Wear 319 (2014) 27–37
Contents lists available at ScienceDirect
Wear
journal homepage: www.elsevier.com/locate/wear
Static friction of stainless steel wire rope–rubber contacts
Arjo J. Loeve n, Tim Krijger, Winfred Mugge, Paul Breedveld, Dimitra Dodou,
Jenny Dankelman
Department of BioMechanical Engineering, Faculty of Mechanical, Maritime and Materials Engineering (3mE), Delft University of Technology
Mekelweg 2, 2628 CD, Delft, The Netherlands
art ic l e i nf o
a b s t r a c t
Article history:
Received 7 February 2014
Received in revised form
8 July 2014
Accepted 10 July 2014
Available online 17 July 2014
Little is known about static friction of stainless-steel wire ropes (‘cables’) in contact with soft rubbers, an
interface of potential importance for rigidifiable medical instruments. Although friction theories imply
that the size and profile of the cables affect static friction, there are no confirmative data for stainlesssteel cable-rubber contacts. Static friction was measured between five cable types (0.18, 0.27 and
0.45 mm diameter, twisted in 1 7, 1 19, or 7 7 strands) and latex, nitrile, and silicone rubber. Mean
static friction coefficients of the cables ranged over 0.27–0.31, 0.25–0.27, and 0.44–0.53 for nitrile,
silicone, and latex, respectively. Overall, the cable type had little effect on static friction. For all cables,
friction was twice as high for latex as for nitrile rubber, which had slightly higher friction than silicone
rubber. The higher static friction for nitrile compared to silicone rubber despite silicone rubber being
significantly softer could be caused by the high polar surface free energy of nitrile rubber. Common
friction theories were valuable in predicting the effect of cable profiles and rubber properties on static
friction but should not be applied without considering interaction effects. Static friction seems to be a
minor factor when selecting cables for practical applications involving cable-rubber contacts.
& 2014 Elsevier B.V. All rights reserved.
Keywords:
Surface topography
Steel
Rubber
Hardness
1. Introduction
Surgeons operate through ever-smaller incisions, reducing
recovery times, scarring, inflammation, and other complications.
In Natural Orifice Transluminal Endoscopic Surgery (NOTES), a long,
flexible endoscope [1] and surgical instruments are inserted into
the body through a natural orifice (see Fig. 1(a) for an example)
[2–6]. Before NOTES can be used to its full potential, some problems
should first be solved. Specifically, during insertion, the endoscope
shaft can buckle and loop due to its flexibility, inhibiting reaching
the target site, whereas during therapeutic actions (Fig. 1(b)), when
tissue is grasped and pulled, the shaft cannot offer sufficient
stability, which hampers precise manipulation [3].
To solve insertion and stability difficulties in NOTES, we
developed a thin-walled aiding shaft called ‘FORGUIDE’. The
FORGUIDE shaft (Fig. 2) consists of stainless steel wire ropes
(further referred to as ‘cables’) that are circumferentially arranged
n
Correspondence to: Room F-0-200, Department of BioMechanical Engineering,
Faculty of Mechanical, Maritime and Materials Engineering (3mE), Delft University
of Technology, Mekelweg 2, 2628 CD, Delft, The Netherlands. Tel.: þ 31 15 2782977.
E-mail addresses: [email protected] (A.J. Loeve),
[email protected] (T. Krijger), [email protected] (W. Mugge),
[email protected] (P. Breedveld), [email protected] (D. Dodou),
[email protected] (J. Dankelman).
http://dx.doi.org/10.1016/j.wear.2014.07.005
0043-1648/& 2014 Elsevier B.V. All rights reserved.
around an inflatable rubber tube and placed inside a stainless steel
spring. The FORGUIDE shaft can be placed in or around a flexible
endoscope and made compliant or rigid at will to hold its pose and
support and guide a flexible endoscope and other instruments. The
key to having a well-rigidified FORGUIDE shaft is to prevent the
cables in the shaft from sliding, by introducing pressure in the
inflatable tube. Earlier work [7] reported on the feasibility of the
FORGUIDE concept and proposed that increasing static friction
between the tube and the cables and between the cables and the
spring would increase the maximum rigidity of the FORGUIDE
shaft. The best cable–spring combination can be readily selected
using static friction data from literature [8], whereas finding the
best cable–rubber combination is less trivial.
Mathematical models for static friction between rubbers and
hard counter surfaces are not yet conclusive about the effect of
cable surface profiles on static friction with rubber [9,10]. Rubber
static friction depends on many factors, such as rubber hardness,
counter surface roughness, time, and temperature [9,11]. To the
best of our knowledge, the only study on friction between steel
cables and a polymer is by Shirong [12], describing the dynamic
friction between a steel cable and polyvinyl chloride, a relatively
hard polymer compared to the rubbers used for inflatable tubes.
There are many reports of studies on friction between rubbers and
steels of various scales of surface profiles, mostly concerning
dynamic friction. Most of the steel surface profile scales tested in
28
A.J. Loeve et al. / Wear 319 (2014) 27–37
Colon
Ligaments
Flexible
endoscope
Anus
(Desired)
(Reality)
Stomach Wall
Flexible
endoscope
Flexible
endoscope
Mouth
Endoscopic
grasper
Tissue
Endoscopic
grasper
(control end)
(Reality)
Esophagus
Stomach
Rigid(ified)
endoscope
(Desired)
Fig. 1. (a) Insertion problems due to buckling while inserting a flexible endoscope into the colon. (b) Lack of stability during therapeutic actions. Tissue should be pulled
toward the endoscope but instead the endoscope bends toward the tissue due to inadequate shaft stiffness.
these studies are in the roughness range of polished or abraded
surfaces with micrometer scale surface profiles [13–16], some are
several centimeters of scale [17,18]. This article focuses on surface
profile scales in the range of 0.01–0.45 mm.
