Sliding distance could be easily calculated given the test time, sliding speed and the test scheme geometry. For pin-on-disk or block-on-shaft schemes you can calculate the wear path length per one rotation as 2Pi*R and then multiply it by the total number of rotations.
In literature we are unable to find the reference of this formula. most of people calculated wear rate in term of sliding distance and use (mm3 / N-m) unit . Have you any reference of this formula???
I understand that your testing scheme was reciprocal movement and in this case your calculations are quite correct.
Another thing is that wear rate is dependent on the wear test time non-linearly. For some first time there is a wear stage called "running-in stage' when wear rate is maximum because of initial roughness. Then there is a stage of normal mild wear and wear rate determined at this stage is usually taken as a characteristic wear rate to be included with further calculations of designing the device.
in your attachment you calculated two different values but both of them are correct and could be used because sliding path length is proportional to the sliding test time.
Method 1 gives you the wear rate dimensionality as mm3/N*min
Method 2 gives you the so-called wear intensity, mm3/N*m
Both approaches tell you the same information but the final figures wiil be of course different. You may use any of them for your paper but make sure that you use the same value for all your samples .
Dear Rana, usually wear rate is expressed and calculated as W=mm3/N.m where mm3 refers to wear volume and N.m is normal load per sliding distance. The value of this equation is that is independent of hardness. The sliding distance can be calculated as the linear speed times the duration of the test. In the case of a reciprocating test you can find the sliding distance as the frequency(f) times the duration of the test(t) time wear track length (wtl), or SD=f*t*wtl
In fact, the Archard's law is not true for many tribological systems and therefore dividing the wear volume by normal load is not approppriate anymore. In such a case, more productive approach will be either defining wear rate as mm3/time or using more general approach such as reconstructing the so-called wear maps invented by Ashby, where the wear rate is plotted against normal load and sliding velocity as a contour map or 3D plot. The advantage of wear maps is that you may identify the mild wear areas and corresponding combinations of load and speed values.