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.     

Unconstrained bending and springback behaviors of aluminum-polymer sandwich sheets

The bending and springback behaviors of sandwich sheets are more complicated than those of monolithic layer metallic sheet due to the extremely large difference in mechanical properties and in the gauges of polymer core and the skin sheet. In the present study, the bending and springback behaviors of aluminum-polymer sandwich sheets were investigated by using analytical method and conducting experiments and numerical simulations. A simplified analytical model was proposed to calculate the bending moments for sandwich sheet in unconstrained bending process through analyzing the strain and stress distributions of skin sheet and core materials. Then, the analytical model was applied to predict the springback of sandwich sheets after bending. Numerical simulations and experiments of unconstrained bending process for aluminum-polymer sandwich sheets were conducted to investigate the influences of mechanical properties of each layer and thickness ratio of two layers on the folding defects, neutral layer location, and springback. The results show that the neutral layer shifts dramatically toward the compression region of the specimen during bending. The folding angle mainly relates to the strength difference between the skin sheet and the core polymer. The springback angle of sandwich sheet is mainly determined by the mechanical properties of skin sheet.     

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。     

An energy approach for predicting springback of metal sheets after double-curvature forming, Part I: axisymmetric stamping

In our previous study (Xue P, Yu TX, Shu E. International Journal of Materials Processing Technology 1999; 89-90:65-71.), based on the membrane theory of shells of revolution and an energy method a mechanics model and corresponding analytical procedure have been proposed to predict springback of circular and square metal sheets after a double-curvature forming operation. The strain hardening of the material is incorporated into the mechanics model. In the present paper, the method is extended to the cases, in which bending effect, as well as bending-and-unbending effect are taken into account. It is shown that the procedure developed is capable of quantitatively predicting the strain distribution and springback of metal sheets after axisymmetric stamping with a relatively minor effort of calculation and a good accuracy. The effect of stretching force applied at the edge of the plate on springback is also considered. Excellent agreement is found between the theoretical prediction of springback and experiment results.     

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.     

精密定位系统的摩擦力建模与补偿

为了提高由直线电机驱动的精密定位系统的定位精度,建立了优化Stribeck摩擦模型,对摩擦力这一影响定位精度的主要因素进行补偿。首先,对于传统的Stribeck摩擦模型进行优化,采用改进的最小二乘算法对模型参数进行辨识。然后,对所建立的摩擦模型补偿算法进行仿真并与扰动观测器的补偿算法进行比较,发现前者速度比后者速度在补偿后提高了4.33%,对摩擦力具有更好的补偿效果。最后,在大行程二维精密定位平台上进行验证,根据平台能够达到的最大速度定义0.005 m/s为低速运动,0.05 m/s为高速运动,在这两种速度下进行实验,并与基于库仑摩擦前馈补偿模型比较。实验结果表明：精密定位平台在速度为0.005 m/s的低速运动时,优化模型的跟随误差减小了67.67%;在速度为0.05 m/s的高速运动时,优化模型的跟随误差减小了51.63%,验证了优化Stribeck摩擦模型补偿算法的有效性。本文提出的优化Stribeck摩擦模型可用于提高由直线电机驱动的精密定位系统的定位精度。     

On the modelling of the bending-unbending behaviour for accurate springback predictions

The prediction of springback is probably the area in sheet forming simulation where the least success has been achieved in terms of solution accuracy. The springback is caused by the release of residual stresses in the workpiece after the forming stage. An accurate prediction of residual stresses puts, in turn, high demands on material modeling during the forming simulation. Among the various ingredients that make up the material model, the hardening law is one of the most important ones for an accurate springback prediction. The hardening law should be able to consider some, or all, of the phenomena that occurs during bending and unbending of metal sheets, such as the Bauschinger effect, the transient behaviour, and permanent softening. The complexities of existing hardening laws do of course vary within quite wide ranges. One of the purposes of the present study was to try to identify a model of reasonable complexity that at the same time can fulfill the requirements concerning accuracy. Five different hardening models have been evaluated in the present investigation. The simplest model, the isotropic hardening one, involves only one history variable, while the most advanced model involves ten history variables and four additional material parameters. In the current report, results for four different materials will be accounted for. The kinematic hardening parameters have been determined by inverse modeling of a three-point bending test. A response surface method has been used as an optimization tool, together with a finite-element model of the bending test set-up. The springback of a simple U-bend has been calculated for one of the materials, and from the results of these simulations some conclusions regarding the choice of hardening law are drawn.     

