lubricants
Article
The Reduction of Static Friction of Rubber Contact
under Sea Water Droplet Lubrication
Yong-Jie Zhou 1 , De-Guo Wang 1,2, * and Yan-Bao Guo 1,2, *
1
2
*
College of Mechanical and Transportation Engineering, China University of Petroleum, Beijing 102249,
China; [email protected]
Laboratory of Tribology and Surface Engineering, China University of Petroleum, Beijing 102249, China
Correspondence: [email protected] (D.-G.W.); [email protected] (Y.-B.G.); Tel.: +86-10-8973-3727
Academic Editor: James E. Krzanowski
Received: 29 March 2017; Accepted: 7 May 2017; Published: 12 May 2017
Abstract: In this work, a series of experimental tests is carried out in laboratory conditions which
set the rubber compound (soft and stiff), the normal load, and the direction of propagation of sea
water droplets into the interface of rubber–steel pipe contact as variables. The results show that
the maximum static frictions (F) of rubber–pipe contacts increase as the normal load increases in
both dry and lubricating conditions, and the values of F for the softer rubber are higher than that
for the stiffer rubber. However, significant reduction in static friction is found due to the lubrication
of sea water droplets. The influence of lubrication is stronger when the droplets propagate into the
contact interfaces at the tail edge than that at the front edge. Capture sequences of the contact region
facilitate the lubrication of seawater droplets by accelerating the progress of separation in the contact
interfaces, thus reducing the static friction force. This investigation improves our understanding of
the lubrication of sea water droplets during pipe-laying operation, and it will help us to conduct
further research on the accuracy and safety of offshore engineering.
Keywords: rubber; sea water droplet; lubrication; static friction
1. Introduction
Rubber-like materials are widely applied in many engineering fields such as sealing,
tire and offshore installation due to their strong mechanical properties, wear resistance and
anti-corrosion [1–4]. Tribological behaviors of rubber-like materials in soft contact have been
investigated both experimentally and theoretically in the last several decades. It is well known
that the friction force of rubber is derived as the product of the total area of the real contact. The friction
forces of rubbers on steel increase with normal load, because of the increase in real contact area
resulting from the deformation of rubber asperities [5]. Persson [6] presented a discussion on how the
resulting friction force depends on the nature of the real contact.
The adhesion effect plays a very important role in affecting rubber friction on certain contact
conditions. According to Schallamach [7] and Barquins [8], the friction force is velocity dependent
and takes a maximum value around a few centimeters per second. Johnson and Greenwood [9]
revealed an adhesion map for choosing appropriate mechanical models as a solution of the adhesion
between elastic spheres. Schwarz [10] gave a generalized analytical model for the elastic deformation
of adhesive contact between a sphere and a flat surface.
In addition, static frictional contacts between rubber and rigid materials have been widely studied
and the adhesion effect and viscoelastic properties of rubber cannot be neglected. Galligan et al. [11]
discussed the nature of static friction and creep. Roberts and Thomas [12] tested the static friction
of smooth clean vulcanized rubber. Loeve et al. [13] investigated the static friction of stainless steel
wire rope–rubber contacts. Deladi et al. [14] modeled the static friction for contact between rough
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rough rubber
and
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2017, 5, 12
metal surfaces. As described in several works by Barquins et al [15,16], Savkoor
2 of 13
[17,18] or more recently by Scheibert et al [19] or Audry and co-workers [20], the static friction of
rubber contacts involves complex peeling and micro-slip phenomena which deserve a fracture
rubber
and description.
metal surfaces. As described in several works by Barquins et al [15,16], Savkoor [17,18] or
mechanics
more Moreover,
recently byrubber-like
Scheibert etmaterials
al [19] or sliding
Audry and
co-workers
[20], the
static
friction
of rubber
contacts
against
rigid metals
under
wet
conditions
is a common
involves
complex
and micro-slip
phenomena
which
deservebehaviors
a fractureofmechanics
description.
process for
manypeeling
engineering
applications
[21–24]. The
frictional
rubber-like
materials
Moreover,
rubber-like
materials
sliding
against
rigid
metals
under
wet
conditions
is
a common
with liquid lubricant are of great importance for steady performance and safety of the equipment.
process
for many
many authors
engineering
[21–24].
The frictional
of rubber-like
materials
Therefore,
have applications
focused on water
lubricating
rubberbehaviors
contacts. The
well-known
Stribeck
with
liquid
lubricant
are
of
great
importance
for
steady
performance
and
safety
of
the
equipment.
curve helped us to identify the lubrication regime for each specific contact condition [25]. J. K.
Therefore,
authors
focused
on water
lubricating of
rubber
contacts.
The on
well-known
Stribeck
Lancaster many
reviewed
the have
friction
and wear
performances
polymers
sliding
metal with
water
curve
helped he
us tosuggested
identify the
lubrication regime
specific
contact
[25]. J. K. Lancaster
lubrication;
complicated
trends for
of each
friction
forces
due condition
to the interaction
between
reviewed
wear performances
of also
polymers
sliding
onthe
metal
with water
lubrication;
he
adhesion the
andfriction
surfaceand
properties
[26]. Roberts
explained
that
mechanical
properties
of the
suggested
complicated
trends
of
friction
forces
due
to
the
interaction
between
adhesion
and
surface
vulcanized rubber were modified by liquid absorption [27]. Persson et al. took the phenomenon of
properties
[26]. Roberts
alsocontext
explained
thatrubber-road
the mechanical
properties
the vulcanized
rubberseveral
were
water entrapment
into the
of tire
contact
[28]. A. of
Koenen
et al. revealed
modified
by
liquid
absorption
[27].
Persson
et
al.
took
the
phenomenon
of
water
entrapment
into
influencers on the friction properties of wiper blade and windscreen contact [29]. Moreover, the
the
context
tire rubber-road
contact
[28].water
A. Koenen
et al. revealed
several
influencers
on observed
the friction
special of
contribution
to friction
by thin
film under
high contact
pressure
has been
in
properties
of
wiper
blade
and
windscreen
contact
[29].
Moreover,
the
special
contribution
to
friction
several studies at nanoscale [30].
by thin
water film
underthis
highprogress,
contact pressure
has of
been
observed
in several
studies
at nanoscale
[30].
However,
despite
the project
static
frictional
behaviors
of soft-rigid
contact
However,
despite this
progress, the
project ofhas
static
frictional
behaviors of
soft-rigid contact
during
during
the deep-water
pipe-laying
operations
rarely
been discussed.
Deep-water
pipe-laying
is
the
deep-water
pipe-laying
operations
has
rarely
been
discussed.
Deep-water
pipe-laying
is
known
known as a standard industrial process for the installation or maintenance of offshore equipment
as
a standard
the installation
or splash
maintenance
offshore
equipment
[31–34].
[31–34].
It is industrial
inevitable process
that seafor
water
droplets will
on theofpipe
surface
during pipeline
Itinstallation.
is inevitable
that
sea water
droplets
splash
on the
pipe surface
during
pipeline
installation.
