Keywords: tube hydroforming process, reliability analysis, uncertainty, optimization, forming limit curve.

Hydroforming processes have been widely implemented in many industries due to their advantages compared with conventional stamping and assembly processes. In this paper, we consider the tube hydroforming process. The principle of this process is to apply an inner pressure that is used to expand the tube with an axial force that allows compensating the thinning in the expanded zone. In metal forming processes, the parameters relative to the numerical simulations (material constants, friction coefficients, loads, geometric dimensions, etc.) were assumed deterministic. However, these parameters exhibit unavoidable scatter and must be defined with a probability law. Deterministic design optimizations (DDO) of the process that do not consider uncertainties are not reliable and can lead to failure. In this paper, we present a rigorous and practical approach to optimize the tube hydroforming process incorporating uncertainty inherent to the most important parameters of the process. In this paper, we consider the loading conditions defined by a B-spline curve.

During the process different kinds of plastic instability may occur, among these plastic instabilities striction may occur. It occurs when we apply a high level of pressure, with buckling and wrinkling occuring when we apply a large displacement.

A probabilistic approach is proposed to impose probabilistic constraints on the failure modes. The parameters of interest are the loading conditions (i.e. axial feed and internal pressure) and the limit state function taking advantage from the forming limit curve (FLC) defined by Keeler and Backofen [1]. This curve divides the space into two domains: the failure domain (above the curve) and the safe domain (under the curve).

To assess the probability of failure many methods were proposed in the literature such as approximation methods and direct Monte Carlo simulations. However, these methods require a high computational time. To overcome this problem we use Monte-Carlo simulations based on the response surface methodology [2] with robust central composite design (CCD) and sequential quadratic programming to solve the reliability design optimisation.

Tube hydroforming is used as an example to demonstrate the robustness of the proposed approach to solve the problem in a reasonable time. With reliability based design optimization, satisfactory results are obtained and we show that the risk of rupture and wrinkling can be decreased considerably.

1

S.P. Keeler, W.A. Backofen, "Plastic Instability and Fracture in Sheets Stretched over Rigid Punches", Trans. ASM., 56(1), 25-48, 1963.

2

R.H. Myers, D.C. Montgomery, "Response surface methodology: process and product optimization using designed experiments", 2nd ed., John Wiley and sons, USA, 2002.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £145 +P&P)