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 .     

PREFORM DIE SHAPE DESIGN IN METAL FORMING USING AN OPTIMIZATION METHOD

An optimization algorithm for preform die shape design in metal-forming processes is developed in this paper. The preform die shapes are represented by cubic B-spline curves. The control points of the B-spline are used as the design variables. The optimization objective is to reduce the difference between the realized and desired final forging shapes. The sensitivities of the objective function with respect to the design variables are developed in detail. The numerical examples show that the optimization method and the sensitivity analysis developed in this paper are very useful and the design results are satisfactory. Importantly, the preform die shapes designed by this method are easily manufacturable and can be implemented in practical metal-forming operations. This optimization method and the sensitivity analysis can also be applied in the preform design of complex industrial metal-forming problems. © 1997 by John Wiley & Sons, Ltd.     

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.     

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.     

Buster Die Shape Design of a Track Link Forging Using FEMBased Back-Tracing Method

For the preform design of a complex track link forging, fifteen critical sections were selected for two dimensional back-tracing using FEM. The preform shapes of the critical sections are designed and integrated into an ideal 3D busting shape. The buster dies are finally designed according to the ideal busting shape with a little of modification. The 3D simulation of the busting stage is carried out.     

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.     

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.     

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 .     

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.     

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。     

An efficient memetic algorithm for 3D shape matching problems

Shape representation plays a vital role in any shape optimization exercise. The ability to identify a shape with good functional properties is dependent on the underlying shape representation scheme, the morphing mechanism and the efficiency of the optimization algorithm. This article presents a novel and efficient methodology for morphing 3D shapes via smart repair of control points. The repaired sequence of control points are subsequently used to define the 3D object using a B-spline surface representation. The control points are evolved within the framework of a memetic algorithm for greater efficiency. While the authors have already proposed an approach for 2D shape matching, this article extends it further to deal with 3D shape matching problems. Three 3D examples and a real customized 3D earplug design have been used as examples to illustrate the performance of the proposed approach and the effectiveness of the repair scheme. Complete details of the problems are presented for future work in this direction.     

预制坯形状对扭力梁内高压成形的影响分析

针对复杂截面扭力梁内高压成形容易出现咬边和开裂的问题,以轿车V型扭力梁为例,采用数值模拟和试验方法,分析了预制坯形状对扭力梁内高压成形的影响,重点研究了压下量（Y）和侧向宽度（B）对预制坯形状和内高压成形的影响.结果表明,当Y、B分别为0.83D（D为管材直径）、0.73D和0.78D、0.78D时,得到的预制坯形状在...     

A numerical study on the elements of shape optimum design

This paper discusses the main elements of shape optimization. The material derivative of a stress function using the continuum approach is derived by introducing an adjoint problem, which is then transformed into shape design sensitivity by replacing the velocity field with the change of the design variables. The difficulty related with the appearance of the concentrated adjoint loads is discussed, with two proposals for the modelling of the adjoint problem. A numerical example is used to demonstrate the accuracy of the proposed formulation for different adjoint loads.

Two shape optimization examples are used to investigate the numerical characteristics of the optimization process. Two kinds of design boundary modelling are employed, namely the linear and cubic spline boundary representation. The difference of the final design shapes under different design variables and mesh distributions are also studied.     

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.     

Shape design sensitivity analysis with respect to the positioning of features in composite structures using the boundary element method

This paper presents the application of the boundary element method to the shape design sensitivity analysis of composite structures with holes and cutouts. A two-dimensional (2D) anisotropic domain, which contains a number of voids of arbitrary shapes will be considered. The objective is to perform the design sensitivity analysis of the structure with respect to the translation and rotation of the voids using the boundary element method. A directly differentiated form of the boundary integral equation, with respect to geometric design variables is used to calculate the shape design sensitivities for anisotropic materials. The response sensitivity analysis, with respect to the design variables such as feature positions and orientations, is achieved by the definition of appropriate design velocity fields for these variables. To find the optimum positions of the features within an anisotropic structure with the highest stiffness, the elastic compliance of the structure has been minimized subject to constraints upon stresses and geometry. Due to the non-linear nature of the mean compliance and stresses, the numerical optimisation algorithm used is the feasible direction method, together with the golden section method for the 1D search. A couple of test cases have been performed to verify the proposed method.     

