Davim J.P. Tribology for Engineers: A Practical Guide

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Tribology in manufacturing

applying solid lubricants is to incorporate them within a

synthetic resin binder and to paint or spray them onto a

surface. Some of the formulations cure in air, but others

require oven drying and curing. According to Lancaster

(1984), several common constituents of bonded-ﬁ lm lubricants

are MoS

, WS

, graphite, PTFE, pthalocyanine, CaF

/BaF

Pb, PbO, PbS, Sb

, Au, Ag, and In. Sonntag (1960) has

tabulated data for the static and kinetic friction coefﬁ cient of

solid lubricants on metals, and indicated whether or not they

exhibited tendencies for stick-slip. A selection of these data is

provided in Table 5.16. Since the conditions of use vary greatly

and may differ signiﬁ cantly from Sonntag’s testing conditions,

these values are only provided as an example of relative

Lubricant

S-S

None (steel-on-steel) 0.40 – 0.80 0.40

Molybdenum disulﬁ de 0.05 – 0.11 0.05 – 0.093 N

Tungsten disulﬁ de 0.098 0.09 N

Selenium disulﬁ de, titanium — 0.25 Y

Mica, talc — 0.25 N

Graphite — 0.25 N

Boron nitride (hexagonal) — 0.25 Y

Vermiculite 0.167 0.160 N

Beeswax (at 60–63°C) 0.055 0.05 N

Parafﬁ n (at 47–77°C) 0.112 0.104 N

Calcium stearate (157–163°C) 0.113 0.107 N

Carnauba wax (83–86°C) 0.169 0.143 N

Sodium stearate (198–210°C) 0.192 0.164 Y

Lithium 12-hydroxystearate

(210–215°C)

0.218 0.211 N

S-S, tendency for stick-slip; Y, yes; N, no.

Friction coefﬁ cients for steel lubricated by solid

lubricants

Table 5.16

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Tribology for Engineers

differences in the solid lubricating behaviour of various

materials at room temperature.

Solid lubricants are also used at elevated temperatures or in

high vacuum applications where most liquid lubricants would

volatilize, oxidize, or otherwise become unstable. Table 5.17

lists the friction coefﬁ cients of several candidate solid

lubricants obtained under the same high-temperature sliding

conditions (7.7 kgf and 7.6 mm/sec on steel at 704°C), as

reported by Peterson et al. (1969). A later compilation of

high-temperature solid lubricant friction coefﬁ cients was

produced by Allam (1991). Table 5.18 provides room-

temperature friction values of compressed powder pellets

sliding on stainless steel from a compilation by Clauss (1972).

Many of the most important solid lubricating materials

exhibit what has been called lamellar behaviour. That is,

there tend to be weak shear planes within the structure of the

material that can yield preferentially to reduce friction, if

they are properly aligned to the sliding direction. Many of

the compounds in Table 5.18 form hexagonal crystal

Kinetic friction coefﬁ cients for

several oxides at 704°C

Table 5.17

Lubricating solid

PbO 0.12

0.14

MoO

0.20

0.28

O 0.44

SnO 0.42

TiO

0.50

MnO

0.41

MoO

0.20

0.17

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Tribology in manufacturing

structures in which the shear strength is lowest parallel to the

basal planes. In the case of molybdenum disulﬁ de, there are

weak van der Waals’ bonds between covalently bonded

Mo–S layers. Moisture and air tend to reduce the effectiveness

of MoS

as a solid lubricant, since they penetrate these layers

and raise their shear stresses. On the other hand, graphite is

observed to be more lubricious in moist environments, since

interlayer species reduce the shear strength. Therefore,

molybdenum disulﬁ de is very effective in low vacuum (space)

applications, but graphite is more effective in moist

environments. Table 5.19 illustrates some of these effects,

but it should be noted that solid lubricants used in powdered

form might produce different effects on friction than the

same compositions applied by other methods.

