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

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Tribology for Engineers

active, two other parts of the piezo elements are used to move

the tip in a plane parallel to the surface to scan over the surface.

In the scanning process, every time that the last atom of the

tip is precisely over a surface atom, the tip needs to be retracted

a little bit, while it has to be brought slightly closer when

the tip atom is between the surface atoms. This automatically

leads the tip to follow a bumpy trajectory, which replicates the

atoms of the surface. Information about the trajectory is

available in the form of the voltages that have been applied by

the feedback electronics being visualized in the form of a

collection of individual height lines or in the form of grey scale/

colour scale representation or in some three-dimensional

perspective views.

More recently, the atomic force microscope (AFM) has

been developed to investigate surfaces of both conductors

and insulators on an atomic scale. Like the STM, the AFM

relies on a scanning technique to produce very high-

resolution, three-dimensional images of sample surfaces. In

the AFM, the ultra-small forces (less than 1 nN) present

between the AFM tip and sample surface are measured by

the motion of a very ﬂ exible cantilever beam having an ultra

small mass. The AFM combines the principles of the STM

and the stylus proﬁ ler, but the important difference between

the AFM and the STM is that in the AFM, the tip gently

touches the surfaces. The AFM does not record the tunnelling

current but the small force between the tip and the surface:

the AFM tip is attached to a tiny leaf spring, the cantilever,

which has a low spring constant, and the bending of the

cantilever is detected with the use of a laser beam, which is

reﬂ ected from the cantilever. The AFM thus measures

contours of constant attractive or repulsive force. The

detection is made very sensitive such that the forces as small

as a few pico-Newton can be detected. Forces below 1 nano-

Newton are usually sufﬁ ciently low to avoid damage to

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Surface topography

either the tip or the surface. Since AFM does not rely on the

presence of a tunnelling current, it can also be used on non-

conductive materials. Soon after the introduction of the

AFM, it was realized that the same instrument could also be

used to measure forces in the direction parallel to the surface,

i.e., the friction forces. When modiﬁ cations are incorporated

for atomic scale and microscale studies of friction, it is

termed as the friction force microscope (FFM) or the lateral

force microscope (LFM). The FFM usually detects not only

the deﬂ ection of the cantilever perpendicular to the surface,

but also the torsion of the cantilever resulting from one

lateral force. Schematic of the AFM/FFM commonly used

for measurements of surface roughness, friction, adhesion,

wear, scratching, indentation and boundary lubrication from

micro to atomic scales is shown in Fig. 1.14.

In all surface proﬁ lometric methods, roughness (small-

scale irregularities) and form error (deviation from its

Schematic operation of AFM/FFM

Figure 1.14

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intended shape) remain coupled in the recorded data. Form

error may be subtracted from the recorded data to provide

only the roughness features by different means. The two

most common methods used in stylus proﬁ lometer are the

use of datum-generating attachments and the use of large

radius skids or ﬂ at shoes. With these the average local

level is used, as datum and form error or waviness is not

recorded. Other methods include the use of ﬁ ltering the

displacement signal corresponding to waviness. Table 1.2

summarizes the comparison of the different roughness

measuring methods.

1.8 Summary

Solid surfaces always contain deviations (roughness) from

the prescribed geometrical form. Surface roughness is

commonly characterized by average amplitude parameters:

and R

. Height distribution and autocorrelation functions

are used to completely characterize a random and isotropic

surface. A surface contains a large number of length scales of

roughness superimposed on each other, so commonly

measured roughness parameters depend on the resolution of

the measuring instrument and thus are not unique. Fractal

analysis, Fourier transform and the wavelet transformation

method can be used to characterize the multiscale nature of

rough surfaces and various measurement techniques are used

for roughness measurements. For on-line measurements,

optical techniques such as specular reﬂ ection and diffuse

reﬂ ection are commonly used. For off-line measurements,

stylus proﬁ lers, atomic force microscopes and optical

interferometers are very common.

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Method Quantitative

data

3-D

data

Resolution at maximum

magniﬁ cation (nm)

On-line

measurement

capability

Limitations/Comments

Horizontal Vertical

Stylus method Yes Yes 15–100 0.1–1 No Operates along linear track, contact type

can damage sample, slow speed in 3-D

mapping

Optical methods

Light sectioning Limited Yes 500 0.1–1 No Qualitative

Taper sectioning Yes No 500 25 No Destructive, tedious specimen preparation

Specular reﬂ ection No No 10

–10

0.1–1 Yes Semiquantitative

Diffuse reﬂ ection Limited Yes 10

–10

0.1–1 Yes Smooth surfaces (<100 nm)

Speckle pattern Limited Yes Yes Smooth surfaces (<100 nm)

Optical interference Yes Yes 500–1000 0.1–1 No

SEM Limited Yes 10 0.1 No Operates in vacuo, limits on specimen size

TEM Limited Yes 0.5 0.02 No Operates in vacuo, requires replication

of surface

STM Yes Yes 0.2 0.02 No Requires a conducting surface, scans

small areas

AFM Yes Yes 0.2–1 0.02 No Scans small areas

Summary and comparison of roughness measurement methods

Table 1.2

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1.9 References

Abbott, E. J. and Firestone, F. A. (1933), ‘Specifying surface

quality’, Mech. Eng. 55: 569–72.

Anonymous (1985), Surface Texture (Surface Roughness,

Waviness, and Lay), ANSI/ASME B46.1, ASME, New

York.

Bhushan, B. (1996), Tribology and Mechanics of Magnetic

Storage Devices (2nd edn), Springer, New York.

