As I mentioned in "Re: Millrite MVI spindle bearing repair - Second report" posted on 5 September 2010, I'm looking for a way to measure total runout without use of a $250 precision test bar, and Rollie's Dad's Method of Lathe Alignment was suggested as an approach that could be adapted to the task. We will call this the RDM method, or just RDM.
Reading various postings about attempts to use RDM, people seemed to be having some problems getting it to work. As did I. I may now know why. A simple but fundamental error may have crept in over the years.
Consider a circle rotating about an axis displaced from the center of the circle. (This is all in 2D, and the various axes are perpendicular to the plane of the circle.) Using RDM's nomenclature, the radius of the circle is R, and the distance between rotation axis and circle center is X. In other words, X is the runout.
Using a dial indicator or a dial test indicator, we will rotate the circle about the rotation axis and measure the maximum and minimum values. We have adjusted the indicator so that measurements are all positive (or all negative), with greater absolute values signifying greater distances from the axis of rotation. We will assume positive measurements in the following paragraphs.
Now, by geometry, the maximum reading will be (R+X), and the minimum reading will be (R-X).
By RDM, we compute 0.5*[(R+X)+(R-X)]= 0.5*[2R]= R, which is the radius of the circle, regardless of the runout X. If we measure the diameter D with a micrometer and compute R-D/2 as suggested, what we get is a measure of the departure from roundness of the circle. We do not get the runout, which has already cancelled out.
If we instead compute the difference, subtracting the smaller measurement from the larger measurement, it's the circle radius that cancels out instead, and we now get the runout 0.5*[(R+X)-(R-X)]= 0.5*[2X]= X that we seek, uncontaminated by the radius R of the circle. (Assuming that the "circle" is in fact round enough.)
Wherever we compute this difference, the radius R of the circle at that location will cancel, yielding the total runout X at that location.
Now, I bet that Rollie's Dad knew this and was solving for X and not for R, so a small error crept in as the method was passed along.
If one measures X at different locations along a round rod, it is possible to fit the data to a linear equation, and this equation can be used to predict total runout as a function of position along the rod.
I made the needed measurements on my Millrite, so will use the data in the following example:
Close to collet: Max=0.0020", Min=0.0015", so X=0.00025".
Away from collet by 4.135" (from the DRO):Max=0.0040", Min=0.00145", X=0.001275".
Now, fit these data points to the equation y=a*x+b (X and x are not the same), with all runouts multiplied by 1000 for convenience:
0.25=a*0+b, so b=0.25 mils.1.275= a*4.135+0.25, so a=0.2479 mils per inch.
The full equation is thus y= 0.2479*x+0.25, yielding mils of total runout as a functionm of distance in inches from where the "close to collet" measurement was taken.
In other words, the total runout is a quarter mil plus a quarter mil per inch along the rod.
As mentioned earlier, the Millrite MVI specs are 0.0005" total runout near the spindle nose, and 0.001" at 8" from the spindle nose, using a test bar. This yields the equation y=0.5+0.0625*x.
Near the spindle nose, we are seeing only 0.00025" total runout, half the allowed 0.0005" runout. This is probably due solely to the lateral runout of the bearing closest to the nose, and cannot be much improved.
At 8", we would see about 0.25+8* 0.2479= 2.2332 mils, or 0.002233" total runout, which exceeds the 8" total limit by a factor of 2.233.
The key problem is the angular error, 0.2479 versus 0.0625 mils per inch.
A machine made in 1965 need not apologize for having only twice the runout it had in its youth. That said, properly orienting the outer races may help a great deal.
I should also list the fundamental assumptions underlying the above methods:
First, while the rod need not be straight, it must be quite round at all places measured, so a piece of raw stock will not work. What will likely work the best is precision ground shafting, which is quite round but may have a few thousandths of curve per foot.
Second, in the above linear fit, we implicitly assumed that the line between the two measurements does not cross the axis of rotation. While this is usually true, it is not guaranteed. A quick test is to measure in at least three places along the rod, and plot the value of X as a function of position along the rod. If they fall in a line, no significant crossover. If they form a V, there is crossover. If necessary, one can keep track of runout directions and fit to the actuals.
Third, we implicitly assume that the measurements all fall on a common line (are colinear), and that this common line and the axis of rotation together define a common plane (in other words, the lines are not skewed with respect to one another). This is never quite true, although is is usually true enough. To detect skew, one measures both runout and clock angle at a minimum of three places along the bar and does some fancy math.
I hasten to add that the machine accuracy specs make the same assumptions.
Joe Gwinn