板管成形的快速有限元模拟研究
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摘要
板管成形在材料加工中占有相当大的比重,广泛应用于汽车、航空、航天、船舶、电机电器等领域,尤其是型材弯曲和管材胀形,顺应轻量化、降低能耗和成本的需要,在零部件生产中扮演着重要的角色。在这些成形过程的数值模拟研究中,增量分析和一步及多步模拟互补长短,相辅相成。增量法能反映加载历史、处理坯料与模具间的接触,可以比较全面的考虑板料成形中的各类影响因素,是可以对板管成形过程进行精确计算的方法,相对比较成熟。而一步和多步法则主要致力于对成形过程的快速模拟,可以在设计方案还比较模糊,没有工模具信息,或者是只有初步设计的时候,考察产品的成形质量,优化板坯,使用起来也非常容易。
目前一步和多步法的研究主要是针对初始构形为平面的板料成形。本文的研究目标则是建立一个应用范围更广、可计算一般的板管成形、可考虑弯曲效应的一步和多步正反向快速模拟系统OMSTEP。本文的主要研究内容和成果如下:
通常针对板料成形问题的一步和多步法在考虑弯曲效应时,将公式局限于初始构形为平面的一步反向计算,若将该公式应用于一般的板管成形过程,则会引入转动自由度,增加计算规模,并使一步和多步法的处理相对复杂。为此,本文引入BST壳单元描述变形。该单元没有转动自由度,膜变形的计算与传统一步法所使用的膜单元完全等价,曲率计算不限于初始构形是否为平面的条件,也不局限于反算,同时能够保持一步法公式的简洁性和计算效率。基于极值功原理,将全量本构关系应用于一步法,将由标量预测-回归映射方法得到的本构关系应用于多步法,推导建立了一种适用于一般板管成形的正反向快速模拟公式。
现有的各类初始猜测值生成方法都是针对板料成形问题的,其中的几何方法难以通用,其中基于计算机图形学理论的参数化方法也要求预先完成边界节点的映射后才能使用。因此,本文首先借助边界调整法将板料的边界映射到平面上,保持板料边界的形状特征,再将其与参数化方法结合,实现通用的板料初始猜测值生成方法。为型材弯曲和管材胀形提供合适的初始解,则是个新的课题,本文提出了两种方法,一种是简单有效的几何方法,通过展开型材和管材的扫掠线来实现网格映射,效率比较高,但没有很好的通用性;另一种是将参数化方法由平面拓展到圆柱坐标系中,将工件节点映射到截面形状复杂的型材表面,或者半径尺寸任意的圆柱面上,这种方法高效、通用。此外,还给出了一种思路简单的中间构形初始解生成方法,该方法与参数化方法结合,可高效地得到较精确的中间构形初始猜测值。
接触的处理是一步和多步法中的关键技术,对外力的施加、计算的收敛性和准确性有着重要的影响。但传统的滑动约束算法主要是针对板料的,无法适用于型材和管材。为此,本文提出了接触滑动约束算法。该算法通过接触搜索找到与工件节点最近的滑动约束面单元,通过罚函数法的方式引入法向刚度,由弹簧单元模拟所受到的工模具摩擦,保持节点只在滑动约束面(可以是截面形状封闭的复杂曲面)上运动,从而将滑动约束方法应用于型材和管材成形。此外,为了能够直观考察脱离接触面的缺陷,如起皱、截面的畸变等,本文对多步正向计算中的实际接触状态的模拟进行了一些尝试,引入LS-DYNA中的方法进行全局搜索,采用高效的内外侧算法进行局部搜索找到接触对,使用罚函数法计算实际的接触力,考察了规则化摩擦模型,并针对大穿透量问题,做了些设置,通过选取合适的参数使接触计算稳定。
对板料成形过程进行了一步和多步正反向模拟计算,检验了OMSTEP系统求解板料成形问题的可行性。其中一步反算高效易用,多步模拟则可以获得更接近实际状况的结果。算例表明采用滑动约束计算更容易收敛,而采用罚函数法处理接触,可以观察到脱离接触面而产生的成形缺陷。
将一步和多步正反向模拟推广应用于一般的管材和型材成形过程。进行了矩形管3点弯曲试验和复杂截面异型材的拉弯实验。通过矩形管弯曲试验模拟考察截面畸变问题,通过复杂截面异型材的拉弯实验模拟考察型材的壁厚变化和回弹情况。一步模拟所得到的截面畸变、壁厚变化结果与增量分析及实验结果非常接近。多步模拟由于中间构形的引入,计算结果较一步法有所改进,可以捕捉到更为细微的变化趋势,基于多步模拟结果的回弹计算也比基于一步模拟结果的回弹更接近实验结果。在对复杂截面异型材的模拟中,采用滑动约束,避免填充物与型材间的接触处理。在胀形计算中,实现了一步正反向计算的结合,通过反算为正算提供优化的管坯,而多步法也自然地与多工步的胀形过程相匹配。
Sheet, tube and profile formings take up a large proportion in the material forming, being widely used in the fields such as automobile, aerospace, aviation and shipping etc. Particularly, profile bending and tube hydroforming play an important role in the metal manufacturing to meet the needs of lightweight, reduction of energy consumption and cost. In the study of numerical simulations concerning such formings, the incremental analysis and the one- and multi- step simulation have complemented each other. Incremental analysis is a relatively accurate finite element computation method for sheet, tube and profile forming since the deformation history, contacts and frictions between blank and forming tools, and other factors influencing forming and product performance can be considered in the round, while the one- and multi-step approach is a kind of fast finite element computation method and can be used to inspect formability and possible forming defects, optimize blank shape without the information of tools and dies, or only with simplified tool surfaces.