Buckley, D. H. (1981), Surface Effects in Adhesion, Friction,

Wear and Lubrication, Elsevier, Amsterdam.

Ganti, S. and Bhushan, B. (1995), ‘Generalized fractal

analysis and its applications to engineering surfaces’, Wear

180: 17–34.

Ling, F. F. (1990), ‘Fractals, engineering surfaces and

tribology’, Wear 136: 141–56.

Majumdar, A. and Bhushan, B. (1990), ‘Role of fractal

geometry in roughness characterization and contact

mechanics of surfaces’, ASME J. Tribology 112: 205–16.

Sahoo, P. and Roy Chowdhury, S. K. (1996), ‘A fractal

analysis of adhesion at the contact between rough solids’,

Proc. IMechE. Part J: J. Engineering Tribology 210:

269–79.

Thomas, T. R. (1982), Rough Surfaces, Longman, London,

UK.

Whitehouse, D. J. (1994), Handbook of Surface Metrology,

Institute of Physics Publishing, Bristol, UK.

Williamson, J. B. P. (1968), ‘Topography of solid surfaces’,

in Interdisciplinary Approach to Friction and Wear (P. M.

Ku, ed.), SP-181, pp. 85–142, NASA Special Publication,

NASA, Washington, DC.

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Friction and wear

A.-E. Jiménez and M.-D. Bermúdez,

Universidad Politécnica de

Cartagena, Spain

Abstract: This chapter is an introduction to the dry friction

and wear for sliding contacts. The concepts of friction

and wear, their corresponding coefﬁ cients and their main

mechanisms are described, including stick-slip effects,

adhesion and ploughing. Adhesive, abrasive, erosive

and erosion-corrosion wear mechanisms are described.

Friction–wear relationships are discussed and wear maps

are introduced.

Keywords: dry friction and wear, friction and wear

mechanisms.

2.1 Friction

Friction between contacting bodies is manifested as the force

that must be overcome to initiate or sustain motion, and as

the energy dissipated during relative motion (Bogdanovich

et al., 2009). The term friction describes the gradual loss of

kinetic energy for materials or bodies in relative motion

(Röder et al., 2000), while the dry friction of materials can

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be deﬁ ned as the resistance to the relative movement between

two surfaces in contact (ASM Handbook, vol. 18, 1992;

Bushan, 2001; Czichos, 1978). From an engineering point of

view, friction is a major cause of energy waste dissipated as

heat, and a major cause of components and equipments

failure (Bayer, 2002).

2.1.1 Friction coefﬁ cient, friction laws

Sliding friction has been described by the following laws

(Hutchings, 1992; Williams, 1996):

First law of friction

The ﬁ rst law states that the friction force F between a pair of

loaded sliding surfaces is proportional to the normal load W

(Fig. 2.1), that is, the tangential force required to slide

a body along a surface is proportional to the weight of the

body. The proportionality constant between F and W is

known as the coefﬁ cient of friction, μ.

Scheme of two contacting bodies in relative

motion

Figure 2.1

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Coefﬁ cient of friction: Deﬁ nition

The ﬁ rst law can be expressed by the simple equation:

F = μW [2.1]

where μ is called the coefﬁ cient of friction. This expression

also implies the second law.

Second law of friction

The second law of friction is derived from the ﬁ rst:

The friction force is independent of the apparent area

of contact.

Once sliding stops, the force needed to initiate sliding (static

friction) is greater than the force needed to sustain sliding

(kinetic friction). The dependence of friction force with

sliding velocity is very small.

Third law of friction

Kinetic friction is independent of sliding velocity, which

is really an approximation.

The ﬁ rst two laws are known as Amontons’ laws, who

formulated them in the Proceedings of the French

Academy of Sciences in 1699. The third law is due to

Coulomb.

These laws are not derived from fundamental principles, but

they are rather empirical ones based on experimental

observations. In order to understand when these laws can be

applied, it is necessary to analyse their physical origins

(Santner et al., 2005).

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2.1.2 Static and kinetic friction

When considering how friction originates at the atomic level,

it is convenient to separate the problem into two regimes:

1. Static friction: the force needed to overcome the potential

energy barriers between atoms in order to initiate sliding.

2. Kinetic friction: the mechanisms for dissipating energy as

atoms slide over each other.

Figure 2.2 shows a friction curve as a function of sliding

displacement. The maximum friction value appears after a

short sliding distance from the origin.

2.1.3 Stick-slip

In practice, friction-distance records obtained in tribological

tests are not smooth curves. Sliding surfaces often exhibit

stick-slip behaviour rather than continuous forces (Berman

et al., 1996; Chatelet et al., 2008; Rapoport, 2009; Yoshizawa

et al., 2003).

Figure 2.3 shows the real-time variation of friction with

sliding distance for a pin-on-disc metal-metal contact. After

a maximum friction value during the running-in period, a

Variation of the friction coefﬁ cient with sliding

distance

Figure 2.2

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Friction and wear

steady-state is reached, where oscillations of friction are

observed due to the stick-slip effect.

Stick-slip, or interrupted motion rather than smooth

uninterrupted motion (Fig. 2.4) occurs in many different

phenomena such as friction, ﬂ uid ﬂ ow, material fracture

Friction coefﬁ cient–sliding distance record

obtained in a pin-on-disc test for a metal–metal

contact under dry conditions

Figure 2.3

Stick-slip effect

Figure 2.4

Adapted from Hutchings (1992).

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