Solid State Phenomena Vols. 147-149 (2009) pp 380-386
Online available since 2009/Jan/06 at www.scientific.net
© (2009) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/SSP.147-149.380
The Effect of Controlled Frequency and Amplitude
of Vibration on Friction
Jamil Abdo1, a, Amer Al-Yhmadi1, b
1
Mechanical Engineering Dept., Sultan Qaboos University, P O Box 33, AlKhod 123, Oman
a
[email protected], [email protected]
Keywords: pin-on-disc machine, vibration, amplitude of vibration, friction
Abstract. An in-house pin-on-disc apparatus is designed and constructed to perform the tests and
the design of experiments technique is utilized to determine the effect of vibration, amplitude of
vibration, surface roughness, and sliding speed and their cross influence on coefficient of friction
for 304 stainless steel and Alloy 6061 Aluminum. The design is performed using response surface
method (RSM). The coefficient of friction (CoF) is analyzed as a nonlinear function of the factors
and predicted by a second-order polynomial equation. Results suggested that the presence of
vibration affect the friction function CoF considerably for both metals. The friction function linearly
decreases with the increases of vibration and amplitude of vibration, non-linearly decreases with the
increases of sliding speed and linearly increases with the increases of the surface roughness until the
middle range is reached and then there is non-linearly decrease thereafter. Similar trends of friction
functions are observed for Alloy 6061 Aluminum with a reduction of almost 15% except for the
case with amplitude of vibration where the variation showed more significant affect on the friction
function when Alloy 6061 Aluminum disk is used.
Introduction
The complex friction phenomena can cause detrimental effects in sliding components in many
engineering applications such as railway wheels, automotive and aircraft brake systems, clutches
bearings, mechanical joints and computer storage drives. It is important to identify the factors that
influence the friction characteristics in order to improve the design or performance of frictional
components. The problem of establishing exactly which attributes of the contact conditions and the
materials contribute most of friction forces is a major one for developing friction tests and
analytical friction models. Since the number of potential friction-affecting factors is large, it is
necessary to identify the set of key variables applicable to each particular case in order to select the
appropriate test methods or simulation instead of just studying the effect of one variable. Several
authors observed the reduction of friction force with the vibration, amplitude of vibration, relative
sliding speed, roughness of rubbing surfaces, type of material, humidity, temperature, lubrication
[1-12]. However, the combined effect of different levels of these parameters has not been yet
investigated. In this study the combined effect of vibration, amplitude of vibration, surface
roughness, and sliding speed on coefficient of friction of different metals is investigated by utilizing
experimental design technique.
Material and methods
Apparatus and measuring instruments. Since the number of potential friction affecting factors is
large, it is necessary to identify the set of key variables to each particular case in order to construct
appropriate apparatus and to select the appropriate test method or simulation.
The constructed pin-on-disc machine mainly consists of the carriage, spindle, and arrangement to
generate vertical vibration. It is connected to a custom PC, that has the capability for both spindle
motion control and carriage vertical applied load control, and data acquisition and display unit
(monitor). The machine has a linear vertical and horizontal motion system for positioning the pin
and a rotational motion control system that controls the spindle speed through the control of the
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Solid State Phenomena Vols. 147-149
381
motor speed. The pin is attached directly to the friction and load sensors; the latter provides
feedback to the force versus displacement servo-loop. The disc specimen is attached to the spindle
and has rotational movements through a compound V-pulley above the top supporting square plate
and fixed with the shaft to transmit rotation to the shaft from the motor. The vertical shaft passes
through two close-fit bush bearings which are rigidity fixed with two-square plates and clamped
with screw from the bottom surface of the rotational plate. The pin-on-disc apparatus is designed so
it has the capability of vibrating the disc at different frequencies and amplitudes. A compression
spring is fitted with the shaft between the first and the second supporting plates in order to restrain
any vertical movement of the shaft. There are two circular plates near the bottom of the shaft. One
is fixed with the shaft end and another is fixed with the base plate with the help of a height adjusted
screw. The upper circular plate has a spherical ball extended from the lower surface of this plate.
