What it is
A polygon turning process performed on a CNC machine that synchronizes two axes—the C-axis (work-spindle) and a linear X-axis carrying a special polygon cutter head (or a small tool spindle). By electronically “gearing” the spindle speed to the cutter motion, the tool continuously intercepts the rotating workpiece and generates non-circular polygons, including curved-flank (lobed) profiles such as tri-lobes, multi-lobes, and gerotor-type forms, in one chucking.

Kinematic principle

• The control sets an electronic gear ratio between workpiece RPM (nW) and cutter rotation/oscillation (nT) and a phase angle (φ).
• Each revolution, the tool engages the work at timed intervals; the envelope of these timed cuts forms the polygon.
• By adjusting gear ratio, phase, eccentricity/offset, and the number/spacing of cutter inserts, you obtain flat-flank polygons (e.g., hex, square) or curved-flank polygons (lobes).
• No index stops; the profile is generated dynamically along Z (axial) while X maintains the programmed radial depth.

Machine configuration

• Axes: X (radial feed) + C (spindle) are mandatory; Z is used for axial length feed (straight or helical lobes).
• Tooling: polygon turning head (2–6 inserts typical) or a compact live cutter spindle; positive-rake carbide with small nose radius for lower cutting force on interrupted cuts.
• Workholding: high-stiffness collet/chuck; run-out ≤ 0.01 mm recommended.

Process setup (typical)

1. Chuck and probe the blank; verify C-axis zero.
2. Program electronic gearing (nT : nW) and phase φ for the target number of lobes and flank shape.
3. Set X-depth of cut (ap) and axial feed (Fz or mm/rev); enable constant surface speed if available.
4. Rough pass (larger ap), then finish pass with reduced ap and higher φ accuracy.
5. Optional spring pass to stabilize size after heat/stress.

Key control parameters

• Electronic gear ratio (G = nT/nW) and phase φ → determines lobe count and profile curvature.
• Eccentricity/offset (e) or insert radial position → sets lobe amplitude (inscribed/circumscribed size).
• Insert count & spacing → affects tooth entry frequency and surface continuity.
• ap, feed, and RPM → manage load on interrupted cuts and heat.

Capability & quality (with a rigid setup and finish pass)

• Diameters: typically Ø8–120 mm (application-dependent).
• Form accuracy: ±0.01–0.03 mm on lobe radius/inscribed size; better with in-process gauging.
• Surface finish: Ra ≈ 0.8–3.2 µm (finish pass, sharp inserts).
• Materials: alloy steels (pre-hard ~35–45 HRC), stainless, brass, Al; hard turning up to ~55–60 HRC possible with CBN/ceramic.

Typical applications

• Tri-lobed shafts/couplings, wrench-engagement ends, anti-rotation features.
• Curved-flank rotors (pump/compressor), gerotor-like sealing profiles.
• Polygon fits for press/locating connections without broaching.

Advantages vs. milling/broaching/grinding

• One-chucking, very fast cycle (no indexing), excellent concentricity to the turned datum.
• No dedicated broach or EDM electrode; profile changes are software-driven (gear ratio/phase).
• Works on small shoulders and short overhangs where milling heads won’t fit.

Limitations / cautions

• Inside corner radius limited by insert nose radius (can’t make sharp internal corners).
• Intermittent cutting → manage vibration; keep overhangs short, use balanced cutter heads.
• Requires accurate C-axis and spindle-phase control; weak C-axis brakes can degrade form.

Rule-of-thumb starting data (steel, roughing)

• Cutting speed: 80–150 m/min (carbide), ap 0.2–0.6 mm, feed 0.05–0.15 mm/rev (per lobe).
• Finish: reduce ap to 0.05–0.15 mm; add 0.5–1° phase refinement.