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.     

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。     

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.     

Incremental forming path-generated method based on the intermediate models of bulging simulation

This paper discusses the strategy of incremental forming and presents a novel forming strategy for tool path generation. To equalize the strain distribution of sheet metal and improve the forming limit, multistage forming is made to reference a hydraulic bulging forming. Under the liquid pressure, a plate sheet gradually approaches the final shape. A hydraulic bulging numerical simulation is used to obtain a series of intermediate surfaces. Then, CNC codes can be generated in CAM software based on the surfaces. The codes are the tool spatial feed paths for single-point incremental sheet metal forming. The paper focuses on the feasibility investigation, and the experiment proved it. The behaviors of forming and the distribution of thickness are also discussed and concluded that the forming limit of the sheet can be improved by imitating the approach between intermediate surfaces.     

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.     

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.     

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。     

板材多点成形使用弹性垫后回弹的数值模拟

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。使用3mm厚的弹性垫抑制板材成形产生的压痕,但弹性垫的使用加上板材的回弹会导致成形误差的增大。基于数值模拟的结果,提出了修正基本体群成形面补偿回弹。经过两次补偿,精度得到了很好的提高,证明该方法可以很好地补偿多点成形中的回弹。     

铜铝复合板渐进成形回弹缺陷研究

为了讨论不同工艺参数对复合板渐进成形回弹的影响,建立了包含工具头、复合板材和复合界面的三维有限元模型,通过对比T形剥离结果得到复合界面内聚力单元参数,通过实验验证了有限元模型的可靠性。实验结果表明,成形角对双金属复合板渐进成形回弹最敏感,工具头直径对回弹敏感度最低,另外,内聚力单元能有效模拟双金属复合板结合界面,模拟误差仅为7.9%。分析结果表明,单层下压量、板厚、工具头直径都与回弹量成正相关,成形角与回弹量成负相关,成形角从30°增大至60°时回弹量减小21%。     

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。     

平面变形回弹迭代补偿的收敛准则及应用

针对板材平面变形过程中的回弹问题,基于迭代法建立了迭代补偿机制,给出了迭代参量收敛性的判定准则。对于简单应力状态下平板单向拉伸和双向拉伸的弹塑性变形过程,证明了参量轴向长度对迭代补偿机制具有收敛性。对于宽板V形自由弯曲工艺,通过理论和实验验证了弯曲曲率和弯曲角的收敛性。进而,将迭代补偿机制应用于宽板自由弯曲工艺的回弹控制,对曲率和弯曲角分别进行了迭代补偿实验,结果表明,根据每次试验的回弹量,迭代补偿机制可以预测下一次补偿值,使弯曲工艺经过2～3次迭代,就获得了误差小于0.1%的目标曲率和误差小于0.5%的目标弯曲角,收敛速度很快。而且,对于同一材料的同一成形工艺,每次的补偿量只取决于回弹前后的迭代参量差值。     

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.     

采用试错接触算法的板料成形有限元模拟技术－

以金属板料成形过程为对象,采用基于板壳理论的８节点壳单元,以Ｋｉｒｃｈｈｏｆｆ应力张量和Ｇｒｅｅｎ应变张量作为应力与应变的度量,采用有限变形的Ｕｐｄａｔｅｄ　Ｌａｇｒａｎｇｉａｎ列式,研究有限元方法模拟成形过程的技术。在此基础上,提出了一种直接试错的接触算法,将非线性的接触边界条件线性化处理,接触处理与有限元计算相对独立。通过试验结果与计算结果的比较,说明采用的模拟算法是合理可行的。     

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.     

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。     

Tooling design in sheet metal forming using springback calculations

A method to design tooling in sheet metal forming using springback calculations is presented. The designed tooling produces a part which matches the desired shape, thereby compensating for springback. To design the appropriate tooling, traction distributions on the sheet in the fully loaded deformed state are computed using the finite element method. The calculated tractions are then used to numerically reproduce springback of the desired part shape by elastic unloading of the part in a reverse manner. The method is examined for materials covering a range of steel strength and hardening, and is found to produce parts with negligible shape error. The success of the tooling design algorithm leads to a proposal for an experimental method to design tooling based on traction distribution measurements.     

