Multi-objective optimization of forming parameters for tube hydroforming process based on the Taguchi method

Tube hydroforming is an attractive manufacturing technology which is now widely used in many industries, especially the automobile industry. The purpose of this study is to develop a method to analyze the effects of the forming parameters on the quality of part formability and determine the optimal combination of the forming parameters for the process. The effects of the forming parameters on the tube hydroforming process are studied by finite element analysis and the Taguchi method. The Taguchi method is applied to design an orthogonal experimental array, and the virtual experiments are analyzed by the use of the finite element method (FEM). The predicted results are then analyzed by the use of the Taguchi method from which the effect of each parameter on the hydroformed tube is given. In this work, a free bulging tube hydroforming process is employed to find the optimal forming parameters combination for the highest bulge ratio and the lowest thinning ratio. A multi-objective optimization approach is proposed by simultaneously maximizing the bulge ratio and minimizing the thinning ratio. The optimization problem is solved by using a goal attainment method. An example is given to illustrate the practicality of this approach and ease of use by the designers and process engineers.     

Global sensitivity analysis and multi-objective optimisation of loading path in tube hydroforming process based on metamodelling techniques

Tube hydroforming process is widely used in various industrial applications which consists of combining internal pressure and axial displacement to manufacture tubular parts. Inappropriate choice as small changes in such variables may affect the process stability and, in some cases, lead to failure. Consequently, loading path should be optimised to better control the process and to guarantee hydroformed parts with desired specifications. However, optimisation procedure requires several evaluations of the real models which induces a huge computational time. To cope with this limitation, we propose to compare two metamodelling techniques to solve the problem efficiently: the response surface method and the least squares support vector regression. To enhance the metamodels precision, optimal latin hypercube design is used to generate sampled points. It is obtained through iterative optimisation procedure based on a modified version of the simulated annealing algorithm by minimising simultaneously two optimality criterions. Then, multi-objective optimisation problem is formulated to search for the Pareto optimal solutions. Fuzzy classification is then applied to rank the non-dominated solutions which helps designers in the decision-making phase. Before optimising the process, a global sensitivity analysis is carried out using the variance-based method by coupling metamodels and Monte Carlo simulations in order to identify the relative importance of the design variables in terms of internal pressure and axial displacement on the variance of the responses of interest defined to control the process.     

Process analysis of two-layered tube hydroforming with analytical and experimental verification

Two-layered tubular joints are suitable for special applications. Designing and manufacturing of two layered components require enough knowledge about the tube material behavior during the hydroforming process. In this paper, hydroforming of two-layered tubes is investigated analytically, and the results are verified experimentally. The aim of this study is to derive an analytical model which can be used in the process design. Fundamental equations are written for both of the outer and inner tubes, and the total forming pressure is obtained from these equations. Hydroforming experiments are carried out on two different combinations of materials for inner and outer tubes; case 1: copper/aluminum and case 2: carbon steel/stainless steel. It is observed that experimental results are in good agreement with the theoretical model obtained for estimation of forming pressure able to avoid wrinkling.     

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.     

Experimental study and finite element analysis of simple X- and T-branch tube hydroforming processes

The tube hydroforming process is a relatively complex manufacturing process; the performance of this process depends on various factors and requires proper combination of part design, material selection and boundary conditions. Due to the complex nature of the process, the best method to study the behaviour of the process is by using numerical techniques and advanced explicit finite element (FE) codes. In this work, X- and T-branch components were formed using a tube hydroforming machine and experimental load paths (forming pressure and axial feed) were obtained for the processes via a data acquisition system integrated with the machine. Subsequently, the processes were simulated using LS-DYNA3D explicit FE code using the same experimental boundary, loading conditions and the simulation results were compared with the experimental results. It was found that the developed branch height and the wall thickness distribution along different planes were in good agreement with the experimental results.     

Coupled buckling and plastic instability for tube hydroforming

In this paper, the hydroforming limit of isotropic tubes subjected to internal hydraulic pressure and independent axial load is discussed.Swift's criterion is often used in this case for the prediction of diffuse plastic instability. Here, we first highlight the existence of two different Swift's criteria (for sheets and for tubes).Then, we recall that these types of approaches do not take into account buckling induced by axial loading. In fact, buckling may obviously occur before plastic instability; consequently, Swift's criteria must not be used alone to predict instability in the case of tube hydroforming.Numerical simulation was used to confirm these points and to analyse both the buckling and striction phenomena together. The two types of instability must be treated together in a reasonable approach to the hydroforming process.In this paper, the material verifies a “J2-flow” constitutive rate constitutive law. Jaumann's derivative was chosen and the Prandtl–Reuss equations with von Mises’ yield criterion and the associated flow rule were used. Isotropic hardening was taken into account.     

基于Dynaform三通管液压成型分析

提出改进液压成型工艺,并通过Dynaform软件仿真及实际生产验证。该方法舍弃了通常管材液压成形中所需的超高压供给系统以及平衡冲头,进而大大降低设备费用。在验证工艺正确基础上,通过Dynaform软件仿真分析影响三通管液压成型因素。仿真模拟分析为模具设计方案和液压成形工艺方案设计提供了科学的依据,提高了设计效率。     

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.     

