ORIGINAL PAPER

Dynamic In Situ Measurements of Frictional Heatingon an Isolated Surface Protrusion

Alexander I. Bennett • Kyle G. Rowe •

W. Gregory Sawyer

Received: 22 November 2013 / Accepted: 29 April 2014 / Published online: 14 May 2014

� Springer Science+Business Media New York 2014

Abstract Problems in the subject of frictional heating

have been studied extensively, yet their complexity

remains a barrier to further understanding. This study

simplifies the frictional heating problem by examining the

temperature rise due to a heat source of prescribed geom-

etry. A single positive feature on the sliding face of the

countersurface causes a local temperature rise. The cylin-

drical feature has a diameter of 150 lm and aspect ratio of

0.1 and slides under the larger contact area whose contact

width is *600 to *750 lm. An infrared camera, acquiring

at 870 Hz, observed the temperature rise at the contact

interface between the feature and the rubber pin. The

applied force for all tests was 200 mN, and the sliding

velocity was varied from 10 to 200 mm/s. Maximum

temperature rises of *1–17 �C and average temperature

rises of *1–8 �C were measured. Measured values were

compared to the Jaeger’s frictional heating models for

sliding contacts.

Keywords Friction � Wear � Thermal tribology �Elastomer

1 Introduction

Frictional heating in sliding contacts is unavoidable and

may profoundly affect the tribological and mechanical

properties of the materials in the system [1–5]. At the high

sliding speeds and loading conditions that are necessary to

induce measurable frictional heating in ceramic and

metallic contacts, the thermal behavior due to surface

roughness is especially difficult to analyze [6–8]. Due to

high friction, micro-scale elastomeric contacts demonstrate

appreciable temperature rises under much more controlla-

ble and measurable sliding conditions despite unpredict-

able contact geometries.

A broad range of thermal measurement methods, ranging

from thin film and dynamic thermocouples to radiometric

(infrared) measurements [1, 9–17], have been applied to

monitor contact temperature [18–20]. These methods have

largely been limited to spot analysis, which neglect the

spatial distribution of temperature data. A full-field infrared

method, as developed by Rowe et al. [12], is capable of

simultaneously mapping temperature changes over the full

contact area, reducing the analytical difficulties presented by

areal and geometric complexity [17]. This method can be

applied to contacts between any materials for systems with

an infrared (IR) transparent countersample and IR opaque

pin.

Established models for the frictional heating problem

have been proven for ideal circumstances such as smooth

geometries, known systems, and idealized materials [21–

30]. Due to the aforementioned barriers to measurement as

well as the expansive nature of the problem, making fun-

damental measurements becomes increasingly difficult.

The ideal system for infrared measurement of heating in

sliding contacts would involve set geometries with appre-

ciable heating at low speeds and loads.

Building on the work done by Rowe et al. [17], an

experiment has been designed in which the temperature

rise due to a prescribed geometry moving through contact

is measured. A micro-sized positive feature was deposited

A. I. Bennett � K. G. Rowe � W. Gregory Sawyer (&)

Department of Mechanical and Aerospace Engineering,

University of Florida, Gainesville, FL 32611, USA

e-mail: wgsawyer@ufl.ed

W. Gregory Sawyer

Department of Material Science and Engineering, University of

Florida, Gainesville, FL 32611, USA

123

Tribol Lett (2014) 55:205–210

DOI 10.1007/s11249-014-0347-7

on the surface of the CaF2 countersample in the sliding

path of the sample. Local temperature rises of the feature

are appreciable over the temperature rise of the global

contact even at sliding speeds as low as 10 mm/s. The

maximum and average temperature of the feature follows

the classical thermal heating models of Jaeger. Addition-

ally, the range of sliding speeds used may have crossed two

frictional heating regimes, which, with further investiga-

tion, may lead to a better understanding of sliding contact

frictional heating relative to surface roughness.

