Friction

 
Friction is the tangential resistance to motion. The occurrence of friction is a part of everyday
life. It is needed so that we have control on our walking. On the other hand, in most of
running machines friction is undesirable (energy loss, leading to wear of vital parts,
deteriorating performance due to heat generation) and all sorts of attempts (i.e. using low
friction materials, lubricating surfaces with oil or greases, changing design so that sliding can
be reduced) have been made to reduce it.
 
Often coefficient of friction(μ) is considered a constant value for a pair of material. In
addition, the value of μ is accounted much lesser than 1.0. In practice μ greater than 1.0, as
shown in Table 2.1, has been observed. Generally coefficients of friction depend on
parameters such as temperature, surface roughness and hardness.
 
Table 2.1: Coefficient of friction for various metals sliding on themselves. 

 
Fig. 2.1 indicates that under dry lubricant conditions, μ ranges between 0.1 to 1.0 for most of
the materials. Very thin lubrication reduces coefficient by 10 times.
 

Fig. 2.1: Coefficient of friction for various metals.

 
Generally, adhesion(Fig. 2.2) increases the friction. So, while selecting metal pairs, low
adhesion metal pairs must be selected to reduce friction force. Similiar material pair must be
avoided as similar materials have higher tendency of adhesion.
 

Fig. 2.2: Adhesive Friction among various materials.

 
Static & Kinetic Frictions :
 
Before starting friction mechanisms, it is necessary to define static and kinetic friction. Let us
consider a block on the surface getting pushed by a tangential force F. On application of 20 N
load, block does not move. This second point on the graph(Fig. 2.3) shows that on application
of 40 N, still block does not move. There is static force equilibrium between application force
and friction force. On application of 50 N load, block just start sliding. At this point of load
application friction force remains equal to 50 N, but friction resistance decreases subsequently
to 40 N. In other words, static friction is higher than kinetic friction. Table 2.2 shows few
published results of static/kinetic coefficient of friction. This table indicates that coefficient of
friction is statistical parameter. It is difficult to obtain same value under various laboratory
conditions. Further, there is a possibility of substantial decrease in kinetic friction relative to
static friction. Stick-slip is a phenomenon where the instantaneous sliding speed of an object
does not remain close to the average sliding speed. Stick-slip is a type of friction instability.
 

Fig. 2.3: Difference between the static and kinetic friction may initiate
‘stick-slip’.
 
Table 2.2: μ for wood-on-wood reported in various articles. 

 
A friction is statistical parameter depends on a number of variable. There is a need to
understand science of friction.
 
To understand the effect of material pair, role of lubrication, and environmental factors let us
start with dry friction. The dry friction is also known as solid body friction and it means that
there is no coherent liquid or gas lubricant film between the two solid body surfaces. Four
theories given by Leonardo da Vinci, Amonton, Coulomb and Tomlison for dry lubrication are
explained in following paragraph.
 

Fig. 2.4: Amonton`s work.

 
Leonardo da vinci(Earliest experimenter, 1452-1519) :

As per Leonardo, “Friction made by same weight will be of equal resistance at the beginning
of movement, although contact may be of different breadths or length”.

“Friction produces the double the amount of effort if weight be doubled”. In other words, F α
W.
 
G.Amontons, 1699 : The friction force is independent of the nominal area (F ≠ A) of contact
between two solid surfaces. The friction force is directly proportional F α N to the normal
component of the load. He considered three cases(Fig. 2.4) and showed that friction force will
vary as per the angle of application of load. As per Amontons μ = 0.3 for most of materials.
 
C.A.Coulomb 1781 (1736-1806) :

• Clearly distinguished between static & kinetic frictions. Friction due to interlocking of rough
surfaces.

• Contact at discrete points μstatic ≥ μkinetic.

• f ≠ func(A).

• f ≠ func(v).
 

Fig. 2.5: Coulomb friction model.

 
As per coulomb friction force is independent of sliding speed. But this law applies only
approximately to dry surfaces for a reasonable low range of sliding speeds, which depends on
heat dissipation capabilities of tribo-pairs.
 
TOMLINSON’s Theory of Molecular attraction, 1929 :

Tomlison based on experimental study provided relation between friction coefficient & elastic
properties of material involved.
 

Fig. 2.6: Examples on Tomlison formula.

 
As per Tomlison due to molecular attraction between metal, cold weld junctions are formed.
Generally load on bearing surface is carried on just a few points. These are subjected to
heavy unit pressure, and so probably weld together. Adhesion force developed at real area of
contact. 
Fig. 2.6 provides illustration related to Tomlison`s friction formula. This figure indicates f =
0.6558 for clean steel and aluminium, f = 0.742 for aluminium and titanium, and f = 0.5039
for clean steel and titanium.
 
Scientific Explanation of Dry Friction :
 
There are two main friction sources: Adhesion and Deformation. Force needed to plough
asperities of harder surface through softer. In lubricated tribo-pair case, friction due to
adhesion will be negligible, while for smoother surfaces under light load conditions
deformation component of friction will be negligible.
 
Fig. 2.7 demonstrates the adhesion (cold weld) between two surfaces. Some force, F a, is
required to tear the cold junction. Fig. 2.8 demonstrates the deformation process. It shows a
conical asperity approaching to a softer surface. To move upper surface relative to lower
surface some force is required.
 
• Two friction sources : Deformation and Adhesion.

• Resulting friction force (F) is sum of two contributing (F a & Fd) terms.

• Lubricated tribo-pair case -- negligible adhesion.

• Smoother surfaces under light load conditions – Negligible deformation.

