Optimization of IHPF loading path for monolithic centralizer based on NSGA-II

During the process of internal high-pressure forming (IHPF) in a centralizer, the relationship between axial feed at both ends and liquid pressure loading inside the tube blank significantly influences the forming results. Insufficient axial feed can lead to a reduction in wall thickness and the formation of cracks in the tube blank, while excessive axial feed can result in thickening and wrinkle formation in the wall thickness. Therefore, precise loading path (LP) design is required. A novel multi-objective optimization method for LP, incorporating internal pressure and axial feed curves, is proposed. The objective function is defined as the maximum and minimum wall thickness obtained from simulation, with the LP serving as the design variable. The integration of Non-dominated Sorting Genetic Algorithm-II (NSGA-II) with LS-DYNA finite element simulation software facilitates the reconfiguration of the profiles of the internal pressure loading curve and the axial feed rate curve. This is achieved by adjusting key control points, enabling automated LP optimization within an expanded solution space. The optimization results demonstrate that LP obtained by this method is optimal than LP obtained by formula calculation, empirical curves, and manual optimization. Compared with the empirical LP, the maximum thinning rate of the tube blank under the No.12 optimal LP is reduced from 7.8% to 1%, while the maximum thickening rate under the No.7 optimal LP is decreased from 15.3% to 1%. Consequently, wall thickness distribution becomes more uniform, and significant manpower and material resources can be conserved. Additionally, this method has the capacity to yield multiple Pareto optimal solutions in a single operation, thereby providing a more extensive array of solutions for the formulation of process plans and process parameters. Finally, experimental validation demonstrates that the measured thickness values are in high agreement with the simulation predictions, with a maximum error of merely 4.88%.