Deformation mechanics in single-point and accumulative double-sided incremental forming

Single-point incremental forming (SPIF) uses one small hemispherically ended tool moving along a predefined toolpath to locally deform a completely peripherally clamped sheet of metal such that the sum total of the local deformations yields the final desired shape of the sheet. While SPIF is characterized by greater formability than conventional forming processes, it suffers from significant geometric inaccuracy. Accumulative double-sided incremental forming (ADSIF) is a substantial improvement over SPIF in which one hemispherically ended tool is used on each side of the sheet metal. The supporting tool moves synchronously with the forming tool, therefore acting as a local but mobile die. ADSIF results in considerably enhanced geometric accuracy and increased formability of the formed part as compared to SPIF. In light of the aforementioned advantages of ADSIF as compared with SPIF, an investigation of the mechanics associated with the ADSIF process, which has yet to be presented in the literature, is warranted. The present study sheds light on the differences in deformation mechanisms between SPIF and ADSIF. Finite element analyses are performed to simulate deformation in the two processes, and a detailed analysis of the deformation history is presented. It is shown that the presence of the supporting tool in ADSIF elicits substantial differences in the plastic strain, hydrostatic pressure, and shear strains as compared to SPIF. The implications of these trends on the prevalent modes of deformation in ADSIF along with possible explanations for increased formability observed in the process arediscussed.     

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.     

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.     

Integration of RP and explicit dynamic FEM for the visualization of the sheet metal forming process

This paper develops a FORTRAN program to convert the explicit dynamic finite element method (FEM)-simulated deformed sheet to the stereolithography (STL) format used in the rapid prototyping (RP) apparatus. Such integration of the RP/FEM can rapidly produce a visualized 3D physical part of the sheet deformation state. Three cases – cylindrical drawing, bore expanding and square cup drawing processes, simulated by explicit dynamic FEM – were investigated to verify the integration system. The wrinkled flange in the cylindrical drawing process, the circle hole expansion in the bore expanding process, and the square cup in the square cup drawing were successfully predicted by explicit dynamic FEM, and the rapid prototyping 3D physical parts also showed good visualization of the deformed sheet for the above three cases. It proves that the integration system of RP/FEM will be able to supply a useful method for the visualization of the 3D physical part in the sheet metal forming process.     

Prediction and control of pillow defect in single point incremental forming using numerical simulations

Pillows formed at the center of sheets in Single point incremental forming (SPIF) are fabrication defects which adversely affect the geometrical accuracy and formability of manufactured parts. This study is focused on using FEA as a tool to predict and control pillowing in SPIF by varying tool size and shape. 3D Finite element analysis (FEA) and experiments are carried out using annealed Aluminum 1050. From FEA, it is found out that the stress/strain state in the immediate vicinity of the forming tool in the transverse direction plays a determinant role on sheet pillowing. Furthermore, pillow height increases as compression in the sheet-plane increases. The nature of in-plane stresses in the transverse direction varies from compressive to tensile as the tool-end geometry is changed from spherical to flat. Additionally, the magnitude of corresponding in-plane stresses decreases as the tool radius increases. According to measurements from the FEA model, flat end tools and large radii both retard pillow formation. However, the influence of changing tool end shape from hemispherical to flat is observed to be more important than the effect of varying tool radius, because the deformation zone remains in tension in the transverse direction while forming with flat end tools. These findings are verified by conducting a set of experiments. A fair agreement between the FEM and empirical results show that FEM can be employed as a tool to predict and control the pillow defect in SPIF.

     

NUMERICAL SIMULATION FOR LASER BENDING OF SHEET METAL

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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.     

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。     

A 3-D finite element method for non-isothermal sheet-forming processes

In sheet forming of ductile materials, the forming limit and strain distribution are governed by plastic instability and fracture following strain localization. A number of phenomena influence the localization process, including the best-known plastic properties of strain hardening, strain-rate sensitivity and yield-surface shape. The temperature gradient caused by deformation heating, heat transfer, and friction between sheet and tools also controls strain localization. In this paper, a numerical method for analyzing the non-isothermal, rigid-viscoplastic deformation of sheets is presented. The method consists of two parts: a rigid-viscoplastic finite element model (FEM) to solve the plastic deformation, and transient heat transfer FEM to evaluate the temperature change throughout the specimen during the deformation process. Bishop's step-wise decoupled method is adopted to handle coupling between mechanical deformation and the temperature change. Using this method, the effect of temperature distribution on strain patterns was investigated. As illustrative 3-D examples, hemispherical punch-stretching and square punch-stretching operations have been analyzed, including deformation heating, frictional heating, heat transfer to tooling and air, and internal heat conduction in the workpiece. The role of temperature gradients is revealed by examination of the simulation results.     

