On bend-stretch forming of aluminum extruded tubes — II: analysis

Part II describes a two-dimensional model of the bend-stretch-pressure forming process, which assumes that the tube shape and all applied loads are uniform along the length. This simplification results in a significant improvement in computational time over corresponding three-dimensional models. The model is validated through comparisons with experimental results discussed in Part I and its application to the design process is illustrated. The model is then used to study the current manufacturing process and to evaluate some possible alternative loading histories. The effect of tension and pressure on the cross-sectional distortion, springback and net elongation are discussed in light of the predictions. Additionally, the merits of changing the tension and pressure after forming are discussed. The simulations and corresponding experiments are used as the basis for a design methodology for selecting the order and magnitude of the loads applied during the forming process.     

Three-dimensional effects of the bend–stretch forming of aluminum tubes

Bend–stretch forming is commonly used to shape extruded tubular aluminum parts for automotive applications. The tubes are pre-stretched, pressurized and bent over rigid dies. Tension prevents buckling of the compressed side and significantly reduces springback during unloading. An unwanted byproduct of the process is distortion of the cross section. Small amounts of pressure applied during forming can reduce this distortion. A systematic study of how to select the appropriate amounts of tension and pressure for accurate forming with minimal distortion has been conducted. The problem was first studied experimentally using a custom forming facility. An efficient 2-D model of the process was previously developed which was shown capable of capturing the main deformation features of interest. Its efficiency made this model a useful design tool for optimally selecting the forming parameters. In this paper, a 3-D finite element model of the forming process is used to simulate the complete forming process. By using a specially calibrated non-quadratic yield function, the model accurately reproduces all aspects of the process. The model is used to study 3-D features of the problem such as variations of distortion and springback along the length, the effect of friction, the lifting of a section of the tube around the mid-span off of the die, the effect of post-tension, and forming over a variable radius die.     

A simple analysis for bend-stretch forming of aluminum extrusions

Bend-stretch forming is a cold-forming operation used to bend initially straight aluminum extrusions. The process consists of bending the parts over a curved die in the presence of axial tension. Higher tensions reduce the springback of the part but can induce relatively large, permanent cross-sectional distortions. This work presents an efficient formulation to predict the cross-sectional distortion of extrusions with relatively arbitrary, thin-walled cross-section. The results show good agreement with calculations for simple tubular sections and experimental results in the literature. The numerical implementation has short computer run times and should be useful in the design of extrusion cross-sections and in the optimization of the process variables.     

铝型材多点三维拉压复合弯曲成形工艺

轻量化薄壁型材三维弯曲结构件是高端装备制造业中一种难成形加工的关键零部件。针对此类制件的高精度、低成本的成形需求,提出一种拉弯-压弯相结合的铝合金型材三维弯曲成形工艺,设计多点联动的拉压复合成形单元体结构,通过水平方向由夹钳带动拉弯,垂直方向由各单元体上液压执行机构压弯,实现"W"形三维弯曲零件的成形,并研制成形装备样机。建立分析成形过程及回弹预测的数值仿真模型,通过试验对模型的有效性进行验证,仿真结果与试验结果回弹变形一致,回弹预测最大误差小于15%。此外,研究拉力对矩形截面型材拉压复合成形件回弹变形的影响规律,预拉伸力较补拉伸力对成形件的回弹减小趋势更为明显,当预拉伸力从零达到临界塑性应力Aσ_s时,总回弹减少了26.81%,为保证成形件不发生截面畸变和破裂等成形缺陷,确定了预拉伸力为Aσ_s、补拉伸力为0.3Aσ_s的最优工艺参数。所提出的多点三维拉压复合弯曲成形工艺解决了W形一类型材传统三维拉弯无法实现的多向曲率半径复杂弯曲成形的技术难题,为实现镜面对称结构件的成对一次成形提供了一种新方法。     

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.     

