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。     

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。     

An accelerated springback compensation method

Part shape error due to springback is usually considered to be a manufacturing defect in sheet metal forming process. This problem can be corrected by adjusting the tooling shape to the appropriate shape and/or active process control. In this paper, the focus will be on tooling shape design. The traditional trial-and-error methods are inefficient for complex dies. Several analytical methods have been proposed in recent years. Each of these has their advantages and disadvantages. As expected, all these methods required a few iteration steps before converting to the desired tooling shape. Here, we put all of these proposed methods under the same framework. Additionally, built upon existing methods, a new methodology is proposed by incorporating pure geometry correction with fundamental mechanics analysis. Consequently, the convergence becomes much faster and certain. Tooling design results from the new method, together with three existing methods, are compared with each other and an experiment.     

Die design method for sheet springback

A new method for designing general sheet forming dies to produce a desired final part shape, taking springback into account, has been developed. The method is general in that it is not limited to operations having particular symmetry, die shapes, or magnitude of springback shape change. It is based on iteratively comparing a target part shape with a Finite Element-simulated part shape following forming and springback. The displacement vectors at each node are used to adjust the trial die design until the target part shape is achieved, hence the term “displacement adjustment method” (DA) has been applied. DA has been compared with the “springforward” method of Karafillis and Boyce (K&B), which is based on computing the constraint forces to maintain equilibrium following forming. DA was found to converge in cases when K&B does not, and in cases when both methods converge, DA is many times faster. In general, i.e. nonsymmetric parts, K&B can return inaccurate results whereas DA does not. The suitability and application of the two methods is discussed, along with the origins of the differences.     

A die design method for springback compensation based on displacement adjustment

Springback is a major problem in sheet forming processes. This problem can be corrected by adjusting the tooling shape to the appropriate shape and/or active process control. In this paper, the focus will be on tooling shape design, of which compensation magnitude and compensation direction are the two important aspects. A new method, which takes compensation direction into account based on displacement adjustment, has been developed. The method, which we call “comprehensive compensation method” (CC) is general for it considers the fact that large rotation and displacement would occur during springback, which is more common for automotive panel stamping due to the application of advanced high strength steels (AHSS) and the complexity in automotive panel structure. An angle compensation factor was introduced to determine the compensation direction. Compared to the three existing methods, which compensate in different directions, the new method has a higher precision especially for complex panel with advanced high strength. Additionally, the suitability and application of those four methods is also discussed, along with the origin of the differences.     

A rapid and intelligent approach to design forming shape model for precise manufacturing of flanged part

Adjusting the part shape with complex flanges to compensate springback deformation is key to forming shape design for manufacturing rapidly and precisely. Classical forming shape design by displacement adjustment (DA) method using finite element (FE) simulation is usually time-consuming and not accurate enough for complex surface part in industrial application. In this paper, the forming shape is modeled by changing the relations of geometric features of part model with the new flange control surfaces directly. Control surface processing (CSP) method is presented including control surface trimming, cross section division, springback compensation, and extending to design forming shape model of doubly curved flange part with joggles rapidly. The algorithms of cross section curves division of control surfaces and subsequent subdivision of each curve with circular arc and line segments are proposed. A case-based reasoning (CBR) technique and gray relation analysis (GRA) are used to support the intelligent springback prediction of each bending segment of the cross section curve. The geometric data of control surface is expressed in XML format to realize the integration of the CAD-based tools of control surface division and compensation with the Web-based springback prediction system. The approach is demonstrated on an industrial aircraft wing rib part. The forming shape model could be designed rapidly by comparison with DA method. The part shape deviations of flange angle (?0.465° ~ 0.528°) and surface position (?0.3 mm ~ 0.3 mm) were detected by comparing the desired geometry with the actual digital formed part shape, and the results indicate that the approach can achieve the industrial part manufacturing rapidly and precisely.     

基于回弹的飞机蒙皮拉形模型面修模技术研究

回弹是飞机蒙皮成形中不可避免的现象,影响着零件的形状精度。通过模具型面补偿方法可以降低由回弹引起的形状误差。分析基于回弹补偿的飞机蒙皮拉形模具的修模过程,确定贴模度的计算和模具修模量的计算是修模过程中的关键技术。提出虚拟拉形中的贴模度定义以及计算贴模度的直接投影法和最近单元法,并分析这两种方法的特点,得出最近单元法优于直接投影法。同时,提出基于回弹补偿的虚拟修模计算公式,针对公式中贴模度映射到模具节点修模矢量的方法,提出一次投影法和二次投影法,并针对三类典型的蒙皮零件进行计算验证。结果表明,两种投影方法都是有效的,对最大贴模度的影响不大,但就多次修模的稳定性而言,二次投影法好于一次投影法。     

基于有限元分析的铝合金板料弯曲回弹的影响因素研究

铝合金材料的弯曲成形是飞机板材和型材零件常用的加工方式之一,在卸载过程中,由于板料的弹性回复,不可避免的会出现回弹现象,在实际加工中如何预测工件回弹后的形状,并对模具进行适当修正仍是一个比较难解决的问题。本文利用非线性有限元软件MARC对不同厚度的铝合金板材弯曲加工过程进行了模拟分析,给出了相对弯曲半径,弯曲中心角,及不同弯曲模式与回弹角度之间的关系,并与实验数据进行了比较。结果表明,有限元分析结果与实验结果比较吻合,有限元模拟能有效地分析和预测铝合金板料的弯曲回弹,为实际生产加工过程中工艺参数的选择提供有力的参考。     

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.     