The friction of solid lubricants is sometimes modelled by

assuming that the friction force F in a given sliding system is

Properties and friction coefﬁ cients

characteristic of certain compounds

Table 5.18

Class Compound Crystal structure

␮

Disulﬁ des MoS

Hexagonal 0.21

Hexagonal 0.142

NbS

Hexagonal 0.098

TaS

Hexagonal 0.033

Diselenides MoSe

Hexagonal 0.178

WSe

Hexagonal 0.13

NbSe

Hexagonal 0.12

TaSe

Hexagonal 0.084

Ditellurides MoTe

Hexagonal 0.20

WTe

Orthorhombic 0.38

NbTe

Trigonal 0.70

TaTe

Trigonal 0.53

Graphite C Hexagonal 0.14

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determined by the shear strength τ of the interfacial medium:

[5.55]

where A is the contact area over which shear force F is acting.

As discussed earlier in regard to friction modelling, it has

been found by Bridgman (1935) that

is a function of the

contact pressure p. Thus,

[5.56]

and the pressure coefﬁ cient α determines the change in the

saturation shear stress with pressure. Bednar et al. (1993)

have re-examined the pressure dependence of the yield

strength and, using anvil experiments, determined the

effective friction coefﬁ cient μ

eff

of metals as a function of

applied pressure p and the saturation yield stress (represented

as τ in eq. [5.55]. Thus,

[5.57]

Experimentally determined values for

and

of several

Effects of moisture on the friction coefﬁ cients

of various solid lubricants in air of various

relative humidity

Table 5.19

Solid lubricant

, dry air, RH

< 6%

, moist air,

RH = 85%

(after sliding

in dry air)

, dry air

(after sliding

in moist air)

Molybdenum disulﬁ de

powder

0.06 0.20 0.06

Molybdenum disulﬁ de

bonded ﬁ lm on disk

0.09 0.22 0.09

Molybdenum disulﬁ de

bonded ﬁ lm on both

slider and disk

0.26 0.34 0.31

Graphite powder 0.06–0.10

0.16 0.19

Initial value before ﬁ lm failure.

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metals are listed in Table 5.20. Of the three metals listed as

solid lubricants, silver and tin are used more than indium.

Interestingly, the frictional response of silver is quite suitable

for solid lubrication because there is no signiﬁ cant difference

between μ

and μ

, leading to very smooth sliding with an

absence of stick-slip behaviour.

Graphite and molybdenum disulﬁ de are among the most

commonly used solid lubricants, and it is worthwhile to

consider their frictional behaviour speciﬁ cally. Winer (1967)

compiled an extensive review of molybdenum disulﬁ de as a

solid lubricant that was published in 1967, and Fleischauer

and Bauer (1987) reviewed the chemistry and structure of

sputtered MoS

ﬁ lms. Clauss (1972) has reviewed lubrication

by graphite. Both these materials are anisotropic in properties

due to their hexagonal crystal structures, which contain wide

separations between the basal planes. When properly

oriented, for example, by running in the surface to produce

easy-shear platelet orientations, friction coefﬁ cients for

MoS

can be as low as 0.02–0.1. Graphite typically exhibits

friction coefﬁ cients of 0.10–0.15 in air. Fluorination of

graphite to produce substoichiometric graphite ﬂ uoride

Dependence of saturation shear strength and

friction of metals on the applied pressure

Table 5.20

Metal

␣␶

(MPa)

eff

(at p = 1 MPa)

Fe 0.075 173.82 0.246

Cu 0.049 107.61 0.160

0.036 109.04 0.144

Au 0.029 91.82 0.123

AI 0.035 47.56 0.082

0.012 12.30 0.024

0.006 5.65 0.011

Commonly used solid lubricants.

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Tribology for Engineers

(0.3 ≤ x ≤ 1.1) increases the spacing between the basal

planes, making it a good candidate for future lubricants.

Another method to spread the basal planes and enhance

graphite lubrication is by intercalation. Intercalation involves

the insertion of atoms between basal planes. This process

can result in signiﬁ cant enhancements of ﬁ lm life as well as

frictional performance.

