Czichos H., Saito T., Smith L.E. (Eds.) Handbook of Metrology and Testing

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748 Part D Materials Performance Testing

Category Type of tests

Machinery

field tests

Machinery

bench tests

Systems

bench tests

Components

bench tests

Model tests

Laboratory tests

Symbol

Increasing

cost

Increasing

complexity

Increasing

control

Increasing

flexibility

III

Fig. 13.4

Schematic illus-

tration of types

of tribological

test (after [13.3])

the tribological performance of materials when they are

being developed or selected for a general ﬁeld of ap-

plication, but when the speciﬁc conditions that will be

applied are not well-deﬁned. In this case there is little

information to guide the speciﬁcation of the test param-

eters to be used in any test program, and indeed the

speciﬁc test that should be used is not always clear.

However, it is important to consider carefully how the

materials will be used in order to eliminate inappropri-

ate tests that will only lead to misleading results. Thus,

for materials that are being developed for applications

where abrasion is extremely likely to occur, sliding wear

tests cannot be expected to give relevant data. Neverthe-

less, so long as the likely mode of wear can be predicted,

useful information can be obtained on the likely perfor-

mance of the materials in practice.

The second situation is where there is a requirement

to simulate a speciﬁc application. Here the conditions

that are operating in the tribological contact should be

better deﬁned, so that the design of a program of lab-

oratory wear tests reduces to choosing the appropriate

test and test parameters to achieve the correct simulation

of the practical application. Although in some cases the

best approach is to design and manufacture a speciﬁc

rig that is intended to reproduce the conditions in the

application precisely, in most cases a well-established

test can be used, perhaps with some adjustment of the

test parameters, to provide a reasonable match with the

application. The selection of these parameters is the key

to generating a valid test.

As it is often difﬁcult to achieve an exact simulation

in the laboratory, it is always important to check that

the same mechanisms of wear occur in the laboratory

test as in the real application. When this is achieved,

the laboratory test is likely to give results that will reli-

ably predict performance in the application. Figure 13.5

shows an example of such a comparison, from tests per-

formed to simulate the abrasion of cemented carbide

extrusion tools used to form ceramic roof tiles. The fea-

tures of the worn surfaces of the cermets were very

similar in both laboratory tests and the samples recov-

ered from the practical application, and subsequent ﬁeld

trials showed an excellent match between the results of

the laboratory tests and the lifetimes of the components

in service.

13.2.2 Test Parameters

Many parameters control and deﬁne the conditions in

a tribological contact, and hence inﬂuence the result-

ing wear and friction. Important examples are listed

in Table 13.1. Some of these parameters are only appli-

cable to speciﬁc types of wear; for example the shapes

of abrasive or erodent particles are relevant only to the

processes of abrasion or erosion.

A full description of the effects of these test pa-

rameters is well beyond the scope of this chapter. The

reader should refer to other sources for a fuller descrip-

tion [13.4, 5], but some aspects are discussed brieﬂy

here.

Part D 13.2

Friction and Wear 13.2 Selection of Friction and Wear Tests 749

Table 13.1 List of some important parameters that inﬂuence tribological processes

Parameter Units or type of information

Normal load N

Sliding speed m/s

Materials of triboelements All aspects of composition and microstructure, at surface as well as sub-

surface

Test environment (including any lubricant present) Composition, chemical and physical properties of gas and/or liquid sur-

rounding tribological contact

Temperature

◦

Type of relative motion between surfaces Trajectory: sliding, rolling, impact etc.

Contact geometry (form) Shapes of surfaces

Contact geometry (local) Roughnesses of surfaces

Abrasive/erosive particles Material, shape (and distribution), size (and distribution)

Contact dynamics Stiffness, damping, inertial mass

In laboratory testing it is normal to positively con-

trol only a few test parameters such as the applied

normal load, relative speed and contact geometry. Other

parameters that can have a major effect on the resulting

wear and friction are the presence of lubrication, the en-

vironment and atmosphere of the test (including the air

humidity), the bulk temperature of the samples, and the

mechanical dynamics of the test system. These parame-

ters are normally held constant from one test to another,

either by the application of a speciﬁc control method-

ology, or simply by using the same test system for the

whole sequence of tests in the program.