On the top surface of the lower circular plate there are a number of slots. Rotating the screw will
bring up the lower circular plate to touch the ball. When the shaft rotate, the ball will slide on the
slotted surface and due to spring action, the shaft along with the plate will vibrate. The mode of
vibration is sinusoidal and the direction is vertical. Different values of frequency are generated by
varying the number of slots. The amplitude of vibration values are varied by adjusting the height of
the slotted plate. The rotational speed of the shaft is controlled and programmed to have different
values. A machinable type 304 Stainless Steel disc and an Alloy 6061 Aluminum disc are used to
perform the tests. The surface topography of the discs is controlled. The Mahr profilometer is used
to obtain the profile of aluminum and steel discs. The profile measurement consists of 512 traces
with trace taken over a 10-mm-long distance. The 512 traces are separated so to occupy a width of
1.25 mm, providing a reasonable aspect ratio for the sampled area. The constructed machine has
capability of applied loads servo-controlled with a closed-loop feedback from 1 mN to 50 N and
controlled speed from 0.001 to 2500 rpm with precisely controlled accelerations and positions. The
measured friction force, normal force, CoF, amplitude of vibration and vibration, speed, and applied
load are displayed on the monitor.
Fig. 1 Schematic diagram of the pin-on-disc machine
Response surface method (RSM) and central composite design (CCD). The model used in
RSM is generally a full quadratic equation or diminished form of this equation. The behavior of the
system can be describe by the following second-order polynomial equation
response (CoF ) = β 0 + ∑ β i xi + ∑ β ii xi2 + ∑∑ β ij x i x j
(1)
Where the response is the predicted response, β 0 is the interception coefficient, βi are the linear
terms, β ii are the quadratic terms, β ij are the interaction terms, and xi and x j represent the coded
levels of the independent variables.
Experimental design and data collection. Because the number of possible variables for use in
predictive friction coefficient quite large, it is necessary to identify the set of key variables
382
Mechatronic Systems and Materials III
applicable to each particular case and to conduct screening experiments to reduce the number of the
independent variables. These independent variables are identified and their names, units and levels
are shown in Table 1. The process with a standard RSM design, central composite design (CCD), is
utilized to ascertain the effect of the four factors and their cross influence on the CoF between dry
surfaces of different metals. Four factors are investigated in this study. Their names, units and levels
are shown in Table 1. The effect of speed and roughness on coefficient of friction under no
vibration was investigated first and then the results were compared with the results obtained under
different conditions according to the levels shown in Table 1.
Independent
Factors
Units
level 1
actual &
(coded)
level 2
actual &
(coded)
level 3
actual &
(coded)
level 4
actual &
(coded)
level 5
actual &
(coded)
Frequency of
vibration (A)
Amplitude of
vibration (B)
Hz
120
(-1)
15
(-1)
Low level
actual &
(coded)
240
(-0.5)
75
(-0.5)
480
(+0.5)
175
(+0.5)
600
(+1)
225
(+1)
High
level
actual &
(coded)
2.5
(+1)
Surface
roughness (C)
µm
(RMS)
0.5
(-1)
360
(0)
125
(0)
Middle
level
actual &
(coded)
1.5
(0)
Relative surface
speed (D)
m/s
0.8
(-1)
1.0
(0)
µm
1.2
(+1)
)o
vibration
level
actual
0
0
)o
vibration
level
actual
0
0
Table 1. Levels of the independent factors and coding identification
Test procedure. A series of tests have been performed on the Universal pin-on-disc machine.
Easily interchangeable compatible rotary and linear drives allow for the combination of rotary and
linear motions of test specimens. The applied loads are servo-controlled with a closed-loop
feedback. The applied load is kept at 15 N for all tests. The speed is programmed to have different
values according to Table 1.
In this study the machine is used to measure the friction force, normal force and the CoF. A
machinable type 304 Stainless Steel discs and Aluminum discs with radii 50 mm used to perform
the tests. The surface topography of the discs is controlled. Testing is done in a pin-on-surface mode
where the pin is located at any radius up to 50 mm from the centerline of the spindle.
During testing, parameters are monitored, displayed and stored in the computer for further
analysis. Data is displayed in real time on the monitor. The normal and tangential loads are also
recorded from which the COF ratios are computed. The COF is then collected and analyzed using
analysis of variance. During the analysis of variance, the main and interaction effects are computed.
Those effects that are statistically insignificant are screened out. The significant effects are retained.
Results and discussions
The experiments were designs to determine the effect of the four factors, their quadratic terms and
their cross influence on CoF between dry surfaces. The analysis is done to extract all the
information present in the data, taking account of variability and measurement error. The effects of
the factors as linear, quadratic, cross-products coefficients, or cubic on responses were tested for
adequacy. The results show that the quadratic model is the most significant.
Solid State Phenomena Vols. 147-149
383
Response residual and regression analysis. In order to confirm the adequacy of the model
obtained, the confirmation run experiments are performed for the friction function. The percentage
error ranges between the experimental and the predicted value of the CoF lie within –2.1 to 2.2%.