As discussed by Peace (1967), the maximum use temperatures

for graphite and molybdenum disulﬁ de depend on other factors

than temperature alone. These include relative humidity,

oxygen concentration in the environment, and whether the

material is in powdered or monolithic form. In furnace

oxidation experiments, graphite powder begins to oxidize

signiﬁ cantly at about 585°C, compared with 298°C for

molybdenum disulﬁ de powder. Fusaro (1978) found that

oxidation causes molybdenum disulﬁ de ﬁ lms to blister and

fail. This is explained by the tendency of molybdenum disulﬁ de

to form oxides and sulﬁ des of various stoichiometry in air. In

the case of graphite, the oxidation is highly anisotropic, but the

rates of oxidation are slower than for molybdenum disulﬁ de.

Bisson and Anderson (1964) prepared an extensive review

of solid lubricant properties, including graphite, molybdenum

disulﬁ de, and molybdenum trioxide. For example, the

friction coefﬁ cients of various MoS

and MoO

ﬁ lms on steel

surfaces reaction to increasing sliding velocities is stunning.

Clearly, MoO

is a very poor lubricant. As the temperature

increases in air, molybdenum disulﬁ de undergoes changes in

colour and rate of oxidation. Table 5.21 summarizes these

changes, as discussed by Bisson and Anderson. Molybdenum

disulﬁ de and graphite can each be used as solid lubricants,

but attempts have been made to determine whether mixing

them together would provide synergistic effects. Gardos

(1987), for example, reviewed the use of graphite as an

oxygen scavenger to help molybdenum disulﬁ de ﬁ lms retain

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Tribology in manufacturing

low friction characteristics. Some limited advantages in

enhancing the stability and wear resistance of the

microcrystalline molybdenum disulﬁ de ﬁ lms in air were

reported. About the same time, Bartz et al. (1986) in Germany

studied the friction of bonded ﬁ lms containing various

combinations of graphite, molybdenum disulﬁ de, and

antimony thioantimonate [Sb(SbS

)]. Using a block-on-ring

apparatus, after sandblasting the 100CrMn6 steel ring, they

applied bonded ﬁ lms to it, but left the 90MnCrV8 steel block

untreated. A method of assessing the effectiveness of the

blends was to measure the stable, post-running-in friction

coefﬁ cient. Table 5.22 lists values of μ for several combinations

of lubricants.

Briscoe (1992) has reviewed the mechanisms of organic

polymer friction, stating that two non-interacting contributions,

adhesion and plowing, can be used to model behaviour. In

this treatment, frictional energy is dissipated by an interface

zone (adhesive) and a subsurface zone (deformation and/or

plowing). In the latter zone, behaviour in polymers may

be viscoelastic, plastic, or brittle. The friction coefﬁ cient

Transformations in molybdenum disulﬁ de as

temperature rises

Table 5.21

Temperature range (ºF) Temperature range (ºC) Behaviour

Up to 750 Up to 400 No detectable

oxidation rate

750 – 800 400 – 427 Thin oxide ﬁ lm

forms

800 – 850 427 – 454 Slow, but

appreciable

oxidation

850 – 900 454 – 482 Yellowish white

MoO forms

Over 900 Over 482 Rapid oxidation

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Tribology for Engineers

could be derived from geometric arguments to produce the

form

[5.58]

where the angle θ was associated with the roughness of the

surface. Briscoe found that if PTFE behaved in a more brittle

fashion, as it did after irradiation by gamma rays, the same

expression could be similarly written:

[5.59]

where the value of x, the slope of the dependence of friction

on tan

, varied from 0 to 2 depending on the degree of

embrittlement (i.e., the extent of plastic ﬂ ow). When tan θ

exceeded approximately 2.3, irrespective of x, the PTFE

began to exhibit chip-forming characteristics rather than

ﬂ ow. Like other materials, the shear stress of PTFE was seen

to vary with contact pressure.

