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 .     

多目标优化在锻造毛坯形状优化设计中的应用

以形状相对简单的单工序锻件为研究对象,以同时获得材料消耗最小和变形程度最均匀的终锻件为优化目标,对锻造过程毛坯形状进行多目标优化设计的研究.给出了单工序锻件形状优化设计的总的目标函数及其各子目标函数的表示方法及计算表达式,以毛坯的高径(宽)比作为优化设计的变量,基于刚粘塑性有限元理论,采用黄金分割法进行优化迭代,编制了相应的程序,并对一典型的轴对称H型锻件的毛坯形状进行了多目标的优化设计,取得了明显的效果.     

挤压成形过程灵敏度分析及模具型腔参数优化设计

以高温下的挤压成形加工过程优化设计问题为背景,针对应变率相关粘性固体本构关系的材料稳态非弹性变形过程提出了形状灵敏度分析方法,并对算法的效率进行了讨论,在此基础上研究了挤压成形模具的形状优化设计问题的数学模型和数值求解算法。给出了挤压成形模具的二维形状优化设计算例,数值结果验证了所给出的灵敏度分析算法和优化设计模型的正确性和可用性。     

锻造变形量对7050合金组织和性能的影响

对两种不同锻造变形量的7050铝合金的组织和性能进行研究,分别考察组织均匀性、再结晶分数、粗大第二相比例和拉伸性能、断裂韧性等,分析锻造变形量对7050铝合金组织和性能的影响。结果表明,锻造变形量70%样品的再结晶分数(10%)和粗大第二相比例均小于变形量50%的样品,组织均匀性也更好;并且变形量70%样品的强度高出变形量50%样品约30 MPa,延伸率和断裂韧性也明显优于变形量50%的样品。因此,较大的变形量有利于获得均匀的组织和优异的综合性能。     

高纯铝多向锻造大塑性变形过程的数值模拟及实验研究

采用多向锻造的方法研究室温下锻造道次对高纯铝组织的影响,并用三维DEFORM软件对实验过程进行模拟。结果表明:经3次多向锻造后,高纯铝试样横截面上形成1个X形的细晶区及4个粗晶区,随锻造道次增至9,细晶区的面积不断扩大,粗晶区的面积不断缩小,但细晶区与粗晶区的晶粒尺寸差异并未消除。当高纯铝试样心部的等效应变量达到2.5时,心部再结晶晶粒尺寸达到70μm,继续增加心部的等效应变至6.0,心部的晶粒不再随等效应变量的增加而细化,达到晶粒细化的极限。而当试样边部难变形区和自由变形区的等效应变量增至4.0时,其再结晶晶粒仍随等效应变量的增加而细化,未达到晶粒细化极限。这表明局部等效应变量及局部变形方式均是影响高纯铝晶粒细化的重要因素。     

大规格弥散铜棒材的冷变形能力、性能及均匀性研究

研究了成分、粒度配比对大规格弥散铜棒材的冷变形能力、力学性能和导电性能的影响,并研究了大规格弥散铜棒材的均匀性问题。结果表明,大规格弥散铜棒材的冷变形能力随Al含量的增加而下降;提高细粉比例,冷变形能力降低;弥散铜棒材硬度随Al含量的升高先线性增加,后趋于平缓;导电率随Al含量的升高而下降;极限冷拉拔后,大规格弥散铜棒材性能存在不均匀性,退火可降低其性能的不均匀性。     

低温时效法消除DD8单晶高温合金的拉伸变形不均匀性

研究了消除DD8单晶合金的变形不均匀性的方法和机理,发现增加750C／24h的低温时效处理后,可以消除DD8单晶高温合金中的拉伸变形不均匀现象,同时合金的屈服强度得到提高。观察表明,低温时效能阻止基体通道中应力诱导下小γ^′粒子的不均匀析出,保证滑移变形沿试样均匀分布。     

