Modeling and simulation for multiple-step incremental air-bending forming of sheet metal

Based on Hill’s yielding criterion and plane strain condition, the explicit expressions of elastoplastic constitutive model are derived in this paper which takes into account the effects of transverse stress, neutral surface shifting, and sheet thickness thinning on the sheet springback of air-bending. Then, this model is embedded into ABAQUS software platform by means of programming. Finally, 3D ABAQUS finite-element models (FEM), used to form the semiellipse-shaped workpiece with super length and large opening of sheet metal, are established, and the multiple-step incremental air-bending forming and springback processes are simulated. The simulation and experiment results show that the data predicted with the new constructed constitutive model under the plane strain condition are in much better agreement with experimental data than those predicted with the constitutive model built-in ABAQUS. It can be taken as a valuable mathematical tool used for multiple-step incremental air-bending forming simulation of large area sheet metal.     

Tool path correction algorithm for single-point incremental forming of sheet metal

There exists some error between the manufactured part shape and the designed target shape due to springback of this part after forming. To reduce the error, an iterative algorithm of closed-loop control for correcting tool path of the single-point incremental forming, based on Fast Fourier and wavelet transforms, has been developed. Moreover, the data of the springback shapes, after unloading, of the sheet metal parts formed with the trial and corrected tool paths, used for iterative correction of tool path in the algorithm, are obtained with finite element model (FEM) simulation. Then, a truncated pyramid-shaped workpiece, whose average errors are +0.183/?0.175 mm, was made with the corrected tool path after three iterations solved by the above algorithm and simulation data. The results show that the tool path correction algorithm with Fourier and wavelet transforms is reasonable and the means with FEM simulation are effective. It can be taken as a new approach for single-point incremental forming of sheet metal and tool path design.     

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.     

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.     

大型U形板材工件渐进滚弯成形数值模拟

利用ABAQUS有限元分析平台,对大型U形板材工件渐进滚弯成形及其回弹过程进行数值模拟,其中工件材料类型选择普通低碳钢。针对半椭圆形工件形状,提出用半径不同的五段圆弧逼近的几何规划。在此基础上,根据加工过程可能出现的缺陷,合理设计滚弯道次,调整ABAQUS参数设置。用模拟优化的工艺参数成形加工半椭圆形板材工件,经origin8拟合配准,其各段曲率半径最大误差小于5%。模拟结果表明,用渐进滚弯方法成形加工半椭圆形工件是可行的,且模拟过程满足准静态响应的要求。     

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.     

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。     

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.     

Modelling of kinetic friction in V-bending of ultra-high-strength steel sheets

The Stribeck friction model was investigated in this study to predict springback of high-strength steel sheets. The coefficient of friction in Stribeck curve depends on sliding velocity and contact pressure. The plane-strain bending process is simulated in ABAQUS/Standard. The influence of forming speed, over-pressing and holding time on springback behaviour of sheets was studied numerically. By plotting the variation of bending angle with punch stroke, we found that the loading curve of finite element analysis showed similar results to the experiments. The unloading curves of FE analysis with friction models based on Stribeck curve and Coulomb law showed good agreement with experiments with error less than 1.5%. Forming speed of up to 50 mm/s does not have significant effect on springback. The effect of holding time on reducing springback is small, but over-press has large effect on reducing springback. The results showed that Stribeck model is suitable for sheet metal forming simulations, especially at higher forming speeds and pressures.     

Springback evaluation in hot v-bending of Ti-6Al-4V alloy sheets

In this paper, v-bending of Ti-6Al-4V alloy sheet was conducted from room temperature to 850 °C at a fixed velocity of 0.1 mm/s. Punches with punch radii of 1, 2, 4, and 6 mm, as well as several holding times were used. V-bending and springback behaviors were numerically analyzed with an isotropic hardening model that considered rate-dependent effects. Using a punch radius of 1 mm always leads to negative springback in the temperature range of 550–750 °C. This behavior occurs because an arc formed in the transition side near the end of bending and flattened at the end of bending, leading to an internal bending moment which causes specimen to bow inward after unloading. At a punch radius of 2 mm, positive springback occurs at 300–650 °C, while negative springback occurs at 700–750 °C. At punch radii of 4 and 6 mm, positive springback occurs at 600–750 °C, and the angle decreases as temperature increases. At 850 °C, negative springback occurs at a punch radius of 4 mm due to the decrease in yield strength. At a punch radius of 1 mm, cracking occurs at room temperature and 500 °C, while at 2 mm, it occurs only at room temperature. This discrepancy is ascribed to the greater plastic deformation caused by the smaller punch. As holding time increases, the shape of the deformed specimen more closely matches the desired shape.     

