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.     

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.     

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.     

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.     

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.     

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.     

Influence of constitutive model in springback prediction using the split-ring test

The aim of this paper is to compare several plastic yield criteria to show their relevance on the prediction of springback behavior for a AA5754-0 aluminum alloy. An experimental test similar to the Demeri Benchmark Test [Demeri MY, Lou M, Saran MJ. A benchmark test for springback simulation in sheet metal forming. In: Society of Automotive Engineers, Inc., vol. 01-2657, 2000] has been developed. This test consists in cutting a ring specimen from a full drawn cup, the ring being then split longitudinally along a radial plan. The difference between the ring diameters, before and after splitting, gives a direct measure of the springback phenomenon, and indirectly, of the amount of residual stresses in the cup. The whole deep drawing process of a semi-blank and numerical splitting of the ring are performed using the finite element code Abaqus. Several material models are analyzed, all considering isotropic and kinematic hardening combined with one of the following plasticity criteria: von Mises, Hill’48 and Barlat’91. This last yield criterion has been implemented in Abaqus. Main observed data are force-displacement curves during forming, cup thickness according to material orientations and ring gap after splitting. The stress distributions in the cup, at the end of the drawing stage, and in the ring, after springback, are analyzed and some explanations concerning their influence on springback mechanisms are given.     

Finite element simulation of springback for a channel draw process with drawbead using different hardening models

The objective of this work is to predict the springback of Numisheet’05 Benchmark#3 with different material models using the commercial finite element code ABAQUS. This Benchmark consisted of drawing straight channel sections using different sheet materials and four different drawbead penetrations. Numerical simulations were performed using Hill's 1948 anisotropic yield function and two types of hardening models: isotropic hardening (IH) and combined isotropic-nonlinear kinematic hardening (NKH). A user-defined material subroutine was developed based on Hill's quadratic yield function and mixed isotropic-nonlinear kinematic hardening models for both ABAQUS-Explicit (VUMAT) and ABAQUS-Standard (UMAT). The work hardening behavior of the AA6022-T43 aluminum alloy was described with the Voce model and that of the DP600, HSLA and AKDQ steels with Hollomon's power law. Kinematic hardening was modeled using the Armstrong-Frederick nonlinear kinematic hardening model with the purpose of accounting for cyclic deformation phenomena such as the Bauschinger effect and yield stress saturation which are important for springback prediction. The effect of drawbead penetration or restraining force on the springback has also been studied. Experimental cyclic shear tests were carried out in order to determine the cyclic stress-strain behavior. Comparisons between simulation results and experimental data showed that the IH model generally overestimated the predicted amount of springback due to higher stresses derived by this model. On the other hand, the NKH model was able to predict the springback significantly more accurately than the IH model.     

复杂形状板料冲压件回弹评价指标研究

对于 3- D复杂形状板料冲压件 ,现有的回弹评价指标均有一定的片面性 ,难以满足工程实践和理论研究多方面的要求。本文从弹性变形能概念出发 ,提出一种新的回弹评价指标。新指标反映了冲压件回弹过程的几何和力学本质 ,能客观全面地评价复杂零件的整体回弹水平。新指标以相同的参数衡量 2 - D弯曲件和 3- D复杂冲压件的回弹水平 ,做到了评价指标相对于不同评价对象的一致性。     

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。     

Measurement of springback

Springback, the elastically-driven change of shape of a part after forming, has been measured under carefully-controlled laboratory conditions corresponding to those found in press-forming operations. Constitutive equations emphasizing low-strain behavior were generated for three automotive body alloys: drawing-quality silicon-killed steel; high-strength low-alloy steel; and 6022-T4 aluminum. Strip draw-bend tests were then conducted using a range of die radii (3<R/t<17), friction coefficients (0<μ<0.20), and controlled tensile forces (0.5<F_b/F_y<1.5). Springback angles and curvatures were measured for bend and bend–unbend areas of the specimen, the latter corresponding to the “sidewall curl” region, which dominates the geometric change and the dependence on process variables. Friction coefficient and R/t (die-radius-to-sheet-thickness) greater than 5 have modest but measurable effects over the ranges tested. As expected, strip tension dominates the springback sensitivity, with higher forces reducing springback. For 6022-T4, springback is dramatically reduced as the tensile stress approaches the yield stress, corresponding to the appearance of a persistent anticlastic curvature. The presence of this curvature, orthogonal to the principal curvature, violates the simple two-dimensional models of springback reported in the literature. The measured springback angles and curvatures are reported both in graphical summary and tabular form for use in assessing analytical models of springback.     