2 Asperity Contact Temperature Testing

2.1 Instrumentation and Analysis

A pin-on-disk, in situ thermal micro-tribometer was used

for all tests conducted in this experiment where contact is

made between a rubber hemisphere on a 3-mm-thick

cylindrical optical window [17]. The rubber, Viton A, is

pressed into contact with the calcium fluoride disk, and the

sample is held stationary, while the disk is rotated in a ring-

bearing stage, driven by a servo motor. Loading and

positioning of the sample are controlled by manual

micrometer stages and held constant during testing. Two

capacitance probes attached to a rectilinear cantilever

transduce displacements into voltages which are then

converted into force measurements.

The work done to overcome the friction between the

rubber pin and the rotating calcium fluoride (CaF2) disk

causes heat to be generated within the contact. The infrared

radiation emitted by the sample is then measured by an IR

camera (FLIR SC7650) and related to temperature. The

indium antimonide detector is sensitive to radiation wave-

lengths between 3 and 5 lm where the CaF2 countersample

transmits up to 92 % of incident IR. At quarter frame res-

olution (128 9 160 pixels at 5 lm/pixel), the camera is

capable of acquiring at 870 Hz. LabVIEWTM was used for

instrument control and data acquisition. Post-processing of

data was performed in MATLAB�.

Tests were conducted at a prescribed load of 200 mN

and contact pressure of *620 kPa. One sliding speed

was used for each test and varied from 10 mm/s up to

200 mm/s. Each test lasted *22 s and was imaged at

870 Hz. Frames were acquired for each pass of the feature

through the field of view of the camera (Fig. 1c). The

asperity was tracked frame by frame using an algorithm,

designed in house, that assigns a region of interest to the

cylindrical asperity for all frames in which it was visible

between the pin and the countersample (Fig. 1b).

For every video, the frames where the feature appeared

were separated from the rest of the video. Image-editing

tools in MATLAB were applied to each of the frames

which isolated the feature from the rest of the image using

a region of interest overlay. As the frames progressed, the

region of interest moved according to predicted values of

the features location. The dimensions and location of the

ROI were then applied to the temperature data of the

image. The average and maximum temperatures of the

isolated regions were recorded. The distance, s, is mea-

sured from the center of the image to the center of the

ROI.

21.5 °C

19.8 °C

19.1 °C

18.4 °C

17.7 °C

17.0 °C

16.3 °C

15.9 °C

Nominal Contact Area Field of View

s

Feature

t = 2.3 ms

150 µmV(asperity velocity)

Ff(friction force)

P(pin)

Fn(normal load)+s

at edge of contact: s = rr

18 µm

~20 µm

21.5 °C

19.8 °C

19.1 °C

18.4 °C

17.7 °C

17.0 °C

16.3 °C

15.9 °C

t = 0 ms

t = 5 ms

Rubber Impengement

Temperature Developmentthrough Contact

a b

c

800 µm

640 µm

s = 0

Fig. 1 a Schematic of contact

between the pin, countersurface,

and positive feature. As the

feature moves into contact, it

displaces the Viton A pin.

b Data analysis scheme of the

feature as it moves through the

global contact. The position of

the pin is measured from the

center of apparent contact of the

pin with the countersurface to

the center of the feature. c The

temperature development as the

feature moves under contact

shows a correlation with the

pressure distribution in the

contact. Highest temperatures

manifest near the center of

contact where the highest local

pressures exist

206 Tribol Lett (2014) 55:205–210

123

2.2 Materials

Viton A half-spheres were used as the pin material in these

studies. Viton A is considered hard relative to other rubbers

with a rating of 70A on the shore durometer scale, an

elastic modulus of 4–8 MPa, and a thermal conductivity of

0.22 W/m K. The average surface roughness, measured

using a scanning white light interferometer (Veeco�

NT7100), was found to be 1.46 lm.

