Tribological analysis of thin films by pin-on-disc: Evaluation of frictionand wear measurement uncertainty

R. Novak a, T. Polcar a,b,n

a Department of Control Engineering, Faculty of Electrical Engineering, Czech Technical University in Prague, Technicka 2, Prague 6, Czech Republicb nCATS, Faculty of Engineering and Environment, University of Southampton, Highfield Campus, SO17 1BJ Southampton, UK

a r t i c l e i n f o

Article history:Received 9 August 2013Received in revised form3 February 2014Accepted 13 February 2014Available online 12 March 2014

Keywords:Pin-on-discCoatingsUncertaintyFriction and wear

a b s t r a c t

Pin-on-disc is widely used to evaluate tribological properties of thin films. However, the results are oftenpresent without standard uncertainties; moreover, in many cases the standard uncertainty is replaced bystandard deviation, which is a strong underestimation of real uncertainty. In this study we have followedISO and NIST guidelines to investigate the possible sources of uncertainties related to friction and wearrate measurement and to apply them on two selected coating systems – TiN and DLC. We show thatinfluence of operator is a significant contribution to the uncertainty of the wear rate, particularly in thecase of very low wear of DLC coatings. We discuss why variance should be used instead statisticdeviation and suggest a method to calculate uncertainties in case of small number of measurements. Thepaper could be used as a guide to evaluate friction and wear data of thin films and coatings using thepin-on-disc technique.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The experimental evaluation of friction coefficient and wearrate using pin-on-disc is a common laboratory procedure. Despitethe simplicity of measurement and calculation, there are practicalchallenges to quantify these basic tribological parameters accu-rately. Friction is a typical non-equilibrium process and slidingoften leads to wear, which is highly stochastic. The values offriction coefficients and wear rates reported in the literaturetypically show wide variation even for nominally identical tests;the origin of these variations is often not known. To assessuncertainty of tribological measurement is thus a complex pro-blem. Due to the high spread of measured data, a high number ofidentical measurements is required to estimate values of frictionand wear. The tribological measurement is a lengthy and expen-sive process; therefore, an optimum number of repetitive mea-surements must be found to satisfy both precision and economy ofthe testing. Moreover, in some cases the number of samples andthus number of available tests is limited.

Tribological analysis of thin protective films is in many waysdifferent from that of bulk materials. The thickness of the film is inthe range 0.1–10 mm with 1–3 mm being the typical value. The

films are quite often composed of bonding interlayer improvingadhesion (metals, carbides, nitrides, gradient interlayers) and topfunctional coating. To evaluate the latter the maximumwear depthis limited to approx. 80% of its thickness to avoid influence ofbonding layer. As a consequence, the worn volume is very low andtraditional measure of material mass loss cannot be used; thus,mechanical and optical profilometry is required. In some casesthe wear is extremely low and the depth of the wear track isclose to surface roughness, which leads to high uncertainty of thewear rate.

Unfortunately, the standard procedures [1,2], which should beused to estimate measurement uncertainties, are not always fol-lowed. As a consequence, the friction and the wear rate values areoften presented without measurement uncertainty; moreover, theuncertainty is sometimes replaced by standard deviation, which ismisleading and significantly lower than standard uncertainty.

Uncertainty of tribological measurements has been addressedin several papers for various measurement conditions [3,4,5].Detailed uncertainty analysis of low friction coefficient measure-ments with a reciprocating pin-on-disk tribometer has beenshown in Refs. [6,7]. In these studies the predominant source ofvariations originated from the misalignment of the force transdu-cer axis relative to the specimen surface. Nevertheless, the scatterof friction coefficient values was larger than estimated uncertain-ties related to the experimental apparatus. Krick et al. [8] exam-ined the influence of the ratio of the wear track radius, r, andcontact width, 2a, on uncertainty of friction coefficient measured

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Tribology International

http://dx.doi.org/10.1016/j.triboint.2014.02.0110301-679X & 2014 Elsevier Ltd. All rights reserved.

n Corresponding author at: Department of Control Engineering, Faculty ofElectrical Engineering, Czech Technical University in Prague, Technicka 2, Prague6, Czech Republic. Tel.: þ420 224 357598.

E-mail address: polcar@fel.cvut.cz (T. Polcar).

Tribology International 74 (2014) 154–163

by pin-on-disc. They concluded that the increase of uncertaintywas significant only for very small wear track radii. For r=a Z 4,the relative uncertainty was lower than 1%.

In this paper we follow guidelines provided in Refs. [1,2] toanalyze in detail the uncertainty of friction coefficient measuredby the standard pin-on-disc apparatus and the correspondingcoating wear rate. Then we report application of the method totwo large set of substrates, one coated by titanium nitride (TiN),the second with hydrogenated diamond like carbon coating (DLC).We determine the most significant contributors to the overallmeasurement uncertainty, which could help to either re-designthe experiment procedure to reduce the measurement uncertaintyor to simplify it by neglecting some parameters. We show thatestimation of uncertainties could help to distinguish betweenrandom value variation and true trends (i.e. dependence ofmeasured values on selected variable or set of variables). Finally,we suggest an optimum process to estimate uncertainties.

