Proceedings of the Institution of Mechanical
Engineers, Part H: Journal of Engineering in
Medicine
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Development and experimental validation of a mathematical model for friction between fabrics and a
volar forearm phantom
A M Cottenden, D J Cottenden, S Karavokiros and W K R Wong
Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 2008 222: 1097
DOI: 10.1243/09544119JEIM406
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1097
Development and experimental validation of a
mathematical model for friction between fabrics
and a volar forearm phantom
A M Cottenden1, D J Cottenden1*, S Karavokiros1, and W K R Wong2
1
Department of Medical Physics and Bioengineering, University College London, UK
2
SCA Hygiene Products AB, Gothenburg, Sweden
The manuscript was received on 8 February 2008 and was accepted after revision for publication on 9 April 2008.
DOI: 10.1243/09544119JEIM406
Abstract: An analytical mathematical model for friction between a fabric strip and the volar
forearm has been developed and validated experimentally. The model generalizes the common
assumption of a cylindrical arm to any convex prism, and makes predictions for pressure and
tension based on Amontons’ law. This includes a relationship between the coefficient of static
friction (m) and forces on either end of a fabric strip in contact with part of the surface of the
arm and perpendicular to its axis. Coefficients of friction were determined from experiments
between arm phantoms of circular and elliptical cross-section (made from Plaster of Paris
covered in Neoprene) and a nonwoven fabric. As predicted by the model, all values of m calculated from experimental results agreed within ¡8 per cent, and showed very little systematic variation with the deadweight, geometry, or arc of contact used. With an appropriate
choice of coordinates the relationship predicted by this model for forces on either end of a fabric strip reduces to the prediction from the common model for circular arms. This helps to
explain the surprisingly accurate values of m obtained by applying the cylindrical model to experimental data on real arms.
Keywords:
1
skin, friction, mathematical model, experimental validation
INTRODUCTION AND BACKGROUND
Wearers of incontinence pads often experience skin
damage, soreness, and discomfort in the diaper area
[1, 2]. When skin is occluded by (wet) pad materials,
the skin becomes over-hydrated, thereby compromising its barrier function and making it susceptible
to abrasion damage by friction against the pad and
vulnerable to chemical irritation and bacterial colonization [3–5].
In an earlier paper [6], the present authors described the development and validation of a new method for determining the coefficient of friction between
volar forearm skin (a commonly used surrogate for
diaper area skin) and nonwoven materials of the
*Corresponding author: Department of Medical Physics and
Bioengineering, University College London, Archway Campus
Clerkenwell Building, Highgate Hill, London N19 5LW, UK.
email: d.cottenden@ucl.ac.uk
JEIM406 F IMechE 2008
kind used to face incontinence pads. The apparatus
(see Fig. 1) and the experimental procedure are described in detail in the earlier paper [6] but, in essence, the strip of nonwoven fabric under test is
dragged across the volar forearm using a tensometer.
A weight (mass m) is attached to the free vertical end
of the fabric and the tensometer force F is plotted
against displacement. Following the example of
Gwosdow et al. [7], the maximum force (Fmax) on
the plot is taken to be that needed to overcome static
friction and the coefficient of friction is calculated
using
2
Fmax
m~ ln
ð1Þ
p
mg
Equation (1) assumes the arm to be a rigid cylinder
and the nonwoven fabric to be inextensible (as in
Fig. 1).
In spite of these highly unrealistic assumptions,
coefficients of friction measured using the authors’
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1098
A M Cottenden, D J Cottenden, S Karavokiros, and W K R Wong
Fig. 2 A diagram of the arm. It is assumed that the
arm is a prism over the length considered. The
major variables and functions are illustrated
2
MATHEMATICAL MODEL
The new mathematical model characterizes the
system in terms of the following quantities, many
of which are illustrated in Fig. 2:
Fig. 1
The set-up used by the authors in an earlier
paper [6]: (a) shows the equipment in use,
while (b) shows the assumed geometry, where
the circle represents a cross-section of the arm
new method [6] agreed remarkably well with values
measured using a mathematically simpler but experimentally more difficult method in which fabric
samples were dragged over regions of the volar forearm that could be well approximated as flat. Measurements were made on the wet and dry volar
forearms of five young women using three different
nonwoven materials. The correlation coefficient for
the two methods was 0.95.
