Fast thickness prediction and blank design in sheet metal forming based on an enhanced inverse analysis method

In sheet metal forming process, inverse analysis codes serve a useful purpose at the early product design stage when an approximate analysis is required to determine if the initial concept part can be made and where the failures and defects will occur. In this paper, a robust energy-based 3D mesh mapping algorithm is used to obtain the initial solution and is followed by a reverse deformation method to improve its accuracy. The novel initial solution scheme can consider the material and the process parameters, and thus lead to fewer Newton–Raphson iterations. The actions of the punch, die, blank holder and the drawbead are fully considered. A fast and reliable boundary condition treatment method is implemented to workpiece without binder and addendum information. Contact treatment between punch and die is an essential issue which greatly affects the convergence of Newton–Raphson iterations. A reliable contact treatment based on topological relations of workpiece is proposed to define the force direction between die and punch. Equivalent drawbead forces are also considered with a simplified model. With the improved aspects, the in-house inverse analysis code InverStamp is developed. Application to a square box and a clover-shaped cup are presented with demonstrations of the validity of the code and the efficiency of the proposed modified approaches.     

Optimization of drawbead design in sheet forming using one step finite element method coupled with response surface methodology

In a sheet forming process, drawbead plays an important role on the control of the material flow. In this paper, a numerical procedure for the design of forming processes is described. It is based on the coupling of an optimization technique and the simplified one step finite element method (also called inverse approach). The optimization technique allows adjustment of the process parameters so that specified criteria are fulfilled. Response surface methodology (RSM) is a global approximation method, which is ideally suited for solving highly nonlinear optimization problems. The finite element method, in addition to predicting the response of the process to certain parameters, allows assessment of the effect of a variation in these parameters on this response. The authors utilize the one step method at the preliminary design stage to supply stress or strain information for the following optimization using RSM. The procedure for this optimization process is fully described. The front fender for Numisheet 2002 is presented and the real defect free workpiece is produced to demonstrate the usefulness of the proposed optimization procedure. A comparison between the two forming limit curves (FLC) before and after optimization and results obtained using the precise incremental commercial software DYNAFORM based on the explicit dynamic approach verify that the optimization design method of drawbead could be successfully applied in designing actual tools of auto body cover panels.     

等效拉延筋模型及其在板料成形数值模拟中的应用

讨论等效拉延筋的建模方法、常用模型及其在板料成形数值模拟中的应用情况,并指出研究中仍存在的问题及今后的发展方向。     

Electromagnetic blank restrainer in sheet metal forming processes

Electromagnetic blank restrainer (EMBR) is a new technology that was recently developed to control material movement in sheet metal forming processes. Magnetic attraction on the ferrous sheet metal is the intrinsic property of EMBR. Such magnetic force is quantified using Maxwell's stress tensor to assess the feasibility of EMBR in the sheet metal forming process. The 3D finite element analysis (FEA) of an electromagnetic system is conducted to determine the distribution of magnetic flux density on contacting surfaces of the sheet metal. The distribution is then used to estimate the magnetic force. Experiments have been conducted to measure the magnetic force and compare with results from the FEA. Biaxial-loading apparatus has been built to measure restraining forces on the sheet metal with blankholder, drawbead, and EMBR. All the restraining forces are put together in a chart to see where each method stands with respect to one another. In order to evaluate the quality of forming with each method, an experimental die has been built. The die forms a channel in a single stroke and provides a direct indication of how each restraining method controls blank movement in the die. The real advantage of EMBR lies in the effectiveness of force control and its flexible location in a sheet metal forming die. To prove this, a prototype has been built in a tryout die where house appliance panel is formed with blankholder and EMBR. EMBRs are locally installed in the die and actively controlled during the forming process. The part formed with EMBR shows a significant improvement in the forming quality. At the end of this paper, two immediate impacts that EMBR can bring to the sheet metal forming industry are also discussed.     

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.     