2. Measurement uncertainties

The standard uncertainty of measurements is determined usingType A and Type B uncertainty evaluations [1,2]. To evaluate TypeA uncertainty the measurement is repeated under the sameconditions and the statistical methods are applied to the set ofmeasured values. However, the tribological tests are destructiveand the test cannot be repeated under the repeatability conditionsstated in Refs. [1,2]. It is clearly demonstrated by the wear ratedata dispersion for which orders-of-magnitude variations arecommon [9]. Thus, the results of the set of measurements cannotbe (at least in general) treated with statistical methods; in otherwords, uncertainties Type A cannot be evaluated. Nevertheless, thetesting procedure involves some steps, such as instrument calibra-tion, which fulfill the repeatability conditions and thereforecould be evaluated by means of a statistical methods and Type Auncertainty could be determined. The standard uncertainty oftribological measurement is dominated by Type B uncertainties.The uncertainty Type B is evaluated by an engineering and/orscientific judgment based on all available information. In our caseit is the estimation of instrument and method errors and operatorinduced uncertainties.

2.1. Standard uncertainty of the friction coefficient

In this study we consider traditional pin-on-disc tribometer witha ball pressed against a rotating sample (Fig. 1(a)). The pin 1 ismounted on a stiff lever 2, designed as a frictionless force transducer.The dead weight 3 produces the normal force Fn. The friction force Ffis evaluated from the deflection of the elastic arm 4 measured byinductive displacement transducers 5; the calibration referred toabove is used to calculate force from measured deflection.

If umA and umB denote the Type A and Type B uncertainties, thestandard uncertainty um of the friction coefficient m is givenby [1,2]

u2μ ¼ u2

μAþu2μB: ð1Þ

Since the friction measurement cannot be repeated under iden-tical conditions due to progressive destruction of the surfaces inthe contact, Type A uncertainty is related only to the calibrationprocedure. Calibration is provided by a dead weight (5 N) appliedto a ball holder (Fig. 1(b)) giving offset for frictional force gauge(zero load is obviously used as the second point). However, itshould be pointed out that the calibration could be only consid-ered as an uncertainty Type A provided it is carried out before anyindividual measurement. In normal testing practice it is not thecase – the equipment is calibrated after a certain number of tests

or when the material couple is changed. This practice is reasonablewhen the friction offset (and thus uncertainty Type A) is muchlower than total uncertainty of friction coefficient. We carried outnumber of calibrations giving statistical set of frictional forceoffsets; standard deviation of the data was then used to estimateuncertainty Type A denoted umA.

Based on our experience in the field of tribological measure-ments we assume the uncertainty Type B consists of instrumentuncertainty and uncertainty given by the dispersion of measuredvalues. The origin of the latter is not known; however, it can beestimated on the basis of data difference. We can thus summarizethat the Type B uncertainty umB is given by

u2μB ¼ u2

μ iþu2μ v; ð2Þ

where umi is the instrument uncertainty and umv is the uncertaintydue to data difference.

Fig. 1. Tribometer measuring head and scheme of calibration: 1 – pin, 2 – stifflever, 3 – dead weight, 4 – elastic arm, 5 – inductive displacemant transducer,6 – dead weight 5 N, 7 – pulley, 8 – string, 9 – pin holder (stiff lever).

R. Novak, T. Polcar / Tribology International 74 (2014) 154–163 155

The coefficient of friction μ is defined as the ratio of themeasured frictional force Ff and the normal force Fn

μ¼ FfFn

: ð3Þ

The friction and normal forces in the contact are measuredseparately using the combination of force transducer and deadweight load, respectively. Since both Ff and Fn are measuredindependently and the combined standard uncertainty is afunction of the standard uncertainties uFf and uFn and the asso-ciated sensitivity coefficients, the expression for the combinedstandard uncertainty uμi could be given as

u2μi ¼

∂μ∂Ff

� �2

u2Ffþ ∂μ

∂Fn

� �2

u2Fn : ð4Þ

Zero covariance, i.e. no correlation between the separate inputvariables, is assumed in our analysis. Combining of Eq. (4) andEq. (1) yields

u2μ i ¼

1

F2nu2FfþF2fF4n

u2Fn : ð5Þ

Eq. (5) can be simplified using relative standard uncertainties to

u2μi;r ¼ u2

Ff ;rþu2

Fn;r ; ð6Þ

where

uμi;r ¼uμiμ; uFf ;r ¼

uFf

Ff; uFn ;r ¼

uFn

Fn: ð7Þ

The friction force Ff is calculated from the elastic deformation ofthe arms measured by shift transducer. Since the value of forceFf depends linearly both on the transducer ratio and the armsdeformation, the relative uncertainty uFf,r is

u2Ff ;r

¼ u2t;rþu2

d;rþu2h;r ; ð8Þ

where ut,r is the relative uncertainty of deformation transducerdata, ud,r is the relative uncertainty due to vertical ball holdermisalignment and uh,r is the relative uncertainty due to horizontalball holder misalignment. The value of ut,r can be easily obtainedfrom data given by the transducer manufacturer [1,2]. Thus, the ut,rvalue could be calculated as

ut;r ¼τþδ

100ffiffiffi3

p μ0

μ; ð9Þ

where τ is the sensitivity tolerance (%), δ is the linearity deviation(%), and μ0 is the tribometer range.

