一步成形模拟中初始场预示、效率优化及弯曲修正的算法研究
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摘要
随着计算机技术的迅猛发展，在汽车覆盖件模具的设计和制造过程中，广泛采用CAD/CAE/CAM技术已成为提高质量，缩短研制周期，降低成本，提高市场竞争的最有效手段。对CAD/CAE/CAM技术的研究系统应用，已成为衡量一个国家科技和工业化水平的重要标志之一。
本文结合国家自然科学基金重点项目“冲压成形与模具设计的基础理论、计算方法和关键技术”，重点研究了一步成形模拟初始场预示算法，以及在该过程中初始坯料面积对计算效率的影响，并提出了一种可弯曲修正的膜单元来考虑板料冲压成形过程中的弯曲效应。研究内容主要如下：
论文第一章绪论考察了汽车工业中板材冲压成形技术的发展概况，提出了覆盖件成形过程中快速模拟技术的必要性，分析了可用于工艺设计早期的一步成形模拟方法的发展趋势，以及在板料成形的工艺设计中的广泛应用。
论文第二章系统地阐述了一步成形模拟法的基本思想，基本假设和特征，并在此基础上论述了一步成形模拟的有限变形理论：利用薄板弯曲理论和膜理论给出了大变形的几何关系；根据Hill厚向异性屈服准则和理想型变理论，在比例加载条件下，给出了弹塑性板材积分形本构关系；论述了一步模拟中板料和模具接触的简化问题；然后，根据力平衡的概念和虚功原理，建立了一步成形模拟的计算方程，并采用Newton-Raphson方法进行求解；最后给出了一步成形模拟算法的程序流程图。
论文第三章在参阅大量文献并探讨前人成果的基础上，经过不断的尝试，从计算效率和稳定性出发，提出了几种有效可靠的初始场预示算法，能够为一步成形模拟提供一个比较合理的初始解，获得比较理想的分析结果，在很多情况可以满足工程应用的需要。其一，基于有限元模型修正技术的思想，提出了立面（负角）修正法。该方法就是在立面和负角单元的最高节点上建立旋转轴，将单元其他两个节点绕其旋转一定小角度，使其单元法线与z轴夹角小于90o，然后进行垂直投影得到初始场，从而避免出现单元投影时出现重叠，进而导致有限元方程的收敛性问题。其二，基于汽车覆盖件的多样性和复杂性，按照冲
压工艺分类，将其分为拉延件和弯曲件，并针对冲压件这两种主要成形特点，提出了两种基于截面线展开的算法。其主要思想是：以不动点轨迹线（或基准点）为中心，以展开节点与不动点（或基准点）构成的矢量方向为延展方向，其矢量长度为延展长度，将构件上所有节点做几何展开，得到毛坯形状的一个初始解。其三，考虑到由于几何法不能精确考虑到材料的性能和变形的特点，得到的初始解可能不能保证求解的稳定性和收敛性，为了改善几何法得到的近似解，本文利用弹性有限元的基本原理提出了面积迭代方法对其做力学修正，得到有效的初始场。该方法的基本思想是：完全按照线弹性的本构理论，并且不考虑各种等效的外载荷的情况下，根据输入的板料终了构形，将板料人为地、强行地拉成初始时刻的平板。然后进行平衡迭代，使得求得的初始解构形在线弹性意义下满足应力平衡条件。
论文第四章研究的是一步成形中初始场面积对一步成形迭代计算时间的影响。通过对不同高度的四种典型件（球冠，方盒，花形件，L形件）的考察，发现冲压构件面积与初始场面积的比值等于1时，计算效率并不如前人的文献中提到是最高的。本章建立了四个不同的构件特征，通过特征曲线可以优化复杂构件的面积比，从而达到有效加快收敛速度，提高计算效率的作用。最终确定构件表面积与投影面积之比更能反映构件的普遍特征，复杂构件可通过这一特征与最佳面积比构成的曲线图进行面积优化。
论文第五章研究了一步成形模拟方法中如何考虑弯曲效应的问题。在分析薄板成形问题时，主要是考虑弯曲、拉深引起的弹塑性变形，采用膜单元模拟拉伸占主导地位的胀形一类的问题是有效的，但是对于弯曲效应比较明显的问题，误差将是显著的。尤其是在冲头和模具的圆角附近这样容易发生破坏的区域，这种误差会更加突出。本章根据单元节点内力及弯矩平衡的原理，提出了一种可进行弯曲修正的膜单元，这种单元能够简便有效地计算板材冲压成形过程中弯曲变形引起的节点内力，提高了计算精度，同时计算工作量远远小于壳单元。
With the fast development of computer technology, CAD/CAE/CAM has been widely used in the designing and making of auto body panels in order to increase the competitive ability effectively with high quality, in a short time and at a low cost. The systemic application of CAD/CAE/CAM has become an important symbol to weigh the level of industry, science and technology of a country.
