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

[Shadowdog500]

I uploaded the spreadsheet as a zip file in the Downloads, Calculators for Metal Working category. http://www.hobby-machinist.com/resources/socket-taper-calculation-by-two-ball-method.3098/


John, I plugged the numbers from my SolidWorks drawing into your formula and it comes out with an angle of 5.4502º. I also checked the Excel spreadsheet against the SolidWorks drawing and the angles agree to eight decimal places so I'm quite sure that my equations are correct. (On the original drawing, the dimensions for d1, d2, and h were rounded off which I corrected in the drawing in the spreadsheet.)

I would be curious to see how you arrived at your equation.

RJ,

I was going through your equations, and they do work similar to mine but approach the solution in a different way. The height "h" is measured differently, so the same numbers can't just be plugged in both equations. You are measuring h as the difference between the two horizontal plains where the ball touches the taper. John and my equation measures h as the difference between the center of the two balls.

I will draw a picture or do a video when I get home tonight that shows the derivation of my equation. In addition I will show a comparison to your equations and my equation.

Thanks,

Chris

 

[John Hasler]

I uploaded the spreadsheet as a zip file in the Downloads, Calculators for Metal Working category. http://www.hobby-machinist.com/resources/socket-taper-calculation-by-two-ball-method.3098/


John, I plugged the numbers from my SolidWorks drawing into your formula and it comes out with an angle of 5.4502º. I also checked the Excel spreadsheet against the SolidWorks drawing and the angles agree to eight decimal places so I'm quite sure that my equations are correct. (On the original drawing, the dimensions for d1, d2, and h were rounded off which I corrected in the drawing in the spreadsheet.)

I would be curious to see how you arrived at your equation.

I did it by noting that a radius from the center of a ball to the line of contact (your d1/2 and d2/2) forms a right angle with the wall of the cone and then using similar triangles.

Your h is not the center to center distance. The distance between the center of the ball and the center of the circle of contact is proportional to the diameter of the ball.

 

[RJSakowski]

RJ,

I was going through your equations, and they do work similar to mine but approach the solution in a different way. The height "h" is measured differently, so the same numbers can't just be plugged in both equations. You are measuring h as the difference between the two horizontal plains where the ball touches the taper. John and my equation measures h as the difference between the center of the two balls.

I will draw a picture or do a video when I get home tonight that shows the derivation of my equation. In addition I will show a comparison to your equations and mine and my equation.

Thanks,

Chris

Your method does give the correct value for the taper and it is a more elegant solution. I am looking forward to seeing your derivation. Thanks!

 

[Shadowdog500]

Your method does give the correct value for the taper and it is a more elegant solution. I am looking forward to seeing your derivation. Thanks!

Thanks!!

I will do a video tonight but I made the attached PDF comparing our two measurements.

page 1 is the basic setup where we both start. Page 2 is your setup, Page 3 is my setup.

Thanks,

Chris

 

[RJSakowski]

Thanks!!

I will do a video tonight but I made the attached PDF comparing our two measurements.

page 1 is the basic setup where we both start. Page 2 is your setup, Page 3 is my setup.

Thanks,

Chris

I did it by noting that a radius from the center of a ball to the line of contact (your d1/2 and d2/2) forms a right angle with the wall of the cone and then using similar triangles.

Your h is not the center to center distance. The distance between the center of the ball and the center of the circle of contact is proportional to the diameter of the ball.

Got it John and Chris! From your pdf, if the distances from the vertex to the center of the balls is l1 and l2 and the diameters of the balls are d1 and d2,and the half angle of the taper is a, then sin a = d1/2 * l1 = d2/ 2 * l2 and the distance between the centers of the balls , h, = l1-l2 or h = d1/2 *sin a -d2/2 *sin a. Simplifying, h = (d1 - d2)/(2*sin a). Solve for sin a =(d1-d2)/2*h and a = arcsin(d1-d2)/2h.

Sometimes I overthink things! A solution elegant in its simplicity.

 

[Shadowdog500]

Got it John and Chris! From your pdf, if the distances from the vertex to the center of the balls is l1 and l2 and the diameters of the balls are d1 and d2,and the half angle of the taper is a, then sin a = d1/2 * l1 = d2/ 2 * l2 and the distance between the centers of the balls , h, = l1-l2 or h = d1/2 *sin a -d2/2 *sin a. Simplifying, h = (d1 - d2)/(2*sin a). Solve for sin a =(d1-d2)/2*h and a = arcsin(d1-d2)/2h.

Sometimes I overthink things! A solution elegant in its simplicity.

RJ,
Here is the derivation as well as a comparison to your solution.

Thanks,
Chris

 

[RJSakowski]

Chris, an even simpler analysis.

 

[Shadowdog500]

Chris, an even simpler analysis.

Thanks!!

Chris

 

[Andre]

I always wondered what gauge balls could be used for. Thanks for posting

Sent from my XT1053 using Tapatalk