Master's Thesis in Structural Engineering
Friction of wood on steel
Authors: Radek Koubek, Karolina Dedicova
Surpervisor LNU: Michael Dorn, Erik Serrano
Examiner, LNU: Johan Vessby
Course Code: 4BY05E
Semester: Spring 2014, 15 credits
Linnaeus University, Faculty of Technology
I
Abstract
This thesis deals with the experimental description of friction between steel
and wood materials, specifically laminated veneer lumber (LVL) and pine
wood with two types of annual rings. It studies the influence of a number of
different parameters on the coefficient of friction such as contact pressure,
moisture content, fiber orientation in relation to the load direction, steel
surface roughness, and horizontal load rate. First, the theoretical mechanical
and physical properties as well as the coefficient of friction itself are
described. This is followed by the description of the test setup including the
test method and how the obtained data is exported, handled and processed
and how the coefficient of friction is determined.
The results study the influence of different parameters and show that the
coefficients of friction for the smooth sliding plate tests vary in between 0.1
and 0.3, whereas tests with the rough sliding plate vary around 0.7.
Factors influencing the coefficient of friction were found to be the different
moisture content under all tested pressures, the different fiber direction
under low contact pressure, the contact pressure itself, though under higher
pressures the influence was found to be low, and the horizontal load rate
under low pressures. The outcomes are further discussed in the discussion
chapter.
Key words: Friction, wood, steel, moisture, coefficient of friction, contact
pressure, LVL, laminated veneer lumber, pine, fiber direction
II
Acknowledgement
We would like to thank the supervisors of our thesis Michael Dorn and Erik
Serrano for providing us with time, guidance and assistance during the
conduction of the experiments and for contributing with valuable
information, comments and advice during analysis of the data and the actual
writing process. Furthermore we would like to thank to the personnel of the
laboratory of Linnaeus University for providing us with the necessary
equipment and machinery.
III
Table of contents
1. INTRODUCTION............................................................................................ 1
1.1 BACKGROUND ...................................................................................................................... 1
1.2 PURPOSE AND AIM ................................................................................................................ 2
1.3 HYPOTHESIS AND LIMITATIONS ............................................................................................ 2
1.4 RELIABILITY, VALIDITY AND OBJECTIVITY ........................................................................... 3
1.5 LITERATURE REVIEW ............................................................................................................ 4
1.5.1 History of friction determination.................................................................................. 4
1.5.2 Research on friction between wood and steel .............................................................. 5
1.5.3 Wood friction characteristics during exposure to high pressure ................................. 5
2. THEORY .......................................................................................................... 8
2.1 MECHANICAL PROPERTIES OF WOOD..................................................................................... 8
2.1.1 Strength and stiffness of wood...................................................................................... 8
2.1.2 Compression parallel to the fiber direction ................................................................. 8
2.1.3 Compression perpendicular to the fiber direction ....................................................... 9
2.1.4 Compression stresses at an angle to the grain ............................................................. 9
2.1.5 Orthotropic elasticity ................................................................................................. 10
2.1.6 Stress at an angle to the grain - Hankinson's formula ............................................... 11
2.2 PHYSICAL PROPERTIES OF WOOD ........................................................................................ 12
2.2.1 Moisture and wood..................................................................................................... 12
2.2.2 Density ....................................................................................................................... 13
2.2.3 Shrinkage and swelling .............................................................................................. 14
2.3 DESCRIPTION OF FRICTION AND THE COEFFICIENT OF FRICTION .......................................... 14
3. METHOD ....................................................................................................... 17
3.1 MATERIALS ..................................................................................................................... 17
3.2 SPECIMEN PREPARATION AND PHYSICAL PROPERTIES ...................................... 19
3.3 EXPERIMENTAL PART .................................................................................................. 24
3.3.1 Test procedure............................................................................................................ 20
3.3.2 Methodology of experiments ...................................................................................... 22
3.4 ANALYTICAL PART....................................................................................................... 24
4. RESULTS ....................................................................................................... 25
4.1 OBTAINING THE COEFFICIENT OF FRICTION OF A SINGLE SPECIMEN .................................... 25
4.2 STATISTICAL EVALUATION OF A SINGLE TEST SERIES .......................................................... 28
4.3 STATISTICAL EVALUATION FOR VARYING CONTACT PRESSURE ........................................... 28
5. ANALYSIS ..................................................................................................... 29
5.1 VARIATION OF CONTACT PRESSURE .................................................................................... 29
5.2 VARIATION OF MOISTURE CONTENT .................................................................................... 31
5.3 VARIATION OF FIBER DIRECTION ......................................................................................... 33
5.4 VARIATION OF ROUGHNESS OF THE STEEL SLIDING SURFACE .............................................. 35
5.5 VARIATION OF LOAD RATE .................................................................................................. 36
6. DISCUSSION ................................................................................................. 38
7. CONCLUSIONS ............................................................................................ 39
REFERENCES ................................................................................................... 40
APPENDICES .................................................................................................... 42
IV
1. Introduction
Friction is everywhere where there is contact between two surfaces of
materials. Depending on the amount of friction, it plays an important role in
determining the behavior of the materials in contact. In timber applications,
contact between wood and steel appears nearly in every construction, mostly
in connections.
A commonly used connection is the dowel-type steel-to-timber joint in
structural timber engineering. Joints are often considered as the weaker part
of the structure. Therefore estimating the load-bearing capacity and stiffness
of the connection should be done in an accurate and reliable manner
(Dorn, 2012). Previous researches on the influence of friction between wood
and steel in connections has proved that using different values of the
coefficient of friction can give a significant difference in the final results
(Sjödin et al. 2008; Dorn, 2012).
Nowadays, Eurocode 5 (EC5) is used for designing timber constructions.
EC5 does not include the coefficient of friction as a parameter in the
designing. Friction, of course, exists and should be applied during the
designing process, but the coefficient of friction changes depending on
various parameters. But also the properties of wood widely vary from one
tree to another and from sawn wood to engineered wood products, which
again affect frictional properties.
Whether and how the coefficient of friction changes in dependence on
different parameters can bring very important knowledge for timber design.
1.1 Background
Broadly speaking, the current calculations and literature for timber
constructions provide relatively poor information about the coefficient of
friction and its values are seldom precisely determined. For contact between
wood and a steel surface, coefficients of friction between 0 and 1 (and
above) are commonly found in literature (American Forest & Paper
Association, 1997; Residential structural design guide, 2010), but the values
given are seldom rationalized. In general, frictional resistance to slipping of
connection members is conservatively ignored in design equations, although
in some cases coefficient of friction is taken into account (American Forest
& Paper Association, 1997).
Friction is usually not accounted for in wood connection design because the
amount of frictional force is difficult to predict and in many instances may
not exist, if a wood member shrinks or a connection relaxes. (American
Forest & Paper Association, 1997). The effect of friction between wood and
steel is supposed to be dependent on a variety of parameters such as surface
1
texture, roughness, wood density, moisture content, applied pressure,
orientation of annual rings in respect to the sliding plane and the direction of
sliding, etc. (Sjödin et al., 2008) show, in their experimental and numerical
study of effect of friction in single dowel joints, how the coefficient of
friction is changing by using different surfaces of dowels. From the work of
(Sjödin et al., 2008) it is obvious, that there, in some cases, can be a
substantial effect of friction that could be taken into account in calculations.
Nevertheless, the current version of Eurocode 5, does not explicitly involve
friction in design as a parameter.
1.2 Purpose and Aim
The purpose of this thesis is laying down a range of coefficients of friction
for different situations involving pine wood and laminated veneer lumber
(LVL) coming into contact with steel. For obtaining results it is also
necessary to design the experiments including the MTS machine used in
order to obtain reliable data and being able to evaluate the coefficients of
friction.
The aim of this work can be split into three sub-goals:
1) Carry out experiments on two wooden materials with different
combinations of selected parameters (moisture content, surface of the
steel sliding plane, applied pressure, orientation of annual rings and load
rate).
2) Calculate the coefficient of friction for different types of wood species
and combinations of parameters.
3) Generate data from the measurements (forces) and evaluate the data.
1.3 Hypothesis and Limitations
Hypotheses
1) The machine setup and the way the specimens are mounted will provide
data that makes it possible to obtain the necessary information regarding
differences between e.g. wood species and different steel surfaces.
2) There is a correlation between all the studied parameters – contact
pressures, fiber directions, moisture contents of pine wood and LVL
materials - and the coefficient of friction measured.
2
Limitations and assumptions
In regard to the hypotheses above, there are several limitations and
assumptions that have to be considered in this work. For instance:
1) There is only one machine setup.
2) A limited amount of tests for each parameter variation can be conducted
3) There is no possibility to measure roughness of the used materials.
4) Some mechanical properties are taken from literature.
1.4 Reliability, validity and objectivity
The experiments have been performed using a MTS Frame machine 322,
which has high reliability in functions provided by a hydraulic system. The
load cells and actuators of the machine are designed for laboratory testing of
materials and every test is controlled by a computer. The setup of the MTS
Frame machine 322 has been done by professional employees of Linnaeus
University laboratory.