As a significant part of the national key project of nature science fund of china, called the Basic Theories, Simulation Method and Key Technique of Sheet metal Stamping and Tool’s Design (19832020), this paper deals with the initial guess arithmetic in one-step forming simulation and the effect of initial blank areas on computing efficiency in this process. What’s more, a membrane element is introduced to consider the bending of blank in stamp forming. The main research content is as follows:
The introduction of this paper points out the general situation of the development of blank stamp forming technology in auto industry. The necessity of fast simulation technology in the auto body panels’ forming process is also presented. Then the introduction analyzes the developing trend and wide use of one-step forming simulation approach which can be applied to the preliminary stage of process design in sheet metal forming.
The second chapter of this thesis exploits systemically the basic ideas, hypothesis and character of one-step forming simulation approach, on the basis of which I study the finite forming theory. Then I deduct kinematic relation of large elasto-plastic strains using the sheet metal forming theory and membrane theory. After that, on the basis of Hill’s anisotropic yield criterion and ideal deformation theory, I deduct integral constitutive equation of elasto-plastic flat blank by the assumption of proportional loading. Afterwards, I discuss the simplified method as to the contact of blank and tools. Whereafter, using the conception of force’s balance and the principle of virtual work, I construct the calculation equation of one-step forming simulation and give the solution by Newton-Raphson method. Finally, the program flow chart of one-step forming is given.
In the chapter 3, after reading a lot of literature and discussing their results, I introduce a few of valid and reliable arithmetics of initial guess in view of calculative efficiency and stability. All of them can provide reasonable initial solution for one-step forming simulation and obtain ideal analytic results, which can satisfy the need of engineering project in general. First of all, I introduce a correcting method of vertical plane elements (VPE) and negative plane elements (NPE) on the basis of finite element model’s correcting technique. In this method, we create a rotation axis
through the upmost node of VPE or NPE. And then we make the other two nodes of this element rotate around the axis for a small angle letting the inclination angle of element’s normal and Z axis be less than 90 degree. After that we project the geometry model vertically to get the initial guess avoiding the elements’ superposition which can’t result in constringency of finite element equation. Secondly, we classify the various complicated auto panels as drawing parts and bending parts by their process. And then we propose two arithmetics of section line spreading schemes considering the mainly forming characters of these two stamped parts. The basic ideas of them are: let the trochoid of the fixed points (or datum points) be the center. Then create a vector from the fixed points (or datum points) to spreaded points. Let this vector’s direction be the spreading direction and it’s length be the spreading length. Then spread all of the nodes on the part to obtain an initial solution of the blank. The third one: in view of geometry method’s being unable to take material performance and deformation into account accurately so that it can’t get initial guess which assure solution’s stability and constringency. This paper introduces an area’s iteration approach to cor
本文结合国家自然科学基金重点项目“冲压成形与模具设计的基础理论、计算方法和关键技术”，重点研究了一步成形模拟初始场预示算法，以及在该过程中初始坯料面积对计算效率的影响，并提出了一种可弯曲修正的膜单元来考虑板料冲压成形过程中的弯曲效应。研究内容主要如下：
论文第一章绪论考察了汽车工业中板材冲压成形技术的发展概况，提出了覆盖件成形过程中快速模拟技术的必要性，分析了可用于工艺设计早期的一步成形模拟方法的发展趋势，以及在板料成形的工艺设计中的广泛应用。
论文第二章系统地阐述了一步成形模拟法的基本思想，基本假设和特征，并在此基础上论述了一步成形模拟的有限变形理论：利用薄板弯曲理论和膜理论给出了大变形的几何关系；根据Hill厚向异性屈服准则和理想型变理论，在比例加载条件下，给出了弹塑性板材积分形本构关系；论述了一步模拟中板料和模具接触的简化问题；然后，根据力平衡的概念和虚功原理，建立了一步成形模拟的计算方程，并采用Newton-Raphson方法进行求解；最后给出了一步成形模拟算法的程序流程图。
论文第三章在参阅大量文献并探讨前人成果的基础上，经过不断的尝试，从计算效率和稳定性出发，提出了几种有效可靠的初始场预示算法，能够为一步成形模拟提供一个比较合理的初始解，获得比较理想的分析结果，在很多情况可以满足工程应用的需要。其一，基于有限元模型修正技术的思想，提出了立面（负角）修正法。该方法就是在立面和负角单元的最高节点上建立旋转轴，将单元其他两个节点绕其旋转一定小角度，使其单元法线与z轴夹角小于90o，然后进行垂直投影得到初始场，从而避免出现单元投影时出现重叠，进而导致有限元方程的收敛性问题。其二，基于汽车覆盖件的多样性和复杂性，按照冲
压工艺分类，将其分为拉延件和弯曲件，并针对冲压件这两种主要成形特点，提出了两种基于截面线展开的算法。其主要思想是：以不动点轨迹线（或基准点）为中心，以展开节点与不动点（或基准点）构成的矢量方向为延展方向，其矢量长度为延展长度，将构件上所有节点做几何展开，得到毛坯形状的一个初始解。其三，考虑到由于几何法不能精确考虑到材料的性能和变形的特点，得到的初始解可能不能保证求解的稳定性和收敛性，为了改善几何法得到的近似解，本文利用弹性有限元的基本原理提出了面积迭代方法对其做力学修正，得到有效的初始场。该方法的基本思想是：完全按照线弹性的本构理论，并且不考虑各种等效的外载荷的情况下，根据输入的板料终了构形，将板料人为地、强行地拉成初始时刻的平板。然后进行平衡迭代，使得求得的初始解构形在线弹性意义下满足应力平衡条件。
