Numerical Simulations and Parameter Optimization for Rotary Draw Bending of Tubes

Date: 06.2007–06.2008
My role: main modeling analyst

Rotary draw bending is the metal forming process widely used in aerospace and automotive industries to form straight metal tubes into designed spatial geometric shapes. Viewed from the perspective of analysis, the process is severely nonlinear from multiple sources—the geometric nonlinearity due to the large rotation, the material nonlinearity due to metal plasticity, and the state nonlinearity due to complex contact interactions between dies, mandrels and tubes. An accurate solution that can predict the defects of material during forming and capture the geometric features of tubes after bending as well as after springback is essential. This solution is only viable through finite element analysis.

We used the finite element code LS-DYNA as the core solver. In the bending process the tube’s kinetic energy produced by motion is negligible compared to its internal energy by deformation, the forming process is quasi-static, thus was modeled by the explicit solver so the convergence issue caused by nonlinearities could be avoided. The springback of bent tubes was computed by the implicit solver, which was realized by LS-DYNA’s feature of seamless transfer from explicit to implicit.

Movements of parts

Belytschko-Tsay reduced integration shell elements were used in the forming simulation to discretize the whole model. Stiffness-based hourglass control was used to inhibit hourglass mode. The reduced integration elements were switched to full integration after the model was transferred into the implicit solver so that stresses during the unloading is more accurately computed.

Mesh

The first pack of tubes were made of a kind of DQAK steel, whose complete elasto-plastic behavior was modeled. The plasticity was modeled as the power law isotropic strain hardening with Von Mises yield criterion. All the dies, clamps, and mandrels are modeled as rigid bodies to save computational cost; yet their geometric features are important to the forming shape of tubes, so their geometric features were preserved as much as possible in the model and a high density mesh were used for small features like fillets. Mechanisms between the last mandrel ball and mandrel axel, and between mandrel balls themselves were models by spherical joints type of kinematic constraints. Both time scaling and mass scaling were used to accelerate computation, the sensitivities to results were carefully tested,.

The analysis were not only developed to investigate the bending process for the DQAK steel, they were also intended to serve as a predictive tool that would be ultimately integrated in the design and optimization process for other material and geometry demands. An automatic means of pre-processing would save significant modeling effort. Thus, a parametric model was created to cover a wide range of scenarios and was implemented by ANSYS APDL. The abstracted model has 66 parameters to completely describe the geometry, material, contact, and processing aspects of the problem. Hence, the pre-processing labor left was to input values of those parameters. Then the FEA model would be automatically created and the corresponding keyword file of LS-DYNA would be submitted for computation.

In post-processing, we analyzed tube’s stress/strain, thickness variation, section distortion, and wrinkling under certain working conditions. With the aid of the parametric modeling, we conducted stacks of computation to optimize processing parameters for specific targets, for example, the rotary angle of bend die according to the final formed angle of tube after springback.