The contact geometry is a crucial parameter in the

design of a wear test where two bulk surfaces are in

moving contact, as in sliding. The ideal situation, in

which the nominal contact area, and hence nominal con-

tact pressure, would not vary during the test, would be to

achieve self-aligning conformal contact between the test

samples. This can be achieved in some cases by careful

design of the samples and their holders, but often it can-

not be achieved, and then high initial contact stresses

occur at the edges of the misaligned contacts. To avoid

this uncontrolled nonconformal geometry, it is common

to use a controlled nonconformal geometry with one tri-

boelement in the form of a ball or spherically-ended

pin loaded against a ﬂat sample. A ball diameter of

about 10 mm is typically used. The disadvantage of this

approach is that although the initial contact geometry

is well controlled, the initial contact stresses are high.

The ball or pin then wears rapidly until a larger con-

tact area is produced, resulting in a substantially lower

contact pressure. This change may lead to a change in

Fig. 13.5a,b Example of comparison of worn surfaces

from a laboratory simulation and a practical application.

The SEM images show WC/Co tools used to manufac-

ture concrete tiles: (a) worn surface from production tool;

(b) worn surface of sample after laboratory wear testing 

Part D 13.2

750 Part D Materials Performance Testing

wear mechanism from the initial high-stress regime to

a subsequent low-stress, larger contact area regime. An

approach that reduces this effect is to use one triboele-

ment with a large contact radius so that although the

initial contact geometry is still well deﬁned, the initial

contact pressure is lower, and changes in mechanism are

less likely.

The temperatures of the contacting triboelements

can affect the tribological behavior through changes in

their mechanical and chemical properties. As well as

these bulk effects, the areas of the samples in contact

become hotter through frictional heating; the power dis-

sipated in the contact is given by μNv where μ is the

friction coefﬁcient, N is the normal load, and v is the

relative sliding velocity. The local temperatures at the

contact areas can therefore become much higher than

the bulk temperatures [13.6]. This factor needs to be

taken into account when designing wear tests or inter-

preting test results.

As outlined in Sect. 13.1.3, lubrication of the con-

tacts will also affect the wear, often in terms of

mechanism as well as amount. Under certain condi-

tions of sliding speed, load and lubricant viscosity,

the two surfaces become separated by a continuous,

hydrodynamically-generated lubricant ﬁlm, and the

wear rate can fall to a very low level, as indicated

in Fig. 13.3. Hydrodynamic lubrication (a thick lubri-

cant ﬁlm) is favored by low normal pressure, high

lubricant viscosity, and high sliding speed. For con-

ditions where the lubricant ﬁlm thickness becomes

comparable with the roughness of the triboelements,

elastic deformation of these bodies becomes important

and the pressure in the lubricant is high enough to

cause a signiﬁcant local increase in viscosity; this is

the regime of elastohydrodynamic lubrication (EHL).

For even thinner ﬁlms (at low speeds or high contact

pressure), the system enters the regime of boundary lu-

brication, where appreciable interaction occurs between

asperities on the two surfaces. Here the chemical com-

position of the lubricant has a major effect on the nature

and properties of the chemically formed surface ﬁlms

and on the wear that occurs.

13.2.3 Interaction with Other Degradation

Mechanisms

Other degradation mechanisms such as chemical reac-

tion and fatigue can also make a major contribution to

the overall loss of material from moving contacting sur-

faces. Interactions often occur with the test environment

through chemical reactions of the test materials. In wear

corrosion, the triboelements are exposed to an aqueous

medium, and corrosion of the materials acts in conjunc-

tion with mechanical processes to alter the amount of

material lost. There is positive synergy in most cases,

so that the mass loss is greater than the sum of the con-

tributions expected from pure corrosion or pure wear

alone. Exceptionally, in negative synergy, corrosion can

form a mechanically stronger layer on the surface which

acts to protect the surface and thus reduce the total wear

rate. Tribochemical reactions of materials may also oc-

cur; ceramics, for example, can react with water vapor

to form hydroxides that reduce friction and protect the

wearing surface.