Substepping algorithms with stress correction for the simulation of sheet metal forming process

The finite element analysis of the sheet metal forming process involves various nonlinearities. To predict accurately the final geometry of the sheet blank and the distribution of strain and stress and control various forming defects, such as thinning, wrinkling and springback, etc., the accurate integration of the constitutive laws over the strain path is essential. Our objective in this paper is to develop an effective and accurate stress integration scheme for the analysis of three-dimensional sheet metal forming problems. The proposed algorithm is based on the explicit “substepping” schemes incorporating with the stress correction scheme. The proposed algorithms have been implemented into ABAQUS/Explicit via User Material Subroutine (VUMAT) interface platform. The algorithms are then employed to analyze a typical deep-cup drawing process and the accuracy of these algorithms has been compared with the implicit “return” algorithm and explicit forward algorithm. The results indicate that the explicit schemes with local truncation error control, together with a subsequent check of the consistency conditions, can achieve the same or even better level of accuracy as “return” algorithm does for integrating large plastic problems like sheet metal forming process.     

Two-directional toolpath correction in single-point incremental forming using model predictive control

Incremental sheet forming (ISF) is an emerging forming technology that promises high flexibility and formability. These properties make it suited for small-scale and customised production. However, the poor geometric accuracy of ISF limits the wide application of this flexible forming technology. This paper presents a two-directional toolpath correction approach to enhance ISF forming accuracy using a model predictive control (MPC) algorithm. A toolpath optimisation method for vertical toolpath correction has been validated in our previous work (Lu et al., Int J Adv Manuf Technol 72:1–14, 2015), and it helps to reduce errors in the base of the test shapes to a suitable level while its major limitation is that horizontal geometric errors are relatively large. This paper extends our previous work (Lu et al., Int J Adv Manuf Technol 72:1–14, 2015) by augmenting the vertical control module with a new control module for horizontal toolpath correction. The proposed control algorithm was experimentally validated in single-point incremental sheet forming (SPIF) using two forming case studies. In the first case study (a truncated pyramid), two control approaches with different assumptions for the horizontal springback distribution along the horizontal cross-sectional profile were tested and compared. Then, the developed MPC control algorithm was applied to form a more complex asymmetric shape. The results show that the developed strategy can reduce the forming errors in the wall and base of the formed shape compared to the existing works. The ISF process with MPC control leads to significant accuracy improvement in comparison with the typical ISF process that is without toolpath control.     

金属板料渐进成形有限元仿真过程中复杂成形路径的构建方法

提出一种用于获得复杂空间运动轨迹的方法——虚拟靠模导向法。该方法借鉴了数控加工中COPY铣的思想,利用轨迹生成球在由零件派生出的虚拟靠模表面上的持续运动来模拟实际成形工具的运动过程,从而获得最终成形路径。基于该思想和简单的运动学原理,轨迹球与虚拟靠模有限元模型被构建起来。通过对计算过程进行分析,确定运用该法时适合的加载力、成形速度及计算精度的影响因素。因该法完全基于有限元模拟计算,故获得的成形路径可直接导入至后续的金属板料成形过程的模拟分析。该法已在有限元软件PAMSTAMP平台上得以实现,并主要用于金属板料渐进成形过程的有限元仿真。     

Effect of electropulsing on springback during V-bending of Ti-6Al-4V titanium alloy sheet

Because the intermediate-stage forming surface and the intermediate-stage forming tool path of the complex shape model are difficult to generate, the existing multi-stage CNC incremental forming takes the regular rotary body model or the square model as the research objects, and all adopt the three-axis CNC incremental forming mode. In this paper, a method for generating the intermediate-stage surface by using a longitude line that can reflect the personality of the surface and the five-axis CNC multi-stage incremental forming tool path was proposed. Firstly, the vertexes of the triangular facets of the STL model are used to generate the longitude lines which can reflect the characteristic of the surface, then the longitude lines are offset according to the multi-stage forming strategy and the characteristics of each surface associated with the longitude lines so that the intermediate-stage longitude lines could be generated, and then the intermediate-stage surfaces are built using the intermediate-stage longitude lines. Finally, the cutter location points of each intermediate stage are obtained by cutting the intermediate-stage surfaces, and the postures of the five-axis CNC pressing tool are determined according to the normal vector of the cutter location points. The case studies show that the proposed method can well generate the five-axis CNC multi-stage incremental forming path for the complex shape sheet metal part. The results of the numerical simulation analysis and forming experiments show that the proposed method is applicable.