MATERIALES DE CONSTRUCCIÓN
Vol. 64, Issue 315, July–September 2014, e030
ISSN-L: 0465-2746
http://dx.doi.org/10.3989/mc.2014.03913
Static and kinetic friction coefficients of Scots pine
(Pinus sylvestris L.), parallel and perpendicular to grain direction
J.R. Airaa*, F. Arriagaa, G. Íñiguez-Gonzáleza, J. Crespob
a. Universidad Politécnica de Madrid. (Madrid, Spain)
b. Universidad de Santiago de Compostela (Santiago de Compostela, Spain)
*joseramonaira@gmail.com
Received 30 May 2013
Accepted 7 November 2013
Available on line 25 July 2014
SUMMARY: In this study the static (μe) and kinetic (μd) coefficients of friction were obtained for Pinus
sylvestis L. sawn timber of Spanish origin. Friction between transverse surfaces sliding perpendicular to the
grain (tangential direction) and radial surfaces sliding parallel to the grain was analyzed. A specifically designed
device was used for tests, which makes it possible to apply contact pressure and measure displacements and
applied loads simultaneously. Coefficients of friction between transverse surfaces (μe = 0,24; μd = 0,17) were
about twice of the coefficients of friction between radial surfaces (μe = 0,12; μd = 0,08). Furthermore, these values
are located within normal values of those commonly reported for softwood. The results are considered preliminary due to the small number of specimens.
KEYWORDS: Friction; Wood; Physical properties
Citation / Citar como: Aira, J.R.; Arriaga, F.; Íñiguez-González, G.; Crespo, J. (2014). Static and kinetic friction
coefficients of Scots pine (Pinus sylvestris L.), parallel and perpendicular to grain direction. Mater. Construcc. 64
[315], e030 http://dx.doi.org/10.3989/mc.2014.03913.
RESUMEN: Coeficientes de rozamiento estático y dinámico en la madera de pino silvestre (Pinus sylvestris L.),
según las direcciones paralela y perpendicular a la fibra. En este estudio se determinaron los coeficientes de
rozamiento, estático (μe) y dinámico (μd), en madera aserrada de Pinus sylvestris L. de procedencia española,
diferenciando si se produce el contacto entre secciones de corte transversal con deslizamiento en dirección perpendicular a la fibra (en dirección tangencial), o entre secciones de corte radial con deslizamiento paralelo a la
fibra. Para la realización de los ensayos se ha utilizado un dispositivo, diseñado específicamente, que posibilita
la aplicación de una presión de contacto y la medición del desplazamiento y de la fuerza aplicada de manera
simultánea, permitiendo la obtención de los coeficientes de rozamiento estático y dinámico. Los coeficientes de
rozamiento obtenidos entre secciones transversales (μe = 0.24; μd = 0.17) fueron del orden del doble de los coeficientes de rozamiento entre secciones radiales (μe = 0.12; μd = 0.08). Además, estos valores se encuentran dentro
de los valores que aparecen habitualmente en la bibliografía para madera de coníferas. Debido al escaso tamaño
de la muestra los resultados se consideran preliminares.
PALABRAS CLAVE: Rozamiento; Madera; Propiedades físicas
Copyright: © 2014 CSIC. This is an open-access article distributed under the terms of the Creative Commons
Attribution-Non Commercial (by-nc) Spain 3.0 License.
1. INTRODUCTION
In traditional or carpentry joints, forces are transmitted from one piece to the other through contact
surfaces. These forces lead to normal and tangential
stresses between surfaces, and the friction forces
that oppose sliding between the elements forming
the joint. Knowledge of friction or friction forces
is important to correctly analyze the mechanical
behavior of traditional joints of wooden structures,
2 • J.R. Aira et al.
and it is commonly used in finite element simulation of timber joints (1–4).
Friction is a force that opposes the sliding or rolling motion of bodies when they are in contact at
one of their surfaces. The origin of friction forces is
due to roughness or surface irregularities present in
most bodies, while molecular attraction between the
contact surfaces may cause microwelding that must
be broken to start sliding, figure 1.