When metals are heated, either through a bulk

increase in temperature or by frictional heating, con-

siderable oxidation can occur. At ﬁrst this may reduce

wear, as seen in the mild wear of steels, but as the

temperature increases further, the production of weak

oxide may increase to such an extent that the wear rate

increases once more [13.4].

In many tribological systems, the surfaces of

the contacting materials are subjected to alternating

stresses. These stresses may be high enough to initi-

ate and grow fatigue cracks in the material that may

contribute to the material loss caused by other wear

processes. Rolling contact fatigue is an important degra-

dation mechanism in certain applications of materials,

but lies outside the scope of this chapter.

13.2.4 Experimental Planning

and Presentation of Results

When planning a program of tribological tests, the

choice of test conditions must be determined, either

by the relevant engineering application, or in order to

achieve the appropriate mechanism of wear in more

fundamental studies. In the development of materials,

a range of conditions can be chosen to represent those

likely to occur during actual use of the material.

There are many test factors that need to be con-

trolled during a test. These can be grouped into those

concerned with the mechanical test conditions (such

as contact load or pressure, speed, motion type and

test environment), and sample parameters (such as

material composition, microstructure and the initial

surface ﬁnish of the samples). A full program of test-

ing under all combinations of these factors would be

time-consuming and costly, and may not be required.

Often a single factor can be identiﬁed as key to the

material response, and in this case a good approach

is to set all the other factors at constant values and

Part D 13.2

Friction and Wear 13.3 Tribological Test Methods 751

vary the chosen factor in a controlled way in a se-

ries of tests. This approach is termed a parametric

study. More complex statistical, experimental design

procedures can be used, but care needs to be taken

in the design of experiments to account for the vari-

ability that is normally observed in the results of wear

tests.

Mapping techniques can be used where two (or

more) factors are changed in a controlled way (normally

more coarsely than in parametric studies), with the fric-

tion and wear results plotted either as individual points

or as contours. Regions on the map are then delin-

eated on a mechanistic basis, with the region boundaries

either deﬁned by identifying the wear mechanism by

microstructural techniques, or by identifying transitions

in friction and wear behavior as sudden changes in wear

rate or friction coefﬁcient. The mapping procedure is

a very efﬁcient way of determining the overall behav-

ior of a material because it provides useful information

about the position of transitions in wear behavior in

a systematic and controlled way. This comes at the ex-

pense of a reduction in the detailed knowledge of the

variation of friction and wear with any one factor, but

once the regime of interest is better deﬁned through the

use of mapping studies, then a more detailed parametric

study can be conducted.

13.3 Tribological Test Methods

This section gives some information on the tribologi-

cal tests that are in common usage, and which have in

many cases been standardized, particularly through the

American Society for Testing and Materials (ASTM).

Due to constraints on space, only a brief description

can be given. Further information can be obtained from

other sources [13.5, 7–12]. The main test parameters,

the measurements that can be made, and the standards

associated with each type of test are listed.

13.3.1 Sliding Motion

Wear tests for materials in sliding contact are character-

ized by continuous contact between the two samples in

tribological contact. There are two distinctly different

types of test.

In many tests, the extent of relative movement is suf-

ﬁciently large (typically greater than 300 μm) so that all

contact points on at least one of the bodies are out of

contact for some of the test period. This is in contrast

to the case of fretting, where at least part of the contact

area on both samples is always in contact. In fretting

tests, the debris is trapped at the interface between the

two samples, leading to different behavior from that in

tests involving larger extents of movement, in which the

debris is more readily lost from the contact region.

Common tribological test geometries involving slid-

ing motion are shown in Fig. 13.6. Pin-on-disc and

reciprocating geometries are used most often, but pin-

on-disc testing with continuous rotary motion is often

not appropriate since many applications involve recipro-

cating motion. This difference is important, as it affects

the retention of debris at the wear interface and the

stress history on the surfaces. Fretting tests are always

Pin on disc Pin on ring

Pin on flat Crossed cylinder Thrust washer

Fig. 13.6 Examples of test geometries used for tribological

tests involving sliding motion

carried out with a reciprocating geometry; particular

care is needed in apparatus design as the elastic defor-

mation of the test system can be similar in magnitude

to the required sample motion, leading to difﬁculties

controlling and measuring sample displacement.