基于试验设计和灰色关联度的橡皮囊成形回弹影响因素显著性分析

橡皮囊成形是飞机钣金零件的一种重要成形工艺方法,回弹问题是橡皮囊成形的难点,对其影响因素进行显著性分析可有效控制回弹。基于橡皮囊成形有限元数值模拟,将正交试验设计方法与灰色关联度相结合用于分析橡皮囊成形回弹影响因素的显著性,以某实际长直U形件为例分析压力、最大充液速率、最大节点速度、保压时间、弯曲半径、板料厚度以及轧制方向等因素对回弹的影响程度,结果表明,模具圆角半径、压力、板料厚度、保压时间是橡皮囊成形回弹的主要影响因素,而最大充液速度、最大节点速度、轧制方向对回弹的影响较小。分析结果与工艺试验结果相吻合,从而验证了该方法的有效性。     

Shape error compensation in flexible forming process using overbending surface method

In this article, the design of the flexible forming process considering die shape compensation using an iterative overbending method based on numerical simulation is carried out. In this method, the springback shape obtained from the final step of the first forming simulation is compared with the desired objective shape, and the shape error is calculated as a vector norm with three-dimensional coordinates. The error vector is inversely added to the objective surface to compensate both the upper and lower flexible die configuration. The flexible dies are made up of several punches that make a forming die that is equivalent to a solid die, thus the forming surface shape can be reconfigurable with regard to the compensated die shapes. The flexible die shapes are recalculated, and the punch arrays are adjusted according to the overbent forming surface. These iterative procedures are repeated until the shape error variation converges. In addition, experimental verification is carried out using a 2,000-kN flexible forming apparatus for thick plates. Finally, the configuration of the prototype obtained from the experiment is compared with the numerical simulation results, which have consideration of the springback compensation. Consequently, it is confirmed that the suggested method for compensating the forming error could be used in the design of the flexible forming process for thick-curved plates.     

Applying forming simulation to process and tooling designs for minimizing springback in split dowel manufacturing

In this study, FEA simulations were conducted to analyze the forming and springback of a split dowel forming process. Through 96 simulations, the best dimensional quality product from the current production tooling was obtained. However, it still cannot meet the customer’s geometrical requirement, so a metal finish process (secondary operation) is required. In order to minimize manufacturing cost and time, the secondary operation is not desired. Therefore, a new forming process and die design were developed through many iterative FEA simulations. This new design adds a short coin bead on the seam line area of the split dowel. It has been found that the springback amount is almost eliminated and the product quality exceeds the customer’s geometry requirement. Through this real industry case study, it is shown that FEA simulation can be used to not only optimize the current process but also design a new process and tooling.     

Characterising material and process variation effects on springback robustness for a semi-cylindrical sheet metal forming process

Variation in the incoming sheet material and fluctuations in the press setup is unavoidable in many stamping plants. The effect of these variations can have a large influence on the quality of the final stamping, in particular, unpredictable springback of the sheet when the tooling is removed. While stochastic simulation techniques have been developed to simulate this problem, there has been little research that connects the influence of the noise sources to springback. This paper characterises the effect of material and process variation on the robustness of springback for a semi-cylindrical channel forming operation, which shares a similar cross-section profile as many automotive structural components. The study was conducted using the specialised sheet metal forming package AutoForm™ Sigma, for which a series of stochastic simulations were performed with each of the noise sources incrementally introduced. The effective stress and effective strain scatter in a critical location of the part was examined and a response window, which indicates the respective process robustness, was defined. The incremental introduction of the noise sources allows the change in size of the stress–strain response window to be tracked. The results showed that changes to process variation parameters, such as BHP and friction coefficient, directly affect the strain component of the stress–strain response window by altering the magnitude of external work applied to forming system. Material variation, on the other hand, directly affected the stress component of the response window. A relationship between the effective stress–strain response window and the variation in springback was also established.     

