A little birdie told me that i could cut radiuses by calculating the "steps" for that radius and then bled the steps with a large file.. This got me curious.. How do i create one of these stepping diagrams? I couldnt find any description in my machinist books or in my CAD software.
Guy Lautard wrote that up in one of his
Machinist's Bedside Reader books. Basically, you trig out the corner of your (square edged) tool at points around the radius of your ball.
Let's say that you want to turn a R1.000 inch ball using cuts every 10° around its circumference. You will need two tables -- one for the tailstock side of the cut (i.e. to the right on most lathes) and one for the headstock side of the cut (i.e. to the left on most lathes). Further, you are going to use a .250 inch wide cutter for the task. (Your assumptions will vary.)
Setup: You have the bar firmly chucked or colleted in your lathe. The cutter protrudes at least 1.000 from the toolholder. The tailstock end of your bar has been dressed to a nice clean and square end. You pick that face up with the left-hand face of your cutter using a shim to establish a true position and set your longitudinal measuring device (DRO, travel dial indicator, etc.) to -1.000. Using the same type of technique, set your cutter to the centerline radius of your bar (ø2.000 assumed for the sake of ease) and set your radial measuring device to +1.000. You are now at your
operational zero point.
In a spreadsheet, set a cell (A1 assumed for simplicity) value to 10*pi()/180 (i.e. 10° expressed in Radians). Set (B1 assumed for simplicity) to a value of 1.000 (i.e. the radius of your ball). Set a cell (C1 assumed) to .250 (i.e. the width of your cutter).
Lay out an array of cells (call it A5 through I5) to increment the angle from 0° (A5) to 90° such that cell B5 is set to =A5+$A$1 to increment the angle. Copy that value (B5) across from C5 through I5. You should now have an array of angles going: 0, 10, 20, 30, ... 90. Row 6 is going to be the longitudinal offset value and Row 7 is going to be the radial offset value. Thus, the value for cell A6 is going to be: =-1*$B$1*cos(A5). The value for cell A7 is going to be: =$B$1*sin(A5). When you copy those values out from A6/7 through I6/7, you will have your table of values for the tailstock side of the cut.
The headstock side of the cut is the same -- lets place it using Row 8 for longitudinal and Row 9 for radial offsets. A8 will be defined as =-1*A6+$C$1. A9 will be defined as: =A7. Copy them across from A8/9 through I8/9 and you will have values for the headstock side of the cut -- though it should be obvious that you are going to stop before you reach the 90° mark, right?
Just remember that spreadsheets use
Radians for all their trig functions. pi()/180 is the factor for converting degrees into Radians.