The aim of the current experiment is to investigate the static
friction between AISI 316 stainless steel cables and smooth
rubbers used to manufacture expandable tubing. It is explored to
what extent predictions based on literature on friction between
smooth soft and rough hard surfaces hold for contact between soft
rubbers and stainless steel cables. The tests this work describes
primarily provide further data to complete the literature, but will
also be used to determine which steel cable–tube combination
provides the highest static friction and thus maximizes the rigidity
of a rigidified FORGUIDE shaft.
1.1. Interface description
In essence, the contact between steel cables longitudinally
aligned around an inflatable rubber tube is identical to the contact
between a rough, flat, steel surface pressed onto a smooth flat
rubber surface. The tube surface has only microscopic roughness.
Microscopic roughness on rubbers is known to have a minor
effect – which diminishes for loads above about 0.2 MPa – on
sliding friction in contact with roughened surfaces [18].
A.J. Loeve et al. / Wear 319 (2014) 27–37
29
Spring
Cable
Expandable tube
Tip
(Compliant)
Water
(pressure)
3D
(Rigid)
Fig. 2. (a) Transverse (left) and longitudinal (right) cross sections of the FORGUIDE shaft concept. (Inset) 3D impression of the shaft layers. (b) FORGUIDE shaft prototype. The
shaft consists of three layers: an expandable tube filled with fluid, a ring of cables lying around it, held together by a closed coiled spring. These layers are rigidly connected at
the tip. The spring and tube are attached to a syringe at the base. In its neutral state the shaft is compliant. When the shaft bends, the cables slide between the tube and
spring to compensate for length differences between inner and outer bend curves. Raising the fluid pressure (locking pressure) expands the tube and clamps the cables
between tube and spring due to friction between tube, cables, and spring: the cables can no longer slide, the curve lengths cannot change (assuming negligible material
deformation), the shape of the shaft is fixed and thus the shaft is rigidified.
30
A.J. Loeve et al. / Wear 319 (2014) 27–37
Multi strand cable (7x7)
Cable-level roughness with size ~ ØCable
Sub-strand-level roughness with size ~ Ø Sub-strand
Wire-level roughness with size ~ Ø Wire
Soft rubber
Soft rubber
Single wire
Single strand cable
Multi strand cable
Rubber
Soft rubber
Hard rubber
Fig. 3. (a) Schematic side (left) and front (right) view of macroscopic contact between a layer of multi strand cables (twined of seven strands twisted of seven wires each)
pressed on soft rubber, and the different levels of macro-roughness. (b) Impression of contact changes due to changing cable roughness or rubber hardness.
If the steel surface consists of a dense layer of parallel-aligned steel
cables (as in the FORGUIDE shaft), it contains several scales of
roughness (Fig. 3a). Each cable is twisted from a set of wires or
twined from a set of sub-strands, with each sub-strand twisted from a
set of wires (Fig. 3). Three levels of macro-roughness (here defined as
roughness heights of 0.01–0.45 mm) can be distinguished (Fig. 3a) on
a surface formed by such cables: cable-level roughness, consisting of
the bumps formed by the nominal cable diameter perpendicular to
the longitudinal direction of the cables; sub-strand-level roughness,
consisting of the bumps formed by the nominal sub-strand diameter;
and wire-level roughness, consisting of the bumps formed by the wires
in the (sub-)strands, with bump sizes of about the diameter of the
wires (Fig. 3b). On top of the macro-roughness, a cable has microscopic roughness on the (often polished) surface of the wires (Fig. 3b).
1.2. Hypotheses
Static friction is hard to define for rubbers due to its timedependent nature. In this study, ‘static friction’ is defined as the
maximum shear force before macroscopic sliding starts. The main
component of static rubber friction is adhesive friction, which is
determined by the real contact area and the adhesion strength
between the contact pair [9,19].
Because of the multiple levels of macro-roughness on the
cables and the viscoelastic properties of rubber, one can expect
that under identical loading magnitudes and times, a layer of
multi-strand cables will provide a larger real contact area than a
layer of single strand cables of the same diameter [20]. Similarly,
one can expect that a layer of small diameter cables will provide a
larger real contact area than a layer of large diameter cables of the
same structure. Additionally, increasingly softer rubbers mold into
increasingly smaller voids in the counter surface profile. Consequently, the real contact area (Fig. 3b) and thus static friction
increases with decreasing rubber hardness. [19,21–23] Also, softer
rubbers show larger bulk deformation, which increases the surface
free energy, generally increasing adhesion [9,24,25].
Based on the above considerations static friction between a
layer of rubber and a layer of AISI 316 stainless steel cables is
expected to increase with: (Hypothesis 1, cable-effect) decreasing
size of the macro-roughness levels of stainless steel cables;
(Hypothesis 2, cable-effect) increasing number of distinct levels of
macro-roughness present on stainless steel cables; (Hypothesis 3,
rubber-effect) decreasing rubber hardness; and (Hypothesis 4,
rubber-effect) increasing rubber surface free energy.
2. Materials and methods
2.1. Test setup
Static friction between flat rubber surfaces and flat surfaces made
of longitudinally aligned steel cables was measured using a tensile
tester (Zwick 1484 with HBM 26–3 tensile force sensor). Apparent
contact areas of 3 3 cm2 were used. Increasing the contact pressure
will eventually lead to saturation of the real rubber–steel contact
area and reduction of the static friction coefficient [9,18,21,26,27].
Pilot tests with contact pressures of 0.25–0.49 MPa (corresponding to
earlier FORGUIDE test pressures [7]) showed that results were more
consistent at high pressures and that saturation did not occur within
this range. To obtain such pressures, a clamping module was
designed (Fig. 4a) based on earlier clamping concepts [15,28,29].
The clamping module had two horizontal jaws – one fixed and
one mobile – clamping a vertically pulled block from two sides.
