Osborne maneuver

In his book, Home Machinist's Bedside Reader #2 (pg. 159), Guy Lautard describes the "Osborne Maneuver" for accurately centering round stock in the milling machine using nothing more than an edge finder.

It works like this. Accurately measure the diameter of the stock. For description purposes, let's assume that the y axis is along the 12-6 o'clock line of the stock and the x axis is along the 3-9 o'clock line. Align the edge finder by eye to the 3 o'clock position and locate the edge of the workpiece. Now move by half the diameter towards the center of the stock along the x axis. Now, use the y axis controls to find the edge of the stock near the 12 o'clock position. Move half the diameter towards the center of the stock along the y axis.

Now do it again. Use the x axis controls to find the edge of the stock near the 3 o'clock position. Move half the diameter towards the center of the stock along the x axis. Use the y axis controls to find the edge of the stock near the 12 o'clock position. Move half the diameter towards the center of the stock along the y axis.

As you repeat this procedure again and again you will approach the center of the stock with ever increasing accuracy. (In mathematical terms, the procedure converges to the center of the stock.)

The question becomes, "How often do I have to do this?". The answer is, "Probably fewer times than you think!". I wrote OSBORNE.EXE to examine how fast the process converges. For example:

OSBORNE MANEUVER

Workpiece diameter [2] ?
Initial offset [0.1] ?

iteration: del1,del2,error= 1: 0.10000000, 0.00501256, 0.10012555
iteration: del1,del2,error= 2: 0.00501256, 0.00001256, 0.00501258
iteration: del1,del2,error= 3: 0.00001256, 0.00000000, 0.00001256
iteration: del1,del2,error= 4: 0.00000000, 0.00000000, 0.00000000
iteration: del1,del2,error= 5: 0.00000000, 0.00000000, 0.00000000
iteration: del1,del2,error= 6: 0.00000000, 0.00000000, 0.00000000

Here we have a 2 (we'll say inch but units don't matter) diameter workpiece and we initially aligned with an error of 0.1". That is to say, we initially aligned by eye to the x axis at the 3 o'clock position with an error of 0.1". If your eyes are that bad, you need better glasses! After the first iteration we're still 0.1" off the x axis (del1), but we're within 0.005" (del2) of being on the y axis. Our radial error (distance from the center of the workpiece) is the root-sum-squared of del1 and del2 or 0.100126". On the second iteration, del1 becomes the del2 of the previous iteration and that puts us within 0.0000126 on the x axis. The iterations continue in this fashion with del1 always becoming the del2 of the previous iteration.

As you can see, even with a hideous initial error we've converged to a nearly unmeasurable* error after only three iterations. You can use the program to experiment with other combinations of workpiece diameter and initial error. Personally, I do it twice and don't worry about it.

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* For readability, I used fixed point rather than scientific formatting in the printout. In the last iterations, the errors are smaller than the specified fixed point size (10^-8) so they show as zero. In fact they're non-zero but less than 10^-8; for our purposes essentially zero.

Marv's ability to illustrate an issue, and describe solutions is uncanny, and typifies highest level of mentoring. To write software and offer it gratis, is beyond generosity. Today alone, there've been 2-3 programs already suiting what I have to do regularly. We are literally fortunate to be his students. Not only in personal benefit, but to emulate and broaden the ranks of those we associate via other means. And that's good for all of us.

Or in for-profit situation, use stock a little oversize. 4 hits X +/- Y +/- will do the trick. Knowing your backlash makes it partly, but reasonably accurate.
With a DRO, something rigid i.e. endmill shank or dowel works well. I don't hit one side [say X-] then 6 o'clock one of the Y's; going all the way across first. Divide the reading x.5, and transit to the axis thus calculated and repeat touching off two sides of second axis. Done. A corner, is 'found' the same way, but 2 hits + half contact diameter will give the coordinates. An actual edgefinder is more accurate, but requires a toolchange.
Round, square no matter; really it's a CMM variety of size determination, by subtracting stylus diameter.

An added mathematical insight...

If you're centering conventionally, i.e. by rotating a DTI around the stock until you get the same reading at +/- X, +/-Y there's no reason to check -Y which may have the DTI dial facing away from you.

Given cylindrical stock, there's no way you can have the same reading at +/-X and +Y and not have the same reading at -Y.