Concentricity of a Tube

Date: 05/09/2003 at 10:33:23
From: Joel
Subject: Concentricity of a tube

I am having trouble finding the concentricity of a tube with a very 
small inner and outer diameter. 

I have searched for a definition of concentricity and still do not 
fully understand the definition. It is my understanding that 
concentricity is the difference of the center point of two or more 
circles (i.e. the roundness of the tube).

radius = 1/2d; therefore, I should be able to locate the center by 
finding the radius of both the inner and outer circles, but cannot 
specifically determine the difference of the center points. I can 
only determine the difference of the two radii. For example:
outer d = 1
inner d = 1/2
therefore,
outer radius = 1/2
inner radius = 1/4
How do I determine the center of the two circles that make up the 
tube?

Date: 05/09/2003 at 16:59:23
From: Doctor Douglas
Subject: Re: Concentricity of a tube

Hi Joel,

Thanks for writing to the Math Forum.

Yes, concentricity refers to "how far apart the centers are". So 
knowing the diameters and radii of both circles does not tell you 
anything about the concentricity - in fact it doesn't even say that 
the inner circle is inside the outer circle.

Because you have a tube, you do know that the inner circle is inside 
the outer circle, and so you have some upper limit on how non-
concentric the circles can be.  

The way I would proceed is to measure the tube's wall thickness, and 
search for the thinnest point, shown as A-B in the figure below:

             |
             *              + is the center of the outer diameter.
       *     |    *          [outer diameter = D]
     *      ooooo   *        [inner diameter = d]
    *     o  |    o  *     
 ---*-----o--+O---A--B---  The center of the inner diameter (O) is 
    *     o  |    o  *     then displaced from + by 
     *      ooooo   *         (D/2)-(AB)-(d/2)
       *     |    *
           * | *  
             |

If this is zero or very small, then the two circles are very nearly 
concentric.                   

- Doctor Douglas, The Math Forum
  http://mathforum.org/dr.math/