The pulled block had two surfaces covered by longitudinally
aligned steel cables (Fig. 4b) and was attached directly to the
force sensor of the tensile tester. Each of the two jaws held a
clamping block (Figs. 4b and d) covered with rubber on one side.
The mobile jaw was bolted to two rigidly connected precision
carriages (Ball Carriage R165181321, Bosch Rexroth AG, Germany)
running over a linear rail (Ball Rail R160583331, Bosch Rexroth AG,
Germany) fixed on the base plate. The friction coefficient between
carriages and rail was o0.003 [30]. From the carriage plate a
pulling cord ran over a low friction pulley (NSK 6202 bearings,
Brammer B.V., The Netherlands) down through the base plate
(Fig. 4c) to a mass holder (Fig. 5a).
Weights were gently applied to the pulling cord to close the
jaws and clamp the pulled block. Simultaneously, a release switch
on the bottom of the mass holder triggered a control box (Fig. 5) to
count-down a preset static loading time, after which the test run
was triggered electronically and a red sync-light was switched on
synchronically. A digital video camera (25 fps, 720 576 pixels)
was positioned close to the contact surface between the rubber on
the static jaw and the cables on the pulled block, with the synclight visible to the camera. This provided a macroscopic recording
of slip initiation with a visual indication of the start of the test run,
enabling synchronization of force data from the tensile tester with
the video recordings.
2.2. Calibration
The weights of the masses used in the tests were determined
using a calibrated compression force sensor (HBM U2, Hottinger
A.J. Loeve et al. / Wear 319 (2014) 27–37
31
Static jaw
Sample block
Mobile jaw
Sample
block
Pulley
Hook to
tensile
tester
Carriage
Sample
block
Base plate
Pulled block
Pulling cord
running
over pulley
Sample
block
Steel
cable
Pulled
block
Rubber
layer
Pulling force
Clamping
force
Sample
block
Mobile jaw
Steel cable
Pulled block
Rubber layer
Sample
block
Static jaw
Fig. 4. (a) Clamping module for friction tests at normal loads up to 1 kN. A pulled block is clamped between clamping blocks in the mobile and the static jaw during the tests.
(b) Close-up of a pulled block clamped between two clamping blocks. The jaws each hold a clamping block covered with a layer of rubber. The pulled block has both sides
covered with longitudinally aligned steel cables. (c) Pulling cord running from the carriages over the pulley, down through the base plate to a set of masses (see Fig. 5).
(d) Diagram of the clamping and pulling mechanism.
32
A.J. Loeve et al. / Wear 319 (2014) 27–37
1x7
1x19
Clampling module
SubStrand
Wire
7x7
Tensile tester
Moving table of
tensile tester
Control
box
Pulling
cord
Adapted
mouse
Ø 0.45 mm
Ø 0.27 mm
Ø 0.18 mm
Set of
masses Pallet
hand
truck
To force sensor
Digital video
camera
Ø 0.45 mm
Ø 0.45 mm
Fig. 6. Tested cable types. Cable structures are denoted as ‘# strands’ ‘# wires per
strand’ (e.g., 7 7 indicates a cable twined of seven strands twisted of seven wires
each) and shown above the cross sections. Tested cable sizes are shown below their
corresponding structures.
The three selected rubbers are widely available as expandable,
small-diameter, thin-walled tubing in various sizes: nitrile butadiene rubber (NIT), silicone rubber (SIL), and natural rubber (LAT).
Table 1 lists supplier information, hardness and surface free
energies of the tested rubbers. Tubes of 10 mm outer diameter
and 1.5 mm wall thickness were opened longitudinally and glued
as strips on the clamping blocks. All samples were oriented such
that the direction of sliding was the same as when used in the
FORGUIDE shaft [7]. Each rubber was tested with each of the five
types of cables, giving a total of 15 cable-rubber test combinations.
2.4. Test parameters
Moving table of
tensile tester
Control box
Sync light
Fig. 5. (a) Overview of the test setup. (b) Devices placed on the moving table of the
tensile tester.
Baldwin Messtechnik, Darmstadt, Germany). Friction losses in the
pulley and carriages were measured seven times by closing the
jaws (by 478 N weight, including the holder) with the compression
force sensor placed between the clamping blocks. The average loss
of applied weight due to friction was about 1% (mean 5.7 N,
standard deviation 1.2 N) for the entire clamping module.
2.3. Materials
Fig. 6 illustrates the cable structures and diameters tested. All
cables were AISI 316 stainless steel cables obtained from Carl Stahl
GmbH, Germany. For each of the five cable types a pulled block was
prepared by winding the steel cable tightly around the pulled block.
The roughness of the surface finish of the wires that form the (sub-)
strands was determined (using a Veeco Wyko NT3300 Optical
Profiler) to be a typical random sub-micrometer-scale surface roughness of highly polished surfaces. Because all the cables tested in this
study were made of the same material and produced similarly, any
effects of varying surface free energies on static friction can be
assumed to be due entirely to the rubbers used.
A pilot test of 240 runs was carried out to check for effects of
pulling speed, normal load and static loading time. Static friction
increased with pulling speed for all cable–rubber combinations.
Therefore, a low pulling speed of 0.5 mm/s was chosen to mimic an
unfavorable situation for the FORGUIDE shaft. When successive runs
were carried out without interruption on a single rubber sample,
friction increased rapidly with each run and stabilized after 40
repetitions at a value more than twice that of the first run. Keeping
an unloaded waiting time of 2 min between test runs was sufficient
to such avoid repetition effects. The effect of unintended spacing
between the rubber strips on the clamping blocks was checked using
a set of 3 3 cm2 samples with the rubber strips spaced 1 mm apart.
Even with this exaggerated rubber spacing (maximally 0.1–0.3 mm in
the samples) there was no significant effect on the measured static
friction. Although static friction has been reported to increase with
static loading time [15,31], increasing the static loading time from 3 s
to 30 s showed no significant effect on static friction in the pilot tests,
justifying a static loading time of 3 s in the main experiment.
