A finite element model for thermomechanical analysis of sheet metal forming

A thermal model based on explicit time integration is developed and implemented into the explicit finite element code DYNA3D to model simultaneous forming and quenching of thin‐walled structures. A staggered approach is used for coupling the thermal and mechanical analysis, wherein each analysis is performed with different time step sizes. The implementation includes a thermal shell element with linear temperature approximation in the plane and quadratic in the thickness direction, and contact heat transfer. The material behaviour is described by a temperature‐dependent elastic–plastic model with a non‐linear isotropic hardening law. Transformation plasticity is included in the model. Examples are presented to validate and evaluate the proposed model. The model is evaluated by comparison with a one‐sided forming and quenching experiment. Copyright © 2004 John Wiley & Sons, Ltd.     

Multiobjective robust optimization method for drawbead design in sheet metal forming

It is recognized that fracture and wrinkling in sheet metal forming can be eliminated via an appropriate drawbead design. Although deterministic multiobjective optimization algorithms and finite element analysis (FEA) have been applied in this respect to improve formability and shorten design cycle, the design could become less meaningful or even unacceptable when considering practical variation in design variables and noises of system parameters. To tackle this problem, we present a multiobjective robust optimization methodology to address the effects of parametric uncertainties on drawbead design, where the six sigma principle is adopted to measure the variations, a dual response surface method is used to construct surrogate model and a multiobjective particle swarm optimization is developed to generate robust Pareto solutions. In this paper, the procedure of drawbead design is divided into two stages: firstly, equivalent drawbead restraining forces (DBRF) are obtained by developing a multiobjective robust particle swarm optimization, and secondly the DBRF model is integrated into a single-objective particle swarm optimization (PSO) to optimize geometric parameters of drawbead. The optimal design showed a good agreement with the physical drawbead geometry and remarkably improve the formability and robust. Thus, the presented method provides an effective solution to geometric design of drawbead for improving product quality.     

板料成形中韧性断裂准则应用研究进展

对板料成形中的成形极限应力图、最大变薄率、成形极限图以及韧性断裂准则等预测成形极限的方法,进行了综述和分析。指出利用韧性断裂准则,不但能够较好地预测塑性差的板料成形极限,而且还能考虑应变路径的变化。利用有限元方法模拟时,韧性断裂准则既可以应用到完全耦合的弹塑性损伤模型的增量方法中,也可以应用到一步有限元逆算法中。为了准确地预测成形极限,除了提高有限元模拟精度外,应找到一种本质地反映材料性能的韧性断裂准则。     

基于FEA的板料成形工艺优化及评价函数研究

基于有限元和优化方法的板料成形工艺优化设计技术已经成为新的研究热点,建立合理的评价标准以形成目标函数,从而用于评价冲压件的成形性是其关键技术之一.提出局部成形性、整体成形性和综合成形性评价函数.基于试验设计法,结合方盒形件拉深以及发动机罩外板成形,验证了本文提出的评价函数具有良好的可靠性和易用性.     

Effects of yield surface shape on sheet metal forming simulations

Three phenomenological yield criteria are adopted to describe the plastic behaviour of sheet metals with normal plastic anisotropy. The sheet metals are assumed to be elastic-plastic, rate-sensitive and incompressible. A rate-sensitive thin shell finite element formulation based on the virtual work principle is derived for the three yield criteria. The effects of the yield surface shapes based on the three yield criteria with the same value of the plastic anisotropy parameter R on the strain distribution and localization are investigated under a hemispherical punch stretching operation and a plane strain rawing operation. The results of the simulations show that the yield surface shape, in addition to the plastic anisotropy parameter R, controls the punch force, strain distribution and strain localization for the punch stretching operation. However, the yield surface shape does not affect the punch force and the strain distribution significantly for the plane strain drawing operation. © 1998 John Wiley & Sons, Ltd.     

