Optimization of springback for AZ31 magnesium alloy sheets in the L-bending process based on the Taguchi method

Springback is a primary issue which is encountered during most sheet metal bending processes. Using the Taguchi method, this study investigates the springback of L-bending with a step in the die through simulation and experiments for AZ31 magnesium alloy sheets at different temperatures. The process parameters for bending springback in this study include: lower punch radius, die clearance, step height, and step distance; we use a Taguchi L9 orthogonal array to design the combinations for the experiments. The results of ANOVA analysis show that, for each bending temperature, the process parameters that affect springback occur in the following order: step height (greatest), lower punch radius (next), die clearance (smaller), and step distance (smallest). In addition, with the increase of the bending temperature, the angle of springback decreases. The optimal parameter combinations at each bending temperature from the signal-to-noise response are all the same, namely, a die radius of 2?mm, die clearance of 0.5?mm, step height of 0.1?mm, and step distance of 2?mm. When the bending temperatures are 100°C, 150°C, and 200°C, the angles after springback of the optimal experimental parameter combination are 91.06°, 90.63°, and 89.84°, respectively.     

Comparison between Gurson and Lemaitre damage models in wiping die bending processes

This paper is devoted to a finite element prediction of material damage distribution within the workpiece during wiping die bending processes. The damage mechanics approach has been used in this investigation in order to describe the progressive damage evolution within the sheet. A comparative study between the results obtained by the simulations using the Lemaitre and Gurson damage models is presented and discussed. The elastoplastic constitutive laws are integrated by means of an incremental formulation which has been implemented in the finite element code ABAQUS. The punch load, influenced by the friction coefficient, is investigated for different cases of die radius. The springback angle, which depends on the elastic properties of the material, is computed for all cases. Both models give similar results in the modelling of bending operations. The Gurson one is shown to have more flexibility for applications.     

考虑接触演变的板材回弹过程建模与优化

回弹是由工件在卸载后的弹性变形引起的。板料成形过程中为了控制成形件的最终形状,必须进行回弹设计优化。准确预测回弹对于板料成形过程的模具设计非常重要。降低回弹模拟结果与试验结果的偏差是设计过程中的难题。基于NUMISHEET’02的自由弯曲标准考题考虑板材与模具间的接触演变过程,建立了一个有限元模型来预测回弹。采用一个常规的优化方法对有限元分析中的材料和单元模型进行了分析,研究发现不同模型对回弹结果有较大影响。模拟结果与参考文献中的试验结果比较表明了模型的正确性和可行性。     

基于改进粒子群算法和小波神经网络的高强钢扭曲回弹工艺参数优化*

针对高强钢复杂件冲压后出现的扭曲回弹现象,运用有限元仿真软件DYNAFORM对复杂件的冲压、回弹过程进行数值模拟,提出了评价复杂件扭曲回弹程度的指标,并运用试验设计和小波神经网络代理模型方法对扭曲回弹进行了优化研究。以某弯曲梁为研究对象,以扭曲回弹为成形目标,通过正交试验设计筛选出对扭曲回弹影响较大的工艺参数作为影响因素。利用拉丁超立方对影响因素进行抽样,通过数值模拟获得样本数据,建立影响因素与成形目标之间的小波神经网络代理模型,利用改进的粒子群算法对该模型迭代寻优获得最优参数。结果表明：采用优化后的工艺参数能有效地减小该弯曲梁的扭曲回弹,该方法为减小复杂件的扭曲回弹提供一种有益的指导。     

Mould correction for sheet-metal multi-step incremental air-bending forming based on close-loop control and FEM simulation

There exist errors between the manufactured workpieces and the CAD models due to the springback of sheet-metal incremental air-bending forming. To reduce these errors, an off-line closed-loop control iterative algorithm, combined by fast Fourier and wavelet transform, is developed from the displacement adjustment method (DAM), smooth displacement adjustment method (SDAM) and deformation transfer function method (DTFM) for die surface. With this algorithm, the mould surface of sheet-metal incremental air-bending forming could be properly corrected, and the springback errors of the formed workpieces could be effectively reduced. In order to reduce mould cost and labor cost, the springback tests of workpieces forming, needed in the iterative process of closed-loop control system, are substituted by finite element model (FEM) simulation. The above correction algorithm was used in a semiellipse-shape workpiece incremental air-bending forming. Its average errors are +0.74/−0.39 mm. The results show that the mould correction algorithm with Fourier and wavelet transform is reasonable and the means of FEM simulation are effective. It can be taken as a new approach for sheet-metal multi-step incremental air-bending forming and mould design.     

