An investigation of the optimal load paths for the hydroforming of T-shaped tubes

This paper proposes a new method to design the optimal load curves for hydroforming T-shaped tubular parts. In order to assess the mathematical models, a combination of design of experiment and finite element simulation was used. The optimum set of loading variables was obtained by embedding the mathematical models for tube formability indicators into a simulated annealing algorithm. The adequacy of the optimum results was evaluated by genetic algorithm. Using this method, the effect of all loading paths was considered in hydroforming of T-shaped tubes. Eliminating of variables with lower effect could simplify the problem and help designers to study the effect of other parameters such as geometrical conditions and loading parameters. Applying the optimal load paths obtained with the proposed method caused an improvement in the thickness distribution in the part as well as a decrease in maximum pressure.     

Analysis and finite element simulation of the tube bulge hydroforming process

To investigate the effect of the loading path on the forming result and get the reasonable range of the loading path in tube bulge hydroforming process, a mathematical model considering the forming tube as an ellipsoidal surface is proposed to examine the plastic deformation behavior of a thin-walled tube during the tube bulge hydroforming process in an open die, and thus different loading paths are gained based on this model. The finite element code Ls-Dyna is also used for simulating the tube bulge hydroforming process. The effect of the loading paths on the bulged shape and the wall thickness distribution of the tube are discussed, and then the reasonable range of the loading path for the tube bulge hydroforming process is determined.     

Analysis and finite element simulation of the tube bulge hydroforming process

To investigate the effect of the loading path on the forming result and get the reasonable range of the loading path in tube bulge hydroforming process, a mathematical model considering the forming tube as an ellipsoidal surface is proposed to examine the plastic deformation behavior of a thin-walled tube during the tube bulge hydroforming process in an open die, and thus different loading paths are gained based on this model. The finite element code Ls-Dyna is also used for simulating the tube bulge hydroforming process. The effect of the loading paths on the bulged shape and the wall thickness distribution of the tube are discussed, and then the reasonable range of the loading path for the tube bulge hydroforming process is determined.     

Die shape design for T-shape tube hydroforming

In this paper, two design methods for T-shape tube hydroforming dies are proposed, namely, the extrusion-cutting-fillet method (ECFM) and the intersection-fillet method (IFM). Simulations on hydraulic expansion and axial feeding of T-shape tube hydroforming with two dies using the program DEFORM-3D were performed. The influence of the two dies on workpiece formability of T-shape tube hydroforming was examined. Experiments were carried out with SUS304 stainless steel tube at room temperature. A qualified product of T-shape tube, without wrinkling or bursting, was obtained using the die designed by the IFM method.     

Feasibility study on optimized process conditions in warm tube hydroforming

Feasibility study has been performed to estimate the optimized process conditions in warm tube hydroforming based on the simulated annealing optimization method. Precise prediction and control of process parameters play an important role in forming at warm conditions. Optimal pressure and feed loading paths are obtained for aluminium AA6061 tubes through the simulated annealing algorithm in conjunction with finite element simulations. Numerous axisymmetric geometries are investigated and the effects of expansion ratio, corner fillet to thickness ratio, and initial diameter to thickness ratio are studied. For the feasibility estimation, warm hydroforming experiments have been conducted on aluminum AA6061 under optimal designed conditions. The results show that the optimization procedure used in this research is a reliable and feasible tool in determination of optimal process conditions for the sound warm hydroforming process.     

The effect of tube dimensions on optimized pressure and force loading paths in tube hydroforming process

The precise control of internal pressure and axial force loading paths significantly affects the final product quality. In this study, the effect of tube dimensions on the pressure and force loading paths in tube hydroforming process is investigated by using simulated annealing optimization method linked to a commercial finite element code. The optimized loading paths, obtained for different tube geometries with a constant expansion ratio, are then compared. The effects of initial diameter and wall thickness on shape conformation, optimal internal pressure and axial force (or feed) are discussed on the basis of optimal loading paths. Several guidelines in prediction and determination of tube hydroforming parameters are obtained by optimization analysis.     

加载路径对液压胀形管材成形性能的影响

在管材液压胀形过程中,加载路径对管材成形性能有着重要的影响,一直是研究热点。本文介绍了目前管材液压胀形中的各种加载路径如线性加载、折线加载、脉动加载和由模糊逻辑控制加载路径方式,阐述了各种加载路径的特点、原理及其对管材成形性能的影响,指出了深入研究加载路径要解决的几个关键问题。     

Hydroforming of aluminum extrusion tubes for automotive applications. Part II: process window diagram

Based on the mathematical formulations for predicting forming limits induced by buckling, wrinkling and bursting of free-expansion tube hydroforming, a theoretical “Process Window Diagram” (PWD) is proposed and established in this paper. The theory developed in the first part of the present work was formulated within the context of free-expansion tube hydroforming with both combined internal pressure and end feeding. The PWD is designed to provide a quick assessment of part producibility for tube hydroforming. The predicted PWD is validated against experimental results conducted for 6260-T4 60×2×320 (mm) aluminum tubes. An optimal loading path is also proposed in the PWD with an attempt to define the ideal forming process for aluminum tube hydroforming. Parametric studies show that the PWD has a strong dependency on tube geometry, material property and process parameters. To the authors’ knowledge, this is the first attempt that a PWD is being formulated theoretically. Such a concept can be advantageous in deriving design solutions and determining optimal process parameters for tube hydroforming processes.     