Often balls are used instead of pins, and in some

cases blocks (with large contact areas) are also used.

The choice of a conformal or nonconformal contact ge-

ometry and the frictional generation of heat are factors

that need to be carefully considered.

13.3.2 Rolling Motion

Tribological contacts often involve rolling motion. Suit-

able test geometries are shown in Fig. 13.7.Ifthe

application is concerned with bearing races, then this is

Part D 13.3

752 Part D Materials Performance Testing

Four ball test Balls in bearing race

Roller on roller

Fig. 13.7 Examples of test geometries used for tribological

tests involving rolling motion

one situation where laboratory tests can be carried out

relatively easily on the components themselves. This is

clearly appropriate for roller bearing applications, but

the complexity of the test geometry means that it is of-

ten difﬁcult to develop a fundamental understanding of

the wear and friction processes that occur.

The four-ball test has been popularly used for many

years to test, in particular, the maximum load and speed

for failure at the contact points in this test geometry,

from mechanisms such as scufﬁng and seizure. How-

ever, results from this test, which can involve very high

contact pressures and frictional power dissipation, are

not readily extended to practical applications, and the

method also suffers from a lack of control of the detailed

motion of the balls during the test.

In two-roller testing, on the other hand, there is in-

dependent control of the motion of the rollers, and it is

possible to adjust the amount of relative sliding between

Pin on rotating

abrasive disc

Plate against rotating

wheel with feed of abrasive

Block on a moving plate

in a bath of slurry

Pin on rotating abrasive

disc with spiral track

Wear of pin in rotating

pot of slurry

Micro-scale abrasion test

with rotating ball on plate

in presence of abrasive

Drive shaft

Abrasive

slurry

Fig. 13.8 Examples of test geometries

involving abrasion

them as well as the rolling speed. The cylindrical edge

of the rollers sometimes has a ﬂat cross-section, but is

also commonly crowned.

13.3.3 Abrasion

Abrasion testing can be carried out with a range of tests,

asshowninFig.13.8. The simplest type of testing is car-

ried out by loading a sample pin against abrasive-coated

paper supported on a solid backing. As well as using

a rotating abrasive-covered disc, tests can also be car-

ried out with abrasive paper held on to a drum, or with

a belt of abrasive paper. An important issue with these

tests is that, as abrasion of the test sample takes place,

the abrasive paper degrades by clogging with wear de-

bris and due to damage to the contacting regions of the

abrasive particles, so that the wear of the test sample

will typically decrease as the test progresses; in extreme

cases the wear mechanism may change as sliding then

occurs predominantly against debris rather than against

the abrasive particles. The use of a spiral track on the

abrasive paper can achieve a steady process of wear by

ensuring abrasion against fresh particles.

In another common type of abrasion test, a sam-

ple is pressed against a rotating wheel in the presence

of a continuous supply of free abrasive particles. An

important parameter in these tests is the stiffness of

the wheel or other counterbody. Tests can also be car-

ried out dry or in ﬂuids of different types, allowing

tests to be made in the presence of corrosive media.

Some tests with rotating wheels involve the recir-

culation of abrasive during a single test (ASTM B

611 [13.8]), while in others a continuous stream of

Part D 13.3

Friction and Wear 13.3 Tribological Test Methods 753

abrasive passes through the wear interface and is not

reused (such as the dry sand rubber wheel abrasion test,

ASTM G 65 [13.8]).

A test that has received some prominence recently

is the microscale abrasion test, in which a ball is rotated

against a ﬂat sample in the presence of abrasive. This

test is particularly suited to determining the abrasion

rateofacoating.

13.3.4 Erosion by Solid Particles

There are two main groups of particulate erosion tests,

in which the particles either strike the sample in a gas

(usually air), or are transported in a liquid, which is

usually termed slurry erosion. Examples are shown

in Fig. 13.9.

