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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: [email protected] 2 Graduate Student of Nagaoka University of Technology; E-mail: [email protected]
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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