Substepping algorithms with stress correction for the simulation of sheet metal forming process

The finite element analysis of the sheet metal forming process involves various nonlinearities. To predict accurately the final geometry of the sheet blank and the distribution of strain and stress and control various forming defects, such as thinning, wrinkling and springback, etc., the accurate integration of the constitutive laws over the strain path is essential. Our objective in this paper is to develop an effective and accurate stress integration scheme for the analysis of three-dimensional sheet metal forming problems. The proposed algorithm is based on the explicit “substepping” schemes incorporating with the stress correction scheme. The proposed algorithms have been implemented into ABAQUS/Explicit via User Material Subroutine (VUMAT) interface platform. The algorithms are then employed to analyze a typical deep-cup drawing process and the accuracy of these algorithms has been compared with the implicit “return” algorithm and explicit forward algorithm. The results indicate that the explicit schemes with local truncation error control, together with a subsequent check of the consistency conditions, can achieve the same or even better level of accuracy as “return” algorithm does for integrating large plastic problems like sheet metal forming process.     

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.     

Numerical simulation of the electromagnetic sheet metal bulging process

Electromagnetic forming (EMF) is an uncommon metal working process that relies on the use of electromagnetic forces to deform metallic workpieces at high speeds. It is expected to overcome some formability barriers of materials. EMF process analysis is the foundation of theoretical analysis. However, the electromagnetic sheet metal process is very difficult to describe, because of the complexity of magnetic pressure distribution. In this paper, a numerical modeling of the electromagnetic sheet metal process is performed using a finite element method, and a series of simulations on free bulging are carried out using the FEA program ADINA. The dynamic deformation process of sheet metal is investigated. At last, some experiments are made and those simulations agree well with the experimental results.     

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.     

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.     

On the prediction of side-wall wrinkling in sheet metal forming processes

Prediction and prevention of side-wall wrinkling are extremely important in the design of tooling and process parameters in sheet metal forming processes. The prediction methods can be broadly divided into two categories: an analytical approach and a numerical simulation using finite element method (FEM). In this paper, a modified energy approach utilizing energy equality and the effective dimensions of the region undergoing circumferential compression is proposed based on simplified flat or curved sheet models with approximate boundary conditions. The analytical model calculates the critical buckling stress as a function of material properties, geometry parameters and current in-plane stress ratio. Meanwhile, the sensitivities of various input parameters and integration methods of FEM models on the prediction of wrinkling phenomena are investigated. To validate our proposed method and to illustrate the sensitivity issue in the FEM simulation, comparisons with experimental results of the Yoshida buckling test, aluminum square cup forming and aluminum conical cup forming are presented. The results demonstrate excellent agreements between the proposed method and experiments. Our model provides a reliable and effective predictor for the onset of side-wall wrinkling in sheet metal forming processes.     

Improvement of formability for the incremental sheet metal forming process

In order to obtain competitiveness in the field of industrial manufacture, a reduction in the development period for the small batch manufacture of products is required. In order to meet these requirements, an incremental sheet metal forming process has been developed. In this process, a small local region of a sheet blank deforms incrementally by moving a hemispherical head tool over an arbitrary surface. In this work, an incremental sheet metal forming process controlled three dimensionally by a computer has been accomplished. It has been shown by the experiments that a sheet blank is mainly subject to shear-dominant deformation. Therefore, the final thickness strain can be predicted. The uniformity of thickness throughout the deformed region is one of the key factors to improve the formability in the sheet metal forming processes. Using the predicted thickness strain distribution, the intermediate geometry is decided in the manner that a shear deformation is restrained in the highly shear-deformed region and vice versa. This double-pass forming method is found to be very effective so that the thickness strain distribution of a final shape can be made more uniform.     

Quality design of fixture planning for sheet metal assembly

Fixturing plays an important role in enhancing weld quality of the sheet metal assembly process. However, traditional experience-based fixturing schemes and purely optimal fixturing schemes are often sensitive to location fluctuation of the designed locators. In this paper a mathematical representation of deterministic locating and total fixturing for a flexible workpiece is developed first, then a virtual beam model is proposed to evaluate the degree of flexibility of the locating points. A quality design model of fixture planning for sheet metal assembly with resistance spot welding is then developed; both the performance expectation and the variance are considered in the formulation of the objective function; a prescribed factor is used to weight the two objectives. The finite element model based on ANSYS software is set up with a spot weld feature employed and genetic algorithm is used in the optimization process. A simple example and an industrial case illustrate the feasibility of the developed model. This work provides a basis for improving the quality of sheet metal assembly in the design phase.     