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。     

润滑点接触粗糙表面滑动摩擦因数的实验研究

利用多功能微摩擦试验机,在轻载荷条件下测量了具有横向纹理圆盘表面的摩擦因数,得到了包括流体润滑、混合润滑和边界润滑完整的Stribeck曲线。考虑了载荷和时间对实验结果的影响,对不同粗糙度表面的Stribeck曲线进行了比较。实验的初步结果表明:增加载荷与实验时间,会获得更加稳定的实验结果;表面越粗糙,从混合润滑向流体润滑转换的临界速度越大;表面越光滑,Stribeck曲线的“谷底”越明显。     

On bend-stretch forming of aluminum extruded tubes — I: experiments

Tubular aluminum frame parts for automotive applications are best produced by extrusion. The tubes are then cold formed to the required shape by prestretching, pressurizing and bending them over rigid dies. Tension prevents buckling of the compressed side and significantly reduces the springback on unloading. An unwanted byproduct of the process is distortion of the cross section. It has been found that modest levels of pressure can reduce this distortion. The selection of the level of tension and pressure for optimum forming is presently empirical. The study discussed herein seeks to develop a scientific basis for optimizing forming processes such that buckling is avoided and distortion and springback are minimized. Part I describes a custom bend-stretch-pressure forming facility developed for the study. The facility is operated by one pneumatic and two servohydraulic closed-loop systems. This allows computer control of the process, and affords selectable loading histories. The planar forming process was modeled by approximating the tube as a nonlinear elastic–plastic beam which can undergo large rotations. The model was shown capable of reproducing accurately the loading history experienced by different sections along the length of the part during forming. Representative results from forming experiments involving rectangular aluminum are presented. The results are used to discuss the effect of friction, tension and pressure on the cross-sectional distortion, springback and net elongation of the part. Part II presents a model for establishing the cross-sectional distortion induced during forming. The model is used in conjunction with experimental results to establish ways of optimizing the process.     

Coupled bending and torsional vibration of a rotor system with nonlinear friction

Unacceptable vibrations induced by the nonlinear friction in a rotor system seriously affect the health and reliability of the rotating machinery. To find out the basic excitation mechanism and characteristics of the vibrations, a coupled bending and torsional nonlinear dynamic model of rotor system with nonlinear friction is presented. The dynamic friction characteristic is described with a Stribeck curve, which generates nonlinear friction related to relative velocity. The motion equations of unbalance rotor system are established by the Lagrangian approach. Through numerical calculation, the coupled vibration characteristics of a rotor system under nonlinear friction are well investigated. The influence of main system parameters on the behaviors of the system is discussed. The bifurcation diagrams, waterfall plots, the times series, orbit trails, phase plane portraits and Poincaré maps are obtained to analyze dynamic characteristics of the rotor system and the results reveal multiform complex nonlinear dynamic responses of rotor system under rubbing. These analysis results of the present paper can effectively provide a theoretical reference for structural design of rotor systems and be used to diagnose selfexcited vibration faults in this kind of rotor systems. The present research could contribute to further understanding on the self-excited vibration and the bending and torsional coupling vibration of the rotor systems with Stribeck friction model.     

冲压工艺参数对回弹的影响及改进方法比较

板料成形都存在回弹,因回弹使得板料零件无法满足使用要求。论文围绕实际工件回弹的情况,通过有限元CAE方法,探讨了预成形压力、摩擦系数、间隙等主要因素对回弹的影响。并提出了减小回弹的几种方法,经实际验证效果良好。     

A friction model evaluated with results from a bending-under-tension test

The friction in stamping is an important process parameter to control the flow of material in the tool. Consequently, it is also an important parameter in the design process of new stamping tools when numerical simulations of the forming operations are performed. In this work an advanced friction model is evaluated, which considers properties of surface topography, lubricant, sheet material, and process parameters such as sliding speed and pressure. The evaluation is made by comparing theoretical results with experimental ones obtained in a bending-under-tension friction test. The results show conformance in behaviour between the friction model and the experimental work. Furthermore, a model, which considers the influence of bulk plastic strains on the real area of contact, is investigated. The developed model predicts that the effective hardness of a surface is reduced by the presence of underlying plastic flow. It is found that when the strain rates are increased, the Stribeck curve becomes flatter and mixed lubrication is introduced at lower Hersey values. The friction model clearly shows the potential of improving the FE simulations of sheet metal forming operations, in comparison to the use of the classical Coulomb's friction model.     