In the centrifugal accelerator, the erodent particles

are accelerated along radial tubes in a rotor so that

a stream of erodent particles emerges at some angle to

the rotor periphery (which depends on the detailed de-

sign) to strike one or more samples located in a ring

around the rotor. This test has the advantage that several

different samples can be tested simultaneously, but there

is usually some uncertainty in the angle with which

the particles strike the samples, and only a fraction of

the particles fed into the apparatus actually strike the

samples. Some designs of centrifugal accelerator impart

signiﬁcant rotation to the particles, which may inﬂuence

the resulting erosion rate. In the gas-blast test a com-

pressed gas stream (usually air) accelerates the erodent

particles along a nozzle towards the sample, which is

held at a controlled angle to the stream. In this case only

one sample can be tested at a time.

In slurry erosion testing a pump can be used to gen-

erate liquid ﬂow through a nozzle. Erodent particles are

incorporated into the jet, being either picked up through

a venturi system or suspended in the erodent slurry. The

resulting jet of slurry is directed against the test sample

held at a controlled angle.

In all erosion tests the particle impact speed and the

angle of impingement of the erodent stream against the

sample are the most important variables.

13.3.5 Scratch Testing

Scratch testing was originally developed to evaluate the

adhesion of coatings. In the scratch test an indenter of

well-deﬁned geometry is pressed onto and moves rel-

ative to a sample under a ﬁxed or increasing normal

load. The tangential force resisting the motion (usually

described as the friction force) and acoustic emission

Gas in

Test chamber

Funnel

Flow

gauge

Pump

Test

solution

Specimen

Sand bed

Ejector

Pressure

gauge

Fig. 13.9a–c Examples of tests involving erosion by solid

particles: (a) gas-blast test; (b) centrifugal accelerator;

from the sample are often both measured continually.

The acoustic emission signal typically increases sharply

when a brittle coating is cracked, or the coating delam-

inates from the substrate.

When the test was developed, the adhesion of typi-

cal engineering coatings was quite poor and the scratch

test provided reasonable results, representative of the

adhesion of the coating. More recent coatings are much

more adherent, and although the scratch test remains an

extremely valuable test for coatings, the results are more

difﬁcult to interpret, giving information on the complex

response of the coating–substrate composite system to

the movement of the indenter.

In the context of wear testing, scratch testing can be

used as a model abrasion test; the response of a ma-

terial to the scratching of the indenter is treated as

Part D 13.3

754 Part D Materials Performance Testing

an analog of its response to a hard asperity or abra-

sive particle. Parameters such as the frictional force

generated and the scratch width can be measured.

Multiple scratches can be made both in the same po-

sition or intersecting one another to extend the model

range.

13.4 Friction Measurement

As discussed in Sect. 13.1.1, the measurement of fric-

tion involves the measurement of the friction force.

For a rotating component it may be useful to deﬁne

the friction torque, the measurement of which also in-

volves a force measurement combined with a length

measurement.

13.4.1 Friction Force Measurement

A friction force measurement system is made up of one

or more force transducers mounted between one of the

triboelements and the base frame of the tribometer, and

their associated instrumentation. A practical force trans-

ducer usually consists of a chain of several transducers.

For example, the force may act upon and bend a metal

beam, and the bending then alters the electrical resis-

tance of a strain gauge bonded to the surface of the

beam by an amount proportional to the force. For many

types of force measurement system, the term load cell

is commonly used in place of force transducer.

Most force transducers employ some type of elas-

tic load-bearing element or combination of elements.

Application of force to the elastic element causes it

to deﬂect, and this deﬂection is then sensed by a sec-

ondary transducer which converts it to an output. The

output may be in the form of an electrical signal (as

from a strain gauge or LVDT, a linear variable differ-

ential transformer), or a mechanical indication (as in

proving rings and spring balances). However, the most

common method is for longitudinal and lateral strains

to be sensed, and when this is done by electrical resis-

tance strain gauges the transducer is known as a strain

gauge load cell.