During preparation of the experiments, there was an effort to obtain as much
numerical data as possible. Stress was put also on the selection of specimen
and their preparation. All specimens were cut by professional personnel of
Linnaeus University Växjö, measured by appropriate tools and marked and
placed in a climate chamber with constant temperature and moisture content.
All measured values were noted to excel files.
The specimens are made from two materials (pine wood and LVL) and they
have approximately the same dimensions (30 x 30 x 10 mm3). Each
specimen dimensions has been measured before the actual testing using a
digital sliding gauge and all data are noted in an Excel document.
For each combination of parameters used in this work, five repetitions have
usually been made. All data has been recorded by the machine computer and
afterwards evaluated with help of suitable software (Matlab, Excel).
All the above described procedures aimed at minimizing variability and
assuring the methodology used was objective.
3
1.5 Literature review
This section addresses previous research relating to measuring coefficients
of friction and its dependency on various parameters. It includes a short
history of determination and establishment of friction in a general way and
later research about friction between wood and steel.
1.5.1 History of friction determination
Looking back into history, (Jost, P., 1966) found that huge financial losses
were occurring as a result of wear, friction and corrosion. The ancients as far
back as Paleolithic times understood the need to control these forces. Also
drawings from ancient Egypt, 2400 years BC, show that lowering friction by
using grease in transporting heavy statues and building the pyramids
facilitated the works.
However, defining friction as an actual science started 500 years ago.
(Beek, A., 1995) describes that the first deep study of friction was conducted
in the 15th century by Leonardo Da Vinci (1452-1518) who realized that it
is important to take friction into account, while he was designing his
machines (Figure 1.1). He stated two basic laws of friction - “1st the size of
the areas in contact has no effect on friction and 2nd if the load of an object is
doubled, the frictional force will also be doubled”. Also other scientists who
were concerned with the definition of friction, observing its values and its
dependency on various parameters; the most famous are Guillaume
Amontos (1663-1705) whose work was based on the theory of friction as a
result of roughness of two surfaces and he rediscovered the basic laws of
friction of Da Vinci. Charles August Colomb (1736-1806) who expanded
Amontons’ work by stating “strength due to friction is proportional to a
compressive force” so the “Amontons-Coulomb Law” was established
(Beek, A., 1995).
Figure 1.1: Sketches from da Vinci's notebook, ca. 1480 demonstrating
some of his coefficient of friction experiments (Hart, 2011).
4
In the late 1930s, F. Philip Bowden and David Tabor found that the true area
of contact is formed by asperities and with the increasing normal force the
area of contact increases. They also gave the researched discipline about
friction the name tribophysics, but that term was never generally accepted,
leaving the way clear for H. Peter Jost, author of the eponymous report, to
give the science its name: tribology (Hart, 2011).
Tribology is defined as the science and engineering of surface phenomena
such as friction, wear, lubrication, adhesion, surface fatigue and erosion
(Sinha S.K., 2010). Today, friction is mainly studied in scientific tribology.
1.5.2 Research on friction between wood and steel
In regard to friction between wood and steel, experiments mainly addressing
issues related to the mechanics of cutting wood have been done.
(Murase et al., 1980) conducted extensive evaluation of the influence of
change in various factors such as surface roughness, sliding speed, moisture
content on the friction characteristics during processing (cutting/shaving)
wood with tools during exposure to relatively low pressure (up to 0.1 MPa).
(McKenzie and Karpovich, 1968) worked on determining the more
important variables affecting friction between wood and steel by using a
milling machine for cutting wood; they found that sliding speed as well as
moisture content and roughness of steel have a significant influence on the
value of the coefficient of friction.
(Ning, et al., 1982) studied the friction between Swedish wood and steel by
using the same set-up as (McKenzie and Karpovich, 1968) and they obtained
the same results, in addition they obtained evidence for two basic relations:
a) the softer the wood surface, the higher the coefficient of friction and
b) the higher the surface roughness of steel, the higher the coefficient.
1.5.3 Wood friction characteristics during exposure to high pressure
The friction between wood and steel is becoming a widely discussed
phenomenon, especially due to the increased use of wooden structures with
e.g. dowel type joints, where high pressure occurs. Proof about the fact, that
friction is an important factor that should be taken into account has been
verified for example in (Seki et al., 2012). (Sjödin et al., 2008) showed by
experimental and numerical methods that the value of the coefficient of
friction has a significant effect on the load-bearing capacity of single dowel
connections.
(Seki et al., 2012) published a study on friction of wood and steel during
exposure to high pressure, where contact pressures 1, 5 and 10 MPa were
used. The effect of metal surface (polished and grinded) and effect of wood
5
surface (planed, rim sawn, band sawn) was tested on two moisture states of
wood specimens; oven dried and water saturated. In the case of different
surfaces of the steel, the value of the coefficient of friction was
approximately twice as high for a grinded steel surface as compared to a
polished surface on oven dried wood during exposure to different pressure.
For water saturated wood the value of the coefficient of friction was the
same or higher in comparison to the oven dried wood at all load levels.
Studying the effect of the wood surface on the friction characteristics it was
shown, that wood surface finishing has less impact on the coefficient of
friction. The irregularities on a coarse wood surface were deformed and
became smooth since the wood surface is much softer than the metal tool
surface. In every case, the value of the coefficient of friction tended to be
higher with water saturated wood than with oven dried wood.
In case of dowel connections used in structural engineering, a lot of previous
research has been done, e.g. by (Sjödin et al., 2008) and (Dorn, 2012).
(Sjödin et al, 2008) estimated the coefficient of friction between the dowel
and the surrounding timber for two groups of dowels – with a smooth
surface of the dowel and with a rough one. For joints with smooth dowel
surfaces, the value of the coefficient of friction µ was estimated to lie
between 0 and 0.3. For joints with a rough surface dowel µ, was estimated to
be between 0.3 and 0.5. Experimental investigations also show, that the
load-bearing capacity increases for single dowel joints when rough surface
dowels are used compared to when smooth dowels are used.
(Dorn, 2012) performed structural experiments on single dowel-type timber
connections using different roughness of the dowels and density of the wood
and studied the influences of the coefficient of friction and the effects on the
behavior and failure of the connection. The outcomes verified the expected
influence of increased dowel roughness on connection behavior: increase of
both maximum load and maximum displacement at failure. In finite
elements simulations of dowel connections, (Dorn, 2012) used variations of
the coefficient of friction from 0.0 up to 0.8 and observed the results being
significantly influenced; increased friction positively affected load bearing
capacity, while stiffness was less significantly influenced (see Figure 1.2).
6
Figure 1.2: Load-displacement curves and the stiffness course for variation
of frictional properties (Dorn, 2012).
7
2. Theory
The first two parts of the theory chapter is oriented towards mechanical and
physical properties of wood, such as behavior in compression with different
fiber directions as well as moisture influence on wood properties. The third
part describes friction itself and the coefficient of friction including formulas
necessary to obtain its value.
2.1 Mechanical properties of wood
The mechanical properties such as strength and stiffness of wood, in
compression parallel to the fiber direction and in compression perpendicular
to the fiber direction, are often given for "clear" wood. The term “clear”
refers to the fact that effects of growth features, such as spiral grain, knots,
splits or checks are not included. (Kretschmann, D., 1999) describes in wood
mechanics that clear wood specimens are considered as homogeneous.
2.1.1 Strength and stiffness of wood
(Kretschmann, D., 1999) says that wood may be described as an orthotropic
material which means that it has unique and independent mechanical
properties in different directions of the three mutually perpendicular axes
(Figure 2.1). The longitudinal axis L is parallel to the fiber (grain); the radial
axis R is perpendicular to the grain direction (normal to the growth rings);
tangential axis T is perpendicular to the grain but tangential to the growth
rings.
Radial R
Tangential T
Longitudinal L
Figure 2.1: Three principal axes of wood with respect to grain direction and
growth rings.
2.1.2 Compression parallel to the fiber direction
Loading wood parts parallel to the fiber direction is (together with bending)
the most common method of straining wooden constructions. It is necessary
8
to take the difference between buckling pressure and simple pressure into
account.
There are some aspects that have to be taken into account in designing and
evaluating wood in compression parallel to the grain:
1. load capacity is calculated based on a linear relation between stress and
deformation,
2. strength and stiffness are dependent on moisture content, the rate of loading
and the duration of loading,
3. particular damages vary and depend on many factors, for example on the
layout of the volume of loaded particular cells among other things (i.e.
that kind of damage is hard to predict for untested specimens)
Characteristic strength of wood in compression parallel to the fiber direction
is given by standards and it is in turn referred to Eurocode 5.
2.1.3 Compression perpendicular to the fiber direction
Compression perpendicular to the fiber direction is a very common kind of
loading. Current knowledge about this type of loading is based on long-time
experience and rules are empirically determined. These are used in
contemporary standards and design rules for wooden constructions.