All the experimental values for the confirmation run are within 95% prediction interval. This
indicates that the quadratic model of friction function is accurate.
The analysis of variance (ANOVA) is done on the experimental data to evaluate the statistical
significance of the model. The ANOVA confirms the adequacy of the quadratic model. For 304
Stainless Steel, vibration (A), amplitude of vibration (B), surface roughness (C), speed (D),
quadratic term of surface roughness (D)2 and quadratic term of speed (C)2 are significant model
terms. The final response equation for the CoF for 304 Stainless Steel is obtained in terms of coded
factors as follows,
CoF = 0.324 - 0.152 * A - 0.0362 * B - 0.0467 * C - 0.110 * D - 0.0811 * C 2 + 0.0559 * D 2
(2)
For Alloy 6061 Aluminum, vibration (A), amplitude of vibration (B), surface roughness (C),
speed (D), quadratic term of surface roughness (D)2, quadratic term of speed (C)2 and the
interaction between vibration and speed are significant model terms. The final response equation for
the CoF for Alloy 6061 Aluminum is obtained in terms of coded factors as follows,
CoF = 0.273 - 0.121 * A - 0.0481 * B - 0.0401 * C - 0.096 * D - 0.0677 * C 2 + 0.0469 * D 2
+ 0.0296 * (A * D)
(3)
Equations 2 & 3 are fitted regression model representations of the RSM experiments for CoF.
Model graphs and analysis. The mathematical models furnished in previous section can be
employed to predict the friction function of 304 Stainless Steel and Alloy 6061 Aluminum for the
range of factors used in the investigation by substituting their respective values in coded form.
Fig. 2 (a, b, c) show how the friction function of the 304 stainless steel changes as each factor
moves from the chosen reference point, with other factors held constant at the reference value. In
Fig. 2a, the reference point is set at the middle of the design space that is the coded zero level of the
vibration, amplitude of vibration, surface roughness, and sliding speed and corresponded to the
actual factor levels of 360 Hz, 125 µm, 1.5 µm, 1.0 m/s. In Fig. 2b, the reference point is set at the
lowest level of the design space that is the coded -1 level of each factor and corresponded to the
actual factor levels shown in Table 1. In the same manner the reference point in Fig. 2c is set at the
highest level of the design space that is coded +1 of each factor. The friction function changes
linearly from 0.5 to 0.177 as the level of vibration changes from 120 Hz to 600 Hz while other
factors held at the coded zero level (Fig. 1a, curve A). The friction function in Fig. 2b is linearly
decreased from 0.66 to 0.33 as the levels of vibration increased from 120 Hz to 600 Hz (Fig. 1b,
curve A) with other factors held constant at coded level -1. In Fig. 1c, the friction function is also
linearly decreased from 0.25 to 0.02 as the actual level of vibration increased from 120 Hz to 600
Hz with other factors held at coded level +1. The second significant factor is the sliding speed
represented by curves D in Fig. 2 (a, b, c). It is observed the from these three curves that the friction
function is non-linearly decreases with the increases of the sliding speed until the middle range is
reached and the effect is less significant thereafter. In Fig. 2a, the friction function is non-linearly
decreased from 0.5 to 0.278 with the increases of sliding speed from 0.8m/s to 1.2m/s with other
factors held constant at reference point at the middle of the design space that is the coded zero level
of each factor. Similar behaviors are observed with the reference point held at coded -1 and +1 of
each factor as shown in Fig. 1 (b, c) curves D. Curves C in Fig. 2 (a, b, c) show the behavior of the
friction function with the changes of the surface roughness. It is observed that there is non-linearly
increase of friction function until the middle range is reached and then there is non-linearly decrease
thereafter. Same trend is observed with the reference points held at -1 and +1 of each factor as
shown in Fig. 2 (a, b, c) curves C. The effect of amplitude of frequency on friction function for 304
stainless steel is shown in Fig. 2 (a, b, c) curves B. The friction function linearly reduced from
384
Mechatronic Systems and Materials III
0.385 to 0.3 as the actual values of the amplitude of vibration changes from 15 µm to 225 µm with
the other factors held at the middle of the design space that is the zero coded level of each factor.
Curves B of Fig. 2 (a, b, c) shows same trend at the other referenced points.
