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Influence of vibration on the kinetic friction between plastics and ice
Wear, I15
(1987)
131
131
- 138
INFLUENCE OF VIBRATION PLASTICS AND ICE*
ON THE KINETIC
FRICTION
BETWEEN
A. LEHTOVAARA Laboratory of Machine Design, SF-331 01 Tampere (Finland)
Tampere
University
of Technology,
P.O. Box
527,
Summary Influence of vibration on the average kinetic friction between plastics and ice was studied within a range 0.005 - 1 kHz, concentrating on the low frequencies. Vibration was induced in the test specimen by an exciter while the test specimen was sliding on smooth ice. Measurements were performed at a speed of 5 m s-l and a load of 215 N at different temperatures. The results of the study show that low frequency vibration reduces the kinetic friction in a remarkable way at temperatures below -1 “C, even when the acceleration of the vibrating body was much lower than the acceleration of gravity. The mechanism of kinetic friction of ice is also discussed.
1. Introduction In the past and at present the subject of kinetic friction between plastics and ice or snow has been studied in terms of materials, surface finish, load, speed, temperature, apparent contact area etc. [ 1 - 61. However, no attention has been paid to the influence of contact dynamics on kinetic friction. Contact surfaces are never absolutely smooth and contain different kinds of surface irregularities and corrugations which induce vibration at the contact area. This paper describes the measurement arrangements and initial results of an experimental investigation of the effect of vibration on the average kinetic friction between plastic and ice in the case of high speeds and loads under laboratory conditions. As is known from earlier research [ 11, the frictional behaviour of snow is almost similar to ice except for the macroscopic ploughing of snow. Therefore the plastic-ice friction measurements also give information about the frictional behaviour between plastics and snow.
*Paper Technology,
presented at the Nordic Lulei, Sweden, June 15 -
0043-1648/87/$3.50
Symposium
on
Tribology,
Lule”a University
of
18, 1986. @ Elsevier
Sequoia/Printed
in The Netherlands
132
2. Measurements 2.1, Apparatus The friction apparatus, which is described in detail elsewhere j2f. was placed in a cold box and modified to take into account the demands of the vibration studies. A general view of the apparatus is shown in Fig, I
, kR:C
Fig.
1. The friction
I ION
CYNAMOMi
‘F .
apparatus
The temperature T of the cold box could be varied within a range -20 - +2 “C. Because the test specimen in the cold box could be handled through a plastic cover the air conditions in the cold box were kept constant. The specimen was observed through a window in the box. An electric motor with adjustable speed u control (0 - 12 m s ’ ,I was placed outside the cold box to eliminate heat and vibration from the measuring system. The rotating turntable was connected to the motor by a flexible shaft and a V-belt. Vibration was caused by the exciter which was connect,ed to the loading arm. Forced vibration was controlled by the exciter amplitude and frequency, and the vibration of the test specimen was measured by
133
accelerometers. The test specimen was fixed to the loading arm which could move freely in the horizontal and vertical planes. The frictional force dynamometer was connected in the horizontal plane between the loading arm and immovable arm. The normal force FN could be adjusted by weights. The frictional force was measured by a strain gauge dynamometer whose signal was low pass filtered at 2 Hz and the mean value was monitored continuously by a plotter and a Data Precision 6000 analyser (trend curve). The natural frequency of the dynamometer at a load of 215 N was adjusted to 7 Hz to partly filter frequencies above 10 Hz. This eliminates the normal vibration influence on tangential (frictional) sliding causing the system to slide smoothly during excitation. However, the dynamometer was still stiff enough to keep the test specimen tangentially at the same position at different frictional forces. The acceleration of the test specimen was measured by the piezoelectric accelerometers, masses 20 and 4 g, and monitored by the Data Precision 6000 and Hewlett Packard HP 3582A spectrum analyser. The possible frequency range of the vibration controlling system was from 0.002 to 8 kHz. The normal acceleration was measured at point A in Fig. 1 and the side displacement was controlled at point B. Thermocouples were used for measuring temperatures inside the cold box and inside the ice about 3 mm below the track surface. Tap water was used for preparing the ice. The ice was smoothed by grinding when the turntable was rotating. The ice was ground so that the sliding track was raised and had a width of 40 mm. Because the width of the test specimen was 44 mm (slightly greater than that of the track) side effects on the specimen from the track were eliminated. 