The
frictional
behaviors
ofwill
the soft
contact
between
the rubber
block
and pipe
with sea
The
frictional
behaviors
of
the
soft
contact
between
the
rubber
block
and
pipe
with
sea
water
droplets
water droplets are of importance for the accuracy and safety of the pipe-laying operation. Three
main
are
of importance
for the accuracy
andrubber
safety of
thepipe
pipe-laying
Three
main
kinds
of contact
kinds
of contact situations
between
and
with theoperation.
lubrication
of sea
water
droplets
are
situations
between
rubber
and
pipe
with
the
lubrication
of
sea
water
droplets
are
schematically
shown
schematically shown in Figure 1. Sea water droplets can splash at the central, front and tail parts of
in
FigureIn
1. this
Sea study,
water droplets
can
splash at the
front and tail
parts
of contact.
In lubrication
this study,
contact.
a series of
experiments
forcentral,
soft rubber–rigid
pipe
contact
with the
aofseries
of experiments
soft
rubber–rigid
pipe friction
contact with
the lubrication
of sea
carried out
sea water
is carriedfor
out
with
a home-built
instrument
based on
the water
three is
fundamental
with
a
home-built
friction
instrument
based
on
the
three
fundamental
lubricating
conditions,
the
lubricating conditions, with the aim of investigating the static friction behaviors under with
different
aim
of
investigating
the
static
friction
behaviors
under
different
lubricating
processes.
The
evolution
lubricating processes. The evolution of the contact area caused by increasing the tangential load has
of
the contact
areaincaused
increasing thecomparison
tangential load
has effect
been discussed
in detail.
Furthermore,
been
discussed
detail.byFurthermore,
of the
of sea water
droplets
for each
comparison
of
the
effect
of
sea
water
droplets
for
each
condition
has
been
discussed.
condition has been discussed.
Figure 1.
1. Schematic
diagram
of the
lubricating
conditions
in pipe-laying
operation.
(a) The
Figure
Schematic
diagram
of major
the major
lubricating
conditions
in pipe-laying
operation.
central
part of part
lubrication;
(b) The(b)
front
ofpart
lubrication;
(c) The(c)
tailThe
part
ofpart
lubrication.
(a)
The central
of lubrication;
Thepart
front
of lubrication;
tail
of lubrication.
2. Experimental
Experimental
2.
2.1. Samples
Samples
2.1.
Figure2 2illustrates
illustrates
shapes
of rubber
and
pipe samples.
special
mould
is used to
Figure
the the
shapes
of rubber
and pipe
samples.
A special A
mould
is used
to manufacture
manufacture
vulcanized
rubber
samples
in athe
shape
of a half
oblique
frustum
cone, the
to simulate
the
vulcanized
rubber
samples
in the
shape of
half
oblique
frustum
cone,
to simulate
contacting
contacting of
conditions
of rubber
blockswith
in tension
with
pipe the
wallpipe-laying
during the process.
pipe-laying
process.
conditions
rubber blocks
in tension
the pipe
wallthe
during
Meanwhile,
Meanwhile,
mould to
is polished
unify the
surface roughness
of the
rubberUniaxial
sample.
the
surface ofthe
thesurface
mouldofisthe
polished
unify thetosurface
roughness
of the rubber
sample.
Uniaxial
tensile
tests are
using a test
universal
test(model
machine
(model
Lina™ WDTII-20,
tensile
tests
are carried
outcarried
using out
a universal
machine
Lina™
WDTII-20,
Shenzhen
Shenzhen
Lina Instrument
Ltd., Shenzhen,
China) according
to the standard
ISO
Lina
Instrument
TechnologyTechnology
CO., Ltd., CO.,
Shenzhen,
China) according
to the standard
ISO 37:1994.
The crosshead displacement rate is set at 500 mm/min, and the initial separation distance between
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37:1994. The crosshead displacement rate is set at 500 mm/min, and the initial separation distance
between two clamp holders is 36 mm. The hardness of samples is tested by a LX-A tester according
two
clamp
holders
36 mm. The
hardness
of samplesparameters
is tested byofa rubber
LX-A tester
according
to the
to the
standard
ISOis7619:2004.
Specific
corresponding
and pipe
samples
are
standard
ISO
7619:2004.
Specific
corresponding
parameters
of
rubber
and
pipe
samples
are
listed
in
listed in Table 1.
TableSix
1. black lines are drawn on the surface of the rubber with a marker pen to identify the
Six
black differences
lines are drawn
on the
surface
of the
rubber
with aand
marker
pen to identify
deformation
deformation
in the
contact
area.
When
normal
tangential
load arethe
applied
to the
differences
in
the
contact
area.
When
normal
and
tangential
load
are
applied
to
the
rubber–pipe
rubber–pipe contact system, each black line will bend due to the shearing deformation of the contact
rubber
system,
black line
will
bend
the line
shearing
deformation
rubber
surface.
extentThe
of
surface. each
The extent
of the
bend
ofdue
the to
black
indicates
the levelof
ofthe
shear
stress
at that The
location.
the
bend
of
the
black
line
indicates
the
level
of
shear
stress
at
that
location.
The
higher
the
shear
stress
higher the shear stress level, the greater the extent of bend of the black line. Therefore, the distribution
level,
thestress
greater
of of
bend
the black
line.
Therefore,
the distribution
of shear stress
on the
of shear
onthe
theextent
surface
theof
rubber
can be
deduced
qualitatively
by identifying
the different
surface
of
the
rubber
can
be
deduced
qualitatively
by
identifying
the
different
extents
of
bend
of test
the
extents of bend of the black lines. Even though the marker pen ink contributes negligibly to the
black
lines.
Even
though
the
marker
pen
ink
contributes
negligibly
to
the
test
records,
the
relative
records, the relative displacement of the contact surfaces can be noticed when the ink moves away
displacement
the contact surfaces can be noticed when the ink moves away from the black line.
from the blackofline.
Figure 2. The shapes of rubber and pipe samples. Two types of rubber samples: rubber A and B; Two
Figure 2. The shapes of rubber and pipe samples. Two types of rubber samples: rubber A and B;
types of pipe samples: steel pipe and polymethyl methacrylate (PMMA) pipe.
Two types of pipe samples: steel pipe and polymethyl methacrylate (PMMA) pipe.
Table 1. Mechanical properties of the unfilled nitrile butadiene rubber (NBR) samples and pipe
Table 1. Mechanical properties of the unfilled nitrile butadiene rubber (NBR) samples and pipe samples.
samples.