The purpose of the work described in the current paper was to extend the mathematical model
to address convex prisms of arbitrary cross-section
and to explain why the earlier model produced such
accurate values for coefficients of friction in spite of
its obviously unrealistic assumptions.
(a) the shape of the arm immediately before initial
slippage, described in terms of a polar function
R(h) around an arbitrary coordinate centre
within the arm: as shown in Fig. 2, first contact
between the vertical hanging fabric and the arm
is taken as h 5 0 and the loss of contact near the
tensometer is taken as h 5 H;
(b) the tension in the fabric at an angle of h, T(h):
from Fig. 2 it follows that T(0) 5 mg and T(H) is
the tension in the fabric between the tensometer and the arm;
(c) the element of normal reaction force from the
arm at an angle h, denoted dN;
(d) the element of angle through which the arm surface turns when h R h + dh, denoted dx (Fig. 3).
2.1
Assumptions
The present model makes certain assumptions on
both the arm geometry and the physical mechanisms at play. A diagram of the geometry (including
relevant variables) is shown in Fig. 2.
The assumptions are as follows.
1. The arm is a strictly convex prism at the instant of
slip. It is assumed that contact between the fabric
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Mathematical model for friction between fabrics
1099
tangent of the angle between that function’s graph
and the x axis, and considering Fig. 3 it follows that
dR
dx~dh{d tan{1
dl
1 dR
~dh{d tan{1
RðhÞ dh
ð3Þ
Fig. 3
The angular change on the arm surface for a
change of dh in coordinates. The tangential are
length l is defined as R(h)dh
and the skin is maintained all around the curve
r 5 R(h);h g [0,H].
2. Amontons’ law is obeyed. The friction force at the
instant of slip locally obeys Amontons’ law,
Ff 5 mN, where Ff is the friction force, N is the
normal force, and m is the coefficient of static
friction. m is assumed not to vary with N. m is also
assumed not to vary intrinsically with fabric
tension.
3. Total slip occurs when each location is at its local
maximum loading. Neither real arms nor real
fabrics are inextensible. As deformation and
stretching will occur, this will act anomalously
to load the arm over some of the arc of contact
and to unload other parts, in turn meaning that
some locations will reach the limit of the shear
they can support before others. Local slip or creep
will occur in these regions. This assumption
implies that local creep will simply act to remove
regions of anomalous loading without causing
general slip. This ensures that it is locally true that
dF f 5 mdN when general slip occurs. If the
coefficient of dynamic friction were equal to the
static coefficient, then the system would certainly
behave this way.
It should be noted that it is not necessary to
assume that the arm does not deform as it is loaded,
nor is it assumed that the fabric does not stretch.
The sole condition on arm deformation is that
whatever occurs does not cause any concavity.
2.2
At the point of slippage all forces are in equilibrium.
In particular
ð2Þ
at h. The derivative of a function is equal to the
JEIM406 F IMechE 2008
ð4Þ
where the last equality in equation (3) follows by
identifying a tangential arc length l with R(h)dh.
Substituting this result into equation (2) produces
d
1 dR
tan{1
dN ~T ðhÞdh 1{
dh
RðhÞ dh
ð5Þ
By assumption, at the point of slippage dFf 5 mdN.
Further, it is clear that the tension T(h) comprises the
deadweight mg and the total frictional force accrued
between the fabric and arm up to the angle h, i.e.
T ðhÞ~mgzFf ðhÞ
ð6Þ
? dT ~dFf
where Ff(h) is the integral of dFf between 0 and h.
Combining equations (5) and (6) and Amontons’
law, a closed equation for the system can be written
dT
d
1 dR
{1
~T ðhÞdh 1{
tan
m
dh
RðhÞ dh
ð7Þ
This can easily be solved by separation of variables
to give
T ðhÞ~T ð0Þexp mh{m tan
{1
1 dR
RðhÞ dh
h !
ð8Þ
0
hence
!
1 dR H
{1
T ðHÞ~mg exp mH{m tan
RðhÞ dh 0
ð9Þ
by applying the boundary conditions mentioned at
the start of this section.
