Hello All! This is my first post here. I have lurked around quite a bit, but I have a more specific question that I have not been able to find a 100% clear answer too. So, my goal right now is to make a nice cylindrical square for the shop I work at. We just had our 18x24 granite surface plate resurfaced to grade A, and are now looking to get some more tools and gauges for inspection. From what I've read so far on the net, cylindrical squares are made by taking a solid bar (or thick walled pipe) chucking it up in a lathe, center drill both ends then either hold the bar with only a dead center on the tailstock, or turn it between dead centers. with the tail stock having a half dead center. you take a cut on the face of the bar then take a cut on the tail stock end all the way up to the center drilled hole then undercut the end leaving 0.375" ring of material around the circumference of the bar end. Then, a parting tool is used on the head stock end. the face at the tail stock end of the bar should now be very close to 90 degrees if the machine itself is in good condition, and in proper alignment. the other end that was cut by the parting tool should be close, but from what I have read the parting tool can give somewhat less predictable results as far as accuracy is concerned. Anyways, after all that you harden and temper the steel then either use a tool post grinder or a cylindrical grinder to get the necessary finish. So, assuming one does everything right on a well built machines, and measured everything making sure there is no taper you would have a cylindrical square with +/- 0.0001" accuracy. So, I guess my question is what is the next step after that to get it more precise assuming you could measure to those tighter tolerances? Does one lap it, or can one spot it on a surface plate, and perhaps file or scrape the high spots like on flat surfaces while being careful not to work a taper into it ( I'm not sure if this can even be done as I have not read any info on such methods)? Just curious really. I'm one of those people who have a thirst for knowledge, and experience. To make sure not to confuse anyone I'm aware that there are probably many more ways for turn a cylindrical square on a lathe, and to grind to good precision, but I'm more concerned with A) methods of verifying a cylindrical square (means of self checking), B) methods of how a more accurate and precise grade cylindrical square is made after initial turning, grinding.
Thanks in advance.