Ultrasonic Method for Measuring Frictional Temperature Rise

in Rubbing Surface

Ikuo IHARA 1, and Shingo AOKI 2

1 Department of Mechanical Engineering, Nagaoka University of Technology; Nagaoka, Japan

Phone: +81 258 479720, Fax: +81 258 479720; E-mail: ihara@mech.nagaokaut.ac.jp 2 Graduate Student of Nagaoka University of Technology; E-mail: s113002@stn.nagaokaut.ac.jp

Abstract

An ultrasonic thermometry is applied to temperature measurements during the friction process between an

acrylic resin and felted fabric plates. Temporal variations in the temperatures at and near the friction surface of

the acrylic plate has been examined. Both the temperature at the friction surface and temperature distribution

beneath the surface are quantitatively determined by the ultrasonic thermometry. The ultrasonic pulse echo

measurements at 2 MHz are performed for an acrylic resin plate of 10 mm thickness whose single side is being

heated by rubbing with a felted fabric plate. The influence of the loading pressure between the acrylic resin and

fabric plate on friction temperature rise has been examined. Rapid temperature rise more than 30 K at the friction

surface is observed within 0.5 s immediately after rubbing starts. It has also been observed that the temperature

at the friction surface increases with the loading pressure. Thus, it has been demonstrated that the ultrasonic

thermometry is a useful tool for measuring temperature rise in friction surface.

Keywords: Ultrasonic thermometry, Frictional temperature, Rubbing surface, Acrylic resin, In-situ observation

1. Introduction

Accurate knowledge about temperature rise due to friction between rubbing surfaces has long

been a topic of great interest in the field of tribology as well as any other relating fields in

science and engineering. This is basically because such temperature rise is closely related to

the mechanical and physicochemical properties of the rubbing materials. Such temperature"

also influences tribological properties and lubrication efficiency of the rubbing surfaces [1]-

[4]. Although there have been many theoretical and experimental works on the topics, few

studies on direct measurements of the temperature rise at the friction surface have so far been

made. This is because of extreme difficulty in measuring such temperature rise at the rubbing

surface. Unfortunately, little is known about the temperature measured at the interface of two

rubbing materials. Therefore, measuring such temperature rise due to friction and examining

its variation comprehensively are important issues. In particular, in-situ and real-time

monitoring technique for the temperature could be quite beneficial not only for basic research

in tribology but also for making an effective quality control of material manufacturing with

tribological processes.

Ultrasound, because of its capability to probe the interior of materials and high

sensitivity to temperature, is considered to be a promising tool for measuring internal

temperature of materials. Since there are some advantages in ultrasonic measurements, such

as non-invasive and faster time response, several studies on the temperature estimations by

ultrasound have been made [5]-[11]. In our previous works [12]-[15], an effective ultrasonic

methods for measuring internal temperature distributions of heated materials were developed

and applied to internal temperature profiling of heated materials. Since the ultrasonic method,

so-called ultrasonic thermometry, can determine surface temperature at a heated surface

without using any thermal boundary conditions at the heated surface, it is quite attractive and

highly expected to apply the ultrasonic thermometry to temperature measurements at a

friction surface between two rubbing materials. In this work, the ultrasonic thermometry has

been applied to frictional temperature measurements in a rubbing acrylic plate. The influence

of the loading pressure at the rubbing surface on frictional temperature rise has been

examined.

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2. Method for determining internal temperatures of heated material

When a material slides over another material, heat is generated at the interface due to friction

and the heat is transferred from the interface to each material. The generated heat and its

transfer depends on the thermal properties of the materials and sliding conditions such as

contact surface geometry and sliding speed. Figure 1 shows a schematic an internal

temperature gradient in a material whose single side is uniformly heated due to friction. To

investigate the temperature gradient, a one-dimensional unsteady heat conduction with a

constant thermal diffusivity is considered. Assuming that there is no heat source in the

material, the equation of heat conduction is given by [16]

2

2

T T

t xc• •?• • , (1)

where T is temperature, x is the distance from the heated or cooled surface, t is the elapsed time

after the heating or cooling starts, c is the thermal diffusivity. It is known that the temperature

distribution can be estimated by solving Eq. (1) under a certain boundary condition. In an

actual heating process such as a frictional heating, however, the boundary condition at the

frictional surface is quite difficult to know and often being changed transiently during heating.