Calcium fluoride was used as the countersample. Similar

to other ionic solids, CaF2 is transmissive in the infrared

spectrum and exhibits 92–95 % transmission throughout

the 0.2- to 6.5-lm wave band; this range encompasses the

3–5 lm range in which the FLIR SC7650 is capable of

measuring. Due to its hardness and thermal conductivity of

9.71 W/m K, as well as optical transmission, CaF2 is an

ideal choice as a countersample.

To produce the positive feature on the surface of the

countersample, an 18-lm layer of a common photoresist epoxy,

SU-8, was spun coat onto the CaF2. A photomask was then

applied for UV curing in order to produce patterns on the disk.

The desired pattern was a single cylinder, 18 lm tall and

150 lm in diameter at a disk radius of 15.725 mm. After cur-

ing, the excess uncured photomask was dissolved away using

propylene glycol monomethyl ether acetate. The deposition

process left an optically smooth positive feature on the CaF2 as

seen in Fig. 2. SU-8 has a thermal conductivity of 0.2 W/m K

which matches well with the thermal conductivity of the pin.

3 Results

The average temperature rise of the surface feature (above

ambient) ranged from 0.5 �C, for the slowest sliding

speed test, to 7 �C, for the fastest. The maximum tem-

perature rise followed the same trend with temperature

rises from 1 to 18 �C. A characteristic image for each test

is displayed in Fig. 3. Ambient and global contact tem-

perature, friction coefficient, and load did not change

appreciably during the experiments. Maximum and aver-

age temperatures of the feature for each test are given in

the table in Fig. 6.

The center of the feature’s position, s, as measured from

the center of global contact, was recorded for all frames

where the feature was in view. Position data were then

binned in 25-lm increments; the standard deviation of the

temperature for each bin is plotted in Fig. 4. In some tests,

18.25 µm

18.69 µm

b Worn

a Nascent

Fn Ffω

IR ImageArea 640 x 800 µm

CaF2 counter-sample

pinsurfacefeature

Sliding Direction

Sliding Direction

A

A

18.5 µm

150 µm

152.83 µm

Fig. 2 The SU-8 feature rotates

with the disk and slides under

contact once per revolution. IR

radiation from the sliding

contact is measured by the 39

lens which then focuses the

radiation on the indium

antimonide detector. A scan

from a scanning white light

interferometer shows the

unworn feature (a) and the worn

feature (b)

32.0 °C

29.5 °C

27.0 °C

25.3 °C

23.9 °C

21.0 °C

19.6 °C

16.5 °C

200 mN

10 mm/s

25 mm/s

50 mm/s

75 mm/s

100 mm/s

150 mm/s

200 mm/s

Fig. 3 Schematic of contact between pin, countersurface, and

positive feature. As the feature moves into contact, it displaces the

Viton A pin. The position of the pin is measured from the center of

apparent contact of the pin with the countersurface to the center of the

feature

Tribol Lett (2014) 55:205–210 207

123

two distinct peaks form near s = 0. It has been documented

that increased speeds can cause rubber pins in tribological

sliding experiments to bifurcate into two zones separated

by a section of non-contact [17]. This could explain the

drop in feature temperature and also bolsters the correlation

between local contact pressure and temperature rise.

While rubber wear debris is characteristic of sliding tests

with completely roughened surfaces, no wear debris was

observed or recovered during these tests. Neither the pin

nor the raised feature showed appreciable degradation as

observed by white light interferometer scans.

4 Discussion

The average and maximum temperature is plotted for a

particular feature position in Fig. 5 (left) and Fig. 5 (right),

respectively. Position (s) is measured from the center of

global contact to the center of feature (local) contact; each

temperature point corresponds to a locus of positions

25 lm wide. As the feature first enters contact, it begins to

heat; for low-speed tests, the temperature throughout global

contact plateaus, but at higher-speed test, there are distinct

temperature peaks around s = 0. This trend alludes to a

correspondence between the maximum temperature and the

location of the highest pressure under the contact. The

parabolic pressure distribution in circular contacts has been

studied before and the findings correlate well with the data

of this experiment [28].