A solution
dN ~T ðhÞdx
d
1 dR
{1
tan
dx~dh 1{
dh
RðhÞ dh
2.3
Choice of coordinate centre
As equation (9) will be the most regularly used the
free choice of coordinate centres will be used to
simplify it. If the coordinate centre is chosen to be
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1100
A M Cottenden, D J Cottenden, S Karavokiros, and W K R Wong
d [arc length]2 5 (Rdh)2 + dR2, hence
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
dR2
dh
d ½arc length~ RðhÞ2 z
dh
1
dN
P ðhÞ~ h
i1=2
dh
2
2
w RðhÞ zR0 ðhÞ
ð12Þ
From equation (6) and Amontons’ law it follows that
dT 5 mdN at the point of slip, hence
Fig. 4
the point of intersection of perpendicular bisectors
to tangents to R(h) at h 5 0, h 5 H (see Fig. 4) then by
definition
dR dR
~
~0
dh 0 dh H
Substituting this result into equation (9) greatly
simplifies it by making both the upper and lower
limits of the integral in the exponent vanish
T ðHÞ~mg expðmHÞ
ð10Þ
This is identical with the expression connecting T(H)
and mg on a cylinder [7]. It is frequently more useful
to rearrange this equation to give m in terms of the
other variables
m~
2.4
dN 1 dT
~
dh
m dh
If the centre of coordinates is taken as the
intersection of the perpendicular bisectors to
the tangents to the arm at h 5 0, H then the
relationship between the forces on either end of
the fabric strip simplifies significantly
1
T ðH Þ
ln
H
mg
2
2
0
2
3
00
6RðhÞ z2R ðhÞ {RðhÞR ðhÞ7
P ðhÞ~4
h
i3=2 5T ðhÞ
2
2
0
w RðhÞ zR ðhÞ
ð13Þ
immediately before slip occurs. It is important to
recall that if this expression is used for general values
of h then the complete form of T(h) (equation (8))
must also be used: the simplified version (equation
(10)) applies only to h 5 0 or h 5 H.
3
3.1
EXPERIMENTAL VALIDATION
Materials
The mathematical model was investigated experimentally using two model arms made from Plaster of
ð11Þ
Pressure
If the normal force is known at any point around the
surface of the arm then the pressure can be
calculated. If the width of the fabric strip is w and
the pressure P
P ðhÞ~
1
dN
w d½arc length
The arc length of the arm can be determined easily
by considering Pythagoras’ theorem
Fig. 5 Model arms were constructed from Plaster of
Paris wrapped around with Neoprene. The join
in the Neoprene was avoided in all experiments
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JEIM406 F IMechE 2008
Mathematical model for friction between fabrics
Fig. 8
Fig. 6
An optical micrograph of the test fabric used in
all experiments
Paris covered with a layer (1 mm thick) of Neoprene
(Fig. 5). One arm was circular (diameter, 66 mm) and
the other elliptical (major and minor axes, 67 and
45 mm). It was not the intention to imitate accurately the shape or mechanical properties of real
arms or the friction behaviour of real skin. Rather the
need was for prisms of well-defined cross-section
that could be made easily.
All friction experiments were conducted with
strips of a spunlaid, thermal-calendered polypropylene material with area density 17 g/m2 and fibre
diameter 30 mm (see Fig. 6), denoted fabric A in
the earlier study [6]. Strips were 30 mm wide and
450 mm long.
3.2
Method
With the cylindrical arm, experiments were run for
starting arc of contact H0 5 63.5u, 76u, 90u, 111.5u,
131.5u (see Fig. 8 later). Similarly, a range of H0
values were used with the elliptical prism arm
(H0 5 70u, 80u, 90u, 105u, 120u) with the major axis
at 0u, 90u, and 135u to the horizontal (Fig. 7). All
experiments were run with masses m 5 10 g, 30 g,
1101
The angle of contact, H approaches p/2 as the
displacement of the cross-head increases
50 g, and 70 g (Fig. 2) and there were five repeats for
each mass, for each of three fabric test pieces for the
cylindrical arms and two test pieces for the elliptical
prism. The tensometer (Model MTT170, Dia-Stron,
USA) cross-head speed was 150 mm/min. In each
experiment the tensometer force F was plotted
against cross-head displacement, and the first maximum in the graph – corresponding to initial
slippage between the fabric and the arm – was used
to calculate the coefficient of static friction.
For H 5 p/2 the calculation is simple because
F 5 T(H) and H does not change with cross-head
displacement. For H ? p/2 two corrections have to
be made.
