I just got a copy of Graham T. Smiths book Machine Tool Metrology
People on here are always talking about Airy points as where you support a surface plate. Turns out that isn't correct. Airy points are where you support an end standard so that the end faces are parallel.
To properly support a surface plate you use Bessell points. The Bessel points will support an evenly-loaded bar or plate at the point of minimum deflection.
Airy points are 1/ square root of 3 = 0.577L
Bessell points are given as 0.554L The text doesn't say how that number was derived.
This is an interesting book there is also a biography of George Schlesinger
Interesting stuff
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99.99999% of time i do not work on simple rectangular objects. when you deal with complex shapes the weight or density varies so you do not normally support part in Airy points based on size so much as weight distribution.
....in general make a best guess and bring supports in from ends a bit the exact amount is hard to determine exactly.
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i have often seen big parts weighing over 10 tons when i removed 1/2 ton of chips and coolant that are on and in part the center of the part springs up of course. .0005" over 10 feet is perfectly normal.
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sometimes i get inspection reports telling exactly how a part is off in flatness, perpendicular, twisted, etc. i can use the data to either
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1) jack up corner of part .001" and machine it so when inspected it will be in tolerance
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2) or move a pad location the part sits on closer to Airy points determined by inspections results. often a best guess is a foot or 2 off and pad needs to be moved based on inspection results
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names like "Airy" dont mean much. i have worked in other countries where a billion people call stuff other names. who's to say what is correct name. i wouldnt get too concern with terminology
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the other thing is of course large metal parts like castings have different hardness and other properties in different locations of part. i have often seen harder sections typically in certain locations usually due to part thickness in that section and the rate that part section cooled. the different metal properties in different locations of large parts can make them distort not just from gravity but from different sections pushing and pulling on other sections. similar to cold rolled steel. if you mill the skin off one side a longer cold rolled piece will often bend like a banana.
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2nd picture shows a casting on its side that typically warps curved shape and needs multiple finish cuts to get within .0005". that part warpage in that case is not caused by weight but internal stress in the metal
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airy is 2 dimensional part sitting on 2 supports
bessel is 3 dimensional part sitting on 3 supports
or at least i believe thats the difference and i might call both airy points. if you talk to average operator and mention airy or bessel points good chance they never heard of either name but most understand the principle of not supporting a long flimsy part on its ends