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。     

确定拉延筋约束阻力的一种数值模拟方法

利用率形式的虚功原理和考虑弯曲影响的 Mindlin曲壳单元 ,根据塑性变形体积不可压缩的假设 ,将大变形弹塑性有限元应用于板料成形过程中 ,建立了接触摩擦模型。在此基础上 ,利用自行开发的软件 Sheet Form模拟板料流经拉延筋的过程 ,确定板料成形数值模拟中建立等效拉延筋模型需要的拉延筋约束阻力、塑性厚向应变和最小压边力 3个边界条件 ,并与Nine等人的实验结果进行对比 ,证明了该方法的有效性     

Simulation and experimental verification of flexible roll forming of steel sheets

Roll forming is a sheet metal forming process that has been used for decades. Usually roll-formed sections have a constant cross section. Flexible roll forming is a brand new forming process that produces parts with variable cross sections, in which the rollers translate back and forth in a direction that is perpendicular to the sheet feeding direction. Theoretical analysis gives an explanation of the plane strain state, compressive stresses, tensile stresses, and shear stresses in flexible roll forming. In order to analyze the mechanics and the deformation characteristics of flexible roll forming, the finite element method (FEM) model of a 17-step flexible roll forming process is established. The yield criterion used in the FEM simulation is Hill 48, and the parameters of which are solved with the yield stresses under different loading conditions and are firstly verified with a plane strain tensile test. The complicated roller paths are realized with data extracted from the computer-aided design (CAD) files with VC++ programs developed by the authors. We developed the first flexible roll forming prototype machine in China, with which the roll forming experiment of a side door beam is performed. Final shapes of the experimental and numerical results are compared. It is shown that the numerical results based on Hill 48 yield criterion that is solved with yield stresses agree well with the experimental results, which indicates that the simulation model can well reflect the real forming process. Detailed analysis of the distribution and history of plastic strain, longitudinal strain, shear strain, and thickness of both the constant cross section and the variable cross section is performed, which is of great help to understand this forming process.     

Contact simulation for predicting surface topography in metal forming

A surface contact model that takes account of flattening, roughening and tool elastic microwedge effects on workpiece surface is developed. The model can be implemented in FEM codes to predict the final surface qualities of the products in metal forming. As an example, the proposed model has been combined with a membrane finite element code of sheet metal forming process to predict the contact area ratio, surface roughness and mean asperity spacing. Numerical results showed good agreement with the experiments.     

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。     

金属板料冲压成形的数值模拟

本文采用有限元动力显式算法模拟金属板料冲压成形的加工过程。四结点蜕化壳单元和刚体壳单元分别用来建立权和模具的有限元模型;更新Ｌａｇｒａｎｇｅ法和速率型本构关系被用来处理板料变形中的大应变和大转动;材料模型采用塑性各向异性屈服与等向强化模型;通过主从面模型定义板料和模具的接触,接触算法采用运动约束法,摩擦力用库仓定律计算;并利用动力松弛法对回弹过程进行了计算。模拟结果和实际零件比较,证明模型合理,算法稳定,结果可靠,具有良好的应用价值。     

The formability of annealed and pre-aged AA-2024 sheets in single-point incremental forming

The formability of AA-2024 sheets, an aerospace grade material, in the annealed and pre-aged conditions has been investigated in the single-point incremental forming (SPIF) process. The major operating parameters, namely step size, tool radius, and forming speed, of SPIF process were varied over wide ranges, and their effect on the formability was quantified through a response surface method called as central composite rotational design. It was found that the interaction of step size and tool radius is very significant on the formability. Moreover, a variation in the forming speed does not affect the formability of annealed AA-2024 sheet. However, the formability of pre-aged AA-2024 sheet decreases with the increase in the forming speed. Furthermore, the annealed sheet shows higher formability than the pre-aged sheet.     

Experimental evaluation of coating delamination in vinyl-coated metal forming

In this paper, a new evaluation and prediction method for coating delamination during sheet metal forming is presented. On the basis of the forming limit diagram (FLD), the current study evaluates the delamination of PET coating by using a cross-cut specimen, dome test, and rectangular-cup drawing test. Dome test specimens were subjected to biaxial, plane strain, and uniaxial deformation modes. Rectangular cup-drawing test specimens were subjected to the deep-drawing deformation mode, and compression deformation mode. A vinyl-coated metal (VCM) sheet consists of three layers of polymer on the sheet metals: a protective film, a PET layer and a PVC layer. The areas with coating delamination were identified, and the results of the evaluation were plotted according to major and minor strain values, depicting coating delamination. The constructed delamination limit diagram (DLD) can be used to determine the forming limit of VCM during the complex press-forming process. ARGUS (GOM) was employed to identify the strain value and deformation mode of the delaminated surface after the press forming. After identifying the areas of delamination, the DLD of the PET coating can be constructed in a format similar to that of the FLD. The forming limit of the VCM sheet can be evaluated using the superimposition of the delamination limit strain of the coating onto the FLD of VCM sheet. The experimental results showed that the proposed test method will support the sheet metal forming process design for VCM sheets. The assessment method presented in this study can be used to determine the delamination limit strain under plastic deformation of other polymer coated metals. The experimental results suggested that the proposed testing method is effective in evaluating delamination for specific applications.     

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.     

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。     

Dynamic analysis on laser forming of square metal sheet to spherical dome

Laser forming (LF) is a new die-less forming technique that employs the energy from a laser beam to modify and adjust the curvature of sheet metals. In order to advance the LF process further for realistic application industry, it is necessary to consider large scale three-dimensional laser forming (3DLF). The main problem of 3DLF is the understanding of the mechanism and the planning of laser scanning strategy. This paper illustrates the temperature field, stress–strain field, and deformation field in the process of 3DLF of square sheet to spherical dome with spider-lines strategy with a finite element method (FEM). The explicit dynamic integral is used in the work presented in the paper rather than implicit method for improving the computational efficiency and accuracy. The FEM results showed that the inner stress induced by the laser beam propagates through the sheet as a stress wave, and the thermal stress and the stress wave in the sheet are the main influence factors in 3DLF. Also, the FEM results have been verified against experimental data, and a reasonable correlation has been found. The work showed in the paper would be beneficial of the parameter optimization of laser scanning strategy and the control of the formed precision of the sheet in 3DLF.