Rubber
Type
Rubber
Type
AA
B B
Pipe
Type
Pipe
Type
Steel
Steel
PMMA
PMMA
MechanicalProperties
Properties
Mechanical
Elastic
Modulus
[MPa] Tensile
Tensile Strength
Strength [MPa]
[Ra]
Elastic
Modulus
[MPa]
[MPa] Shore
ShoreHardness
Hardness Roughness
Roughness
[Ra]
2.26
13.2
2.26
13.2
3737
3.13.1
12.79
5151
3.23.2
3.73.7
12.79
MechanicalProperties
Properties
Mechanical
Elastic
Modulus
[MPa]
HRCHRC
Roughness
[Ra]
Elastic
Modulus
[MPa]
Roughness
[Ra]
5
2.12.1
× 10
80 80
1.71.7
× 105
× 3103
3 ×3 10
99 99
1.61.6
It is
is necessary
necessary to
to note
note that
that the
the major
major difference
difference between
between rubber
rubber A
A and
and B
B is
is the
the elastic
elastic modulus
modulus
It
which is
is resulted
resulted from
from the
the different
different densities
densities of
of the
the crosslink
crosslink [35].
[35]. Therefore,
Therefore, the
the two
two rubber
rubber samples
samples
which
behave
remarkably
differently
in
the
viscoelastic
aspect.
Moreover,
the
surfaces
of
both
kinds
of pipe
pipe
behave remarkably differently in the viscoelastic aspect. Moreover, the surfaces of both kinds of
samples are
arepolished
polisheddesignedly
designedly
to unify
roughness
of them.
Therefore,
the influence
of the
samples
to unify
the the
roughness
of them.
Therefore,
the influence
of the surface
surface
roughness
difference
is
not
discussed
in
this
study.
roughness difference is not discussed in this study.
The sea
seawater
watersolution
solution
study
is prepared
according
the standard
ASTM1141-98
as
The
in in
thisthis
study
is prepared
according
to thetostandard
ASTM1141-98
as shown
shown
2. This solution
is used
widely
by researchers
as a substitute
of sea[36].
water [36].
in
Tablein2.Table
This solution
is widely
byused
researchers
as a substitute
of sea water
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Table 2. Chemical composition of sea water solution.
Table 2. Chemical composition of sea water solution.
Compound
Compound
Concentration (g/L)
(g/L)
Concentration
NaCl Na
Na22SO
SO44 MgCl
2 2 CaCl
2 2 SrCl
2 2
MgCl
CaCl
SrCl
NaCl
24.53
4.09
5.20
1.16
24.53
4.09
5.20
1.16 0.025
0.025
KCl
KCl
0.695
0.695
NaHCO
3 3 KBrKBr H3 BO
NaHCO
H33BO3 NaFNaF
0.201
0.201
0.101
0.101 0.027
0.027 0.003
0.003
2.2.Tribological
TribologicalInstrument
Instrument
2.2.
schematicdiagram
diagramof
ofthe
thetribological
tribologicalinstrument
instrumentisisshown
shownin
inFigure
Figure3.3.The
Theinstrument
instrumentmainly
mainly
AAschematic
consists of
of three
threecomponents:
components: normal
normal loading
loading module;
module; rubber-pipe
rubber-pipe contact
contact testing
testing module;
module; and
and
consists
tangential
loading
module.
Normal
load
is
applied
to
the
rubber
samples
via
the
lever
arm.
The
pipe
tangential loading module. Normal load is applied to the rubber samples via the lever arm. The pipe
sampleisismounted
mountedatatthe
thetop
topofofthe
thelinear
linearslide
sliderail
railsoso
that
can
slide
Y-direction
smoothly.
sample
that
it it
can
slide
in in
thethe
Y-direction
smoothly.
It isIt
is necessary
to note
that
coefficient
of friction
(COF)
of the
linear
slide
without
normal
loading
necessary
to note
that
thethe
coefficient
of friction
(COF)
of the
linear
slide
railrail
without
normal
loading
is
is nearly
0.12,
and
it will
increase
much
(5%)
whenthe
therange
rangeofofthe
thenormal
normalload
loadisisfrom
from00N
Nto
to
nearly
0.12,
and
it will
notnot
increase
soso
much
(5%)
when
100N.
N.The
Thetangential
tangentialload
loadisisdriven
drivenby
byaamotor
motorand
andreducer
reducerthrough
throughwire
wirerope
ropewhich
whichconnects
connectsthe
the
100
sidesof
ofthe
thepipe
pipeand
andreducer.
reducer.AAspring
springisisused
usedto
toeliminate
eliminaterigid
rigidmotional
motionaltendency
tendencyand
andvibration
vibration
sides
whichare
arecaused
causedby
bythe
therunning
runningof
ofthe
themotor
motorand
andreducer.
reducer.The
Thenormal
normalload
loadand
andtangential
tangentialload
loadare
are
which
detectedby
byforce
forcesensors.
sensors.The
Thedisplacement
displacement of
ofpipe
pipeisistested
testedby
byaalaser
laserdisplacement
displacementsensor
sensor(model
(model
detected
Panasonic™HG-C1030L;
HG-C1030L;Panasonic
Panasonic
industrial
devices
SUNX
Suzhou
CO., Suzhou,
Ltd., Suzhou,
Panasonic™
industrial
devices
SUNX
Suzhou
CO., Ltd.,
China) China)
which
is mounted
on the
of the instrument.
All data
testing
data is recorded
in a computer.
iswhich
mounted
on the base
of base
the instrument.
All testing
is recorded
in a computer.
Figure3.3.Schematic
Schematicdiagram
diagramof
ofthe
thetribological
tribologicalinstrument.
instrument.The
Theinstrument
instrumentmainly
mainlyconsists
consistsof
ofthree
three
Figure
components: normal
normal loading
loading module;
module; rubber-pipe
rubber-pipe contact
contact testing
testing module;
module; and
and tangential
tangentialloading
loading
components:
module.
A
portable
video
camera
is
positioned
perpendicular
to
the
contacting
surface
across
the
module. A portable video camera is positioned perpendicular to the contacting surface across the
PMMA
pipe
to
provide
a
macroscopic
recording
of
the
contact.
PMMA pipe to provide a macroscopic recording of the contact.
In order to observe the frictional behaviors of the contact area between rubber and polymethyl
In order to observe the frictional behaviors of the contact area between rubber and polymethyl
methacrylate (PMMA), the portable video camera (model Supereys™ A005; Shenzhen Deyufu
methacrylate (PMMA), the portable video camera (model Supereys™ A005; Shenzhen Deyufu
Instrument Technology CO., Ltd., Shenzhen, China) is positioned perpendicular to the contact
Instrument Technology CO., Ltd., Shenzhen, China) is positioned perpendicular to the contact surface
surface across the PMMA pipe. This digital camera provides a macroscopic recording in a whole test
across the PMMA pipe. This digital camera provides a macroscopic recording in a whole test run.
run.
2.3. Experimental Procedures
2.3. Experimental Procedures
A contact area is formed between rubber and pipe samples when normal load is applied to
A contact area
is formed
between
rubber andload
pipestarts
samples
when
normal
load
is applied
to the
the rubber-pipe
contact
system.
Then, tangential
to be
imposed
with
a pre-set
constant
rubber-pipe
contact
system.load
Then,
tangential load
starts to
be imposed
a pre-set
constant
increasing
rate.
As tangential
is continuously
increasing,
macroscopic
slipwith
between
the surface
of
increasing
rate.