The rubber surfaces were degreased with ethanol, rinsed with
water, and dried at room temperature for 24 h in the main
experiment. Before each test run the surfaces were gently
brushed [11]. The cable surfaces were brushed, rinsed with acetone and dried for at least 30 min. Each cable surface was dragged
over the tested rubber surface three times before commencing the
tests to remove any remaining acetone.
Lab temperature and relative humidity were logged throughout
the tests at 21.9 1C (standard deviation 0.4 1C) and 46.7% (standard
deviation 1.4%), respectively. All tests were conducted at 478 N
normal load, which corresponds to the load at 0.53 MPa locking
pressure in the FORGUIDE shaft.
2.5. Sample size & randomization
Based on sample size calculations (using Lehr's formula [32] for
90% power, two-sided significance level of 0.05 for unpaired
A.J. Loeve et al. / Wear 319 (2014) 27–37
33
Table 1
Tested rubbers. Property γ is the average surface free energy, with superscripts T, D and P indicating the total, dispersive and polar components, respectively, and the values
between brackets indicating the standard deviation. All surface free energy values are averages of 5 values. Each value was determined using the Owens/Wendt theory [30]
with up to 180 contact angles obtained with dynamic advancing contact angle measurements on a Krüss DSA100 Drop Analyser at 21( 7 1)oC with water and diiodomethane.
NIT
SIL
LAT
Rubber type
Measured hardness
Product at supplier
Supplier
γT [mJ/m2]
γD [mJ/m2]
γP [mJ/m2]
Nitrile butadiene
Silicone
Natural
65 Shore A
45 Shore A
40 Shore A
RSNI0710
Siliconen Rubber Slang 4
40 Shore A Saint Gobain GA
Het Rubberhuis, The Netherlands
Benetech, The Netherlands
Rubber B.V., The Netherlands
24.90 (2.92)
31.25 (3.95)
24.34 (1.93)
23.42 (2.31)
31.09 (3.82)
19.07 (2.21)
1.49 (0.80)
0.16 (0.19)
5.27 (1.37)
t-tests, and 0.15 as detectable difference in static friction coefficient, which was selected to target considerable improvement of
the FORGUIDE shaft rigidity [7]) each cable-rubber combination
was tested seven times. For the five cables to be tested, this
resulted in 35 test runs conducted in a pre-randomized order – to
minimize wear effects – in each rubber group.
2.6. Data analysis
Because the pulled block was clamped on two sides, the static
friction coefficient was calculated by dividing the pulling force at the
instance of slip initiation by twice the normal load. The instance of
slip initiation was determined from the force-displacement graphs by
assuming that until that instance the rubber surface deforms linearelastically under pure shear. Under this assumption, the instance of
slip initiation coincides with the moment that the forcedisplacement curve departs from the linear trend in the beginning
of the curve (Fig. 7). Therefore, for each repetition the first part of the
graph was fitted linearly using Matlabs‘s fit’ function. The instance of
slip initiation was taken as the displacement at which the linear
approximation line crosses the þ 1.96 standard deviation line. At that
point, the linear approximation of that repetition deviates significantly from the average, suggesting that the assumption of linearity
does no longer hold, which should indicate the initiation of macroscopic slip.
To validate the linearization method, the instance of macroscopic slip initiation was also obtained manually by a single
observer from the video recordings for all LAT test runs (i.e. the
rubber with the least linear behavior). The instance of macroscopic
slip initiation was found by zooming in on the steel cable–rubber
contact (Fig. 8), choosing a pair of prominent points (irregularities)
on the two surfaces and taking the instance that the two selected
points departed from each other as the instance of macroscopic
slip initiation. For each of the 35 test runs with LAT this was done
five times, each time for different prominent points, and averaged
for each test run over the five observations.
2.7. Statistics
All measurements were unpaired. Matlabs's ‘normplot’ function and Lilliefor’s test [33] were used to check whether all data
were normally distributed. Levene’s test [34] was used to check for
equal variances. A two-way ANOVA was used to check for
significant cable, rubber, and interaction effects (p ¼0.05) on the
mean coefficients of static friction. Individual one-way ANOVAs
and multiple comparison of means with Bonferroni correction
were used to investigate any underlying effects within sub-groups.
3. Results
The Ra roughness of the wire surfaces was within 0.07–0.16 μm
for all cables. Fig. 7a shows some typical test results of the cablerubber static friction measurements. Fig. 7b illustrates the method
used to find the instance of slip initiation. In Fig. 7c plus signs
indicate the instances of slip initiation determined by linearization
and circles indicate the instances of macroscopic slip initiation
determined manually from the captured videos. There was no
significant difference between the instances of slip initiation
determined by linearization and those determined manually from
the video footage, supporting the validity of the used methods.
All static friction coefficient data were distributed approximately normally and are provided as median and quartile distribution box plots in Fig. 9 and as mean (and standard deviation)
in Table 2 for all tested cable-rubber pairs. NIT and SIL data had
equal variances. The variances of the LAT data were equal in the
LAT group, but larger than the NIT and SIL variances. Yet, the
complete absence of overlap between the LAT group and the NIT
and SIL group made the significant difference between LAT and the
other groups obvious, and NIT and SIL were further compared
separately. Due to unknown cause the data of one test run for NIT
with the 7 7–0.45 mm cable were missing, resulting in a sample
size of 6 for that measurement.
The two-way ANOVA indicated that rubber, cable, and interaction effects were all significant, with effect sizes (η2) of 0.906,
0.009 and 0.024, respectively. LAT static friction coefficients were
significantly higher and up to about twice as high as those of NIT
and SIL for all cable types (Table 2). Overall, SIL static friction
coefficients were slightly but significantly lower than those of NIT.