A model of one-surface cyclic plasticity and its application to springback prediction

This paper presents an elasto-plastic constitutive model based on one-surface plasticity, which can capture the Bauschinger effect, transient behavior, permanent softening, and yield anisotropy. The combined isotropic-kinematic hardening law was used to model the hardening behavior, and the non-quadratic anisotropic yield function, Yld2000-2d, was chosen to describe the anisotropy. This model is closely related to the anisotropic non-linear kinematic hardening model of Chun et al. [2002. Modeling the Bauschinger effect for sheet metals, part I: theory. International Journal of Plasticity 18, 571-95.]. Different with the model, the current model captures in particular permanent softening with a constant stress offset as well as the Bauschinger effect and transient behavior under strain path reversal. Inverse identification was carried out to fit the material parameters of hardening model by using uni-axial tension/compression data. Springback predicted by the resulting material model was compared with experiments and with material models that do not account for permanent softening. The results show that the resulting material model has a good capability to predict springback.     

Simulation of springback

Springback, the elastically-driven change of shape of a part after forming, has been simulated with 2-D and 3-D finite element modeling. Simulations using solid and shell elements have been compared with draw-bend measurements presented in a companion paper. Plane-stress and plane-strain simulations revealed the dramatic role of numerical tolerances and procedures on the results. For example, up to 51 integration points through the sheet thickness were required for accuracy within 1%, compared with 5–9 typically acceptable for forming simulations. Improvements were also needed in the number of elements in contact with the tools, and in the numerical tolerance for satisfying equilibrium at each step. Significant plastic straining took place in some cases upon unloading; however the choice of elastic–plastic unloading scheme had little effect on the results. While 2-D simulations showed good agreement with experiments under some test conditions, springback discrepancies of hundreds of percent were noted for one alloy with sheet tension near the yield stress. 3-D simulations provided much better agreement, the major source of error being identified as the presence of persistent anticlastic curvature. Most of the remaining deviation in results can be attributed to inaccuracies of the material model. In particular, the presence of a Bauschinger effect changes the results markedly, and taking it into account provided good agreement. Shell elements were adequate to predict springback accurately for R/t greater than 5 or 6, while solid elements were required for higher curvatures. As R/t approaches 2, springback simulated with solid elements tends to disappear, in agreement with measurements presented in the companion paper and in the literature.     

Springback prediction for sheet metal forming process using a 3D hybrid membrane/shell method

To reduce the computational time of finite element analyses for sheet forming, a 3D hybrid membrane/shell method has been developed and applied to study the springback of anisotropic sheet metals. In the hybrid method, the bending strains and stresses were calculated as post-processing, considering the incremental change of the sheet geometry obtained from the membrane finite element analysis beforehand. To calculate the springback, a shell finite element model was used to unload the sheet. For verification purposes, the hybrid method was applied for a 2036-T4 aluminum alloy square blank formed into a cylindrical cup, in which stretching is dominant. Also, as a bending-dominant problem, unconstraint cylindrical bending of a 6111-T4 aluminum alloy sheet was considered. The predicted springback showed good agreement with experiments for both cases.     

Direct generation of die surfaces from measured data points based on springback compensation

Reverse engineering is an approach for constructing a CAD model from a physical part through dimensional measurement and surface model. For sheetmetal parts, when removed from dies after forming, are subject to springback due the resultant in-plane forces and moments throughout the sheet at the end of the forming processing. Therefore, springback should be compensated for integrating reverse engineering into the system of forming sheet metal with a complex surface. However, CAD modelling from measured points data is a roadblock to the automation of the duplication procedure. The difficulties here arise from surfaces fitting to measured points, which is well-known to be time-consuming. To avoid the roadblock, based on the convex hull property of B-spline, a new strategy for direct generation of die shapes from digitized points with springback compensation is presented in this paper. The proposed algorithm has been applied to a part of complicated geometry with good results.     