Surfaces have more protuberances when they are
rougher. These protuberances keep elements in contact and determine the actual area in contact. When
the pressure between contact surfaces increases, the
actual area in contact increases as protuberances are
deformed when they are crushed.
A body with a weight P which is resting on a horizontal surface is considered, Figure 2. By applying a
force F parallel to the surface that does not change
the rest position of the body, forces F and P give the
resultant force F1. The equilibrium of forces occurs
when force F1 is balanced by force F2. If force F2
is decomposed into its vertical and horizontal components, two forces are obtained: N, which is the
reaction or force that a horizontal plane exerts on
the body due to its own weight, and R which is the
force that opposes the motion of the body or friction
force.
Figure 3 shows the friction force R depending on
the applied force F.
As the applied force, F, is increased from point 0
to point A, the static friction force, Re, is increased in
the same module until a time when the body is about
to slide. That time corresponds to maximum static
friction, and its value is obtained by the expression:
Re max = μe·N, where μe is the static friction coefficient. If the applied force, F, remains equal to Re max,
point B, the body starts moving with an acceleration
of: a = (Re max −Rd)/m, where m is the mass of the
body. If the applied force, F, is increased, point D,
the net force on the body increases as does acceleration of the body. At point C, the applied force, F,
is equal to the kinetic friction force, Rd, so that the
net force on the body is zero and it moves with a
constant velocity. At point E, the applied force, F,
drops to zero so that the force acting on the body
FIGURE 1.
is - Rd, the acceleration is negative and the velocity
decreases until the body stops.
Therefore, once the body is in motion for any
value of the applied force, F, the kinetic friction force
is always: Rd = μd·N. If the applied force, F, is equal
to Rd, the body moves with constant velocity and no
inertial forces oppose the motion. If the force F is
greater than Rd, the movement will be accelerated,
while it will decelerate if it is lower (5).
For any two surfaces in contact, the static friction
coefficient is usually higher than the kinetic friction
coefficient (μe > μd).
Friction coefficients for wood depend primarily
on moisture content and surface roughness, which
is in turn determined by, among other factors,
anatomical properties, hardness and machining
characteristics. In species without a high content of
elements on their surface which favour the sliding,
such as oily or waxy exudations, coefficients do not
vary much from one species to another (6).
Friction coefficients increase with moisture
content, up to the point of fiber saturation. After
that moment, values remain constant until there is
a substantial amount of free water on the surface,
causing reduction again. Moreover, kinetic friction
depends on the sliding velocity, so that at moisture
contents of less than 20%, the kinetic friction coefficient varies little with the sliding velocity, while at
high moisture contents kinetic friction decreases relevantly with increasing velocity (6).
Wood is considered to be an orthotropic material, and each principal plane of wood has a different
degree of roughness, so friction coefficients depend
on the surfaces which are in contact. In general the
friction between two pieces of wood can be studied
for each cut surface corresponding to material symmetry planes: transverse surfaces (cut perpendicular
to the grain) and two cut surfaces parallel to the grain
(radial and tangential). Within each plane, sliding can
be studied in two perpendicular directions (radial and
tangential for the transverse surfaces, and parallel and
perpendicular to the grain for parallel surfaces). It is
also possible to combine two different cut surfaces, so
the possibilities multiply. For this reason, the study of
friction will be particularized for each situation.
Roughness between contact surfaces.
Materiales de Construcción 64 (315), July–September 2014, e030. ISSN-L: 0465-2746. doi: http://dx.doi.org/10.3989/mc.2014.03913
Static and kinetic friction coefficients of Scots pine (Pinus sylvestris L.), parallel and perpendicular to grain direction • 3
TABLE 1.
Timber friction coefficients (8 y 9)
Friction coefficients
Material
Static (μe)
Kinetic (μd)
Timber-Timber
0.25–0.50
0.20
Waxed timber-Wet snow
0.14
0.10
Waxed timber-Dry snow
–
0.04
parallel to the grain
0.62
0.48
perpendicular to the grain
0.54
0.34
parallel-perpendicular
0.43
0.19
Timber-Stone
0.38
<0.7
Timber-Concrete
0.62
–
Timber-Brick
0.60
–
Oak-Oak
FIGURE 2.
