锻造过程中变形均匀性控制及模具优化设计

以直接设计预成形模具形状为目标 ,提出并建立了一种控制变形均匀性的灵敏度分析理论和模具形状优化设计方法 .以任意单元的等效应变与所有单元的平均等效应变的差值的平方和作为目标函数 ,B样条曲线表示模具形状 ,B样条曲线控制点坐标作为优化设计变量 ,优化设计的目标就是通过设计预成形模具形状使目标函数最小 ,即使整个工件的变形尽可能均匀 .给出了目标函数的表达形式 ,详细推导了目标函数、单元等效应变率和单元各应变率分量对优化设计变量的灵敏度 .并对圆柱体平面镦粗工艺进行预成形优化设计 ,给出了相应的优化设计结果 .     

Sensitivity Analysis Based Multiple Objective Preform Die Shape Optimal Design in Metal Forging

The multiple objective preform design optimization was put forward. The final forging＇s shape and deformation uniformity were considered in the multiple objective. The objective is to optimize the shape and the deformation uniformity of the final forging at the same time so that a more high integrate quality of the final forging can be obtained. The total objective was assembled by the shape and uniformity objective using the weight adding method. The preform die shape is presented by cubic B-spline curves. The control points of B-spline curves are used as the design variables. The forms of the total objective function, shape and uniformity sub-objective function are given. The sensitivities of the total objective function and the sub-objective functions with respect to the design variables are developed. Using this method, the preform die shape of an H-shaped forging process is optimally designed. The optimization results are very satisfactory.     

Optimal Preform die Design through Controlling Deformation Uniformity in Metal Forging

A finite element based sensitivity analysis method for preform die shape design in metal forging is developed.The optimization goal is to obtain more uniform deformation within the final forging by controlling the deformation uniformity.The objective function expressed by the effective strain is constructed.The sensitivity equations of the objective function,elemental volume,elemental effective strain rate and the elemental strain rate with respect to the design variables are constituted.The preform die shapes of an H-shaped forging process in axisymmetric deformation are designed using this method.     

基于有限元灵敏度分析的预锻模具形状优化设计

在控制锻件几何形状的前提下 ,采用有限元灵敏度分析方法 ,对预锻模具形状进行优化设计 .针对下模速度为零时 ,速度灵敏度边界条件为零 ,其形状在优化迭代过程中得不到优化的情况 ,对速度灵敏度边界条件提出改进措施 ,使上下模具形状同时能够得到优化 .最后给出了优化设计实例 ,验证该方法的可靠性 .     

Sensitivity analysis and shape optimization for preform design in thermo‐mechanical coupled analysis

In complex forging processes, it is essential to find the optimal deformation path and the optimal preform shape that will lead to the desired final shape and service properties. A sensitivity analysis and optimization for preform billet shape in thermo‐mechanical coupled simulation is developed in this work. Non‐linear sensitivity analysis of temperatures, flow‐stresses, strains and strain‐rates are presented with respect to design variables. Both analytical and finite‐difference gradients are employed to validate the effectiveness of sensitivity analysis developed in this work. Numerous iterations of coupled thermo‐mechanical analysis are performed to determine an optimum preform shape based on a given criterion of minimizing the objective function on effective strain variance within the final forging. The design constraints are imposed on die underfill, material scrap, folding defects and temperatures. In addition, a method for material data processing is given in order to determine the flow stress and its derivatives. The shape optimization scheme is demonstrated with the preform designs of an axisymmetric disk and a plane strain problem. Copyright © 1999 John Wiley & Sons, Ltd.     

3D preform shape optimization in forging using reduced basis techniques

Three-dimensional preform shape optimization of complex forgings with a weighted summation of multiple basis shapes is presented in this article. Currently, 2D preform shape optimization is well developed; however, in cases in which the parts are neither axisymmetric nor plane strain, 2D assumptions do not hold well. The number of design variables required to define the 3D preform shape is high, making most iterative design methods impractical for shape optimization. The goal here is to make design optimization practical and efficient by developing reduced-order modeling techniques for 3D preform shape optimization. The preform shape is treated as a linear combination of various billet shapes, called basis shapes, with the weights for each basis shape used as design variables, thereby reducing the number of design variables. It is very difficult to obtain the necessary gradient information for 3D forging simulations, so a non-gradient method is used to build the surrogate model on which optimization is performed. The optimization problem is formulated to minimize strain variance while placing constraints on underfill. Representative problems are used to demonstrate the effectiveness of the approach.     

