Mean volume can be another useful way of describing a particle size distribution if the standard distribution holds a tolerance that is centered around the mean of the distribution. Mean volume is a calculated algorithm based on the volume that a particle occupies in the measuring medium-i.e., a particle will displace its own volume if it is submerged in a liquid, and that volume can then be calculated by measuring the height of displaced liquid.
Even if no other variables about the abrasive material are known, basic predictions about the behavior of the abrasive can be made based on its particle size distribution. For example, a d50 of one 15-micron (µ) material will not be as aggressive as a d50 of another 15-µ material if one of the distributions contains a higher value at the d10 mark in the same species of abrasive.
For submicron abrasive applications, the "span" of the particle size distribution is also important. This characteristic is defined as the d90-d10/d50-the lower the value, the tighter the distribution. The span provides a relative measure between the points of distribution and therefore signals the quality of the distribution. For example, if we specified a mean of 0.17 µ with a standard deviation of less than or equal to 0.050 µ on a 0-0.25-µ material, we could receive a material with a d50 = 0.167 µ, a d90 = 0.237 µ and a d10 = 0.119 µ. If we add span control to the same specified material at less than or equal to 0.068, we might receive a d50 = 0.164 µ, d10 = 0.118 µ and a d90 = 0.230 µ. While the differences may seem trivial, the tighter specification can generate a higher quality finished part.
It should be noted that a number of different devices can be used to calculate these distributions, and all devices are not equal. Abrasive users should insist that the particle size analysis conform to the accepted norms of the gage reproducibility and repeatability (R&R) studies developed for use in the automotive industry.
As with particle size distribution, the instrumentation used by the abrasive supplier can affect the reported coarse channel measurements and should conform to the appropriate industry standards.
For example, let's say we're producing aluminum oxide faucet seals and we want to lap for flatness as the first step. We would probably want a fairly coarse particle size distribution-i.e., the d10 of the distribution will not be as critical as the d50 or d90, because the coarse end of the distribution does most of the material removal work. However, this does not mean that the distribution should primarily be on the coarse end. While an abrasive with a higher level of coarse particles will provide a higher material removal rate, using too many coarse particles will take material off in such large quantities with such deep valleys that a secondary polishing operation might not be able to remove these valleys to an acceptable finish. For our rough lapping operation of the ceramic seal, the specification might be a d50 range of 10 to 20 µ, with a d90 of less than or equal to 20.5 µ and a hard stop on the coarse channel of 32.5 µ, meaning that the largest particle should not exceed this value.
In the second step of the operation, we'll want to polish the part. To select the appropriate abrasive characteristics for this step, we must first define the ideal level of polishing required for the final application. For example, when polishing ceramic seals, the material removal rate (Ra) and root mean square (RMS) of the peaks and valleys of the polishing process are the important considerations. If these values are too low (i.e., a highly polished surface), the seal will have a tendency to "stick" to the mating surface. In faucet seal applications, an extremely low Ra/RMS will cause excessive strain on the mechanical holding mechanism, while in mechanical pump applications, it might cause the spring tension device holding the seal to fail. In either case, the product will probably fail to perform as designed.
In our example of aluminum oxide faucet seals, we would want a surface roughness that is high enough to provide a positive seal against liquid seepage while still being low enough to ensure useful operation. We would probably select a 2 to 4 µ material with a high aspect ratio (1.4 to 1.0) and a particle morphology in which the surface characteristics exhibit a certain degree of surface striations on the particle.
In glass texturing operations, the abrasive requirements would be quite different. For instance, in automotive glass edging, the surface needs to be rough to the edge of the glass to ensure a tight fit against the elastomeric window frame seal. The edge of the glass also needs to have a uniform roughness to ensure a good seal and an aesthetically pleasing finish. For this type of application, we would select a narrow particle size distribution, such as 15-25 µ with a mean of 19.5 µ and a standard deviation of less than or equal to 2.6 µ, with a tight standard deviation and a low aspect ratio (1.3 to 1.0 or less).