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What is the angle of BT40 taper?

T

tok-tokkie

Plastic
Joined
Sep 13, 2011
Location
cape Town, South Africa
All the references I find list the BT40 taper as 3.5" in a foot = 7 in 24.
The diagrams I have seen all give the half taper angle as 8° 17' 50"
Here is my confusion. 8° 17' 50" = 8.297222°
Calculating the taper angle by trigenometry it is ArcTangent of 7/24. That is 16.260205°. Halve that for the half angle gives 8.130102°. That is different to the stated angle.
Where am I making a mistake?
What is the actual angle?
I tried 8.297° on my machine & it does not seem to match my spindle.
 
Taper setting angles are an old machine shop trap.

You gotta work conical tapers on the half angle because they are bodies of symmetry and revolution that is, generated from an axis. Half the tangent of the included angle is not the same as the tangent of the half angle. The half angle is what you have to set the taper attachment, compound, grinder platen, etc. Same when you set the bench center up with a sine bar for inspecting the taper angle.

The half angle for a 7/24 taper is 8.2971 degrees or 8 degrees 17 min 50 sec and you can take that to the bank.

If you're having trouble picking up an existing taper it isn't likely to be the result of competent calculation. Your tool height or indicator contact absolutely positively HAS to be in the plane of the spindle axis lying parallel to the tool path. 1/32 high or low and the spindle won't blue to the gage. Ideally the spindle mouth should be +.0000/-0.0002 with the gage. You got a gage?

Then again it is possible some blithering dufus re-ground the spindle wrong and you get to deal with it now.

Good luck.
 
Last edited:
Directly from ASA B5.10 Machine Taper Standard- the taper is 3.5in/ft. Also from the standard- 16 deg,35 min,39.4 seconds.
Initially I made the same mistake as you did- I think. You have to calculate the tangent form the ½ angle- not the inverse tangent of 3.5/12.
Lay out the taper on a piece of paper- the 3.5/12 is not a right angle, and that's where you get into trouble using the arc tan directly.

Take the arc tan of 1.75/12 and then work it backward- The actual angle is 16 deg,35 minutes and 39.443 minutes.
Also your half angle was not exact- its 8 deg,17minutes 49.72 miinutes.
 
Forrest beat me to it while i was scraching my head figuring out where you went wrong. The clue to me was when I calculated the arc tan of the 3.5/12, the result did not match the deg,min.sec value in the standard.
Dan
 
And...

The taper you are trying to mate may not be a perfect taper so you may have to measure and then fit.

To find the existing taper you can set an indicator inside and at center line of the spindle taper and set to zero. Move out exactly an inch so the indicator point is off and above the wider area of the taper. Raise the spindle or lower the axis holding the indicator to make indicator zero with measuring exactly the amount of travel.

With knowing taper per inch you can manufacture what ever you wish to use in the spindle.

Grind or turn the taper with leaving a little stock to blue the fit to exact finish.

Certainly you can do the same in millimeters.

Buck
 
tok-tokkie said:
Many thanks. I get it now. Pathetic in retrospect.
Click to expand...

You are not alone..

If ever i get too arogant, complaiscent, and self important I inevitably recall humiliating events I brought on myself working the machinist trade. A trade where there is no end to the delusion, folly, and plain bad luck lurking behind every simple-seeming job. Suitably humbled I continue, sobered, humbled, clear eyed - until the next time.
 
For what it's worth, this is a very common error. So you are in good company. The downside is that the error is so common, we can recognize exactly the mistake in the work you didn't show. :)
 
Hi,

8.297222 doesn't look right on my spindle. So 8.130102 maybe? I'm using mach4 lathe to grind the spindle.
 
JRIowa said:
Steep taper holders all have the same angle 3.5000" / foot. NMTB, CAT, BT, and ISO all use that taper. Don't know about any of your "diagrams".
JR
Click to expand...
I guess I missed this post. Calculating 3.5"/per foot gives me 16.71126 degree so half angle is 8,3556.
 
Full angle, half angle.. my head is spinning.
Why is this stuff so complicated?
Wait until you grind B&S tapers. :)

This not a easy task to get right. Frank at Mari must be smiling.
 
Last edited:
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