As
tangential
load
is
continuously
increasing,
macroscopic
slip
between
the
surface
the rubber and pipe takes place. The increasing rate of tangential load can be controlled by altering
the
of the rubber
and
pipeoftakes
place. and
The reducer.
increasing rate of tangential load can be controlled by altering
output
rotation
speed
the motor
the output
of the out
motor
and reducer.
A seriesrotation
of tests speed
was carried
to investigate
the effect of the lubrication of sea water droplets in
A
series
of
tests
was
carried
out
to
investigateofthe
effect of the
of sea
the rubber-steel contact system. The combinations
parameters
are lubrication
given in Table
3. water droplets
in the rubber-steel contact system. The combinations of parameters are given in Table 3.
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Table 3. Parameters of friction tests.
Rubber
Pipe
Normal Load [N]
Increasing Rate of Tangential Load [N/s]
A
B
Steel, PMMA
Steel, PMMA
10, 20, 30, 40
0.062, 1.5
Specifically, procedures of injecting sea water into the contact system for the three fundamental
lubricating conditions are slightly different. In order to lubricate the central part of contact, sea water
is sprinkled onto the surface of the pipe before rubber is squeezed on the pipe in normal direction.
The amount of sea water should be sufficient to ensure that a steady water film region is spread on the
surface of the pipe to cover the contact area completely. On the contrary, for lubricating conditions
which are at the front part and tail part of the contact system, sea water is applied to the front edge
and the tail edge of contact respectively after the contact area is stably formed.
Simultaneously, other groups of tests with the same independent variables between rubber and
PMMA pipe were carried out to uncover the similarities between rubbers in contact with steel and
PMMA. Moreover, digital recordings were exploited to investigate the behaviors of the contact areas
between rubber and PMMA samples.
At the beginning of a test, only normal load was applied, and maintained for 180 s without
changing any other parameter of the test. The procedure was operated before tangential load was
applied to ensure the same normal loading condition. During this time, the radius of the contact area
increases gradually to the maximum value and becomes unchanged; the principle of the changing
contact radius is revealed by Lee and Radok who took the creep property of the rubbery material into
account in studying soft-rigid contact [37]. Furthermore, maintaining the unloading time above three
minutes between each test run considerably minimizes the repetition effects during tests including
viscoelastic rubber samples [38].
After finishing the first test run, we needed to unload the samples and move the pipe to the initial
position for the second test run. The residual sea water on the counter surfaces was removed artificially.
It is necessary to note that tangential force data tend to be stable after seven successive test runs. As a
consequence, 10 runs for each variable combination were carried out and the last three groups of data
are regarded as test values to eliminate the deviation of data at the initial stage of the test [39].
The temperature and relative humidity of the laboratory remained at 25 ◦ C (StDev 0.1–0.5) and
40% (StDev 3–5%) respectively throughout the tests via central air-conditioning.
2.4. Confirmation of the Maximum Static Friction
Figure 4a illustrates a combination of test records of the rubber A-steel contact system for the
central part lubricating condition. These tests are carried out at 10 N normal load with increasing
rates of tangential load at 0.062 N/s and 1.5 N/s, respectively. The results are reproducible for each
combination of normal load and increasing rate of tangential load which are tested.
A local enlargement of a single testing curve is shown in Figure 4b to demonstrate how the
maximum static friction and maximum partial displacement are confirmed. At the beginning of the
test, the tangential load curve starts to increase with a constant increasing rate. The entire curve
does not show any significant fluctuation until a sudden drop emerges from the top of the curve.
The displacement curve also shows a surprising increase at the same time. This time point is chosen as
the instant of macroscopical slip, and the values of tangential load and displacement at that time point
are treated as the maximum static friction and the maximum partial displacement, respectively.
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Figure 4. Confirmation of the maximum static friction. (a) Combination of two test records under 10
Figure 4. Confirmation of the maximum static friction. (a) Combination of two test records under 10 N
Figure
4. Confirmation
of the
static
friction.rate
(a) Combination
of two(b)
test
records
under 10
N
normal
load with a 0.062
N/smaximum
and 1.5 N/s
increasing
of tangential load;
Local
enlargement
normal load with a 0.062 N/s and 1.5 N/s increasing rate of tangential load; (b) Local enlargement of a
N
normal
load
with
a
0.062
N/s
and
1.5
N/s
increasing
rate
of
tangential
load;
(b)
Local
enlargement
of a single testing curve.
single testing curve.
of a single testing curve.
3. Results
3.3.Results
Results
3.1. The
The Maximum
Maximum Static
Static Friction
Friction
3.1.
3.1. The Maximum Static Friction
All the
the test
test results
results are
areshown
shown with
with the
the maximum
maximum static
static frictions
frictions in
in respect
respect to
to rubber
rubber types;
types; dry
dry
All
All
the
test
results
are
shown
with
the
maximum
static
frictions
in
respect
to
rubber
types;
dry
and lubricating
lubricatingconditions;
conditions;normal
normalloads;
loads;and
andincreasing
increasingrates
ratesof
oftangential
tangentialload.
load.
and
and A
lubricating
conditions;
normal
loads;
and
increasing
rates
of
tangential
load.
series of
of maximum
maximum static
static frictions
frictions (F)
(F) of
of rubber
rubber A
A and
and BB in
in contact
contact with
with steel
steel for
for dry
dry and
and
A series
A series
of maximum
static
frictions
(F)respectively.
of rubber A In
and
B in contact
with
steel
for dry
and
lubricating
conditions
is
plotted
in
Figure
5a,b,
general,
the
trends
of
F
for
each
testing
lubricating conditions is plotted in Figure 5a,b, respectively. In general, the trends of F for each testing
lubricating
conditions
is
plotted
in
Figure
5a,b,
respectively.
In
general,
the
trends
of
F
for
each
testing
conditionare
arethe
thesame;
same;values
valuesof
ofFFincrease
increasewith
withincreasing
increasingnormal
normalload.
load.ItItis
is obvious
obviousthat
that the
the friction
friction
condition
condition
are
the same;
values
ofwater
F increase
withinto
increasing
normal
load.
It is obvious
that the
friction
of
each
test
decreases
when
sea
is
added
the
central
part
of
rubber-steel
contact
systems.
of each test decreases when sea water is added into the central part of rubber-steel contact systems.
of each
test
decreases when
sea water is added
intofriction
the central
part
of rubber-steel
contact systems.
Sea
water
shows
levels
with
quite
a high
proportion.
The
Sea
water
shows strong
stronglubrication
lubricationability
abilitytotoreduce
reduce
friction
levels
with
quite
a high
proportion.
Sea
water
shows
strong
lubrication
ability
to
reduce
friction
levels
with
quite
a
high
proportion.
The
lubrication
of
seawater
is
more
active
for
rubber
A
than
that
for
rubber
B.
When
compared
with
dry
The lubrication of seawater is more active for rubber A than that for rubber B. When compared with
lubrication
of
seawater
is
more
active
for
rubber
A
than
that
for
rubber
B.
