Friction is not a simple or fundamental force by any means. There are different mechanisms behind frictional force which grow or weaken depending on many factors (normal force, velocity, lubrication, materials, temperature, area, etc. etc) and even then not all of them are understood.

The coefficient of friction on a macroscale is higher than that on a microscale for comparable contact stresses. When measured for the small apparent area of contact and very small loads used in microscale measurements, the indentation hardness and modulus of elasticity on a microscale are higher than that at the macroscale. This reduces the degree of wear at the microscale. In addition, small apparent areas of contact in microscale measurements reduces the number of particles trapped at the interface and thus minimizes the ploughing contribution to the friction force. Based on this study, it is concluded that measured values of the coefficient of friction on a microscale are a strong function of normal load and the apparent area of contact.

if want to see in details.

http://www.sciencedirect.com/science/article/pii/0040609095081380

A coefficient of friction is a value that shows the relationship between the force of friction between two objects and the normal force between the objects. The coefficient of static friction is the friction force between two objects when neither of the objects is moving. It has to be measured experimentally, and cannot be found through calculations. Rougher surfaces tend to have higher effective values.

An examination of the surface topography, by means of an electron microscope, has shown that the earlier type of slip ceases because surface scratches extend the boundaries of real contact both the force of adhesion and the tangential force vary linearly with the real and apparent areas of contact.

To see more.

http://iopscience.iop.org/0370-1301/63/3/305/pdf/0370-1301_63_3_305.pdf

http://www.sciencedirect.com/science/article/pii/0020740388900021

I think that contact area has nothing to do with the coefficient of friction, although it could have something to do with friction.

Friction, static or dynamic, is typically described as the normal force between the surfaces multiplied by the coefficient of friction. But another way to think of it is that friction is a function of the pressure between the two surfaces (force per unit area), multiplied by coefficient of friction, multiplied by the contact area.

So, this shows that changing the contact area will affect friction only if you simultaneously increase the normal force between the two objects. It also shows that the coefficient of friction is not affected by either the contact area or the normal force.

Friction is not a simple or fundamental force by any means. There are different mechanisms behind frictional force which grow or weaken depending on many factors (normal force, velocity, lubrication, materials, temperature, area, etc. etc) and even then not all of them are understood.

The coefficient of friction on a macroscale is higher than that on a microscale for comparable contact stresses. When measured for the small apparent area of contact and very small loads used in microscale measurements, the indentation hardness and modulus of elasticity on a microscale are higher than that at the macroscale. This reduces the degree of wear at the microscale. In addition, small apparent areas of contact in microscale measurements reduces the number of particles trapped at the interface and thus minimizes the ploughing contribution to the friction force. Based on this study, it is concluded that measured values of the coefficient of friction on a microscale are a strong function of normal load and the apparent area of contact.

if want to see in details.

http://www.sciencedirect.com/science/article/pii/0040609095081380

Dr Tanzeel Areeb

Thank you

For the enclosed link of paper I am not able to download those papers if possible kindly attach the pdf will be helpful to go through

you have mentioned that increase in surface roughness will increase co efficient of friction, I know that surface roughness will increase friction kindly explain the relationship between surface roughness and coefficient of friction weather any standard data are available.

Dr Albert Manfredi 

Thank you

For your answer it was clearly stated in answer that co efficient of friction doesn't depends on the contact area kindly provide some article related to that and also by today I will update the problem similar to which I am working on kindly provide your valuable input

Regards

These papers will help you

Thank you very much Dr Tanzeel Areeb

I will go through and reply back I will update the problem similar to which I am working on kindly provide your valuable input

Prabhakar, on a macro scale, see for example these simple explanations:

http://www.physlink.com/Education/AskExperts/ae140.cfm

http://hyperphysics.phy-astr.gsu.edu/hbase/frict3.html

https://answers.yahoo.com/question/index?qid=20110619004221AArNcif

On the micro level, this may not hold true, depending on how the surfaces deform and recover.

