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

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

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

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.

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)

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

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
Figure 3 shows that aromatic and olefinic hydrocarbons give better wear protection in air
than paraffinic and naphthenic hydrocarbons of comparable viscosity (comparable molecular
size). For comparable hydrocarbon type, higher viscosity (larger molecule) hydrocarbons
give better wear protection even under boundary lubrication conditions.
Additives
Additives that adsorb at surfaces generally contain both base-oil and surface-attracting
portions as illustrated in Figure 4. Molecules of this type cluster in “micelles” with their
surface attracting portions on the interior and oil-solubilizing portions on the exterior. These
54 CRC Handbook of Lubrication
FIGURE 3. Effect of hydrocarbon type and viscosity on wear. Four-
ball 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 lu-
bricant additives.
Copyright © 1983 CRC Press LLC
additives may be considered as “dispersed” in the oil rather than being dissolved. Inorganic
solid lubricants can also be made to form stable dispersions in oil by making the particles
sufficiently small and covering their surfaces with oil-solubilizing chemical groups.
Additives may be classified functionally as lubricity, antiwear, and extreme-pressure.
Lubricity additives reduce and smooth friction — particularly at low sliding speeds. Antiwear
additives, as the name implies, reduce wear. EPadditives extend the loads that can be
covered without a transition to unacceptably high friction, wear, or surface damage.
The same additive can perform more than one function. Thus, a zinc dithiophosphate,

to prevent catastrophic wear and surface damage (scuffing) at the highest load. Incidentally,
tendency for wear protection to increase with load below the lowest transition load is often
observed with antiwear additives. In most cases, increasing severity by increasing surface
roughness decreases load-carrying capacity. However, the reverse is true for the last two
EPadditives listed in Table 4.
5
Surface Films
Cumulative evidence indicates that lubricity additives provide lubrication by covering each
of the sliding surfaces with a thick film of molecules. These films can be formed from
additives with molecular shapes that preclude close packing of the hydrocarbon chains.
Lastly, typical lubricity additives can give chemically complex reaction products, at least
for steel surfaces.
6,7
Similarly, EPadditives produce complex organic material-containing surface films in
contrast to the widely held view that they give simple inorganic films (e.g., iron sulfide
from an active sulfur EPadditive). Films formed from neat base oils and oiliness or EP-
additive oils all contain each chemical element present in the bearing metal and the lubricant
as well as oxygen from ambient air.
6,7
The films generally contain organic and inorganic
materials present as both chemically bound (soaps) and physical mixtures. EPfilms are
generally solid-like, and contain the order of the same number of organic carbon and oxygen
atoms as they do iron atoms.
6
Generally, hydrocarbons give predominantly organic reaction products when wear is low
and inorganic products when wear is high. The organic materials are polymeric, partially
oxidized, metal-soap-containing material. The inorganic portion from steel generally contains
iron oxides. Lubricity additives generally give organic complex metal-soap-containing films
under low-wear conditions. Films from both hydrocarbons and additives usually appear to
be liquid-like dispersions of chemical reaction products and bulk lubricant.

and a plowing or deformation component.
1
Considering Figure 7, shear component, F
s
,
predominates except when asperities sink too deeply into a boundary lubricant film or a soft
opposing surface. When sliding occurs, the shear friction force depends on the shear re-
sistance 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 film shear resistance, S, has been assumed equal to the plastic
flow shear stress, τ
p
, of an ideal elastic, plastic solid.
1
Such a solid gives shear stress
independent of strain (and strain rate) at strains sufficiently large to cause plastic flow. This
traditional picture did not explain how Newtonian liquid lubricants give friction coefficients
similar to those of organic solids.
Recent research
8
provided the unifying picture of flow properties shown in Figure 8.
Materials such as mineral oils that approximate ideal liquids at atmospheric pressure and
common shear rates can act like plastic solids at the high pressures and shear rates between
sliding asperities. The conditions that produce the “glass transition” from liquid to plastic-
like 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