0.500
D
A
0.710
C
AB
D
0.607
Friction Function
Friction Function
0.419
B
0.338
C
B
D
B
C
0.505
D
0.256
0.402
C
A
A
0.175
-1.00
-0.500
0.000
0.500
0.300
1.00
0.000
Deviation from Reference Point
0.500
1.00
1.50
2.00
Deviation from Reference Point
a)
b)
0.250
A
Friction Function
0.182
D
0.114
C
B
0.0453
C
DBA
-0.0230
-2.00
-1.50
-1.00
-0.500
0.000
Deviation from Reference Point
c)
Fig. 2 (a, b, c) Variation of coefficient of friction from reference point (a: vib. =360Hz , amp. of
vib.=125 µm, sur. roug.=1.5 µm, sl. speed=1.0 m/s, (coded: 0,0,0,0) ; b: vib. =120Hz , amp. of
vib.=15 µm, sur. roug.= 0.5 µm, sl. Speed = 0.8 m/s, (coded:-1,-1,-1,-1); c: vib. =600Hz , amp. of
vib.=225 µm, sur. roug.= 2.5 µm, sl. Speed = 1.2 m/s, (coded:+1,+1,+1,+1); normal load 12 N, test
sample = 304 stainless steel.
Fig. 3 (a, b, c) shows how the friction function of the of the Alloy 6061 Aluminum changes as
each factor moves from the chosen reference point, with other factors held constant at the reference
value.
The reference point is set at the middle of the design space that is the coded zero level of each
factor. It is observed that the trend of the effect of amplitude of vibration, surface roughness and
sliding speed are the same as that for 304 stainless steel. However, it is observed a non-linearity
effect of the vibration on the friction function. On the other hand the values of the friction function
is reduced by about 15% in all cases except for the in cases that of moving of the amplitude of
vibration from the reference points. The amplitude of vibration is much more significant when
Alloy 6061 Aluminum is used. Note that the results with reference to no vibration and no amplitude
conditions are reported elsewhere [13].
In investigating of the effect of all factors at all levels on the friction function for both 304
stainless steel and Alloy 6061 Aluminum the vibration effect is shown to be most significant factor.
The lower the friction function the higher the vibration might be due to the reduction of actual
rubbing surface, because there is always more separation between the rubbing surfaces due to
reduction in the mean contact area of the two sliding objects for vibration. In addition vibration
Solid State Phenomena Vols. 147-149
385
reduces load momentarily, which causes of effective normal force resulting in reduction of metalto-metal contact and hence friction coefficient. The decreases of the friction function with the
increases of amplitude of vibration is due to the fact that the greater the amplitude of vibration, the
higher the actual rubbing time. Therefore, the separation of contact surfaces as the higher the
amplitude the higher the separation of rubbing surfaces. As the amplitude increases, keeping the
frequency of vibration constant, the acceleration of vibration will also increase and that might cause
momentary vertical load reduction, which causes the reduction of effective normal force resulting in
reduction of friction function with the increase of amplitude of vibration [1]. The reduction of
friction function with the increase of sliding speed is due to the reduction of actual rubbing surface
and to the fact that the disc material interfaces softened and decreased in shear strength as
temperature increased, leading to lower friction force. As temperature increases, the possibility of
forming oxides increases as well. Certain oxides have lubricating characteristics and could assist for
further reduce friction. Friction function is high at low to moderate roughness because of the growth
of real of area of contact; it tends to be high at very high roughness because of mechanical
interlocking. The non-linear effect of sliding speed and surface roughness in Fig. 2 (a, b, c) are due
to the significance of the quadratic terms of these factors in eq. 2. The nonlinearity effects of the
vibration in Fig. 3 (a, b, c) are to the significant of the interaction term between vibration and
sliding speed as indicated in eq. 3.
0.42
A
0.65
AC
B
D
D
0.57
Friction Function
Friction Function
0.36
B
0.29
C
DB
0.23
C
C
B
0.49
0.40
D
A
A
0.17
0.32
-1
-0.5
0
0.5
1
0
Deviation from Reference Point
0.5
1
1.5
2
Deviation from Reference Point
b)
a)
0.21
A
Friction Function
0.16
D
0.11
B
C
0.05
C
B
D A
0.00
-2
-1.5
-1
-0.5
0
Deviation from Reference Point
c)
Fig. 3 (a, b, c) Variation of coefficient of friction from reference point (a: vib. =360Hz , amp. of
vib.=125 µm, sur. roug.=1.5 µm, sl. speed=1.0 m/s, (coded: 0,0,0,0) ; b: vib. =120Hz , amp. of
vib.=15 µm, sur. roug.= 0.5 µm, sl. Speed = 0.8 m/s, (coded:-1,-1,-1,-1); c: vib. = 600Hz , amp. of
vib.=225 µm, sur. roug.= 2.5 µm, sl. Speed = 1.2 m/s, (coded:+1,+1,+1,+1); normal load 12 N, test
sample = Alloy 6061 Aluminum
386
Mechatronic Systems and Materials III
Conclusions
A homemade pin-on-disc apparatus was designed and constructed study the influence of frequency
of and amplitude of vibration and other factors such as sliding speed, surface roughness on friction.
