Springback predictions for three-dimensional thick-walled tubes based on the cylindrical helix splines

This article analyzed the forming process of thick-walled three-dimensional tubes under combined bending and twisting loads and performed the springback predictions based on the cylindrical helix splines. The equations to calculate the two kinds of moments consider the hardening effect, and they can be well applied to most materials. The cylindrical helix spline is adopted creatively to approximate the objective tube axis, and the curvature and the torsion of each cylindrical helix segment can represent the bending angle and the twisting angle per unit length of the corresponding tube element, respectively. All the cylindrical helix segments after springback are obtained based on the calculated moments and the final shape of the tube axis is achieved by connecting all of them through an appropriate splicing technology. Then, the whole deviations of the calculated shapes can be obtained. The method proposed is applied on a typical three-dimensional tube forming and it has got good effect.