Shape optimization of the initial blank in the sheet metal forming process using equivalent static loads

In the sheet metal forming process, forming the final desired shape is difficult to obtain due to wrinkling, tearing, failure of material, etc. Various conditions of the forming process should be controlled for the desired shape. These conditions are the velocity of the punch, the friction factor, the blank holding force, the initial shape of the blank and others. Many researchers have conducted studies to predetermine the initial blank shape. The structural optimization technique is one of them. Non‐linear response structural optimization is required because non‐linearities are involved in the analysis of the metal forming process. When the conventional method is utilized, the cost is extremely high due to repeated non‐linear analysis for function and sensitivity calculation. In this paper, the equivalent static loads (ESLs) method is used to determine the blank shape which leads to the final desired shape and reduced wrinkling. The ESLs method is a structural optimization method where non‐linear dynamic loads are transformed into ESLs, and these ESLs are utilized as external loads in linear response optimization. The design is updated in linear response optimization. Non‐linear analysis is performed with the updated design and the process proceeds in a cyclic manner. An optimization formulation is defined for the examples, the formulated problems are solved to verify the proposed method and the results are discussed. Non‐linear analysis is performed using the commercial software LS‐DYNA, NASTRAN is used for calculating the ESLs and linear response optimization, and an interface program for LS‐DYNA and NASTRAN is developed. Copyright © 2010 John Wiley & Sons, Ltd.     

汽车板精益成形技术

建立了面向零件成形特征的合理选材方法,发明了高效的拉延筋阻力混合优化设计方法,构建了变压边力控制实验平台。从降低成形质量对材料和工艺过程波动敏感性的角度出发,研究面向材料和工艺参数随机波动的成形质量的稳健控制。形成了基于“合理选材、工艺优化、稳健设计”思想的汽车板精益成形技术体系。通过在宝钢股份和多家汽车厂10多年的成功应用,支持宝钢汽车板的市场占有率稳步达到50％,有效地推动了国产汽车板使用技术的发展。     

A computationally efficient metamodeling approach for expensive multiobjective optimization

This paper explores a new metamodeling framework that may collapse the computational explosion that characterizes the modeling of complex systems under a multiobjective and/or multidisciplinary setting. Under the new framework, a pseudo response surface is constructed for each design objective for each discipline. This pseudo response surface has the unique property of being highly accurate in Pareto optimal regions, while it is intentionally allowed to be inaccurate in other regions. In short, the response surface for each design objective is accurate only where it matters. Because the pseudo response surface is allowed to be inaccurate in other regions of the design space, the computational cost of constructing it is dramatically reduced. An important distinguishing feature of the new framework is that the response surfaces for all the design objectives are constructed simultaneously in a mutually dependent fashion, in a way that identifies Pareto regions for the multiobjective problem. The new framework supports the puzzling notion that it is possible to obtain more accuracy and radically more design space exploration capability, while actually reducing the computation effort. This counterintuitive metamodeling paradigm shift holds the potential for identifying highly competitive products and systems that are well beyond today’s state of the art.     

Radial basis functions and level set method for structural topology optimization

Level set methods have become an attractive design tool in shape and topology optimization for obtaining lighter and more efficient structures. In this paper, the popular radial basis functions (RBFs) in scattered data fitting and function approximation are incorporated into the conventional level set methods to construct a more efficient approach for structural topology optimization. RBF implicit modelling with multiquadric (MQ) splines is developed to define the implicit level set function with a high level of accuracy and smoothness. A RBF–level set optimization method is proposed to transform the Hamilton–Jacobi partial differential equation (PDE) into a system of ordinary differential equations (ODEs) over the entire design domain by using a collocation formulation of the method of lines. With the mathematical convenience, the original time dependent initial value problem is changed to an interpolation problem for the initial values of the generalized expansion coefficients. A physically meaningful and efficient extension velocity method is presented to avoid possible problems without reinitialization in the level set methods. The proposed method is implemented in the framework of minimum compliance design that has been extensively studied in topology optimization and its efficiency and accuracy over the conventional level set methods are highlighted. Numerical examples show the success of the present RBF–level set method in the accuracy, convergence speed and insensitivity to initial designs in topology optimization of two‐dimensional (2D) structures. It is suggested that the introduction of the radial basis functions to the level set methods can be promising in structural topology optimization. Copyright © 2005 John Wiley & Sons, Ltd.     

