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 .     

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。     

温挤压微成形系统及其数值模拟研究

零件尺寸微型化带来了"尺度效应"等问题,对塑性成形理论、设备和工艺等都提出了更高的要求.针对微挤压中冷热成形的不足,提出了温挤压微成形工艺.在借鉴现有微成形装置的基础上给出了自行设计的温挤压微成形系统,并对其工作原理进行了阐述.为了探索坯料在微挤压筒内的流动行为,利用ABAQUS/Explicit模块对温挤压微成形进行了数值模拟,着重分析了210℃时温挤过程中的应力分布以及不同摩擦条件下金属的流变行为,揭示了不同工艺参数对温挤压微成形规律的影响,从而为其模具优化设计提供科学的理论依据.     

传动轴万向节叉精密成形研究与试验

采用三维有限元法对万向节叉锻件热挤压成形过程进行了数值模拟仿真分析.针对其成形过程中出现的缺陷进行模具优化设计.生产实践表明,改进后的模具结构从根本上解决了改进前出现的充不满及形状尺寸不能满足要求的问题,并且提高了材料利用率,延长了模具寿命,降低了工人劳动强度,同时工件获得较高的尺寸和形状精度,较好的纤维流向和机械性能.     

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 .     

基于 Deform-3D 的车用下轴套零件冷挤压模具结构优化设计

目的分析挤压成形中车用下轴套零件成形表面出现的折叠缺陷,优化挤压上凹模的底部出口斜度、下凹模的入口斜度和挤压深度等主要成形工艺参数。方法采用DEFORM-3D软件,对汽车下轴套零件的冷挤压成形工艺进行了系统的有限元数值模拟试验。结果挤压成形模具结构设计不合理,导致在成形过程中模具分型面处金属出现汇流并形成折叠。结论通过优化挤压模具结构,使金属成形良好,无折叠缺陷出现,最终获得了较为合理的冷挤压模具结构。     

声场-结构耦合系统灵敏度分析及优化设计研究

给出了低频声－结构耦合系统的有限元方程，并在此基础上提出声一结构耦合系统的包含尺寸和形状设计变量的优化设计模型，建立基于灵敏度分析求解的优化设计方法，重点推导了耦合系统的特征频率和声压级响应关于设计变量的灵敏度方程。在JIFEX软件中实现上述理论和算法，并通过灵敏度比较和优化设计的数值算例，进一步说明该研究方法对声结构耦合系统的工程设计具有实用意义。     

复合材料层合板屈曲稳定性优化设计及其灵敏度计算方法

笔者在有限元分析基础上研究了以屈曲稳定性作为约束条件或优化目标的复合材料层合板结构优化设计及其灵敏度分析方法,重点讨论了屈曲临界荷载灵敏度对内力场和载荷的依赖关系及其在铺层优化、尺寸优化和形状优化问题中的不同计算方法,并在JIFEX软件中实现了复杂结构复合材料层合板优化设计方法。数值算例验证了本文算法和程序的有效性。     

亚热精密成形过程模具磨损的数值模拟研究

采用数值模拟技术分析了亚热挤压成形阶段坯料及模具上的参量变化。基于修正的磨损模型,将其引入到有限元数值模拟软件中,对亚热挤压过程中模具磨损量的变化情况进行了分析,得到了不同变形阶段的瞬时磨损曲线及一次成形结束时的综合磨损曲线。利用研究结果对模具的磨损寿命进行了预测,与实际情况对比,两者吻合较好。     

模具在工件反挤压过程中的变形模拟研究

模具在金属塑性成形过程中起着十分重要的作用.就一般而言,模具在金属成形过程中的变形被忽略,将之视为刚性体.然而在金属精密成形中,模具的变形对成形件的尺寸精度将产生较大的影响.利用SuperForm软件针对模具在工件挤压过程中的变形进行了有限元数值模拟,对这一问题作了初步分析与探讨,为工厂实际生产的工艺制定、模具设计提供理论参考与依据.     

OPTIMAL DESIGN FOR NON-STEADY-STATE METAL FORMING PROCESSES—II. APPLICATION OF SHAPE OPTIMIZATION IN FORGING

This paper is the second part of a two-part article about shape optimization of metal forming processes. This part is focused on numerical applications of the optimization method which has been described in the first paper. The main feature of this work is the analytical calculations of the derivatives of the objective function for a non-linear, non-steady-state problem with large deformations. The calculations are based on the differentiation of the discrete objective function and on the differentiation of the discrete equations of the forging problem. Our aim here is to show the feasibility and the efficiency of such a method with numerical examples. We recall the formulation and the resolution of the direct problem of hot axisymmetrical forging. Then, a first type of shape optimization problem is considered: the optimization of the shape of the initial part for a one-step forging operation. Two academic problems allow for checking the accuracy of the analytical derivatives, and for studying the convergence rate of the optimization procedure. Both constrained and unconstrained problems are considered. Afterwards, a second type of inverse problem of design is considered: the shape optimization of the preforming tool, for a two-step forging process. A satisfactory shape is obtained after few iterations of the optimization procedure.     