However, most one- and multi-step approaches are only applied in the sheet metal forming with a flat blank. This paper is to achieve a more widely-used fast simulation system named OMSTEP, with which sheet, tube and profile forming proecesses can be generally simulated forward or inversely with bending effects being considered. The main research content is concluded as follows.
When the bending effects are considered in the traditional one-step approaches which are based on the sheet metal forming, the resulted formulation is limited in the one-step inverse simulation with flat initial configuration, not suited to the general forming processes of sheet, tube and profile. Therefore, the BST shell element is introduced here to describe deformation without sacrificing the efficientcy of computation and the simplicity of formulation. In the BST element, the membrane compuation results equal to those gained by traditional one-step membrane elements and the curvature is calculated without using rotational DOF, not limited either by the condition whether the initial blank is flat or by the inverse simulation. Then based on the extreme principle, total deformation theory adopted for one-step and the constitutive equations from scalar prediction-return mapping method adopted for multi-step, the basic fast FE inverse and forward formulation is deduced.
Traditional methods to get initial guess solutions are all proposed for the sheet metal forming, among which the geometrical methods are not generally suited while the parameterization method in computer graphics can only be used after mapping the edge of sheet onto plane. So the edge tweaking method, which is shape-preserved, is firstly adopted here to map the outer edge of sheet, and then combined with the parameterization method to get initial satisfactory mesh of sheet by solving linear equations. It is a new issue to get initial guess solutions for profile bending and tube hydroforming. Two mehods are presented in this dissertation. One is a simple geometrical method in which the mesh is mapped by developing the sweepling line (center line) of profile and the other is an effective and general-suited parameterization method in which the column coordinate system is used to map mesh. Besides, a simple effective method is put forward to get good initial guess solutions for mid-configures.
Traditional sliding constrait algorithm is mainly proposed for the sheet metal forming too, not suited to profile and tube forming. Therefore, a new contact sliding constraint method is presented, in which the nearest constraint surface element of a node is found by contact search, and then the node normal stiffness is calculated by the penalty method and the friction is computed by the spring element. This method avoids the problem of geometrical adjustment of coordiate in traditional sliding constraints and is suited to profile and tube forming. Some attempts are also made to employ the penalty method to treat real contacts between blank and tools for multi-step forward simulation. Effective inside-outside algorithm is utilized to search contact pairs, the regularized friction model is investigated and some parameters are set up to deal with the problem of big penetration.
Sheet metal forimg processes are simulated inversely and forward by the developed in-house one- and multi- step program OMSTEP. It is shown that the one-step inverse simulation is highly efficient and easy to use and the simulation results can be improved by the multi-step approach. Besides, the numerical examples show that the convergence can be more easily achived by the sliding constraint than by the penalty method. However, the wrinkling can be oberserved directly only when the penalty method is used to treat real contacts.
The applications of one- and multi- step approach are extended to general forming processes of profile and tube, which is hard for the traditional one- and multi- step approach based on the sheet metal forming. The experiment of three point bending of rectangular tube, in which the cross-sectional distortions are inspected, and the experiment of stretch bending of profile with a complicated cross-section, in which the variation of thickness and the springback are inspected, is conducted to inspect the suitability of OMSTEP system to the profile bending. The variation of wall thickness and cross-section distortions gained from the one-step simulation show good agreements with the incremental analyses and experimental results, but the detailed deformation tendency can only be achieved correctly from multi-step simulations since the mid-configurations are increased and the deformation history is considered. The springback values based on the results of multi-step simulation are also closer to the experimental results than those based on the one-step simulation. In the simulation of profile bending, the sliding constraint is adopted to avoid the contacts between the fillers and profile. In addition, the inverse simulation affords optimized tube blank for the forward simulation in the one step simulation of hydroforming while the multi-step approach matches with the multi-stage hydroforming.