Determination of stretch-bendability of sheet metals

Today's sheet-metal forming industry relies mostly on experience-based methods for finding the forming limits which assure successful forming processes. Such methods are inefficient and there is an obvious need for cost-effective knowledge-based computer-aided techniques.In this paper, a mathematical model for the stretch-bending processes is introduced. The model is capable of performing all calculations necessary to determine the effect of material properties on the process parameters such as forming loads, product geometry, springback, and residual stresses. From this model, the significance of various material parameters from productivity, ease of fabrication, and tool design viewpoints can be evaluated. This should contribute to the development and optimum use of sheet materials with improved properties.Notation c,d distances on the cross-section of the beam, m - h depth of the cross-section of the beam, m - K,n material constants in the power law equation: =K ⁿ - M bending moment, Nm - M _e maximum elastic bending moment, Nm - m non-dimensional bending moment,M./M _e - N axial tensile force, N - N _e maximum elastic tensile force, N - n _r non-dimensional axial force,N/N _e - non-dimensional parameter,c/(h ₂) - non-dimensional parameter,d/(h ₂) - effective stress, MPa - effective strain     

切边工艺对冲压件回弹影响的研究

作为冲压产品生产的重要工序之一,切边对零件形状精度产生明显影响。针对目前关于切边回弹研究比较少的情况,以某矿用防爆灯灯罩为研究对象,在Dynaform平台下,对切边回弹的产生、构成、切边线位置变化及切边工序安排对冲压件形状精度的影响进行了仿真分析,研究结果认为:切边回弹一方面是由于切边导致零件形状结构变化、内应力重新分布而引起的,另一方面是因为切边线附近应力、应变状态变化而产生的。其中前者占主导地位,在冲压加工中必须予以充分考虑,后者占总体回弹比例较小,对大型、复杂冲压件拉深成形后的切边可忽略其影响;另外,切边线位置变化、切边工序的顺序安排,对零件回弹变形影响明显,实际生产中,可通过适当选择切边线位置、合理安排切边工序在整个工艺路线中的顺序来有效控制切边回弹。     

Semi-implicit numerical integration of Yoshida-Uemori two-surface plasticity model

A semi-implicit integration scheme was used to implement the Yoshida-Uemori two-surface model into the finite element method. Hill’s quadratic yield function was employed to account for the orthotropic behaviour of the metal sheet. The model was used to predict the cyclic simple shear response of DP-600. In order to evaluate the capability of the model for sheet metal forming, the model was used to simulate both the forming stage of a channel draw process in the presence of drawbeads and the subsequent springback stage. The results show that the model predicts the springback profile very well, especially at deeper drawbead penetrations.     

Role of plastic anisotropy and its evolution on springback

Springback angles and anticlastic curvatures reported for a series of draw-bend tests have been analyzed in detail using a new anisotropic hardening model, four common sheet metal yield functions, and finite element procedures developed for this problem. A common lot of 6022-T4 aluminum alloy was used for all testing in order to reduce material variation. The new anisotropic hardening model extends existing mixed kinematic/isotropic and nonlinear kinematic formulations. It replicates three principal characteristics observed in uniaxial tension/compression test reversals: a transient region with low yield stress and high strain hardening, and a permanent offset of the flow stress at large subsequent strains. This hardening model was implemented in ABAQUS in conjunction with four yield functions: von Mises, Hill quadratic, Barlat three-parameter, and Barlat 1996. The simulated springback angle depended intimately on both hardening law after the strain reversal and on the plastic anisotropy. The springback angle at low back forces was controlled by the hardening law, while at higher back forces the anticlastic curvature, which depends principally on yield surface shape, controlled the springback angle. Simulations utilizing Barlat's 1996 yield function showed remarkable agreement with all measurements, in contrast to simulations with the other three yield functions.