Sheet Metal & CNC Forming

Flow Forming & Shear Spinning Sine Law Vector Prepress Guide

Master the CNC toolpath prepress, mandrel clearance profiles, and volumetric Sine Law transformations for precision shear spinning and multi-pass flow forming.

1. Mechanics of Shear Spinning & The Sine Law

Shear spinning (also known as shear forming or power spinning) is a high-precision rotary forming process wherein a rotating flat circular blank or tubular preform is plastically deformed over a rigid mandrel by one or more CNC-controlled forming rollers. Unlike conventional manual metal spinning—which involves radial stretching and drawing—shear spinning deliberately reduces wall thickness via pure shear deformation while keeping the outer diameter of the blank unshifted.

The core governing physical principle is the Sine Law:
t_f = t_0 · sin(α)
where t_0 is the original flat blank thickness, t_f is the final finished cone wall thickness, and α is the half-included cone angle relative to the mandrel rotational centerline axis.

When generating 2D CAD/CAM DXF toolpaths for the forming roller, deviation from the Sine Law leads directly to catastrophic part failure:

• Under-reduction (Roller clearance > Sine Law tf): The roller fails to enforce sufficient thickness reduction, causing compressive hoop stress in the unformed flange, triggering severe flange buckling and wrinkling.
• Over-reduction (Roller clearance < Sine Law tf): The roller attempts to displace more material than mathematically permitted, creating high axial tensile stresses that pull the wall apart, resulting in circumferential tensile fracture.

2. Engineering Specifications & Tolerances

3. CNC Vector CAD/CAM Toolpath Preparation Rules

• Mandrel Clearance Profile: Ensure the internal mandrel DXF contour accounts for thermal expansion during high-speed spinning and includes a 0.5° to 1.0° release taper for seamless part stripping.
• Tangent Lead-In Arcs: Program tangential roller engagement vectors (minimum radius equal to 2x roller nose radius) to eliminate impact shock and contact witness marks at the blank edge.
• Scallop Height Control: Calculate axial feed per revolution (fz) relative to roller nose radius (rR) using h_s = f_z^2 / (8 * r_R) to maintain surface roughness below Ra 1.6 µm without post-machining.
• Multi-Pass Intermediate Vectors: For cylindrical tube flow forming requiring >60% total wall reduction, export discrete multi-pass DXF layers representing balanced 25-35% progressive reduction steps with inter-pass stress relief annealing.
• Closed Vector Validation: Verify that all CAD profiles exported for CNC spinning CAM systems are 100% closed, zero-intersecting spline or tangent arc polylines.