The local feature temperature distribution is more likely

related to the Peclet number. Because the feature width is

small compared to the contact width and because the pin

material can accommodate large strains, pressure across the

feature can be assumed to be constant. As the sliding speed

increases, the distribution of heat shifts from the leading

edge of the feature to the trailing edge. The thermal gra-

dient at low speeds is fairly shallow, but as speed increases,

the gradient across the feature can realize half of the total

temperature rise due to the feature moving through contact.

An analytical model for the average and maximum

temperature rise in sliding contacts has been solved for and

verified experimentally [25]. The model partitions the heat

between the two sliding bodies based on their individual

thermo-mechanical properties. In the performed experi-

ments, the feature becomes a third body and must be

accounted for in the heat-partitioning equations. According

to the models, the lowest temperature rise will be realized

when contact consists of only the pin and countersample

which is the state of lowest contact pressure. The highest

contact pressure would then be found when the load is

0

2

4

6

8

10

12

14

16

18

Ave

rage

)C°(,TΔ

Max

imum

)C°(,TΔ

Feature Position, s (µm)

0

2

4

6

8

10

12

14

16

18

Feature Position, s (µm)

0

2

4

6

8

10

12

14

16

18

Feature Position, s (µm)

0

2

4

6

8

10

12

14

16

18

Feature Position, s (µm)

0

2

4

6

8

10

12

14

16

18

Feature Position, s (µm)

-500 -250 0 250 500 750

0

2

4

6

8

10

12

14

16

18

Feature Position, s (µm)

200 mm/s150 mm/s100 mm/s

200 mm/s150 mm/s100 mm/s

direction oftravel

-500 -250 0 250 500 750 -500 -250 0 250 500 750

-500 -250 0 250 500 750-500 -250 0 250 500 750-500 -250 0 250 500 750

Fig. 4 Average and maximum temperature rise of and within the region of interest of the positive feature at varying speeds

208 Tribol Lett (2014) 55:205–210

123

applied only to the contact area of the feature. Applying

these two conditions to Jaeger’s model provides bounds for

the measured data and are given in Fig. 6.

The analysis process predicts feature position fairly

well; however, the final judgment on feature position lies

with the experimentalist. A small portion of frames exists

in which the feature is obscured and the experimentalist

must decide, based on prior frames and localized heating in

the current frame, where the feature is located. This con-

tributes to the error in Fig. 4.

5 Conclusions

A method to measure the temperature rise due to the input

of heat from a single perturbation into such a system was

developed. This method provides a way to study the effects

of frictional heating on a simple and fundamental level. A

positive, cylindrical SU-8 micro-feature was cured onto a

calcium fluoride countersurface. The rubber pin and mod-

ified countersample were tested in a pin-on-disk configu-

ration, and sliding experiments were conducted at various

sliding speeds.

The feature created an average of 8 �C and maximum of

16 �C temperature rise over the bulk sliding temperature.

Feature temperature rises increased with increasing sliding

speeds. The measured average and maximum feature

temperature was compared to predicted temperature values

predicted by Jaeger’s heating model for sliding contacts.

The predicted average and maximum temperature values

provided lower and upper bounds, respectively, to the

measured data.

Acknowledgments The authors would like to thank Jon Bart Ten

Hove at the University of Florida for his assistance with countersur-

face fabrication. Additionally, the authors would like to thank Dr.

Dylan Morris and Olivier Gerardin for their useful insight and guid-

ance throughout ideation and experimentation. This work was sup-

ported by Michelin North America and could not have been

completed without the help of the Tribology Lab at the University of

Florida.