Manufacturing tolerances, sample shape and adjustment, andposition of the pin holder in the lever (see points 1 and 2 in Fig. 1(a)) inevitably produce misalignment of the normal and tangentialaxes (Fig. 2). Firstly, we must treat the potential misalignmentbetween the normal of the sample surface and the pin holder axisin the tangential plane (Fig. 2(a)). The arm of friction force R/ islonger than R:

R= ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2þa2 sin 2α

q; ð10Þ

and the relative uncertainty due to this instrument misalignmentis then

ud;r ¼R=�RR

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þa2

R2 sin2α

s�1: ð11Þ

We proceed by calculating the first-order Taylor series approxima-tion resulting in

ud;r �a2

2R2 sin2α� a2

2R2α2: ð12Þ

Secondly, the incorrect adjustment of horizontal level of the stifflever should be taken into account (Fig. 2(b)). It is evident that thelength of friction force arm, R//, can be approximated as

R== ¼ R cos βþa== sin β: ð13ÞThe normal force F//n then differs from the dead load

F==n ¼ GR cos β

R cos βþa== sin βð14Þ

and the momentum M// of friction force Ff acting on the lever is

M== ¼ μF==n R== ¼ μGR cos β ð15ÞThe relative uncertainty uh,r created with this misalignment isdetermined as

uh;r ¼M==�M

M¼ 1� cos β ð16Þ

Again we proceed by applying the first-order Taylor series approx-imation giving

uh;r ¼β2

2: ð17Þ

Fig. 2. Geometry of pin misalignments. G is the gravitation force produced by deadweight. The numbers correspond to Fig. 1.

R. Novak, T. Polcar / Tribology International 74 (2014) 154–163156

The Eq. (8) may be then written as

u2Ff ;r ¼

τþδ100

ffiffiffi3

p μ0

μ

� �2

þ a2

2R2α2

� �2

þ β2

2

!2

: ð18Þ

The force Fn in Eqs. (3) and (5) is the normal component of forceacting on the pin and the uncertainty of this value is calculatedusing Eq. (19)

u2Fn ¼

∂Fn∂m

� �2

u2mþ ∂Fn

∂γ

� �2

u2γ ; ð19Þ

where um is the uncertainty of the dead weight and uγ is theuncertainty caused by deviation of the normal of sample surfaceplain from the sample axis of rotation.

If ε(m) denotes the error of scales used for dead weight scalingand g for the gravity acceleration, the first term in Eq. (19) is

∂Fn∂m

� �2

u2m ¼ g2

εðmÞffiffiffi3

p� �2

: ð20Þ

The relative uncertainty of gravity acceleration, given by latitudeand altitude of the measurement place, is of the order 10�4 andcould be neglected. The coefficient 1/√3 in Eq. (20) has beenapplied according to Refs. [1,2].

The effect of deviation of the normal of sample surface plainfrom the sample axis of rotation is illustrated in Fig. 3, whereγ denotes the angle of deviation, r the radius of wear track, R thedistance of the pin holder axis from the level axis of rotation, J themoment of inertia of the pin holder lever and z the instantaneousheight of the pin over horizontal plane. The time dependence of zis described as

z¼ r sin γ cos ωt; ð21Þwhere ω denotes the angular velocity of the sample. Due to thecontribution of inertial forces to the weight G, the instantaneousforce on the pin is

Fn ¼ gmþ J

R2þm� �

d2zdt2

¼ gmþ J

R2þm� �

ω2r sin γ cos ωt: ð22Þ

Considering low deviation γ we can simplify

uγ ¼ sin γ � γ ð23Þto obtain

Fn ¼ gmþ J

R2þm� �

ω2rγ cos ωt: ð24Þ

In tribological tests linear speed v is traditionally used, v¼ω � r.The sensitivity coefficient of Fn with respect to γ written as

∂Fn∂γ

¼ J

R2þm� �

v2

rcos ωt ð25Þ

is time dependent with the period T¼2πr/v. If the samplingfrequency of friction data is high compared to frequency ofrotation ω/2π and the measurement duration long enough, themean value of the coefficient ∂Fn/∂γ could be considered as zero.Nevertheless, this coefficient could be still responsible for theperiodical fluctuation of the measured instantaneous value offriction coefficient, particularly for higher deviation angle γ.If the sensitivity coefficient of Fn is negligible, the relative instru-ment uncertainty of the friction coefficient μ is

u2μi;r ¼

τþδ100

ffiffiffi3

p μ0

μ

� �2

þ a2

2R2α2

� �2

þ β2

2

!2

þ εðmÞm

ffiffiffi3

p� �2

: ð26Þ

The uncertainty umi is, however, only a part of umB; its remainingcomponent umv is often predominant. To obtain umv it is necessaryto repeat the measurements with the same type of samples underidentical conditions. The best estimation of the friction coefficientis the arithmetic mean of the registered values m1, m2,…, mN. Thedifference Δm between highest and lowest values of mi should beused as a base for estimation of umv. Supposing the rectangulardistribution of the probability of values mi in the interval betweenthe highest and the lowest values, in agreement with [1,2]we obtain

uμv ¼Δμ2ffiffiffi3

p : ð27Þ

Then we combine Eqs. (2), (26) and (27) giving

u2μB ¼ ðμuμi;rÞ2þ

ðΔμÞ212

: ð28Þ

The value of uncertainty of friction coefficient uμ is then given as

uu ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2uAþðμuμi;rÞ2þ

ðΔμÞ212

s: ð29Þ

We should point out here that we do not consider any inertialeffects caused by dead load. When the coating and/or ball surfacesare rough or have topographical defects, the load would varyduring one rotation and thus calculated friction. However, theseeffects are negligible in the case of hard protective coatings. Thesurface roughness of the coatings is typically very low (substratesare polished) and counterparts are very smooth (bearing balls).Topographic features in the wear track could be producedby severe plastic deformation of the substrate or by localizedaccumulation of adhered wear debris. For hard coatings the plasticdeformation is negligible and worn volume minimal; moreover,the wear debris is typically removed from the contact area to thewear track borders. In fact, the surface roughness measured in thewear track in direction parallel to sliding distance is often lowerthan that of as-deposited coating surface.