In the LAT group, all cable effects were small but significant, both
when considered as a single factor and when cable size effects and
cable structure effects were considered separately (Fig. 9 indicates
p-values for two sub-groups in each rubber group: the leftmost
sub-group contains identically structured cables of different sizes,
indicating the cable size effect; the rightmost sub-group contains
identically sized cables of different structures, indicating the cable
structure effect). In the SIL group the cable effect did not reach
significance. In the NIT group there was a small but significant
overall cable effect, which proved to be due to cable structure.
4. Discussion
Static friction coefficients for friction pairs involving LAT were
much higher than for SIL or NIT, with static friction coefficients
slightly lower for SIL than for NIT. LAT and NIT showed a small but
significant cable effect, whereas SIL did not. For LAT static friction
increased with decreasing cable size and with increasing cable
structure complexity (toward the 7 7 structure). For NIT friction
decreased with increasing cable structure complexity.
4.1. Rubber effects
NIT showed slightly but significantly higher static friction than
SIL (Table 2), even though SIL is not only considerably softer than
NIT but also has higher surface free energy (Table 1), which at first
sight contradicts both Hypotheses 3 and 4 on rubber effects.
Additionally, the literature reports higher dynamic friction for SIL
than for NIT low loads [18,21,24,35]. Yet, the stainless steel cables
most likely have a surface layer of chromium trioxide, which is
highly polar, implying that adhesion should increase with the
polar surface free energy of the rubber. On reviewing the rubber
34
A.J. Loeve et al. / Wear 319 (2014) 27–37
Pull direction
NIT, SIL, and LAT on
1x7-0.45mm cables (N=7)
1000
Sample block
Force [N]
500
Rubber
Cables
Rubber
LAT
NIT
SIL
Cables
0
0
0.5
1
1.5
2
2.5
3
Displacement [mm]
5 mm
Sync
light
Pulled
block
+1.96 STD
Linearization of
repetition X
Mean
Departure of
linear behavior
of repetition X
Force
Macroscopic
slip initiation
of repetition X
Repetition X
-1.96 STD
1mm
Fig. 8. (a) Video stills showing contact between cables and rubber (clamping block
in the static jaw) and the red light indicating the measurement has started. (b–e)
Zoomed-in images used to determine instance of macroscopic slip initiation. Solid
and dotted circles indicate reference points on rubber and cables, respectively.
(b) No movement. (c) Movement without macroscopic slip. (d) Initiation of
macroscopic slip. (e) Gross slip. (For interpretation of the references to color in
this figure legend, the reader is referred to the web version of this article.)
surface free energies in detail (Table 1), the polar components did
agree with the trends of the static friction coefficients. In fact, the
effect of an increasing polar component of the rubber surface free
energy seems to exceed the effect of decreasing rubber hardness,
which may be why NIT showed higher static friction than SIL. LAT
showed up to about two times higher static friction than NIT or SIL,
which supports Hypotheses 3 and 4 as LAT is both the softest
rubber and the rubber with the highest polar surface free energy.
The much lower hardness of LAT compared to NIT should increase
the contact area [9,19]. Furthermore, the capstan effect, known
from ropes wrapped around a capstan, causes friction to increase
exponentially with the extent to which a rubber wraps around the
profile of a counter surface [36]. The capstan effect may have
amplified any static friction increase caused by increased indentation depth and real contact area for LAT compared to NIT.
Displacement
LAT on 1x7-0.45mm
cables (N=7)
500
Force [N]
4.2. Cable effects
Macroscopic slip
initiation from video
Macroscopic slip
initiation from linearization
0
0
0.5
1
1.5
Displacement [mm]
Fig. 7. Typical test results. (a) Force–displacement graphs for 1 7 structure 0.45 mm
diameter cable on NIT, SIL, and LAT. (b) Illustration of utilized method for finding the
instance of macroscopic slip initiation. Average, þ 1.96 and 1.96 standard deviation
lines were determined from the data set. A linear approximation line was placed on the
first part of each repetition. The displacement where the linear approximation line
crosses the þ 1.96 standard deviation line was taken as the instance of macroscopic slip
initiation. (c) Comparison of macroscopic slip initiation instances obtained from the
videos stills vs. from the linearization method.
The effect of the cable type tested significant for LAT and NIT
but the trends differed between both rubbers. On considering the
effects of size and structure as separate factors of the cable effect,
structure effect (rightmost sub-groups of cables in each rubber
group in Fig. 9) tested significant for both LAT and NIT but with
opposing trends. The size variation of the 1 7 structure cables
from 0.18 mm to 0.45 mm tripled the size of all macro-roughness
levels without changing any other properties of the surface profile.
Yet, this tripled macro-roughness size had a significant effect on
static friction for LAT only.
As all cable effects tested significant for LAT it seems at first
sight that static friction in LAT is affected by both the size of the
bumps at all macro-roughness levels and the number of distinct
macro-roughness levels. Because of its multi-strand structure, the
7 7–0.45 mm cable had similar large bumps as the single strand
1 7–0.45 mm cable but with down-scaled ‘copies’ of these
bumps distributed over the large bumps (self-affine fractal on
A.J. Loeve et al. / Wear 319 (2014) 27–37
p<0.05
35
p>0.05
p<0.05
0.6
Friction coefficient at slip [-]
0.5
0.4
p<0.05
p<0.05
*
0.3
p>0.05
0.2
p<0.05
p>0.05
p>0.05
0.1
NIT
SIL
7x7−0.45mm
1x19−0.45mm
1x7−0.45mm
1x7−0.27mm
1x7−0.18mm
7x7−0.45mm
1x19−0.45mm
1x7−0.45mm
1x7−0.27mm
1x7−0.18mm
7x7−0.45mm
1x19−0.45mm
1x7−0.45mm
1x7−0.27mm
1x7−0.18mm
0
LAT
Cable−Rubber combination
Fig. 9. Box plots of all results, showing the effect of the cable type on the static friction coefficient at the instance of macroscopic slip initiation. Data are grouped per rubber type. For
all cable-rubber pairs N¼7, except for the one marked with ‘*’, for which N¼ 6. The top, middle and bottom lines of each box represent the upper quartile, median, and lower quartile,
respectively. Whiskers represent the data range. Outliers are represented by a ‘þ ’. Triangles border the 95% confidence interval for the true median. If these intervals of two tests do not
overlap, there is strong evidence that their true medians are significantly different (po0.05). The p-values given at the top of each rubber group, indicate whether the cable type effect
was significant in that rubber group. The p-values below the dashed lines indicate whether there was an effect of the sub-group of cables grouped by the same dashed line. In each
rubber group, the leftmost and rightmost sub-groups of cables are used to test for effects of the cable size and the cable structure, respectively.