 

Fig. 2.7: Adhesion

 

Fig. 2.8: Abrasion(Deformation)[1]

 

 
Adhesion and Ploughing in Friction
 
This theory is based on the fact that all surfaces are made of atoms. All atoms attract
one another by attractive force. For examples, if we press steel piece over indium piece
(as shown in Fig. 2.9) they will bind across the region of contact. This process is
sometimes called "cold welding," since the surfaces stick together strongly without the
application of heat. It requires some force to separate the two surfaces. If we now apply
a sideways force to one of surfaces the junctions formed at the regions of real contact
will have to be sheared if sliding is to take place. The force to do this is the frictional
force. Fig. 2.10 shows carbon graphite material adhered to stainless steel shaft.
 

Fig. 2.9: Cold welding in steel and indium

 

Fig. 2.10: Carbon graphite and stainless steel.

 
Theory of ADHESIVE Friction :
 
Bowden and Tabor developed theory of adhesive friction. As per this theory on
application of W, initial contact at some of higher asperity tips occurs. Due to high stress
those asperities suffer plastic deformation, which permits strong adhesive bonds among
asperities. Such cold formed junctions are responsible for the adhesive friction. The real
area of contact, A can be estimated by applied load W and hardness of the soft material,
H. If s is shear stress of softer material, then force Fa required to break these bonds can
be estimated by Equation Fa = As. The coefficient of friction due to adhesive friction is
given by ratio of friction force to applied load W. Fig. 2.11 shows the formulation and
breakage of cold junctions.
 
• Two surfaces are pressed together under load W.

• Material deforms until area of contact (A) is sufficient to support load W, A = W/H.

• To move the surface sideway, it must overcome shear strength of junctions with force
Fa. 

• μ = Fa ⁄ W = s ⁄ H.
In other words shear strength(s) and hardness(H) of soft material decides the value of μ.
This means whatever properties of the other harder pairing material, μ would not
change.
 

Fig. 2.11: Adhesion theory.

 
For most of untreated materials H = 3 σy & s = σy/1.7321. Expected value of μ = 0.2, as
μ = s ⁄ H. But for most of the material pair(shown in Fig. 2.12) μ is greater than 0.2.
There is a huge difference between measured values of friction coefficient and estimated
by theory of adhesion.

Theory is unable to estimate different μ for steel on indium and steel on lead alloy.
Theory related to deformation needs to be explored.
 

Fig. 2.12: Friction coefficients for various material pairs.

 
FRICTION due to DEFORMATION :
 
This theory is based on the fact that contact between tribo-pairs only occurs at discrete
points, where the asperities on one surface touch the other. The slope of asperities
governs the friction force. Sharp edges cause more friction compared to rounded edges.
Expression for coefficient of friction can be derived based on the ploughing effect.
Ploughing occurs when two bodies in contact have different hardness. The asperities on
the harder surface may penetrate into the softer surface and produce grooves on it, if
there is relative motion.
 

Fig. 2.13: Deformation theory[1].

 
Contact between tribo-pairs only occurs at discrete points. Assume n conical asperities of
hard metal in contact with flat soft metal, vertically project area of contact.
 

 
μd = (F/W), substituting the equations of F and W, we get μ d = (2/π)cot θ : This relation
shows important of cone angle, θ. Table 2.3 lists the μ d for various θ values.
 
Table 2.3

In practice slopes of real surfaces are lesser than 10 0 (i.e. θ > 800),
therefore μd = 0.1. If we add this value(μd = 0.1), total μ, should not
exceed 0.3. Total μ, representing contribution for both ploughing and
adhesion terms.

 
Ploughing By Spherical Asperity :
 
If we consider asperities on solid surfaces are spherical, vertical projected area of
contact :
 

Fig. 2.14: Spherical asperity.

 
 
Generally h << R, therefore μd Ξ 0.1. This means total μ, should not exceed 0.3.
 
Summary of theories related to adhesion and ploughing effects.
 

Fig. 2.15: Summary of adhesion and

ploughing.
 
Three frictional theories were discussed :

• In first expression it is shown that friction depends on the lowest shear strength of the
contact tribo-pair. Reducing shear strength and increasing the hardness reduces the
coefficient of friction.

• Second expression shows the dependence of coefficient of friction on the angle of

conical asperity.

• Third expression indicates lesser sensitivity of coefficient of friction compared to that of

conical asperity. 

None of these expression provides reliable estimation of coefficient of friction which we

observe during laboratory tests. Bowden and tabor improved that theory of adhesion and
Junction Growth
 
Bowden and Tabor were motivated to think that contact area(shown in Fig. 2.16) might
become much enlarged under the additional shear force and they proposed junction
growth theory. They considered two rough surfaces subjected to normal load W and
friction force at the interface. To explain their hypothesis they considered two
incorporated
dimensional stressthe limiting shear stress
system(Eq.(2.1)). concept.
If W force is in y-direction and force in x-direction is
zero,  then principle stresses can be expressed by Eq.(2.2) and Eq.(2.3).
 

 
....Eq.(2.1)
 

Fig. 2.16: Two contacting surfaces.

 

....Eq.(2.2)
 
Where σ1 is first principal stress, and δ is elemental area.
 

....Eq.(2.3)
 
Substracting Eq.(2.3) from Eq.(2.2) 

Where σ2 is second principal stress.

 

....Eq.(2.4)
 
If yield strength of material is σy = σ1 - σ2 

and shear strength and τy = 0.5τy. On substituting and rearranging.

 

....Eq.(2.5)
 
In Eq.(2.5) τy and W remain constant and this indicates that area of contact will increase
with increasing friction force, till force reaches its limiting value. We can state that on
application of additional incremental tangential force, there will be further plastic flow at
constant shear stress, resulting in an incremental contact area of A. Bowden and Tabor
called this increase the junction growth. Assume τi is shear stress of fractured interface.