References

1. Grosch, K.A., Schallamach, A.: Tyre wear at controlled slip.

Wear 4, 356 (1961)

0

2

4

6

8

10

12

14

16

18

Feature Position, s (µm)-500 -250 0 250 500 750-500 -250 0 250 500 750

0

2

4

6

8

10

12

14

16

18

Tem

pera

ture

Ris

e,T

,(°C

)

Feature Position, s (µm)

10 mm/s 25 mm/s 50 mm/s 75 mm/s 100 mm/s 150 mm/s 200 mm/s

Maximum Temperature Rise Average Temperature Rise

Slid

ing

Spe

ed

Slid

ing

Spe

ed

Fig. 5 (Left) Average

temperature rise of positive

feature region of interest as it

moves through global contact.

(Right) Maximum temperature

rise within the positive feature

region of interest as it moves

through global contact. The

position of the 150-lm feature

was determined from the center

of global contact between the

pin and disk

Sliding Speed Avg. Max.(mm/s)

10255075100150200

(ΔT, °C)0.71.42.02.23.34.25.0

(ΔT, °C)1.74.05.65.512.914.216.7

Avg. Max.(ΔT, °C)

4.37.210.010.516.119.122.4

(ΔT, °C)0.81.92.92.85.66.98.0

Predicted Measured

0 50 100 150 2000

2

4

6

8

10

12

14

16

18

20

22

24

Sliding Speed, v (mm/s)

Predicted Maximum ΔTPredicted Average ΔT

Maximum Measured ΔTAvgerage Measured ΔT

Fig. 6 Measured maximum and

average temperature rises for

each sliding speed. Jaeger’s

solution for average and the

modified solution for maximum

temperature rises within contact

provide bounds for the data

Tribol Lett (2014) 55:205–210 209

123

2. Grosch, K.A.: Relation between friction and visco-elastic prop-

erties of rubber. Proc. R. Soc. Lond. A-Math. Phys. Sci.

274(1356), 21 (1963). doi:10.1098/rspa.1963.0112

3. Tabor, D.: The mechanism of rolling friction. II. The elastic

range. Proc. R. Soc. Lond. 229(1177), 198–220 (1955)

4. Lancaster, J.K.: Estimation of the limiting PV relationships for

thermoplastic bearing materials. Tribology 4(2), 82–86 (1971).

doi:10.1016/0041-2678(71)90136-9

5. Barquins, M.: Rubber friction variation with rate and tempera-

ture: some new observations. Physics 19, 547–563 (1985)

6. Siroux, M., Kasem, H., Thevenet, J., Desmet, B., Dufrenoy, P.:

Local temperatures evaluation on the pin–disc interface using

infrared metrology. Int. J. Therm. Sci. 50(4), 486–492 (2011).

doi:10.1016/j.ijthermalsci.2010.11.001

7. Ingram, M., Reddyhoff, T., Spikes, H.A.: Thermal behaviour of a

slipping wet clutch contact. Tribol. Lett. 41(1), 23–32 (2011).

doi:10.1007/s11249-010-9669-2

8. Bos, J., Moes, H.: Frictional heating of tribological contacts.

J. Tribol. 117(1), 171–177 (1995)

9. Bushan, B. (ed.): Modern Tribology Handbook, 1st edn. CRC

Press LLC, Boca Raton (2001)

10. Gulino, R., Bair, S., Winer, W.O., Bhushan, B.: Temperature

measurement of microscopic areas within a simulated head tape

interface using infrared radiometric technique. J. Tribol. Trans.