Since PTFE has a relatively low hardness, various additives

are mixed with it to improve its wear resistance. Table 5.23

shows the effects of certain additives on the friction coefﬁ cient

and wear of PTFE sliding on steel at 0.01 m/sec. Comparing

the ﬁ rst and last row of data shows how it is possible to increase

wear resistance by more than three orders of magnitude while

Steady-state friction coefﬁ cients for solid

lubricant combinations

Table 5.22

Film composition

, Steady state

Graphite alone Unstable

MoS

alone 0.05

Graphite + MoS

(about 1:2 wt% ratio) 0.01 – 0.02

Graphite + Sb(SbS

) (about 3:4 wt% ratio) Unstable

MoS

+ Sb(SbS

) (about 4:5:1 wt% ratio) 0.1 – 0.03

Graphite + MoS

+ Sb(SbS

) 0.04 – 0.05

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Tribology in manufacturing

raising the sliding friction coefﬁ cient of the material by at most

about 0.03. Erdemir (1994) reviewed some of the important

mechanisms responsible for the lubricating action of solid ﬁ lms

on ceramics such as silicon carbide, silicon nitride, and

aluminium oxide. He stated that solid lubrication may be the

only option available to help lubricate ceramics in severe

environments, but noted that like other types of lubricants,

solid lubricants suffer from ﬁ nite lifetimes. He discussed the

use of boric oxide (B

) and its product with water, and boric

acid (H

) in particular. Boric acid resembles other lubricants

with layered structures, and produces favourable friction

reductions under some circumstances. However, when the

temperature rises above about 170°C, boric acid decomposes

to boric oxide and loses its layered structure.

5.4 Tribology of rolling

Rolling is a process that cannot be conducted without friction

as friction is needed to draw the work piece into the roll gap

and to deform it. The minimum value of friction is twice that

needed for continuous rolling. The effects of friction are

connected to the geometric description of the process known

as the L /h ratio, where L is the projected length of the arc of

Effect of additives on the friction of blended

PTFE

Table 5.23

Material composition Wear rate improvement

Unﬁ lled PTFE 1 0.10

15 wt% graphite 588 0.12

15 wt% glass ﬁ bre 2857 0.09

12.5 wt% glass ﬁ bre and 12.5

wt% MoS

3333 0.09

55 wt% bronze and 5 wt% MoS

4000 0.13

Ratio of the wear rate of unﬁ lled PTFE to that of the given material.

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Tribology for Engineers

contact and h is the mean strip thickness. At L/h > 2, deformation

is homogeneous and the limiting strip thickness may be

reached. At L/h < 2, there is an inhomogeneity and at L/h < 1,

sticking friction occurs, so lubricants are applied to reduce

friction and wear. In cold rolling, lubricants are used to reduce

friction, although a minimum amount is required. Surface

ﬁ nish requirements are friction dominated. In hot rolling,

lubricants are used to control adhesion between material and

roll. Lubricants may be oil or water based, and extreme

pressure additives are used where there is a mixed-ﬁ lm

lubricating mechanism. The most commonly used lubricants in

rolling are shown in Table 5.24.

Commonly used lubricants and typical

(friction coefﬁ cient) values in cold and hot

rolling

Table 5.24

Material Hot rolling

– lubricant

Hot rolling

–

Cold rolling –

lubricant

Cold rolling

–

Steel Water

Emulsion of

fat + EP

additive

Fat (ester) +

EP additive

+ water

Sticking

0.4

0.3

3–6% emulsion

of palm oil

0.01 – 0.03

Al and Mg

alloys

Emulsion,

2–15% of

mineral oil

0.4 Mineral oil with

1–5% fatty

acid

0.01 – 0.03

Cu and Cu

alloys

Emulsion,

2–8% of

mineral oil

0.3 2–10%

concentration

of mineral oil

with fat

0.01 – 0.03

Ti alloys Fat + water Sticking Esters or soap

Castor oil

Compounded

mineral oil

0.2

Refractory

metals

Dry 0.3 Mineral oil with

boundary and

EP additives

0.01–0.03

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