Using Three (3) Gage Pins to Check Hole

Proud Liberal

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Using Three (3) Gage Pins to Check Hole Ø

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.
 

bobdoering

Stop X-bar/R Madness!!
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Re: Using Three (3) Gage Pins to Check Hole Ø

This may be an aside, but in general what tolerance are you trying to measure using this technique? Do you know if there is lobing in the hole, and if so two or three lobe?
 

Kales Veggie

People: The Vital Few
Re: Using Three (3) Gage Pins to Check Hole Ø

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.

This seems a complicated method to measure hole size. Have you considered alternatives (and measure variable data).
 

Tim Folkerts

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Re: Using Three (3) Gage Pins to Check Hole Ø

Here is a solution for drawing such a circumscribed circle around three circles, but you would have to do a bit a math to calcualte the sizes
http://mathforum.org/library/drmath/view/55110.html

Here is a research paper on the problem. You would have to pay for the full paper (or perhaps contact the authors directly).
http://www.springerlink.com/content/lbyfy3kr1anr9gqy/

Neither looks like a simple project! I expect that buying some more pins of the proper sizes will be cheaper and easier in the end.

I suspect that if you did get it to work, the best solution would be to basically create a table with all the combinations of pin sizes you have, sort it by the final diameter, and then look up the closest size in the table.


Tim F

P.S. the problem of packing IDENTICAL circles in a larger circle is well known. That might be a place to start. http://en.wikipedia.org/wiki/Packing_problem
 

bobdoering

Stop X-bar/R Madness!!
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Re: Using Three (3) Gage Pins to Check Hole Ø

I suspect that if you did get it to work, the best solution would be to basically create a table with all the combinations of pin sizes you have, sort it by the final diameter, and then look up the closest size in the table.

Yes, and consider the error of multiple "fits", as well as the feel of overall fit. You might have to verify the calibration and GR&R with some ring gages to see how close you are getting, depending on the tolerance. Man, if you have taper and lobing in the hole, you might as well just put spaghetti in there! :tg:

After all, all gages are 'bad', but they might be 'good enough'! This technique might be good enough if the tolerances are wide open.
 

Proud Liberal

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Re: Using Three (3) Gage Pins to Check Hole Ø

The process is plastic injection molding (fairly large tolerances). Thanx all for the help. I'm on the right path.
 
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