Such boundary condition can usually not be measured. Because of little knowledge about the

boundary condition, temperature gradient is hardly determined from Eq. (1). This kind of

problematic situation usually occurs in frictional heating processes. To overcome the problem

mentioned above, we have applied an effective method, so-called the ultrasonic thermometry

[13-15], to the evaluation of the temperature of the friction surface as well as the temperature

distribution beneath the surface. This method consists of an ultrasonic pulse-echo measurement

and an inverse analysis coupled with a one-dimensional finite difference calculation. The

advantage of the method is that no boundary condition at the heating surface is needed. A one-

dimensional finite difference model consisting of a large number of small elements and grids is

used for analyzing heat conduction in the heated material. Using two information, the initial

temperature distribution and the temperature dependence of the ultrasonic velocity of the

material to be evaluated, not only the temperature at the heating surface but also the

temperature distribution in the material can be determined by the method. Temporal variations

Figure 1. Schematic of a one-dimensional temperature distribution in a rubbing material whose single side

is heated by friction.

of the determined temperatures can also be obtained as long as the transit time of ultrasound

propagating in the direction of temperature gradient of the heated material is continuously

being measured using an ultrasonic transducer as shown in Figure 1. It is noted that both the

temperature at B which is the outer surface and the temperature dependence of the material

should be given as known information in the inverse analysis. The detailed procedure for

temperature determination by the method is described in References [13-15].

3. Experiment

An acrylic resin plate (50 mm x 50 mm x 10 mm thickness) is used as a specimen and its

surface is rubbed with a felted fabric of 5 mm thickness so that the rubbed surface of the

acrylic plate is heated by frictional heat. Figure 2 shows a schematic of the experimental setup

used. This system provides not only ultrasonic pulse-echo measurements but also internal

temperature measurements of the acrylic plate using thermocouples inserted in the plate, so

that the validity of the ultrasonically determined temperatures can be verified by comparing

with those measured using the thermocouples. Three thermocouples, TC1, TC2 and TC3, are

inserted in the acrylic plate, at three locations, 1, 5 and 9 mm from the bottom (friction

surface), respectively. Another thermocouple, TC4, is placed on the top surface of the plate to

measure the surface temperature which is used as a known data in the ultrasonic thermometry.

The acrylic plate is forced on the surface of the rotating felted fabric so that an appropriate

rubbing between the felted fabric and acrylic plate can occur. The loading force is changed

from 60 N to 90 N. The loading pressure is then calculated from the compress load measured

using a load-cell. The diameter of the felted fabric is 150 mm and the speed of rotation is 200

rpm. The sliding velocity between the fabric and acrylic plate is approximately 0.5 m/s at the

location of the ultrasonic measurement. A longitudinal ultrasonic transducer of 2 MHz is

installed on the top surface of the acrylic plate and ultrasonic pulse-echo measurements are

performed. Ultrasonic pulse-echoes from the bottom surface (friction surface) of the acrylic

plate are continuously acquired every 30 ms with a PC based real-time acquisition system.

The sampling rate of ultrasonic signal is 100 MHz. Signal fluctuation due to electrical noise in

measurements is reduced by taking the average of fifty ultrasonic signals. Such ultrasonic

signals are used for determining both the temperature at the friction surface and temperature

distribution beneath the friction surface of the acrylic plate.

Thermocouples

Ultrasonic transducer

Specimen:

Acrylic resin

plate

Felted fabric on

rotating discAmp.

Ultrasonic

pulser/receiver

A/D board

PC

TC3TC2

TC1

TC4

Ultrasonic transducer

Acrylic resin plate

Felted fabric

Rotating disc

Loading

Figure 2. Schematic of the experimental setup: acrylic plate on a rotating felted fabric disc and schematic

diagram of measurement system (left); cross sectional view of the setup (right).

4. Results and discussion

Figure 3 shows ultrasonic pulse echoes measured from the acrylic plate. Two echoes, the first

and second reflected echoes, are clearly observed. The transit time through the acrylic plate

can precisely be determined from the time delay between the two echoes by taking a cross-

correlation between them. Using the transit times acquired during the rubbing process, the

temperature at the friction surface and internal temperature distribution of the acrylic plate are

obtained as a function of measurement time. It is noted that the temperature dependence of the

longitudinal wave velocity of the acrylic resin plate used is found to be approximately v(T) =–

0.0214T2–1.9749T+2769.3 (m/s). The temperature dependence and the initial temperature of

the acryl plate before heating, 22.5 oC, are used in the estimation.