2.2. Test specimen The test specimen was a cantilever wedge-like sandwich beam structure (Fig. 1) 260 mm long, 44 mm wide and 14 mm thick at its thickest point and with the same curvature as the turntable. High density polyethylene was used as the sliding material. The base of the test specimen was ground with a series of emery papers (Numbers 120, 240 and 400) and waxed with paraffin. After waxing, the paraffin was removed as thoroughly as possible by scraping and the specimen was then corked. 2.3. Test procedure After freezing water to the turntable and placing the test specimen in the cold box, the system was left to stabilize overnight. In the morning the ice was smoothed by grinding. After 2 h it was then ready for measurement. Before the vibration measurements the test specimen was allowed to run in for a distance of approximately 3 km to ensure that a steady state friction process had been achieved. In the case of sinusoidal sweep, the sweep rate was 20 Hz mini’ within a range of 5 - 250 Hz and 200 Hz mini’ for 0.25 1 kHz and the vibration velocity of the shaker was kept constant. Vibration
134
measurements were done at a constant speed of 5 m s ’ and a constant normal load of 215 N at different temperatures.
3. Experimental
results
The influence of vibration on kinetic friction was measured within a range of 0.005 - 1 kHz. At first the frequency range was swept and the frictional force and the acceleration response were monitored continuously. The frictional force reduction was observed only at low frequencies. The reduction was greatest at the first natural frequency of the test specimen where the vibration amplitude was large compared with the amplitudes of the antiresonance frequencies. Many specific frequencies were also excited by random and sinusoidal vibration to confirm that higher frequencies (greater than 70 Hz) have no effect on the kinetic friction even when the acceleration level at point A is more than ten times higher than the aeceleration level without external excitation at specific frequencies. Next, the first natural frequency of the test specimen, 11.8 Hz, was examined more closely because it gave the clearest vibration--friction dependence. The typical frequency spectrum of the test specimen without external vibration is shown in Fig. 2. It can be seen that the r.m.s. acceleration amplitude at a frequency of 11.8 Hz is about 0.05 m se2. The two peaks at frequencies 54 and 70 Hz are the natural frequencies of the apparatus. The friction behaviour as a function of the normal acceleration at point A can be seen in Fig. 3. At the beginning of the curves the frictional force is stable and the normal acceleration (about 0.04 m sC2) comes from surface irregularities and apparatus vibration. When the exciter is turned on the acceleration increases and the frictional force decreases in a remarkable way.
0
Fig. 2. Typical normal r.m.s. external excitation (FN = 215
FREQ Hz
250
acceleration response of test specimen N, ~1= 5 m s-‘, T = -4.5 “C).
at point
A withour
135 FRICTION
ACC m s-2
N
+4
1
-j
I 0
TIME
s
4
10
Fig. 3. Frictional force (lower curve) behaviour as a function (upper curve) (FN = 215 N, u = 5 m s-l, 2’ = -13 “C).
or normal
acceleration
When the exciter is turned off the frictional force increases back to its normal level. At all times the frictional force seems to follow the normal acceleration very closely. The influence of vibration on the kinetic friction is shown in Fig. 4 at different temperatures. The normal acceleration of the test specimen was measured at point A. The friction behaviour is described by the friction reduction percentage DF which is the change in frictional force caused by the excitation divided by the frictional force without excitation. Also the 3c
0.5
I .o
I .5
2.0
2.5 ACCELERATION
3.0 m s-2
Fig. 4. Frictional force reduction percentage DF as a function of normal different temperatures: X, T = -13 “C; A, T = -4.5 “C; 0, T = -2.0 “C.