For deriving and assessing wood loaded in compression perpendicular to the
fiber direction it is necessary to take the following aspects into account:
1. strength and stiffness is dependent on the moisture content and its changes,
and on the duration of loading as well,
2. loading capacity is given by a relation between stress and deformation, which
is non-linear.
The maximum stress level in compression loading perpendicular to the grain
is between 3 and 5 MPa and failure stress is defined as the stress level that
gives 10% remaining deformations (Johansson et al. 2011). There is a
difference in the amount of deformation depending on the orientation of the
annual rings – the modulus of elasticity perpendicular to the grain is higher
in the thick-walled latewood than in the thin-walled earlywood.
2.1.4 Compression stresses at an angle to the grain
Being a strongly orthotropic material angle of loading in relation to the fiber
direction must be taken into account in design.
9
According to (Johansson et al., 2011), the strength of the wood material
changes considerably depending on the angle between the applied load and
the grain direction. A correlation for calculating compression strength
depending on angle (α) was proposed by Hankinson. The relationship
between the failure strength and the angle (α) according to Hankinson is
shown in Figure 2.2.
f0
α
f90
90°
0°
Figure 2.2 - The relationship between the failure strength f and the angle α
between the fiber direction and the force direction according to Hankinson
(Johannson et al, 2011).
2.1.5 Orthotropic elasticity
Applying the theory of orthotropic elastic materials involves several
assumptions. The tree log is for instance idealized to have the shape of a
perfect cylinder, of which the longitudinal axis is identical to the fiber
direction. Another idealization is the assumed concentric orientation of the
annual rings.
Orthotropic solid occurs when the three mutually perpendicular symmetric
planes of elastic properties go through each point of its body. If there is such
a case in a solid, it holds true that there are three mutual perpendicular axis
directions, e.g. longitudinal (L), radial (R) and tangential (T). Hooke's law
establishes a linear relation between each stress component and all the strain
components. The relation between stresses and strains can then be written
as:
10
(1)
In simple linear elasticity symmetry gives
(2)
From where it is concluded that:
(3)
Due to the symmetry, nine independent constants define the compliance
matrix:
EL, ER, ET, GLR, GRT, GLT, υLR, υRT, υLT.
The moduli of elasticity in tension and compression, EL, ER, ET, the shear
moduli GLR, GRT, GLT, and Poisson’s coefficients υLR, υRT, υLT
2.1.6 Stress at an angle to the grain - Hankinson's formula
There is no general formula describing cracking of wood. Empirical
relations for the determination strength boundaries have been used until
now. These can give relatively accurate results. One of these methods is
Hankinson's formula for plane stress giving the strength at angle α to the
grain:
11
=
,
,
.
,
(4)
,
Where:
,
... Compression strength parallel to the grain.
,
... Compression strength perpendicular to the grain.
... Deviation of grain from the axis system given by two mutual
perpendicular planes.
n
… Exponent which value can be determined experimentally, for the
time being the most common value used is n = 2.
2.2 Physical properties of wood
There are a number of physical properties of wood that influence the
behavior of wooden materials and they have to be taken into account. The
well-known are moisture content, density, shrinkage and swelling.
2.2.1 Moisture and wood
Wood is a hygroscopic material; therefore the moisture content plays a very
important role. The amount of water absorbed in wood is determined
primarily by the relative moisture of the surrounding environment.
The mechanical properties of wood are affected by the moisture content
therefore its influence is usually taken into account in design code by
reducing strength values for timber used in environments where high
moisture content can occur (Johannson et al. 2001).
There are two kinds of water in wood, bounded water and free water. Free
water does not influence strength or elasticity or other aspects, while
bounded water has a significant effect on entire characteristics including all
kinds of strength. Bound water is the moisture absorbed within the cell wall;
this water is molecularly bound to the wood molecules of the cell (Figure
2.2) (Department of Natural Resources, 2013).
12
Figure 2.2 – Anatomy of longitudinal cells, in relation to moisture loss
(Department of Natural Resources, 2013).
There is no effect on strength of wood in the loss of free water, however
when wood loses its bounded water, most strength properties increase
(Department of Natural Resources, 2013). Therefore it is important to relate
e.g. all mechanical tests to the moisture content (MC). This is usually
expressed as a percentage and can be calculated from
=
. (100%)
(6)
Where mwater is the mass of water in wood and mwood is the mass of the
ovendry wood.
The moisture content of a given piece of wood can be calculated by
=
$
%
%
. (100%)
(7)
Where mwet is the mass of the specimen at given moisture content and mdry is
the mass of the ovendry specimen.
2.2.2 Density
Wood is a porous material made of cells of various kinds; therefore
depending on the nature of these cells, some wood have more or less solid
wood substance for a given sized piece. Density is determined by the
amount of wood substance for a given volume. Density is dependent on
volume and weight, which are in turn dependent on the moisture content; it
is also an indicator of wood strength – the higher the density the stronger the
wood (Department of Natural Resources, 2013).
13
Values of density for wood are usually determined for moisture content 12%
which is referred to as a standard condition. The density of wood varies
significantly between species; between about 320 and 721 kg/m3 (Glass et
Zelinka, 1999).
2.2.3 Shrinkage and swelling
With respect to dimensional stability, wood is an anisotropic material. It
shrinks (swells) most in the direction of the annual growth rings
(tangentially), about half as much across the rings (radially), and only
slightly along the grain (longitudinally) (Glass et Zelinka, 1999).
Shrinkage occurs when the moisture content is reduced; the micro fibrils
(surface of cells where water is bonded) come closer to each other. The
shrinkage is usually very small but for large lengths this can be necessary to
take into account (Johannson et al. 2011).
2.3 Description of friction and the coefficient of friction
There are several types of friction, but only dry static friction is relevant for
this thesis since it is a study of solid surfaces in contact (wood and steel).
According to (Wikipedia, 2014), dry friction is defined as the force resisting
a relative motion between two solid surfaces and it is subdivided into static
friction (between non-moving surfaces) and kinetic friction (between
moving surfaces).
Friction converts kinetic energy into heat whenever relative movement
between two surfaces in contact occurs. Another inevitable consequence
whenever friction occurs is wear, which may lead to damage of the surfaces
exposed to friction and/or performance degradation.
According to (Persson B.N.J., 2000) friction is not itself a fundamental force
but arises from fundamental electromagnetic forces between the charged
particles constituting the two contacting surfaces. The interactions between
these particles results in the calculation of friction from first principles being
impractical, thus use of empirical methods for analysis and the development
of theories are required.
The coefficient of friction, denoted μ, is defined as the ratio between the
friction force F and the normal force N, both acting in the contact surface
(Figure 2.3), resulting in
'
&=(=
)
(8)
*
14
L
P
F
N
Figure 2.3 - The friction force F and the normal force N
As can be seen from the equation (8), there is no area that would influence
the friction, meaning that for a small block of wood, the calculated
coefficient of friction will be the same as for a larger one, if the ratio of
acting forces remains the same. Further observations made in (Persson
B.N.J., 2000) show that the coefficient of friction is also often almost
independent of velocity, except for extreme cases of low or high velocity.
The coefficient of friction is also nearly independent of the surface
roughness, except for extreme cases, where either of the surfaces is smooth
or rough.
The friction force equals the shear stress integrated over the area of real
contact. Because of surface roughness, the area of real contact is usually
much smaller than the apparent area of contact.
Macroscopic bodies always have rough surfaces, at least on a microscopic
level, and if one places two solid materials in contact, some regions on their
surfaces will be so close together that the surface atoms of one material
"touch" the surface atoms of the other material, while in other regions, the
surface atoms are separated by relatively large distances. The regions of
contact are referred to as junctions, and the sum of all the junctions is called
the area of real contact. The rest of the apparent area of contact is usually
much larger than the real area of contact, but plays essentially no part in
determining the sliding friction.
The real area of contact in most practical cases can be estimated accurately
by assuming that plastic deformation has occurred at each junction and that
all the junctions are in a state of incipient plastic flow. This assumption
gives
∆, = -/
(9)
where N is the load and σc (the penetration hardness) the largest compressive
stress that the materials can bear without plastic yielding.
15
Coulomb’s friction law then states that the force F necessary to shear the
junctions with the total area ΔA equals
/ = 0 ∆,
(10)
where τc is the yield stress in shear. Inserting this into equation (9) gives
/ = (0 / )-
(11)
i.e. the coefficient of friction
&=0 /
(12)
This derivation not only explains why the friction force is proportional to the
load but also why it is independent of the surface area A and of the nature of
the surface roughness (as long as the surfaces are not too rough or too
smooth). This follows from the fact that the 0 and
are of similar
magnitude.
Coulomb’s law in (Persson B.N.J., 2000) states that
F=μ N
(13)
The coefficient of friction tends to increase with increasing velocity.
16
3. Method
This thesis work is divided into two parts - experimental and analytical.