Estimation of springback in double-curvature forming of plates: Experimental evaluation and process modeling

This paper presents the results obtained from a series of experiments on double-curvature forming of 300 mm square and 15 mm thick plates of type 316L(N) stainless steel to evaluate the inherent springback and also to validate finite element method (FEM) based process model developed for forming of multiple-curvature sectors of large size vessels. The experimental results show that twisting of the plate occurs during pressing, which is unavoidable in an actual forming setup on the shop floor. Twisting increases with increase in slope of the die cavity. Springback in the plate changes in an ascending order towards the centerline of the plate from the edges. The final radius of curvature (ROC) on the pressed plate after springback does not remain constant along a particular axis although the die and the punch had constant ROC along that axis because of varying constraint to opening up of the plate from centerlines to the edges. Springback also increases with reduction in the stiffness of the die and punch. The simulated plate profiles obtained from the FEM process model for multiple-curvature plate forming compared well with the experiments, the maximum error being within 6%. The process model used a sequential dynamic explicit formulation for the plate pressing phase and a static implicit formulation for the unloading (springback) phase in the Lagrangian framework. Reduced integration shell elements were used for the plate and the die and the punch were considered rigid. Dynamic explicit FEM for pressing and static implicit FEM for the unloading phase are adequate and economic for modeling of plate forming process by using FEM. The necessary material and frictional property data needed for the FEM process model were generated in-house. This model can be applied to design of dies and punches for forming the petals of large pressure vessels. The FEM process model predicts the final shape of the product and the residual cold work level for a given die, punch and plate configuration and this information can be used to correct the die and punch shapes for springback to manufacture the petals to the desired accuracy.     

Comparison between three optimization methods for the minimization of maximum bending load and springback in wiping die bending obtained by an experimental approach

The sheet metal bending process is widely used in the automotive industries, and it is actually one of the most important manufacturing processes. The robustness and the reliability of the bending operation, like many other forming operations, depend of several parameters (geometry, material, and process). In this paper, the die radius and the clearance between the punch and the sheet are optimised in order to reduce the maximum bending load and the springback. Two optimization problems are formulated, and three optimization procedures based on the response surface method are proposed and used to find the optimum solutions. Global and local approximations are used to replace the initial optimization problem, which is implicit by an explicit problem, and the optimum is localised using two algorithms: a sequential quadratic programming and an evolution strategies. The objective functions are evaluated experimentally into a limited points number, which are defined using a design of experiments technique. Good results are obtained from the three optimization procedures. The ability of each technique to find the optimal solution is evaluated, and the results show a good agreement between those three methods.     

Numerical simulations on reducing the unloading springback with multi-step multi-point forming technology

Multi-point forming (MPF) is an innovative flexible manufacturing technology for three-dimensional sheet metal forming. It replaces the conventional solid dies with a set of height-adjustable discrete punches, called the “punch group”. A set of punches can construct various three-dimensional curved surfaces freely and conveniently, through adjusting the relative position of each punch. MPF technology not only saves a significant amount of money and time in the design, manufacture, and adjusting of the dies but it can also be applied to change the deformation path and to improve the forming quality. Unloading springback is an inevitable phenomenon in sheet metal forming using MPF. To control and reduce springback, numerical simulations for the MPF process and the unloading springback are carried out using the explicit-implicit coupled finite element method. Subsequently, influencing factors such as thickness, deformation amount, and material properties of MPF springback are researched to investigate the MPF springback tendency. Next, the multi-step MPF technology is introduced to reduce MPF springback. Based on numerical simulation analysis, it is obviously validated that the unloading springback is decreased when the multi-step MPF method is applied. Finally, it is verified that the equidifferent deformation path and small deformation amount of each forming step can improve the workpiece stress state and minimize the unloading springback effectively by an evaluation result of the deformation path effect on the multi-step MPF.     

