FANUC polygon turning: why 1∶2 synchronization can make a hexagon without producing exact flats
The 0i-F polygon-turning model separates side count from flatness. Original ellipse-semiaxis and tangent-deviation calculations explain the limits of approximately straight sides, without equating a hexagonal outline with exact planar surfaces.
Contents
Polygon turning uses synchronized tool and workpiece rotation to generate a multi-sided profile. Its efficiency must be considered alongside its shape. A correct speed ratio and side count do not imply that every side is mathematically straight.
Side count and contour accuracy are different questions
The FANUC 0i-F lathe operator's manual B-64604EN-1/01, §7.1, pages 298–302 (public mirror of the original manual) explains that rotation ratio and number of cutting edges jointly determine the shape, which is not an exact polygon. In the workpiece-to-tool speed-ratio model of 1∶2, two cutting edges can produce four sides and three can produce six. Actual use requires the corresponding synchronization control, drives and tooling structure; entering G51.2 alone does not establish machine support.
Why the sides still have curvature
The section's simplified model places the tool center at distance A from the workpiece center, with tool-tip rotation radius B. Under its same-direction 1∶2 rotation convention, the tip trajectory in a frame rotating with the workpiece is x=(A−B)cosθ, y=(A+B)sinθ. This is an ellipse; the equations identify A−B and A+B as semiaxis lengths. The discussion concerns a tool-tip locus, not the final envelope produced by arbitrary installed inserts.
Original geometry: a short side looking flat does not mean zero curvature
Choose original example values A=60 mm and B=40 mm, giving semiaxes a=20 mm and b=100 mm. Near the ellipse's rightmost end, deviation from the tangent x=20 is δ=20−20√(1−y²/10000).
| y from the center | Trajectory x | Deviation δ from the tangent |
|---|---|---|
| 0 mm | 20 mm | 0 |
| 5 mm | About 19.97498 mm | About 0.02502 mm |
| 10 mm | About 19.89975 mm | About 0.10025 mm |
In this model, extending the inspected range from ±5 to ±10 mm increases deviation approximately fourfold. A nearly straight appearance near the center does not prevent curvature becoming apparent over a wider effective side. The table is neither a FANUC accuracy promise nor measured flatness from a particular tool set.
Using the result for process selection
First establish whether the drawing requires a wrench-gripping profile, an across-flats dimension, or strict flatness and mating surfaces. Then calculate the envelope from actual tool geometry. The synchronization ratio cannot determine the latter requirements by itself; cutting-edge radius, tool-center distance, cutter count and effective contact region all affect the final shape.
If the part requires a controlled planar surface, a program that generates a hexagon does not replace contour validation. Compare appropriate milling or interpolation methods against the workpiece's requirements. Further advanced functions are in the OPTION section.