Experimental design is performed using response surface method (RSM) to provide an impetus to
develop analytical model, based on experimental results for obtaining friction function model. The
validity of the model has been enhanced by screening out the non-significant factors. Coefficient of
friction (CoF) is analyzed as a nonlinear function of the factors and predicted by a second-order
polynomial equation. The investigations of this study indicate that the factors vibration, amplitude
of vibration, surface roughness and its quadratic form, sliding speed and its quadratic form are the
primary factors influencing the friction function of 304 stainless steel with different degree of
significant. The factors vibration, amplitude of vibration, surface roughness and its quadratic form,
sliding speed and its quadratic form, and the interaction between vibration and sliding speed are the
primary factors influencing the friction function of Alloy 6061 Aluminum with different degree of
significant. The friction function linearly decreases with the increases of vibration and amplitude of
vibration, non-linearly decreases with the increases of sliding speed and linearly increases with the
increases of the surface roughness until the middle range is reached and then there is non-linearly
decrease thereafter. Similar trends of friction functions are observed for Alloy 6061 Aluminum with
a reduction of almost 15% except for the case with amplitude of vibration where the variation
showed more significant affect on the friction function for Alloy 6061 Aluminum.
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Mechatronic Systems and Materials III
10.4028/www.scientific.net/SSP.147-149
The Effect of Controlled Frequency and Amplitude of Vibration on Friction
10.4028/www.scientific.net/SSP.147-149.380
DOI References
[1] Chowdhury MA, Helali MM: The effect of frequency of vibration and humidity on the oefficient of
friction, Tribol Int 2006, 39, 958-62.
doi:10.1016/j.triboint.2005.10.002
[5] Berger EJ, Krousgrill CM, Sadeghi F: Stability of sliding in a system excited by a rough surface. SME
1997; 119, 672-80.
doi:10.1115/1.2833868
[8] Bengisu, M. T.and Akay A., 1997: Relation of Dry-Friction to Surface Roughness, Journal of ribology,
119, 18-25.
doi:10.1115/1.2832457
[9] Wang J. and Rodkiewicz C. m., 1994: Temperature maps for pin-on-disk configuration in dry liding,
Tribol. Int., 1994, 27, 4, 259-265.
doi:10.1016/0301-679X(94)90005-1
[11] Godfrey D.: Vibration reduces metal to metal contact and causes an apparent reduction in riction, ASME
Trans 1967, 10, 183-92.
doi:10.1080/05698196708972178
[12] Hess DH, Soom A.: *ormal vibrations and friction underharmonic loads: part I-hetzian ontacts. J tribo
1991, 113, 80-6.
doi:10.1115/1.2920607
[13] Abdo J.: Experimental Technique to Study Tangential to *ormal Contact Load Ratio, ribology
Transactions, 2005, 48, pp. 389-403.
doi:10.1080/05698190500225334
[1] Chowdhury MA, Helali MM: The effect of frequency of vibration and humidity on the coefficient of
friction, Tribol Int 2006, 39, 958-62.
doi:10.1016/j.triboint.2005.10.002
[2] Abdo J. and Shamseldeen E.: Experimental technique for characterization of friction in dry contact,
Journal of solid mechanics and materials Engineering 2007, 1/10, 1197-1208.
doi:10.1299/jmmp.1.1197
[8] Bengisu, M. T.and Akay A., 1997: Relation of Dry-Friction to Surface Roughness, Journal of Tribology,
119, 18-25.
doi:10.1115/1.2832457
[9] Wang J. and Rodkiewicz C. m., 1994: Temperature maps for pin-on-disk configuration in dry sliding,
Tribol. Int., 1994, 27, 4, 259-265.
doi:10.1016/0301-679X(94)90005-1
[10] Suh, A., Polycarpou, A., and Conry, F.: Detailed surface roughness characterization of engineering
surfaces undergoing tribological testing leading to scuffing, Wear, 2003, 255, 556-69.
doi:10.1016/S0043-1648(03)00224-2
[12] Hess DH, Soom A.: ormal vibrations and friction underharmonic loads: part I-hetzian contacts. J tribo
1991, 113, 80-6.
doi:10.1115/1.2920607