Analytical springback modelling of helical metal tubes in 6-axis free bending considering dynamic constitutive effects

Helical metal tubes, valued for their unique spatial configurations, are critical components in heat-exchange and fluid-transport systems, serving indispensable roles in high-precision engineering applications. Such tubes can be manufactured seamlessly and consistently using six-axis free bending (6FB) technology. However, the helical structure leads to enhanced bending-torsional coupling effects, complicating the springback mechanism. To reveal the springback effect of tubes, this paper proposes mathematical models for the 6FB processing of three typical helical metal tubes based on the Frenet frame. By integrating the Johnson-Cook (JC) constitutive model and the power-hardening model, a springback prediction analytical model suitable for 6FB is established. This model can capture the springback behavior during the forming process based on the tube’s dynamic constitutive relationship, cross-sectional morphology, and spatial structural characteristics. Based on finite element (FE) analysis and bending experiments, the central axis characteristics of helical tubes are analyzed and compared, verifying the accuracy of the springback prediction analytical model. Furthermore, the stress–strain distribution law of the tube during bending is analyzed and summarized. Simultaneously, the influence of the correction parameter k on the springback of the helical tube is discussed based on the finite element results. The results show that the bending accuracy is highest when the k value is between 1.25 and 1.26.