I have a part (it's a tire balancer cone) of an unknown taper. When I first saw the cone I figured I'd use the right triangle rule but that's not correct because the right triangle's tip isn't the tip of the cone- because the 'cone' doesn't have a point. What's the best way to find its taper angle?
Ah! thanks. So the resulting number will be the large diameter? the height stays unchanged? e.g. say the small end is 1" the large end is 3" so 3-1=2 - I'll use 2 as the bottom diameter.
In other words: X=Inv Tan (Opposite/Adjacent)
X= Inv Tan (1.6/1)
If you want to know taper, that is normally expressed as inches per foot. The taper of a ramp in the example above would be R-r (in inches) divided by H (in feet). If you want the machine taper, you need to define if you want included angle or not. For included angle it would be D-d (in inches) divided by H (in feet). Check here and you'll see that different standards calculated taper differently (included vs non-included angle). I've encountered this confusion many times. https://en.wikipedia.org/wiki/Machine_taper
As far as the angle calculation in post #6, that is as fundamental as it gets -indisputable.
Right, I was doing Arctan (H/(R-r) which gave me the angle from the other end but subtracting from 90 would set that straight. Thanks again guys. Now I can't wait to get home and see if the compound slide angle follows the part
Well that worked guys, the taper's angle based on my measurements came out to be 12.3deg, which was confirmed by the angle gauge/protractor too. My guess is it was 12deg even when it was made. Thanks everyone!
The taper is the difference in diameters divided byr the distance separating them but the half angle (measured between center line and the taper is the arctan of half the taper. The total include angle is twice that angle. Taking the arctan of the taper is close to the total angle but only when the angle is small. For small angle measured in radians, a = tan a = sin a. As the angle increases this equality falls a part. For example , for a 1º angle a = .017453 radians, tan a = .0174655, and sin a = .017452 but for a 45º angle a = .7854 radians, tan a =1, and sin a =.7071. For this reason the equality a = 2 arctan a/2 is not true.
???? See the pictogram from top to bottom. Assuming the dimensions are H =1.6, D = 3 and d = 2 then, the angle wrt horizontal axis is arctan (R-r)/H = 17.35 degrees. The included angle is twice that. The angle at the base end is 90-17.35.
OP here...per post# 13 above I was able to calculate and verify the correct angle using the ArcTan(R-r/H) forumla.
Ray you're absolutely correct...however, the dimensions I used in this thread were not the actual dimensions of the cone though, hence my results in post #13 were different but the formula was spot on. Thank you and everyone else for that.
Mark, There were two errors in your previous post. The first is that to find the angle, you use the arctangent function not the tangent. The second is that you have to use the radii rather than the diameters to determine the angle as stated by Ray in posts 6 & 9. arctan(D/2-d/2)/H = arctan(.5/1.6) =17.354º while (arctan(D-d)/H/2 = 16.00º.
You guys are absolutely right! I am doing my compound setting using taper per foot. Heres what I was thinking. Taper foot is tpf over 24 equals tangent angle. Or not really thinking at all I guess Thanks guys learn something everyday and realize just how much I need to hit the books again. Been away some twenty years after doing for it for twenty. Started in screw machines while doing and app. Program doing general machining. Took a job across country as a general machinist. Not enough work and life. Driven a Zambonii for the last twenty in another town now for work. Lost some people in my life. Realized i miss machining. Seeing something your making evolve. Good for the soul. Sold my two motorcycles and took out the credit card and back into machining at fifty. Still driving a zamboni for now. I Can ramble a bit! But guys I am not too proud and Always willing to learn. Thanks And another realization there is so much and machining is definite. No Horseshoes! Need to sharpen up I guess. Just another great challenge on it s own to learn and be interested!
Holy cow up at 4 am. With my better halfs alarm going off to watch the queen get married. First thing I do is grab my calculater over this trig and my post. I Don t care who is right or wrong. For me its am I That out of touch being out for so long and another question to me if what I am doing with my life crazy. Taking a run at getting my own shop going. Lost all my confidence and second guess myself. Took my old books to verify. Well the trig worked out as I thought after braking it down to a proper triangle? I have a story to tell and been meaning to start a thread about it.
One thing is I Should really think more about what I post especially when i ve had a few. I ll be better and more respectful to all and this forum!