Force balance in a resting body.
Moreover, the cuts made along surfaces parallel
to the grain (radial and tangential) give rise to a
slight orientation of the roughness on the cut plane.
This effect is commonly called “with the woodgrain
and against the woodgrain”, which also influences
friction values.
In research works carried out with products
derived from wood, Laminated Strand Lumber
(LSL) and Laminated Veneer Lumber (LVL), the
existence of a relationship between the values of the
friction coefficients and contact pressure was determined, so that friction coefficients decrease nonlinearly with increasing contact pressure (7).
The usual kinetic friction coefficient values for
wood are said in the scientific literature to vary from
0.3 to 0.5 for dry and smooth wood against hard
smooth surfaces, 0.5 to 0.7 for intermediate moisture content and 0.7 to 0.9 for near fiber saturation
(6). Other values reported in the literature are shown
in table 1.
Design values of static friction coefficients between softwood and between softwood and concrete are indicated in the UNE-EN 1995-2 standard
(10), for the design of stress-laminated deck plates,
table 2.
Currently there is no European standardized test
method for determining friction coefficient. The
American standard ASTM G115-10 (11) specifies
general methodology. In recent years some research
has been conducted in Spain, leading to a proposed
testing methodology. The friction between transverse surfaces (sliding perpendicular to the grain) in
glued laminated timber specimens of Picea abies L.
Karst with a moisture content of 12% was analyzed,
obtaining a static coefficient of 0.47 and a kinetic
coefficient of 0.31 (12). Glued laminated timber specimens of the same species with a moisture content of
10% were also tested to obtain the friction between
dovetail joint flanks, resulting in a static coefficient
of 0.42 and a kinetic coefficient of 0.27 (2).
In this work, as will be explained in the next section, friction coefficients necessary to study halved
and tabled timber scarf joints are obtained. The
static and kinetic friction coefficients of Scots pine
sawn timber (Pinus sylvestris L.) of Spanish origin
are determined, differentiating if contact occurs
between transverse surfaces sliding perpendicular
to the grain (tangential direction), or radial surfaces
sliding parallel to the grain.
TABLE 2.
Design values for the static friction
coefficient μe (10)
Perpendicular
to the grain
Parallel
to the grain
Moisture content (%)
FIGURE 3.
Graphical representation of the friction force R
according to the applied force F.
Material
≤12
≥16
≤12
≥16
Sawn timber-Sawn timber
0.30
0.45
0.23
0.35
Planed timber-Planed timber
0.20
0.40
0.17
0.30
Sawn timber-Planed timber
0.30
0.45
0.23
0.35
Timber-Concrete
0.40
0.40
0.40
0.40
Note: For moisture content values between 12 and 16% can be
interpolated linearly.
Materiales de Construcción 64 (315), July–September 2014, e030. ISSN-L: 0465-2746. doi: http://dx.doi.org/10.3989/mc.2014.03913
4 • J.R. Aira et al.
2. MATERIAL AND METHODS
To determine the friction coefficients a specific
device is used. It is was designed and manufactured
specifically for this purpose, and it is located in the
laboratory of the Platform for Structural Timber
Engineering (PEMADE) of the University of
Santiago de Compostela (USC), Figure 4.
The test specimens are placed in two plates called
specimen-brackets, one upper and one lower. After
placing the specimens into the specimen-bracket
plates, six weights are coupled together so that surface
normal force, N, is known previously. The weights
exert a total force of 2435.3 N.
The lower specimen-bracket is mobile and receives
an external load through a braided steel 3 mm diameter cable which is fixed to the piston that exerts the
load. The device does not register the load, but only
records the vertical displacement of the piston.