Microstructure optimization design methods of the forging process and applications

A microstructure optimization design method of the forging process is proposed. The optimization goal is the fine grain size and homogeneous grain distribution. The optimization object is the forging process parameters and the shape of the preform die. The grain size sub-objective function, the forgings shape sub-objective function and the whole objective function including the shape and the grain size are established, respectively. The detailed optimization steps are given. The microstructure optimization program is developed using the micro-genetic algorithm and the finite element method. Then, the upsetting process of the cylindrical billet is analyzed using a self-developed program. The forging parameters and the shape of preform die of the upsetting process are optimized respectively. The fine size and homogenous distribution of the grain can be achieved by controlling the shape of the preform die and improving the friction condition.     

Sensitivity analysis of viscoplastic deformation process with application to metal preform design optimization

The sensitivity analysis of rigid viscoplastic deformation processes with application to metal preform design optimization is investigated. For viscoplastic constitutive models, the deformation process is path-dependent in nature and thus the sensitivity analysis of the deformation history is formulated in an incremental procedure. To this end, an algorithm is derived on the basis of the time integration scheme used in the primary finite element analysis, where the contact conditions are treated with the penalty method. The discretized equilibrium equations, as well as the time integration equations, are directly differentiated with respect to the design variables. The discrete form of the sensitivity equations is then solved with procedures similar to those used in the direct analysis, where the secant matrix decomposed in the direct analysis can also be utilized at each time instant. Thus the sensitivity of the deformation history is evaluated in a step-wise procedure. The present algorithm can be employed for the optimization of metal forming processes. The accuracy of the proposed sensitivity analysis as well as its applicability are demonstrated by numerical examples with reference to preform design optimization problems, where the aggregate function method is employed for converting the non-smooth Min–max type objective function into a numerically tractable one.     

A continuum sensitivity method for finite thermo‐inelastic deformations with applications to the design of hot forming processes

A computational framework is presented to evaluate the shape as well as non‐shape (parameter) sensitivity of finite thermo‐inelastic deformations using the continuum sensitivity method (CSM). Weak sensitivity equations are developed for the large thermo‐mechanical deformation of hyperelastic thermo‐viscoplastic materials that are consistent with the kinematic, constitutive, contact and thermal analyses used in the solution of the direct deformation problem. The sensitivities are defined in a rigorous sense and the sensitivity analysis is performed in an infinite‐dimensional continuum framework. The effects of perturbation in the preform, die surface, or other process parameters are carefully considered in the CSM development for the computation of the die temperature sensitivity fields. The direct deformation and sensitivity deformation problems are solved using the finite element method. The results of the continuum sensitivity analysis are validated extensively by a comparison with those obtained by finite difference approximations (i.e. using the solution of a deformation problem with perturbed design variables). The effectiveness of the method is demonstrated with a number of applications in the design optimization of metal forming processes. Copyright © 2002 John Wiley & Sons, Ltd.     

基于双向渐进结构优化的叶片锻件预成形设计

为了实现体积成形的预成形优化设计,基于双向渐进结构(BESO)优化的思想,提出了一种针对体积成形预成形设计的新方法——拓扑优化法,并详细给出了该方法的优化策略、单元增删准则、插值处理等关键技术.利用自行开发的优化程序,结合DEFORM-2D有限元模拟软件,以理想充填模腔、最小飞边状态为目标,以静水压力的大小作为单元的增删准则,从毛坯的欠填充状态出发,对二维叶片锻件的预成形结构进行了优化设计.优化结果表明:该方法算法原理清晰明确,实现方便,整个过程集成化后,从模拟到优化均可实现自动进行,运行效率高,并具有较高的优化精度.     