Optimization of the structural and process parameters in the sheet metal forming process

The quality of the sheet metal forming product is determined by defects such as wrinkling, springback, etc. Optimization techniques can avoid such defects while the desired final shape is obtained. The design variables of the optimization process consist of the structural parameters and process parameters. The structural parameters are the initial blank shape, geometry, etc. and the process parameters are the blank holding force (BHF), the drawbead restraining force (DBRF), etc. In this paper, the two groups of parameters are separately optimized. The structural parameters are optimized by the equivalent static loads method for non linear static response structural optimization (ESLSO) and the process parameters are optimized by the response surface method (RSM). A couple of examples are solved by the iterative use of ESLSO and RSM, and the solutions are discussed.     

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.     

Rapid Sheet Metal Manufacturing. Part 1: Indirect Rapid Tooling

Rapid sheet metal manufacturing (RSMM) is a closed loop process for making sheet metal products which uses advanced computer-aided techniques and computer-controlled machines to produce non-ferrous tooling directly or indirectly. The tooling would be suitable for short-run production or design evaluation of sheet metal products for which prototyping cost and lead time are greatly reduced. The key aspect of this closed-loop process is the method used to fabricate and modify the sheet metal forming tool. Various approaches are adopted in the preparation of the tooling for onward embossing on a sheet metal. The three indirect approaches use selective laser sintering (SLS), stereolithography (SLA), and high-speed computer numerical controlled (CNC) milling to build the masters from computer data models. The masters are used in the vacuum casting process to generate the non-ferrous tooling. Comparisons on quality, lead time and cost are presented.     

A novel 3D optical method for measuring and evaluating springback in sheet metal forming process

A novel 3D optical method for measuring and evaluating the springback in sheet metal forming is presented and its principle, program and steps are studied. The optical method includes a measuring method and evaluation indexes. The point cloud, obtained using photogrammetry and surface scanning systems, is used as the workpiece shape after springback. The original mould is regarded as the CAD model before springback. The point cloud and CAD model are aligned in Geomagic Qualify. A cutting line for the point cloud or CAD model can be obtained at any point in any direction of their cross sections. The springback is calculated as the difference between any two corresponding key points on the two cutting lines. The evaluation index S consists of a 3D springback value w and its vectors along x, y and z directions. Feasibility of the optical method is verified by using a refrigerator door shell.     

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.     

Springback prediction of the vee bending process for high-strength steel sheets

The precise prediction of springback is a key to assessing the accuracy of part geometry in sheet bending. A simplified approach is developed by considering the thickness ratio, normal anisotropy, and the strain-hardening exponent to estimate the springback of vee bending based on elementary bending theory. Accordingly, a series of experiments is performed to verify the numerical simulation. The calculation of the springback angle agrees well with the experiment, which reflects the reliability of the proposed model. The effects of process parameters such as punch radius, material strength, and sheet thickness on the springback angle are experimentally tested to determine the dominant parameters for reducing the springback angle in the sheet bending process for high-strength steel sheets. Moreover, the effects of the thickness ratio, normal anisotropy, and the strain-hardening exponent on the springback angle in the vee bending process for high-strength steel sheets are theoretically studied. Therefore, improving understanding on and control of the springback reduction of the vee bending process in practical applications is possible.     

Rapid springback compensation for age forming based on quasi Newton method

Iterative methods based on finite element simulation are effective approaches to design mold shape to compensate springback in sheet metal forming. However, convergence rate of iterative methods is difficult to improve greatly. To increase the springback compensate speed of designing age forming mold, process of calculating springback for a certain mold with finite element method is analyzed. Springback compensation is abstracted as finding a solution for a set of nonlinear functions and a springback compensation algorithm is presented on the basis of quasi Newton method. The accuracy of algorithm is verified by developing an ABAQUS secondary development program with MATLAB. Three rectangular integrated panels of dimensions 710 mmx750 mm integrated panels with intersected ribs of 10 mm are selected to perform case studies. The algorithm is used to compute mold contours for the panels with cylinder, sphere and saddle contours respectively and it takes 57%, 22% and 33% iterations as compared to that of displacement adjustment （DA） method. At the end of iterations, maximum deviations on the three panels are 0.618 4 mm, 0.624 1 mm and 0.342 0 mm that are smaller than the deviations determined by DA method （0.740 8 mm, 0.740 8 mm and 0.713 7 mm respectively）. In following experimental verification, mold contour for another integrated panel with 400 ram~380 mm size is designed by the algorithm. Then the panel is age formed in an autoclave and measured by a three dimensional digital measurement devise. Deviation between measuring results and the panel＇s design contour is less than 1 mm. Finally, the iterations with different mesh sizes （40 mm, 35 mm, 30 mm, 25 mm, 20 mm） in finite element models are compared and found no considerable difference. Another possible compensation method, Broyden-Fletcher-Shanmo method, is also presented based on the solving nonlinear fimctions idea. The Broyden-Fletcher-Shanmo method is employed to compute mold contour for the second panel. It only takes 50% iterations compared to that of DA. The proposed method can serve a faster mold contour compensation method for sheet metal forming.