acceleration
at
136
linear regression line is calculated for the measured points to make the figure easier to examine. The coefficient of determination r* was between 0.95 and 0.98. It can be seen from Fig. 4 that at all three temperatures the kinetic friction decreases in a remarkable way when vibration is induced in the test, specimen. It also seems that a decrease in temperature increases the effect of the vibration. At air temperatures above zero vibration has no effect on or increases friction, depending on the dry/wet friction ratio and the amount of water present. The side r.m.s. displacement amplitude without external vibration was about 0.005 mm and during excitation was between 0.01 and 0.02 mm at an excitation frequency of 11.8 Hz. The effect of the normal load on the kinetic friction (Fig. 51 was also measured at a temperature of -13 “C to analyse the friction behaviour. The measurement was done by increasing and decreasing the statit> normal load. The normal load fluctuation AF during excitation can be determined from the normal acceleration ji by AF = mji, where m is the reduced loading arm mass. For the maximum acceleration amplitude value of 2.X m 5 ’ at the reduced loading arm mass of 12.5 kg, the maximum load fluctuation was 35 N. In Fig. 5 is shown the normal force without excitation FZJIand the minimum and maximum normal forces during excitation. FrniIl and F,,, respectively, which can be expressed by Fmin = F, t .- AF and F,,, = F, 1..+ AF. It can be seen that, within a range of load fluctuation, the frictiona! force is nearly linearly dependent on the load. The same kind of hehaviour was also observed at a temperature of -4.5 “C
r
% .- , ,I’
t, i
‘.
,
?
,‘5:_
‘-
‘.,*.‘,~:
Fig. 5. Frictional
force
as a function
of normal
force
I’<,
-.. ,_.1:
(v = 5 m s l. T = ---I:% t_!
4. Discussion As has been proven the low kinetic friction between plastic and ice is due to a partial water layer formed by frictional heating [ll The total
137
frictional force is a combination be written [2]
of dry and wet friction
components
and can
(1) where A is the area which supports the applied normal force, (Y is the fraction of this area over which the breakdown of the water film has occurred, s is the shear strength of the junctions at the plastic-ice contact in dry friction, n is the viscosity of water, u is the sliding speed, d is the thickness of the water layer, FN is the normal force, k is a constant and $ is the semi-apical angle of a surface asperity. The dry/wet friction ratio and the influence of vibration on kinetic friction are dependent on the temperature. At temperatures below -1 ‘C, where dry friction is dominant [2], vibration has a great effect on friction which can be seen from Fig. 4. At air temperatures above zero, where wet friction (viscous shear of water) is dominant, vibration has no effect or increases friction. This suggests that vibration reduces the adhesive friction or ploughing and in the case of wet friction disturbs the water layer and induces partial dry friction which may increase the overall friction. The mechanism of friction reduction caused by vibration was studied by measuring the frictional force dependence on the normal force and the normal acceleration values. As is shown in Fig. 5 the frictional force is nearly linearly dependent on the normal force within a normal force fluctuation range. Because of linearity the normal force fluctuations caused by excitation have no effect on the average friction value. Thus the friction reduction caused by vibration cannot be explained by the non-linear friction dependence on the normal force which is measured by changing the static normal force. Neither can it be explained by loss of contact caused by the normal acceleration values greater than the acceleration of gravity g because the measurements were performed within a normal acceleration range of 0 - 0.28g. There still seems to be many possibilities to explain the mechanism of friction reduction caused by vibration. However, it cannot be explained via parameters such as loss of contact or the non-linear frictional force dependence on normal force. This is why vibration must influence friction on a microscopic level even when the vibration frequency is low. These microscopic parameters can be, for example, a change in adhesion shear strength or a change in contact area at the surface roughness level. In the case of a steel against steel contact Godfrey [7] has reported that vibration can cause a great reduction in average friction even when the normal acceleration is less than the acceleration of gravity. As was stated earlier vibration has little effect at high frequencies and this study has concentrated on low frequencies. However, this does not mean that high frequency vibration has no effect on friction, i.e. the measurement arrangement was not suited to high frequencies. The excitation point was chosen to be the loading arm. The effect of this is that the high
136
frequency vibration energy may be lost in the composite beam test specimen before reaching the contact zone. Some better positions for the shaker placement, in order to study high frequency vibrations, might he the t,est specimen itself or the turntable. It must be emphasized that the influence of vibration on the kinetic friction is not dependent on one particular frequency (which in this case was 11.8 Hz) and the results are partly dependent on the test specimen and measurement apparatus as is very often the case in dynamical studies.