基于虚载荷变量的无网格法形状优化的研究

将选择施加在"虚结构"控制点上的虚载荷作为形状优化的设计变量,并将它与无网格Galerkin法相结合来开展结构形状优化研究,采用罚函数法来施加边界条件,通过直接微分法建立了结构形状优化的离散型灵敏度分析算法,利用无网格法研究了节点坐标关于设计变量导数的计算。所提出的算法简单明了,它不仅解决了网格的畸变问题,而且简化了优化模型和迭代流程,并可使结构的受力特性得到进一步的改善。最后用2个工程实例验证了所建立的算法,并得到了形状优化结果。     

金属预成形优化设计及凝聚函数方法

研究了金属预成形设计中的形状优化设计问题及相应的求解算法,并讨论了凝聚函数在这类问题中的应用。金属预成形设计在本质上是一类反问题,给出采用形状优化设计方法求解这类问题的数学模型,讨论了目标函数构造方法对数值计算收敛性的影响。提出采用凝聚函数将∞-范数形式的形状误差函数转化为光滑可微的目标函数,显著提高了求解以金属预成形设计为背景的优化问题的收敛性。采用流动模型描述金属材料高温下的变形过程,利用基于梯度的数学规划方法求解了金属预成形优化设计问题。数值算例验证了所提出方法的有效性。     

Structural reliability optimization using an efficient safety index calculation procedure

The objective of this paper is to conduct reliability-based structural optimization in a multidisciplinary environment. An efficient reliability analysis is developed by expanding the limit functions in terms of intermediate design variables. The design constraints are approximated using multivariate splines in searching for the optimum. The reduction in computational cost realized in safety index calculation and optimization are demonstrated through several structural problems. This paper presents safety index computation, analytical sensitivity analysis of reliability constraints and optimization using truss, frame and plate examples.     

Application of a response surface method to the optimal design of the wall temperature profiles in extrusion die

A new approach to the optimal design of the die wall temperature profile in polymer extrusion processes is presented. In this approach, optimization of the design variables is conducted by a Response Surface Method (RSM) and the Sequential Quadratic Programming (SQP) algorithm. Design of experiment (DoE) needed for the construction of the response surface is used to evaluate the objective and the constraint functions on the basis of a finite element method (FEM). Two designs of experiments are used and the performances of the optimization results are compared with respect to efficiency and ability to obtain a global optimum. Typically, for extrusion die design, the objective function states that the average velocity across the die exit is uniform. Constraints are used to limit the pressure drop in the die. For this purpose, we optimize the wall temperature profile of a coat hanger die in a heterogeneous way, (i.e. the wall temperature may not be constant in the entire die). The melt temperature enables us to locally control the viscosity, which influences the flows in the various zones. The effect of the design variables in the objective and constraint functions is investigated using Taguchi method. The flow analysis results are then combined with an automatic optimization algorithm to provide a new profile of the die wall temperature distributions.     

基于目标应变分布的TC17合金双性能盘预成形形状优化设计

目的 研究TC17合金双性能盘目标应变分布下的预成形形状优化设计方法.方法 采用拉丁超立方试验设计方法对预成形形状设计变量抽样选取样本点,并通过Deform有限元数值模拟获得样本设计变量下的局部应变分布.以局部应变分布与目标应变分布之间的方差最小为目标函数,采用Kriging方程建立近似替代模型预测响应应变误差,并结合遗传算法,以锻件的充填率及材料利用率为约束条件,优化设计预成形形状.结果 近似替代模型预测的应变误差与基于有限元数值模拟计算获得的应变误差之间的最大相对误差和最小相对误差分别为10.8％和0.01％.结论 这表明Kriging近似替代模型在预测响应应变误差时的精度较高,具有较好的可靠性,采用优化后的预成形形状经多道次等温锻造后的等效应变分布满足目标应变分布的设计要求.     