The experimental part describes the testing machine MTS Frame machine
322 used for applying force in both vertical and horizontal direction. The
experimental part also shows test parameters and used formulas. All
variations are shown in tables for easy illustration of each experiment. The
descriptions of the used materials, parameters and methodology for the
generation of data of the tested combinations are also in the experimental
part. Characteristics of the used combinations follow the description above.
The analytical part shows statistical formulas used for analyzing the
obtained data and how it was processed in Matlab in terms of finding the
coefficient of friction.
3.1 Materials
The test specimens as well as the steel sliding plates have been provided by
Linnaeus University.
There were two kinds of wooden materials used in this work: pine wood and
laminated veneer lumber (LVL) (Figure 3.1). Both were cut into small
specimens with a cross section of approximately 30 x 30 mm2 and a
thickness of approximately 10 mm. All specimens were carefully selected in
order to not include any knots or cracks. The wood was dry, without any
damages and its moisture was approximately 12%, which is considered as
the reference conditions.
The influence of change in moisture content on the coefficient of friction
was studied. In these tests, dried and wet specimens, respectively, have been
used as well as specimens with the reference moisture content. Dry wood
was achieved by using an oven with temperature set to 105°C, where the
already cut specimens were stored for at least 24 hours before testing. Wet
material was achieved by soaking the specimens in water for at least one
week before cutting and testing. The surfaces were made wet again right
before the test itself.
Area and thickness of each specimen were measured by a sliding gauge and
the dimensions noted in an Excel file. The sliding steel plates were carefully
cleaned by acetone before each test.
17
30 mm
Figure 3.1: Tested specimens, from left: laminated veneer lumber (LVL),
pine wood with wide annual rings and pine wood with narrow annual rings.
Pine wood
Pine (Pinus sylvestris) is softwood mostly available in the Northern
Hemisphere. Despite being lightweight, pinewood is a structurally strong
and inexpensive material, which is used for a variety of purposes such as
carpentry, general constructions, furniture and boat/ship building.
Like all woods, pine products must be sawn and machined from felled trees,
which puts some limits on the range of shapes for which it is suitable. The
structure of pine wood gives the material very low density and good
durability. Pine wood boards frequently contain a number of knots, which
can be problematic during cutting, but the wood is otherwise very easy to
work with.
For this work, pine wood has been divided into two groups with wide and
narrow annual rings. Only clear wood (wood without any knots or damages)
has been used.
Laminated veneer lumber (LVL)
In general, LVL is known as a material with high bending, tension,
compression and shear strength. Also a relatively high modulus of elasticity
is observed. These characteristics are accomplished by gluing thin (3-5 mm
thick) veneer sheets together using a phenolic resin-based adhesive (phenol
formaldehyde). The veneers are dried and the grains of each veneer are
oriented in the same direction. This makes LVL stronger, straighter and
more uniform than solid timber and hence overcomes some of timber’s
natural limitations such as strength-reducing knots. LVL is less prone to
shrinking or wrapping. LVL is mainly used for permanent structural
applications including beams, lintels, purlins, truss chords and formwork
and its main advantages are that it can be manufactured to almost any length
and it can also support heavier loads and span longer distances than normal
timber (Wood Solutions, 2013).
18
Sliding steel plates
Two kinds of steel plates have been used as a sliding part. One plate was
polished and thus had a smooth surface. The surface of the second plate was
sandblasted and it is considered as a rough surface (Figure 3.2).
a)
b)
Figure 3.2: a) The sandblasted rough steel sliding plate and b) the polished
smooth steel sliding plate used in the tests
3.2 Specimen preparation and physical properties
For determining the physical properties of the specimen, mathematical
calculations and special machines have been used. The digital sliding gauge
and a digital scale used to measure the dimensions and mass of the
specimens in order to determine the volumetric mass density 1
1=
2
4
56
7
8
(14)
The specimens were cut from a long piece of wood on a circular saw down
to the thickness of 10 mm and, where necessary, grinded to an approximate
size of 30 x 30 mm2. After cutting and to achieve identical conditions, all
specimens were stored in a climate chamber before being tested.
The steel surface was cleaned by Acetone prior to each test.
3.3 Experimental part
The experimental part has focused on five main types of tests to investigate
the dependence of friction on contact pressure, moisture content, angle of
fiber direction relative to the sliding direction, different roughness of the
sliding plate and different sliding speed. In order to estimate the influence on
individual parameters, different contact pressures have been used (Tables
3.1 – 3.5). In the case of different fiber directions, the tests have been done
19
for a low load pressure (0.3 MPa) and for a high level of contact pressure,
which was different for each angle (Table 3.3). For each variation, the
testing was done for all three groups of wood: LVL, pine wood with wide
rings (PW) and pine wood with narrow rings (PN). Individual experiments
are described in the following chapters.
Table 3.1: Applied pressures for the experiment with dependence on contact
pressure for all three materials (LVL, PW, PN).
Fibre direction
Pressure (MPa)
0°
0.3, 1.0, 10, 30
90°
0.3, 0.6, 1.0, 2.5, 5.0, 7.5, 8.5, 10
Table 3.2: Applied pressures in experiments of dependence on moisture
content for all three materials (LVL, PW, PN).
Fiber direction
Pressure (MPa)
0°
0.3, 5
90°
0.3, 1.0, 2.5
Table 3.3: Applied high pressures in experiments with
directions for all three materials (LVL, PW, PN).
Angle (°) -90 -75 -60 -45 -30 -15 0 15 30 45
Pressures 5 5.3 6.3 8.6 13.3 22.5 30 22.5 13.3 8.6
(MPa) 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
different fiber
60 75
6.3 5.3
0.3 0.3
90
5
0.3
Table 3.4: Combinations of pressures and fiber directions for LVL material
in experiments with different roughness of sliding plate.
Pressure (MPa)
Angles (°)
0.3
-90,-45, 0, 45, 90
Table 3.5: Combination of pressures and load rates in experiments with
sliding speed
Sliding speed (mm/min)
Pressure (MPa)
1
0.3, 5.0
10
0.3, 5.0
100
0.3, 5.0
3.3.1 Test procedure
The experiments were performed on a MTS Frame machine, Model 322,
which had special components designed and constructed for purposes of
these experiments. The tests were performed in the Laboratory of the
Department of Building Technology at Linnaeus University, Växjö.
The MTS Frame machine, Model 322 is able to perform a wide variety of
tests such as tension, compression, fatigue and fracture mechanics tests.
MTS manufactures a variety of grips, mounting fixtures and test area guards.
20
Main components of the MTS Frame machine 322 used for this experiment
are shown in Figure 3.3. Further details about the machine and its particular
components can be seen in Appendix A.
Figure 3.3: Set up for friction testing: 1 – Vertically moving part. 2 –
Sliding steel plate fixed to part 1. 3 – Wooden specimen. 4 – Attachment for
wood specimens. 5 – Horizontally moving bottom part.
All tests were performed as compression tests with horizontal loading. As
was previously stated, some of the components were specifically
manufactured for these experiments: the horizontally moving part which can
fit a plate (see also Figure 3.4) on which the wood specimen is placed and
the vertically moving part for the attachment of the sliding steel plate.
21
Figure 3.4: Horizontally moving machine components: 1 – File plate,
mostly used in this work. 2 – Very rough file, used for verification reliability
of this set up. 3 – Smooth plate, used for glued attachment. 4 - Bearing plate.
Experimental data was automatically recorded to a text file and subsequently
processed to obtain the friction coefficient for each test. All parameters and
their range is shown in Table 3.6.
Table 3.6: Range of values of parameters set for experiments on the MTS
320 machine
Range of contact pressure
0.1 – 30 MPa
Sliding speed (horizontal movement) 1, 10, 100 mm/min
Sliding length
10, 30, 60 mm
3.3.2 Methodology of experiments
The purpose of testing using the MTS Frame machine 322 was to do
primarily a qualitative and, if possible, a quantitative investigation of the
ratio between vertical load N and horizontal load P (Figure 2.3), to estimate
the coefficient of friction µ.
The principle of the tests is to press the steel plate to the surface of a wood
specimen. The steel plate is fixed to the upper part of the machine and the
wood specimen is attached to the bottom part of the machine by a very
rough steel plate (or glued to a smooth steel plate in some tests). The upper
part moves only vertically while the bottom part moves only in the
horizontal direction. The coefficient of friction is obtained by calculating the
ratio of horizontal to vertical load.
22
The machine is controlled by a PC. The system enables the user to define the
testing profile with personalized settings. The following automated steps
were executed during the experiments:
1. The vertical displacement was set to the position where the loading
surface of the machine is only a couple of millimeters away from the tested
surface of the wood.
2. The procedure is switched to vertical load control and the specimen is
loaded until the desired vertical load is achieved. During this period the
horizontal load is being kept constant at 0 N.
3. After the vertical loading procedure is complete, the machine waits for a
couple of seconds to balance both loads
4. A horizontal displacement is initiated with a defined rate (1, 10 or
100 mm/min) during which the vertical load is kept constant at a predefined
value. For the normal speed of movement (10 mm/min) the horizontal
displacement continues until the entire length of one specimen is reached
(30 mm) or until the specimen can no longer withstand the load and fails.