When
compared
with
dry
conditions,
the proportion
for rubber
A ranges
fromfrom
30%30%
to 45%,
while
for rubber
B, the
is 5%–
dry
conditions,
the proportion
for rubber
A ranges
to 45%,
while
for rubber
B, range
the range
is
conditions,
theexception
proportion
for rubber
A ranges
fromB30%
to
45%, is
while
for10
rubber
B, theload
range
is 5%–
30%.
The
only
takes
place
for
the
rubber
test
which
below
N
normal
with
an
5–30%. The only exception takes place for the rubber B test which is below 10 N normal load with an
30%. The only
exception
takes
the rubber B test which is below 10 N normal load with an
increasing
rateof
of
tangential
loadplace
at1.5
1.5for
N/s.
increasing
rate
tangential
load
at
N/s.
increasing rate of tangential load at 1.5 N/s.
Figure 5. A series of maximum static frictions (F) of rubber in contact with steel for dry and lubricating
Figure 5. A series of maximum static frictions (F) of rubber in contact with steel for dry and lubricating
conditions.
Results
of rubberstatic
A tests;
(b) Results
rubber
tests.
Figure 5. A(a)
series
of maximum
frictions
(F) of of
rubber
in B
contact
conditions.
(a)
Results
of rubber A tests;
(b) Results
of rubber
B tests.with steel for dry and lubricating
conditions. (a) Results of rubber A tests; (b) Results of rubber B tests.
Another
Another comparison
comparison can
can be
be easily
easily seen
seen for
for rubber
rubber A
A tests
tests for
for which
which friction
friction levels,
levels, with
with an
an
Another
comparison
can
be
easily
seen
for
rubber
A
tests
for
which
friction
levels,
with
an
increasing
rate
of
tangential
load
at
1.5
N/s,
are
always
higher
than
that
with
an
increasing
rate
of
increasing rate of tangential load at 1.5 N/s,
always higher than that with an increasing rate of
increasing
rate
of
tangential
load
at
1.5
N/s,
are
always
higher
than
that
with
an
increasing
rate
of
tangential
tangentialload
loadat
at0.062
0.062N/s.
N/s. Difference of friction levels between the two different
different tangential
tangential loading
loading
tangential
load
at
0.062
N/s.
Difference
of
friction
levels
between
the
two
different
tangential
loading
conditions
conditions is
is not
not quite
quite apparent
apparent at
at 10
10 N
Nand
and20
20N
Nnormal
normalload
loadconditions.
conditions. However,
However, the
the difference
difference
conditions
is
not
quite
apparent
at
10
N
and
20
N
normal
load
conditions.
However,
the
difference
increases
as
normal
load
increases.
increases as normal load increases.
increases as normal load increases.
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77 of
Even though almost the same tendency is shown in tests of rubber B, the difference of friction
though
the same
tendency
is shown
ofproportion
rubber B, the
difference
of friction
levelsEven
between
twoalmost
tangential
loading
conditions
staysinattests
a low
range.
Moreover,
when
levels
between
two
tangential
loading
conditions
stays
at
a
low
proportion
range.
Moreover,
when
normal load is 40 N, the lubricated friction for the 1.5 N/s increasing rate of tangential load is lower
normal
load
400.062
N, the
lubricated
friction for the 1.5 N/s increasing rate of tangential load is lower
than that
for is
the
N/s
rate.
than that for the 0.062 N/s rate.
3.2. Efficiency of Lubrication
3.2. Efficiency of Lubrication
In order to investigate the different lubricating conditions in the central, the front and the tail
In
to investigate
the of
different
lubricating
in the central,
the front
the tail
contact order
part, we
set α as a ratio
the efficiency
of theconditions
three lubricating
conditions.
The αand
is denoted
contact
part,
we
set
α
as
a
ratio
of
the
efficiency
of
the
three
lubricating
conditions.
The
α
is
denoted
as
as a simple function that
a simple function that
(1)
⁄ lc
α=
= Flx /F
(1)
Flt; these
threethree
factors
represent
the maximum
static friction
of rubberwhere FFlxlx includes
includesFlcF,lcF,lf Fand
Flt ; these
factors
represent
the maximum
static friction
of
lf and
seen
as
the
steel contact contact
under each
the of
three
conditions,
respectively.
Flc can Fbe
rubber-steel
underofeach
the lubricating
three lubricating
conditions,
respectively.
can
be
seen
lc
reference
value tovalue
examine
the lubrication
efficiencyefficiency
for the other
typicaltwo
lubricating
conditions.
as
the reference
to examine
the lubrication
for two
the other
typical lubricating
Therefore, the
values ofthe
α for
the of
central
of the lubricated
constantly
1. Theequal
higher
conditions.
Therefore,
values
α for part
the central
part of thetests
lubricated
testsequal
constantly
1.
value
of α reveals
friction;
the lubrication
efficiencyefficiency
is not asisgood
asgood
that for
the
The
higher
value ofhigher
α reveals
highertherefore,
friction; therefore,
the lubrication
not as
as that
central
part lubricating
condition.
Values Values
of α forofthe
other
typical
lubricating
conditions
which
for
the central
part lubricating
condition.
α for
thetwo
other
two typical
lubricating
conditions
are under
different
loading
processes
are shown
in Figure
6.
which
are under
different
loading
processes
are shown
in Figure
6.
Figure 6a represents a combination of values of αα for
for rubber
rubber A
A tests.
tests. Apparently, most of the
for the
the tail
tail part
part lubricating
lubricating conditions are lower than that for the front part conditions,
values of αα for
except for
for only
only one
one test
test which
which is
is under
under 10
10 N
N normal
normal load
load with
with aa 0.062
0.062 N/s
N/s increasing
except
increasing rate of tangential
load. This
This phenomenon
phenomenonmeans
meansthat
thatlubrication
lubrication
at
the
tail
part
of
contact
is commonly
at the tail part of contact is commonly
moremore
activeactive
than
thanatthat
the part
frontofpart
of contact.
The values
in the
most
tests 1,exceed
1, it indicates
that the
that
theat
front
contact.
The values
of α in of
theαmost
tests
exceed
it indicates
that the levels
of
levels of lubrication
the two
lower
at the
central part.
lubrication
at the twoatside
partsside
are parts
lowerare
than
that than
at thethat
central
part.
In Figure 6b, some similar trends are observed,
observed, for example, lubrication
lubrication at
at the tail part of contact
behaves more
morevigorously
vigorouslythan
thanthat
thatatatthe
thefront
front
part
rubber
B contact
system.
Lubrication
at
behaves
part
forfor
thethe
rubber
B contact
system.
Lubrication
at the
the
central
part
is
also
more
active
than
that
at
the
other
side
parts.
central part is also more active than that at the other side parts.
Figure 6.
6. Lubrication
Lubricationefficiency
efficiencyat at
parts
of contact.
(a) Results
of rubber
(b)
Figure
thethe
twotwo
sideside
parts
of contact.