直拉硅单晶中氧的轴向均匀性控制

本文从气氛、热场、坩锅材料、埚位、埚转、晶转、变参数拉晶等几个方面的论述了ＣＺ硅单晶初始氧浓度和氧的轴向均匀性的控制方法,着重研究了变参数拉晶对氧的轴向均匀性控制的影响。     

铝型材挤压模具的预变形设计

笔者结合多年铝型材挤压模具设计的经验,从铝型材挤压模具出现的挤压缺陷入手,介绍了一种预变形设计方法。通过论述几种典型型材的模具设计实例,表明了该设计方法的可行性,取得了较好的效果,克服了挤压缺陷的产生。     

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.     

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.     

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.     

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.     

A continuum Lagrangian sensitivity analysis for metal forming processes with applications to die design problems

A continuum sensitivity analysis is presented for large inelastic deformations and metal forming processes. The formulation is based on the differentiation of the governing field equations of the direct problem and development of weak forms for the corresponding field sensitivity equations. Special attention is given to modelling of the sensitivity boundary conditions that result due to frictional contact between the die and the workpiece. The contact problem in the direct deformation analysis is modelled using an augmented Lagrangian formulation. To avoid issues of non‐differentiability of the contact conditions, appropriate regularizing assumptions are introduced for the calculation of the sensitivity of the contact tractions. The proposed analysis is used for the calculation of sensitivity fields with respect to various process parameters including the die surface. The accuracy and effectiveness of the proposed method are demonstrated with a number of representative example problems. In the die design applications, a Bézier representation of the die curve is introduced. The control points of the Bézier curve are used as the design parameters. Comparison of the computed sensitivity results with those obtained using the direct analysis for two nearby dies and a finite difference approximation indicate a very high accuracy of the proposed analysis. The method is applied to the design of extrusion dies that minimize the standard deviation of the material state in the final product or minimize the required extrusion force for a given reduction ratio. An open‐forging die is also designed which for a specified stroke and initial workpiece produces a final product of desired shape. Copyright © 2000 John Wiley & Sons, Ltd.     

预成型体渗透率预测及其受压缩变形的影响

建立了织物预成型体单胞内纱线间细观流动和纱线内部微观流动的统一的数学模型。基于最小势能原理建立了织物松弛状态下的单胞几何模型,同时对在模具压缩下的单胞变形进行了分析,并建立了不同压缩状态下的单胞几何模型。通过对单胞内树脂流动数学模型的数值求解,获得了流动速度场及压力场,进而预测了预成型体的渗透率。预测1组不同压缩状态下的单胞渗透率,研究了预成型体压缩变形对渗透率的影响。结果显示:随着压缩量的增加,其渗透率逐渐降低。通过实验测量及数据分析,验证了建模和预测方法的正确性。     

Die shape optimal design in three-dimensional shape metal extrusion by the finite element method

A new approach to die shape optimal design in shape extrusion is presented. In this approach, the design problem is formulated as an optimization problem incorporating the three-dimensional finite element analysis model, and optimization of the die shape is conducted on the basis of the design sensitivities. The approach is applied to the determination of the die shapes for extrusion of parts with various cross sections including polygons and T sections. © 1998 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.     

Shape optimization of axisymmetric preform tools in forging using a direct differentiation method

A method for computing shape sensitivity in the frame of non‐linear and non‐steady‐state forging is presented. Derivatives of tool geometry, velocity and state variables with respect to the shape parameters are calculated by a direct differentiation of discrete equations. Because of the important part played by the accuracy of finite element calculations, an efficient transfer method is used between meshes during remeshings and the contact algorithms are carefully differentiated. The resulting inverse design procedure is successfully applied to two industrial examples of forging of automobile parts, with fold‐over and piping defects occurring during the intermediate designs. It makes it possible to suggest reasonable preform shapes, with or without any available knowledge of the forging process. Copyright © 2001 John Wiley & Sons, Ltd.