[Metrology] Measuring An Internal Taper Using Two Balls. + Question

[Shadowdog500]

I was messing around with the idea of measuring a taper using two balls.
After I worked out the equation (which turned out to be pretty simple) and put it in a spreadsheet, I had to try it out.
I posted the attached video showing the measurement and spreadsheet.

The spreadsheet also has pages on measuring mouth openings of tapers. Joe Pi did a great video on measuring mouth openings with balls that got me thinking about measuring tapers using balls.

Here is Joe's video on measuring mouth openings using a gauge ball:

He is new to youtube, but has excellent machining tips.

I want to post the excel spreadsheet for free distribution.
Any ideas on the best way to do this? Update: link to EXCEL spreadsheet in post #5.

Thanks,

Chris

 

[4GSR]

Chris,

You can post it right here in this thread. You can also post it in the download section of the forum. Look for the tab toward the top of the page.

Ken

 

[Shadowdog500]

Chris,

You can post it right here in this thread. You can also post it in the download section of the forum. Look for the tab toward the top of the page.

Ken

Ken,

Thanks for the info. I've uploaded plenty of pictures, but never an excel spreadsheet. I will look into how to do this.

Hopefully something like this will be useful for others. I mostly played with the idea for my own entertainment.

I like figuring out stuff like this, so if there is anything that would be good to add to the spreadsheet, please let me know.

Thanks,

Chris


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[4GSR]

Chris,

Just upload the excel file as you would a picture file. You can upload just about any file to a posting here of just about any size. We are not like the other forum where you can't load a file bigger than 5Kbits. Ken

 

[caspaincmonster]

Sounds interesting, you can upload it to google docs and share the link, it is free and platform independent and will let people use it on line.
L

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[Shadowdog500]

Sounds interesting, you can upload it to google docs and share the link, it is free and platform independent and will let people use it on line.
L

Sent from my XT1072 using Tapatalk

Thanks,

I just uploaded it onto this thread. I will look into google docs as well.

Thanks,

Chris

 

[Tony Wells]

There is one subtle factor I didn't see addressed in a quick look at your math. That's the effect of the contact line between the ball and the unknown taper NOT being on centerline of the ball. So, in reality, you cannot use the radius of the ball directly in your calculations. Since the bore is tapered, the contact line is below centerline of the ball, and hence the radius value must be somewhat less than the radius of the ball(s). The problem is that you don't know where exactly that contact line is, due to the taper, which is unknown. So it presents a somewhat circular calculation with an unsolved variable. The contact line defines a plane that lies on the tangent point between the taper and the ball.

The ball measurement does work reasonably well on shallow tapers, because that tangent point approaches the radius contact of the ball, but when it does, obviously you then have a cylinder, not a tapered bore. The steeper the taper, the more pronounced this factor becomes. I learned this the hard way a long time ago when making some really critical tapers and decided it would be slick to use 2 balls to measure it. Then the customer sent me a precision ground taper plug to do a blue fit. Took some thinking to see why the methods disagreed. This was before the Internet and all the information it offers, but I did have the Machinery Handbook. And some helpful engineers on the other side of the coin.

This has been discussed on a few other fora plus Googe Groups, etc.

 

[T Bredehoft]

Should you have access to a good drafting program, you can draw the two circles exactly to size, distanced apart (calculated from their depth in the taper) and draw one common center line and one line tangent to both circles and measure the angle between them. Easy Peasy.

 

[Tony Wells]

Sure Tom.....but that's cheating lol

 

[RJSakowski]

The equations for solving the taper measurement by two balls are fairly complicated, at least for this poor soul who last took a trigonometry class in 1959. Here is a drawing of the geometry and the equations derived from it. The last equation gives the taper in terms of the diameters of the two balls and the distance between them as measured by Chris above. Microsoft Excel can be used to solve the equation using an iterative process which converges quickly.

It works like this: d1, d2, and h are fairly straightforward. It is the cos(a) that is the problem. Assume that a = 0 and therefore cos(a) = 1. Substitute in the equation and solve for tan(a). Calculate a new value for a and cos(a) and go through the calculation again. The calculated value will soon converge on the true value, small angles faster than larger ones.

I will upload the Excel spreadsheet to the download section.

I should add that this is not the way that I usually calculate the angle. As Tom stated, I draw the geometry in a good drafting program (I use SolidWorks) and let the CAD program solve the problem.