(a) Results
of rubber
A tests;A(b)tests;
Results
Results
of
rubber
B
tests.
of rubber B tests.
3.3. Deformation of Contact
3.3. Deformation of Contact
The pictures of contact are extracted frame by frame from testing video files (video format: 1600
The pictures of contact are extracted frame by frame from testing video files (video format:
× 1200 pixels, 24 bit, 60 frames per second). We select the image which represents the typical shape
1600 × 1200 pixels, 24 bit, 60 frames per second). We select the image which represents the typical
of the contact region for each deformation phase of the rubber sample. In order to highlight the
shape of the contact region for each deformation phase of the rubber sample. In order to highlight
deformation of the contact region, we keep the image of contact at the center of the picture and crop
the deformation of the contact region, we keep the image of contact at the center of the picture and
the picture to 200 × 200 pixels. Therefore, a series of pictures is demonstrated in Figures 7–9 to identify
crop the picture to 200 × 200 pixels. Therefore, a series of pictures is demonstrated in Figures 7–9 to
the evolution of the contact region throughout the tests of three typical lubricating conditions.
identify the evolution of the contact region throughout the tests of three typical lubricating conditions.
Firstly, the evolution of contact for the central part lubricating condition is shown in Figure 7.
Sea water has spread onto the pipe surface and has formed a stationary lubricating film before rubber
surface of rubber due to the continuously increasing tangential load. Relative displacement of the
counter
counter surfaces
surfaces is
is observed
observed within
within the
the yellow
yellow dotted
dotted ovals,
ovals, as
as shown
shown by
by partial
partial traces
traces of
of ink
ink which
which
are
are separated
separated from
from the
the black
black marker
marker pen
pen lines.
lines. As
As long
long as
as the
the tangential
tangential load
load is
is increasing,
increasing, more
more and
and
more
more separations
separations of
of partial
partial traces
traces of
of ink
ink appear
appear within
within the
the apparent
apparent contact
contact area
area (Figure
(Figure 7e).
7e). The
The
bend
at
the
rear
edge
of
contact
is
more
distinct
than
that
at
the
front
edge.
Finally,
as
soon
as
bend at the rear edge of contact is more distinct than that at the front edge. Finally, as soon as the
the
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2017, 5, 12
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contact
contact separations occupy
occupy most
most of
of the
the contact
contact region,
region, macroscopic
macroscopic slip
slip emerges
emerges (Figure
(Figure 7f).
7f).
Figure 7. Evolution of the apparent contact area in the rubber A-PMMA test, for the central part
Figure 7.
7. Evolution
rubber A-PMMA
A-PMMA test,
the central
central part
part
Figure
Evolution of
of the
the apparent
apparent contact
contact area
area in
in the
the rubber
test, for
for the
lubricating condition. The test is under 20 N normal load with a 0.062 N/s increasing rate of tangential
lubricating
condition.
The
test
is
under
20
N
normal
load
with
a
0.062
N/s
increasing
rate
of
tangential
lubricating condition. The test is under 20 N normal load with a 0.062 N/s increasing rate of tangential
load. The black lines on the surface of the rubber are marked as 1–6. (a) Steady contact between rubber
load. The
onon
thethe
surface
of the
rubber
are marked
as 1–6.
Steady
contactcontact
between
rubber
load.
Theblack
blacklines
lines
surface
of the
rubber
are marked
as (a)
1–6.
(a) Steady
between
and pipe without tangential load; (b) Deformation of the contact at the beginning of tangential load;
and
pipe
without
tangential
load;
(b)
Deformation
of
the
contact
at
the
beginning
of
tangential
load;
rubber and pipe without tangential load; (b) Deformation of the contact at the beginning of tangential
(c) Rubber surface which, at the rear edge of contact, is moving towards with pipe; (d) Partial traces
(c) Rubber
surface
which,which,
at the at
rear
contact,
is moving
towards
with pipe;
Partial
traces
load;
(c) Rubber
surface
theedge
rear of
edge
of contact,
is moving
towards
with(d)
pipe;
(d) Partial
of ink which are separated from the black marker pen lines; (e) More and more separations of partial
of ink which
separated
from thefrom
black
marker
lines;
(e) lines;
More (e)
andMore
moreand
separations
of partial
traces
of ink are
which
are separated
the
black pen
marker
pen
more separations
traces of ink appear within the apparent contact area; (f) Macroscopic slip is emerging. The white
traces
of ink
appear
within
thewithin
apparent
area;
(f) Macroscopic
slip is emerging.
white
of
partial
traces
of ink
appear
thecontact
apparent
contact
area; (f) Macroscopic
slip is The
emerging.
arrows indicate the direction of expansion of the contact region; The red arrows indicate the
arrows
indicate
the
direction
of
expansion
of
the
contact
region;
The
red
arrows
indicate
the
The white arrows indicate the direction of expansion of the contact region; The red arrows indicate
deformation of the rubber surface; The yellow dotted circles indicate the relative displacement of
deformation
of the
rubber
surface;
The
yellow
dotted
the
deformation
of the
rubber
surface;
The
yellow
dottedcircles
circlesindicate
indicatethe
therelative
relative displacement
displacement of
interfaces (the interpretation also applies to figures 8 and 9).
to Figures
figures 8 and 9).
interfaces (the interpretation also applies to
Figure 8. Evolution of the apparent contact area in the rubber A-PMMA test, for the front part
Figure 8. Evolution of the apparent contact area in the rubber A-PMMA test, for the front part
Figure 8. Evolution
the
apparent
area load
in the
rubber
A-PMMA
test, for
the
part
lubricating
condition. of
The
test
is under contact
20 N normal
with
a 0.062
N/s increasing
rate
of front
tangential
lubricating condition. The test is under 20 N normal load with a 0.062 N/s increasing rate of tangential
lubricating
condition.
The
test
is
under
20
N
normal
load
with
a
0.062
N/s
increasing
rate
of
tangential
load. (a) Steady contact between the rubber and pipe without tangential load; (b) Deformation of the
load. (a) Steady contact between the rubber and pipe without tangential load; (b) Deformation of the
load. (a)atSteady
contact between
the rubber
pipe without
tangential
(b) Deformation
of the
contact
the beginning
of tangential
load; and
(c) Rubber
surface
which, atload;
the rear
edge of contact,
is
contact at the beginning of tangential load; (c) Rubber surface which, at the rear edge of contact, is
contact
at
the
beginning
of
tangential
load;
(c)
Rubber
surface
which,
at
the
rear
edge
of
contact,
is
moving towards with pipe; (d) Partial traces of ink which are separated from the black marker pen
moving towards with pipe; (d) Partial traces of ink which are separated from the black marker pen
moving
towards
with
pipe;
(d)
Partial
traces
of
ink
which
are
separated
from
the
black
marker
pen
lines; (e) More and more separations of partial traces of ink appear within the apparent contact area;
lines;
(e) 5,
More
and10.3390/lubricants5020012
more separations of partial traces of ink appear within the apparent contact area;9 of 13
Lubricants
2017,
12; doi:
lines;
(e) More
and
separations of partial traces of ink appear within the apparent contact area;
(f)
Macroscopic
slipmore
is emerging.
