增量体积成形数值模拟技术及其在多道次拔长工艺设计中的应用
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摘要
为了实现对锻件产品精确“控形”和“控性”的目标,需要对成形工艺方案进行合理设计,并对成形产品质量进行准确预报。近几十年来,以有限元法为代表的数值模拟技术和相关计算机软硬件技术都取得了显著进步,从而为实现这一目标带来了巨大机遇。然而,目前的数值模拟技术和计算机软硬件技术还不能完全满足实现精确“控形”和“控性”的要求。例如对于许多增量体积成形工艺,由于其工序很多而且耗时很长,导致对工艺方案进行完整数值模拟的成本很高或者并不现实,因而难以采用数值模拟对工艺方案进行完整设计。因此,如何提高数值模拟对于增量体积成形工艺分析的适用性,以及如何将数值模拟合理地应用于成形工艺方案的设计,仍然是具有重要科学与工程价值的问题。本文从金属体积成形通用数值模拟技术、增量体积成形专用数值模拟技术、多道次平砧拔长工艺设计等几个方面进行了研究和探讨,对现有技术进行了改进并提出了一些新技术。
提出了针对增量体积成形的预指定刚性区自由度缩聚原理,并改进了刚粘塑性有限元的非线性迭代算法与待定刚性区自动判别算法。针对增量体积成形的瞬时局部变形特点,根据刚性区材料对总能量泛函的贡献为零以及刚性区材料仅发生刚体运动,首次推导了预指定刚性区自由度缩聚原理——泛函积分区域缩减原理与刚性区节点自由度凝聚原理,从而降低分析系统的自由度规模。改进了非线性刚粘塑性有限元方程组的直接迭代解法与牛顿-拉夫森迭代解法,以提高迭代收敛的稳健性。改进了待定刚性区的自动判别算法,利用变形历史信息来不断更新当前参考平均等效应变率,从而可以适应不同变形条件。
解决了增量体积成形高效稳健有限元模拟的关键技术,包括采用两套网格描述的预指定刚性区自由度缩聚技术、三维动态接触边界搜索处理技术以及离散型流动应力数据插值技术。针对增量体积成形中变形发生在局部区域而传热发生在全部区域的特点,提出了采用“全网格”和“子网格”的描述方法解决分析系统的计算量问题,其中“全网格”用于计算整体温度场,“子网格”用于计算变形区速度场。通过预指定刚性区自由度缩聚技术实现子网格生成以及两套网格间运动映射,从而构造了热力耦合问题的高效分析方法。提出了同时采用“穿透”判据和“靠近”判据的三维动态接触边界搜索算法以及考虑特殊“穿透”情形的接触节点调整算法,还提出了离散型流动应力数据的两种插值方式——简单分段插值和对数分段插值。
引入基于栅格法中“表面零厚度单元层”概念,对非结构化与分层六面体网格分别提出了一种自动重划分方法,并改进了新旧网格间数据传递方式。对于非结构化六面体网格,提出了通过在旧网格空间域上直接覆盖表面零厚度六面体单元层以生成新网格的方法。针对拔长、扩孔、径向锻造等一类增量体积成形工艺,提出了一种分层六面体网格模型,通过四边形单元层插入、表面零厚度六面体单元层覆盖以及后续的网格平滑处理与边界拟合等步骤来实现网格质量优化。在将旧网格单元物理量传递至旧网格节点时,分别采用内部边外插和单元对角外插获得不同类型边界节点的传递值。在计算新网格节点在旧网格单元中局部坐标时,采用粒子群优化算法以提高算法的求解精度和稳健性。算例结果表明,由所提出的非结构化与分层六面体网格重划分方法生成的新网格具有较好质量,且新旧网格间数据传递具有较高精度。
基于上述原理和技术,开发了具有自主知识版权的增量体积成形有限元模拟系统XFORM,并通过数值算例和物理实验对该系统的有效性进行了验证。算例和实验的结果表明:对于一般金属体积成形过程模拟,XFORM与商业有限元软件DEFORM的计算精度相当,且XFORM的迭代收敛速度具有一定优势;将所提出的预指定刚性区自由度缩聚技术应用于某正八角形截面坯料多工步拔长的有限元模拟后,计算效率提高了约62%,且计算精度并无明显损失,从而验证了该技术对于增量体积成形过程模拟的有效性。
基于解析方法与有限元模拟,建立了一套多道次平砧拔长的工艺设计流程。首先,提出了一种基于Markov变分原理的平砧拔长压下过程解析方法。在该方法中,考虑摩擦及刚性端的影响建立了一组变形区瞬态动可容速度场,并采用增量法对压下过程进行分析。在每个增量步中,利用Markov变分原理对速度场进行求解,并将拉格朗日网格应用于数值积分和变形区构形更新。其次,以上述解析法为基础提出了一个多道次平砧拔长的工艺规划算法,可以快速生成满足成形尺寸要求的工艺方案集。然后,以XFORM为核心分析模块,开发了多道次平砧拔长的连续有限元模拟平台,并且包含了预指定刚性区自由度缩聚技术与分层六面体网格自动重划分技术。此外,从工艺角度对拔长过程中压机与操作机的动作进行了分析,并提出了一种描述压机与操作机联动的代码,以用于拔长过程的精确控制与自动化。利用上述工艺规划算法和连续有限元模拟平台,对某35吨特种钢模块的一个拔长工序进行了工艺设计,并生成了压机与操作机联动代码,从而为实际的锻造生产提供了科学的指导。
In order to precisely control geometry and property of forging products, it is necessary to rationally design process schedules and accurately predict the forging performance. Great opportunities for this goal have arisen due to achievements in numerical simulation technology and computer technology over the recent decades. However, precise control of product geometry and property demands more than what the state-of-the-art can provide. For example, some incremental bulk forming processes are composed of many operations. Complete numerical simulations of these processes are too costly