Die shape design optimization of sheet metal stamping process using meshfree method

A die shape design sensitivity analysis (DSA) and optimization for a sheet metal stamping process is proposed based on a Lagrangian formulation. A hyperelasticity‐based elastoplastic material model is used for the constitutive relation that includes a large deformation effect. The contact condition between a workpiece and a rigid die is imposed through the penalty method with a modified Coulomb friction model. The domain of the workpiece is discretized by a meshfree method. A continuum‐based DSA with respect to the rigid die shape parameter is formulated using a design velocity concept. The die shape perturbation has an effect on structural performance through the contact variational form. The effect of the deformation‐dependent pressure load to the design sensitivity is discussed. It is shown that the design sensitivity equation uses the same tangent stiffness matrix as the response analysis. The linear design sensitivity equation is solved at each converged load step without the need of iteration, which is quite efficient in computation. The accuracy of sensitivity information is compared to that of the finite difference method with an excellent agreement. A die shape design optimization problem is solved to obtain the desired shape of the workpiece to minimize spring‐back effect and to show the feasibility of the proposed method. Copyright © 2001 John Wiley & Sons, Ltd.     

韧性断裂准则在高强钢板料成形中的应用

 针对板料成形中的韧性断裂准则预测成形极限的方法,进行了综述和分析,提出了利用韧性断裂准则能够较好地预测塑性差的板料成形极限,而且还能考虑应变路径的变化．将Cockroft和Latham准则应用到高强度钢板DP590的成形预测中．对高强钢DP590进行了单向拉伸试验,获得了相应的物性参数．同时对该高强钢进行了方盒件成形试验,并进行了相应的有限元模拟．通过对高强钢的极限试验,利用有限元模拟获得了该材料的Cockroft和Latham准则常数．最后利用该常数对方盒件的拉深过程进行了缺陷的预测,模拟结果和试验结果完全吻合．表明韧性断裂准则是可以应用到高强度钢板的成形中的．     

Using genetic algorithm-back propagation neural network prediction and finite-element model simulation to optimize the process of multiple-step incremental air-bending forming of sheet metal

Using neural network to predict punch radius based on the results of air-bending experiments of sheet metal is a high efficiency work in spite of little error. A three-layer back propagation neural network (BPNN) is developed to best fit this discrete engineering problem involving many parameters of air-bending forming. A genetic algorithm (GA) is used to optimize the weights of neural network for minimizing the error between the predictive punch radius and the experimental one. Then, with the predicted punch radius and other geometrical parameters of a tool, 2D and 3D ABAQUS finite-element models (FEM) are established, respectively. The original forming process of multiple-step incremental air-bending of sheet metal, obtained from geometric planning for semiellipse-shaped workpiece, is simulated using the FEM. This process is further adjusted with simulation-optimization results, because of existing large errors in the workpiece simulated with the original forming process. Finally, a semiellipse-shaped workpiece, with average errors of +0.61/−0.62 mm, is manufactured with the optimized adjustment process. The experimental results show that the punch design method is feasible with the prediction model of GA-BPNN, and the means of optimizing process with FEM simulation is effective. It can be taken as a new approach for punch and process design of multiple-step incremental air-bending forming of sheet metal.     

基于支持向量机和重要度抽样的高强度钢板冲压成形工艺稳健设计

高强度钢板成形中噪声因素的存在造成了冲压质量不稳定.提出了基于支持向量机和重要度抽样的板料成形工艺稳健设计方法,量化了噪声因素对成形质量的影响,同时结合优化算法求解即满足质量可靠性又保证质量目标最优的工艺条件.对一高强度钢板冲压实例进行了工艺优化.按优化工艺冲压成形的零件减薄率及回弹均有所改善,验证了该方法的有效性.     

大幅面板材渐进折弯成形的本构建模及模拟

为了提高大幅面板材成形的模拟精度,在板材折弯平面应变假设条件下,推导出基于Hill各向异性屈服准则的弹塑性本构方程.借助ABAQUS有限元软件本构模块用户子程序接口,通过编程将上述推导的应力-应变本构关系显示表达式嵌入ABAQUS分析平台.以超长大开口半椭圆形工件成形为例,建立了大幅面钢板渐进折弯的三维弹塑性有限元模型,并数值模拟了多道次渐进折弯成形及回弹全过程.模拟效果和工程应用结果表明,与传统的基于平面应力假设的本构关系模型相比,采用平面应变假设的本构关系模型的模拟结果更接近实验值.     

