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Adhesive wear - Archard's equation


I am trying to find a derivation of 'Archard's equation' for 'adhesive wear'

Can anyone help, please.

Albert Clyde
- Coleraine, Co Londonderry, Northern Ireland


After considerable searching, I have located several 'incomplete' derivations. Putting these together, I have come up with the following possible solution to my original query - ANY COMMENTS?

Adhesive Wear

Note that the surface asperities will deform until the material yields sufficiently until it is able to carry the applied load. Hence, the pressure generated, P is equal to the yield stress, and this is proportional to the hardness of the softer material.

Assume that all adhesive junctions are circles of diameter 'd'

If there are 'n' junctions then the load carried will be:

L = n * (π / 4) * d^2 * P

i.e., the number of junctions will be:

n = 4 * L / π * d^2 * P

In a sliding distance 'd', all 'n' junctions will be broken and remade.

In a sliding distance 'd', the number of junctions broken and remade will be:

x / d * n = 4 * L * x / π * d^2 * P

If K is the probability of transferring a particle when a junction breaks, then the:

Number of transfer particles = 4 * K * L * x / π * d^3 * P

Thus volume transferred =4 * K * L * x /

π * d^3 * P * ( π * d^3 / 12)

{ Now, the deformation at pressure P, (yield stress), is proportional hardness Rho, i.e., P = const * Rho,

so we may substitute hardness, Rho, in place of P - this only affects the value of the constant.}

i.e., V = K * L * x / 3 * Rho - ARCHARD'S EQUATION


K = wear coefficient

L = load

x = distance of sliding

Rho = hardness of the softer surface

Albert Clyde
- Coleraine, Co Londonderry, Northern Ireland


I've had the opportunity to touch on the subject many times. I'm a Tribologist at a hard drive manufacturer and while I was at another company, I wrote several papers pertaining to the tribomechanical and tribochemical reactions and the contact force between the head/disk interfaces. You can find the papers with a search of "Surface Characteristics for Proximity Recording" in October 1996 issue of Data Storage magazine, and "Techniques Used to Evaluate Robustness of the Head/Disk Interface" in the September/October 1998 issue of IDEMA INSIGHT magazine. In the design of the hard disk drive, the interface between the head and disc needs to take into consideration the wear of the mating surfaces. To measure wear between a disk and head, one needs at least two LDV channels or a system that is capable of measuring the pitch and roll angle of the slider body. I and another person developed a laser beam deflection system, which is capable of measuring small angular changes.

Ronald L. Voights
computer disk drives - Shakopee, Minnesota

August 30, 2008


I am glad to see this derivation - well done. But I have a problem with dimensions. Perhaps I misunderstand the equation's aim as I am not in the industry.

I thought that K, the wear coefficient, is dimensionless. But in that case V cannot be the volume of material removed.

Could you please enlighten me,


Michael McInerney
- Terre Haute, Indiana

April 1, 2009

Hi all
I want to predict the wear rate of gear teeth.I am unable ti understand how to derive and use Archards equation for abrasive wear.Please let me know your suggestions.

Vajralingam Bennuri
employee - Bangalore,Karnataka,India

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