or unpractical, which makes it hard to fully design process schedules with numerical simulations. Therefore the problems, including how to improve applicability of numerical simulation for analysis of incremental bulk forming processes and how to rationally use numerical simulation in design of process schedules, have important scientific and engineering values. This paper researches on general techniques for numerical simulation of bulk metal forming, special techniques for numerical simulation of incremental bulk forming and process design of multi-pass flat-tool stretching, which yields some technical improvements and some new techniques as follows.
The principles for reduction of pre-assigned rigid zone DOFs are presented, and the algorithms for solving nonlinear rigid-viscoplastic finite-element equations and for identifying unknown rigid zone are improved. In order to reduce the system DOFs in analysis of incremental bulk forming, two principles are derived for the first time: the principle of reduction of functional integral region based on the condition that the contribution of the rigid zone material to the total energy functional is zero, and the principle of condensation of rigid-zone nodal DOFs based on the condition that the motion of the rigid zone material is of rigid body type. In order to enhance iteration robustness, the direct iteration algorithm and the Newton-Raphson iteration algorithm are both improved. An approach is proposed for automatic identification of unknown rigid zone. It uses the information of deformation history to update the current reference average effective strain rate and is adaptive to different deformation conditions.
Some key techniques for efficient and robust simulation of incremental bulk forming are discussed. In incremental bulk forming, deformation occurs in the local region while heat transfer occurs in the whole region. According this characteristic, two mesh systems are adopted to improve computation efficiency for the thermo-mechanical coupled analysis of incremental bulk forming. The whole mesh is used for temperature field computation and the sub mesh is used for velocity field computation. A technique of reduction of pre-assigned rigid zone DOFs is proposed for generation of the sub mesh and for mapping of the two mesh systems. A“penetration”criterion and a“near”criterion are used for search of dynamic contact boundaries, and a special“penetration”case is considered in the algorithm for adjustment of the contact boundary nodes. Two interpolation approaches, which are linear piecewise interpolation and logarithmic piecewise interpolation, are proposed for handling discrete flow stress data.