2.2. Standard uncertainty of the wear rate

Assessment of the wear rate uncertainty is more complicateddue to necessity to evaluate the uncertainties of the normal force,the sliding distance, and the wear volume. Two methods aretypically applied to calculate the wear volume: (i) the samplemass loss measured by a precise balance, and (ii) the evaluation ofthe wear track cross section area. The former does not take intoaccount the plastic deformation and possible mass changes(i.e. oxidation, etc); its uncertainty is equal to the uncertainty ofbalance. The effect of the instrument related uncertainties on thewear rate was studied in Ref. [10]. Experiments with the recipro-cating tribometer showed that the primary sources of uncertaintywere the mass loss measurements and the length of the weartrack, i.e. the uncertainties of the instruments. It is obvious thatthis method cannot be used to evaluate wear rate of thin films dueFig. 3. Geometry of sample misalignment.

R. Novak, T. Polcar / Tribology International 74 (2014) 154–163 157

to negligible mass of worn material compared to the mass of thesample. The second method, evaluation of the wear track shape,includes plastic deformation and its uncertainty depends onthe uncertainty of the wear track cross sectional area and theuncertainty of the wear track radius.

The cross section area of the wear track is usually evaluated bycontact (mechanical) or non-contact (optical) surface profil-ometers. We will focus here on the more progressive opticalsystems. The uncertainty of the cross section area depends bothon lateral and vertical resolution of the instrument. Althoughthese values are often provided by the profilometer manufacturer,it is necessary to review supplied data critically. While the lateralresolution is given by the optical characteristics of the objectiveand can be easily determined, the vertical resolution presentscomplex problem. In principle, the value of vertical resolution islimited by Heisenberg's uncertainty principle and optical uncer-tainty principle [11]. The question of the best possible achievedvertical resolution regarding to the interferometer setup isdiscussed in Ref. [12]. The vertical resolution is also influencedby the sample surface roughness [13]. Moreover, there is anothersource of uncertainty, which is difficult to estimate. The wear trackcross-section strongly depends on profilometer operator, whodefines original surface line (i.e. surface before the wear test)and width of the wear track. The operator influence stronglyincreases in case of rough surfaces and irregular shape of the weartrack. It is well demonstrated in Ref. [14], where the significance oferrors due to the variations in the wear track irregularity arecompared with the instrument error and the predominant role ofthe uncertainties of the cross section area scans is clearly shown.To achieve a sufficiently low value of the wear volume uncertainty,a set of scans had to be carried out. As the number of scansincreased, the estimated volume loss was closer to the true valueand the associated uncertainty decreased. The probability that thetrue value was in the confidential interval was about 80% for 10scans and nearly 100% for 50 scans [14]. Nevertheless, thesequantitative conclusions should be assessed critically, since theauthors applied the statistical methods considering individuallyscanned cross-sectional areas as identical, i.e. repeated measure-ment. However, they used the values obtained from differentplaces of the wear track.

We will investigate here the uncertainty of the wear rate. Thewear rate w is defined as

w¼ VFnd

; ð30Þ

where V is the worn volume during the wear test, Fn is the normalforce and d is the total sliding distance. Applying the method ofloss volume evaluation based on the wear track cross section areaA [mm2] and the wear track radius r [m], the wear rate is given as

w¼ 10�3 � AFnN

½mm3ðN mÞ�1�: ð31Þ

where N is the number of sample revolutions (sometimes denomi-nated as cycles or laps). Standard uncertainty uw is given as

u2w ¼ u2

wAþu2wB: ð32Þ

None of the quantities A, Fn and N can be measured repeatedlyunder identical conditions; thus the Type A uncertainty of thewear is zero and uw¼uwB. To simplify the calculations the relativestandard uncertainties uw,r uA,r uFn,r and uN,r are used. Since thepin-on-disc equipment provide precisely defined number of cyclesN, the uncertainty uN,r could be ignored:

u2wB;r ¼ u2

w;r ¼ u2A;rþu2

Fn;r : ð33Þ

The evaluation of the uncertainty uFn,r was discussed above and wewill thus focus on the uncertainty of the cross-section area A. It can

be calculated as

u2A ¼ u2

Aiþu2Aoþu2

Av; ð34Þwhere uAi denotes the instrument uncertainty, uAo the operatorinduced uncertainty and uAv the uncertainty caused by wear trackirregularities.

The evaluation of the wear track area A is based on the wear trackprofile measured with an optical profilometer. Operator determinatesoriginal surface profile together with wear track boundaries; then thearea A is computed. Fig. 4 illustrates problems related to identifica-tion of the wear track edges. This operator uncertainty, uAo, combinesboth inaccuracy of one operator (i.e. repetitive measurement ofidentical profile gives different results) and inaccuracy originated inoperator practice and training. Its estimation is difficult – in presentstudy the measurements of one particular wear track by 5 operatorswere used to analyze the difference of the values in order to estimateoperator induced uncertainty.

The instrument induced uncertainty uAi depends on positioninguncertainty of particular profile points given by lateral and verticalresolutions Δx and Δz of the instrument. To evaluate the effect ofΔx and Δy on the uncertainty of the cross-section area uAi, twoextreme cases are considered: very shallow and wide wear track(Fig. 5(a)) and very narrow and deep wear track (Fig. 5(b)). If bdenotes the wear track width and h its depth, we can write

b⪢h; bΔz⪢hΔx; ΔA= � bΔz; u=Ai;r ¼

ΔA=

A� bΔz

bh¼Δz

hð35Þ

0.0 0.1 0.2 0.3 0.4 0.5

-200

0

200

400

600

800

1000

Hei

ght (

nm)

Hei

ght (

nm)

Surface scan length (mm)

Surface scan length (mm)0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

-80

-60

-40

-20

0

20

P2

P1R2L R1

Fig. 4. Typical cross-sections of the DLC wear tracks measured by optical profil-ometer (offset applied) (a). Selected cross-section demonstrating that neitherborder of the wear track (R1 or R2) nor original profile (P1 or P2) could be easilydefined.