The upper specimen-bracket is coupled to a
bending beam load cell which restricts its horizontal displacement and records the load applied in
the said direction. This load cell has a high nominal sensitivity (2 mv/v) and a loading capacity of
5441.1 N. The rear of the specimen-bracket contains
a threaded 10 mm diameter rod which is inserted
through a hole into the load cell. Finally, a nut
located at the end of the rod is tightened to achieve
perfect adjustment.
FIGURE 4.
The weights are placed directly on the upper
specimen-bracket descending vertically by two steel
guides. Contact is made by two Teflon plates, one
affixed to the bottom of the weights-bracket and the
other affixed to the top of the specimen-bracket.
The upper specimen is positioned at a distance
of approximately 1 cm recessed relative to the lower
specimen to eliminate noise caused by friction between the edges of the specimens when starting
movement, Figure 5.
The test is performed with constant velocity of
piston displacement to prevent the onset of inertial
forces during the sliding between specimens. Thus
the value of kinetic friction coefficient, μd, can be
obtained graphically in a simple manner, since the
modulus of friction force Rd and the modulus of
applied load, F, are equal. By observing Figure 3, the
testing methodology follows the steps below: 0–A,
A–B and B–C. Figure 6 shows schematically the
working of the friction device, together with the balance of forces involved.
A computer connected to the piston and the load
cell records the displacement values and friction
force at all times, while simultaneously calculating
the friction coefficients.
The lower specimen-bracket is subjected to the
friction between the wood specimens, Rmm, at the
top, and friction with the specimen-bracket lubricated steel rails on which slides, Raa, at the bottom.
Device for friction testing.
Materiales de Construcción 64 (315), July–September 2014, e030. ISSN-L: 0465-2746. doi: http://dx.doi.org/10.3989/mc.2014.03913
Static and kinetic friction coefficients of Scots pine (Pinus sylvestris L.), parallel and perpendicular to grain direction • 5
FIGURE 5.
Relative position of friction specimens.
FIGURE 6.
Scheme of the friction test device.
The upper specimen-bracket is subjected to friction between the Teflon plates, Rtt, at the top, and
the friction between the wood specimens, Rmm, at
the bottom. The friction coefficents verify the following relationship: Rmm >> Raa > Rtt. Applying
the external load, F, the upper specimen-bracket
remains in equilibrium due to the friction forces
that oppose movement (Rmm and Raa) verifying
that: F = Rmm + Raa. In turn, load F is transmitted
to the upper specimen-bracket through the friction
between the wood specimens (Rmm). The transmitted load is recorded by the load cell, Rr, verifying the following balance: F = Rr + Rtt. By equalizing
the two equations, the friction between the wood
specimens is obtained: Rmm = Rr + Rtt − Raa, where
Rr is the recording load cell and Rtt − Raa has an
experimental value of − 0.08671·N. The software is
calibrated so that friction between other elements of
the device will not affect the results, i.e. the friction
force between wood specimens is directly calculated
by the equation: Rmm = Rr − 0.08671·N. This calibration is the same for all test series.
The test is performed at a constant speed of
8 mm/min and is interrupted when the kinetic friction coefficient remains constant during piston displacement of 30 mm.
Materiales de Construcción 64 (315), July–September 2014, e030. ISSN-L: 0465-2746. doi: http://dx.doi.org/10.3989/mc.2014.03913
6 • J.R. Aira et al.
This research work is part of a larger project
studying a type of traditional timber joint called the
halved and tabled scarf joint. Figure 7 shows the
contact surfaces of this carpentry joint. For this reason, friction coefficients between transverse surfaces
sliding perpendicular to the grain (tangential direction) and between radial surfaces sliding parallel to
the grain are obtained.
The friction specimens must have the same roughness between contact surfaces as the joint which is
being analyzed. Therefore, wood specimens were
obtained using the same band saw to cut the joint.
The test material consists of Pinus sylvestris L.
wood from the “Valsaín sawmill” (Segovia). 5 test
specimens were cut and consecutively numbered to
obtain the friction coefficients between transverse
surfaces, and 5 other specimens to obtain the friction coefficients between radial surfaces. Each specimen is composed of two parts, upper and lower.
