Multi-objective optimization and sensitivity analysis of tube hydroforming

Tube hydroforming is a manufacturing process used to produce structural components in cars and trucks, and the success of this process largely depends on the careful control of parameters such as internal pressure and end-feed force. The objective of this work was to establish a methodology, and demonstrate its effectiveness, to determine the optimal process parameters for a tube hydroformed in a die with a square cross section. The Taguchi method was used to establish a design of virtual hydroforming experiments, and numerical simulations were carried out with the finite element code LS-DYNA®. A sensitivity analysis was also carried out with analysis of variance. Multi-objective functions that consider necking/fracture, wrinkling, and thinning were formulated, and the response surface methodology was used with the most sensitive factors to obtain a defect-free part. An objective function, based on the final corner radius in the part, was also included in the optimization model. The forming severity of virtual hydroformed parts was evaluated using the forming limit stress diagram and the forming limit (strain) diagram. Finally, the normal-boundary intersection method and the L ₂ norm were used to obtain the Pareto-optimal solution set and the optimal solution within this set, respectively. The hydroforming process for this part was also optimized using the commercial optimization software LS-OPT®, with two different single-objective algorithms. However, the optimum load path predicted with the proposed methodology was shown to achieve a smaller corner radius. The proposed optimization technique helped to define a process window that leads to a robust manufacturing process and improved part quality.     

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.     

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.     

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.     

Bursting failure prediction in tube hydroforming processes by using rigid–plastic FEM combined with ductile fracture criterion

The most common failure in tube hydroforming is the bursting failure due to excessive thinning of large deformation. To evaluate the forming limit of hydroforming processes, the Oyane's ductile fracture integral I was introduced and calculated from the histories of stress and strain according to every element by using the rigid–plastic finite element method. The region of fracture initiation and the forming limit for three hydroforming processes, such as a tee extrusion, an automobile rear axle housing, and a lower arm under different forming conditions are predicted in this study. Also it is shown that the material parameters used in the ductile failure can be obtained from the experimental forming limit diagram. From the results, the prediction of the bursting failure and the plastic deformation for the three hydroforming examples demonstrates to be reasonable so that this approach can be extended to a wide range of practical tube hydroforming processes.     

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.     

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.     

Multi-objective optimization of process parameters for the helical gear precision forging by using Taguchi method

Precision forging of the helical gear is a complex metal forming process under coupled effects with multi-factors. The various process parameters such as deformation temperature, punch velocity and friction conditions affect the forming process differently, thus the optimization design of process parameters is necessary to obtain a good product. In this paper, an optimization method for the helical gear precision forging is proposed based on the finite element method (FEM) and Taguchi method with multi-objective design. The maximum forging force and the die-fill quality are considered as the optimal objectives. The optimal parameters combination is obtained through S/N analysis and the analysis of variance (ANOVA). It is shown that, for helical gears precision forging, the most significant parameters affecting the maximum forging force and the die-fill quality are deformation temperature and friction coefficient. The verified experimental result agrees with the predictive value well, which demonstrates the effectiveness of the proposed optimization method.     

Modelling of localised thinning features in the hydroforming of micro-tubes using the crystal-plasticity FE method

The wall thickness of hydro-formed micro-tubes is not uniform due to the low ratio of the wall thickness and the grain size. The features of localised thinning are different from those of the traditional hydroforming process, and this is related directly to the ratio of the wall thickness and the grain size of the material, and also to the amount of deformation. Macro-mechanics finite element (FE) modelling cannot be used to simulate such effects encountered in micro-tube hydroforming processes. In this paper, a simplified plane-strain crystal-plasticity finite element (CPFE)-based modelling technique has been developed and used to capture the localised thinning features in the hydroforming of micro-tubes. The grain structures within the tube workpiece, and their distributions and orientations, are generated automatically using the developed VGRAIN system. A set of crystal-viscoplasticity models is implemented in ABAQUS/Explicit FE code through the user-defined sub-routine, VUMAT. Single-crystal and multi-crystal structures have been studied, and the localised thinning has been analysed for different microstructures of the material using the CPFE modelling technique. It is confirmed from the analysis that the localised thinning in the hydroforming of micro-tubes is affected significantly by the microstructure and grain orientations of the material.     

Application of the hydroforming strain- and stress-limit diagrams to predict necking in metal bellows forming process

In order to predict the initiation of necking in metal bellows forming process, a methodology for determination of the forming limit diagram and the forming limit stress diagram is represented in this paper. The methodology is based on the Marciniak and Kuczynski (M–K) model. Comparison between the experimental and theoretical results for hydroforming stress and strain-limit diagrams as predicted by different methods indicates that the present approach is suitable for prediction of necking in tube hydroforming processes. Afterwards, the implementation of the hydroforming strain- and stress-limit diagrams into finite element numerical simulations for the forming of the metal bellows is established. A satisfactory agreement between the finite element method (FEM) and test results is achieved.     