By introducing the concept of zero-thickness surface element layer from the grid-based method, two methods are respectively proposed for automatic regeneration of unstructured hexahedral mesh and layered hexahedral mesh. In regeneration of unstructured hexahedral mesh, a new mesh is produced by surface coverage of the old mesh with zero-thickness element layer(s). For a class of incremental bulk forming processes such as stretching, saddle forging and radial forging, a layered hexahedral mesh model is proposed. The new mesh is generated and improved by insertion of quadrilateral element layer(s), surface coverage of the old mesh with zero-thickness element layer(s) and subsequent mesh smoothing and boundary fitting. In data transfer from the old mesh to the new mesh, extrapolation along the inside edge and extrapolation along the element diagonal are respectively used for two types of boundary nodes. When calculating local coordinates of the new nodes in the old elements, a particle swarm optimization algorithm is adopted to improve computation efficiency and robustness. The results of two examples show that the new meshes produced by the proposed methods have good quality and the data transfer procedure leads to small accuracy loss.
On the basis of these principles and techniques, the software XFORM is developed with the capability of finite element simulation of incremental bulk forming. The effectiveness of the software is validated by some numerical examples and a physical experiment. The results show that: (i) for finite element simulation of general bulk metal forming, the accuracy of XFORM are close to that of the commercial finite element software DEFORM and, XFORM has advantage on convergence speed of nonlinear iteration but lack on bandwidth optimization; (ii) in the finite element simulation of a stretching process, the efficiency is improved by about 62% with no significant loss of accuracy after using the technique of reduction of pre-assigned rigid zone DOFs and this result validates effectiveness of this technique for finite element simulation of incremental bulk forming.
By using an analytical method and finite element simulation, process design of multi-pass flat-tool stretching is discussed. Firstly, an analytical method is presented for flat-tool stretching based on the Markov variational principle. In this method, a set of transient kinematically admissible velocity fields are established with considering the influence of friction and rigid ends, and then the reduction in a stretching bite is analyzed with incremental method. In each incremental step, the Markov variational principle is used for approximate velocity field solution, and a Lagrangian mesh is used for numerical integration and configuration update. Secondly, with the analytical method, a fast process planning algorithm is developed for multi-pass flat-tool stretching. This algorithm can produce feasible pass schedules which satisfy the requirement of final dimensions. Thirdly, by using XFORM as the analysis core, a continuous finite element simulation platform is developed for multi-pass flat-tool stretching. This platform includes the rigid zone DOFs reduction technique and the layered hexahedral mesh regeneration technique. Fourthly, the operations of press and manipulator during stretching are analyzed from the process schedule point of view, and then a type of code is proposed for describing the press-manipulator linkage operations. This type of code can be used for precise control and automation of stretching process. With the process planning algorithm and the finite element simulation platform, a stretching process for production of an alloy block is designed and a code for press-manipulator linkage operations is generated. The results show the feasibility of using these techniques in industry.
