Prediction of Longitudinal Curvature Radius of 3D Surface Based on Quadratic Relationship between Strain and Coordinates in Continuous Roll Forming

Abstract

Continuous roll forming (CRF) is a new method for the rapid forming of three-dimensional (3D) surfaces developed in recent years, and the significant advantage of CRF compared with traditional die forming is that the longitudinal dimension of the sheet metal is not limited. By controlling the curvature radius and gap shape of upper and lower bending rolls, three-dimensional parts with different shapes and sizes can be precisely formed. When the elastic deformation is ignored during the forming process, the transversal curvature radius of the three-dimensional surface is consistent with the radius of the roll gap centerline. Therefore, the calculation of longitudinal curvature radius is the key to improve the accuracy of the 3D surface in CRF. In this paper, the basic principle of CRF is described. The modified formulas for calculating the longitudinal curvature radius of convex and saddle surfaces based on the quadratic relationship between the strain and coordinates are deduced in detail, and the corresponding design method of the roll gap is derived. Furthermore, the mathematical equations of convex and saddle surfaces are given. Through numerical simulation and theoretical analysis, it is found that the relative errors of the longitudinal centerline radius are reduced from 13.67% before modification to 4.35% after modification for a convex surface and 6.81% to 0.41% for a saddle surface when the transversal curvature radius is 800 mm and the compression ratio is 5%. The experimental and measured results indicate that the shapes of formed parts are more consistent with the target parts after modification, which further proves the applicability of the modified formulas.