An alternative approach to shape design sensitivity analysis

A novel method is presented in this paper for calculating shape design sensitivity, which is based on the finite difference method (FDM). By analysing the numerical procedure of the FDM, the perturbation of the geometry is replaced by a perturbation load which can be calculated once the stress field of the initial problem and the design boundary perturbation are known. The final shape design sensitivity is obtained by solving the perturbation problem which has the same geometry and the kinematical boundary condition as the initial problem, but under the perturbation loads. Therefore the new method does not require the calculation of the matrices of the perturbed structure, and is independent of the perturbation step. A numerical implementation of the finite difference load method (FDLM) is described in which the boundary element method is used to evaluate the structural response. The numerical examples demonstrate that this new method for shape design sensitivity analysis is very accurate.     

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.     

随机波浪作用下海洋平台响应分析与结构优化设计

根据随机响应分析的确定性算法,提出了随机波浪作用下海洋平台结构响应灵敏度分析方法。采用虚拟激励算法,将随机响应灵敏度分析问题转化为稳态简谐响应分析,进一步求出结构随机响应的均值、方差、协方差等统计量的灵敏度。这一过程可直接利用响应分析的程序模块,避免计算振型导数的困难,具有较高的计算效率和精度。与差分法计算结果的比较验证了该方法的效率和精度。在此基础上,研究了随机波浪作用下海洋平台结构尺寸与形状优化方法。本文方法在有限元分析与优化设计软件系统JIFEX中实现,数值算例验证了算法的有效性。     

Boundary integral equation method for shape optimization of elastic structures

A general method for shape design sensitivity analysis as applied to plane elasticity problems is developed with a direct boundary integral equation formulation, using the material derivative concept and adjoint variable method. The problem formulation is very general and a complete consideration is given to describing the boundary variation by including the tangential component of the velocity field. The method is then applied to obtain the sensitivity formula for a general stress constraint imposed over a small part of the boundary. The accuracy of the design sensitivity analysis is studied with a fillet and an elastic ring design problem. Among the several numerical implementations tested, the second order boundary elements with a cubic spline representation of the moving boundary have shown the best accuracy. A smooth characteristic function is found to be better than a plateau function for localization of the stress constraint. Optimal shapes for the two problems are presented to show numerical applications.     

OPTIMUM SHAPE DESIGN AND POSITIONING OF FEATURES USING THE BOUNDARY INTEGRAL EQUATION METHOD

A design optimization procedure is developed using the boundary integral equation (BIE) method for linear elastostatic two-dimensional domains. Optimal shape design problems are treated where design variables are geometric parameters such as the positions and sizing dimensions of entire features on a component or structure. A fully analytical approach is adopted for the design sensitivity analysis where the BIE is implicitly differentiated. The ability to evaluate response sensitivity derivatives with respect to design variables such as feature positions is achieved through the definition of appropriate design velocity fields for these variables. How the advantages of the BIE method are amplified when extended to sensitivity analysis for this category of shape design problems is also highlighted. A mathematical programming approach with the penalty function method is used for solving the overall optimization problem. The procedure is applied to three example problems to demonstrate the optimum positioning of holes and optimization of radial dimensions of circular arcs on structures.     

Adjoint shape design sensitivity analysis of molecular dynamics for lattice structures using GLE impedance forces

We presented a shape design sensitivity analysis method for lattice structures using a generalized Langevin equation (GLE) to overcome the difficulty of discrete nature in atomic systems. Taking advantage of the GLE forces, the perturbed atomistic region is treated as the GLE impedance forces and the shape design problem of discrete atomic variations is converted into a non-shape problem with GLE impedance forces. We developed an adjoint variable method in order to improve the computational efficiency for molecular dynamics (MD) with many design variables. Due to the translational symmetry in lattice structure, the size of the time history kernel function that accounts for the boundary effects of reduced systems could be reduced to that of a single atoms DOFs. In numerical examples, the convergent characteristic of shape sensitivity according to the amount of shape variations is investigated in MD systems. Also, the results of the derived shape sensitivity turn out to be more accurate and efficient, compared with those of the finite difference ones.     

Finite volume method for simulation of extrusion processes

In this paper, the development of a finite volume method for prediction of plastic flow of metals during cold and hot extrusion processes is described. The method solves the equations governing mass, momentum and heat balance in their integral form, using discretization elements of an arbitrary polyhedral shape. Comparisons of the numerical and experimental results show a very good agreement, implying that the proposed numerical method can be used as a useful tool in designing extrusion processes. Copyright © 2005 John Wiley & Sons, Ltd.     

Design sensitivity analysis and optimization of interface shape for zoned-inhomogeneous thermal conduction problems using boundary integral formulation

A generalized formulation of the shape design sensitivity analysis for two-dimensional steady-state thermal conduction problem as applied to zoned-inhomogeneous solids is presented using the boundary integral and the adjoint variable method. Shape variation of the external and zone-interface boundary is considered. Through an analytical example, it is proved that the derived sensitivity formula coincides with the analytic solution. In numerical implementation, the primal and adjoint problems are solved by the boundary element method. Shape sensitivity is numerically analyzed for a compound cylinder, a thermal diffuser and a cooling fin problem, and its accuracy is compared with that by numerical differentiation. The sensitivity formula derived is incorporated to a nonlinear programming algorithm and optimum shapes are found for the thermal diffuser and the cooling fin problem.     

Boundary elements in shape design sensitivity analysis and optimal design of vibrating structures

A general approach to shape design sensitivity analysis and optimal design for dynamic transient and free vibrations problems using boundary elements is presented. The material derivatives and the adjoint system method are applied to obtain first-order sensitivities for the effect of boundary shape variations. A numerical example of shape sensitivity analysis and optimal design for free vibrations of an elastic body is presented.