Gallery, Projects and General > How do I??
Math for machinist tapers...
NeoTech:
Well i got my filthy hand on this tool holder that states BT40.. after some googling i found that the taper is of the type "7/24".. well that is some ancient way of telling degrees or angle i guess.. 7 inch per foot.. right.. How do i convert that to well.. modern measurements.. like degree of angle....
AdeV:
According to my digital angle gauge, it's 7.8 degrees.
I did try a bunch of maths, but in this case, the universe disagreed :scratch: (this might be because my desk is not totally level, I am not sure, trig suggested an answer of 8.297 degrees = tan-1((7/2) / 24), assuming the ratio really is 7 in 24.
NeoTech:
After way much googling the closes i found was this Angle = atan(7/24). but in the case with the BT40 holder i cant seem to figure out if its included angle or not.. if its included that would be *2..
AdeV:
--- Quote from: NeoTech on February 07, 2013, 04:05:38 PM ---After way much googling the closes i found was this Angle = atan(7/24). but in the case with the BT40 holder i cant seem to figure out if its included angle or not.. if its included that would be *2..
--- End quote ---
Unfortunately, Machinery's Handbook completely glosses over any British Taper standards, mentioning only the BS Standard number (1660) from 1972.
It does go on to mention that the National Machine Tool Builders Assoc. chose a 3 1/2" per foot taper to be standard on milling machines as far back as 1927... i.e. 7/24. so I think we can be reasonably certain that's the BT40 spindle taper.
To get the taper angle, you have to halve the taper-per-foot, so arctan(7/48) should give you the correct result. Do not ask me how I know this...
The above is wrong, see Marv's post below, which is correct!
mklotz:
If the taper is 7" of diameter in 24" then the INCLUDED taper angle is...
arctan (7/24) = 16.2602... deg
and the taper HALF ANGLE is half this value = 8.130... deg.
Note that this is NOT the same as:
arctan (7/48) = 8.297 deg.
Mathematically,
arctan (x/2) is never equal to 0.5*arctan (x)
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