ASME 108(1), 29–34 (1986)

11. Bair, S., Green, I., Bhushan, B.: Measurement of asperity tem-

peratures of a read write head slider bearing in hard magnetic

recording disks. J. Tribol. Trans. ASME 113(3), 547–554 (1991).

doi:10.1115/1.2920658

12. Santini, J.J., Kennedy Jr, F.E.: An experimental investigation of

surface temperatures and wear in disk brakes. Lubr. Eng. 31(8),

402–417 (1974)

13. Nagaraj, H.S., Sanborn, D.M., Winer, W.O.: Direct surface

temperature measurement by infrared radiation in elastohydro-

dynamic contacts and the correlation with the Blok flash tem-

perature theory. Wear 49(1), 43–59 (1978). doi:10.1016/0043-

1648(78)90022-4

14. Tong, H.M., Arjavalingam, G., Haynes, R.D., Hyer, G.N., Ritsko,

J.J.: High-temperature thin-film Pt–Ir thermocouple with fast time

response. Rev. Sci. Instrum. 58(5), 875–877 (1987). doi:10.1063/

1.1139649

15. Schreck, E., Fontana, R.E., Singh, G.P.: Thin-film thermocouple

sensors for measurement of contact temperature during slider

asperity interaction on magnetic recording disks. IEEE Trans.

Magn. 28(5), 2548–2550 (1992). doi:10.1109/20.179552

16. Kennedy, F.E., Frusescu, D., Li, J.: Thin film thermocouple

arrays for sliding surface temperature measurement. Wear

207(1–2), 46–54 (1997). doi:10.1016/s0043-1648(96)07473-x

17. Rowe, K.G., Bennett, A.I., Krick, B.A., Gregory Sawyer, W.:

In situ thermal measurements of sliding contacts. Tribol Int 62(0),

208–214 (2013). doi:10.1016/j.triboint.2013.02.028

18. Archard, J.F., Rowntree, R.A.: The temperature of rubbing bod-

ies; part 2, the distribution of temperatures. Wear 128(1), 1–17

(1988). doi:10.1016/0043-1648(88)90249-9

19. Archard, J.F.: The temperature of rubbing surfaces. Wear 2(6),

438–455 (1959). doi:10.1016/0043-1648(59)90159-0

20. Schallamach, A.: How does rubber slide? Wear 17(4), 301–312

(1971)

21. Carslaw, H.S., Jaeger, J.C.: Conduction of Heat in Solids, 2nd

edn. Clarendon Press, Oxford University Press, Oxford

[Oxfordshire], New York (1986)

22. Blok, H.: The dissipation of frictional heat. Appl. Sci. Res. 5(2),

151–181 (1955). doi:10.1007/bf03184615

23. Blok, H.: The flash temperature concept. Wear 6(6), 483–494

(1963). doi:10.1016/0043-1648(63)90283-7

24. Blok, H.: Theoretical study of temperature rise at surfaces of

actual contact under oiliness lubricating conditions. In: Pro-

ceedings of the General Discussion on Lubrication and Lubri-

cants, vol. 2, pp. 222–235 (1937)

25. Jaeger, J.C.: Moving sources of heat and the temperature at

sliding contacts. J. Proc. R. Soc. N. S. W. 76, 203–224 (1942)

26. Kennedy, F.E., Hussaini, S.Z.: Thermo-mechanical analysis of

dry sliding systems. Comput. Struct. 26(1–2), 345–355 (1987).

doi:10.1016/0045-7949(87)90264-1

27. Kennedy, F.: Frictional heating and contact temperatures. In:

Modern Tribology Handbook, Two Volume Set. Mechanics &

Materials Science. CRC Press, Boca Raton (2000)

28. Tian, X.F., Kennedy, F.E.: Maximum and averate flash temper-

atures in sliding contacts. J. Tribol. Trans. ASME 116(1),

167–174 (1994). doi:10.1115/1.2927035

29. Tian, X., Kennedy, F.: Contact surface temperature models for

finite bodies in dry and boundary lubricated sliding. J. Tribol.

115(3), 411–418 (1993)

30. Bansal, D.G., Streator, J.L.: On estimations of maximum and

average interfacial temperature rise in sliding elliptical contacts.

Wear 278–279, 18–27 (2012). doi:10.1016/j.wear.2011.12.006

210 Tribol Lett (2014) 55:205–210

123