提出了针对增量体积成形的预指定刚性区自由度缩聚原理,并改进了刚粘塑性有限元的非线性迭代算法与待定刚性区自动判别算法。针对增量体积成形的瞬时局部变形特点,根据刚性区材料对总能量泛函的贡献为零以及刚性区材料仅发生刚体运动,首次推导了预指定刚性区自由度缩聚原理——泛函积分区域缩减原理与刚性区节点自由度凝聚原理,从而降低分析系统的自由度规模。改进了非线性刚粘塑性有限元方程组的直接迭代解法与牛顿-拉夫森迭代解法,以提高迭代收敛的稳健性。改进了待定刚性区的自动判别算法,利用变形历史信息来不断更新当前参考平均等效应变率,从而可以适应不同变形条件。
解决了增量体积成形高效稳健有限元模拟的关键技术,包括采用两套网格描述的预指定刚性区自由度缩聚技术、三维动态接触边界搜索处理技术以及离散型流动应力数据插值技术。针对增量体积成形中变形发生在局部区域而传热发生在全部区域的特点,提出了采用“全网格”和“子网格”的描述方法解决分析系统的计算量问题,其中“全网格”用于计算整体温度场,“子网格”用于计算变形区速度场。通过预指定刚性区自由度缩聚技术实现子网格生成以及两套网格间运动映射,从而构造了热力耦合问题的高效分析方法。提出了同时采用“穿透”判据和“靠近”判据的三维动态接触边界搜索算法以及考虑特殊“穿透”情形的接触节点调整算法,还提出了离散型流动应力数据的两种插值方式——简单分段插值和对数分段插值。
引入基于栅格法中“表面零厚度单元层”概念,对非结构化与分层六面体网格分别提出了一种自动重划分方法,并改进了新旧网格间数据传递方式。对于非结构化六面体网格,提出了通过在旧网格空间域上直接覆盖表面零厚度六面体单元层以生成新网格的方法。针对拔长、扩孔、径向锻造等一类增量体积成形工艺,提出了一种分层六面体网格模型,通过四边形单元层插入、表面零厚度六面体单元层覆盖以及后续的网格平滑处理与边界拟合等步骤来实现网格质量优化。在将旧网格单元物理量传递至旧网格节点时,分别采用内部边外插和单元对角外插获得不同类型边界节点的传递值。在计算新网格节点在旧网格单元中局部坐标时,采用粒子群优化算法以提高算法的求解精度和稳健性。算例结果表明,由所提出的非结构化与分层六面体网格重划分方法生成的新网格具有较好质量,且新旧网格间数据传递具有较高精度。
基于上述原理和技术,开发了具有自主知识版权的增量体积成形有限元模拟系统XFORM,并通过数值算例和物理实验对该系统的有效性进行了验证。算例和实验的结果表明:对于一般金属体积成形过程模拟,XFORM与商业有限元软件DEFORM的计算精度相当,且XFORM的迭代收敛速度具有一定优势;将所提出的预指定刚性区自由度缩聚技术应用于某正八角形截面坯料多工步拔长的有限元模拟后,计算效率提高了约62%,且计算精度并无明显损失,从而验证了该技术对于增量体积成形过程模拟的有效性。
基于解析方法与有限元模拟,建立了一套多道次平砧拔长的工艺设计流程。首先,提出了一种基于Markov变分原理的平砧拔长压下过程解析方法。在该方法中,考虑摩擦及刚性端的影响建立了一组变形区瞬态动可容速度场,并采用增量法对压下过程进行分析。在每个增量步中,利用Markov变分原理对速度场进行求解,并将拉格朗日网格应用于数值积分和变形区构形更新。其次,以上述解析法为基础提出了一个多道次平砧拔长的工艺规划算法,可以快速生成满足成形尺寸要求的工艺方案集。然后,以XFORM为核心分析模块,开发了多道次平砧拔长的连续有限元模拟平台,并且包含了预指定刚性区自由度缩聚技术与分层六面体网格自动重划分技术。此外,从工艺角度对拔长过程中压机与操作机的动作进行了分析,并提出了一种描述压机与操作机联动的代码,以用于拔长过程的精确控制与自动化。利用上述工艺规划算法和连续有限元模拟平台,对某35吨特种钢模块的一个拔长工序进行了工艺设计,并生成了压机与操作机联动代码,从而为实际的锻造生产提供了科学的指导。
In order to precisely control geometry and property of forging products, it is necessary to rationally design process schedules and accurately predict the forging performance. Great opportunities for this goal have arisen due to achievements in numerical simulation technology and computer technology over the recent decades. However, precise control of product geometry and property demands more than what the state-of-the-art can provide. For example, some incremental bulk forming processes are composed of many operations. Complete numerical simulations of these processes are too costly or unpractical, which makes it hard to fully design process schedules with numerical simulations. Therefore the problems, including how to improve applicability of numerical simulation for analysis of incremental bulk forming processes and how to rationally use numerical simulation in design of process schedules, have important scientific and engineering values. This paper researches on general techniques for numerical simulation of bulk metal forming, special techniques for numerical simulation of incremental bulk forming and process design of multi-pass flat-tool stretching, which yields some technical improvements and some new techniques as follows.
The principles for reduction of pre-assigned rigid zone DOFs are presented, and the algorithms for solving nonlinear rigid-viscoplastic finite-element equations and for identifying unknown rigid zone are improved. In order to reduce the system DOFs in analysis of incremental bulk forming, two principles are derived for the first time: the principle of reduction of functional integral region based on the condition that the contribution of the rigid zone material to the total energy functional is zero, and the principle of condensation of rigid-zone nodal DOFs based on the condition that the motion of the rigid zone material is of rigid body type. In order to enhance iteration robustness, the direct iteration algorithm and the Newton-Raphson iteration algorithm are both improved. An approach is proposed for automatic identification of unknown rigid zone. It uses the information of deformation history to update the current reference average effective strain rate and is adaptive to different deformation conditions.