R. Novak, T. Polcar / Tribology International 74 (2014) 154–163158

b⪡h; bΔz⪡hΔx; ΔA== � hΔx; u==Ai;r ¼

ΔA==

A� 2hΔx

bh¼ 2Δx

b: ð36Þ

The relative instrument uncertainty uAi,r of the wear track area isthen given as

u2Ai;r ¼ u=2

Ai;rþu==2Ai;r ¼

Δz

h

� �2

þ 2Δx

b

� �2

: ð37Þ

The resolution of a standard optical profilometer is Δx¼(200–400) nm and Δz¼(0.1–1) nm, h and b denote the arithmeticmeans of the quantities h and b, respectively.

Estimation of the operator induced uncertainty uAo depends onthe experimenter choice and could be based e.g. on difference ofthe A value measured on the same sample several times by theparticular operator or on the comparison of values taken on a solesample by several operators.

Considering the irregularities of the wear track cross-section,the measurements are carried out in n positions along the weartrack circumference resulting in a set of values A1, A2,… An. Thearithmetic mean A of values A1, A2,… An as the best availableestimate of expected value A. However, since the obtained datacannot be considered as a series of measurements repeated underthe same conditions, the difference ΔA between the highest andthe lowest values of Ai is used as a base for setting the value of uAv.Supposing the rectangular probability distribution of the Ai valuesin the interval between the highest and the lowest values weobtain

uAv ¼ΔA

2ffiffiffi3

p : ð38Þ

And then

u2A;r ¼ u2

Ai;rþu2Ao;rþu2

Av;r ¼Δz

h

� �2

þ 2Δx

b

� �2

þ uAo

A

� �2

þ 112

ΔA

A

� �2

:

ð39Þ

If the time dependent component in Eq. (25) is maximal (i.e. cosωt¼1), and the Eq. (20) is used, the uncertainty uFn,r is given byEq. (40)

uFn;r ¼ um;r ¼εðmÞm

ffiffiffi3

p : ð40Þ

The standard relative uncertainty of the wear rate w is calculatedusing Eq. (41)

u2w; r ¼

Δz

h

� �2

þ 2Δx

b

� �2

þ uAo

A

� �2

þ 112

ΔA

A

� �2

þ13

εðmÞm

� �2

ð41Þ

and the standard combined uncertainty uw using Eq. (42)

uw ¼w

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiΔz

h

� �2

þ 2Δx

b

� �2

þ uAo

A

� �2

þ 112

ΔA

A

� �2

þ13

εðmÞm

� �2s

ð42Þ

3. Experimental details

The experiments with repeated measurements of frictioncoefficient and wear rate were carried out with two hard coatings,TiN and DLC. To eliminate the effects of any laboratory preparationboth series were deposited in large industrial deposition facilities,each in one batch. Thus, the uniformity of the coatings wasguaranteed (total number of samples was 30 per deposition).The coatings were deposited on steel (ISO 4597: 1.2379 (X153CrMoV12) - AISI: D2) substrates polished to surface roughnessRao50 nm; the hardness of substrates was 6172 HRC. Allsubstrates were ultrasonically cleaned in alcalic bath, rinsed indeionized water and dried in vacuum before deposition. TiNcoatings were deposited in HC4 apparatus (Hauzer Techno Coat-ing) by cathodic arc evaporation from Ti target in ArþN2 mixture.The deposition temperature was 350 1C, the working pressure wasin the range 0.1–0.2 Pa and the substrate bias was – 70 V. Thecoating thickness was 2 μm. DLC coatings were deposited inHauzer Flexicoat 1200. DLC coatings were deposited by PACVDusing C2H2 (purity 99,6%) with substrate pulsed bias in frequencyrange (20–100) kHz. The coating thickness was 1.3 μm includingthin titanium interlayer improving adhesion deposited by magne-tron sputtering.

The tribological tests were performed with CSM Instrumentspin-on-disc tribometer (software TriboX 2.9C). The instrumentwas repeatedly calibrated before and after measurements. Thetests were carried out at room temperature (22–25 1C); theapplied load was 5 or 10 N and the linear speed varied in therange 2–10 cm s�1. Balls with a diameter of 6 mm were used ascounterparts; high speed steel for TiN coatings and alumina forDLC. Both coatings and the balls were cleaned with isopropylalco-hol and acetone before the tests.

To evaluate the Type A uncertainty of friction coefficient, thetribometer calibration was repeated before and after experimentsin total twenty times using the calibration procedure suggested bythe tribometer manufacturer. Obtained individual calibrationcoefficients slightly differed in value and the experimental stan-dard deviation of their mean value was

uμA ¼ 8:9� 10�3 ð43Þ

Type B uncertainty of friction coefficient was calculated fromEq. (26) and (29). According to the inductive displacementtransducer specification, the sensitivity tolerance τ is 1% and thelinear deviation δ is 0.2%. The highest measured friction force Ff0 islimited by software to 10 N; thus, μ0 from Eq. (9) is calculated fromequal to Ff0¼μ0Fn. Estimation of uncertainty components ud,r anduh,r is based on the presumption that the effect of manufacturingtolerances is negligible compared to the effect of the elasticdeformations and clearances. Analyzing stiff lever positions inthe unloaded and loaded state, the highest measured value α,0.006 rad, was obtained for a¼50 mm and R¼90 mm (see Fig. 2(a)). The horizontal deviation of the stiff lever, β, which is adjustedby an operator, did not exceed 0.012 rad. The mass of dead weight

Fig. 5. Cross section of (a) shallow and (b) deep wear track.