论文第四章研究的是一步成形中初始场面积对一步成形迭代计算时间的影响。通过对不同高度的四种典型件（球冠，方盒，花形件，L形件）的考察，发现冲压构件面积与初始场面积的比值等于1时，计算效率并不如前人的文献中提到是最高的。本章建立了四个不同的构件特征，通过特征曲线可以优化复杂构件的面积比，从而达到有效加快收敛速度，提高计算效率的作用。最终确定构件表面积与投影面积之比更能反映构件的普遍特征，复杂构件可通过这一特征与最佳面积比构成的曲线图进行面积优化。
论文第五章研究了一步成形模拟方法中如何考虑弯曲效应的问题。在分析薄板成形问题时，主要是考虑弯曲、拉深引起的弹塑性变形，采用膜单元模拟拉伸占主导地位的胀形一类的问题是有效的，但是对于弯曲效应比较明显的问题，误差将是显著的。尤其是在冲头和模具的圆角附近这样容易发生破坏的区域，这种误差会更加突出。本章根据单元节点内力及弯矩平衡的原理，提出了一种可进行弯曲修正的膜单元，这种单元能够简便有效地计算板材冲压成形过程中弯曲变形引起的节点内力，提高了计算精度，同时计算工作量远远小于壳单元。
With the fast development of computer technology, CAD/CAE/CAM has been widely used in the designing and making of auto body panels in order to increase the competitive ability effectively with high quality, in a short time and at a low cost. The systemic application of CAD/CAE/CAM has become an important symbol to weigh the level of industry, science and technology of a country.
As a significant part of the national key project of nature science fund of china, called the Basic Theories, Simulation Method and Key Technique of Sheet metal Stamping and Tool’s Design (19832020), this paper deals with the initial guess arithmetic in one-step forming simulation and the effect of initial blank areas on computing efficiency in this process. What’s more, a membrane element is introduced to consider the bending of blank in stamp forming. The main research content is as follows:
The introduction of this paper points out the general situation of the development of blank stamp forming technology in auto industry. The necessity of fast simulation technology in the auto body panels’ forming process is also presented. Then the introduction analyzes the developing trend and wide use of one-step forming simulation approach which can be applied to the preliminary stage of process design in sheet metal forming.
The second chapter of this thesis exploits systemically the basic ideas, hypothesis and character of one-step forming simulation approach, on the basis of which I study the finite forming theory. Then I deduct kinematic relation of large elasto-plastic strains using the sheet metal forming theory and membrane theory. After that, on the basis of Hill’s anisotropic yield criterion and ideal deformation theory, I deduct integral constitutive equation of elasto-plastic flat blank by the assumption of proportional loading. Afterwards, I discuss the simplified method as to the contact of blank and tools. Whereafter, using the conception of force’s balance and the principle of virtual work, I construct the calculation equation of one-step forming simulation and give the solution by Newton-Raphson method. Finally, the program flow chart of one-step forming is given.
In the chapter 3, after reading a lot of literature and discussing their results, I introduce a few of valid and reliable arithmetics of initial guess in view of calculative efficiency and stability. All of them can provide reasonable initial solution for one-step forming simulation and obtain ideal analytic results, which can satisfy the need of engineering project in general. First of all, I introduce a correcting method of vertical plane elements (VPE) and negative plane elements (NPE) on the basis of finite element model’s correcting technique. In this method, we create a rotation axis
through the upmost node of VPE or NPE. And then we make the other two nodes of this element rotate around the axis for a small angle letting the inclination angle of element’s normal and Z axis be less than 90 degree. After that we project the geometry model vertically to get the initial guess avoiding the elements’ superposition which can’t result in constringency of finite element equation. Secondly, we classify the various complicated auto panels as drawing parts and bending parts by their process. And then we propose two arithmetics of section line spreading schemes considering the mainly forming characters of these two stamped parts. The basic ideas of them are: let the trochoid of the fixed points (or datum points) be the center. Then create a vector from the fixed points (or datum points) to spreaded points. Let this vector’s direction be the spreading direction and it’s length be the spreading length. Then spread all of the nodes on the part to obtain an initial solution of the blank. The third one: in view of geometry method’s being unable to take material performance and deformation into account accurately so that it can’t get initial guess which assure solution’s stability and constringency. This paper introduces an area’s iteration approach to cor
引文
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