Handbook of Lubrication Episode 1 Part 3 pot

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 coe

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 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 present example 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 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

42 CRC 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.

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,

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 W is 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 W that will initiate sliding If the coefficient of friction remains constant after sliding begins, the weight W will 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 W will, 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 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 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 (µs – µk), the more likely a system will oscillate The transition from µs to µkis influenced by the surface finish of the sliding parts and by the physical and chemical nature of the lubricant In general, µk 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

44 CRC Handbook of Lubrication

FIGURE 10 Simplified model of vibrating sliding system.

Table 2 COEFFICIENTS OF STATIC AND SLIDING FRICTION

46 CRC Handbook of Lubrication

Table 2 (continued) COEFFICIENTS OF STATIC AND SLIDING FRICTION

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

Key to Lubricants Used:

a = oleic acid m = turbine oil (medium mineral)

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 averaging can be aided by using a parallel plate (noncontacting) viscous damper to diminish oscillations during 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 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 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

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 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 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 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, W is normal load, 1 is distance slid, d is depth

of wear, P is normal pressure, Awis area being worn, and A is area of apparent load support For surfaces which are not in continuous “contact” and the sliding and relative motion are parallel:

(2)

in which L is face width of line contact, n is number of passes through load support area,

U is sweep velocity through the area, and Usis 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 P is 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)

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 (Us/U), in-creased surface hardness, and inin-creased 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

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.

During run-in, friction and wear coefficients often change approximately exponentially from beginning values fband kbto steady-state values of fssand kss Instantaneous values at any sliding distance, , tend to follow the equations

(5) and

(6)

Break-in sliding distance, btypically 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

BOUNDARY LUBRICANTS 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 EP additives

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 × 109ppb), 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

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