Machining distortion minimization for the manufacturing of aeronautical structure

The distortion of machined parts is a major concern in the manufacture of aeronautical monolithic structures. We investigated the influence of material removal partition on residual stress in high-strength aluminum alloy parts to minimize machining distortion. In the present study, a methodology of minimizing machining distortion based on an accurate cross-sectional residual stress determination is presented, which can be applied to avoid or minimize part distortions in advance by adapting machining strategies or process conditions. A powerful contour method was used first to measure bulk residual stress within the blank. Next, a finite element model was applied to predict machining distortion based on measured residual stress for analyzing part distortion. Finally, experimental verification was provided by comparing measured distortion and predicted distortion by the finite element analysis. This simulation showed that part distortion is mainly affected by the partition of material removal in T-shaped components. Our results also indicate that distortion can be minimized by optimizing the partition of material removal to ensure a symmetrical distribution of residual stress in the part so that the residual stress-induced bending moment could reach self equilibrium.     

Modeling of springback, strain rate and Bauschinger effects for two-dimensional steady state cyclic flow of sheet metal subjected to bending under tension

An elastic-plastic mathematical model is presented for plane strain flow of sheet metal subjected to strain rate effects during cyclic bending under tension. The model calculates the stress, strain, strain rate, flow profile geometry, springback and residual stresses for steady state flow of sheet metal under plane strain along the width. Stress reversals were experimentally quantified using a pure bending moment test and were included in the model through Bauschinger factors. Modeling results for two materials, mild steel and aluminum alloy, were in good agreement with experimental results from bending under tension test devices. The iterative nature of the model, associated with a representative experimental framework proved a valuable approach to improving the modeling of sheet metal forming and springback control.     

An energy approach for predicting springback of metal sheets after double-curvature forming, Part II: Unequal double-curvature forming

Based on the membrane theory of shells of revolution and an energy method, theoretical predictions of springback of metal sheets after an equal double-curvature forming operation has been given in the part I of this paper (Xue et al., An energy approach for predicting springback of metal sheets after double-curvature forming, Part I: axisymmetric stamping. International Journal of Mechanical Sciences 2001;43(8):1893–1914). In Part II, the prediction of springback of metal sheets after unequal double-curvature forming is illustrated. It is shown that the proposed mechanics model and analytical procedure can be conveniently applied to predicting the springback, as well as the strain and stress distributions of metal sheets after unequal double-curvature forming, which is valuable for design of tools with complicated shapes in manufacturing industries.     

Hydroforming of aluminum extrusion tubes for automotive applications. Part II: process window diagram

Based on the mathematical formulations for predicting forming limits induced by buckling, wrinkling and bursting of free-expansion tube hydroforming, a theoretical “Process Window Diagram” (PWD) is proposed and established in this paper. The theory developed in the first part of the present work was formulated within the context of free-expansion tube hydroforming with both combined internal pressure and end feeding. The PWD is designed to provide a quick assessment of part producibility for tube hydroforming. The predicted PWD is validated against experimental results conducted for 6260-T4 60×2×320 (mm) aluminum tubes. An optimal loading path is also proposed in the PWD with an attempt to define the ideal forming process for aluminum tube hydroforming. Parametric studies show that the PWD has a strong dependency on tube geometry, material property and process parameters. To the authors’ knowledge, this is the first attempt that a PWD is being formulated theoretically. Such a concept can be advantageous in deriving design solutions and determining optimal process parameters for tube hydroforming processes.     

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.     

7075铝板弹性模量退化行为研究及回弹预测

金属板材的弹性模量随塑性变形发生衰退,这一现象对板材成形中的回弹预测影响巨大。为研究7075高强铝板的弹性模量衰退规律,采用传统的循环加载试验进行弹性模量测试,同时借助DIC应变测量系统设计弯曲卸载试验进行测试。试验结果表明：弹性模量随塑性变形发生明显退化且衰退规律受材料变形所处的应力状态影响。将两种试验所得衰退规律用于C形梁成形过程中的有限元回弹仿真,仿真与试验的对比结果表明：弯曲卸载试验所得弹性模量衰退规律对C形梁回弹分析的结果明显优于循环加载试验所得规律的结果,四个回弹角的预测精度分别提高了42%、7%、40%和200%。     