Table 2
Static friction coefficient means (and standard deviations) for the tested pairs of rubbers and cables. Sample size per pair is seven, except for the pair indicated with a
‘*’, which has a sample size of six. The significance of the cable effects are given in Fig. 9. The effect of the rubber type on static friction and the differences between the
static friction coefficients of the three rubber types were all statistically significant (po0.05).
Cable
Rubber
NIT
SIL
LAT
1 7–0.18 mm
1 7–0.27 mm
1 7–0.45 mm
1 19–0.45 mm
7 7–0.45 mm
0.30 (0.01)
0.27 (0.01)
0.50 (0.05)
0.30 (0.01)
0.27 (0.02)
0.52 (0.06)
0.31 (0.01)
0.26 (0.02)
0.44 (0.04)
0.29 (0.01)
0.25 (0.01)
0.48 (0.04)
0.27n (0.01)
0.27 (0.01)
0.53 (0.04)
two length scales [37]). The 1 19 structure resembled the 1 7
structure but with more and smaller bumps. The 7 7-structure
cable is likely to show a higher dynamic friction coefficient than
the other cables due to energy dissipation over a larger frequency
bandwidth [37]. However, for LAT, static friction with the 7 7–
0.45 mm cable did not differ significantly from the 1 7–0.18 mm
cable but did so from the 1 7–0.45 mm. Therefore, it is seems
that the higher friction of the 7 7–0.45 mm cable was not caused
by the addition of an extra macro-roughness level (Hypothesis 2)
or by large frequency bandwidth energy dissipation but by an
increased real contact area through the decreasing size of the
smallest present macro-roughness level (Hypothesis 1).
4.3. Interaction effects
As softer rubbers adapt more readily to finer counter surface
roughness, the difference between the directions of observed cable
structure effects on LAT (upward with increasing cable structure
complexity) and NIT (downward with increasing cable structure
complexity) may be caused by contact area differences. Any
capstan effect or increased adhesion due to bulk deformation
would amplify this difference in cable effects on LAT and NIT. For
LAT, due to decreasing size of the sub-strand level and wire-level
macro-roughness on 1 19 and 7 7 compared to 1 7 structure
cables, the rubber has a larger contact area to mold into. For the
36
A.J. Loeve et al. / Wear 319 (2014) 27–37
harder NIT, this same extra roughness on the 7 7 structure cables
may reduce contact if the small voids become too small for NIT to
mold into under the applied load [9,38].
The fact that no cable effects reached significance on SIL agrees
with friction data on human fingers on roughened metals [39]. These
data showed that friction of human skin—having mechanical properties similar to SIL [40–42] – is independent of counter surface
roughness for roughness430 μm. Evidently, Hypotheses 1 and
2 do not hold for SIL.
other designs where static friction between a rubber layer and
stainless steel cables is of interest. This expands design freedom
for, designers of medical instruments, for instance, allowing them
to base cable choices purely on such other criteria as dimensions
or flexural rigidity, without having to consider the effect on static
friction.
4.4. Limitations
Static friction coefficients for the earliest onset of macroscopic
sliding were about twice as high for LAT compared to NIT or SIL,
which is likely because LAT was the softest rubber tested and had
the highest polar surface free energy. Static friction coefficients
were slightly higher for NIT than for SIL for all cable types, which
may be due to the higher polar free energy of NIT compared to SIL
giving stronger bonding to the chromium trioxide layer on the
stainless steel cables. Overall, there were only minor effects of the
cable diameter or structure within the range of tested stainless
steel cables. Common friction theories were valuable in predicting
the effect of cable profiles and rubber properties on static friction
but clearly should not be applied without considering interaction
effects. For use in a FORGUIDE shaft, when it comes to static
friction LAT seems to be the rubber of choice for the expandable
tube. Generally, the results suggest that static friction can be
considered just a minor factor when selecting cables for practical
applications involving cable-rubber contacts.
Temperature effects were not investigated because of the low
variation of friction with temperature for rubbers well above their
glass transition temperature [11,43,44]. Air humidity can change
friction [45,46] but that effect was not investigated in this study.
Because of the pragmatic focus on off-the-shelf materials, only
a limited number cables and rubbers was tested. Consequently,
rubber hardness and surface free energy were not varied independently. These properties could be decoupled using lubricants
or surface treatments, which would provide better insight into
how hardness and surface free energy interact on static friction.
Additionally, due to the unavoidable geometric dependency, the
cable structure and the size of the smallest level of macroroughness were not tested independently. Testing each cable
structure for each tested cable size may solve this issue, but could
not be readily achieved because stainless steel cables at small
diameters were only available for limited cable structures. For
larger diameter cables, such tests may be easier to achieve.
