Dr. Mohamed M.
Abdelkader
Tribology
Lecture 5
Friction
Dr. Mohamed M. Abdelkader
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Dr. Mohamed M. Abdelkader
What is friction?
Friction is a retarding force that opposes motion.
Friction types:
Static friction Dry or
Coulombic
Kinetic friction friction
Fluid friction
Sources of dry friction
Asperities between contacting surfaces
Interactions at the atomic level
Tribology studies sources of friction, lubrication, wear.
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Dr. Mohamed M. Abdelkader
Friction
• Friction is the resistance to motion during sliding
or rolling, that is experienced when one solid body
moves tangentially over another with which it is in
contact.
• The resistive tangential force, which acts in a
direction directly opposite to the direction of
motion, is called the friction force.
• There are two main types of friction that are
commonly encountered: dry friction and fluid
friction. As its name suggests, dry friction, also
called “Coulomb” friction, describes the tangential
component of the contact force that exists when
two dry surfaces move or tend to move relative to
one another.
• Fluid friction describes the tangential component
of the contact force that exists between adjacent
layers in a fluid that are moving at different
velocities relative to each other as in a liquid or
gas between bearing surfaces.
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Dr. Mohamed M. Abdelkader
Friction
• If the solid bodies are loaded
together and a tangential force (F) is
applied, then the value of the
tangential force that is required to
initiate motion is the static friction
force, Fstatic or Fs.
• It may take a few milliseconds before
relative motion is initiated at the
interface.
• The tangential force required to
maintain relative motion is known as Tangential force as a function of
the kinetic (or dynamic) friction force, time or displacement;
Fkineticor Fk . Fstatic is the static friction force
• The static friction force is either required to initiate motion and
Fkinetic is the kinetic friction force
higher than or equal to the kinetic
required to sustain motion.
friction force,
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Dr. Mohamed M. Abdelkader
Coefficient of Friction
At impending motion:
F = μN
This is the maximum force for a given N.
μ is a coefficient of friction.
for impending relative motion μ = μs
for actual relative motion μ = μk
μk ≤ μs
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Dr. Mohamed M. Abdelkader
Friction
• Friction is not a material property, it is a system response.
• Friction forces can be either good or bad.
• Without friction it would be impossible to walk, use automobile
tires on a roadway, or pick up objects.
• Even in some machine applications such as vehicle brakes and
clutches and frictional transmission of power (such as belt drives),
friction is maximized.
• However, in most other sliding and rotating components such as
bearings and seals, friction is undesirable.
• Friction causes energy loss and wear of moving surfaces in
contact. In these cases, friction is minimized. 6
Dr. Mohamed M. Abdelkader
Solid–Solid Contact
Rules of Sliding Friction
Two basic rules of intrinsic (or
conventional) friction are generally obeyed
over a wide range of applications.
1. The first rule states that the friction
force, F, is directly proportional to the
nominal load, W, that is, F = μW
where μ (also commonly labeled as f) is a
proportionality constant known as the
coefficient of static friction (μs ) or kinetic
friction (μk ) which is independent of the
normal load.
Alternately, it is often convenient to express this rule in terms of constant angle of
repose or frictional angle θ defined by μs = tan θ.
In this equation, θ is the angle such that any body of any weight, placed on a plane
inclined at an angle less than θ from the horizontal, will remain stationary, but if the
inclination angle is increased to θ, the body will start to slide down.
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Dr. Mohamed M. Abdelkader
Friction
2. The second rule states that the friction force (or coefficient of
friction) is independent of the apparent area of contact between
the contacting bodies. Thus two bodies, regardless of their
physical size, have the same coefficient of friction.
3. To these two rules, a third rule is sometimes added which is
often attributed to Coulomb (1785). It states that the kinetic
friction force (or coefficient of friction) is independent of the
sliding velocity once motion starts. He also made a clear
distinction between static friction and kinetic friction.
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Dr. Mohamed M. Abdelkader
Friction
• In summary, the first two rules The effect of normal
are generally obeyed to within a load on the
few percent in many cases. coefficient of
friction for;
• It should be emphasized that μ is
strictly constant only for a given (a) Steel sliding on
pair of sliding materials under a aluminum in air.
given set of operating conditions
(temperature, humidity, normal (b) A copper on
pressure and sliding velocity). copper in air.
• Many materials show
dependence of normal load,
sliding velocity and apparent
area on the coefficients of static (c) AISI 440C
and kinetic friction in dry and stainless steel on Ni3
lubricated contacts. Al alloy in air.
• Therefore, any reported values
should be used with caution! 9
Dr. Mohamed M. Abdelkader
Friction
Coefficient of friction as a
function of sliding velocity for;
(a) Titanium sliding on titanium
at a normal load of 3 N.