13.4.2 Strain Gauge Load Cells

and Instrumentation

A strain gauge load cell is based on an elastic ele-

ment to which a number of electrical resistance gauges

are bonded. The geometric shape and elastic modulus

of the element determines the magnitude and distri-

bution of the strain ﬁeld produced by the force to

be measured. Each strain gauge responds to the lo-

cal strain at its location, and the measurement of force

is determined from the combination of these individ-

ual measurements of strain. Each elastic element is

designed to measure the force acting in a particular di-

rection, and not to be affected by other components

such as side loads. The material used for the elastic ele-

ments is usually tool steel, stainless steel, aluminum or

beryllium–copper. The material should exhibit a linear

relationship between the stress (proportional to the force

applied) and the strain (output), with low hysteresis and

creep in the working range. A further requirement is

a high repeatability between force cycles, with no fa-

tigue effects.

The most common materials used for strain

gauges are copper–nickel, nickel–chromium, nickel–

chromium–molybdenum and platinum–tungsten alloys.

The foil strain gauge is the most widely-used type be-

cause it has signiﬁcant advantages over the other types

and is employed in the majority of precision load cells.

A foil strain gauge consists of a metal foil pattern sup-

ported on an electrically insulating backing of epoxy,

polyimide and glass-reinforced epoxy phenolic resin.

It is constructed by bonding a sheet of thin rolled

metal foil, 2–5 μm thick, on a backing sheet 10–30 μm

thick. The measuring grid pattern including the terminal

tabs is produced by photoetching, in a process sim-

ilar to that used in the production of printed circuit

boards.

Semiconductor strain gauges are manufactured from

n-type or p-type silicon. The output from a semiconduc-

tor gauge is about 40 to 50 times greater than that from

a metal foil gauge. While the output is not linear with

strain, they do exhibit essentially no creep or hystere-

sis and have an extremely long fatigue life. Because of

their high temperature sensitivity, careful matching of

the gauges and a high level of temperature compensa-

tion is required.

Thin ﬁlm strain gauges are produced by sputtering

or evaporation of thin ﬁlms of metals onto an elastic

element. Wire strain gauges are used mainly for high-

temperature transducers. The wire is typically 20 to

30 μm in diameter and is bonded to the elastic element

with ceramic material.

The rated capacities of strain gauge load cells range

from 0.1 N to 50 MN, at a typical total uncertainty of

Part D 13.4

Friction and Wear 13.4 Friction Measurement 755

Cantilever beam

Fixation

1 or 2 strain gauges

(on top and/or bottom)

Strain gauge

(stressed)

Strain gauge

(stressed)

Strain gauge

(stressed)

Strain gauge

(stressed)

Full-bridge strain gauge circuit

Fig. 13.10

Example of

strain gauges

connected into

a full-bridge

circuit

0.02–1% of full scale. The range of capacity depends

on the type of gauges, with thin ﬁlm gauges having

the highest sensitivity (typically 0.1–100 N), followed

by semiconductor gauges (1 N–10 kN), and foil gauges

(5–50 MN).

The response of a load cell can be maximized

using one or more strain gauges aligned to respond

to a longitudinal strain and another set aligned ei-

ther to a longitudinal strain of the opposite sign or to

the transverse strain. When connected electrically in

a Wheatstone bridge conﬁguration, this has the addi-

tional advantage of minimizing temperature effects that

act equally on all gauges. The resistance change is de-

tected by measuring the differential voltage across the

bridge (see for example Fig. 13.10). The load cell forms

part of the measurement chain and requires an ac or

dc excitation voltage to be supplied, and ampliﬁcation

and conditioning of the output signal, before it can be

used. The whole chain must be incorporated into the

calibration procedure.

13.4.3 Piezoelectric Load Sensors

Another commonly used type of force measurement

transducer is based on the piezoelectric phenomenon

exhibited by certain crystalline materials, in which an

electric ﬁeld is generated within a crystal which is pro-

portional to the applied stress. To make use of the

device, a charge ampliﬁer is required to provide an

output voltage signal that is proportional to the ap-

plied force and large enough to measure. Piezoelectric

crystal sensors are different from most other sensing

techniques in that they are active sensing elements. No

power supply is needed for the sensor (although it will

be for the ampliﬁer) and the mechanical deformation

needed to generate the signal is very small, which gives

a stiff sensor and the advantage of a high-frequency

response in the measuring system without introducing

geometric changes to the force measuring path. To en-

able measurement of both tension and compression,

piezoelectric force sensors are usually pretensioned by

a bolt.