R. Novak, T. Polcar / Tribology International 74 (2014) 154–163 159

m¼511.52 g was estimated with maximum error ε(m)¼0.03 ggiven by the digital balance manufacturer. Using Eqs. (9) and(27), the instrument uncertainty of friction coefficient is

u2μi;r ¼

τþδ100

ffiffiffi3

p μ0

μ

� �2

þ a2

2R2α2

� �2

þ β2

2

!2

þ εðmÞm

ffiffiffi3

p� �2

¼ 0:069Fnμ

� �2

þð5:4� 10�6Þ2þð7:2� 10�5Þ2þð2:3� 10�5Þ2

ð44ÞNeglecting the second term in Eq. (44) related to stiff leverposition, the uncertainty umi,r could be simplified to

u2μi;r �

0:069Fnμ

� �2

þ0:57� 10�8 ð45Þ

and the combined standard uncertainty of the friction coefficientuμ is then

u2μ ¼ u2

μAþu2μB ¼ ð8:9� 10�3Þ2þðuuui;rÞ2þ

ðΔuÞ212

¼ 7:9� u2 0:069Fnu

� �2

þ0:57� 10�8

" #þðΔuÞ2

12ð46Þ

The ZYGO 7200 optical profilometer with 5x/Michelson objectiveand software MetroPro were used to measure the wear trackwidth, depth and cross-section area. The samples were cleanedwith isopropylalcohol; the free debris was thus removed from thesurface. Each sample was positioned on rotating holder enablingprecise positioning of the measured section. The cross sectionalarea Ai and the wear track width bi and depth hi were measured ineight points regularly spaced along the wear track circumstance.

Combining the profilometer data provided by manufacturer(vertical resolution Δz¼0.1 nm and lateral resolution Δx¼200 nm) and Eq. (41), the relative uncertainty uw,r could be givenas

uw;r ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi0:1

h

� �2

þ 400

b

� �2

þ uAo

A

� �2

þ 112

ΔA

A

� �2

þð2:3� 10�5Þ2s

:

ð47Þwhere the wear track width b and depth h are in nanometers.

4. Results

4.1. Friction and wear of TiN coatings

The experiments carried out with 10 samples consisted in a setof measurements focused on estimation of (i) operator induceduncertainties of wear rate values, (ii) effect of air humidity and(iii) impact of the wear track radius r on friction coefficient μ andwear rate w values.

In order to find the operator induced uncertainties, the follow-ing pin-on-disc experiment was arranged: the load Fn¼5 N, thelinear speed v¼10 cm s�1 and the number of laps N¼3000. Thenthe cross section areas were measured in eight positions evenlydistributed along the wear track. The measurements were per-formed by five operators with different laboratory skills. Thecomparison of their results, i.e. the arithmetic mean A and thedifference ΔA of these eight values of cross section area measuredby particular operators, is given in Table 1.

If all A values measured by these five operators are consideredas one set, the mean value of the cross-section area and its relativeuncertainty are

A¼ ð119:576:4Þ μm2;uAo;r ¼ 0:053: ð48Þ

To evaluate the effect of the humidity on the tribological proper-ties, 10 samples were tested with identical parameters (Fn, v, r, N)except for air humidity, which was varied in the range 25–45%.Results of this experiment summarized in Table 2 clearly demon-strate that there are no noticeable dependences of measuredvalues on air humidity since all values are within the limits givenby their standard combined uncertainties.

The standard combined uncertainties uμ and uw presented inTable 2 were calculated using Eqs. (50) and (52). By substitutingthe values of Fn and measured difference Δm, we obtain

u2μ ¼ 7:9� 10�5þμ2 0:015

μ

� �2

þ0:57� 10�8

" #þðΔμÞ2

12ð49Þ

By neglecting negligible terms in Eq. (49) we can write

uμ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2:25� 10�4þðΔμÞ2

12

s; ð50Þ

where the first member is related to the instrument uncertaintyuμi of this particular tribometer using the normal force Fn and thesecond member corresponds to the variance of measured values offriction coefficient μ.

The standard combined uncertainties uw were calculated usingEqs. (47) and (48) and measured values of h � 500 nm andb � 5� 104 nm

u2w;r ¼

0:1500

� �2

þ 400

4:7� 105

� �2

þð0:05Þ2þ 112

ΔA

A

� �2

þð2:3� 10�5Þ2

ð51ÞIt is apparent that all instrument uncertainties could be neglectedin comparison with operator induced uncertainty and with var-iance of A values. Thus the uncertainty uw could be given as

uw ¼w

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2:5� 10�3þ 1

12ΔA

A

� �2s

: ð52Þ

The last experiment was aimed to the investigation of the weartrack radius effect on the friction coefficient and the wear rate. Wevaried radius r in the range 3–18 mm using a set of five samples.The results of this experiment are presented in Table 3 andsummarized in Fig. 6. The friction coefficient μ slightly increaseswith radius; the increase in the wear rate w is even more evident.

We can conclude here that the relative humidity in the range25–41% does not affect the tribological measurement. However,

Table 1Cross-section area measured by 5 different operators, TiN coating.

Operator no. 1 2 3 4 5

A (mm2) 115 121 122 119 119

ΔA (mm2) 12 18 22 17 15μAo,r 0.03 0.043 0.041 0.036 0.036

Table 2Friction and wear rate of TiN coating as a function of relative air humidity.