For 1 mm/min rate the displacement is only a third of the element length
(10 mm) and for 100 mm/min rate the horizontal displacement is two
element lengths (60 mm).
After setting all automated steps it is necessary to select output in terms of
graphs to be plotted. Four graphs were used for this work – vertical and
horizontal force and vertical and horizontal displacement as a function of
test time.
An illustration of the methodology of these experiments can be divided into
six steps:
1. Preparing wooden specimens - cutting, grinding, marking and measuring.
2. Setting up the test procedure on the computer such as defining loads and
displacements to be applied during the test.
3. Cleaning the steel sliding plate with acetone.
4. Placing wooden specimen on the mounted parts of the machine.
5. Running the test procedure.
6. Export and analysis of obtained data.
23
3.4 Analytical part - statistical evaluation
A large amount of data was obtained for each group of measured specimens.
This data is necessary to evaluate with statistical relevance. For each tested
group the arithmetic mean (average) was used:
;
9: = ∗ ∑ >; 9
(15)
where n is the number of tested specimens and Xi is the i-th value in the
group of tested values. Regarding the fact that the arithmetical average hides
and smoothens extremes and is also influenced by extremes, it is very
convenient to expand the final results with range R, variance s2, standard
deviation s and average absolute deviation d. The range R is defined as
?=@
AB
−@
(16)
where xmax is the maximum and xmin the minimum value, respectively, within
the sample. Thus it measures the distance between the extreme values, but
doesn’t say anything about the concentration of the extremes around the
mean. For such a measure the variance s2 is used
DE =
;
$;
. ∑ >;(9 − 9:)E
(17)
The standard deviation s is defined as the square root of the variance. It is
used together with variance s2 for characterizing.
For statistical evaluation it is also possible to use the average absolute
deviation d, which is less sensitive to extreme values than the standard
deviation
;
F = . ∑ >;|9 − 9:|.
(18)
All characteristics above have an absolute value and therefore it is necessary
to consider the magnitude of the characteristics with respect to the nominal
value of data in the group of the obtained data, (Hanousek, 1992).
24
4. Results
Large amounts of data were obtained in the tests and these were
subsequently analyzed in Matlab and Excel. The basic data presented here is
given in terms of the static coefficient of friction µ. The experiments were
performed for different conditions such as varying contact pressure,
moisture content, fiber direction, roughness and sliding speed and they are
divided into separate sections.
For clear understanding of the evaluation of the data, the first part of this
chapter describes the step by step process of obtaining the coefficients of
friction by means of a Matlab script for a single specimen. The second part
shows the further evaluation of the results in Excel and the derivation of the
statistics. This is done using LVL specimens in otherwise standard
conditions (0.3 MPa contact pressure, fiber direction 0°, normal moisture,
smooth sliding plate, 10 mm/min load rate).
4.1 Obtaining the coefficient of friction of a single specimen
From each single test the raw data from the MTS Frame machine 322 is first
imported from the text files into Matlab in the form of matrices. In addition,
the Excel file containing all information about the actual specimen is loaded,
which contains specimen number, date of the experiment, dimensions,
applied pressure, moisture content, attachment, plate roughness, fiber
direction, type of wood, and sliding speed.
The first plot (the examples in this chapter are for LVL, fiber direction 0°,
contact pressure 1 MPa, normal moisture, smooth plate, sliding speed
10 mm/min) is then created showing both vertical and horizontal forces as
can be observed in Figure 4.1. Following that, the coefficient of friction
matrix is calculated by dividing the horizontal force by the vertical force.
This is plotted again as a function of time (Figure 4.2).
As can be observed in Figure 4.2 a lot of noise is in the very beginning and
the very end of the test. The noise in the beginning is removed by deleting
the first 50 seconds of the data since at least this timespan of each
experiment contains only data about the loading process. Next all values
with a coefficient below 0.1 is deleted. This eliminates any discrepancies
during the rest of the loading process after the first 50 seconds and also to
find the point where the first slip (movement) of the tested specimen is
measured (marked with a circle in Figure 4.2 and Figure 4.3). Next the first
decreasing value (first occurrence of slip) after the coefficient of friction
reaches 0.1 is selected as a rough estimate of the coefficient of friction. This
serves also as the starting point for finding the static coefficient of friction in
the script.
25
950
Force [N]
750
550
350
150
Vertical
Horizontal
-50
0
50
100
150
200
250
Time [s]
Figure 4.1: An example of the vertical and horizontal force output of the
experiment.
Figure 4.2: The coefficient of friction over time plot calculated from the
exported horizontal and vertical forces.
From that point only the next five seconds are considered in the search for
the coefficient of friction. The Matlab function diff is then used to create a
matrix with differences between the neighboring friction values. In that
matrix the values that are smaller than an adjustable threshold value (0.01
was found to be working properly) are deleted, which only leaves the big
jumps (if there are any more) in the coefficient of friction matrix. By this the
stick-slip motion is removed that can be observed in Figure 4.3 at around
67.5 s before the coefficient is again rising.
The last step is to select the highest value, meaning the next biggest slip in
the selected data (marked with a cross in Figure 4.2 and Figure 4.3). The
26
value of the coefficient of friction and its timestamp is then recorded into a
separate text file.
Figure 4.3: Detail of the significant difference between the occurrence of
the first movement (red circle) and the actual selected coefficient of friction
(black cross), and of the stick and slip motion.
4.2 Statistical evaluation of a single test series
Figure 4.4 and Table 4.1 show the statistical parameters discussed
previously in Section 3.4. Arithmetical average is labeled as @̅ , average
deviation as d, range as R and the value of standard deviation as s in both
positive and negative direction, which is a square root of variance s2.
Conditions: material LVL, normal moisture, smooth plate, sliding speed
10 mm/min, fiber direction 0°, contact pressure 0.3 MPa.
Table 4.1: Statistical results for a single test series
LVL 0°
0.3 MPa
x
0.251
R
s2
d
0.0479 0.00024 0.0126
27
0,30
Coefficient of friction μ [-]
0,28
0,26
s
R
0,24
s
d @̅
d
0,22
0,20
0
Figure 4.4: Graphical interpretation of the statistical results.
4.3 Statistical evaluation for varying contact pressure
The results are then presented and compared varying only a single
parameter, in the following example the variation of contact pressure.
Conditions: material LVL; normal moisture; smooth plate; load rate
10 mm/min; fiber direction 0°; contact pressure 0.3, 1, 10 and 30 MPa.
In Figure 4.5, all measured values are shown as well as the derived average
values, which are connected to show the course of the curve of the
coefficient of friction depending on varying contact pressure.
Coefficient of friction μ [-]
0,35
0,30
0,25
0,20
0,15
0,10
0,05
0,00
0
5
10
15
Pressure [MPa]
20
25
30
Figure 4.5: Pressure variation of LVL, fiber direction 0°, smooth plate,
normal moisture, sliding speed 10 mm/min.
28
5. Analysis
This chapter shows and describes the average values obtained in accordance
with the previous chapter. The following experiments are analyzed with
variations of individual parameters such as contact pressure, moisture
content, fiber direction, steel plate roughness and load rate.
Only the average values for each nominally equal series will be shown.
More detailed figures showing the exact measured values are included in the
Appendix B in form of plots and Appendix C in statistical form.
5.1 Variation of contact pressure
Conditions: smooth steel plate; load rate 10 mm/min; normal moisture
content; fiber direction 0° (Figure 5.1) and 90° (Figure 5.2); attachment by
rough plate; contact pressure in the range of 0.1, 0.3, 10, and 30 MPa.
Coefficient of friction μ [-]
0,30
0,20
0,10
LVL
PW
PN
0,00
0
5
10
15
20
25
30
Pressure [MPa]
Figure 5.1: Dependence of the coefficient of friction on the contact pressure
for fiber direction 0° for LVL and pine wood (with wide and narrow annual
rings).
According to the course of the curve of average values it is visible that the
coefficient of friction is decreasing while contact pressure is increasing, but
after a certain pressure is reached, the decrease is negligible.
29
Coefficient of friction μ [-]
0,30
0,20
0,10
LVL
PW
PN
0,00
0
1
2
3
4
5
6
7
8
9
10
Pressure [MPa]
Figure 5.2: Dependence of the coefficient of friction on the contact pressure
for fiber direction 90° for LVL and pine wood (with wide and narrow annual
rings).
Behavior of the coefficient of friction in the case of fiber direction 90°
evinces a similar course of the curve as in the case of fiber direction 0°. The
highest coefficient of friction has shown in the lowest contact pressure, since
then, only lower values are detected.
30
5.2 Variation of moisture content
Coefficient of friction μ [-]
Conditions: smooth steel plate; load rate 10 mm/min; fiber directions 0°°
and 90°; attachment by rough plate; contact pressure 0.3, 1, 2.5, and 5 MPa;
normal, dry and wet wood.