板料成形中的回弹计算和模具修正

利用动力显式有限元计算程序MSC／DYTRAN,采用动力松弛法模拟了板料成形及回弹过程,计算出板料成形后的回弹量：提出“位移描述－结点修正”法,以回弹量为依据通过反向位移补偿和插值算法,编制程序自动对模具网格结点进行修正,通过反复迭代计算,最终可获得生成理想形状制件所必需的凸,凹模尺寸。     

Metal flow prediction during sheet-metal punching process using the finite element method

In this study, part springback and metal flow caused by punch penetration into a sheet was investigated by punching circular test specimens with concentric circular tools. Strain gauges were bonded on the upper surface of the specimens at radial distances varying from 2 mm to 10 mm from the cutting edge of the punch. The experiments were used to validate a finite element model (FEM) valid for numerical simulation of sheet-metal punching processes. Damage and crack propagation were taken into account by means of an elastoplastic constitutive law. The main difficulty encountered in simulating this operation is describing the behaviour of the sheet continuously from the beginning of the operation up to the total rupture. The choice of a behaviour law is crucial, since each successive step in the whole process has to be described accurately. In this investigation, an elastoplastic behaviour law coupled with damage was retained to describe the progressive damage accumulation in the workpieces. During the analysis, the initiation of a crack is assumed to occur at any point in the structure where the damage reaches its critical value D _c . The crack propagation is simulated by the propagation of a completely damaged area. This is taken into account in the FEM by a decrease in the stiffness of the broken elements. The numerical results obtained by the simulation were compared with the experimental ones in order to verify the validity of the proposed FEM.     

复杂形状的中厚板件拉深成形动力显示有限元分析

将厚向异性屈服函数、单元级双面接触算法的能够反映强烈弯曲效应的M ind lin曲壳单元模型引入动力显式中心差分格式的有限元算法,并组入自主开发的板成形CAE商品化软件KMAS系统中,建立对复杂形状的中厚板件拉深成形有限元模拟分析算法;在此基础上,以轿车摇臂厚板金件为例分析了材料厚向异性参数r值、凹模圆角以及压边力大小对此类成形件成形性的影响。通过数值模拟与实际拉深成形实验的对比,验证了本文方法的有效性;同时,结合实验研究了此类单元对工具弯曲圆角大小的适应性。     

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.     

基于有限元复杂回转体渐进成形过程研究

数字化渐进成形技术是一种新兴的金属板料柔性成形技术。通过有限元数值对其成形过程模拟,能够对渐进成形的研究起理论指导作用。利用有限元分析软件LS-DYNA对金属板料渐进成形的过程进行了模拟。根据试验特点建立了相关的有限元模型,对其中工具头的运动轨迹和加载方式进行了简化,同时根据实际成形特点建立了边界条件和约束,保证了模拟的真实性,并据此模型分析了成形过程中板料上的应力、应变分布特点。     

The study for stability of closed-loop control system based on multiple-step incremental air-bending forming of sheet metal

To solve the springback problem for sheet metal forming, feedback control idea in automatic control theory is introduced to incremental air-bending forming process. The advanced control techniques are used to solve precision forming for workpiece of sheet metal. However, stability, accuracy, and rapidity of closed-loop control can directly affect system normal operation. Aiming to analyze the effect of stability on the quality of the formed workpiece, a closed-loop control system model for incremental air-bending forming is established. The transfer function and characteristic equation of the closed-loop system are solved through theory deduction and minor incremental linearization method. Both simulations with Matlab/Simulink and root locus results show that, as the overall gain is equal to one, the shape of formed part could converge to the target shape at the fastest rate. Finally, a semiellipse-shape workpiece is manufactured with the corrected mold obtained by the closed-loop forming method. The experimental results show that the closed-loop forming way is feasible and the means of correcting the mold parameters by iterative compensation of the stable closed-loop control system is effective. It can be taken as a new approach for sheet metal incremental air-bending forming and mold design.     

基于混合算法的冲压回弹模拟研究

文中对数值模拟算法进行分析,得出对于板料冲压成形问题使用动态显式算法进行模拟比较合适,而对于成形后回弹问题使用静态隐式算法进行模拟更适用,即利用混合算法对冲压回弹问题进行模拟;讨论了有限元模拟中的单元选择、网格技术和凸模虚拟速度的关键技术。利用混合算法在ABAQUS软件中对多角弯曲件冲压成形及回弹进行模拟,对实际模具设计具有很好的指导和参考价值。     

金属板材数控单点渐进成形回弹的实验研究

主要研究了金属板材数控单点渐进成形过程中的回弹问题 ,分析了影响板材渐进成形回弹的主要因素和变化规律 ,提出了一种通过增大成形角度控制回弹的方法。     

A new model for springback prediction in which the Bauschinger effect is considered

Springback prediction is an important issue for the sheet metal forming industry. Most sheet metal elements undergo a complicated cyclical deformation history during the forming process. For an accurate prediction of springback, the Bauschinger effect must be considered to determine accurately the internal stress distribution within the sheet metal after deformation. Based on the foundations for isotropic hardening and kinematic hardening, Mroz multiple surface model, plane strain assumptions, and experimental observations, a new incremental method and hardening model is proposed in this paper. This new model compares well with the experimental results for aluminum sheet metal undergoing multiple-bending processes. As is well known, aluminum is one of the most difficult sheet metals to simulate. The new hardening model proposed in this paper is not only a generic model for springback prediction but also a hardening model for sheet metal forming process simulation.     

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。