Reverse Engineering -Based Approach for Identifying the Loading Curve in Metal Forming

In the tube hydroforming (THF) process, particularly for components with complex geometries like T-shaped tubes, the loading path plays a critical role in determining the quality of the final product. Inappropriate variations in internal pressure or axial feed can result in defects such as tearing, wrinkling, or incomplete filling of the die cavity. Since direct measurement of the loading path is often impractical in industrial applications, it can be estimated using numerical methods based on the geometry of produced samples. This study introduces a reverse engineering approach integrated with the multi-level response surface method (MLRSM) to accurately estimate the pressure-displacement curve in THF. Using ABAQUS software, a finite element (FE) model of the hydroforming process was developed, with wall thickness variation and protrusion height selected as key output parameters. The pressure-displacement diagram was treated as a set of design variables, which were optimized through a stepwise, multi-level approach to minimize the deviation between the model and the physical sample. By refining the variable range at each iteration, the method achieved a precise estimation of the loading path, with an average deviation of less than ۵% from the actual wall thickness distribution, demonstrating its effectiveness for industrial applications.

Keywords:

reverse engineering , multi-level response surface method , finite element , tube hydroforming , loading path