonds must be broken for sliding to occur

There are now two convincing arguments against the interlocking theory First is theobservation 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 andwould soon be separated some distance from the lower body!

The adhesion theory has been criticized for two reasons One is based on the belief thatadhesion 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 arereadily separated after sliding ceases, requiring no force to separate as would be requiredwith adhesive bonding

The modern view is that friction is primarily due to adhesion but an adhesion that islimited 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 ofthe roughness may be due to carbide particles, there may be a second component of frictiondue to asperity collision

Laws of Friction

The earliest law of friction is due to Leonardo DeVinci (1452 to 1519).8 He observedthat F is proportional to N, where F is the force to initiate sliding and N is the normal forceholding 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 isindependent 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 withpork 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 thatfriction 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 thefindings of Amontons, yet today “dry friction” is almost universally known as “Coulombfriction” 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 areBowden and Tabor.1An early model from this school began with the idea that the force offriction is the product of Ar, the summation of the microscopic areas of contact, and theshear strength, Ss, of the bond in that region; i.e., F = ArSs To complete the model, theload, N, was thought to be borne by the tips of asperities, altogether comprising a total area

of contact, Ar, multiplied by the average pressure of contact, N = ArPf, where Pf is theaverage pressure of contact on the asperities Altogether, the coefficient of friction is takenas

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.9Conceptually, the model of the sphere on the flat plate can be applied here As load on thesphere increases, its contact area with the flat plate increases and the stresses pass from theelastic to the plastic regime In the elastic regime, a superimposed shear stress on the spherewould produce an elastic shear strain in the sphere and the contact area between the sphereand flat plate would not be affected In the plastic range, however, after a normal load isapplied that produces plastic flow, a horizontal force producing a shear stress in the spherewould produce a new increment of strain in the direction of the resultant of the initial normalforce and the applied shear force Thus, the shear force causes a further normal strain inasperities 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 stressthat 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 = Si/Ss, and Siis the shear strength of the interface between the sphere and theflat 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 applieduntil the contact and adhesion area is very large In this case, it may not be possible toseparate the surfaces and this is defined as the state of seizure Where some interruption ofsurface adhesion occurs, however, the value of Si is less than Ss The calculated values of

µ for several conditions are shown in the table below

The latest model of Tabor is not totally satisfying because of our inability to comprehend

Si in realistic terms It may be either an average shear strength over a contact region, or thefraction of surface over which very high adhesion occurs leaving other areas to have noadhesion Other uncertainties in the model are due to the manner in which the plastic flowproperties 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 observationthat µ increases as surface finish decreases below a roughness of 10 µin Neither of theTabor models or the interlocking theory explain the influence of close lateral proximity ofasperities which imposes a limit on the high value of µ This is the case in metal workingwhere there is high-contact pressure

COEFFICIENT OF FRICTION

Measurement of Friction

Measurement of the coefficient of friction involves two quantities, namely F, the forcerequired to initiate and/or sustain sliding, and N, the normal force holding two surfacestogether Some of the earliest measurements of the coefficient of friction were done by anarrangement of pulleys and weights as shown in Figure 1 Weight Ps is applied to the panuntil sliding begins and one obtains the static, or starting, coefficient of friction with µs =

Ps/N If the kinetic coefficient of friction µkis desired, a weight is applied to the string andthe 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 thiscase, the final weight Pkis used to obtain µk= Pk/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 theangle of tilt of the plane to θ when the object begins to slide down the inclined plane Bysimple 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 advancedmanually 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

FIGURE 1 String-pulley-weight measurement of coefficient of friction.

FIGURE 2 Tilting plane measurement of coefficient of friction.

high accuracy under a wide range of conditions Force measuring devices for this purposerange 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 normalforces on the sliding pair The deflection can be measured by strain gages, capacitancesensors, inductance sensors, piezoelectric materials, optical interference, acoustic emission,moire fringes, light beam deflection, and several other methods The most widely usedbecause of its simplicity and reliability is the strain gage system

Just as there are many sensing systems available, there are also many designs of frictionmeasuring 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 toload 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 gagesattached to vertical flexible section 3 measure friction force by bending of the beam Designsincorporating 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 tocalibrate the instrument and to maintain it, and (2) the inevitable interaction or “cross talk”between the two force-measuring signals

A more complex system which requires less skill to operate is shown in Figure 4 It iscomposed of two parts Part A can rotate about bearing G in a horizontal plane but isconstrained by a wire between cantilevers x and y Part B is attached to part A by bearing

H on a horizontal axis A slider test pin is inserted in body B When the prime mover ismoved vertically downward, the pin presses the flat plate tending to rotate body B in aclockwise 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 plaguesthe design of Figure 3 The two-part design also is nearly insensitive to the amount ofextension 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 deadweights The above designs are a few of many in use Frequently, it is more convenient touse two flat surfaces, a shaft in a bearing, or three pins instead of one

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.

the temperature becomes high enough to increase the oxidation rate (which usually decreasesµ) Increased temperature will lower the sliding speed at which surface melting occurs (seeFigure 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 beobscured by dynamic effects of the systems

Applied load or contact 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 8.1The 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 lowload, 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

40 CRC 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.

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 thecoefficient of friction and wear rate

Static and Kinetic Friction

The force required to begin sliding is usually greater than the force required to sustainsliding For dry surfaces the reason for the starting (or static) coefficient of friction beinglarger than the sliding (or kinetic) coefficient of friction may most simply be explained interms of the adhesion of asperities It is often found that the static coefficient of frictionincreases with time of standing This suggests diffusion bonding of the points of contactwhich progresses with time Sustained sliding could be viewed as providing a very shortstanding time of one asperity upon another This should also produce a decrease in thecoefficient 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 6-6the 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 v2 Most observers would, however,measure the value of µ at v2 as the static value of µ The reason is that v1 in the presentexample is imperceptibly slow The coefficient of friction at the start of visible sliding at

v2 is higher than at v3 In this case it may be useful to define the starting coefficient of

friction as that at v2and the static coefficient of friction as that at or below v1