The specimens’ dimensions are the following:
to obtain its mass before drying (m1), after which
the sample is dried in an oven at a temperature of
(103 ± 2) °C until the mass difference between two
successive weighings at an interval of 2 hours is less
than 0.1%, and finally the sample is weighed again to
obtain the anhydrous mass (m0). The sample moisture content expressed as a percentage of the mass is
given by the equation: w = ((m1 − m0) / m0)·100.
-
- Static region
-
Contact between transverse surfaces: 2 pieces
of 48 × 148 × 20 mm.
Contact between radial surfaces: 2 pieces of
48 × 150 × 20 mm.
The friction specimens are obtained from other
larger samples designed for the study of halved
and tabled traditional timber scarf joints. These
specimens are conditioned according to the guidelines of the UNE-EN 408 standard (13), i.e. in a
camera with a controlled atmosphere at a temperature of (20 ± 2) °C and air relative humidity
of (65 ± 5)%. Under these conditions, the equilibrium moisture content of most softwood species is
approximately 12%.
Once specimens are conditioned, the moisture
content and density are determined according to the
guidelines of the UNE-EN 408 standard, by cutting a sample according to the UNE-EN 13183-1
standard (14). The sample is measured and weighed
FIGURE 7.
3. RESULTS AND DISCUSSION
3.1. Friction between transverse surfaces
(perpendicular to the grain plane and in the
tangential sliding direction)
To assess the variation of the friction coefficient
during the test, a graph is made showing the friction coefficient on the ordinate axis and the piston
displacement in mm on the abscissa axis, Figure 8.
Two regions are clearly distinguished in Figure 8:
During the initial phase, the applied load
increases linearly to maintain a constant speed of
piston displacement. At this stage, the static friction
force, Re, is at all times equal to the applied external
load, F.
As was pointed out above, the maximum value
of Re corresponds to the upper peak of Figure 8.
At this point, the static friction coefficient is determined by the equation: μe = Re/N, and it is obtained
directly since Re and N are known.
Figure 8 also shows that the maximum value of
Re occurs approximately when the piston has moved
from 2.5 to 5 mm, depending on the test specimen.
This displacement is due to deformation of the steel
cable, and also, although theoretically contact surfaces should not slip against each other, to slight sliding in the static region due to the breakage process of
microwelding between surfaces, and perhaps due to
some shear deformation in both parts of the specimen.
Contact surfaces at the halved and tabled traditional timber scarf joint.
Materiales de Construcción 64 (315), July–September 2014, e030. ISSN-L: 0465-2746. doi: http://dx.doi.org/10.3989/mc.2014.03913
Static and kinetic friction coefficients of Scots pine (Pinus sylvestris L.), parallel and perpendicular to grain direction • 7
FIGURE 8.
Graph of friction coefficients between transverse surfaces.
- Kinetic region
From the upper peak, the friction coefficient
declines sharply to stabilize and becomes nearly
horizontal.
The friction coefficient is considered to be stable
with piston displacement of 15 mm, so that the
kinetic friction coefficient μd is determined as the
average value in the range 15–30 mm.
The friction coefficients obtained are shown in
table 3.
The friction coefficients between transverse surfaces sliding perpendicular to the grain are at the
lower limits of those reported in the scientific literature consulted for general wood. Scots pine wood
and most softwoods have a high resin content that
favors sliding between surfaces. However, the values
reported in the literature do not usually differentiate
between softwood or hardwood, between specific
surfaces which are in contact or the direction of sliding. When the value of the static friction coefficient
obtained (0.24) is compared with the value given
in table 2 for softwood sliding perpendicular to the
grain (0.20), it is within usual values. The coefficient of variation, although slightly higher, is within
normal values for wood.
3.2. Friction between radial surfaces (sliding
direction parallel to the grain)
To assess friction coefficient variation during the
test, a graph was made in the way described for the
test between transverse surfaces, Figure 9.