It is common practice to derive the static friction coefficient from
the peak of the force–displacement graphs, assuming that friction
rises to a maximum just before sliding commences. Fig. 8 shows that
the values obtained from the applied linearization method fall well
below those peaks, which may raise questions on the validity of the
current approach. Camera observations at the contact edges used to
validate the linearization method revealed that macroscopic sliding
indeed commences well before the friction peak. These observations
agree with the results of Chateauminois and Fretigny [47] and of
Ciavarella, Hills and Moobola [48] showing that stress and deformation vary throughout the contact area with rough asperities under
shear loading. The applied linearization method apparently indicates
the earliest instance of macroscopic slip initiation, a safe measure of
static friction, as in the FORGUIDE mechanism, when even the
earliest slipping should be prevented.
The cables – and their sub-strands and wires – wound around
the pulled block may have had slightly differing orientations due
to the differing cable diameters and structures. Yet, these orientations should be irrelevant, since the adhesive friction component
barely depends on the sliding direction [49]. Loading the rubber
layer with a rigid block seemingly deviates from the situation in
the FORGUIDE shaft, where the load is applied through uniform
water pressure. However, the rubber thickness (1.5 mm) and the
wavelength of the largest scale roughness ( 0.5 mm) on the
cables are such that the cable–rubber contact should be nearly
identical to the uniform pressure situation [49]. Pressure distribution in cable–rubber contact may be influenced by tilting of the
clamping blocks and by the material of the clamping blocks when
the cables press deeply into the rubber. However, the close-up
video images did not show any of these effects. Furthermore, the
clamping module was dimensioned with high safety factors,
rendering even slight tilting of the clamping blocks unlikely.
4.5. Practical implications
The current results suggest that it does not really matter which
of the tested cable types is used in the FORGUIDE shaft design or in
5. Conclusion
Acknowledgments
The authors would like to thank Guus Liqui Lung for building
the control box, Erik van den Berg and Jorn Bakker for their help in
the design of the clamping module, and Marijke van der Velden,
Sjarifa Siregar, Patricia Baines and Robbert de Graaff for carrying
out pilot tests on friction between stainless steel cables and
springs. Thanks are also due to Jos van Driel for assisting on the
roughness measurements, to the workers of the fine mechanics
workshop of the Delft University of Technology, 3mE Faculty, for
their advice and for manufacturing the clamping module, to Ger
den Boer (Ridderflex B.V., Ridderkerk, The Netherlands), Jac Gofers
and Klaan Nienhuis (Promolding B.V., Den Haag, The Netherlands)
for the rubber hardness measurements, and to Bogdan Necula for
assisting with the contact angle measurements.
References
[1] J. Baillie, The endoscope, Gastrointest. Endosc. 65 (2007) 886–893.
[2] L. DeCarli, R. Zorron, A. Branco, F. Lima, M. Tang, S. Pioneer, I. Zanin, A. Schulte,
A. Bigolin, M. Gagner, Natural orifice translumenal endoscopic surgery
(NOTES) transvaginal cholecystectomy in a morbidly obese patient, Obes.
Surg. 18 (2008) 886–889.
[3] R.H. Hawes, D.W. Rattner, D. Fleischer, C.J. Gostout, A. Kalloo, M. Kochman,
M. Marohn, J. Ponsky, R. Rothstein, S. Schwaitzberg, C.D. Smith, L. Swanstrom,
M. Talamini, C.C. Thompson, NOTES(TM): where have we been and where are
we going? Gastrointest. Endosc. 67 (2008) 779–780.
[4] C. Palanivelu, P. Rajan, M. Rangarajan, R. Parthasarathi, P. Senthilnathan,
M. Prasad, Transvaginal endoscopic appendectomy in humans: a unique
approach to NOTES—world' first report, Surg. Edosc. 22 (2008) 1343–1347.
[5] S.P. Shih, S.V. Kantsevoy, A.N. Kalloo, P. Magno, S.A. Giday, C.W. Ko,
N.V. Isakovich, O. Meireles, E.J. Hanly, M.R. Marohn, Hybrid minimally invasive
surgery—a bridge between laparoscopic and translumenal surgery, Surg.
Endosc. 21 (2007) 1450–1453.
[6] L. Swanstrom, M. Whiteford, Y. Khajanchee, Developing essential tools to
enable transgastric surgery, Surg. Endosc. 22 (2007) 600–604.
[7] A.J. Loeve, D.H. Plettenburg, P. Breedveld, J. Dankelman, Endoscope shaftrigidity control mechanism: Forguide, IEEE Trans. Biomed. Eng. 59 (2012)
542–551.
[8] H. Nolle, R.S.H. Richardson, Static friction coefficients for mechanical and
structural joints, Wear 28 (1974) 1–13.
[9] E.L. Deladi, Static friction in rubber–metal contacts with application to rubber
pad forming processes, Enschede (2006) 171.
A.J. Loeve et al. / Wear 319 (2014) 27–37
[10] E.L. Deladi, M.B. de Rooij, D.J. Schipper, Modelling of static friction in rubber–
metal contact, Tribol. Int. 40 (2007) 588–594.
[11] M. Barquins, A.D. Roberts, Rubber friction variation with rate and temperature:
some new observations, J. Phys. D: Appl. Phys. 19 (1986) 17.
[12] G. Shirong, The friction coefficients between the steel rope and polymer lining
in frictional hoisting, Wear 152 (1992) 21–29.
[13] G.M. Bartenev, A.I. Elkin, The friction of polymers at the initial stage of sliding
in various temperature ranges, Wear 11 (1968) 393–403.
[14] L. Caravia, D. Dowson, J. Fisher, Start up and steady state friction of thin
polyurethane layers, Wear 160 (1993) 191–197.
[15] J. Kingston, A. Muhr, I. Stephens, The effects of surface texture on natural
rubber/metal friction at high pressures, Plast Rubber Co. 32 (2003) 431–438.
[16] R. Lewis, C. Menardi, A. Yoxall, J. Langley, Finger friction: Grip and opening
packaging, Wear 263 (2007) 1124–1132.
