Rotary Laser Tumbler Wrap & Taper Sizing Calculator
Engraving seamless 360-degree wraps on tapered tumblers (Stanley Quenchers, Yeti Ramblers, Hydro Flasks, pint glasses) requires unrolling a truncated cone (frustum) into a curved 2D vector arc. Calculate the exact top/bottom radii, wrap sector angle, seam overlap, and laser hatch execution time.
Conic Arc Angle (θ)
-- °
Top Outer Radius (R1)
-- mm
Bottom Inner Radius (R2)
-- mm
Top / Bottom Circumference
-- / -- mm
Estimated Engrave Time (Full 360)
-- min
LightBurn & Illustrator Conical Wrap Setup Rule
If your tumbler has a taper (> 0.5mm diameter difference), wrapping a rectangular vector template will cause severe distortion, vertical skew, and misaligned seams where the wrap meets. In Illustrator, use Object > Envelope Distort > Make with Warp (Arc) with the exact bend percentage or unwrap curve calculated above. Ensure your vector artwork has closed loop fills for bidirectional hatch rasterization.
Step-by-Step Rotary Chuck vs Roller Calibration
- Rotary Chuck (Direct Drive): Calibrate by setting Steps Per Rotation (e.g. 12,800 or 25,600 pulses/rev). Diameter is entered directly into LightBurn / EZCAD to calculate surface feed.
- Rotary Roller (Friction Drive): Calibrate using the fixed roller wheel diameter. Note that rubber roller slip can cause 1–3% Y-axis elongation; test with a 50mm calibration box on a sacrificial scrap cylinder.
- Hatch Angle Strategy: For powder coated stainless steel, a bi-directional cross hatch (0° and 90°) at 508 DPI ensures 100% ablation with zero residue or ghost lines.