As was the case in the previous test, the static
and kinetic regions can be clearly distinguished,
Figure 9. It should be noted that the values of specimen 3 are not considered in subsequent calculations
due to the fact that its initial behaviour differs from
that of the other specimens, making it impossible to
differentiate between the static and kinetic friction
coefficients. However, this specimen did not show
any differentiating anatomical feature.
TABLE 3. Friction coefficients between transverse surfaces
Specimen
Density (kg/m3)
Moisture content (%)
μe
μd
1
482
11.84
0.26
0.18
2
464
11.90
0.38
0.25
3
466
11.98
0.18
0.13
4
540
11.67
0.18
0.16
5
483
11.51
0.19
0.14
Averages
487
11.78
CV
6.35%
1.61%
0.24
0.17
36.19%
27.70%
Materiales de Construcción 64 (315), July–September 2014, e030. ISSN-L: 0465-2746. doi: http://dx.doi.org/10.3989/mc.2014.03913
8 • J.R. Aira et al.
Moreover, specimens 4 and 5 show a behaviour
in sawtooth shape and the friction values are slightly
higher than they are for the other specimens. This is
due to excess surface resin which still maintains its
adhesive properties.
Figure 9 also shows that the maximum value of
Re occurs when the piston has moved from approximately 1 to 2.5 mm, a shorter displacement than in
the previous test.
The friction coefficients obtained are shown in
table 4.
The value of the static friction coefficient
obtained (0.12) is lower than the value given in
table 2 for softwood sliding parallel to the grain
(0.17). The difference lies within the expected variability for different species of softwood, and it is
also a consequence of the different test methods
used, supporting the need to standardize this test
methodology.
FIGURE 9.
The coefficient of variation is slightly higher than
in the previous test. This may be due to the fact that
the fibers are cut longitudinally in radial surfaces,
resulting in a less homogeneous surface in terms
of roughness than is the case in transverse surfaces
where the fibers are cut transversally. In this respect
the influence of “woodgrain” should be noted. All
tests were carried out “against the woodgrain”, since
in the initial test no friction was recorded when the
tests were made “with the woodgrain”. Additionally,
the difference between the angles of the “woodgrain”
for each of the parts in contact leads to a greater
spread of the results.
On the other hand, friction coefficients between
transverse surfaces are approximately twice those
between radial surfaces. However, it should be noted
that number of specimens is small in both tests, and
it would be desirable to use a larger sample size in
future works.
Graph of friction coefficients between radial surfaces.
TABLE 4. Friction coefficients between radial surfaces
Specimen
Density (kg/m3)
Moisture content (%)
μe
μd
1
486
11.64
0.05
0.03
2
452
11.87
0.11
0.08
3
465
12.25
–
–
4
550
11.51
0.18
0.12
5
477
11.37
0.12
0.09
Averages
486
11.73
CV
7.82%
2.94%
0.12
0.08
46.29%
46.77%
Materiales de Construcción 64 (315), July–September 2014, e030. ISSN-L: 0465-2746. doi: http://dx.doi.org/10.3989/mc.2014.03913
Static and kinetic friction coefficients of Scots pine (Pinus sylvestris L.), parallel and perpendicular to grain direction • 9
4. CONCLUSIONS
The test device designed to determine friction
coefficient provides an easy way to obtain static
and kinetic friction coefficients. This method is
considered to be appropriate as a possible standard
methodology.
Due to the small sample size these results are preliminary. They may not be considered final until tests
are conducted with a larger number of specimens.
The friction coefficients between transverse surfaces sliding perpendicular to the grain are about
twice the friction coefficients between radial surfaces
sliding parallel to the grain. The values obtained are
among the usual values reported in the scientific literature for softwood.
The effect known as “woodgrain” significantly
affects the friction between surfaces cut parallel to
grain direction, so that when the sliding direction
between contact surfaces is “with the woodgrain”
the friction is negligible.
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Materiales de Construcción 64 (315), July–September 2014, e030. ISSN-L: 0465-2746. doi: http://dx.doi.org/10.3989/mc.2014.03913