Analytical modeling and numerical simulation for three-roll bending forming of sheet metal

The three-roll bending forming of sheet metal is an important and flexible manufacturing process due to simple configuration. It is suitable for forming large sheet parts with complex, curved faces. Most researches on roll bending forming of large workpiece are mainly based on experiments and explain the process through macroscopic metal deformation. An analytical model and ABAQUS finite element model (FEM) are proposed in this paper for investigating the three-roll bending forming process. A reasonably accurate relationship between the downward inner roller displacement and the desired springback radius (unloaded curvature radius) of the bent plate is yielded by both analytical and finite element approaches, which all agree well with experiments. Then, the three-roll bending forming process of a semi-circle-shaped workpiece with 3,105 mm (length)?×?714 mm (width)?×?545 mm (height) is simulated with FEM established by the optimum tool and process parameters. Manifested by the experiment for three-roll bending forming of this workpiece, the numerical simulation method proposed yields satisfactory performance in tool and process parameters optimization and workpiece forming. It can be taken as a valuable mathematical tool used for three-roll bending forming of large area sheet metal.     

Analysis and design of flat-die hot extrusion process 1. Three-dimensional finite element analysis

Non-steady-state-coupled three-dimensional analysis is required for investigating complex material flow in practical flat-die hot extrusion processes of aluminum alloys in various channel sections. It is important since the material flow behavior actually determines the amount of distortion of the extruded product. Thus, a non-steady thermo-rigid-viscoplastic finite element program was developed for numerical simulations of the process. Since severely deforming elements of the workpiece can easily interfere with the sharp edges of the flat-die, an automatic remeshing module based on a simple section-sweeping scheme and new contact algorithm were incorporated to allow continuous simulation without manual intervention with less volume loss and computation time. With developed finite element program, non-steady finite element analyses of extrusion processes were carried out for two types of channel-section with constant bearing length of 5 mm. From simulation results, it was found that the exit velocity of the workpiece varied depending on the cross-sectional thickness of the exit and the amount of deflection of the workpiece was not greatly affected by variations of either the workpiece temperature or punch velocity under the present simulation conditions.     

Optimisation of springback in bending processes using FEM simulation and response surface method

The aim of this work includes the springback optimisation of bending processes using the concept of experimental design and response surface methodology (RSM). The optimisation method includes two phases. The first involves the objective function prediction using design of experiments and response surface method, while the second is an optimisation process using a FORTRAN gradient algorithm. Springback of sheet parts during bending processes is simulated using finite element model (FEM) including damage evolution effects within the sheet. The numerical simulation of the damage evolution has been modelled by means of continuum damage approach. The Lemaitre damage model, taking into account the influence of triaxiality, has been implemented into ABAQUS/Standard code in order to predict the external fibres rupture evolution during the process and the material characteristics changes after bending. The simulation included die corner radius and punch-die clearance as the main variables.     

Study on multiple-step incremental air-bending forming of sheet metal with springback model and FEM simulation

A mathematical model of springback radius was developed with dimensional analysis and orthogonal test. With this model, the punch radius could be solved for forming high-precision semiellipse-shaped workpieces. With the punch radius and other geometrical parameters of a tool, a 2D ABAQUS finite-element model (FEM) was established. Then, the forming process of sheet metal multiple-step incremental air bending was simulated with the FEM. The result showed that average errors of the simulated workpiece were +0.68/?0.65 mm, and provided the process data consisting of sheet feed rate, punch displacement and springback angle in each step. A semiellipse-shaped workpiece, whose average errors are +0.68/?0.69 mm, was made with the simulation data. These results indicate that the punch design method is feasible with the mathematical model, and the means of FEM simulation is effective. It can be taken as a new approach for sheet metal multiple-step incremental air-bending forming and tool design.     