above 7 and no known hard or sharp asperities or particles). Abrasion can also lead to
indirect wear. As illustrated in Figure 10, plastic deformation creates ridges on either side
of a plowed groove. The ridges represent new sharp asperities which tend to preferentially
fatigue from the surface.
Adhesion— Is the mechanism of wear mentioned most frequently as the primary process
in review articles and reference works. Particles which are removed from one surface are
either permanently or temporarily attached to the other surface by solid-phase welding. It
is the author’s belief that adhesion is likely a secondary mechanism in boundary lubrication
because of the difficulty of achieving the proper conditions.
6
High vacuum studies show
that surfaces must be atomically clean and within atomic distances of each other to adhere
strongly. Further, atomically clean surfaces are extremely difficult to obtain except by
generation of fresh surface via plastic extension. Hence, under effective lubrication condi-
tions, adhesion of material from one bearing surface to the other surface probably results
from plowing. This would be expected when a trapped third body, such as a fatigued asperity
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
Volume II61
FIGURE 9.Microchip wear particle from effective lubrication under
sliding.
Copyright © 1983 CRC Press LLC
carrying zones between interacting asperities. If the film is liquid, the amount of entrainment
will depend on viscosity. If the film is solid, elastic-plastic resistance to deformation will
determine the entrainment. Whether liquid or solid, the film can protect surfaces only if it
deforms coherently. If the film breaks and exposes substrate, those exposed areas will have
substantially reduced protection.
As previously discussed, additives, many base oils, and some antiwear additives (under
mild conditions) likely give boundary films that are much more viscous than the bulk
lubricant.

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 to the substrate
must be much more shear-resistant than that farther from the surface. This often seems to
be the case: the film closest to the substrate is thickened by inorganic substrate elements
while that farther away is more like the bulk lubricant. Decreased frictional heating also
increases the viscosity of the bulk lubricant with a consequently thicker ehd or hydrodynamic
film. The reduction in substrate bearing temperatures also increases entrainment tendencies
of the boundary film. The increase in surface separation reduces stresses on asperities and,
thus, damage by fatigue or plastic deformation. Increased entrainment of boundary films
also reduces the corrosive wear that occurs when boundary film (which contains reacted
substrate metal) is removed from the surface by forces that push it aside in entrance regions
to macro- and microconjunctions.
Coherence and Friability
Approach of bearing metal surfaces to atomic dimensions over sufficiently large areas of
welding to occur seems to require considerable extension of the surfaces. Extension thins a
boundary film and brings nascent metal to the surface-film interface. This nascent metal
interacts with similar nascent metal unless its chemical bonding tendency is satisfied by the
availability of boundary film material (including gases). Maximum extension before exposure
of nascent metal occurs when the superposed boundary films do not fracture as they thin.
Thus, the boundary films can protect against welding of the surfaces by thinning coherently
in addition to reducing surface stresses. Probably this coherence is enhanced by the organic
components that are an integral part of solid-like EPfilms.
Once a weld has been produced, the extent of surface damage will be minimized if the
welded material is friable. If brittle and the resultant fragments are small, plastically de-
forming welds break at an early stage of deformation. Friability can be caused by surface
films which inhibit emergence of dislocations from the surface. Oxide films cause embrit-
tlement. An active sulfur EPoil has similarily been shown to embrittle steel.

Occasionally different lubricant/atmosphere combinations are in-
cluded in these tabulations. Similarily, tabulations of representative wear coefficients are
available
14
for calculation of expected wear life.
Various factors associated with the boundary lubrication requirement are given in Table
9. Values above threshold levels in the left-hand two columns lead to increasing needs for
Volume II 65
Table 8
DIMENSIONLESS FACTORS FOR ESTIMATING
BOUNDARY LUBRICATION REQUIREMENTS
a
Significant factor only when surface separation by ehd or hydrodynamic film is less
than about 5 µm (200 µ in.).
Table 9
ESTIMATED EFFECT OF FACTORS ON BOUNDARY
LUBRICATION REQUIREMENT
a
Difficult only with high thermal factor.
Copyright © 1983 CRC Press LLC