Position deviation in V-die bending process with asymmetric bend length

Novel finite element analyses and a series of experiments are performed to clarify basic characteristics of high-strength steel sheet metal during fabrication by asymmetric V-die bending processes. The proposed strategy for elastic–plastic FE simulation is used to simulate asymmetric V-die bending process to test its viability for friction contact processes. Accordingly, a series of experiments is performed to verify the numerical simulation. The calculation agrees well with the experiment. The effects of process parameters such as lubrication (contact friction), material properties, and process geometries on position deviation in bending point were experimentally tested to determine the dominant parameters for minimizing position deviation in sheet metal bending processes. Moreover, springback phenomenon is also discussed to minimize bending defects and to obtain a precise asymmetric bent component. This study could be used as a process design guideline for asymmetric bending of high-strength steel sheets.     

An experimental investigation on passive water cooling in laser forming process

The effect of passive water cooling in laser forming of thin sheets made of AISI 304 stainless steel is experimentally investigated. Indeed, since each laser scan can produce only small bending angles, multiple laser scans are required to produce a given deformation with a significant increase of production time due to cooling between consecutive scans. Therefore, passive water cooling is tested to verify its influence on minimum time between consecutive scans (cooling time), bending angle, and surface quality. A parametric approach is involved in the investigation and main process parameters are changed among the experiments by varying laser scanning speed, laser beam power, sheet thickness, and cooling media among several levels. It was discovered that the employment of passive water cooling in laser forming of thin sheets would be beneficial since the capability to dramatically reduce the cooling time and oxidation of both irradiated and cooled surfaces. In addition, the bending angle is only marginally affected by employment of water cooling. The effect of water cooling on stress and deformations are discussed by developing a numerical model based on finite element model.     

TA2M钛合金板材U形件弯曲回弹研究

应用PAM—STAMP冲压模拟软件,对TA2M钛合金板材U形弯曲成形及回弹过程进行了数值模拟预测,并对模拟结果进行了工艺试验验证,得到了板料厚度、轧制方向以及相对弯曲半径等参数对回弹影响的数值结果,并对结果进行了分析。     

Springback prediction and optimization of variable stretch force trajectory in three-dimensional stretch bending process

Most of the existing studies use constant force to reduce springback while researching stretch force. However, variable stretch force can reduce springback more efficiently. The current research on springback prediction in stretch bending forming mainly focuses on artificial neural networks combined with the finite element simulation. There is a lack of springback prediction by support vector regression(SVR). In this paper, SVR is applied to predict springback in the three-dimensional stretch bending forming process, and variable stretch force trajectory is optimized. Six parameters of variable stretch force trajectory are chosen as the input parameters of the SVR model. Sixty experiments generated by design of experiments(DOE) are carried out to train and test the SVR model. The experimental results confirm that the accuracy of the SVR model is higher than that of artificial neural networks. Based on this model, an optimization algorithm of variable stretch force trajectory using particle swarm optimization(PSO) is proposed. The springback amount is used as the objective function. Changes of local thickness are applied as the criterion of forming constraints. The objection and constraints are formulated by response surface models. The precision of response surface models is examined. Six different stretch force trajectories are employed to certify springback reduction in the optimum stretch force trajectory, which can efficiently reduce springback. This research proposes a new method of springback prediction using SVR and optimizes variable stretch force trajectory to reduce springback.     

Deformation path and springback behavior in double-curved bending at high temperature

In this work, integrated double-curved bending-sizing-unloading is simulated for a Ti6Al4V titanium alloy sheet. Bending radii R30 mm × R30 mm and R30 mm × R15 mm are used in the bending tests at 700 °C and 750 °C, respectively. A holding time of 0–600 s is applied to explore the effect of sizing time on forming accuracy. Similar experimental tests are performed for comparison with the finite element analysis results. Results show that bending behavior varies remarkably with the bidirectional radii. As for equal bidirectional curvature, bending along each direction occurs simultaneously. Given that bidirectional radii are different, the sheet consecutively experiences single small-, single large-, and double-curved bending. The deformation path results in nonuniform plastic strain distribution. The springback amount increases from the center to the marginal middle zone. Sizing at 700 °C or 750 °C in 600 s or 180–600 s can remarkably reduce the springback amount, respectively. The springback prediction via finite element method is consistent with that of the experiment.

     

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%。     

空间弯管仿真与回弹补偿

回弹是空间弯管成形的主要成形缺陷。为了预测和补偿空间弯管成形中的回弹,通过编写用户幅值子程序（UAMP）,将有限元法应用于空间弯管的成形和回弹分析,提出了一种从仿真结果中提取管材中心线的方法。通过圆柱螺线形弯管成形的仿真计算,建立了管材回弹前后中心轴线曲率、挠率的关系。提出了一种基于求解曲线基本方程的空间弯管模具型面补偿方法,论述了曲线几何补偿的数学依据。通过对曲率和挠率(均为非常值)曲线进行补偿计算和成形仿真,对该方法进行了验证。结果表明该方法能够有效补偿回弹误差,保证弯管精度。