Springback prediction of high-strength sheet metal under air bending forming and tool design based on GA�CBPNN

Based on orthogonal test for air bending of high-strength steel sheets, 125 values of sheet thickness (t), tool gap (c), punch radius (r), ratio of yield strength to Young??s modulus (?? _y /E), and punch displacement (e) are used to model the springback for air bending of high-strength sheet metal using the genetic algorithm (GA) and back propagation neural network (BPNN) approach, where the positive model and reverse model of springback prediction are established, respectively, with GA and BPNN. Adopting the ??object-positive model?Creverse model?? learning method, air bending springback law is studied with positive model and punch radius is predicted by reverse model. Manifested by the experiment for air bending forming of a workpiece used as crane boom, the prediction method proposed yields satisfactory effect in sheet metal air bending forming and punch design.     

薄壁深抛物线形零件固体颗粒介质成形工艺

薄壁抛物线形壳体成形过程为拉深和胀形两种变形模式的复合,极易发生起皱和破裂。固体颗粒介质成形是采用固体颗粒代替刚性凸模或凹模(或弹性体、液体)对板料进行成形的工艺。板材在颗粒介质内压的作用下成形,可以有效防止抛物线形件拉深成形过程中侧壁的起皱;由于颗粒内压是非均匀分布的,故可以有效控制抛物线形件成形过程中的破裂,提高板材的成形极限。根据固体颗粒介质成形工艺的特点,提出了两次成形薄壁深壳体零件的工艺,建立了数值分析模型,通过数值模拟和试验对该成形过程和工艺参数进行了分析。结果表明,采用固体颗粒介质成形工艺过程简单、成形工件壁厚分布均匀、表面质量好、回弹小。     

基于ANSYS/LS-DYNA的板材多点成形中回弹的数值模拟

利用有限元软件LS-DYNA对板材冲压成形的回弹进行数值模拟,采用动态显式算法模拟板材成形过程,隐式算法模拟卸载回弹过程;对于不同曲率半径、不同屈服强度的圆柱面成形件进行数值模拟,分析得出回弹趋势和回弹分布,这些结果对于减小因回弹带来的误差、提高成形件的成形精度具有十分重要的现实意义。     

An optimization strategy for die design in the low-density polyethylene annular extrusion process based on FES/BPNN/NSGA-II

An optimization strategy for die design in the polymer extrusion process is proposed in the study based on the finite element simulation, the back-propagation neural network, and the non-dominated sorting genetic algorithm II (NSGA-II). The three-dimensional simulation of polymer melts flow in the extrusion process is conducted using the penalty finite element method. The model for predicting the flow patterns in the extrusion process is established with the artificial neural network based on the simulated results. The non-dominated sorting genetic algorithm II is performed for the search of globally optimal design variables with its objective functions evaluated by the established neural network model. The proposed optimization strategy is successfully applied to the die design in low-density polyethylene (LDPE) annular extrusion process. A constrained multi-objective optimization model is established according to the characteristics of annular extrusion process. The minimum of velocity relative difference, δu, and the minimum of swell ratio, S _w, that, respectively, ensure the extrinsic feature, mechanical property, and dimensional precision of the final products are taken as optimization objectives with a constrained condition on the maximum shear stress. Three important die structure parameters, including the die contraction angle α, the ratio of parallel length to inner radius L/R _i, and the ratio of outer to inner radius R _o /R _i, are taken as design variables. The Phan-Thien–Tanner constitutive model is adopted to describe the viscoelastic rheological characteristics of LDPE whose parameters are fitted by the distributions of material functions detected on the strain-controlled rheometer. The penalty finite element model of polymer melts flowing through out of the extrusion die is derived. A decoupled method is employed to solve the viscoelastic flow problem with the discrete elastic-viscous split-stress algorithm. The simulated results are selected and extracted to constitute the learning samples according to the orthogonal experimental design method. The back propagation algorithm is adopted for the training and the establishment of the predicting model for the optimization objective. A Pareto-optimal set for the constrained multi-objective optimization is obtained using the constrained NSGA-II, and the optimal solution is extracted based on the fuzzy set theory. The optimization for die parameters in the annular extrusion process of low-density polyethylene is performed and the optimization objective is successfully achieved.     