In lubricated systems the starting friction is often higher than the kinetic friction Whenthe 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

FIGURE 9 Coefficient of friction pattern for a typical lubricated contact Z is lubricant cosity, N′ shaft speed, and P the unit load transferred radially by the shaft to the bearing.

vis-is given in units of ZN′/P where Z vis-is the vvis-iscosity of the lubricant, N′ vis-is the shaft rotatingspeed, and P is the load transferred radially from the shaft to the bearing.

ROLLING FRICTIONThe force required to initiate rolling motion may be larger than the force to maintainmotion if the contacting surfaces are very rough Sustained rolling motion requires verylittle 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 withineach of the solid bodies in the region of contact During rolling a point in each body passesthrough 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 contactingbodies This can be seen by pressing the eraser of a pencil into the palm of the hand Duringindentation the skin of the hand stretches, in the contact region as well as outside of it, morethan 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 thedirection of the applied force A misaligned roller slides axially to some extent and a poorlyguided ball spins about the contact region Again, lubrication will reduce the energy lossdue to slip

Frictional resistance of ball and roller bearing assemblies is usually much greater than therolling resistance of simple rolling elements because of the cages, grooves, and shouldersintended 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 accuratereadings There are two separate effects One effect is achieved by tapping the face of ameter 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 ongears) 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 anO-ring Such motion requires the application of a force to overcome friction Rotation ofthe shaft also requires overcoming friction, but rotation reduces the force required to effectaxial motion In lubricated systems the mechanism may involve the formation of a thickfluid 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 toanisotropic (grooved) frictional behavior Such oscillatory rotation may be referred to asjiggling, fiddling, or coaxing

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 andshape of final parts are affected by the vibration of tool carriers.13

Vibration of sliding systems is usually described as stick-slip, frictional vibration, orfrictional oscillation In the simple model of Figure 10, an object of weight W is connected

to a prime mover by a spring As the prime mover moves at constant speed in the directionshown, the spring stretches until it applies a force to W that will initiate sliding If thecoefficient of friction remains constant after sliding begins, the weight W will advance atthe same speed as the prime mover If on the other hand, the coefficient of friction decreasesafter sliding begins, less force will be required to sustain sliding than the spring force.Weight W will, therefore, accelerate, shortening the spring, and finally overshooting theequilibrium 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 thanbefore and the coefficient of friction may increase To meet the increased force required tosustain or reinitiate sliding, the spring must stretch This produces a never ending cycle withthe 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 differencesdepending upon the speed of the prime mover as shown in Figure 11 The upper trace forslow 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 secondtrace where the velocity is moderately high, force variations are smaller and the weightoscillates between two limiting sliding speeds in frictional oscillation

In the simplest approach, where the coefficient of friction between the sliding object andthe table is taken to be µk when sliding occurs and µs to start sliding, and where µs > µk,motion of the weight would follow simple laws of dynamics Thus, one could reasonablyexpect that the frequency of frictional oscillations would be low at low speeds of the primemover, with a large weight, and with a flexible or compliant spring The frictional oscillationswould 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 minimizevibration In general, the larger the difference (µs – µk), the more likely a system willoscillate The transition from µs to µkis influenced by the surface finish of the sliding partsand by the physical and chemical nature of the lubricant In general, µk rises as velocitydecreases, as lubricant viscosity increases, as chemical reactivity of lubricant with surfacesincreases, and as surface finish decreases.13

In machine design it may be possible to stiffen the connection between the prime moverand sliding object, to reduce the weight of the sliding object, or to provide a thick fluidfilm An additional design consideration is that frictional oscillation can produce pitchingand yawing motion of the moving element if the driving force is applied at a different plane

FIGURE 10 Simplified model of vibrating sliding system.

Table 2 COEFFICIENTS OF STATIC AND SLIDING FRICTION

46 CRC Handbook of Lubrication

Note: Reference letters indicate the lubricant used; numbers in parentheses give sources (see References).

Key to Lubricants Used:

b = Atlantic spindle oil (light mineral) n = olive oil

e = Atlantic spindle oil plus 2% oleic acid r = dry soap

g = medium mineral oil plus 1 / 2 % oleic acid t = water

i = grease (zinc oxide base) v = 3-in-1 oil

k = turbine oil plus 1% graphite x = triolein

l = turbine oil plus 1% stearic acid y = 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, und Mech., 1924; (7) Honda and Yama la, Jour I of M, 1925; (8) Tomlinson, Phil Mag.,

1929; (9) Morin, Acad Roy des Sciences, 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 Standard Handbook for Mechanical Engineers, 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 averagingcan be aided by using a parallel plate (noncontacting) viscous damper to diminish oscillationsduring tests, as shown in Figure 10

TABLES OF COEFFICIENT OF FRICTION

The coefficient of friction is not an intrinsic property of a material or combinations ofmaterials 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 eachsurface quality, and for each shape of contact region Furthermore, it changes with time ofrubbing, and with different duty cycles Very few materials and combinations have beentested over a wide range of more than three or four variables, and then they are usuallytested in laboratories using simple geometries Thus, it is rarely realistic to use a generaltable 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 orhigh reliability must be achieved, the friction should be measured using a prototype deviceunder 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 Bar well, 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