0,30
0,20
0,10
LVL
PW
PN
0,00
dry
normal
wet
dry
normal
wet
Moisture content
a) 0.3 MPa
b) 5 MPa
Figure 5.3: Dependence of the coefficient of friction on the moisture
content with contact pressures 0.3 MPa (a) and 5 MPa (b), fiber direction 0°.
Coefficient of friction μ [-]
In the experiment with varying moisture content for fiber direction 0°, two
levels of contact pressure were used (0.3 MPa and 5 MPa). For fiber
direction 90° the influence of moisture content was measured at three
different levels of contact pressures: 0.3 MPa, 1 MPa and 2.5 MPa
(Figures 5.4 a, b, c).
0,30
0,20
0,10
LVL
0,00
dry
normal
PN
PW
wet
dry
normal
wet
dry
normal
wet
Moisture content
a) 0.3 MPa
b) 1 MPa
c) 2.5 MPa
Figure 5.4: Dependence of the coefficient of friction on the moisture
content with fiber direction 90°.
31
It is evident from Figure 5.3a that moisture content has a significant effect
on the coefficient of friction: the value for PW in wet conditions is twice as
high as in dry conditions. When high contact pressure is used (Figure 5.3b),
the coefficient of friction has a lower value for each material, but its value
still increases with the increase of the moisture content.
The significant influence of the moisture content in wood is clearly visible
in both angle directions of 0º and 90º. The coefficient of friction increases
with increasing moisture content, which was expected as a result of this
experiment. It is also visible that, for higher contact pressures, the values of
the coefficients of friction are smaller than the values of the coefficients of
friction during exposure to the low contact pressure.
32
5.3 Variation of fiber direction
Coefficient of friction μ [-]
Conditions: smooth steel plate; load rate 10 mm/min; contact pressure
0.3 MPa; normal moisture content; fiber directions from - 90° up to +90°.
0,30
0,20
0,10
0,00
-90
-75
-60
-45
-30
-15
0
Angle [°]
15
30
45
60
75
90
Figure 5.5: Distribution of values for each group of tested specimens with
fiber direction variation for LVL.
The data in the experiment with varying fiber direction show a high
variability of the coefficient of friction in each group. Bigger deviation was
recorded compared to the data from other experiments therefore presenting
only average values would not be valuable so that all determined
coefficients are shown (Figure 5.5 and Table 5.1).
Table 5.1: Statistical values for LVL under contact pressure of 0.3 MPa.
d
x
R
s2
-90°
0.189 0.0580 0.00052 0.0158
-75°
0.190 0.0417 0.00023 0.0105
-60°
0.162 0.0539 0.00040 0.0143
-45°
0.154 0.0396 0.00027 0.0114
-30°
0.169 0.0422 0.00035 0.0155
-15°
0.202 0.0727 0.00083 0.0212
0°
0.251 0.0479 0.00024 0.0126
15°
0.161 0.0351 0.00021 0.0119
30°
0.14
0.0556 0.00043 0.0143
45°
0.157 0.1004 0.00149 0.0299
60°
0.170 0.0641 0.00076 0.0214
75°
0.183 0.0700 0.00078 0.1835
90°
0.189 0.0580 0.00052 0.0158
Average values of the coefficient of friction for all three materials under
0.3 MPa contact pressure (Figure 5.6) and under high contact pressure
(Figure 5.7) are presented. The values differed for each fiber direction. The
chosen value of contact pressure was approx. 80% of the respective
maximum load. The applied contact pressures are shown in Table 3.3.
33
Coefficient of friction μ [-]
0,30
0,20
0,10
LVL
PW
PN
0,00
-90
-75
-60
-45
-30
-15
0
15
30
45
60
75
90
Angle [°]
Figure 5.6: Dependence of the coefficient of friction on fiber direction
under the contact pressure of 0.3 MPa, average values.
Coefficient of friction μ [-]
0,30
0,20
0,10
LVL
PW
PN
0,00
-90
-75
-60
-45
-30
-15
0
15
30
45
60
75
90
Angle [°]
Figure 5.7: Dependence of the coefficient of friction on different fiber
direction under a high level of contact pressure.
Comparing Figure 5.6 and Figure 5.7 shows that the coefficient of friction
varies with fiber direction during exposure to low contact pressure. The
highest value of the coefficient of friction is detected in 0° for all three
materials. The coefficient of friction decreases in both fiber directions from
0°, but slight increase is observed again towards ±90°. The coefficient of
friction under high contact pressure does not vary as much with fiber
direction and the differences between the coefficients of friction are
negligible.
34
5.4 Variation of roughness of the steel sliding surface
Conditions: polished and sandblasted surface of steel plate; load rate
10 mm/min; attachment by rough plate; contact pressure 0.3 MPa; normal
moisture content; fiber direction 0°, ±45° and 90°.
Coefficient of friction μ [-]
0,80
0,60
LVL 0.3 MPa 90°
LVL 0.3 MPa, 0°
LVL 0.3 MPa, -45°
LVL 0.3 MPa, 45°
0,40
0,20
0,00
Smooth
Rough
Plate roughness
Figure 5.8: Dependence of the coefficient of friction on the roughness of the
sliding plate.
Figure 5.8 shows that roughness of the steel plate significantly influences
the coefficient of friction. The sandblasted rough plate almost triples the
coefficient of friction compared to the polished surface. The difference
between both surfaces can be seen in Figure 3.4.
35
5.5 Variation of load rate
0,60
0,60
0,50
0,50
Coefficient of friction μ [-]
Coefficient of friction μ [-]
Conditions: polished steel plate; load rate 1, 10 and 100 mm/min;
attachment by rough plate; contact pressure 0.3, and 5 MPa; normal
moisture content; fiber direction 90°.
0,40
0,30
0,20
0,10
LVL
PW
PN
10
0,30
0,20
0,10
LVL
0,00
1
0,40
PW
PN
0,00
100
1
Loading rate[mm/min]
10
100
Loading rate[mm/min]
a) 0.3 MPa
b) 5 MPa
Figure 5.9: Dependence of the coefficient of friction on different loading
rate for fiber direction of 90°.
Figure 5.10: Typical plot of the coefficient of friction over time for a load
rate of 100 mm/min under low contact pressure 0.3 MPa for LVL.
The results from the experiments with different load rate show that the
coefficient of friction changes significantly under low pressure as can be
seen in Figure 5.9a, showing very high values at a rate of 100 mm/min.
Figure 5.10 allows a more detailed look into the evolution of the coefficient
36
of friction over the course of a single test under this high load rate. It shows
that there is a pronounced peak with a coefficient of friction of approx. 0.58
but the ratio between vertically and horizontally applied forces immediately
drops afterwards to levels of around 0.20, the level that has been observed
for the other load rates.
When the high pressure (5 MPa) is applied, the coefficient of friction is less
influenced by the different loading rate, see Figure 5.9b.
37
6. Discussion
This thesis studies influencing parameters on the coefficient of friction
between wood and steel surfaces. The parameters chosen for the
experiments were contact pressure, moisture content, fiber direction,
roughness of the steel plate and loading rate.
The research of the issue results in the following findings:
The coefficient of friction changes due to a variation of the parameters. Big
differences are observed mainly under lower contact pressure. However,
under higher contact pressure the coefficient of friction does not show big
changes (Chapter 5.1).
In the experiment with different moisture content it is again clear that the
value of the coefficient of friction is lower under high contact pressure than
it is when low contact pressure is applied. The coefficient of friction is still
increasing with increasing moisture content for all tested contact pressures.
Other proof of the influence of high pressure on the coefficient of friction is
the experiment with different fiber directions. The results show that under
low contact pressure (0.3 MPa) the coefficient of friction ranges between
0.15 and 0.30, whereas under high contact pressure the coefficient of friction
ranges between 0.12 and 0.22.
Fundamentally influencing the coefficient of friction is the use of the
sandblasted rough steel sliding plate in comparison with the smooth steel
sliding plate. The experiments proved significant changes of the values of
the coefficient of friction for all applied combinations, where the coefficient
of friction was almost tripled on the rough steel sliding plate.
The coefficient of friction for the three tested wood materials (LVL, PW,
PN) only showed slight differences and the shapes of the curves were very
similar for all three wood types.
The results of the experiments used in this thesis are enclosed in the
appendix.
38
7. Conclusions
The results obtained in the experimental part correspond to the expected
outcomes, for example an increasing coefficient of friction with increasing
moisture content of the specimens was found.
While using the sandblasted rough sliding plate the measured coefficients of
friction were almost doubled in comparison to the smooth sliding plate. The
importance of the roughness of the steel in dowel connections was tested in
(Sjödin et al, 2008), where the outcomes showed that using dowels with
higher surface roughness increased the load bearing capacity of the
connection.
It becomes clear that the coefficient of friction is influenced by more factors
and by multiple factors at the same time and that it would be useful to
conduct deeper research into this topic and carry out more experiments with
more combinations that are shown to be most influential (for example
moisture content and steel plate roughness) on the coefficient of friction.