目前一步和多步法的研究主要是针对初始构形为平面的板料成形。本文的研究目标则是建立一个应用范围更广、可计算一般的板管成形、可考虑弯曲效应的一步和多步正反向快速模拟系统OMSTEP。本文的主要研究内容和成果如下:
通常针对板料成形问题的一步和多步法在考虑弯曲效应时,将公式局限于初始构形为平面的一步反向计算,若将该公式应用于一般的板管成形过程,则会引入转动自由度,增加计算规模,并使一步和多步法的处理相对复杂。为此,本文引入BST壳单元描述变形。该单元没有转动自由度,膜变形的计算与传统一步法所使用的膜单元完全等价,曲率计算不限于初始构形是否为平面的条件,也不局限于反算,同时能够保持一步法公式的简洁性和计算效率。基于极值功原理,将全量本构关系应用于一步法,将由标量预测-回归映射方法得到的本构关系应用于多步法,推导建立了一种适用于一般板管成形的正反向快速模拟公式。
现有的各类初始猜测值生成方法都是针对板料成形问题的,其中的几何方法难以通用,其中基于计算机图形学理论的参数化方法也要求预先完成边界节点的映射后才能使用。因此,本文首先借助边界调整法将板料的边界映射到平面上,保持板料边界的形状特征,再将其与参数化方法结合,实现通用的板料初始猜测值生成方法。为型材弯曲和管材胀形提供合适的初始解,则是个新的课题,本文提出了两种方法,一种是简单有效的几何方法,通过展开型材和管材的扫掠线来实现网格映射,效率比较高,但没有很好的通用性;另一种是将参数化方法由平面拓展到圆柱坐标系中,将工件节点映射到截面形状复杂的型材表面,或者半径尺寸任意的圆柱面上,这种方法高效、通用。此外,还给出了一种思路简单的中间构形初始解生成方法,该方法与参数化方法结合,可高效地得到较精确的中间构形初始猜测值。
接触的处理是一步和多步法中的关键技术,对外力的施加、计算的收敛性和准确性有着重要的影响。但传统的滑动约束算法主要是针对板料的,无法适用于型材和管材。为此,本文提出了接触滑动约束算法。该算法通过接触搜索找到与工件节点最近的滑动约束面单元,通过罚函数法的方式引入法向刚度,由弹簧单元模拟所受到的工模具摩擦,保持节点只在滑动约束面(可以是截面形状封闭的复杂曲面)上运动,从而将滑动约束方法应用于型材和管材成形。此外,为了能够直观考察脱离接触面的缺陷,如起皱、截面的畸变等,本文对多步正向计算中的实际接触状态的模拟进行了一些尝试,引入LS-DYNA中的方法进行全局搜索,采用高效的内外侧算法进行局部搜索找到接触对,使用罚函数法计算实际的接触力,考察了规则化摩擦模型,并针对大穿透量问题,做了些设置,通过选取合适的参数使接触计算稳定。
对板料成形过程进行了一步和多步正反向模拟计算,检验了OMSTEP系统求解板料成形问题的可行性。其中一步反算高效易用,多步模拟则可以获得更接近实际状况的结果。算例表明采用滑动约束计算更容易收敛,而采用罚函数法处理接触,可以观察到脱离接触面而产生的成形缺陷。
将一步和多步正反向模拟推广应用于一般的管材和型材成形过程。进行了矩形管3点弯曲试验和复杂截面异型材的拉弯实验。通过矩形管弯曲试验模拟考察截面畸变问题,通过复杂截面异型材的拉弯实验模拟考察型材的壁厚变化和回弹情况。一步模拟所得到的截面畸变、壁厚变化结果与增量分析及实验结果非常接近。多步模拟由于中间构形的引入,计算结果较一步法有所改进,可以捕捉到更为细微的变化趋势,基于多步模拟结果的回弹计算也比基于一步模拟结果的回弹更接近实验结果。在对复杂截面异型材的模拟中,采用滑动约束,避免填充物与型材间的接触处理。在胀形计算中,实现了一步正反向计算的结合,通过反算为正算提供优化的管坯,而多步法也自然地与多工步的胀形过程相匹配。
Sheet, tube and profile formings take up a large proportion in the material forming, being widely used in the fields such as automobile, aerospace, aviation and shipping etc. Particularly, profile bending and tube hydroforming play an important role in the metal manufacturing to meet the needs of lightweight, reduction of energy consumption and cost. In the study of numerical simulations concerning such formings, the incremental analysis and the one- and multi- step simulation have complemented each other. Incremental analysis is a relatively accurate finite element computation method for sheet, tube and profile forming since the deformation history, contacts and frictions between blank and forming tools, and other factors influencing forming and product performance can be considered in the round, while the one- and multi-step approach is a kind of fast finite element computation method and can be used to inspect formability and possible forming defects, optimize blank shape without the information of tools and dies, or only with simplified tool surfaces.