Dear all,

Please find the enclosed attachment of images of problem similar to which I am working on,  for similar conditions

Fa ( axial force) is generated by pneumatic pressure which is considered as 5 bar in constant area (therefore force cannot be varied) is one limitation

i (number of friction surface is 1) is another limitation one surface is of cast iron and another is of steel

Td ( Transmit torque) expected to be maximum as possible

rm (mean radius) can be varied by varying the contact area (b)

As by varying the area friction reduces I want to know the effect of co efficient of friction

Kindly provide your valuable input

Regards

Prabhakar Purushothaman

Dear all,

Please find the second sheet of the problem

sorry for inconvenience I was not able to attach in previous message

Regards

Prabhakar Purushothaman

I have limited experience testing weak planes in a mudstone that was overcored perpendicular to bedding in the roof of a coal mine, I used a double axis direct-shear machine that was servo-controlled, with feedback sensors mounted on the specimen box to control specimen shear as closely as possible. A low direct-shear velocity was applied after a normal force was applied.  Normal force was adjusted in several small linear steps to account for reduction in contact area.  The limiting friction in this case first hardened (increased in amount), and then softened (decreased in amount), both nonlinearly.  The amount of shearing was only 0.9 inch before the test was stopped.  Therefore, a residual friction value was not reached.  The softening proceeded quickly at first, but the rate of decreased slowed.  All of this, I believe is very congruent with Tanzeel's excellent explanation. 

I also performed creep tests of some of these specimens where I had constant normal force, then cyclical constant shear force on for two days, then off for two days, then repeat at higher shear force, all with the same applied normal force.  The relaxation curve was similar in magnitude, but slightly smaller than the creep curve.  In other words, creep had primary phase, but only a small secondary phase, and no tertiary creep.  Rates of creep increased with higher direct shear force.  In one sample, I had 11 such cycles.

I think friction is self generating force when ever there is relative motion between two contact surfaces, surface may be imaginary for fluid flow. and it is function of coefficient of friction and normal force acting on the surface. but the coefficient of friction is a material properties not the contact surface area. as i think when ever there is a relative motion it may possible of material transfer between two surface during  relative motion and that may vary the coefficient of friction as well as the surface finish hence the contact area so that final effect is seen on frictional force.

Hi

F=mu N as we were all taught may be a simplification of a complex phenomenon. You may want to use it cautiously. If possible, conduct a simple experiment to see if your case can be related to this equation or a correction is needed.

Dear all,

Thanks for helping me to come to a conclusion that co efficient of friction doesn't depends on the contact area it is the function of material in contact, kindly help me to select the best coating material and process with Ra value to increase co efficient of friction in hardened steel part

Regards

Check out the the Society of Tribologists and Lubrication Engineers> http://www.stle.org/. (Trboligy is the study of friction and wear)  They publish books on the subject.  My experience is way out of date, but there have been many papers at society meetings that deal with the sujbect.  As Tanzeel Areeb says, it is a very complex subject, and a to think in terms of a single coefficient of friction is a gross simplification.  In dry metal friction, friction s caused by the interaction of asperities on the two surfaces. As such, it will depend on the hardness of the two materials, to some extent on the surface roughness.  .The reason that the friction is relatively independent  on the load is that is that the load is trasferred from one surface to the other by the junctions between asperities.  It some cases, if the martiarl are similar, there can actually be welding and tearing between the asperities. The worst case for this is when both surfaces are the same material, like steel on steel.  Much better is steel on bronze.  As for coatings, there are many available, the most common being lubricating oil or grease.

Answer to this question may be a matter of research.

Normally, experiments to evaluate coefficient of friction between two different surfaces, the contact area is kept constant and load (normal force) is varied. to find the answer to this question, experiments can be conducted with constant normal force and varying area of contact.

A good example of motorcycle Tyre application

The coefficient of friction varies with various physical parameters. For instance, cold rubber is harder and thus less sticky than warm rubber; the same equation applies but μ is lower for the cold rubber. Static friction, the force necessary to start sliding, is greater than the friction created while sliding. In riding, we're concerned with rolling friction, which is somewhere between static and sliding friction. Again, same equation, but three different values of μ.

If you switch to tires with a better coefficient of friction, you'll immediately notice that stickier rubber is also softer; it wears out much more quickly. Motorcyclists accept the need to replace high-performance tires more often than touring-oriented rubber, but the auto types have another option: They can use wider tires to spread the wear over more rubber. And there, finally, is the reason high-performance auto tires are wider. It isn't to get better traction. Better traction comes from stickier rubber. The tires are wider to get acceptable wear from the stickier, softer rubber.

http://www.stevemunden.com/friction.html

Dear Dr Krishnan Umachandran,

Thank you for your answer it was very useful