Analysis of forming limit in tube hydroforming

The automotive industry has shown increasing interest in tube hydroforming. Despite many automobile structural parts being produced from cylindrical tubes, failures frequently occur during tube hydroforming under improper forming conditions. These problems include wrinkling, buckling, folding back, and bursting.We perform analytical studies to determine forming limits in tube hydroforming and demonstrate how these forming limits are influenced by the loading path. Theoretical results for the forming limits of wrinkling and bursting are compared with experimental results for an aluminum tube.     

Increasing the stability of T-shape tube hydroforming process under stochastic framework

Metal forming processes present several sources of uncertainties coming from material properties, geometric characteristics, and loading paths. During the manufacturing phase, such parameters may vary affecting the process stability and increasing the defect parts. Stochastic framework seems more pertinent than classical deterministic approaches to treat such problems since it is intended to include variabilities at the early design stage. In the present work, tube hydroforming process widely used in various industry applications is investigated. To ensure the process stability, loading paths should be optimized with taking into account randomness associated to the input parameters. To control the potential failure modes, the Forming Limit Stress Diagram is implemented in the finite element code to avoid necking while a simple geometrical criterion is defined for wrinkling. A global sensitivity analysis using the variance-based method is done which shows that the selected random parameters impact considerably the variance of failure indicators. Then, a numerical example of T-shape tube hydroforming process is proposed to show the efficiency of the stochastic framework. Statistical and probabilistic observations of the optimum solution show that the stochastic approach yields to an optimum less sensitive to such fluctuations which improves the process stability and minimizes considerably the percentage of defect parts in a mass production environment.     

A hybrid-constrained MOGA and local search method to optimize the load path for tube hydroforming

The production of a tubular hydroformed part often requires a combination of internal pressure and axial force at the tube ends to fully form the tube to its specified geometry. A successful hydroforming process requires not only achieving a part that conforms to the design specifications, but also ensures that the part has a reasonably uniform thickness distribution and is free of defects, such as wrinkles, severe thinning, or fractures. The load path design (pressure vs. end feed history) largely determines the robustness of the process and the quality of the finished parts. In this paper, a hybrid constrained optimization method was proposed to solve this type of multi-objective problem by coupling a multi-objective genetic algorithm and a local search. The load path design procedure was developed by considering five objectives: four formability objectives (i.e., to minimize the risk of wrinkling, global and local thinning, and fracture) and a geometric objective (to minimize the corner radius). A Kriging predictor was used to accelerate the computation of genetic operations and generate new feasible solutions. Finite element simulations of the hydroforming process were also used after each generation to accurately evaluate the objectives of the offspring, and solutions with rank 1 were retained throughout all generations. Once the Pareto solutions were obtained by multi-objective genetic algorithm, a local search was carried out in the regions of interest with the assistance of visualization. This optimization method was applied to the hydroforming of a straight tube to create a part with an expanded region with a square cross section; the optimum load path produced a very safe part with a corner radius of only 9.115?mm and a maximum thinning of only 23.9%.     

Study on the crushing and hydroforming processes of tubes in a trapezoid-sectional die

A study on the bulging processes of tubes in a trapezoid-sectional die has been carried out through finite-element (FE) analysis. A FE model of the single-step hydroforming process and several FE models of crushing combined with subsequent hydroforming processes in a trapezoid-sectional die with different die closing seams are proposed. The simulations are performed using the FE code LS-DYNA. For the single-step hydroforming process, the effects of loading paths on the formability of the trapezoid-sectional part are investigated. In the case of the crushing combined with subsequent hydroforming processes, the effects of die closing seams, tube diameters, and preforming loading paths on the forming process and the final parts are analyzed. A comparison between the parts formed through single-step hydroforming process and through crushing combined with subsequent hydroforming processes is performed. Finally, an experiment of tube hydroforming in a trapezoid-sectional die is carried out on the hydroforming machine developed by Shanghai Jiaotong University. The simulation results show good agreement with the experimental results.     