(b) Pure bismuth and copper
sliding on themselves.
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Dr. Mohamed M. Abdelkader
Friction
Basic Mechanisms of Sliding Friction
• Amontons and Coulomb were the first to propose the mechanism of
friction.
• Coulomb proposed that metallic friction can be attributed to the
mechanical interaction of asperities of the contacting surfaces.
• In the so-called Coulomb model, the action of the wedge-shaped asperities
causes the two surfaces to move apart as they slide from one position to
another and then come close again.
• Work is done in raising the asperities from one position to another and
most of the potential energy stored in this phase of the motion is recovered
as surfaces move back.
• Only a small fraction of energy is dissipated in sliding down the asperities.
• Since friction is a dissipative process, the mechanical interaction theory
was abandoned.
• A realistic friction theory should include mechanisms of energy
dissipation.
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Dr. Mohamed M. Abdelkader
Friction
• Bowden and Tabor (1950) proposed that for two metals in
sliding contact, high pressures developed at individual contact
spots cause local welding and the contacts thus formed are
sheared subsequently by relative sliding of the surfaces.
• Later, it was argued that asperities do not have to weld, but only
the interfacial adhesion between asperities is sufficient to
account for the friction of metals and ceramics.
• In addition to the frictional energy (or force) to overcome
adhesion developed at the real areas of contact between the
surfaces (asperity contacts), energy is required for micro-scale
deformation of the contacting surfaces during relative motion.
• If the asperities of one surface (the harder of the two, if
dissimilar) plow through the other via plastic deformation,
energy is required for this macro-scale deformation (grooving
or plowing).
• Macro-scale deformation can also occur through the particles
trapped between the sliding surfaces. 12
Dr. Mohamed M. Abdelkader
Friction
• In viscoelastic materials (such as polymers),
deformation force arises from elastic
hysteresis losses.
• These theories, first advanced by Bowden
and Tabor, are widely accepted theories for
friction of metals and ceramics.
• The dominant mechanism of energy dissipation in metals and ceramics
is plastic deformation.
• There is a little energy loss during the elastic deformation of interfaces.
• In engineering interfaces, even if deformation is primarily elastic, some
plastic deformation also occurs.
• Regardless of the type of deformation, breaking of adhesive bonds
during motion requires energy.
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Dr. Mohamed M. Abdelkader
Friction
• If we assume that there is negligible interaction between the
adhesion and deformation processes during sliding, we may add
them, and the total intrinsic frictional force (Fi ) equals the force
needed to shear adhered junctions (Fa) and the force needed to
supply the energy of deformation (Fd). Therefore, we can write;
Fi = Fa + Fd
• or the coefficient of friction;
μi = μa + μd
• In polymers (especially elastomers) and rough surfaces in general, μd
may be a significant fraction of μi .
• The distinction between the adhesion and deformation theories is
arbitrary, and the assumption of no interaction is too simplistic.
• In both cases, there is local deformation, and the magnitude of
friction is influenced by the physical and chemical properties of the
interacting surfaces, the load, the sliding velocity, the temperature,
and so forth.
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Dr. Mohamed M. Abdelkader
Friction - Adhesion
• When two nominally flat
surfaces are placed in contact
under load, the contact takes
place at the tips of the
asperities, the load being
supported by the deformation
of contacting asperities, and
discrete contact spots
(junctions) are formed.
• The sum of the areas of all the
contact spots constitutes the
real (true) area of the contact
(Ar) and for most materials Schematic of (a) two rough
under normal load, this will be surfaces in a sliding contact
only a small fraction of the and (b) a corresponding free
body diagram.
apparent (nominal) area of
contact (Aa).
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Dr. Mohamed M. Abdelkader
Friction - Adhesion
• The proximity of the asperities results in adhesive contacts caused
by either physical or chemical interaction.
• When these two surfaces move relative to each other, a lateral force
is required to shear the adhesive bonds formed at the interface in
the regions of real area of contact.
• Rupture occurs in the weakest regions, either at the interface or in
one of the mating bodies.
• After shearing of the existing contacts, new contacts are formed.
• Because adhesion arises from molecular forces between the
surfaces, the adhesive forces are of the same nature as the forces
existing between the molecules themselves. 16
Dr. Mohamed M. Abdelkader
Friction - Adhesion
Consequently, the interface may be as strong as the bulk materials, and
during sliding, the shearing process may actually tear out fragments of
the materials. In that case, the friction force would depend on the bulk
shear strength of the materials.