1. Cross-head displacement. As the cross-head
moves away from the arm the angle of contact
changes (shown in Fig. 8): H decreases with crosshead displacement for H0 . p/2, and increases for
H0 , p/2. By application of trigonometry, and
taking the cross-head displacement DL to be large
compared to the distance l (Fig. 8)
Q~tan
{1
l0 tan Q0
l0 zDL
where Q and Q0 are defined in Fig. 8. As Q 5 p/2 –
H and Q0 5 p/2 – H0
p
l0 tan½ðp=2Þ{H0 H~ {tan{1
2
l0 zDL
Fig. 7 Orientations for elliptical prism arms
JEIM406 F IMechE 2008
ð14Þ
For the test configuration, l0 5 100 mm and
DL ( 3 mm which corresponds to angular shifts
of less than 1u for all experiments. As these
corrections would cause an error in m calculations
of less than 1 per cent they are neglected in
presenting the results.
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1102
A M Cottenden, D J Cottenden, S Karavokiros, and W K R Wong
Fig. 9
Example graphs of F against displacement: (a) corresponds to m 5 70 g and H 5 90u; (b)
corresponds to m 5 30 g and H 5 63.5u. The oscillations are thought to be attributable to
repeated stick and slip between the fabric and the Neoprene
2. Resolution of F. If H ? p/2 then T(H) ? F. Rather, by
resolving forces, F 5 T(H)cosQ 5 T(H)sinH. Equations (10) and (11) can therefore be rewritten as
F
~mg expðmHÞ
sinH
ð15Þ
1
F
mðF,m,HÞ~ ln
H
mg sinH
ð16Þ
The maximum force (Fmax) on the plot of force
against displacement was used to calculate the
coefficient of static friction using equation (16).
3.3
Results
Example plots of F against displacement are shown
in Fig. 9 for experiments on the cylindrical arm. The
plot for H0 5 90u averages to a horizontal line, while
that for H0 5 63.5u increases with displacement, as
expected from equation (15).
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JEIM406 F IMechE 2008
Mathematical model for friction between fabrics
Fig. 10
Example graphs of ln(T(H)/mg) against H for the cylindrical arm (a) and each
orientation of the elliptical prism (b)–(d). The four point and line styles correspond to
the four different applied weights in newtons. For (a) 0.57 , m , 0.66, 0.96 , R2 , 0.98; for
(b) 0.52 , m , 0.60, 0.91 , R2 , 0.96; for (c) 0.61 , m , 0.62, 0.94 , R2 , 0.98; for (d)
0.56 , m , 0.64, 0.93 , R2 , 0.98
Plots of ln(T(H)/mg) against H are given for
an example data set for the cylindrical arm (Fig.
10(a)) and each orientation of the elliptical prism
(Figs 10(b) to (d)). The gradient in each case is m
(from equation (10)). In all, 36 m values were
obtained by linear regression: 0.91 , R2 , 0.99 for
35 (R2 5 0.78 for the other fit; it was not clear why
this correlation was weaker). As predicted by the
model, the graphs in Fig. 11 show little systematic
variation of m with m. There was some variation of m
between data sets (¡8 per cent), but no more than
could be explained by variablity between samples of
the Neoprene and the fabric.
4
1103
DISCUSSION
The mathematical model predicts that m should
be invariant with H, with m, and with the crosssectional shape of the model arm (subject to a
JEIM406 F IMechE 2008
careful choice of coordinate centre) provided it is
convex across the whole area of nominal contact with
the fabric. This has now been experimentally confirmed. The agreement between model and experiments implies that, at least for the majority of the
pressure range involved here, Amontons’ law holds
to a good approximation.
The agreement with Amontons’ law can be further
elucidated by considering Fig. 11, which shows a
steady increase in m with m for each sample data
set, in contradiction with the model. However, the
increase is small compared to the scatter in the data,
and moreover represents a variation in m of less than
5 per cent across the experimental mass range. This
is likely a result of changes in the interacting
Neoprene and nonwoven surfaces as the pressure
increases, and corresponds to a small departure
from Amontons’ law.
