Manual machining
Rotary axis feed rate calculator for 4th axis and rotary table work
For a CNC mill 4th axis or a rotary table, degrees per minute = IPM x 360 / (2 x pi x R); 6.0 IPM at a 2.000 in radius is 171.887 deg/min.
Technical review pending. Formulas and values are cited. This notice comes down after a machinist review.
Rotary feed
deg/min
F_deg = F_lin x 360 / (2 x pi x R) = 6 x 360 / (2 x 3.1416 x 2) = 171.887 deg/min
0.4775 rev/min (F_deg / 360). Circumference at R: 12.5664 in. Same rate as 152.40 mm/min at 50.800 mm radius.
Sample with your numbers, for a CNC mill with an A axis and a control that supports G93 inverse time; check your control's manual.
Source: Circle geometry (arc length = radius x angle in radians); inverse time feed (G93) as defined in CNC control programming manuals (Hurco NC programming, Tormach PathPilot, LinuxCNC and Eding CNC documentation), summarized, not reproduced. Codes vary by control and machine builder.
Feeds are starting points; the chip load the cutter sees is set by the feed at the cutting point. Prove a new 4th-axis program in single block above the part.
How it works
F_deg = F_lin x 360 / (2 x pi x R); F_lin = F_deg x 2 x pi x R / 360
| Symbol | Meaning | Unit |
|---|---|---|
| F_lin | Linear feed at the cutting point, inches per minute (IPM) or mm/min | IPM or mm/min |
| F_deg | Rotary feed | deg/min |
| R | Radius from the rotary axis centerline to the cutting point | in or mm |
| D | Diameter, 2 x R | in or mm |
| 360 / (2 x pi) | 57.29578 degrees per radian, so F_deg = F_lin x 57.29578 / R | °/rad |
Inverse time (G93)
arc = R x dA x pi / 180; L = sqrt(dX^2 + dY^2 + dZ^2 + arc^2); T = L / F_lin; F = 1 / T
| Symbol | Meaning | Unit |
|---|---|---|
| dA | Rotary move | ° |
| dX, dY, dZ | Linear moves made in the same block | in or mm |
| arc | Arc the cutting point travels at R | in or mm |
| L | Path length of the cutting point on the part | in or mm |
| T | Move time | min |
| F (G93) | Inverse time feed, 1 / T | 1/min |
| A | The rotary axis address on a CNC mill with a 4th axis parallel to X | ° |
The rule used here: T = L / F_lin, with L the path the cutting point travels on the part at radius R. That holds the wanted feed along the cut at R. CAM systems may compute T another way, for example from the slowest axis; the control only sees F = 1 / T. With only a rotary axis moving in feed per minute mode (G94), many CNC mill controls read F as degrees per minute; how a control blends F on a combined linear and rotary move in G94 varies by control, which is the reason for G93.
Wrapping
distance = angle x pi x D / 360; angle = distance x 360 / (pi x D)
| Symbol | Meaning | Unit |
|---|---|---|
| D | Diameter of the surface being wrapped | in or mm |
| angle | Rotary move | ° |
| distance | Flat-pattern length at the surface | in or mm |
G93 sample: CNC mill with an A axis
CNC mill with an A axis, control that supports G93 inverse time; check your control's manual. The numbers are worked example 2 below.
G93 G01 X2.000 A90. F3.236 (INVERSE TIME: MOVE TAKES 1/3.236 MIN)
G94 F10.0 (BACK TO FEED PER MINUTE; NEW F REQUIRED)| Word | What it does |
|---|---|
G93 | Sets inverse time feed: F becomes 1 / minutes for the move, on controls that support G93. |
G01 X2.000 A90. | The combined move: X travels 2.000 in while the A axis turns 90°. The sample assumes it starts at X0 A0. |
F3.236 | F = 1 / 0.30906 min = 3.236; the move takes 18.54 s. While G93 is active, every G01, G02 and G03 block needs its own F. |
G94 F10.0 | Cancels inverse time and returns to feed per minute; the next feed move needs a new F. |
Worked example: rotary feed from IPM
You want 6.0 IPM at the surface of a part turning on a 2.000 in radius.
- Circumference = 2 x 3.141593 x 2.000 = 12.5664 in.
- F_deg = 6.0 x 360 / 12.5664 = 171.887 deg/min; 0.4775 rev/min.
- Metric alongside: 152.40 mm/min at a 50.800 mm radius gives the same 171.887 deg/min.
- Reverse check: 171.887 x 12.5664 / 360 = 6.00 IPM.
Result: 171.887 deg/min (0.4775 rev/min).
Worked example: G93 inverse time for a helical cut
A 3.000 in diameter part (R 1.500 in); A rotates 90° while X moves 2.000 in; 10.0 IPM wanted at the surface.
- Arc at R: 1.500 x 90 x 3.141593 / 180 = 2.3562 in.
- L = sqrt(2.000^2 + 2.3562^2) = sqrt(4.0000 + 5.5517) = 3.0906 in.
- T = 3.0906 / 10.0 = 0.30906 min = 18.54 s.
- F = 1 / 0.30906 = 3.236.
- Average rates during the move: X 2.000 / 0.30906 = 6.47 IPM; A 90 / 0.30906 = 291.208 deg/min.
- Rotary only, A 90° at 10.0 IPM: T = 2.3562 / 10.0 = 0.23562 min, F = 4.244; that is 90 / 0.23562 = 381.972 deg/min, the same as 10.0 x 57.29578 / 1.500 = 381.972 deg/min.
Result: G93 F3.236 for the combined move.
Wrapping and metric checks
- 30° on a 3.000 in diameter = 30 x 3.141593 x 3.000 / 360 = 0.7854 in.
- 1.000 in of flat-pattern length on the same diameter = 1.000 x 360 / (3.141593 x 3.000) = 38.1972°.
- 45° on a 50 mm diameter = 19.635 mm.
- Metric inverse time: A 180° at R 30 mm, 200 mm/min: arc 94.248 mm, T 0.47124 min, F 2.122.
Shop notes
- Use the radius at the cutting point, not the stock radius, when the cut is below the surface: an engraved line at depth runs at a smaller radius.
- When the radius changes during a move (a cone or a ramp in depth), CAM breaks the move into short segments and gives each its own G93 F; one F for the whole move holds the feed at one radius only.
- On a manual rotary table, the same deg/min sets the power feed or the handwheel pace; on a 90:1 table one handwheel turn is 4°.
- Check that your control supports G93 before posting it; the code and its rules come from the control's programming manual.
FAQ
How do you convert IPM to degrees per minute?
F_deg = IPM x 360 / (2 x pi x R). 6.0 IPM at a 2.000 in radius is 171.887 deg/min.
What does G93 do on a CNC mill?
On CNC mill controls that support it, G93 sets inverse time feed: F = 1 / minutes for the move. F 3.236 means the move takes 0.30906 min (18.54 s). F goes on every feed block until G94.
What G93 F holds 10.0 IPM on a 90° turn with 2.000 in of X on a 3.000 in diameter?
3.236 on a CNC mill control that supports G93: the path at the surface is 3.0906 in, which takes 0.30906 min at 10.0 IPM.
Why does the 4th axis cut too fast or too slow in feed per minute mode?
With only the rotary axis moving, many CNC mill controls read F as degrees per minute, not IPM. 10.0 IPM at a 1.500 in radius is 381.972 deg/min.
How do you wrap a flat distance around a 4th axis part?
Angle = distance x 360 / (pi x D): 1.000 in on a 3.000 in diameter is 38.1972°. 30° is 0.7854 in.
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