I'm looking for the formulas to calculate what three (3) different sized gage pins that would combine to form the desired final diameter such that three smaller diameters would be tangent to each other and the circumscribed OD (plus the calculation of the reverse).
ØA & ØB & ØC = ØD
The goal is to setup a spreadsheet where an inspector could enter the size hole that they would like to check and the formula would spit out the three (3) pin sizes that would combine to get that number.
Alternatively, the inspector could enter three (3) pin diameters that combine to fit the part and the formula would return the resulting OD.
NOTE: the use of the term OD is this case refers to the larger diameter that would tangent to the three (3) gage pin diameters used to check the part.
Using Three (3) Pin Gages to Check Hole Diameter
OK--since no one has weighed in on this one, I will. First, please be aware that what you are attempting will result in substantial measurement errors AND possible damage to the holes being measured. (Gage pins are HARD--the ends can gouge the parts being measured.) Those objections aside, you might start this process by looking in Machinery's Handbook--find "Circles in a Circle" in the index. The formulas are for multiple LIKE-SIZED pins, but you CAN calculate the outer diameter by using 3 pins of the same size and multiplying the pin diameter by 2.155. I haven't played with this, but I'm certain one will encounter substantial measurement errors. (Are we assuming these holes are perfectly round?)
Depending upon your required tolerance, I would recommend using small hole gages or telescoping gages (for larger diameters) and measuring them with a micrometer OR--for tighter tolerances, bore gages are not really that expensive. Some bore gages have interchangeable tips, making them useful for wide ranges of diameters. Since "round" holes usually are not really round, one needs to condsider whether to use 2-point or 3-point measuring techniques.