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.     

Analytical and numerical approach to prediction of forming limit in tube hydroforming

Analytical and numerical analyses of forming limit in tube hydroforming under combined internal pressure and independent axial feeding are discussed in this paper. To predict the initiation of necking, Swift's criterion for diffuse plastic instability is adopted based on Hill's general theory for the uniqueness to the boundary value problem. In addition, in order to predict fracture initiation, Oyane's ductile fracture criterion is introduced and evaluated from the histories of stress and strain calculated by means of finite element analysis. From the comparison with a series of tube bulge tests, the prediction of the bursting failure based on the plastic instability and the ductile fracture criterion demonstrates to be reasonable so that these approaches can be extended to a wide range of practical tube hydroforming processes.     

Determination of flow stress of thin-walled tube based on digital speckle correlation method for hydroforming applications

The flow stress, used to describe the plastic deformation behavior of thin-walled tube, is one of the most important parameters to ensure reliable finite element simulation in the tube hydroforming process. In this study, a novel approach of on-line measurement based on digital speckle correlation method is put forward to determine flow stress of thin-walled tube. A simple experimental tooling is developed and free-bulged tests are performed for 304 stainless steel and H62 brass alloy tubes. An analytical approach is proposed according to the membrane theory and the force equilibrium equation. The developed method is validated by means of FE simulations. The results indicate that the present method is acceptable to define the flow stress in the tube hydroforming process.     

一种估计管材硬化模型参数的方法

管材力学性能参数的准确性是影响管材塑性成形有限元数值模拟质量的关键因素之一。单向拉伸试验的试件取自滚弯和焊接等制管工序之前的平板坯料 ,所测应力—应变关系无法真实描述管材的塑性变形行为。单向拉伸试验也不能精确反映管材在实际塑性成形中所处的复杂应力状态。基于各向同性硬化假设 ,本文提出了一种轴压胀形、单向压缩试验和数据拟合技术相结合的估计管材硬化模型参数的方法。有限元数值模拟结果显示 ,由这种方法所估计出的管材硬化模型参数是相当准确的。     

采用可移动凹模的板材液压成形技术

提出一种改进的板材液压成形新工艺,即采用可移动凹模,实现拉深与胀形的复合液压成形。在整个变形过程中,板材初始变形部分始终与可移动凹模接触,从而抑制已变形区进一步变形,使变形更加均匀,实现变形的顺序控制,板材成形极限得到提高。从试验和数值模拟两方面对可移动凹模板材液压成形技术进行了研究,分析各种工艺参数,如摩擦因数等对板材成形性的影响,并且分析了可移动凹模对板材成形极限的影响。     

A prediction of bursting failure in tube hydroforming processes based on ductile fracture criterion

Bursting is an irrecoverable failure mode in tube hydroforming, in contrast with buckling and wrinkling. To predict bursting failure in the hydroforming processes, Oyane's ductile fracture criterion is introduced and evaluated from the results of stress and strain productions obtained from finite element analysis. The region of fracture initiation and the bursting pressures are predicted and compared with a series of experimental results. It is shown that the material parameters used in the criterion can be obtained from the forming limit diagram. From the simulation results of tube bulging, the prediction of the bursting failure based on the ductile fracture criterion was demonstrated to be reasonable. This approach can be extended to a wide range of practical tube hydroforming processes.     

工艺参数对21-6-9高强不锈钢管数控弯曲壁厚减薄影响的显著性分析

为实现21-6-9高强不锈钢管数控弯曲精确成形,提高其成形质量与成形极限,需要对弯曲过程中壁厚减薄进行有效控制。基于ABAQUS/Explicit有限元软件平台,建立了21-6-9高强不锈钢管数控弯曲三维弹塑性有限元模型,并对其可靠性进行了验证。通过有限元模拟和正交试验,研究了工艺参数对21-6-9高强不锈钢管数控弯曲壁厚减薄影响的显著性及规律。结果表明,影响壁厚减薄的显著性工艺参数依次为芯棒伸出量、管材与芯棒间隙、管材与防皱块摩擦因数、管材与芯棒摩擦因数、管材与压块摩擦因数和弯曲速度,其影响规律为：壁厚减薄率随着芯棒伸出量、管材与防皱块摩擦因数、管材与芯棒摩擦因数、管材与压块摩擦因数、弯曲速度的增大或管材与芯棒间隙的减小而增大。采用多元线性回归方法建立了最大壁厚减薄率与显著性工艺参数之间的回归预测模型,经对比验证,回归预测模型结果与正交试验结果之间的相对误差不超过5%。     

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.     

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.