Shape optimization of preform tools in forging of aerofoil using a metamodel-assisted multi-island genetic algorithm

Preform design plays an important role in improving the material flow, mechanical properties and reducing defects for forgings with complex shapes. In this paper, a study on shape optimization of preform tools in forging of an airfoil is carried out based on a multi-island genetic algorithm combined with a metamodel technique. An optimal Latin hypercube sampling technique is employed for sampling with the expected coverage of parameter space. Finite element (FE) simulations of multistep forging processes are implemented to obtain the objective function values for evaluating the forging qualities. For facilitating the optimization process, a radial basis function surrogate model is established to predict the responses of the hot forging process to the variation of the preform tool shape. In consideration of the compromise between different optimal objectives, a set of Pareto-optimal solutions are identified by the suggested genetic algorithm to provide more selections. Finally, according to the proposed fitness function, the best solution of multi-objective optimization on the Pareto front is confirmed and the corresponding preform tool shape proves optimal performances with substantially improved forging qualities via FE validation.     

动力可靠度约束下基于概率测度变换-全局收敛移动渐近线法的结构优化设计EI北大核心CSCD

基于动力可靠度的结构优化是实现随机动力系统优化设计的重要途径。针对设计变量为系统中部分随机变量分布均值的情形,提出了一种基于动力可靠度的结构优化设计方法。在该方法中,通过概率密度演化理论实现了结构动力可靠度的高效分析。在此基础上,结合概率测度变换,可以在不增加任何确定性结构分析的前提下,实现动力可靠度对设计变量的灵敏度分析。进而,通过将上述概率密度演化-测度变换方法嵌入全局收敛移动渐近线法,实现了基于动力可靠度的结构优化设计问题的高效求解。数值算例的结果表明,所提方法可以显著降低结构分析次数,具有较高的效率与稳健性。     

Design sensitivity analysis and optimization for minimizing springback of sheet‐formed part

The springback is a manufacturing defect in the stamping process and causes difficulty in product assembly. An impediment to the use of lighter‐weight, higher‐strength materials in manufacturing is relative lack of understanding about how these materials respond to complex forming processes. The springback can be reduced by using an optimized combination of die, punch, and blank holder shapes together with friction and blank‐holding force. An optimized process can be determined using a gradient‐based optimization to minimize the springback. For an effective optimization of the stamping process, development of an efficient design sensitivity analysis (DSA) for the springback with respect to these process parameters is crucial. A continuum‐based shape and configuration DSA method for the stamping process has been developed using a non‐linear shell model. The material derivative is used to develop the continuum‐based design sensitivity. The design sensitivity equation is solved without iteration at each converged load step in the finite deformation elastoplastic non‐linear analysis with frictional contact, which makes sensitivity calculation very efficient. Numerical implementation of the proposed shape and configuration DSA method is performed using the meshfree method. The accuracy and efficiency of the proposed method are illustrated by minimizing the springback in a benchmark S‐rail problem. Copyright © 2007 John Wiley & Sons, Ltd.     

ON THE CHOICE OF OBJECTIVES IN SHAPE OPTIMIZATION

This paper is concerned with the choice of objectives or multiobjectives for the optimal shape design of axisymmetrical structures which are loaded symmetrically or non-symmetrically. The analysis of the structure is performed using the finite element method and the displacements are developed in Fourier series to take into account non axisymmetrical loadings:

The following topics which have been presented in detail in earlier papers are briefly summarized

— definition of the shape and selection of the design variables

— analysis of the structure

— sensitivity analysis and optimization method.In this paper attention is focused on the following topics: — choice of the objective functions

— multicriterion optimization by combining different objective functions — multicriterion optimization by combining different terms of Fourier series — results and applications.     

An alternative approach for addressing the failure probability-safety factor method with sensitivity analysis

The paper introduces a method for solving the failure probability-safety factor problem for designing engineering works proposed by Castillo et al. that optimizes an objective function subject to the standard geometric and code constraints, and two more sets of constraints that simultaneously guarantee given safety factors and failure probability bounds associated with a given set of failure modes. The method uses the dual variables and is especially convenient to perform a sensitivity analysis, because sensitivities of the objective function and the reliability indices can be obtained with respect to all data values. To this end, the optimization problems are transformed into other equivalent ones, in which the data parameters are converted into artificial variables, and locked to their actual values. In this way, some variables of the associated dual problems become the desired sensitivities. In addition, using the proposed methodology, calibration of codes based on partial safety factors can be done. The method is illustrated by its application to the design of a simple rubble mound breakwater and a bridge crane.