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frwillia
Guest
Questions from the inexperienced:
If one uses a 12" Grizzly rod, that is held at its end in a tail stock chuck, to indicate a spot that is 2" down the breech end of the bore, and the indicator is as close as it can be to the end of the barrel, and there is a small weight hanging from the rod to take the slack out of the assembly, would the actual amount of runout be approximately 10/12ths of what the indicator showed, and if the tip of the rod was advanced into the bore to a point that was 6" from the end, would it be 6/12ths?
You are almost there but it's the inverse. In your example the actual runout (bushing movement) would be 12/10 of what the indicator shows (or .00012" per division on a 0.0001" DTI).
To see this visualize the radial movement: set a pencil on the table with the point against your thumb. The point on your thumb is the end in the tail stock. The eraser is the bushing. Pick a point on the pencil, then move it through an angle my moving the eraser and leaving the point against the thumb. You can see the eraser moves a longer distance than the point on the pencil. So the runout, eraser movement, is greater than the indicator movement.
The rod pivots through an angle. The bushing, being farther from the pivot point (at the tail stock chuck), moves farther than the point the indicator touches which is closer to the pivot point. So in your example the indicator shows 10/12 of the actual runout, or the runout is 12/10 bigger than the indicator shows.
Said differently, arc length at a constant angle is directly proportional to radius.
I realize that these ratios ignore the length of engagement in the tail stock chuck, and the distance from the end of the barrel to the closest position that the indicator tip can be positioned, but I am talking round numbers, to see if I have a grasp on the concept. Beyond this, if I have the ratios right, why would the information thus generated not be useful?
You have the ratios upside down but you are on the right track. The information thus generated is definitely useful. One is centering, correcting for small deltas from a constant. The "sensitivity" of the measurement in your example is reduced from 0.0001"/div to 0.00012"/division, which I submit is not a significant degredation.
Also, of a longer whisker is fitted to a test best type of indicator, does it not reduce the resolution in a similar way, unless it was originally manufactured and calibrated that way?
Yes. If the length of the whisker is doubled, the resolution of the indicator is reduced by a factor of 2. This is the same as the resolution that happens if a 12" Grizzly rod is inserted 5-1/2" into the barrel and the DTI presses against it about a half inch outside the breech.
Fitch