From the classical theory of adhesion to a very rough first approximation,
the friction force (Fa) is defined as follows;
For a dry contact,
Fa = Ar τa
and for a contact with a partial liquid film,
𝜼𝒍 𝑽
Fa = Ar [ατa + (1 − α)τl ] , and 𝜏𝒍 =
𝒉
Where;
τa : The average shear strengths of the dry contact.
τl : The average shear strengths of the lubricant film.
α : The fraction of the unlubricated area.
η : The dynamic (absolute) viscosity of the lubricant.
V : The relative sliding velocity.
h : The liquid film thickness. 17
Dr. Mohamed M. Abdelkader
Friction - Adhesion
Fa = μaW
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Dr. Mohamed M. Abdelkader
Friction - Adhesion
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Dr. Mohamed M. Abdelkader
Friction - Adhesion
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Dr. Mohamed M. Abdelkader
Friction - Adhesion
Coefficient of friction as a
function of surface roughness
for;
(a) a thin-film magnetic rigid
disk with sputtered
diamond like carbon
overcoat against a Mn-Zn
ferrite slider at 0.1 N load
and 1 m/s.
(b) copper against copper at 10
N and 0.1 mm/s.
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Dr. Mohamed M. Abdelkader
Friction- Deformation
• Two types of interactions can
occur during the sliding of two
surfaces with respect to each
other: the microscopic
interaction where primarily
plastic deformation and
displacement of the
interlocking surface asperities
are required, and the more
macroscopic interaction where
the asperities of the harder
material either plow grooves in
the surface of the softer one Schematic of interactions;
via plastic deformation or (a) asperity interaction, and
result in fracture, tearing or (b) macroscopic interaction of two
fragmentation. sliding surfaces.
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Dr. Mohamed M. Abdelkader
Friction- Deformation
• Plowing of one or both surfaces can also occur by wear particles
trapped between them, and truly macroscopic plowing of the softer
material by the harder, with the dimensions of the plowed groove
being orders of magnitude greater than those of the asperities on
either surface.
• Plowing deals with relatively large-volume deformations and small
strains, whereas the shearing mechanism and local asperity
interactions involve very thin, interfacial regions (a fraction of a
nanometer thick) and large strains.
• During any relative motion, adhesion and asperity interactions are
always present.
• The plowing contribution may or may not be significant; its
magnitude depends on the surface roughnesses and relative
hardnesses of the two surfaces, and on the size, shape and hardness
of any wear debris and reaction products trapped between them.
• Before the onset of sliding between two surfaces, μd largely controls
the coefficient of static friction.
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Dr. Mohamed M. Abdelkader
Friction- Deformation
• Energy can be dissipated through the deformation of contacting
bodies during sliding where no groove (macroscale deformation)
is produced.
• The usual approach to the analysis of the micro-scale
deformation of a single asperity is the slip-line field theory of a
rigid perfectly Material.
• If one of the sliding surfaces is harder than the other, the
asperities of the harder surface may penetrate and plow into the
softer surface and produce grooves if shear strength is
exceeded.
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Dr. Mohamed M. Abdelkader
Friction- Deformation
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Dr. Mohamed M. Abdelkader
Friction- Deformation
This expression can be written in terms of the
apex semi-angle of the cone α = 90◦ − θ,
𝟐𝒄𝒐𝒕𝜶
𝝁𝒑 =
𝝅
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Dr. Mohamed M. Abdelkader
Friction- Deformation
• For most engineering surfaces, the angles of asperities with the
horizontal surface (roughness angles) are very small and the
plowing component of friction is correspondingly small.
• For example, for a conical asperity with a roughness angle of 5◦
on a very rough surface, the plowing component of friction is only
0.056.
• This is a low value because the piling up of the material ahead of
the sliding asperity is neglected in the analysis.
• Abrasive materials and impacted wear particles may be very
angular with large θ values which would result in large values of
plowing component of friction. 27
Dr. Mohamed M. Abdelkader
Friction- Deformation
Next we consider a spherical
asperity of radius R in contact
with a softer body.
The expression for μp is;
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Dr. Mohamed M. Abdelkader
Friction- Deformation
For a relatively large width of the groove as compared to radius of sphere,
an expression for μp is given by (Suh and Sin, 1981)
Coefficient of plowing friction as a function of the ratio of
groove width to asperity diameter for a spherical asperity. 29
Dr. Mohamed M. Abdelkader
Example
A hard ball is slid against a soft and flat surface at two different loads. At
one load, the coefficient of friction is 0.20 and the groove width is 0.5 mm
and at another load, the coefficient of friction is 0.25 and the groove width
is 1 mm. Calculate the radius of the ball and the adhesive component of the
coefficient of friction. Assume that the dominant sources of friction are
adhesion and plowing and that these are additive.
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