Quick Measurement Of Small Taper Angle

Further taper thoughts: As I continue to reflect on this issue, it has become obvious to me that there is no easy way to accurately measure a taper when you are not measuring normal to the taper axis. A measurement at any other angle is measuring the major axis of an ellipse. I know that it is possible to determine the diameter from the ellipse measurement but it will involve the taper angle that we are trying to determine (I know because Solidworks can do the math LOL). I suspect it will be an iterative solution.

Plan C: OxTool (YouTube) showed an interesting way to determine tapers. His tool was a cylinder with well defined different i.d.'s on either end. The taper would be mounted in a lathe, indicated for zero runout. The cylinder would carefully placed on the taper and tapped lightly until it was seated true to the lathe axis, thus assuring the the end plane was perpendicular to the taper axis. The position of the opposite end of the cylinder was determined with a dial indicator and his DRO. The cylinder was reversed and the process repeated. Since the cylinder length is the same in both measurements, the difference in position is the distance between the two diameters on the taper. There are two concerns. The edge of the holes in the cylinder have to be sharp or at least have the exact same fillet or chamfer. Also the diameters have to be very well known.

This is similar to the 123 block method above.

I think that I am all tapered out. It was an interesting exercise but it is time to let it go.
 
randyc said:
I started sketching a simple alignment tool but it turned out NOT to be so simple. I couldn't justify making a tool to align the taper when I might measure a taper every two years or so, LOL. I think I'd better forget this method (unless someone can come up with a simple centering technique) and go back to the 1-2-3 block procedure :)

P.S. Thanks for pointing this out !
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Simple, All you need for your method is a bench center :lol: I have put a tapered collet between centers on my lathe and used a dial test indicator to adjust the compound to make my er40 collet chuck. Now I make inboard boat shafts now. last one was 3"dia x21" long
 
Having realized that I had omitted a couple of pieces that went along with my suggestion in the middle of the night. I will attempt to describe what I can not show you visually because of my computer ineptness. When I originally posted , it was with a recently completed job for a magneto shaft in mind . It was a straight shaft with a taper on the end that needed a keyway. Obviously a straight shaft is no problem to lay on a sine bar against a angle plate so you just coordinate in the x for your centerline. What everyone is describing here obviously is a cone, a morse taper for instance. I have used the x-y coodordinate move back and forth to find the high spot method and it works for my use. However there is one more way. A sinebar typically has a little fence or stop at the end. Measure the od of the cone at each end ( measuring the small end is difficult and is a approximation at best to tight tolerances.) Place the part on the sinebar with the small end toward the stop which is also the end your gage stack goes under. Now place a gage pin between the cone, the stop and the dialed in face of your angle plate protruding at least as high as your cone. This gage pin is just a approximated size at this point. A size that gives the appearance of parallelism between angle plate and cone. Place a similar sized pin on the other side touching the cone and stop. Mike across outside of pins. Add or subtract difference from large o.d. end. Select 2 gage pins of 1/2 the difference each and remeasure until outside of pin dimension and large o.d. are equal. This does 2 things. It centers your part in y and it also gives a means of measuring the taper. Tool makers use ball dimensions for finding angles to a sharp edge which is what this method does. Having a known dia. pin hard against your fixed angleplate, the stop and the cone gives you a exact known center point and a right angle between stop and angle plate. With these values you can draw a hypotenuse through the center of your pin and find known lengths and angles all the way to your sharp edge on the small diameter. This requires solving for several different triangles. Of course this exercise eliminates the dti altogether because you already have solved the taper. A long drawn out solution for what started as a simple way I guess. Clear as mud? I will see if I can find a example of using ball dimensions on the net and post if I do. Or possibly this is something you are already aware of.

Darrell
 
I think I see what you are doing. By using two equal diameter pins in a stack with your taper the equals the larger diameter, you ensure that the taper axis is parallel to the angle plate. Using the pins against the stop gives you a measurement point at a good diameter a known distance from the stop as opposed to trying to measure the small end of the taper. If you measure the length of the taper and subtract half the pin diameter, you have your axial distance. At his point, the difference between the two diameters should be twice the pin diameter. Dividing the pin diameter by the distance between should give you the taper in inch/inch. Take the arctan to get the half angle.
:aok:
 
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Exactly. your description is far better than mine.

Darrell
 
Darrell, after two glasses of wine I'm not following that very well.

But the little bit that I THINK I understand suggests that if the large end and the small end of the taper have been accurately measured then the only thing left (to calculate the angle) is to measure the length between the large end and the small end, right ?

What am I missing, can you post a sketch or a photo ? RJSakowski obviously understands your method (and the method obviously works since you've made acceptable parts using it) but both of your brains are clearly a lot more agile than mine :)
 
Just because I can describe it and was shown how many years ago doesn't mean I have a clue how to make and post a drawing with a computer Randy! LOL That is a job for Mr. Sakowski who obviously could whip us up a nice CAD drawing if he would do us the favor. Also if I recall there is a method to use two balls or pins of different dia. a given distance apart between the angle plate and the side of a cone and with the appropriate formula the taper can be resolved.

Darrell
 
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18w said:
Just because I can describe it and was shown how many years ago doesn't mean I have a clue how to make and post a drawing with a computer Randy! LOL That is a job for Mr. Sakowski who obviously could whip us up a nice CAD drawing if he would do us the favor. Also if I recall there is a method to use two balls or pins a given distance apart between the angle plate and the side of a cone and with the appropriate formula the taper can be resolved.

Darrell
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Darrell, a photo would be nice. I am not sure that I understand how the sine bar comes into it from your description. If you can provide a photo, I will be happy to draft the setup.
BTW, Darrell & Randy, since we seem to be getting downright friendly here, the name is Bob
 
Thanks Bob, my fingers were getting sore from typing out your nom de plume.

There is a short chapter in "Machinery's Handbook" regarding setting up tapers. Apparently sine bars weren't considered, I don't know why, as the first choice. Mostly it seems that the old guys preferred to use a couple of known and different diameter discs spaced a precise distance apart. A pair of straight edges (vise jaw or whatever) on each side of and tangent to the discs established the angle. There are lots of tables and math expressions to support this technique in "the book". It makes for interesting reading even if the application won't be used ..

I suppose that the technique might be useful for devising a measuring tool, maybe along the lines of Darrell's sine bar method -
 
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