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。     

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。     

TA2Mδ2.0钛合金外缘翻边成形过程中的形状畸变现象

由于外缘翻边成形过程中应力应变在变形区分布不均匀,以及钛合金板材具有明显的各向异性,导致外缘翻边成形及卸载回弹过程产生诸多形状畸变现象。本文针对料厚为2.0mm的TA2M钛合金板材,采用PAM-STAMP软件对外缘翻边成形及回弹过程进行了有限元数值分析,预测出卸载回弹后的制件将产生翻边壁厚分布不均、翻边高度分布不一致、外翻线端头明显向外隆起、竖边与腹板平面不垂直等畸变现象。室温条件下的一系列外缘翻边成形工艺试验与有限元模拟预测的结果吻合效果良好。     

基于包辛格效应的回弹仿真分析

金属材料在一个方向上的应变硬化降低了反方向的屈服强度,材料包辛格效应的存在对车身成形仿真精度产生了重要影响,尤其现今高强钢和铝合金的大量应用,使车身成形件的回弹问题日益突出,车身模具制造对有限元回弹预测的准确性提出更高的要求。为了提高回弹的仿真精度有必要对材料的包辛格效应进行研究,利用一套夹具对DC06和DP600两种材料的薄板进行拉伸压缩试验,获得不同预应变下的位移加载曲线,通过拉伸压缩试验结果与仿真结果的对比分析,得到能反映材料包辛格效应的非线性混合硬化模型材料参数。开展U形件成形试验,并建立试验的仿真模型,计算DC06和DP600薄板的U形件成形回弹量,分析等向强化、混合强化和随动强化本构模型对回弹预测精度的影响,针对回弹仿真结果和试验结果的差别,对影响仿真精度的材料模型因素进行分析。结果表明,DC06和DP600的包辛格效应大小存在差别,考虑包辛格效应有助于回弹仿真精度的提高,但小曲率弯曲成形回弹计算对材料本构模型的敏感性,限制了回弹仿真精度的提高。     

管轴压成形失稳起皱力学过程的研究

管轴压成形的先进性、优势及成形过程的成功实施受到变形区开裂和传力区起皱等失稳因素的制约,为此采用理论解析与试验相结合的方法,对失稳起皱的力学过程、影响因素及影响规律进行了研究,并给出了失稳判据,以实现稳定成形时变形参数的取值范围的确定。研究表明:成形过程的失稳起皱受到几何参数、材料参数及摩擦边界条件的共同作用。其中,模具圆角曲率半径是决定性因素,并且存在一个最大和最小圆角半径区域使成形过程顺利进行而不发生失稳起皱;增大管坯材料硬化指数,减小相对厚度及接触面的摩擦,有利于减少失稳的发生。对牌号为5052,原始管平均直径d_0=31.0mm,41.0mm铝管的应用表明所提出的判据是可靠实用的。     

Analysis of forming limit in tube hydroforming

The automotive industry has shown increasing interest in tube hydroforming. Despite many automobile structural parts being produced from cylindrical tubes, failures frequently occur during tube hydroforming under improper forming conditions. These problems include wrinkling, buckling, folding back, and bursting.We perform analytical studies to determine forming limits in tube hydroforming and demonstrate how these forming limits are influenced by the loading path. Theoretical results for the forming limits of wrinkling and bursting are compared with experimental results for an aluminum tube.     

FE modeling of warm flanging process of large T-pipe from thick-wall cylinder

The large T-branch pipe made from the thick-wall cylinder is an important part in power, petroleum, and chemical equipment. The warm flanging process is used to manufacture the high-performance large T-branch pipe from thick-wall cylinder. The warm flanging process has a bulk-forming characteristic with heterogeneous temperature field and represents very different from the sheet flanging process. The finite element method is adopted to study the warm flanging process of large T-branch pipe due to complex local heating and local deformation. A viscoplastic FE model was built to simulate the whole process in the same process, including heating, forming, cooling, and relevant elastic springback. Only one set of mesh was used to ensure the connection of heating and forming, which was never proposed in the warm flanging process before. The experiment was conducted to verify the proposed model by comparing the geometry and defects. Accordingly, two kinds of typical defects, buckling and wrinkling, were found in both of the simulation and experiment results. And, the reasons of defects were investigated with the stress and metal flow analysis. The short lower die leads to the buckling. Due to the ellipse outer edge, the uneven rebound makes wrinkling at the ends of the process. Three relevant improved methods, lengthening the lower die, increasing the fillet of the upper die, and increasing the radius of the upper die, were proposed and studied to decline the defects.     

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。