The oscillatory stick–slip behaviour seen in Fig. 9 is
caused by the inability of the smaller dynamic friction
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1104
A M Cottenden, D J Cottenden, S Karavokiros, and W K R Wong
Fig. 11
Graphs showing the variation of m with mass corresponding to the graphs in Fig. 10. m is
calculated for all {F, H, m} groups and all are plotted against m. The horizontal lines
denote the mean of all m, and the mean m for each mass is shown as a large square.
Letters (a)–(d) correspond to those in Fig. 10
force to maintain the deformation caused by the static
friction force at the point of slip. As the ‘yield force’
(and so surface deformation before slip occurs) is
proportional to the normal force, the magnitude of the
stick–slip oscillation would be expected to increase
with m, as was indeed observed.
Inspection of Fig. 10 shows that the spread of data
from experiments with different masses is of the
same order as the spread of data from replicates of
experiments with the same mass, leading to variations in m of ¡8 per cent for each configuration. This
is very similar to the spread of m values between
configurations. This degree of variation is consistent
with the likely variations of material properties,
within a given sample and between samples.
These results also provide the opportunity to
address some related issues.
4.1
Robustness of the m values
In practice, it is simplest to conduct experiments
with H 5 90u as F 5 T(H) and H0 5 H for all displacements. Given that it is difficult to fix H exactly in
experiments on real arms, it is important to establish
how sensative the m value derived from an experiment is to inaccuracies in H.
If the coefficient of friction calculated on the basis
of measured values of F and m, and an (inaccurately)
~, and the difference
assumed H 5 p/2 is denoted m
~ and the true m (calculated using the
between m
correct H 5 p/2 + DH) is denoted D~
m then the fractional error is
D~
m mðF,m,ðp=2ÞÞ{mðF,m,ðp=2ÞzDHÞ
~
~
m
mðF,m,ðp=2ÞzDHÞ
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Mathematical model for friction between fabrics
1105
From equation (16) it follows that to first order in DH
D~
m
LH mðF,m,p=2Þ
~{DH
?
~
m
mðF,m,p=2Þ
D~
m
fmðF,m,ðp=2ÞÞ=p=2g{f1=½p=2 tanðp=2Þg
~DH
~
m
mðF,m,ðp=2ÞÞ
D~
m 2DH
~
~
m
p
ð17Þ
as 1/tan(p/2) 5 0. This means that if an error less
than 5 per cent were required, then the angular
deviation would have to be less than 4.5u. In practice,
a 4.5u deviation from horizontal is easy to detect by
eye: the potential error introduced by inaccurate
angle measurement is small, making the method
suitable for routine and frequent use.
4.2
Variation of pressure with h
It is worth considering pressure and shear stress sf
(owing to friction) around the arc of contact. As
dFf ~mdN
~
?
sf : ~
m
dN
w d½arc length
1
dFf
w d½arc length
?
sf ~mP
where the last step used equation (13), and w is the
width of the fabric strip. In this context, discussing
pressure is equivalent to discussing shear stress.
In Fig. 12 calculated pressure is plotted against h
for each of the three ellipse orientions used in these
experiments. It is interesting and important to note
that for each orientation (w) the pressure at h 5 0 is
the same for high m (1.3) and low m (0.3), that is P(0)
depends only on arm geometry and applied weight
(Fig. 2). Equation (13) makes it clear that P(h) is
determined by the product of a geometrical prefactor and the local tension. Equation (9) shows that
ln T(h) 5 mg(h): a low m leads to a slow increase in T,
while a larger m causes rapid increase (compare parts
(a) and (b) in Fig. 12). This increase is significantly
modulated by the geometry for low m values, even
causing an almost uniform pressure for the ellipse
with a horizontal major axis. However, for large m, P
increases very rapidly with h so that local pressure at
h 5 p/2 is 5–10 times larger than the initial pressure.
This result underlines the potential for serious skin
damage to occur if wet incontinence pads are
removed carelessly. For example, if a wet pad is
JEIM406 F IMechE 2008
Fig. 12 Graphs of pressure against h (calculated using
equation (13)) at two values of m for ellipses of
the dimensions used in these experiments. The
three lines correspond to the three orientatations used, described by the angle w of the major
axis to the horizontal (Fig. 7). The two values of
m correspond to typical values between a nonwoven and wet skin (m 5 1.3, part (a)), and a
non-woven and dry skin (m 5 0.3, part (b)),
found by the authors in a previous in vivo study
of volar forearm skin [6]
pulled from beneath a supine user such that it is in
contact with an arc of the buttocks, the skin near
where the pad loses contact will experience shear
stresses far higher than the average values. The
situation will be still worse than suggested by this
model, as the normal pressure is not only caused by
the force in the pad, but is supplemented by the
patient’s weight.