Considering the machine set-up and the experiment itself it could be
beneficial to create and try out new ways of attaching the wood specimen to
the bearing place (by for example gluing) to see how much the set-up is
influenced by the attachment of the specimen.
It is important to continue with research on this topic. It is obvious that the
changes of coefficient of friction are significant and might be influential for
the calculation and design of timber constructions. The aim should be to
integrate the coefficient of friction into Eurocode 5.
39
References
American Forest & Paper Association (1997): General Dowel Equations for
Calculating Lateral Connection Values. American Wood Council
Available at: http://www.awc.org/pdf/tr12.pdf [Accessed 2014-05-28]
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Persson, B.N.J. (2000): Sliding friction Physical Principles and Applications.
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41
Appendices
Appendix A: The scheme of a MTS Frame machine 320.
Appendix B1: Plots for pressure variation.
Coefficient of friction μ [-]
0,30
0,20
0,10
0,00
0
1
2
3
4
5
6
Pressure [MPa]
7
8
9
10
(a)
Coefficient of friction μ [-]
0,30
0,20
0,10
0,00
0
1
2
3
4
5
6
Pressure [MPa]
7
8
9
10
Figure B1.1: Pressure variation at 0° fiber direction for PW (a) and PN (b).
(b)
Coefficient of friction μ [-]
0,30
0,20
0,10
0,00
0
1
2
3
4
5
6
7
8
9
10
7
8
9
10
7
8
9
10
(a)
Pressure [MPa]
Coefficient of friction μ [-]
0,30
0,20
0,10
0,00
0
1
2
3
4
5
6
(b)
Pressure [MPa]
Coefficient of friction μ [-]
0,30
0,20
0,10
0,00
0
1
2
3
4
5
6
Pressure [MPa]
(c)
Figure B1.2: Pressure variation at 90° fiber direction for LVL (a), PW (b) and
PN (c).
Appendix B2: Plots for moisture content variation
Coefficient of friction μ
0,4
0,3
0,2
0,1
0
dry
normal
wet
dry
(a) LVL
normal
Moisture
wet
dry
(b) PW
normal
wet
(c) PN
Figure B2.1: Moisture content variation for 0° fiber direction, 0.3 MPa contact
pressure.
Coefficient of friction μ
0,3
0,2
0,1
0
dry
(a) LVL
wet
dry
wet
Moisture
(b) PW
dry
wet
(c) PN
Figure B2.2: Moisture content variation for 0° fiber direction, 5 MPa contact
pressure (no data for normal moisture).
Coefficient of friction μ
0,4
0,3
0,2
0,1
0
dry
normal
wet
dry
(a) LVL
wet
normal
Moisture
dry
(b) PW
normal
wet
(c) PN
Figure B2.3: Moisture content variation for 90° fiber direction, 0.3 MPa contact
pressure.
Coefficient of friction μ
0,4
0,3
0,2
0,1
0
dry
normal
(a) LVL
wet
dry
normal
Moisture
(b) PW
wet
dry
normal
wet
(c) PN
Figure B2.4: Moisture content variation for 90° fiber direction, 1 MPa contact
pressure.
Coefficient of friction μ
0,4
0,3
0,2
0,1
0
dry
normal
(a) LVL
wet
dry
normal
Moisture
(b) PW
wet
dry
normal
wet
(c) PN
Figure B2.5: Moisture content variation for 90° fiber direction, 2.5 MPa contact
pressure.
Coefficient of friction μ [-]
Appendix B3: Plots for fiber direction variation
0,30
0,20
0,10
0,00
-90
-75
-60
-45
-30
-15
0
15
30
45
60
75
90
Angle [°]
Coefficient of friction μ [-]
(a)
0,30
0,20
0,10
0,00
-90
-75
-60
-45
-30
-15
0
Angle [°]
15
30
45
60
75
90
(b)
Coefficient of friction μ [-]
0,30
0,20
0,10
0,00
-90
-75
-60
-45
-30
-15
0
Angle [°]
15
30
45
60
75
90
(c)
Figure B3.1: Fiber direction variation, 0.3 MPa contact pressure for LVL (a),
PW (b) and PN (c).
Coefficient of friction μ [-]
0,30
0,20
0,10
0,00
-90
-75
-60
-45
-30
-15
0
Angle [°]
15
30
45
60
75
90
(a)
Coefficient of friction μ [-]
0,30
0,20
0,10
0,00
-90
-75
-60
-45
-30
-15
0
Angle [°]
15
30
45
60
75
90
(b)
Coefficient of friction μ [-]
0,30
0,20
0,10
0,00
-90
-75
-60
-45
-30
-15
0
Angle [°]
15
30
45
60
75
90
(c)
Figure B3.2: Fiber direction variation, high contact pressure (list of pressures in
Table 3.3) for LVL (a), PW (b) and PN (c).
0,80
0,80
0,60
0,60
Coefficient of friction μ [-]
Coefficient of friction μ [-]
Appendix B4: Plots for plate roughness variation
0,40
0,20
0,00
0,40
0,20
0,00
smooth
rough
Roughness
0,80
0,80
0,60
0,60
0,40
0,20
0,00
rough
smooth
Roughness
(c) 45°
Roughness
rough
(b) 0°
Coefficient of friction μ [-]
Coefficient of friction μ [-]
(a) -45°
smooth
0,40
0,20
0,00
smooth
Roughness
rough
(d) 90°
Figure B4.1: Plate roughness variation, 0.3 MPa contact pressure for LVL.
Appendix B5: Plots for load rate variation
Coefficient of friction μ [-]
0,60
0,40
0,20
0,00
1
10
100
1
10
100
Load rate [mm/min]
(a) LVL
1
(b) PW
10
100
(c) PN
Figure B5.1: Load rate variation, 90° fiber direction, 0.3 MPa contact pressure.
Coefficient of friction μ [-]
0,60
0,40
0,20
0,00
1
10
(a) LVL
100
1
10
100
Load rate [mm/min]
(b) PW
1
10
100
(c) PN
Figure B5.2: Load rate variation, 90° fiber direction, 5 MPa contact pressure.
Appendix C1: Statistical values for experiments with different contact pressures
Table C1.1: Pressure variation for 0° fiber direction.
Wood
LVL
Wide
Narrow
x
R
s2
d
x
R
s2
d
x
R
s2
d
0.3 MPa
0.251
0.0479
0.00024
0.0126
0.295
0.0540
0.00033
0.0153
0.244
0.0678
0.00035
0.0134
1 MPa
0.197
0.0694
0.00040
0.0138
0.224
0.0486
0.00021
0.0115
0.203
0.0494
0.00027
0.0127
10 MPa
0.172
0.0439
0.00026
0.0135
0.199
0.0426
0.00019
0.0109
0.199
0.0353
0.00021
0.0124
30 MPa
0.166
0.0585
0.00030
0.0133
Table C1.2: Pressure variation for 90° fiber direction.
Wood
LVL
Wide
Narrow
x
R
s2
d
x
R
s2
d
x
R
s2
d
0.3 MPa
0.189
0.0580
0.00052
0.0159
0.242
0.1706
0.00418
0.0459
0.203
0.0305
0.00012
0.0073
0.6 MPa
0.178
0.0401
0.00022
0.0106
0.194
0.0323
0.00061
0.0188
0.170
0.0376
0.00023
0.0116
1 MPa
0.168
0.0276
0.00013
0.0088
0.225
0.0446
0.00030
0.0135
0.183
0.0629
0.00055
0.0154
2.5 MPa
0.165
0.0279
0.00011
0.0071
0.220
0.0286
0.00013
0.0089
0.179
0.0662
0.00069
0.0189
5 MPa
0.179
0.0340
0.00024
0.0128
0.219
0.0506
0.00035
0.0131
0.157
0.0168
0.00004
0.0042
7.5 MPa
0.161
0.0600
0.00041
0.0159
0.203
0.0557
0.00063
0.0215
0.162
0.1031
0.00095
0.0242
8.5 MPa
0.170
0.0347
0.00020
0.0092
0.175
0.0174
0.00006
0.0061
0.178
0.0364
0.00034
0.0131
10 MPa
0.169
0.0201
0.00020
0.0100
Appendix C2: Statistical values for experiments with different moisture contents
Table C2.1: Statistical values for experiments with different moisture content for LVL.
Angle
0°
Pressure
0.3 MPa
x
Dry
90°
R
s
5 MPa
2
d
x
R
s
0.3 MPa
2
d
R
s
1 MPa
d
x
R
s
2.5 MPa
2
d
x
R
s2
d
0.185 0.0674 0.02979 0.0223 0.117 0.0106 0.00002 0.0031 0.180 0.0248 0.00011 0.0089 0.127 0.0135 0.00004 0.0049 0.122 0.0089 0.00004 0.0048
Normal 0.251 0.0479 0.00024 0.0126
Wet
x
2
0.189 0.0580 0.00052 0.0159 0.168 0.0276 0.00013 0.0088 0.165 0.0279 0.00011 0.0071
0.279 0.0838 0.00049 0.0182 0.257 0.0640 0.00067 0.0213 0.315 0.0277 0.00014 0.0093 0.247 0.0888 0.00135 0.0303 0.338 0.0321 0.00014 0.0080
Table C2.2: Statistical values for experiments with different moisture content for PW.