5. Conclusions Low frequency vibration reduces kinetic friction in a remarkable way at temperatures below -1 “C, even when the acceleration of the vibrating body is much lower than the acceleration of gravity. The reduction in friction caused by vibration cannot be explained by the non-linear frictional force dependence on the normal force. The reduction in frictional force is almost linearly dependent on the normal acceleration and a decrease in temperature increases the effect of the vibration.
Acknowledgments This study is a part of a research project carried out at the Tampere University of Technology in co-operation with Karhu-Titan Co. The author thanks Professor K. Aho for his valuable advice and Karhu-Titan Co. for financing the project.
References F. P. Bowden and T. P. Hughes, The mechanism of sliding on ice and snow, ?‘r,x. !: Sot. London Ser. A, 217 (1939) 280 - 298. A. Lehtovaara, Friction between plastics and ice. Il’ribologia I;‘inn, .i. 7‘rliiv:., ? (3i (1985) 14 26. H. Suominen, Friction between ski and snow, SlTRA Rep. series 4, nurnho~‘ i i. 1983 (SITRA, Finnish National Fund for Research and Development, Helsinki) D. C. B. Evans, J. F. Nye and K. J. Cheeseman, The kinetic friction of ice, I’XW ii Sot. London Ser. A, 34 7 (1976) 493 - 512. P. Oksanen and J. Keinonen, The mechanism of friction OC ice. WVUT. 18 (1982) 316.324. D. Kuroiwa, The kinetic friction on snow and ice, J. Glacial.. 19 (1977) i 1 i 152. D. Godfrey, Vibration reduces metal to metal contact and causes an apparent reduction in friction. ASLE Trans., 10 (1967) 183 _ 192.
(1987)
131
131
- 138
INFLUENCE OF VIBRATION PLASTICS AND ICE*
ON THE KINETIC
FRICTION
BETWEEN
A. LEHTOVAARA Laboratory of Machine Design, SF-331 01 Tampere (Finland)
Tampere
University
of Technology,
P.O. Box
527,
Summary Influence of vibration on the average kinetic friction between plastics and ice was studied within a range 0.005 - 1 kHz, concentrating on the low frequencies. Vibration was induced in the test specimen by an exciter while the test specimen was sliding on smooth ice. Measurements were performed at a speed of 5 m s-l and a load of 215 N at different temperatures. The results of the study show that low frequency vibration reduces the kinetic friction in a remarkable way at temperatures below -1 “C, even when the acceleration of the vibrating body was much lower than the acceleration of gravity. The mechanism of kinetic friction of ice is also discussed.
1. Introduction In the past and at present the subject of kinetic friction between plastics and ice or snow has been studied in terms of materials, surface finish, load, speed, temperature, apparent contact area etc. [ 1 - 61. However, no attention has been paid to the influence of contact dynamics on kinetic friction. Contact surfaces are never absolutely smooth and contain different kinds of surface irregularities and corrugations which induce vibration at the contact area. This paper describes the measurement arrangements and initial results of an experimental investigation of the effect of vibration on the average kinetic friction between plastic and ice in the case of high speeds and loads under laboratory conditions. As is known from earlier research [ 11, the frictional behaviour of snow is almost similar to ice except for the macroscopic ploughing of snow. Therefore the plastic-ice friction measurements also give information about the frictional behaviour between plastics and snow.
*Paper Technology,
presented at the Nordic Lulei, Sweden, June 15 -
0043-1648/87/$3.50
Symposium
on
Tribology,
Lule”a University
of
18, 1986. @ Elsevier
Sequoia/Printed
in The Netherlands
132
2. Measurements 2.1, Apparatus The friction apparatus, which is described in detail elsewhere j2f. was placed in a cold box and modified to take into account the demands of the vibration studies. A general view of the apparatus is shown in Fig, I
, kR:C
Fig.
