selecting values for macrogrit size ranges

M

Mr.Wizard

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Feb 28, 2015
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I am calculating median grain sizes directly from sieve specifications for the next revision of my grit chart (GLGC) as I have become dissatisfied with the estimates provided by organizations like FEPA and UAMA.

For bonded macrogrits (sieve grades #4 to #220) the coarse limits follow a regularly spaced series. For most of the grits the fine limits also follow this spacing but grits 150, 180, and 220 have an expanded range allowing a finer distribution to pass grading. If for my charted value I take the arithmetic mean of the limits this shifts these three grits in the fine direction relative to their coarse limits.

Are these three grits better represented by the mean value, creating a gap between 120 and 150 despite the coarse limits continuing on the regular spacing, or with a value biased toward the coarse limit, hiding the expanded fine limits allowed by the standard?

For the visually inclined here is a graph of the sieve specifications for each of the grits. For each the gray line represents the coarse limit, the orange the fine, and the black dot (one way to calculate) the mean. The cumulative plot of the particle size distribution of an acceptable grit would be contained in the shaded area between the two lines.

FortyTwoBlades FortyTwoBlades I am tagging you since you are in the business.

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In my experience, the finer side of the PSD doesn't matter as much as the coarser side, so I would use the mean. I think the fines are more filler than anything.
 
D Diemaker Thank you. I think I understand except for "so I would use the mean." That (arithmetic mean) weights the fines as much as the coarse, no?
 
I was thinking of the black dot mean in your chart, which looks to me to be the theoretical size. I would say don't shift to account for the fines, use what the size should be. In reality, it all depends on how well the abrasive is sized, which for the common ones is pretty poor. I always laugh when I see Shapton list their abrasive size to the tenth micron for aluminum oxide. You are trying to overthink what is far from exact, and varies quite a lot batch to batch. Just use the theoretical size and don't worry about mean, median, or mode sizes for your chart.
 
D Diemaker Okay, I see. I appreciate the reminder that this is all far from exact. I want to do the best job I can but it's easy to get lost in the weeds. The Shapton numbers seem particularly absurd after seeing this post by ToddS showing ~100µ grains in a "1.84µ" stone. The black dot is actually midway (arithmetic mean) between the main coarse limit (where the gray line first jumps to 100%) and a log-linear interpolation of the fines sieves at 50%. Here is what a regular geometric spacing looks like; note the shift to the right for 150, 180, 220.

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I'd say my experiences are in line with Diemaker's remarks. Coarse grit has a proportionally greater influence than fine in a mix.
 
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