A velocity field level set method for shape and topology optimization

In this paper, we propose a new implementation of the level set shape and topology optimization, the velocity field level set method. Therein, the normal velocity field is constructed with specified basis functions and velocity design variables defined on a given set of points that are independent of the finite element mesh. A general mathematical programming algorithm can be employed to find the optimal normal velocities on the basis of the sensitivity analysis. As compared with conventional level set methods, mapping the variational boundary shape optimization problem into a finite‐dimensional design space and the use of a general optimizer makes it more efficient and straightforward to handle multiple constraints and additional design variables. Moreover, the level set function is updated by the Hamilton‐Jacobi equation using the normal velocity field; thus, the inherent merits of the implicit representation is retained. Therefore, this method combines the merits of both the general mathematical programming and conventional level set methods. Integrated topology optimization of structures with embedded components of designable geometries is considered to show the capability of this method to deal with general design variables. Several numerical examples in 2D or 3D design domains illustrate the robustness and efficiency of the method using different basis functions.     

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.     

Parametric design and optimization of high speed train nose

Aiming at shortening the design period and improve the design efficiency of the nose shape of high speed trains, a parametric shape optimization method is developed for the design of the nose shape has been proposed in the present paper based on the VMF parametric approach, NURBS curves and discrete control point method. 33 design variables have been utilized to control the nose shape, and totally different shapes could be obtained by varying the values of design variables. Based on the above parametric method, multi-objective particle swarm algorithm, CFD numerical simulation and supported vector machine regression model, multi-objective aerodynamic shape optimization has been performed. Results reveal that the parametric shape design method proposed here could precisely describe the three-dimensional nose shape of high speed trains and could be applied to the concept design and optimization of the nose shape. Besides, the SVM regression model based the multi-points criterion could accurately describe the non-linear relationship between the design variables and objectives, and could be generally utilized in other fields. No matter the simplified model or the real model, the aerodynamic performance of the model after optimization has been greatly improved. Based on the SVR model, the nonlinear relation between the aerodynamic drag and the design variables is obtained, which could provide guidance for the engineering design and optimization.     

Geometric mapping of yarn structures due to shape change in 3-D braided composites

The internal yarn structure in 3-D braided preforms possesses a certain topological character which is unique to the braiding method used. Hence, preforms of different shapes but braided by the same method have topologically similar yarn structures. This unique property offers the possibility that the yarn structure in preform of one shape may be geometrically mapped to that in another shape, and vice versa.

This study discusses a geometric mapping methodology, the objective of which is to obtain the appropriate mapping which analytically links the yarn structures in two preforms of different shapes; if the yarn structure in one preform is known, the yarn structure in the other can be determined by the derived geometric mapping.

Two broad classes of mapping are discussed. The first concerns mapping between two preforms that are braided directly in two different shapes; the second concerns mapping between the initial and final shapes of one single preform which is deformed after braiding. In each case, the mathematical forms of the desired mapping functions are obtained, satisfying the geometric constraints imposed by the internal yarns in the respective preforms. The determined mapping functions are then used to investigate the braidability and/or deformability of the considered preforms. Specifically, limiting windows for the braiding parameters that insure the braidability and/or deformability of the preforms are obtained using the appropriately derived mapping functions.

The 4-step 1 × 1 braiding method is used throughout this paper to illustrate the general mapping procedure; rigorous and explicit geometric relationships are derived leading to mapping functions between preforms of rectangular and curvilinear cross-sections. Numerical examples involving mapping between preforms of rectangular and tubular cross-sections are investigated in detail, along with examination of the preform braidability and/or formability.