1. The friction
I ION
CYNAMOMi
‘F .
apparatus
The temperature T of the cold box could be varied within a range -20 - +2 “C. Because the test specimen in the cold box could be handled through a plastic cover the air conditions in the cold box were kept constant. The specimen was observed through a window in the box. An electric motor with adjustable speed u control (0 - 12 m s ’ ,I was placed outside the cold box to eliminate heat and vibration from the measuring system. The rotating turntable was connected to the motor by a flexible shaft and a V-belt. Vibration was caused by the exciter which was connect,ed to the loading arm. Forced vibration was controlled by the exciter amplitude and frequency, and the vibration of the test specimen was measured by
133
accelerometers. The test specimen was fixed to the loading arm which could move freely in the horizontal and vertical planes. The frictional force dynamometer was connected in the horizontal plane between the loading arm and immovable arm. The normal force FN could be adjusted by weights. The frictional force was measured by a strain gauge dynamometer whose signal was low pass filtered at 2 Hz and the mean value was monitored continuously by a plotter and a Data Precision 6000 analyser (trend curve). The natural frequency of the dynamometer at a load of 215 N was adjusted to 7 Hz to partly filter frequencies above 10 Hz. This eliminates the normal vibration influence on tangential (frictional) sliding causing the system to slide smoothly during excitation. However, the dynamometer was still stiff enough to keep the test specimen tangentially at the same position at different frictional forces. The acceleration of the test specimen was measured by the piezoelectric accelerometers, masses 20 and 4 g, and monitored by the Data Precision 6000 and Hewlett Packard HP 3582A spectrum analyser. The possible frequency range of the vibration controlling system was from 0.002 to 8 kHz. The normal acceleration was measured at point A in Fig. 1 and the side displacement was controlled at point B. Thermocouples were used for measuring temperatures inside the cold box and inside the ice about 3 mm below the track surface. Tap water was used for preparing the ice. The ice was smoothed by grinding when the turntable was rotating. The ice was ground so that the sliding track was raised and had a width of 40 mm. Because the width of the test specimen was 44 mm (slightly greater than that of the track) side effects on the specimen from the track were eliminated. 2.2. Test specimen The test specimen was a cantilever wedge-like sandwich beam structure (Fig. 1) 260 mm long, 44 mm wide and 14 mm thick at its thickest point and with the same curvature as the turntable. High density polyethylene was used as the sliding material. The base of the test specimen was ground with a series of emery papers (Numbers 120, 240 and 400) and waxed with paraffin. After waxing, the paraffin was removed as thoroughly as possible by scraping and the specimen was then corked. 2.3. Test procedure After freezing water to the turntable and placing the test specimen in the cold box, the system was left to stabilize overnight. In the morning the ice was smoothed by grinding. After 2 h it was then ready for measurement. Before the vibration measurements the test specimen was allowed to run in for a distance of approximately 3 km to ensure that a steady state friction process had been achieved. In the case of sinusoidal sweep, the sweep rate was 20 Hz mini’ within a range of 5 - 250 Hz and 200 Hz mini’ for 0.25 1 kHz and the vibration velocity of the shaker was kept constant. Vibration
134
measurements were done at a constant speed of 5 m s ’ and a constant normal load of 215 N at different temperatures.
