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Joseph Gwinn Joseph Gwinn is offline
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Default Mathematical analysis of Rollie's Dad's Method

In article ,
Ade V wrote:

did gone and wrote:

[snippage]

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.


[snippage]


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.


Unless I'm mistaken, RDM is _trying_ to cancel the runout? The runout is
getting in the way of determining how accurately the spindle is aimed
relative to the bed. Whilst runout is its own issue, it's not what RDM
is trying to fix...


Although the article doesn't say that, it may be that RDM is ultimately trying
to measure bed twist, but the method as published cannot achieve that. The
published method measures rod diameter despite runout, and there is no way to
deduce bed twist from rod diameter.

What the article claims to be measuring is the deviation of the spindle rotation
axis from parallelism with the ways, in two dimensions, horizontal and vertical.
The published method cannot do this, but changing only the math from summing the
runout max and min to taking the difference allows this deviation to be measured.

What was done with the information was to cleverly shim the headstock where it
rests on the bed, to achieve parallelism.

Actually, with the sum, we don't get the full radius, we get the change from
some unknown constant, because we never zero the dial indicator at the unknown
center of rotation, we set the dial indicator up at some convenient offset, and
go from there.