基于复合优化方法立式数控加工中心的多目标优化设计

为实现加工中心动静态性能不低于优化前性能,达到整机重量最轻的要求,本文提出了一种复合优化方法来研究多变量、多约束和多目标的数控加工中心优化设计。采用有限元分析和实验模态测试方法分析各大件动态性能,并验证了有限元模型的精确性。然后以该有限元模型为基础进行静态分析,得出各大件的最大变形及应力等。以柔度为目标,采用变密度法拓扑优化设计立柱结构的外形框架;以固有频率为目标,基于元结构的可适应性动态优化方法设计加工中心的筋板结构;以固有频率和质量为目标,基于响应面法的尺寸优化确定各结构的最优尺寸。最后将优化后的各大件进行整机装配,分析校核整机动静态性能。分析结果表明,优化后的整机在保证加工中心动静态性能的条件下,整机质量从12749kg减少到12127kg,减重达到4.9%,达到了整机的优化设计要求,说明该方法具有较高的精度和较强的工程实用性。     

A Structural Reliability Analysis Method Based on Radial Basis Function

The first-order reliability method (FORM) is one of the most widely used structural reliability analysis techniques due to its simplicity and efficiency. However, direct using FORM seems disability to work well for complex problems, especially related to high-dimensional variables and computation intensive numerical models. To expand the applicability of the FORM for more practical engineering problems, a response surface (RS) approach based FORM is proposed for structural reliability analysis. The radial basis function (RBF) is employed to approximate the implicit limit-state functions combined with Latin Hypercube Sampling (LHS) strategy. To guarantee the numerical stability, the improved HL-RF (iHL-RF) algorithm is used to assess the reliability index and corresponding probability of failure based on the constructed RS model. The effectiveness of the proposed method is demonstrated through five numerical examples.     

基于RBF网络和NIRS的绿茶水分含量分析模型

基于径向基函数(RBF)和反向传播(BP)神经网络分别建立了绿茶水分含量的近红外光谱分析模型.结果表明:RBF网络预测模型的相关系数r(p)=0.933,预测标准误RMSEP=0.528%;BP网络预测模型的相关系数r(p)=0.914,预测标准误RMSEP=0.598%.RBF网络模型优于BP网络模型.     

Optimal process design in non-isothermal,non-steady metal forming by the finite element method

A new approach to process optimal design in non-isothermal, non-steady-state metal forming is presented. In this approach, the optimal design problem is formulated on the basis of the integrated thermo-mechanical finite element process model so as to cover diverse objective functions and design variables, and a derivative-based approach is adopted for conducting optimization. The process model, the formulation for process optimal design, and the schemes for the evaluation of the design sensitivity, and an iterative procedure for optimization are described in detail. The validity of the schemes for the evaluation of the design sensitivity is examined by performing a series of numerical tests. The capability of the proposed approach to deal with diverse process parameters and objective functions is demonstrated through applications to some selected process design problems. © 1998 John Wiley & Sons, Ltd.     

Material model calibration for superplastic forming

Superplastic forming is a slow forming process. The forming time can be minimized by optimizing the pressure profile applied to the forming sheet. The optimization of the superplastic forming pressure is usually done such that a target strain rate at a high strain rate sensitivity is maintained. Careful consideration of the strain rate is required, since localized thinning can occur when the material is strained too quickly. This paper demonstrates that it is essential to explicitly include strain rate sensitivity data, obtained from strain rate jump tests, during the calibration of material model used for superplastic forming simulations. Conventional calibration methods only consider stress–strain data at different strain rates. Such an approach implicitly assumes that a material model that matches the stress–strain data at the different strain rates, will automatically match strain rate sensitivity data. However, by explicitly including the strain rate sensitivity data, the selected material model is more susceptible to localized thinning as the applied strain rate is increased. It is essential for the selected material model to exhibit this behaviour to prevent superplastic forming simulations at high strain rates from predicting stable deformation, when in fact localized thinning will occur.