Figure 4 shows the estimated temperature distribution and its variation with elapsed

time, where the numbers shown in Figure 4 denote the elapsed time after rubbing starts. It is

noted that this result is obtained under the loading pressure of approximately 28 kPa. It can be

seen in Figure 4 that the temperature distributions estimated ultrasonically almost agree with

those measured using thermocouples, while the estimated value of thermocouples are slightly

higher than those of ultrasonic results. It is worth noting that there occurs a steep temperature

gradient in the shallow area of near-surface even at 0.5 s immediately after the rubbing started,

and the temperature at the friction surface increases with the elapsed time and accordingly, the

temperature distribution becomes deeper. Similar tendency to that shown in Figure 4 is

observed in the results obtained under the loading pressures of 38 kPa and 42 kPa.

Figure 5 shows the temperature variations at the friction surface and 1mm beneath the

friction surface of the acrylic resin plate. The temporal variation in the loading pressure is also

depicted in the figure. It has been found in the ultrasonic result shown in Figure 5 (a) that the

temperature at the friction surface increases rapidly just after the rubbing due to the loading

occurs and then drastically decreases when the loading is removed and gradually decreases

with the elapsed time. It is noted that the friction surface temperature reaches almost 80 oC by

the friction heating due to the loading pressure of 28 kPa for 2.2 s. On the other hand, the

internal temperature at 1mm beneath the friction surface increases slowly a little later after the

rubbing starts and then decreases very slowly. The temperature rise is not significant and it

reaches only 36 oC at most. Although the internal temperature at the same location measured

using the thermocouple shows a similar tendency to that of the ultrasonic result, there is a

Figure 3. Measured ultrasonic pulse echoes from the bottom surface of the acrylic resin plate of 10 mm

thickness.

certain discrepancy between them. The reason for the discrepancy is currently being

investigated. Figures 5 (b) and 5 (c) which are obtained under the loading pressures of 38 kPa

and 42 kPa, respectively show the similar tendency to that of Figure 5 (a). It should be noted

that the friction surface temperature increases with the loading pressure and it can reach

Figure 4. Temperature distribution near friction surface of the acrylic resin plate and its variation, measured

by the ultrasonic method and thermocouples.

0

10

20

30

40

50

20

60

100

140

0 20 40

Pre

sure

(k

Pa

)

Tem

per

atu

re (

oC

)

Elapased time (s)

Ultrasound (friction

surface)

Ultrasound (1 mm

from friction surface)

Thermocouple (1 mm

from friction surface)

Pressure

Pressure

0

10

20

30

40

50

20

60

100

140

0 20 40P

resu

re (

kP

a)

Tem

pera

ture

(oC

)

Elapased time (s)

Ultrasound (friction

surface)

Ultrasound (1 mm

from friction surface)

Thermocouple (1 mm

from friction surface)

Pressure

Pressure

(a) (b)

0

10

20

30

40

50

20

60

100

140

0 20 40

Pre

sure

(k

Pa

)

Tem

per

atu

re (

oC

)

Elapased time (s)

Ultrasound (friction

surface)

Ultrasound (1 mm

from friction surface)

Thermocouple (1 mm

from friction surface)

Pressure

Pressure

(c)

Figure 5. Temperature variations at the friction surface and 1mm beneath the friction surface of the acrylic

resin plate, measured by the ultrasonic method and thermocouple, under the loading pressure (a) 28 kPa,

(b) 38kPa, and (c) 42 kPa.

almost 110 oC due to the loading pressures of 42 kPa. Thus, it seems reasonable to think that

the ultrasonic thermometry properly detect and estimate the temporal variation in the

temperature at friction surface during the rubbing process.

5. Conclusion

An ultrasonic thermometry has been applied to temperature measurements during the friction

process between an acrylic resin and felted fabric plates. Temporal variations in the

temperatures at and near the friction surface of the acrylic plate has been examined. Rapid

temperature rise due to frictional heating has clearly been observed by the ultrasonic method.

It has also been found through the experiments that the friction surface temperature increases

with the loading pressure and it can reach almost 110 oC due to the loading pressures of 42

kPa. Thus, in-situ temperature measurements of frictional heating surface by the ultrasonic

thermometry has been demonstrated. Although further study is necessary to improve the

accuracy in the measurement, it is highly expected that the ultrasonic method could be a

useful tool for on-line monitoring of temperatures at friction surface and beneath the surface

during friction process.

Acknowledgment

Financial supports by the Grant-In-Aid for Scientific Research (B25289238) from the JSPS

and Toyota Motor Co. are greatly appreciated.

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