ACKNOWLEDGEMENTS
The authors acknowledge with thanks SCA Hygiene
Products AB, the Engineering and Physical Sciences
Research Council, and the General Hospital of
Rhodes who funded the work.
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A M Cottenden, D J Cottenden, S Karavokiros, and W K R Wong
REFERENCES
1 Schnelle, J. F., Cruise, P. A., Alessi, C. A., Samarrai,
N. A., and Ouslander, J. G. Individualised nighttime
incontinence care in nursing home residents. Nursing Res., 1998, 47(4), 197–204.
2 Brown, D. S. Diapers and underpads. Part 1: skin
integrity outcomes. Ostomy Wound Mgmnt, 1994,
40, 20–22, 24–6, 28.
3 Lyder, C. H., Clemes-Lowrance, C., Davis, A., Sullivan, L., and Zucker, A. Structured skin care regimen to prevent perineal dermatitis in the elderly. J.
Enterostomal Therapy Nursing, 1992, 19(1), 12–16.
4 Berg, R. W. Etiology and pathophysiology of diaper
dermatitis. Adv. Dermatology, 1988, 3, 75–98.
5 Ersser, S. J., Getliffe, K., Voegeli, D., and Regan, S. A
critical review of the inter-relationship between skin
vulnerability and urinary incontinence and related
nursing intervention. Int. J. Nursing Stud., 2005, 42,
823–835.
6 Cottenden, A. M., Wong, W. K. R., Cottenden, D. J.,
and Farbrot, A. Development and validation of a new
method for measuring friction between skin and
nonwoven materials. Proc. IMechE, Part H: J. Engineering in Medicine, 2008, 222(H5), 791–803.
7 Gwosdow, A. R., Stevens, J. C., Berglund, L. G., and
Stolwijk, J. A. J. Skin friction and fabric sensation in
neutral and warm environments. Textile Res. J., 1986,
56, 574–580.
DL
m
N
P
R(h)
T(h)
w
h
H
DH
H0
l
APPENDIX
m
Notation
F
Ff
Fmax
g
g(h)
h
l
l0
L
experimentally measured force
applied to the nonwoven
frictional force at a location
experimentally measured force
required to initiate slippage
gravitational field strength
an unknown function of h
vertical distance between the point
of loss of contact between the
nonwoven and the arm phantom,
and the tensometer cross-head
arc length around the surface of the
arm phantom
initial distance between the point of
last contact between the nonwoven
and arm phantom, and the cross-head
distance at slippage between the
point of last contact between the
,
m
,
Dm
sf
Q
Q0
x
nonwoven and arm phantom, and
the cross-head
distance moved by the tensometer
cross-head to cause slippage
mass of the dead weight hung on the
nonwoven
normal force exerted by the arm
phantom
pressure of the nonwoven against the
arm phantom
radius of the arm (from an arbitrary
coordinate centre) at the angle h
tension in the nonwoven at the
angle h
width of the nonwoven strip
angle (measured from an arbitrary
coordinate centre) from the point of
first contact between nonwoven and
arm phantom
value of h at which the nonwoven
parts from the arm phantom
difference between the assumed
value of H and the actual value
value of H at which an experiment
was set up
distance between the initial loss of
contact between the nonwoven and
arm phantom and the final one
coefficient of static friction between
the nonwoven test material and the
arm phantom
value of m calculated owing to an
incorrect estimation of H
difference between the true value of
m and the value calculated owing to
an incorrect estimation of H
frictional shear stress at the interface
between the nonwoven and arm
phantom
angle of depression or elevation of
the fabric strip from horizontal at the
point of slippage
initial angle of depression or
elevation of the fabric strip from
horizontal
angle by which the surface of the arm
phantom has changed between one
location and another
Proc. IMechE Vol. 222 Part H: J. Engineering in Medicine
Downloaded from pih.sagepub.com at SWETS WISE ONLINE CONTENT on November 21, 2011
JEIM406 F IMechE 2008