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 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.     

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.     

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.     

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.