Bursting failure prediction in tube hydroforming using FLSD

In tube hydroforming, circular components are hydrobulged or hydroformed from tubular blanks with internal pressure and simultaneous axial loading. Thus the tube can be fed into the deformation zone during the bulge operation allowing more expansion and less thinning without any defects such as wrinkling, buckling, and bursting. By contrast with the buckling and the wrinkling, the bursting is generally classified as an irrecoverable failure mode. Hence in order to obtain the sound hydroformed products, it is necessary to predict the bursting behavior and to analyze the effects of process parameters on this failure condition in hydroforming processes. In this study, a forming limit stress diagram (FLSD) is constructed by plotting the calculated principal stresses based on the local necking criterion. Using the theoretical FLSD, we carry out the numerical prediction of bursting failure in a hydroforming process, which usually has non-linear strain path. Finite element analyses are carried out to find out the state of stresses during simple hydroforming operation, in which the FLSD is utilized as the forming limit criterion for assessment of the initiation of necking, and influences of the material parameters on the formability are investigated. In addition, the numerical results obtained from the FEM combined with the FLSD are confirmed with a series of bulge tests in view of bursting pressure and show a good agreement. Consequently, it is shown that the theoretical and numerical approach to bursting failure prediction proposed in this paper will provide a feasible method to satisfy the increasing practical demands for assessment of the forming severity in hydroforming processes.     

Probabilistic modeling of stress-based FLD in tube hydroforming process

Recently a stress-based FLD due to its path-independency has become a new mainstream technology for prediction of forming limit in tube hydroforming processes, which usually have non-linear strain path. However, the random characteristics owing to experimental errors, inherent measuring equipment errors, dimensional tolerance of as-received blank, inconsistent lubrication condition and so on lead to uncertainty with regard to the position of the forming limit curve on the stress-based FLD. In this work, to take into account the uncertainty on the stress-based FLD, a probabilistic modeling on the stress-based FLD with confidence level is firstly attempted. With the assumption of all experimentally measured data as normally distributed random variables, stochastic evaluation of the reliability of the stress-based FLD is carried out. Moreover the statistical correlation between measured data during a bulge test and the material parameters is investigated by using the first-order approximated mean value and variance. The reliability is analytically calculated based on first-order reliability method (FORM) and verified with Monte-Carlo simulation (MCS). Finally, at a given deviation of measured data, the band width of forming limit curve on the stress-based FLD to be able to satisfy the required confidence level is determined.     

Influence of end-conditions during tube hydroforming of aluminum extrusions

Tube hydroforming experiments were conducted to develop the forming limit diagram of AA6082-T4 by utilizing three types of end-conditions: (i) “free-end”, (ii) “pinched-end” or “fixed-end” and (iii) “forced-end”. It was found that “free-end” hydroforming gives the lowest forming limits followed by “pinched-end” and “forced-end” hydroforming. It was noticed that the tube failure occurs within 5° to the extrusion weld in the “free-end” experiments, within 7° in the “pinched-end” condition and extended up to 10° in the “forced-end” hydroforming experiments. Finite element simulations were carried out to capture the effects of the weld geometry, weld mechanical properties and the end-conditions of the extruded tube on the maximum induced stress and location of the maximum von Mises stress. It was found that the anisotropy of the weld material and the end-condition used during hydroforming experiments have the largest influence on the failure location with respect to the weld center.     

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.     

微型客车车身静态灵敏度分析及优化

通过HyperMesh软件建立了某微型客车车身的有限元分析模型,并验证了有限元模型的正确性。进行了车身弯曲刚度和扭转刚度对板件厚度的灵敏度分析。根据灵敏度分析结果,选择优化设计变量,以车身质量为目标函数,以车身弯曲刚度和扭转刚度为状态变量,对车身进行结构优化。     

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.     

基于KBE的管状液压成型件CAD系统研究

介绍了基于KBE的管状液压成型件CAD/CAE系统的体系结构，阐述了CAD系统的组成、各个功能模块的为能以及系统开发的技术难点，并以UG作为开发平台，在Windows NT4.0环境下，利用UG/API开发出CAD系统。     

离心泵遗传算法多目标优化与压力脉动分析

为了改善离心泵在运行过程中存在的效率低、性能曲线有驼峰和抗汽蚀性能差的情况,以遗传算法和数值模拟相结合的方法对离心泵模型进行优化.建立以离心泵能量损失最小、抗汽蚀性能最强和性能曲线无驼峰为目标函数的数学模型,使用MATLAB遗传算法工具箱对叶轮7个主要变量进行优化,对优化后的模型进行流场分析,并在蜗壳流道内设置3个监测...     

An approach to improve thickness uniformity within tailor-welded tube hydroforming

Both experimental and simulation studies were run to investigate the effects of deformation sequence on stress and strain states and thickness distribution during tailor-welded tube hydroforming. The effects of geometrical boundary condition were also studied. Then, an approach to improve thickness uniformity was put forward. Both stress and strain histories indicate that the deformation states of thinner and thicker tubes were obviously different duo to the difference in thickness during tailor-welded tube hydroforming. These induce tensile strain concentrates to happen near weld seam on thinner tube, but compressive strain on thicker tube, which lead to strain mutation around weld seam on tailor-welded tube components. As result, bigger thinning takes place on thinner tube. The difference in thinning ratio between thinner and thicker tubes reaches about 6.6%. By deformation sequence optimization, thickness distribution uniformity can be improved obviously. When deformation sequence altered from thicker tube to thinner tube, the difference in thinning ratio between two segments can be decreased to 1.5%. At last, the effects of geometrical parameters of preform component were analyzed and the suitable parameters were given.