On the prediction of the effect of process parameters upon forming limit strains in sheet metals

Plasticity analysis of sheet metal forming requires a detailed knowledge of the influence of process parameters on the stress–strain relationships from yielding up to localized necking, for accurate prediction of forming limits. Achievable strain and stress–strain relationships are sensitive to modulations in process parameters, chiefly temperature and strain rate. However, the effects of changes in strain rate and temperature are often complex as they also depend on the levels of strain, strain rate and the temperature employed. Such variations could be either triggered by the process dynamics of the forming operation or imposed for optimal exploitation of the material ductility. In this study, the influence of such process parameter modulations upon formability has been theoretically modelled, following the Sing–Rao prediction approach. The limit strains thus predicted compare favourably with experimental results for a drawing steel, thus validating the present formalism. This approach can also be adopted to accommodate non-linear straining conditions. Thus, theoretical modelling of strain-path-dependent forming limits, which has not been explored adequately so far, now becomes feasible.     

基于多目标遗传算法优化板料拉深成形工艺参数

利用人工神经网络构建了板料拉深成形的目标函数模型,建立了板料拉深成形工艺参数和性能评价指标之间的映射关系.以多种工艺参数(压边力、摩擦因数等)作为优化变量,多种成形缺陷(起皱、破裂等)作为优化目标,结合多目标遗传算法和数值模拟,建立了板料拉深成形工艺参数的优化设计模型,大大提高了优化的效率.以油底壳下盖为例,对其拉深成形工艺参数进行了优化,通过对优化结果进行数值模拟可以看出,该优化参数完全避免了各种缺陷的产生,这说明该优化算法具有较好的优化结果.     

A continuum sensitivity method for the design of multi-stage metal forming processes

A novel, efficient and mathematically rigorous continuum based sensitivity method is introduced that can be used to accurately evaluate the gradients of the objective function and constraints in the optimization-based design of multi-stage deformation processes. Weak sensitivity equilibrium equations are derived for the large deformation of the workpiece in each forming operation. This sensitivity kinematic problem is linearly coupled with the corresponding continuum sensitivity constitutive, contact and thermal sub-problems for the particular process. Thus a linear sensitivity problem with appropriate driving forces is identified and the analysis is carried out in an infinite dimensional framework. The multi-stage continuum sensitivity analysis takes a form similar to the updated Lagrangian sensitivity framework developed earlier for the design of single-stage deformation processes. It allows us to treat in a unified manner shape and parameter sensitivity analyses that are both present in a typical design problem of multi-stage deformation processes. The effectiveness of the proposed methodology is demonstrated with the solution of three practical problems in the design of two-stage metal forming processes.     

Modified membrane finite element formulation for sheet metal forming analysis of planar anisotropic materials

A finite element formulation is derived for sheet metal forming analysis of planar anisotropic materials. The formulation incorporates membrane elements whereas it takes the bending effect into account explicitly. The strain energy term in the formulation is decomposed into the membrane energy term for mean stretching and the bending energy term for pure bending. This procedure needs careful evaluation for the orientation of the anisotropic axes. The formulation is then combined with an effective algorithm to calculate distribution of the blank holding force in each step according to the thickness in the flange region. The calculation employs a special relation between the thickness and the blank holding force. The simulation examples demonstrate the validity and versatility of the developed computer code by showing that the thickness variation in the flange region redistributes the blank holding force during the deformation. The present algorithm can predict accurate deformed shapes and thickness strain distribution with the anisotropy of materials and the variable blank holding force.     

冲压成形薄板厚度变化与回弹量工程估算

研究了忽略薄板厚度变化对有限元仿真计算时间和计算结果的影响 ,得到薄板冲压成形过程中压边力和材料特性与薄板回弹量的关系曲线     

汽车覆盖件冲压成形仿真研究进展

汽车覆盖件冲压成形仿真技术的发展,突破了原有汽车冲压件模具及工艺设计的设计方法,对保证工件质量、减少材料消耗、缩短产品开发周期、降低制造成本具有重要意义.概述了目前汽车覆盖件冲压成形仿真所涉及到的热点领域,如摩擦与接触、回弹分析、模具系统和工艺参数、材料屈服模型和板料形状设计,讨论了这些领域的研究进展和进一步研究的发展方向.