3. Experimental
results
The influence of vibration on kinetic friction was measured within a range of 0.005 - 1 kHz. At first the frequency range was swept and the frictional force and the acceleration response were monitored continuously. The frictional force reduction was observed only at low frequencies. The reduction was greatest at the first natural frequency of the test specimen where the vibration amplitude was large compared with the amplitudes of the antiresonance frequencies. Many specific frequencies were also excited by random and sinusoidal vibration to confirm that higher frequencies (greater than 70 Hz) have no effect on the kinetic friction even when the acceleration level at point A is more than ten times higher than the aeceleration level without external excitation at specific frequencies. Next, the first natural frequency of the test specimen, 11.8 Hz, was examined more closely because it gave the clearest vibration--friction dependence. The typical frequency spectrum of the test specimen without external vibration is shown in Fig. 2. It can be seen that the r.m.s. acceleration amplitude at a frequency of 11.8 Hz is about 0.05 m se2. The two peaks at frequencies 54 and 70 Hz are the natural frequencies of the apparatus. The friction behaviour as a function of the normal acceleration at point A can be seen in Fig. 3. At the beginning of the curves the frictional force is stable and the normal acceleration (about 0.04 m sC2) comes from surface irregularities and apparatus vibration. When the exciter is turned on the acceleration increases and the frictional force decreases in a remarkable way.
0
Fig. 2. Typical normal r.m.s. external excitation (FN = 215
FREQ Hz
250
acceleration response of test specimen N, ~1= 5 m s-‘, T = -4.5 “C).
at point
A withour
135 FRICTION
ACC m s-2
N
+4
1
-j
I 0
TIME
s
4
10
Fig. 3. Frictional force (lower curve) behaviour as a function (upper curve) (FN = 215 N, u = 5 m s-l, 2’ = -13 “C).
or normal
acceleration
When the exciter is turned off the frictional force increases back to its normal level. At all times the frictional force seems to follow the normal acceleration very closely. The influence of vibration on the kinetic friction is shown in Fig. 4 at different temperatures. The normal acceleration of the test specimen was measured at point A. The friction behaviour is described by the friction reduction percentage DF which is the change in frictional force caused by the excitation divided by the frictional force without excitation. Also the 3c
0.5
I .o
I .5
2.0
2.5 ACCELERATION
3.0 m s-2
Fig. 4. Frictional force reduction percentage DF as a function of normal different temperatures: X, T = -13 “C; A, T = -4.5 “C; 0, T = -2.0 “C.
acceleration
at
136
linear regression line is calculated for the measured points to make the figure easier to examine. The coefficient of determination r* was between 0.95 and 0.98. It can be seen from Fig. 4 that at all three temperatures the kinetic friction decreases in a remarkable way when vibration is induced in the test, specimen. It also seems that a decrease in temperature increases the effect of the vibration. At air temperatures above zero vibration has no effect on or increases friction, depending on the dry/wet friction ratio and the amount of water present. The side r.m.s. displacement amplitude without external vibration was about 0.005 mm and during excitation was between 0.01 and 0.02 mm at an excitation frequency of 11.8 Hz. The effect of the normal load on the kinetic friction (Fig. 51 was also measured at a temperature of -13 “C to analyse the friction behaviour. The measurement was done by increasing and decreasing the statit> normal load. The normal load fluctuation AF during excitation can be determined from the normal acceleration ji by AF = mji, where m is the reduced loading arm mass. For the maximum acceleration amplitude value of 2.X m 5 ’ at the reduced loading arm mass of 12.5 kg, the maximum load fluctuation was 35 N. In Fig. 5 is shown the normal force without excitation FZJIand the minimum and maximum normal forces during excitation. FrniIl and F,,, respectively, which can be expressed by Fmin = F, t .- AF and F,,, = F, 1..+ AF. It can be seen that, within a range of load fluctuation, the frictiona! force is nearly linearly dependent on the load. The same kind of hehaviour was also observed at a temperature of -4.5 “C
r
% .- , ,I’
t, i
‘.
,
?
,‘5:_
‘-
‘.,*.‘,~:
Fig. 5. Frictional
force
as a function
of normal
force
I’<,
-.. ,_.1:
(v = 5 m s l. T = ---I:% t_!
