Amateur Machinists' Tools, Techniques and Materials

Archive for May, 2013

Ratios for the lathe compound

Posted by hammerscale on May 25, 2013

This is a popular trick for advancing the tooling in very small increments, but often the ratio to use eludes one’s memory.

Let us review, for today, the relationship between compound angle and its effect on relative movement of the cutting piece into the work.

For this discussion, we will measure degrees as follows:
0 degrees is along (parallel to) the work piece axis.
90 degrees is perpendicular to the work piece axis.
It’s as though a protractor is placed up against the work piece with 0 marking touching the work and 90 degrees marking pointing at your belly button.
The preceding conventions help illustrate what’s going on and also clarify the issue, as different lathe compounds have different protractor angles etched on them.
When the compound is set at an angle other than 90, and you crank the compound handle in, the movement indicated by the micrometer dial is governed by the pesky laws of trigonometry. For instance, at 45 degrees, advancing the compound 1 increment causes a movement that corresponds to a ratio of 1.408 in either the X or Y axis.
So, a movement of 1 thousandth of an inch @ 45 degrees equals 0.71 thousandths in X or Y.
(1 / 1.408 = 0.71)
It’s a right triangle, with 1 as the hypotenuse and 0.71 as either leg. The ratio differs depending on the angle (trigonometry.)
It’s the sine of the angle, (with the above conventions), or could be the cosine if 90 degrees is parallel to the work and 0 degrees @ a right angle to it.

Enough trig. Below are popular ratio’s for using the compound:

1:1 ratio (90 degrees off workpiece)
1:2 ratio (30 degrees off workpiece)
1:5 ratio (11.5 degrees off workpiece)
1:10 ratio (about 6 degrees off workpiece) (5.8, actually, if you can read your compound dial that precisely!)

The following shows kind of what I’m talking about, and shows an example of 30 degrees off the lathe workpiece:


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