TiN coating: Fn¼5 N, v¼10 cm s�1, r¼6.5 mm, t¼2371 1C

Rel. humidity (%) μ w (10�6 mm3 N�1 m�1)

25–30 1.08870.035 8.770.931–40 1.05670.029 9.871.341–45 1.07370.037 9.271.7

R. Novak, T. Polcar / Tribology International 74 (2014) 154–163160

the radius is an important parameter significantly influencing thefriction and, particularly, the wear rate.

4.2. Friction and wear of DLC coatings

The experiments carried out with 10 samples consisted inrepeated measurements focused on the following parametersand their effect on friction and wear rate: (i) operator induceduncertainties of w values and further on determination of testparameters impact on values of m, w and their uncertainties;(ii) relative humidity RH; (iii) normal force Fn; (iv) pin velocity v.

(i) This experiment was arranged in the same way as for TiNcoatings referred to above. The pin-on-disc test with parametersFn¼5 N, v¼10 cm/s and N¼3000 was carried out and five opera-tors measured the wear track cross section area in eight positionsevenly distributed along the wear track. The comparison of theirresults, i.e. the arithmetic mean A and the difference Δ A of theseeight values of cross section area, is shown in Table 4.

While the uncertainties achieved by particular operators arerelatively low, the substantial difference in values A obtained bydifferent operators originated from the different altitudes toestimate the wear track boundaries and this wear track width(see Fig. 4). If all A values measured by these five operators aretaken as one set and the mean value and its uncertainty wasevaluated, the result is

A¼ ð1:8570:30Þ μm2 and uAo;r ¼ 0:16: ð53Þ

Eq. (52) could be then modified to

uw ¼w

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi14:4� 10�3þ 1

12ΔA

A

� �2s

ð54Þ

(ii) The effect of air relative humidity in the laboratory environ-ment was evaluated by means of measurements at seven differentvalues RH whereas the tests conditions were held fixed. Theresults are presented in Table 5.

(iii) The effect of normal force Fn was investigated by means offive measurements with Fn¼5 N and five ones with Fn¼10 N. Theresults are shown in the Table 6.

(iv) The effect of pin velocity v was measured at v¼2.5 cm s�1

(5 measurements) and v¼10 cm/s (5 measurements) and theresults are shown in Table 7.

We can conclude that in this particular case the relative airhumidity in the range 29–47%, the normal force 5 and 10 N and thepin velocity 2.5 and 10 cm s�1 do not influence measured values ofthe friction and the wear rate.

5. Discussion

Although the measurement of friction and wear by pin-on-discapparatus is relatively easy and straightforward, an estimation ofuncertainties is a difficult task. We show that the misalignmentbetween the normal of the sample surface and the pin holder axisin the tangential plane (see Fig. 2(a)) is negligible compared toother sources of instrument uncertainty (Eq. 26). In case of thewear rate, we have found that the major contribution to theuncertainty is the evaluation of the cross-section area of the weartrack. If the wear track borders are not well defined and the weartrack is shallow, the uncertainty of the cross-section area isdominated by operator. We compared 8 measurements of 5 experi-enced operators; although repeatability of each operator wasreasonable, the difference between two operators could be as highas could be as high as 50% (Table 4). However, for deeper weartracks, such as those of TiN coating in this study, the maximumdifference between two operators dropped to an acceptable 6%(Table 1).

Correct evaluation of measurement uncertainties is essential tointerpret tribological results correctly. It helps as well to establishminimum number of measurements. Fig. 6 clearly illustrates theissue showing a mean of five values obtained for friction and wearrate. It is evident that the friction and, particularly, the wear rateincrease with radius. However, if we measure each point just onceor even twice, we would obtain almost random results due to highuncertainties of measured parameters. For DLC coatings, weconcluded that humidity, pin velocity and load in selected rangesdid not influence the values of the friction and the wear rate. Suchassessment would not be possible without precise estimation ofmeasurement uncertainty.

It is evident that the uncertainty of the result of one-timemeasurement, given by umA and umi only, cannot characterize thetrue standard uncertainty. The measurement has to be repeated;however, how many measurements are required to estimate

Table 3The effect of radius on friction and wear rate of TiN coatings.

TiN coating: Fn¼5 N, t¼22–25 1C, RH¼38–40 %

r (mm) 3 6 9 12 15 18

μ 0.9170.13 0.9370.08 0.9170.04 0.9770.04 0.9970.04 1.0670.02w (10�6 mm3 N�1 m�1) 5.671.6 6.572.1 6.971.4 9.670.4 11.370.7 9.770.9

2 4 6 8 10 12 14 16 18 20

0.6

0.7

0.8

0.9

1.0

1.1

FC WR

Radius (mm)

Fric

tion

coef

ficie

nt

4

6

8

10

12

14

Wea

r rat

e (1

0-6m

m3 N

-1m

-1)

Fig. 6. TiN – the effect of the wear track radius on friction coefficient m and wearrate w.

Table 4Cross-section area measured by 5 different operators, DLC coating.

Operator no. 1 2 3 4 5

A (mm2) 1.90 1.85 2.08 1.38 2.04

ΔA (mm2) 0.41 0.4 0.29 0.31 0.78μAo,r 0.06 0.06 0.04 0.06 0.11

R. Novak, T. Polcar / Tribology International 74 (2014) 154–163 161

uncertainty? If the test duration and economy is not taken intoconsideration, the following procedure should be carried out:After every test the value of Δm is evaluated. This value isincreasing sharply during first tests but after certain numberof the tests the increase will be negligible and Δm could beconsidered as Δmmax. Then Δmmax defines the full variance and

uμv ¼Δμmax

2ffiffiffi3

p : ð55Þ

Using Eq. (58) in Eqs. (28)–(30) the standard uncertainty um couldbe determined. The same procedure can be applied to the standarduncertainty uw of the wear rate.

