Optimization of the loading path for the tube-hydroforming process

Abstract

In general, hydroforming optimization aims to make a desired shape of a plastically deformed structure under dynamic forces. The automotive industry has shown great interest in tube hydroforming, which is a metal-forming process. The forces from the hydraulic fluid are utilized to deform a tube. The internal pressures and the axial feedings (of the axial forces) determine the quality of the deformed product. In this research, an optimization process is employed to evaluate the appropriate external forces but defects are prevented. The equivalent static loads method for non-linear static response structural optimization is used for the optimization process because the tube-hydroforming process is analysed by non-linear dynamic response analysis. The equivalent static loads are the static loads that generate the same response field as that of non-linear dynamic analysis and are utilized as the loading conditions in linear static response optimization. A novel process is added to the original equivalent static loads method for non-linear static response structural optimization to address the objective function and the design variables for tube-hydroforming optimization. A new technique is proposed to use the external forces as the design variables in linear static response optimization. A few hydroforming examples are solved by using the newly proposed techniques.

Non-linear dynamic response structural optimization for frontal-impact and side-impact crash tests

“…2, 6–8, 10–12, 32–39 In the late 1990s, Choi et al 12 introduced the ESLM for linear dynamic response optimization, and the method has been expanded to various disciplines such as flexible multi-body dynamic systems, 34, 40–42 rigid-body dynamic systems, 43 non-linear static systems, 10, 36, 37 and non-linear dynamic systems. 5–8, 11, 32, 33, 35, 39, 44, 45 Jeong et al 6 compared the ESLM and the response surface method with regard to the roof structure of a vehicle. Kim and Park 8 compared the ESLM and the conventional method subject to stress constraints.…”

“…combination such as (M, S). In this example, the combinations of (M, S) are (2, 1), (4, 5), (5,8), (4,6), (6,7) and (5,7). The case of the combination (5, 8) is explained in detail using Figure 7.…”

“…4 The ELSM was proposed to overcome these problems, and it has been applied to large and practical examples. 5–11 This method has an analysis domain and a design domain. 12 Non-linear dynamic analysis is performed in the analysis domain, equivalent static loads (ESLs) are generated and gradient-based linear static structural optimization is carried out with the ESLs in the design domain.…”

A comprehensive damage criterion in tube hydroforming

“…2 In fact, hydroforming is the process of producing different parts of machines by applying fluid pressure. 3 This fluid usually, is oil or water. 4 Using the hydroforming process, it is possible to produce a tube component that its cross-section is varied along its axis.…”

“…Shinde et al investigated the effect of internal pressure, without axial feeding, on the success of tube hydroforming process numerically. 3 They analyzed the tube hydroformed in square cross- section die using LS-Dyna explicit solver. They found that the internal pressure that can cause the tube to burst can be determined using the Formation Limit Diagram (FLD).…”