Some key techniques for efficient and robust simulation of incremental bulk forming are discussed. In incremental bulk forming, deformation occurs in the local region while heat transfer occurs in the whole region. According this characteristic, two mesh systems are adopted to improve computation efficiency for the thermo-mechanical coupled analysis of incremental bulk forming. The whole mesh is used for temperature field computation and the sub mesh is used for velocity field computation. A technique of reduction of pre-assigned rigid zone DOFs is proposed for generation of the sub mesh and for mapping of the two mesh systems. A“penetration”criterion and a“near”criterion are used for search of dynamic contact boundaries, and a special“penetration”case is considered in the algorithm for adjustment of the contact boundary nodes. Two interpolation approaches, which are linear piecewise interpolation and logarithmic piecewise interpolation, are proposed for handling discrete flow stress data.
By introducing the concept of zero-thickness surface element layer from the grid-based method, two methods are respectively proposed for automatic regeneration of unstructured hexahedral mesh and layered hexahedral mesh. In regeneration of unstructured hexahedral mesh, a new mesh is produced by surface coverage of the old mesh with zero-thickness element layer(s). For a class of incremental bulk forming processes such as stretching, saddle forging and radial forging, a layered hexahedral mesh model is proposed. The new mesh is generated and improved by insertion of quadrilateral element layer(s), surface coverage of the old mesh with zero-thickness element layer(s) and subsequent mesh smoothing and boundary fitting. In data transfer from the old mesh to the new mesh, extrapolation along the inside edge and extrapolation along the element diagonal are respectively used for two types of boundary nodes. When calculating local coordinates of the new nodes in the old elements, a particle swarm optimization algorithm is adopted to improve computation efficiency and robustness. The results of two examples show that the new meshes produced by the proposed methods have good quality and the data transfer procedure leads to small accuracy loss.
On the basis of these principles and techniques, the software XFORM is developed with the capability of finite element simulation of incremental bulk forming. The effectiveness of the software is validated by some numerical examples and a physical experiment. The results show that: (i) for finite element simulation of general bulk metal forming, the accuracy of XFORM are close to that of the commercial finite element software DEFORM and, XFORM has advantage on convergence speed of nonlinear iteration but lack on bandwidth optimization; (ii) in the finite element simulation of a stretching process, the efficiency is improved by about 62% with no significant loss of accuracy after using the technique of reduction of pre-assigned rigid zone DOFs and this result validates effectiveness of this technique for finite element simulation of incremental bulk forming.
By using an analytical method and finite element simulation, process design of multi-pass flat-tool stretching is discussed. Firstly, an analytical method is presented for flat-tool stretching based on the Markov variational principle. In this method, a set of transient kinematically admissible velocity fields are established with considering the influence of friction and rigid ends, and then the reduction in a stretching bite is analyzed with incremental method. In each incremental step, the Markov variational principle is used for approximate velocity field solution, and a Lagrangian mesh is used for numerical integration and configuration update. Secondly, with the analytical method, a fast process planning algorithm is developed for multi-pass flat-tool stretching. This algorithm can produce feasible pass schedules which satisfy the requirement of final dimensions. Thirdly, by using XFORM as the analysis core, a continuous finite element simulation platform is developed for multi-pass flat-tool stretching. This platform includes the rigid zone DOFs reduction technique and the layered hexahedral mesh regeneration technique. Fourthly, the operations of press and manipulator during stretching are analyzed from the process schedule point of view, and then a type of code is proposed for describing the press-manipulator linkage operations. This type of code can be used for precise control and automation of stretching process. With the process planning algorithm and the finite element simulation platform, a stretching process for production of an alloy block is designed and a code for press-manipulator linkage operations is generated. The results show the feasibility of using these techniques in industry.
引文
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