CNC Rotary Chuck & 4-Axis Laser Toolpath Utility

Tube Laser Coping, Saddle Joint & Rotary DXF Unwrapping Calculator

Calculate flat unrolled DXF circumference, saddle fishmouth cope depth, intersection geometry, weld root gap offset, rotary A-axis coordinate bounds, and cycle time for round, square, and rectangular tube laser cutting.

1. Tube & Joint Parameters

Joint Configuration

Branch Tube Outside Dia (mm)

e.g. 1.75" = 44.45 mm

Header / Main Pipe Outside Dia (mm)

Diameter of the pipe being attached to

Wall Thickness (mm)

e.g. 0.083" = 2.11 mm

Intersection Angle (°)

Angle between pipe axes (90° = Tee, 45° = Brace)

Weld Prep Root Gap (mm)

Spacing allowance for TIG/MIG penetration

Laser Beam Kerf Width (mm)

Fiber laser focal spot / cut kerf

Laser Cut Feed Rate (mm/min)

Linear surface feed rate

Pierce Delay (seconds)

Laser dwell before rotary motion

2. Unwrapped DXF & Cutting Metrics

Unrolled Flat DXF Width

139.64 mm

Circumference (π × OD) = Y/A-axis span

Max Saddle Cope Depth (X)

31.43 mm

Peak-to-valley axial fishmouth stroke

Total Cut Perimeter

168.2 mm

Contour length traveled by laser

Estimated Cut Cycle Time

4.0 sec

Piercing + rotary chuck motion

Internal Slag / Spatter Risk Level

Low / Moderate (Anti-Spatter Tube Recommended)

Clearance inside ID allows normal extraction.

Unrolled 2D Flat Pattern DXF Preview 0° to 360° Rotary A-Axis

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Mathematical Formulas for Tube Laser Coping

When two cylindrical tubes of diameters d (branch) and D (main header) intersect at an axial angle θ, the 3D space curve of intersection unrolls into a 2D flat coordinate plane (x, y) where:

y(φ) = (d / 2) × φ [where φ is the rotation angle from 0 to 2π radians] x(φ) = [ (D/2) / sin(θ) ] - [ sqrt((D/2)² - ((d/2) × sin(φ) + e)²) / sin(θ) ] - [ (d/2) × cos(φ) / tan(θ) ] - RootGap

Where:

d: Branch tube outside diameter (mm).
D: Main header tube outside diameter (mm).
θ: Axis intersection angle (15° to 90°).
e: Lateral axis offset (eccentricity, 0 for centered intersections).
RootGap: Axial gap allowance subtracted from the cope peak to allow full-penetration weld root pass.

Key Considerations for CNC Rotary Laser CAM

Rotary Axis Kinematics: Tube lasers map linear Y-axis motion to the A-axis (or B-axis) rotational chuck (A = Y / (π · d) × 360°). If the 2D DXF vector contains excessive polyline segments instead of true arcs and smooth splines, the rotary chuck will stutter and create thermal burn marks.
Slag & Anti-Spatter Management: During tube cutting, laser pierce slag shoots inside the pipe ID and fuses to the opposite inner wall. Use a sacrificial internal spatter shield or apply water-soluble anti-spatter paste inside the tube before cutting.
Weld Beveling Compensation: For wall thicknesses > 3 mm, square-cut tube edges require excessive weld filler. 3D tilting laser heads (5-axis) rotate the nozzle perpendicular to the header surface, creating variable V-bevels along the saddle contour.

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