However, most one- and multi-step approaches are only applied in the sheet metal forming with a flat blank. This paper is to achieve a more widely-used fast simulation system named OMSTEP, with which sheet, tube and profile forming proecesses can be generally simulated forward or inversely with bending effects being considered. The main research content is concluded as follows.
When the bending effects are considered in the traditional one-step approaches which are based on the sheet metal forming, the resulted formulation is limited in the one-step inverse simulation with flat initial configuration, not suited to the general forming processes of sheet, tube and profile. Therefore, the BST shell element is introduced here to describe deformation without sacrificing the efficientcy of computation and the simplicity of formulation. In the BST element, the membrane compuation results equal to those gained by traditional one-step membrane elements and the curvature is calculated without using rotational DOF, not limited either by the condition whether the initial blank is flat or by the inverse simulation. Then based on the extreme principle, total deformation theory adopted for one-step and the constitutive equations from scalar prediction-return mapping method adopted for multi-step, the basic fast FE inverse and forward formulation is deduced.
Traditional methods to get initial guess solutions are all proposed for the sheet metal forming, among which the geometrical methods are not generally suited while the parameterization method in computer graphics can only be used after mapping the edge of sheet onto plane. So the edge tweaking method, which is shape-preserved, is firstly adopted here to map the outer edge of sheet, and then combined with the parameterization method to get initial satisfactory mesh of sheet by solving linear equations. It is a new issue to get initial guess solutions for profile bending and tube hydroforming. Two mehods are presented in this dissertation. One is a simple geometrical method in which the mesh is mapped by developing the sweepling line (center line) of profile and the other is an effective and general-suited parameterization method in which the column coordinate system is used to map mesh. Besides, a simple effective method is put forward to get good initial guess solutions for mid-configures.
Traditional sliding constrait algorithm is mainly proposed for the sheet metal forming too, not suited to profile and tube forming. Therefore, a new contact sliding constraint method is presented, in which the nearest constraint surface element of a node is found by contact search, and then the node normal stiffness is calculated by the penalty method and the friction is computed by the spring element. This method avoids the problem of geometrical adjustment of coordiate in traditional sliding constraints and is suited to profile and tube forming. Some attempts are also made to employ the penalty method to treat real contacts between blank and tools for multi-step forward simulation. Effective inside-outside algorithm is utilized to search contact pairs, the regularized friction model is investigated and some parameters are set up to deal with the problem of big penetration.
Sheet metal forimg processes are simulated inversely and forward by the developed in-house one- and multi- step program OMSTEP. It is shown that the one-step inverse simulation is highly efficient and easy to use and the simulation results can be improved by the multi-step approach. Besides, the numerical examples show that the convergence can be more easily achived by the sliding constraint than by the penalty method. However, the wrinkling can be oberserved directly only when the penalty method is used to treat real contacts.
The applications of one- and multi- step approach are extended to general forming processes of profile and tube, which is hard for the traditional one- and multi- step approach based on the sheet metal forming. The experiment of three point bending of rectangular tube, in which the cross-sectional distortions are inspected, and the experiment of stretch bending of profile with a complicated cross-section, in which the variation of thickness and the springback are inspected, is conducted to inspect the suitability of OMSTEP system to the profile bending. The variation of wall thickness and cross-section distortions gained from the one-step simulation show good agreements with the incremental analyses and experimental results, but the detailed deformation tendency can only be achieved correctly from multi-step simulations since the mid-configurations are increased and the deformation history is considered. The springback values based on the results of multi-step simulation are also closer to the experimental results than those based on the one-step simulation. In the simulation of profile bending, the sliding constraint is adopted to avoid the contacts between the fillers and profile. In addition, the inverse simulation affords optimized tube blank for the forward simulation in the one step simulation of hydroforming while the multi-step approach matches with the multi-stage hydroforming.
引文
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