A typical piezoelectric transducer deﬂects by only

0.001 mm under a force of 10 kN. The high frequency

response, typically up to 100 kHz due to the high stiff-

ness, makes piezoelectric crystal sensors very suitable

for dynamic measurements. The typical range of rated

capacities for piezoelectric crystal force transducers is

from a few N to 100 MN, with a typical total uncertainty

of 0.3–1% of full scale. While piezoelectric transducers

are ideally suited to dynamic measurements, they can-

not perform truly static measurements because there is

a small leakage of charge inherent in the charge ampli-

ﬁer, which causes a drift of the output voltage even with

a constant applied force.

Piezoelectric sensors are suitable for measurements

in laboratories as well as in industrial settings because

of their small dimensions, the very wide measuring

range, rugged packaging, and their insensitivity to over-

load (typically by > 100% of full scale). They can

operate over a wide temperature range (up to 350

◦

C),

and can be packed to form multicomponent transduc-

ers (dynamometers) to measure forces in two or three

orthogonal directions.

13.4.4 Other Force Transducers

Interesting but less commonly-used examples of force

measurement transducers are the vibrating-wire trans-

ducer and the gyroscopic load cell. The ﬁrst uses a taut

ferromagnetic wire which is excited to resonate in trans-

verse vibration. The resonant frequency is a measure of

Part D 13.4

756 Part D Materials Performance Testing

Friction force signal (arb. units)

Friction force signal

TiO

400 °C

1 m/s 10 N

0 35030025020015010050

Time (ms)

Fig. 13.11 Friction force signal from a load cell recorded with high

time resolution, showing vibration at its resonant frequency super-

imposed on the more slowly varying friction force

the wire’s tension and hence the applied force at that

instant. The advantage is its direct frequency output,

which can be handled by digital circuitry, eliminating

the need for analog-to-digital conversion.

Gyroscopic load cells exploit the force-sensitive

property of a gyroscope mounted in a gimbal or frame

system. The force to be measured is applied to the lower

swivel and a couple is produced on the inner frame,

causing the gimbals to precess. The time taken for the

outer gimbal to complete one revolution is then a mea-

sure of the applied force. The gyroscopic load cell is

essentially a rapidly responding digital transducer and

is inherently free of hysteresis and drift.

Friction force (N)

Material

/Si

Test-No.: LB1504_A

r.h.: 50 %

Position (mm)

–1–2–3–4–5 5

–15

–10

–5

43210

Fig. 13.12 Friction force signal for one sliding cycle of a silicon ni-

tride couple in reciprocating sliding, showing asymmetric behavior

due to differences in the stiffness of the system in the two sliding

directions (after [13.13]) (r.h. =relative humidity)

13.4.5 Sampling and Digitization Errors

In the case of a strain gauge load cell, the output sig-

nal from the whole force measurement chain depends

on the mechanical properties of the elastic element to

which the strain gauges are bonded and on the elec-

tronic circuitry used to convert the resistance changes

in the strain gauges (caused by the bending force ap-

plied to the elastic element) into a recordable electrical

signal proportional to the force. Similar considerations

apply to other types of load cell. The design of the elas-

tic element deﬁnes the resonance frequency of the load

cell. If the dynamic properties of the force to be meas-

ured excite this natural frequency, then the output signal

will no longer be proportional to the applied force.

Figure 13.11 shows the output signal from a strain

gauge load cell, recorded with a high sampling rate;

the friction force was generated between a pair of ti-

tania specimens sliding at 1 m/s at a temperature of

400

◦

C. The dominant component of the alternating sig-

nal occurs at the natural resonant frequency of the load

cell, due to vibration induced by the friction between

the triboelements. Derivation of a friction force from

such a signal will clearly lead to error. Such effects

will still occur but not be obvious if the sampling rate

is too low or if the electronic circuitry used has a long

time constant, integrating over the rapid signal varia-

tions. Recording the output from a load cell with an

analog chart recorder usually ﬁlters out such fast signal

changes and integrates them.

Another example of a dynamic friction signal is pre-

sented in Fig. 13.12. The friction signal, measured with

a piezoelectric sensor, for one sliding cycle of a silicon

nitride couple exhibits different extents of variation for

the two half-cycles, indicating that the sliding couple

under these test conditions tends to stick/slip motion.