[17] J.M. Degrange, M. Thomine, P. Kapsa, J.M. Pelletier, L. Chazeau, G. Vigier,
G. Dudragne, L. Guerbe, Influence of viscoelasticity on the tribological
behaviour of carbon black filled nitrile rubber (NBR) for lip seal application,
Wear 259 (2005) 684–692.
[18] D.F. Denny, The influence of load and surface roughness on the friction of
rubber-like materials, Proc. Phys. Soc. B 66 (1953) 7.
[19] K.L. Johnson, K. Kendall, A.D. Roberts, Surface energy and the contact of elastic
solids, Proc. R. Soc. London A Mater. 324 (1971) 301–313.
[20] B.N.J. Persson, O. Albohr, U. Tartaglino, A.I. Volokitin, E. Tosatti, On the nature
of surface roughness with application to contact mechanics, sealing, rubber
friction and adhesion, J. Phys-Condens. Mater. 17 (2005) R1–R62.
[21] A. Schallamach, The load dependence of rubber friction, Proc. Phys. Soc. B 65
(1952) 657–661.
[22] D. Tabor, Surface forces and surface interactions, J. Colloid Interface Sci. 58
(1977) 2–13.
[23] K.L. Johnson, J.A. Greenwood, An adhesion map for the contact of elastic
spheres, J Colloid Interface Sci. 192 (1997) 326–333.
[24] K. Maeda, A. Bismarck, B. Briscoe, Effect of bulk deformation on rubber
adhesion, Wear 263 (2007) 1016–1022.
[25] D.K. Owens, R.C. Wendt, Estimation of the surface free energy of polymers,
J. Appl. Polym. Sci. 13 (1969) 1741–1747.
[26] G.M. Bartenev, V.V. Lavrent’ev, V.S. Voevodskii, Friction properties of highly
elastic materials at high contact pressures, Mech. Compos. Mater. 7 (1971)
115–120.
[27] M.A. Jiménez, J.M. Bielsa, R. Rodríguez, S. Dobón, The influence of contact
pressure on the dynamic friction coefficient in cylindrical rubber–metal
contact geometries, IUTAM Symp. Comput. Methods Contact Mech. (2007)
257–275.
[28] R. Brown, Friction and Wear. Physical Testing of Rubber, Springer, Boston, MA,
USA (2006) 387, ISBN 978-0-387-29012-6.
37
[29] D.I. James, W.G. Newell, A new concept in friction testing, Polym. Test. 1 (1980)
9–25.
[30] A.G. Bosch Rexroth, Kugelschienenführungen—Katalog, Schweinfurt, 2004.
[31] E.P. Chan, J.M. Karp, R.S. Langer, A self-pinning adhesive based on responsive
surface wrinkles, J. Polym. Sci. B: Polym. Phys. 49 (2011) 40–44.
[32] R. Lehr, Sixteen S-squared over D-squared: a relation for crude sample size
estimates, Stat. Med. 11 (1992) 1099–1102.
[33] H.W. Lilliefors, On the Kolmogorov–Smirnov test for normality with mean and
variance unknown, J. Am. Stat. Assoc. 62 (1967) 399–402.
[34] A.S. Petrie, Caroline, Medical Statistics at a Glance, 2nd Ed., Blackwell Publishing Ltd, Oxford, UK, 2005.
[35] A.D. Roberts, S.A. Jackson, Sliding friction of rubber, Nature 257 (1975)
118–120.
[36] P. Gabriel, A.G. Thomas, J.J.C. Busfield, Influence of interface geometry on
rubber friction, Wear 268 (2010) 747–750.
[37] B.N.J. Persson, Theory of rubber friction and contact mechanics, J. Chem. Phys.
115 (2001) 3840–3861.
[38] M. Modifi, B. Prakash, Influence of counterface topography on sliding friction
and wear of some elastomers under dry sliding conditions, Proc. Inst. Mech.
Eng. J.–J. Eng. 222 (2008) 667–673.
[39] S.E. Tomlinson, R. Lewis, M.J. Carré, The effect of normal force and roughness
on friction in human finger contact, Wear 267 (2009) 1311–1318.
[40] S.A. Johnson, D.M. Gorman, M.J. Adams, B.J. Briscoe, The friction and lubrication of human stratum corneum, Tribol. S. 25 (1993) 663–672.
[41] C. Pailler-Mattéi, H. Zahouani, Study of adhesion forces and mechanical
properties of human skin in vivo, J. Adhes. Sci. Technol. 18 (2004) 1739–1758.
[42] M.A. Meyers, P.Y. Chen, A.Y.M. Lin, Y. Seki, Biological materials: structure and
mechanical properties, Progress Mat. Sci. 53 (2008) 1–206.
[43] D. Fritzson, Friction of elastomer composites: influence of surface temperature, sliding speed and pressure, Wear 139 (1990) 17–32.
[44] S. Derler, F. Kausch, R. Huber, Analysis of factors influencing the friction
coefficients of shoe sole materials, Saf. Sci. 46 (2008) 822–832.
[45] X. Tian, B. Bhushan, The micro-meniscus effect of a thin liquid film on the
static friction of rough surface contact, J. Phys. D: Appl. Phys. 29 (1996)
163–178.
[46] B. Bhushan, Modern Tribology Handbook, CRC Press LLC, Boca Raton, FL, USA,
2001. ISBN 978-0-8493-7787-7.
[47] A. Chateauminois, C. Fretigny, Local friction at a sliding interface between an
elastomer and a rigid spherical probe, Eur. Phys. J. E 27 (2008) 221–227.
[48] M. Ciavarella, D.A. Hills, R. Moobola, Analysis of plane and rough contacts,
subject to a shearing force, Int. J. Mech. Sci. 41 (1999) 107–120.
[49] G. Carbone, B. Lorenz, B.N.J. Persson, A. Wohlers, Contact mechanics and
rubber friction for randomly rough surfaces with anisotropic statistical
properties, Eur. Phys. J. E 29 (2009) 275–284.