(f) Macroscopic slip is emerging.
(f) Macroscopic slip is emerging.
Figure
thethe
apparent
contact
area in
thein
rubber
A-PMMA
test, for the
part
lubricating
Figure 9.9.Evolution
Evolutionofof
apparent
contact
area
the rubber
A-PMMA
test,tailfor
the
tail part
condition.
The
test
is
under
20
N
normal
load
with
a
0.062
N/s
increasing
rate
of
tangential
load.
lubricating condition. The test is under 20 N normal load with a 0.062 N/s increasing rate of tangential
(a)
Steady
contact
between
the the
rubber
andand
pipe
without
tangential
load;
load.
(a) Steady
contact
between
rubber
pipe
without
tangential
load;(b)
(b)Deformation
Deformation of
of the
the
contact
at
the
beginning
of
tangential
load;
(c)
Rubber
surface
which,
at
the
rear
edge
of
contact,
contact at the beginning of tangential load; (c) Rubber surface which, at the rear edge of contact, is
is
moving
towards with
with pipe;
pipe; (d)
(d) Partial
traces of
of ink
moving towards
Partial traces
ink which
which are
are separated
separated from
from the
the black
black marker
marker pen
pen
lines;
of partial
partial traces
traces of
of ink
ink appear
appear within
within the
the apparent
apparent contact
contact area;
area;
lines; (e)
(e) More
More and
and more
more separations
separations of
(f)
Macroscopic
slip
is
emerging.
(f) Macroscopic slip is emerging.
Even though the contact areas are deformed in different scales, Figures 8 and 9 show a similar
evolution of contact for the front part and the tail part lubricating conditions to the central part
lubrication tests.
4. Discussion
There are two major factors that influence friction levels not only in the sliding condition but
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Firstly, the evolution of contact for the central part lubricating condition is shown in Figure 7. Sea
water has spread onto the pipe surface and has formed a stationary lubricating film before rubber is
normal loaded against to the pipe. Figure 7a illustrates steady contact between the rubber and pipe
with seawater lubrication after a certain time which is mentioned in the experimental procedures
section. As soon as the tangential load is imposed, the shape of the contact area starts deforming. At the
beginning of tangential loading, as shown in Figure 7b, the white arrows indicate that the front edge of
contact shrinks backward slightly, while the rear edge expands smoothly. The red arrow is pointing in
the opposite shearing direction to the rear edge of the contact region. It is obvious that the scale of
deformation at the front edge is slightly lower than that at the rear edge. This phenomenon of contact
can be regarded as a consequence of integral elastic deformation of the rubber sample. The bend of
line 2 which is shown in Figure 7c indicates that the rubber surface, at the rear edge of contact, is
moving towards with pipe and no relative displacement of counter surfaces takes place during this
status. The increasing bend of line 2 in Figure 7d reveals remarkable shear of the surface of rubber
due to the continuously increasing tangential load. Relative displacement of the counter surfaces is
observed within the yellow dotted ovals, as shown by partial traces of ink which are separated from
the black marker pen lines. As long as the tangential load is increasing, more and more separations of
partial traces of ink appear within the apparent contact area (Figure 7e). The bend at the rear edge of
contact is more distinct than that at the front edge. Finally, as soon as the contact separations occupy
most of the contact region, macroscopic slip emerges (Figure 7f).
Even though the contact areas are deformed in different scales, Figures 8 and 9 show a similar
evolution of contact for the front part and the tail part lubricating conditions to the central part
lubrication tests.
4. Discussion
There are two major factors that influence friction levels not only in the sliding condition but
also in the static contact system [40]. The principal factor is the adhesion force between the counter
surfaces, which primarily influences the level of friction. The second factor is the viscoelastic property
of rubber, which can be seen as an inherent response to external environmental conditions. In this
study, adhesion force is still playing a very important role which affects the levels of static friction
within the real contact area.
In most of the tests, values of F at the 1.5 N/s increasing rate of tangential load are higher than that
at 0.062 N/s. This phenomenon may be caused by the viscoelastic property of rubber. The explanation
is based on previous research by Schallamach [7] and Barquins [8]. Adhesion load increases as relative
displacement velocity increases, however, the end of the adhesion phase decreases. Therefore, it is
deduced that there is a critical speed for which the friction takes the maximum value. The relative
displacement velocities in our tests are apparently lower than the critical speed; therefore, the friction
increases with a higher increasing rate of tangential load. This phenomenon can also indicate that the
viscoelastic property of rubber still works at the level of static friction for lubricating conditions.
The lubrication of water has complicated influences on the static friction level of rubber. The water
film can be entrapped within the apparent contact area due to the convenient elastic deformation
of rubber [27]. The sealing effect of the water film is introduced when the rubber is normal against
the rough surface of the substrate [28]. The entrapment of water and the sealing effect belong to the
essential principle that the water film, within the apparent contact area, supports the normal load and
smoothens the counter surfaces, consequently leading to a reduction of adhesion force in the contact
system, thus reducing the rubber friction [41]. However, the thin water film and the tacky condition
may generate the influence of the capillary effect. The capillary effect establishes capillary bridges
among the surface asperities of rubber and the water film, resulting in the enhancement of adhesion
and resistance to shear [42]. Therefore, the lubrication of water has two opposite effects on rubber
friction based on the certain investigating condition. It is known that a sufficient amount of water
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leads to the large thickness of the lubricating film and the complete wetting condition. The capillary
effect cannot be highlighted during such a testing situation in our study.
4.1. The Central Part Lubrication
The Stribeck curve provides guidance to identify the lubricating regime in the central part
wetting tests. Even though the tests aim to investigate the static frictional behaviors of rubber, and no
macroscopical displacement takes place during most tests, the relative partial displacement emerges
as soon as the tangential load is imposed. Therefore, the contact system can be seen as an assemblage
of the real contact area surrounded by a circle of the partial sliding zone. We can deduce the relative
sliding velocity at the level of a few centimeters per second due to the displacement–time curves. We
can clearly conclude that the central part lubrication is belong to the scope of boundary lubrication.
In the boundary regime, water lubrication follows the principle of reducing the static friction. Therefore,
the maximum static friction for the central part lubricating condition is universally lower than that in
the dry condition for both rubber A and B tests.
The different extent of bend between line 2 and 5 (Figure 7) reflects the strong difference of the
shear stress between the rear edge and the front edge of the contact zone. This phenomenon is well
established with previous results obtained in the dry condition [15,38]. Lubrication in the central part
of contact can be seen as a function that weakens the adhesion effect within the entire contact zone
rather than changing the deformation principle of the rubber surface. Under this assumption, the
difference of the maximum static friction between the two rubber types can be understood with the
same explanation as for dry condition tests: the lower the elastic moduli, the stronger the contact
deformation; therefore, the static friction increases as the real contact area increases. Furthermore, the
maximum static friction decreases due to the creep of the rubber surface when sheared for a certain
period of time [15]. The improvement of static friction which is achieved at a higher increasing rate of
tangential load is also good evidence to prove the assumption.