Loading path optimization of a hydroformed part using multilevel response surface method

In tube hydroforming, the loading path that is the relationship between axial feeding and internal fluid pressure is of important significance. Researchers have employed various optimization approaches to find an optimum loading path. In this research, a statistical method based on finite element analysis has been developed. An accurate FEA has been used to simulate the process and to find the response of the process to the loading. By performing an experimental test, the model is verified in comparison with the actual T part. The multilevel response surface method (MLRSM) has been used to model the responses from the finite element analysis. The behavior of the process can be predicted using the response surface methodology (RSM) model, and then, the obtained model is used to optimize the process. The optimum point in the RSM highly depends on the initial range of design variables. Thus, after finding the optimum point in each level, the ranges of variables are adjusted around the last optimum point. Then, the optimization process can be continued as a multilevel process. In the performed optimizations, the thickness variance has been considered as the objective function and the protrusion height as the constraint. The thickness variation based on the optimum loading path is highly improved, and it shows that multilevel RSM is very effective in improving the results.     

Investigation of T-Shape Tube Hydroforming with Finite Element Method

In this paper, the finite element method is used to investigate the cold hydroforming process of a T-shape tube. A series of simulations on hydraulic expansion, axial feeding and the counterforce of the tubes was carried out using the program DEFORM-3D. The influences of the process parameters such as the internal pressure, the fillet radius, and counterforce on the minimum wall thickness of formed tube are examined. A suitable range of the process parameters for producing an acceptable T-shape tube that fulfils the industrial demand was also found. ID="A1"Correspondance and offprint requests to: Dr C.-T. Kwan, Department of Mechanical Manufacturing Engineering, National Huwei Institute of Technology, 64 Wunhua Road, Huwei, Yunlin, 632, Taiwan. E-mail: ctkwan@sunws.nhit.edu.tw     

液压成形管件中心轴线抽取算法

管材液压成形技术是一个相对新颖的技术，其在应用过程中仍然有许多问题需要研究和解决。基于有限元法的管材液压成形数值模拟技术发展的时间更短，有待进一步研究和发展。针对这种发展要求，提出了管材液压成形数值模拟中分析模型的构造方法，并且重点介绍了逆向构造中管件中心轴线的抽取算法即边界递进搜寻法，这个算法不仅运行速度快，实现简单，而且具有较强的适应性。     

液压成形管件中心轴线抽取算法

管材液压成形技术是一个相对新颖的技术,其在应用过程中仍然有许多问题需要研究和解决。基于有限元法的管材液压成形数值模拟技术发展的时间更短,有待进一步研究和发展。针对这种发展要求,提出了管材液压成形数值模拟中分析模型的构造方法,并且重点介绍了逆向构造中管件中心轴线的抽取算法即边界递进搜寻法,这个算法不仅运行速度快,实现简单,而且具有较强的适应性。     

基于成形应力极限的管材液压成形缺陷预测

基于塑性应力应变关系及Hill79屈服准则,推导出极限应力与极限应变间转化关系,进而建立2008T4铝合金的成形应力极限图(Forming limit stress diagram,FLSD)。采用LS-DYNA软件对三通管液压胀形过程进行模拟,应用FLSD预测胀形过程中破裂的发生及成形压力极限,并与传统成形极限图(Forming limit diagram,FLD)结果进行了对比。研究表明,FLD与FLSD预测结果中破裂缺陷位置相同,但极限内压力值存在很大差别,而FLSD预测结果与物理试验结果较吻合。考虑到FLD受应变路径影响显著的因素,将FLSD作为管材液压成形等复杂应变路径下的成形极限的判据更加方便可靠。     

Study on experimental approaches of forming limit curve for tube hydroforming

This paper proposes a set of experimental approaches to establish the forming limit curve (FLC) in different forming modes for tube hydroforming. In tension–compression strain state, analytical models are constructed to determine the linear strain paths at the pole of the hydroformed tube, and a self-designed free hydroforming apparatus with axial feeding and internal pressure are used to carry out the bulge tests. In plane strain state, the difference is that both ends of the tube are fixed with different punches. In tension–tension strain state, a novel hydroforming apparatus are designed. The novel device requires the simultaneous application of lateral compression force and internal pressure to control the material flow under tension–tension strain states. The linear strain paths for the right hand side of FLC by finite element method simulation are calculated. The linear strain paths in different strain states are verified and the FLC of roll-formed QSTE340 seamed tube is constructed through the proposed experimental approaches. Comparison between simulation and experimental results for hydroforming process of front crossmember shows that the experimental FLC is accurate and valid for tube hydroforming.     

Numerical analysis and design for tubular hydroforming

To get an optimum deformation path for tubular hydroforming, the hydroforming limit of isotropic and anisotropic tubes subjected to internal hydraulic pressure, independent axial load or torque is firstly proposed based on the Hill's general theory for the uniqueness to the boundary value problem and compared with those of the conventional sheet forming. The influences of the deformation path, the material properties and the active length–diameter ratio on the nucleation and the development of wrinkling during the free tubular hydroforming are also investigated. The above theory is used as a criterion and implemented with some new functions in our ITAS3D, an in-house finite element code for simulating the sheet forming, to control the materials flow and to prevent the final failure modes from occurring. Finally, the tubular hydroforming of an automobile differential gear box is taken as an example to show the efficiency and usefulness of the algorithm.