Three-Dimensional Tube Geometry Control for Rotary Draw Tube Bending, Part 2: Statistical Tube Tolerance Analysis and Adaptive Bend Correction

Abstract

The control of each individual bend and overall process is presented in Part 1 of the paper. In Part 2 of the paper, statistical methods are used to analyze and improve 3-D tube bending accuracy. The relationship between bending process error and tube geometry error is obtained with Monte Carlo simulation. For the same tube tolerance requirement, the required process tolerance varies in a large range based on tube geometry. Among the three bending errors: bend angle, bend plane and distance between bends, bend angle error has the largest influence on tube error. For a tube with multiple bends, the overall tube geometry error can be minimized by intentionally modifying the nominal values of the bends to be made based on the errors in the existing bends. The required modification of the bending commands is calculated with an adaptive bend correction algorithm.