Numerical Optimization of the Blank Dimensions in Tube Hydroforming Using Line-Search and Bisection Methods

Abstract

The change from a consolidated manufacturing practice to a new solution is often a complex problem because of the operative limits of technologies and the strict constraints of industrial parts. Moreover, the new process must reflect or enhance the characteristics of the product and, overall, it must be more competitive in performances and costs. Accordingly, the development of a new process is a multilevel and multivariate problem that requires a systematic and hierarchical approach. The present paper focuses on the development of a Tube Hydroforming process capable to replace the current practice for production of T-Joint parts made of AISI 316L for the water pipes market. In particular, the problem must withstand many process and product constraints. Therefore, it was split in three steps focused on specific aspects of the process: identification of process parameters and configuration, numerical optimization of the blank tube dimensions (length and thickness), experimental tests and final improvements. In particular, two numerical methods were implemented in the optimization step: the line–search method to approach to the optimum point and Bisection method to refine the search. These approaches allowed us to identify the optimum process configuration and, in particular, the optimal dimensions of the blank tube that allows one to achieve the product requirements with the minimum cost of material.

Exploración comparativa de los métodos numéricos de Newton-Raphson y bisección para la resolución de ecuaciones no lineales

“…A diferencia del método de Newton-Raphson, el método de bisección no requiere conocimiento de la derivada de la función y garantiza la convergencia hacia la raíz bajo ciertas condiciones, como la continuidad de la función en el intervalo dado (Gulshan et al, 2023). Aunque el método de bisección tiende a converger más lentamente que el método de Newton-Raphson, su simplicidad y robustez lo hacen adecuado para una variedad de problemas en los que otros métodos pueden fallar (Fiorentino et al, 2020). El objetivo de este artículo fue realizar una exploración comparativa de los métodos numéricos de Newton-Raphson y bisección para la resolución de ecuaciones no lineales.…”

Effect of loading paths on hydroforming ability of stepped hollow shaft components from double layer pipes

“…Tube hydroforming is a highly sought-after alternative to traditional forming methods, becoming increasingly prevalent [1,2]. The outcomes of this forming process are utilized across numerous industries, such as automotive, aerospace, shipbuilding, and oil and gas [3][4][5][6].…”

An Analytic Solution for an Expanding/Contracting Strain-Hardening Viscoplastic Hollow Cylinder at Large Strains and Its Application to Tube Hydroforming Design

“…Recent reviews on this technology are provided in [18,19]. Despite the wide use of numerical methods for hydroforming process designs [20,21], simple semi-analytic solutions are essential for estimating the optimal values of the process parameters [22,23]. In particular, it has been shown in [24] that a simple plane-strain solution for the expansion of a two-layer tube supplies an accurate prediction for the maximum internal pressure value.…”