The difference in behavior is caused by the difference

in the stiffness of the construction elements in the two

directions. For such a system it is not possible to de-

ﬁne a quantitative friction level because the measured

signals are dominated by the vibrations of the elastic

sensor element and are thus not proportional to the fric-

tion forces. Results of this type only allow the tendency

to stick/slip motion to be deduced.

13.4.6 Calibration

Even with good transducers and a good overall sys-

tem design, measurements of forces cannot be relied

upon without calibration. Instruments capable of per-

forming force calibrations are known as force standard

Part D 13.4

Friction and Wear 13.4 Friction Measurement 757

Table 13.2 Types of force standard machine

Type Principle Uncertainty attainable Category

Deadweight

machines

A known mass is suspended in the Earth’s gravita-

tional ﬁeld and generates a force on the support

< 0.001% Primary or secondary

Hydraulic ampli-

ﬁcation machines

A small deadweight machine applies a force to

a piston-cylinder assembly and the pressure thus gen-

erated is applied to a larger piston-cylinder assembly

< 0.02% Secondary

Lever ampliﬁca-

tion machines

A small deadweight machine with a set of levers

which amplify the force

< 0.02% Secondary

Strain-gauged

hydraulic

machines

The force applied to an instrument is reacted against

strain-gauged columns in the machine’s framework

< 0.05% Secondary

Reference force

transducer

machines

A force transfer standard is placed in series with the

instrument to be calibrated

< 0.05% Secondary

machines. Primary standards in force measurement are

machines whose uncertainty can be veriﬁed directly

through physical principles to the fundamental base

units of mass, length and time. Secondary standards can

be compared with primary standards through the use of

a force transfer standard, which is a calibrated force

transducer, frequently a strain gauge load cell. Stan-

dards document ISO 376 describes the calibration and

classiﬁcation of transfer standards.

Table 13.2 lists types of force standard machines

that have been developed for the calibration of static

forces acting along a single well-deﬁned axis. The prin-

ciples used for the calibration of multicomponent force

sensors remain the same, but cross-talk between the

different axes must also be considered. For the mea-

surement of dynamic forces it is assumed that the

statically-derived force transducer sensitivities are ap-

plicable, but attention must also be paid to the natural

frequencies of the load cell.

The calibration of a force transducer can be per-

formed with the transducer in its permanently installed

position by using a transfer standard, or prior to its

installation and by removal as required for further cali-

bration.

More information on force measurement and cali-

bration can be found elsewhere [13.14,15].

For very small forces, as measured with an atomic

force microscope (AFM), special calibration procedures

are needed. An AFM can be used to measure fric-

tion forces in the nN range. The calibration methods

used for this force-measuring machine also use known

masses under gravity, but the lowest attainable uncer-

tainty is much greater than that described above for

macroscopic forces. The AFM scans a probe tip over

the surface under examination. It operates like a sty-

lus proﬁlometer with constant contact force, which is

maintained by steering the bending of the cantilever

beam carrying the probe tip using a piezoelectric el-

ement (Fig. 13.13). The bending of the cantilever is

sensed by a segmented photodiode which measures the

intensity of laser light reﬂected from the back of the

cantilever. The piezoelectric driving voltage is adjusted

during the scan over the surface to hold the resulting dif-

ference in photocurrent between segments (1+2) and

segments (3 +4) constant. A constant photocurrent im-

plies constant beam deﬂection, which is equivalent to

a constant force. The piezoelectric voltage needed to

hold the photocurrent constant is thus a measure of the

topographical height at the instantaneous position of the

tip. The height resolution of an AFM is in the range of

atomic dimensions.

If the direction of scanning is perpendicular to the

axis of the cantilever, the torsion of the cantilever pro-

vides a measure of the friction force between the tip and

the sample. The torsion is measured by the difference

between the photocurrents from segments (1+3) and

Segmented

photodiode

Piezo

Laser

Cantilever

Sample surface

AFM tip

Fig. 13.13 Principle of friction measurement with an AFM

(atomic force microscope)

Part D 13.4