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.     

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.     

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.     

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.     

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.     

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.     

A comparative study of implicit and explicit FEM for the wrinkling prediction in the hydroforming process

The recent application of tube hydroforming in the automotive industry demands finite element analysis, since it is rapidly being used as an effective tool for the evaluation and optimisation of the design of hydroforming dies and processes. In this paper, attention is paid to the comparison of an implicit and an explicit FEM widely used for the hydroforming process. The influences of time scaling and mass scaling, which have been commonly used in order to save computational time in the explicit method, are especially investigated. The comparisons focus on the predictability of wrinkling and stress with various scaling factors in the explicit method. Through verifications with experimental results, a useful guideline in determining the scaling factors is proposed.     

Analytical model for planar tube hydroforming: Prediction of formed shape, corner fill, wall thinning, and forming pressure

An analytical model for planar tube hydroforming based on deformation theory has been developed. This analytical model can be used to predict hydroformed shape, corner fill, wall thinning, and forming pressure. As the model is based on a mechanistic approach with bending effects included, local strain and stress distribution across the wall thickness can be determined. This includes strain and stress distributions for the outer layer, inside layer, and middle layer. The model is validated using finite element analysis and tube hydroforming experiments on irregular triangular, irregular quadrilateral, and pentagonal hydroformed shapes.     

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.     

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。     

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.     

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.     

A contribution to determining the friction coefficient in hydroforming of tubes

Hydroforming is a relatively new technology, which enables complex shaped hollow parts to be produced efficiently. Compared to alternative methods, this technology is characterised by significant potential advantages, such as complex shape production, lightweight design, high accuracy, and process integration. The tribological aspects of hydroforming are very significant, as friction influences all the main process parameters practically in a direct or indirect way. However, there is a paucity of information relating to hydroforming tribology. In most reports on this subject only qualitative data regarding the friction coefficient are given. However, for finite‐element method simulation and optimal process and tool design, quantitative data are indispensable. This paper describes an attempt to determine the coefficient of friction in both the elastic and plastic states of a workpiece during tube hydroforming processes. Push‐through tests were carried out in order to determine the coefficient of friction in the elastic state, and tube upsetting tests were conducted for the plastic state. Various commercial lubricants were used in the experiments.     

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.     

Development of automotive engine cradle by hydroforming process

The hydroforming technology may bring many advantages to automotive applications in terms of better structural integrity of the parts, lower cost from fewer part count, material saving, weight reduction, lower springback, improved strength and durability and design flexibility. In this study, the whole process of front sub-frame parts development by tube hydroforming using steel material having tensile strength of 440 MPa grade is presented. At the part design stage, it requires feasibility study and process design aided by CAE (Computer Aided Design) to confirm hydroformability in details. Effects of parameters such as internal pressure, axial feeding and geometry shape in automotive engine cradle by the hydroforming process were carefully investigated. Overall possibility of hydroformable engine cradle parts could be examined by cross sectional analyses. Moreover, it is essential to ensure the formability of tube material on every forming step such as pre-bending, preforming and hydroforming. At the die design stage, all the components of prototyping tool are designed and interference with the press is examined from the point of deformed geometry and local thinning.     

A gradient-based decomposition approach to optimize pressure path and counterpunch action in Y-shaped tube hydroforming operations

In tube hydroforming, the concurrent actions of pressurized fluid and mechanical feeding allows obtaining tube shapes characterized by complex geometries such as different diameters sections and/or bulged zones. Main process parameters are material feeding history (i.e., the punches velocity history), internal pressure path during the process, and (in T- or Y-shaped tube hydroforming) counterpunch action. What is crucial, in such processes, is the proper design of operative parameters aimed to avoid defects (for instance underfilling or ductile fractures). Actually, the design of tube hydroforming operations is mainly aimed to prevent bursting or buckling occurrence and such issues can be pursued only if a proper control of process parameters is performed. In this paper, a design procedure for Y-shaped tube hydroforming operations was developed. The aim of the presented approach is to calibrate both internal pressure history during the process and counterpunch action in order to reach a sound final component. The approach utilized to optimize the aforementioned parameters is founded on gradient-based techniques and the optimization problem here addressed depends on a considerable number of design variables. In order to reduce the total number of numerical simulations/experiments necessary to reach the optimal values of the design variables, the basic idea of this paper is to develop a sort of decomposition approach aimed to take into account subsets of design variables in the most effective way. The proposed decomposition approach allows avoiding about 50% of the numerical simulations necessary to solve the same problem by traditional gradient technique.     

A study of process and die design for ball valve forming from stainless steel tube

In this paper, two process and die design methods for ball valve forming from stainless steel tubes are compared: one is the tube hydroforming method (THFM), and the other is the tube nosing method (TNSM). Simulations on hydraulic expansion, axial feeding, and tube nosing of the ball shell forming with the two methods using the program DEFORM-3D are carried out. The influence of the two methods on workpiece formability and wall thickness distribution of ball valve forming is examined. A tube nosing experiment is carried out with a SUS304 stainless steel tube at room temperature. An accepted product of ball valve satisfying the industrial demand is obtained using TNSM.     

Optimization of loading path in hydroforming T-shape using fuzzy control algorithm

The loading path is crucial to the quality of forming parts in the process of tube hydroforming, and thus the design and optimization of loading path is an important issue for tube hydroforming. Wrinkling is a catastrophic defect for thin-walled tube hydroforming. In order to avoid wrinkling, an adaptive simulation approach integrated with a fuzzy control algorithm is used to optimize the loading path of hydroforming a T-shaped tube. The tubular material used is stainless steel and has an outer diameter of 103 mm and the wall thickness of 1.5 mm. The controlled variables are the axial feeding, the counterpunch displacement, and the internal pressure. A code is developed to make the optimization automatically, which works together with LS-DYNA. Six evaluation functions are adopted for identifying geometrical shape and quality of T-shape. Failure indicators obtained from the simulation results are used as the input of the fuzzy control, and then process parameters are adjusted according to the expert experiences in the fuzzy controller. In this way, a reasonable loading path for producing a sound T-shape is obtained, and also a T-shaped product is successfully hydroformed by experiment. The result shows that the fuzzy control algorithm can provide an adequately reliable loading path for hydroforming T-shaped tubes.