However, this lengthy procedure is rarely applicable in practiceand the number of measurements typically does not exceed five.Following the recommendation in [1,2], the expanded standarduncertainties Umv or UAw given in Eq. (56) should be used instead ofthe standard combined uncertainties umv and uAw

Uμi ¼ kuμi; UAw ¼ kuAw ð56Þ

The coverage factor k is in the range 2 to 3 [1,2] and the selectionof the k value from this interval depends on the particular case andon the experimenter choice. Eq. (29) will be then modified and thevalue of expanded uncertainty Um will be given as

Uμ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2μAþk2ðμuμi;rÞ2

q: ð57Þ

Consequently, Eq. (42) will be transformed and the value Uw willbe

Uw ¼ kw

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiΔz

h

� �2

þ 2Δx

b

� �2

þ uAo

A

� �2

þ13

εðmÞm

� �2s

: ð58Þ

It is essential to note that the above described procedures ofuncertainties calculations do not involve other phenomena affect-ing the results of friction coefficient and wear rate measurements.In our calculations we assumed constant friction coefficient duringthe test, or, more precisely, during steady-state wear regime. Thiscondition is fulfilled for many material combinations and slidingconditions; the friction value only oscillates regularly around mean

friction values (here the mean means average from actual frictioncoefficient measured during one sliding test). However, sliding is avery complex process and sometimes the steady state wear withstabilized friction is not obtained. In such case the uncertainty offriction will be higher and must be further analyzed. Anotherpossibility is regular oscillation of the friction value during onerevolution of the disc. Local imperfection, such as pores, micro-cracks, or sudden wear debris release, could lead to local changesin the wear track and consequently local change in friction. Theaverage value of friction could be still treated in the same way asabove, but the uncertainty will again increase. We will deal withthese phenomena in our future study.

Our analysis helps to calculate uncertainty of the most usedtribological parameters, friction and wear rate. Although demon-strated on pin-on-disc system, the method could be easily adoptedfor similar techniques. The tribological analysis of thin film istypically comparative – different coatings tested at identicalconditions are compared, or the effect of test conditions on onecoating is studied. The knowledge of uncertainty helps to distin-guish real difference (e.g. increase in friction) from randomfluctuations and thus improve reliability of tribological measure-ments. We should stress here that uncertainty evaluation is a partof tribological measurement; therefore, brief description of uncer-tainty evaluation should be always.

Based on our analysis of the equipment, measurement practiceand friction and wear results obtained for two fundamentallydifferent coatings, we can suggest following simplification to theprocess of friction and wear rate uncertainty evaluation describedabove:

� Sample and pin misalignment could be neglected and theinstrument uncertainty of friction coefficient then depends onthe tribometer range and sensitivity (Eq. (9)).

� Data difference, i.e. difference between the highest and thelowest value in the set of data measured at identical conditions,should be used to calculate variance. In general, the uncertaintyof friction due to variance is significantly higher than theinstrument uncertainty.

� To evaluate uncertainty of the wear rate, the most importantare uncertainty of the wear track cross-section area (operatorinfluence) and the difference between the highest and thelowest measured cross-section area. Other components inEq. (42) could be neglected.

� Single tribological measurement should not be used; theminimum of three identical measurement is required andcoverage factor should be used to increase uncertainties esti-mates (see Eqs. (57) and (58)).

6. Conclusion

We evaluated standard uncertainty of the friction and the wearrate of thin films measured by pin-on-disc measurement. Westrictly followed uncertainty guidelines (ISO and NIST) and ana-lyzed different parts of standard uncertainties, such as the effect of

Table 5Friction and wear rate of DLC coatings vs. relative air humidity.

DLC coating: Fn¼5 N, v¼10 cm s�1, r¼7 mm

RH 29 30 35 36 39 42 47 Average

μ 0.076 0.08 0.085 0.095 0.092 0.084 0.096 0.08770.016w (10�7 mm3/Nm) 1.23 0.96 1.18 1.28 1.04 1.24 1.43 1.1970.17

Table 6The friction and wear rate for two loads, DLC coating.

DLC coating: v¼10 cm s�1, r¼8 mm, t¼2371 1C, N¼3000

Fn (N) μ Δμ w (10�7 mm3 N�1 m�1) ΔA/A

5 0.08770.015 0.020 1.1970.20 0.4010 0.09170.016 0.028 1.1370.19 0.41

Table 7The friction and wear rate for two sliding speeds, DLC coating.

DLC coating: Fn¼5 N, r¼7 mm, t¼2371 1C, N¼3000

v (cm s�1) μ Δμ w (10�7 mm3 N�1 m�1)

5 0.07370.015 0.041 1.1370.1710 0.07870.019 0.046 1.1170.16

R. Novak, T. Polcar / Tribology International 74 (2014) 154–163162

pin holder misalignment or the role of operator in estimation ofthe wear track cross-section area. Due to nature of sliding processwe suggest variance computed from the difference betweenmaximum and minimum measured value instead of standarddeviation. We applied standard uncertainty to a set of measure-ments on two different coatings, TiN and DLC, and showed valuesof friction and the wear rate with corresponding uncertainties.We showed that many uncertainties could be neglected andthe procedure to estimate the uncertainties for low number ofmeasurement.

Acknowledgments

This work was supported by the Czech Science Foundationthrough the project 108/10/0218.

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R. Novak, T. Polcar / Tribology International 74 (2014) 154–163 163