Angle
0°
Pressure
0.3 MPa
x
Dry
90°
R
s
2
5 MPa
d
x
R
s
0.3 MPa
2
d
R
s
1 MPa
d
x
R
s
2.5 MPa
2
d
x
R
s2
d
0.172 0.0526 0.00044 0.0167 0.143 0.0170 0.00006 0.0066 0.171 0.0534 0.00045 0.0155 0.136 0.0149 0.00005 0.0064 0.123 0.0157 0.00004 0.0046
Normal 0.295 0.0540 0.00033 0.0153
Wet
x
2
0.242 0.1706 0.00418 0.0459 0.225 0.0446 0.00030 0.0135 0.164 0.0480 0.00040 0.0142
0.343 0.0724 0.00095 0.0257 0.279 0.0591 0.00053 0.0174 0.333 0.1405 0.00309 0.0442 0.279 0.1482 0.00372 0.0485 0.215 0.1420 0.00297 0.0395
Table C2.3: Statistical values for experiments with different moisture content for PN.
Angle
0°
Pressure
x
Dry
90°
0.3 MPa
R
s
2
5 MPa
d
x
R
s
0.3 MPa
2
d
x
R
s
2
1 MPa
d
x
R
s
2.5 MPa
2
d
x
R
s2
d
0.181 0.0273 0.00010 0.0073 0.150 0.0544 0.00050 0.0157 0.159 0.0357 0.00023 0.0128 0.154 0.0199 0.00008 0.0068 0.134 0.0324 0.00015 0.0093
Normal 0.244 0.0678 0.00035 0.0134 0.199 0.0353 0.00021 0.0124 0.203 0.0305 0.00035 0.0073 0.183 0.0629 0.00055 0.0154 0.179 0.0662 0.00069 0.0189
Wet
0.253 0.0180 0.00004 0.0045 0.263 0.0970 0.00125 0.0248 0.321 0.0979 0.00186 0.0362 0.306 0.1765 0.00462 0.3061 0.275 0.1702 0.00422 0.0492
Appendix C3: Statistical values for experiments with different fiber directions
Table C3.1: Fiber direction variation for low pressure (0.3 MPa).
Wood
LVL
Wide
Narrow
x
R
s2
d
x
R
s2
d
x
R
s2
d
-90°
0.189
0.0580
0.00052
0.0159
0.232
0.0930
0.00152
0.0325
0.203
0.0305
0.00012
0.0073
-75°
0.190
0.0417
0.00023
0.0106
0.197
0.0365
0.00022
0.0114
0.202
0.0517
0.00060
0.0181
-60°
0.162
0.0540
0.00040
0.0143
0.186
0.0270
0.00013
0.0077
0.173
0.0398
0.00028
0.0113
-45°
0.155
0.0397
0.00027
0.0115
0.199
0.0487
0.00046
0.0172
0.197
0.0511
0.00034
0.0122
-30°
0.170
0.0422
0.00035
0.0155
0.189
0.0344
0.00020
0.0098
-15°
0.202
0.0727
0.00083
0.0213
0.189
0.0301
0.00014
0.0092
0.197
0.0328
0.00020
0.0119
0°
0.251
0.0479
0.00024
0.0126
0.295
0.0540
0.00033
0.0153
0.244
0.0678
0.00035
0.0134
15°
0.162
0.0351
0.00021
0.0120
0.211
0.0300
0.00016
0.0098
0.217
0.0244
0.00012
0.0094
30°
0.147
0.0557
0.00043
0.0144
0.197
0.0841
0.00091
0.0200
45°
0.157
0.1005
0.00149
0.0299
0.219
0.0339
0.00020
0.0100
0.195
0.0774
0.00080
0.0199
60°
0.170
0.0641
0.00076
0.0215
0.199
0.0234
0.00011
0.0077
0.179
0.0129
0.00003
0.0041
75°
0.184
0.0701
0.00078
0.1835
0.182
0.0203
0.00008
0.0070
0.164
0.0233
0.00010
0.0082
90°
0.189
0.0580
0.00052
0.0159
0.232
0.0930
0.00152
0.0325
0.203
0.0305
0.00012
0.0073
Table C3.2: Fiber direction variation for high pressure (see list of pressures in Table 3.3).
Wood
LVL
Wide
Narrow
x
R
s2
d
x
R
s2
d
x
R
s2
d
-90°
0.179
0.0340
0.00024
0.0128
0.219
0.0506
0.00035
0.0131
0.157
0.0168
0.00004
0.0042
-75°
0.143
0.0312
0.00014
0.0089
0.153
0.0347
0.00018
0.0101
0.130
0.0398
0.00023
0.0108
-60°
0.128
0.0582
0.00047
0.0161
0.176
0.0531
0.00048
0.0141
0.143
0.0125
0.00003
0.0041
-45°
0.146
0.0405
0.00023
0.0102
0.154
0.0386
0.00036
0.0160
0.123
0.0146
0.00003
0.0043
-30°
0.144
0.0347
0.00017
0.0098
0.174
0.0429
0.00027
0.0109
0.135
0.0197
0.00006
0.0058
0.167
0.0197
0.00005
0.0051
0.150
0.0294
0.00015
0.0086
-15°
0°
0.166
0.0585
0.00030
0.0133
0.197
0.0426
0.00019
0.0109
0.199
0.0353
0.00021
0.0124
15°
0.151
0.0174
0.00005
0.0049
0.185
0.0427
0.00025
0.0112
0.192
0.0415
0.00037
0.0167
30°
0.178
0.0523
0.00041
0.0159
0.182
0.0197
0.00005
0.0053
0.181
0.0438
0.00033
0.0143
45°
0.186
0.0411
0.00025
0.0116
0.186
0.0481
0.00056
0.0197
0.157
0.0173
0.00005
0.0050
60°
0.158
0.0676
0.00083
0.0206
0.195
0.0257
0.00013
0.0081
0.183
0.0179
0.00006
0.0055
75°
0.153
0.0221
0.00011
0.0091
0.157
0.0350
0.00020
0.0113
0.152
0.0664
0.00083
0.0237
90°
0.179
0.0340
0.00024
0.0128
0.219
0.0506
0.00035
0.0131
0.157
0.0168
0.00004
0.0042
Appendix C4: Statistical values for experiments with different sliding plate roughness
Table C4.1: Roughness variation for LVL.
Angle
0°
Pressure
0.3 MPa
x
R
90°
s
2
-45°
0.3 MPa
d
x
R
s
2
1 MPa
d
x
R
s
45°
0.3 MPa
2
d
x
R
s
2
0.3 MPa
d
x
R
s2
d
Smooth
0.251 0.0479 0.00024 0.0126 0.189 0.0580 0.00052 0.0159 0.168 0.0276 0.00013 0.0088 0.155 0.0397 0.00027 0.0115 0.157 0.1005 0.00149 0.0299
Rough
0.582 0.1331 0.00309 0.0440 0.554 0.0948 0.00129 0.0260 0.550 0.0738 0.00102 0.0267 0.626 0.1697 0.00325 0.0442 0.609 0.1894 0.00349 0.0424
Appendix C5: Statistical values for experiments with different loading rate
Table C5.1: Loading rate variation for LVL.
Angle
0°
90°
Pressure
0.3 MPa
0.3 MPa
x
R
s
1 mm/min
0.189
0.0854
10 mm/min
0.251
100 mm/min
0.561
2
5 MPa
d
x
R
s2
d
0.00087
0.0219
0.139
0.0256
0.00011
0.0083
0.0580
0.00052
0.0159
0.179
0.0340
0.00024
0.0128
0.1566
0.00358
0.0452
0.171
0.0162
0.00005
0.0057
d
x
R
s
0.00143
0.0321
0.190
0.0703
0.0479
0.00024
0.0126
0.189
0.0951
0.00119
0.0290
0.526
2
Table C5.2: Loading rate variation for pine wood.
Wood
Pine Wide
Pine Narrow
Angle
90°
90°
Pressure
0.3 MPa
5 MPa
x
R
s
1 mm/min
0.175
0.0786
10 mm/min
0.242
0.1706
100 mm/min
2
0.3 MPa
d
x
R
s
0.00148
0.0335
0.156
0.0530
0.00418
0.0459
0.219
0.0506
2
5 MPa
d
x
R
s2
d
0.00153
0.0315
0.133
0.0558
0.00043
0.0152
0.0305
0.00012
0.0073
0.157
0.0168
0.00004
0.0042
0.1315
0.00236
0.0342
d
x
R
s
0.00042
0.0143
0.180
0.0977
0.00035
0.0131
0.203
0.465
2
Faculty of Technology
351 95 Växjö, Sweden
Telephone: +46 772-28 80 00, fax +46 470-832 17 (Växjö)