4. Discussion As has been proven the low kinetic friction between plastic and ice is due to a partial water layer formed by frictional heating [ll The total
137
frictional force is a combination be written [2]
of dry and wet friction
components
and can
(1) where A is the area which supports the applied normal force, (Y is the fraction of this area over which the breakdown of the water film has occurred, s is the shear strength of the junctions at the plastic-ice contact in dry friction, n is the viscosity of water, u is the sliding speed, d is the thickness of the water layer, FN is the normal force, k is a constant and $ is the semi-apical angle of a surface asperity. The dry/wet friction ratio and the influence of vibration on kinetic friction are dependent on the temperature. At temperatures below -1 ‘C, where dry friction is dominant [2], vibration has a great effect on friction which can be seen from Fig. 4. At air temperatures above zero, where wet friction (viscous shear of water) is dominant, vibration has no effect or increases friction. This suggests that vibration reduces the adhesive friction or ploughing and in the case of wet friction disturbs the water layer and induces partial dry friction which may increase the overall friction. The mechanism of friction reduction caused by vibration was studied by measuring the frictional force dependence on the normal force and the normal acceleration values. As is shown in Fig. 5 the frictional force is nearly linearly dependent on the normal force within a normal force fluctuation range. Because of linearity the normal force fluctuations caused by excitation have no effect on the average friction value. Thus the friction reduction caused by vibration cannot be explained by the non-linear friction dependence on the normal force which is measured by changing the static normal force. Neither can it be explained by loss of contact caused by the normal acceleration values greater than the acceleration of gravity g because the measurements were performed within a normal acceleration range of 0 - 0.28g. There still seems to be many possibilities to explain the mechanism of friction reduction caused by vibration. However, it cannot be explained via parameters such as loss of contact or the non-linear frictional force dependence on normal force. This is why vibration must influence friction on a microscopic level even when the vibration frequency is low. These microscopic parameters can be, for example, a change in adhesion shear strength or a change in contact area at the surface roughness level. In the case of a steel against steel contact Godfrey [7] has reported that vibration can cause a great reduction in average friction even when the normal acceleration is less than the acceleration of gravity. As was stated earlier vibration has little effect at high frequencies and this study has concentrated on low frequencies. However, this does not mean that high frequency vibration has no effect on friction, i.e. the measurement arrangement was not suited to high frequencies. The excitation point was chosen to be the loading arm. The effect of this is that the high
136
frequency vibration energy may be lost in the composite beam test specimen before reaching the contact zone. Some better positions for the shaker placement, in order to study high frequency vibrations, might he the t,est specimen itself or the turntable. It must be emphasized that the influence of vibration on the kinetic friction is not dependent on one particular frequency (which in this case was 11.8 Hz) and the results are partly dependent on the test specimen and measurement apparatus as is very often the case in dynamical studies.
5. Conclusions Low frequency vibration reduces kinetic friction in a remarkable way at temperatures below -1 “C, even when the acceleration of the vibrating body is much lower than the acceleration of gravity. The reduction in friction caused by vibration cannot be explained by the non-linear frictional force dependence on the normal force. The reduction in frictional force is almost linearly dependent on the normal acceleration and a decrease in temperature increases the effect of the vibration.
Acknowledgments This study is a part of a research project carried out at the Tampere University of Technology in co-operation with Karhu-Titan Co. The author thanks Professor K. Aho for his valuable advice and Karhu-Titan Co. for financing the project.
References F. P. Bowden and T. P. Hughes, The mechanism of sliding on ice and snow, ?‘r,x. !: Sot. London Ser. A, 217 (1939) 280 - 298. A. Lehtovaara, Friction between plastics and ice. Il’ribologia I;‘inn, .i. 7‘rliiv:., ? (3i (1985) 14 26. H. Suominen, Friction between ski and snow, SlTRA Rep. series 4, nurnho~‘ i i. 1983 (SITRA, Finnish National Fund for Research and Development, Helsinki) D. C. B. Evans, J. F. Nye and K. J. Cheeseman, The kinetic friction of ice, I’XW ii Sot. London Ser. A, 34 7 (1976) 493 - 512. P. Oksanen and J. Keinonen, The mechanism of friction OC ice. WVUT. 18 (1982) 316.324. D. Kuroiwa, The kinetic friction on snow and ice, J. Glacial.. 19 (1977) i 1 i 152. D. Godfrey, Vibration reduces metal to metal contact and causes an apparent reduction in friction. ASLE Trans., 10 (1967) 183 _ 192.