Smoothing Parametric Design of Addendum Surfaces for Sheet Metal Forming

The manual design of addendum surfaces on common CAD platforms is very tedious which requires many trialscorrections, which will certainly a ect the construction e ciency and quality of addendum surfaces, and then a ect the formability and quality of the workpiece in the process of sheet forming. In this paper, an automatic procedure based on parametric design method is proposed for the rapid construction of the addendum surfaces. The kernel of the parametric method is constructing boundary curves based on the shape of surfaces of workpiece and designing guide curves based on Hermite curve interpolation. By some simple parameters, the shape of the addendum surfaces could be controlled and adjusted easily. In addition, a minimum energy optimization method is employed to further optimize the constructed addendum surface. A finite element analysis for the sheet forming process is performed to evaluate the forming quality of constructed addendum surfaces. The instance illustrates that the addendum surface constructed by the proposed method could ensure both the overall smoothing of surfaces and the final forming quality, and it has a good e ect on springback after forming. This research proposes a smoothing parametric design method for addendum surfaces construction which could construct and optimize addendum surfaces rapidly.     

Optimization of drawbead design in sheet forming using one step finite element method coupled with response surface methodology

In a sheet forming process, drawbead plays an important role on the control of the material flow. In this paper, a numerical procedure for the design of forming processes is described. It is based on the coupling of an optimization technique and the simplified one step finite element method (also called inverse approach). The optimization technique allows adjustment of the process parameters so that specified criteria are fulfilled. Response surface methodology (RSM) is a global approximation method, which is ideally suited for solving highly nonlinear optimization problems. The finite element method, in addition to predicting the response of the process to certain parameters, allows assessment of the effect of a variation in these parameters on this response. The authors utilize the one step method at the preliminary design stage to supply stress or strain information for the following optimization using RSM. The procedure for this optimization process is fully described. The front fender for Numisheet 2002 is presented and the real defect free workpiece is produced to demonstrate the usefulness of the proposed optimization procedure. A comparison between the two forming limit curves (FLC) before and after optimization and results obtained using the precise incremental commercial software DYNAFORM based on the explicit dynamic approach verify that the optimization design method of drawbead could be successfully applied in designing actual tools of auto body cover panels.     

Die design optimization for axisymmetric hot extrusion of metal matrix composites

Strain rate sensitive materials such as Ti alloys, superplastic materials and metal matrix composites (MMCs) can be deformed only in very narrow range of strain rate. In this work, a new process design method for controlling strain rate in workpiece during hot extrusion process is proposed. In this approach, a coupled numerical approach of finite element analysis and optimization technique to optimal profiled die which yields more uniform strain rate distribution in the deforming region is applied to the hot extrusion process of MMCs. Extrusion die profiles are defined by Bezier curves, and FPS (flexible polyhedron search) method is used as optimization technique. The change of relative deviation of strain rate, the progressive development of die profiles with increase of iteration for optimization and the corresponding strain rate distributions are investigated. In addition, the die profiles by optimization scheme for different extrusion ratios are compared with those by analytical solution.     

Fast thickness prediction and blank design in sheet metal forming based on an enhanced inverse analysis method

In sheet metal forming process, inverse analysis codes serve a useful purpose at the early product design stage when an approximate analysis is required to determine if the initial concept part can be made and where the failures and defects will occur. In this paper, a robust energy-based 3D mesh mapping algorithm is used to obtain the initial solution and is followed by a reverse deformation method to improve its accuracy. The novel initial solution scheme can consider the material and the process parameters, and thus lead to fewer Newton–Raphson iterations. The actions of the punch, die, blank holder and the drawbead are fully considered. A fast and reliable boundary condition treatment method is implemented to workpiece without binder and addendum information. Contact treatment between punch and die is an essential issue which greatly affects the convergence of Newton–Raphson iterations. A reliable contact treatment based on topological relations of workpiece is proposed to define the force direction between die and punch. Equivalent drawbead forces are also considered with a simplified model. With the improved aspects, the in-house inverse analysis code InverStamp is developed. Application to a square box and a clover-shaped cup are presented with demonstrations of the validity of the code and the efficiency of the proposed modified approaches.