Finding Taper Angle

Well Mark, persuming that you are machining a shaft that has a one in six taper and it is the INCLUDED taper of the part, then you should divide the length (6) by one-half of the change (1 x.5 =.5) which will give you the cotangent of the angle (12.000000) which equals approximately 4 degree 46 minutes. Base Length/Altitude=Cotangent Of Angle Adjacent Of Base.

Presuming that you are machining an angle, say through the milling process and you must produce a one in six taper, then you should divide the length (6) by one x one (1 x 1) of the change which which will again give you the cotangent of the angle (6.000000) which equals approximately 9 degrees 28 minutes-nearly double the former statement.

I presume the first scenario is your situation. Still today, a common blueprint callout for the U.S.A. when machining a shaft or hub that has a precision taper still called out as taper per foot included, and what you have equals 2" taper per foot. Not what we would call a self-holding taper.

Ing. Robert Forbus

Shouldn't a turned taper of 1~6 have an included angle of twice arctan 1/6 and not half it as suggested ?

Presuming the angle is being machined on an engine lathe, the taper attachment is usually graduated in both degrees, and taper per foot. One has to be careful, as different manufacturers used different methods. For some, the indicated taper or angle is inclusive, for others, it is per side of centreline. It is the same way on universal grinders.

Since the word used was "taper" instead of "angle" I presumed the poster was talking about a turned part. Hence my advice for determining the angle on one (1) side of the centreline. I remember his question of wanting to determine the included angle of the part, which of course just means to multiply the per side answer times 2.

Ing. Robert Forbus

Thank you Robert. The part in question is a steering knuckle and the taper is on a hole that is machined into one of the "fingers" of the knuckle. I assume that the 1:6 notation means for every 1 unit of length there is 6 units of taper???? From there I guess I could trig out the angle but I wanted to make sure of the notation.

Thanks again.

Mark Smith

Precision Devices

Rather: "for 6 units length, a Δ diameter of 1 unit".

Good Morning Mr. Forbus.

I have a question about how to gage the taper shapes. Currently I made tubing reduction with taper shape, (0.299" small end, 0.315" large end and lenght 0.750") is the #6 taper (American National Standard Taper) and I have some problems at the time when i need to check the cone. I don't know where to find gages to for this taper. I send a picture of my currently gage, (our customer provide it), and what I have doubts at the time when I use it. The gage has the taper shape in it, with a step of 1/16", this step is my tolerance (go), to use the nogo I twist the gage and now it's the nogo. But if i twist the piece a little bit goes into the section and they told me, this is a bad piece. I read the Machinery's Handbook, but i need more info about the taper shapes and try to find the correct gage.

I hope that you can help me.

Thanks.

agustib

Included angle = arc tan of 1/6 = 9.46 degrees = 9 degress 27 minutes 44 sec

Regards

Neville Eve

Thank you all. This information helps a lot. It is what I was thinking it was but I needed your comfirmation.

Thanks again

Mark

Hola Mark. I think the hole is needed for a taper pin. You may check on the Machinery´s Handbook 25th edition, page 1582, American National Standard Taper Pins, dimensions table.

Also check on table 5 American National Standard Self-Holding Tapers-Basic Dimensions.

I can´t figure out what exactly 1:6 means for taper nomenclature. I t may be a 1/6 of an inch per foot, or taper no. 6 or it is a metric designation?. For machining purposes it needs more specific data on the taper. But if you can find how it will work you may have your answer. Regards.

Luis

The expression "1 in 6" taper means that in inches, the part increases diameter by 1" every 6" along the centreline. In other words-if the part is 6" long and is 1" diameter on the small end, it will be 2" diameter on the large end. That is a classic example. When we use the term "taper" we are usually referring to a turned shaft or bore. We tend to use the word "angle" for flat surfaces.

For the metric system of course it is the same. Just substitute units for units and you will be fine. As far as how to calculate the included angle, just apply the trigonometric formula that I used as an example and multiple the sum times 2.

We often speak of American pipe threads in taper per foot. In that case, the callout is 3/4" taper per foot or 1 degree 47' 24" per side approximately. The included angle is approximately 3 and 1/2 degrees.

Ing. Robert Forbus

Thanks again. You all have been a great help.

Mark