4.2. Comparison of the Two Side Parts of Lubrication
The effect of lubrication on the contact of the two side parts is quite different from that on the
central part lubricating condition; this is because sea water solution is applied to each part of the
contact zone until the contact is stably formed. Therefore, there is no entrapment of water or sealing
water before the tangential load is imposed. If the counter surfaces are smooth enough, then the
lubricating film would be propagated along with the boundary of the central contact area and partial
slip zone. The counter surfaces in this study are not as smooth as the ideal assumption, and the water
film can propagate into the contact zone through gaps between asperities in contact due to seepage
flow mechanics. Therefore, the lubricating film can reduce the adhesion force around the crack line of
the interfaces. However, the effect of lubricating water within the apparent contact zone is smaller
than that at the central part lubricating condition. Figure 10 provides evidence to compare the extent
of deformation at the rear edge of the apparent contact zone for the three lubricating conditions. The
largest shear stress is shown in Figure 10b and sea water is concentrated at the front part of contact.
There is no lubrication at the tail part of contact; the distance to the initiate position at the rear edge
of contact is 2.08 mm, so the maximum static friction stays at a high level. The deformation which
is shown in Figure 10c is evidently smaller than that in Figure 10b; it indicates that lubrication acts
more efficiently and results in lower static friction for the tail part lubricating conditions. However,
its deformation (1.51 mm) is still larger than that for the central part lubricating tests (1.25 mm).
Furthermore, the contact displacement for each lubricating condition is shown in Figure 10d; we can
observe the variation tendency of the maximum displacements in the three tests, and the tendency is
similar with the variation of the deformations at the rear edge of the contact. This phenomenon can
also prove the different effects of lubrication for the three lubricating conditions. Therefore, values of α
are always greater than 1. It is necessary to note that the maximum contact displacement is apparently
higher than the deformation distance at the rear edge, because there are two major deformation
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styles—elastic deformation of the whole rubber sample and tangential deformation which is located at
the rear edge—which contribute to the contact displacement from the initiate position. An obvious
exception
for5,the
of α is obtained in rubber A tests; the value is under 10 N normal load and
at13a
Lubricants
2017,
12; value
doi: 10.3390/lubricants5020012
11 of
1.5 N/s increasing rate of tangential load. This is possibly because the static contact system undergoes
an unstable
status
which
under
relatively
low
loading
a high
increasing
rate.
high
increasing
shear
rate. is
The
unusual
value of
thenormal
maximum
staticwith
friction
which
is shownshear
in Figure
Themay
unusual
value of evidence;
the maximum
static friction
which is shown
in Figure
5b may
be than
convincing
5b
be convincing
the friction
of the lubricating
condition
is slightly
higher
that in
evidence;
the friction
the lubricating
slightly
than thatrate
in the
dry condition
the
dry condition
testof
which
is under 10condition
N normalis load
withhigher
an increasing
of tangential
loadtest
at
which
1.5
N/s.is under 10 N normal load with an increasing rate of tangential load at 1.5 N/s.
Figure 10. Comparison of deformations at the rear edge of contact for the different lubricating
Figure 10. Comparison of deformations at the rear edge of contact for the different lubricating
conditions. (a) Deformation of the rear edge for the central part lubricating condition; (b) Deformation
conditions. (a) Deformation of the rear edge for the central part lubricating condition; (b) Deformation
of the rear edge for the front part lubricating condition; (c) Deformation of the rear edge for the tail
of the rear edge for the front part lubricating condition; (c) Deformation of the rear edge for the tail
part lubricating condition. (d) Comparison of the maximum displacements of contact for the three
part lubricating condition. (d) Comparison of the maximum displacements of contact for the three
lubricating
N normal
normal load,
load, with
with aa 1.5
1.5 N/s
N/s increasing
lubricating conditions;
conditions; the
the tests
tests were
were conducted
conducted under
under 20
20 N
increasing
rate
of
tangential
load.
rate of tangential load.
The above discussions may not completely explain the accurate lubricating effects among all of
The above discussions may not completely explain the accurate lubricating effects among all of
the experimental results. However, the results of this study suggest that the static friction behaviors
the experimental results. However, the results of this study suggest that the static friction behaviors of
of rubber are affected by different lubricating conditions. The maximum static friction decreases with
rubber are affected by different lubricating conditions. The maximum static friction decreases with
the lubrication of sea water. These results may provide experimental support for further systematic
the lubrication of sea water. These results may provide experimental support for further systematic
studies on tensioner design and more accurate investigation of the tribological behavior of static
studies on tensioner design and more accurate investigation of the tribological behavior of static
rubber contact.
rubber contact.
5. Conclusions
5. Conclusions
A series of experimental tests was carried out using a home-built friction instrument to
A series of experimental tests was carried out using a home-built friction instrument to investigate
investigate the static friction behaviors of contact between rubber and pipe. The maximum static
the static friction behaviors of contact between rubber and pipe. The maximum static friction decreases
friction decreases due to the lubrication of sea water; the extent of the decline ranges from 30% to
due to the lubrication of sea water; the extent of the decline ranges from 30% to 45% for the relative
45% for the relative soft rubber compound; the range is not greater than 30% for the relative stiff
soft rubber compound; the range is not greater than 30% for the relative stiff rubber compound. All
rubber compound. All tests in this study are believed to be in the boundary lubrication condition.
tests in this study are believed to be in the boundary lubrication condition. The water film can be seen
The water film can be seen to weaken the adhesion effect of the contact system rather than changing
to weaken the adhesion effect of the contact system rather than changing the deformation principle of
the deformation principle of the rubber surface. The differences of frictions between 0.062 N/s and
1.5 N/s and the increasing rate of tangential load indicate that the effect of rubber’s viscoelastic
property still works at the level of static friction for the lubricating conditions. Lubrication at the two
side parts of contact shows lower efficiency than that in the central part of contact due to the different
extent of lubricating film.
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the rubber surface. The differences of frictions between 0.062 N/s and 1.5 N/s and the increasing rate
of tangential load indicate that the effect of rubber’s viscoelastic property still works at the level of
static friction for the lubricating conditions. Lubrication at the two side parts of contact shows lower
efficiency than that in the central part of contact due to the different extent of lubricating film.
Acknowledgments: This research is sponsored by the National Natural Science Foundation of China
(No. 51375495), the Tribology Science Fund of State Key Laboratory of Tribology (No. SKLTKF14A08) and
the Science Foundation of China University of Petroleum, Beijing (No. 2462017BJB06, C201602).
Author Contributions: Yong-Jie Zhou set up the test devices, performed tribology, and wrote the manuscript;
Yan-Bao Guo performed mechanical testing, analysis, and contributed in writing the manuscript; and
De-Guo Wang conceived research, analyzed results.
Conflicts of Interest: The authors declare no conflict of interest.
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