I've run across a term in some grinding manufacturing research papers called the specific material removal rate. The units given for this term are [mm$^3$/mm$\cdot$s] (I don't really like this style of formatting because it makes it unclear as to whether the [s] is in the numerator or denominator, but that is the style that has been used in all of the papers that I have seen with this term). I am familiar with the general machining term material removal rate (or $MRR$), which is the volume of material removed per second from a workpiece in [mm$^3$/s], but what is the "specific" part of the "specific material removal rate"?
Usually in machining when we say "specific" we're talking about per unit volume removed. So the specific energy of machining is normally expressed as unit energy per unit volume removed (e.g. [J/mm$^3$]). But for the specific $MRR$ it is a volume per second per unit length (after all, it wouldn't make any sense to have volume removed per unit volume removed). So I guess the real question is, what is this length that we are dividing the $MRR$ by to get the specific $MRR$? Why is this term useful?
This seems like a pretty basic question, but I have been unable to find a definition for the specific material removal rate anywhere. I've looked at several papers and from context in the papers it is rather unclear. I've checked my textbook, Fundamentals of Modern Manufacturing 5th Ed. by Mikell P. Groover, no answer there. It may be a term that is specific to grinding operations.
I would appreciate it if any answers could be backed up with a source.