薄壁管数控弯曲成形过程失稳起皱的数值模拟研究
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摘要
薄壁管数控弯曲精确成形技术是管弯曲技术向先进塑性加工技术发展的必然趋势。然而这是一个多因素耦合交互作用下可能发生失稳起皱的复杂物理过程。特别是航空、航天高技术的发展要求弯管零件的壁更薄、口径更大、弯曲半径更小和成形精度更高，这使得对失稳起皱的预测和控制成为薄壁管精确弯曲成形技术研究与发展迫切需要解决的难题。因此本文采用有限元模拟技术与起皱能量预测准则相结合的方法，实现对薄壁管数控弯曲过程起皱缺陷的分析和预测，对提高薄壁弯管制品的质量，缩短产品开发周期，降低成本具有重要意义。
本文系统深入地研究了薄壁管数控弯曲成形过程三维刚塑性有限元模拟分析中的关键技术问题，提出了有效的算法和处理方法：提出了相对自由度与绝对自由度相结合的壳单元，使得速度边界条件的处理可通过简单、有效的置“1”法或置大数法来实现；采用了三次因式法确定收敛因子，不仅提高了有限元求解过程的计算效率，同时也保证了有限元迭代过程的收敛性。
本文提出了描述薄壁管弯曲过程中失稳起皱波形的数学模型；进而基于薄壳小挠度弯曲理论和最小能量原理建立了预测起皱的能量准则；将预测准则与有限元模拟系统有机结合，可实现对起皱的数值预测。
本文自主开发了薄壁管数控弯曲成形过程的起皱数值预测系统TBWS-3D，包括模具型腔曲面的几何描述、管坯初始网格的自动划分、动态边界条件的处理和摩擦问题的处理、刚塑性有限元模拟分析、变形体几何构形与场变量的显示以及起皱预测等功能。该系统不仅可以实现对成形过程的数值模拟分析，而且可用于对成形过程中失稳起皱现象的数值预测。
采用所开发的薄壁管数控弯曲成形过程起皱数值预测系统深入研究了铝合金和不锈钢薄壁管数控弯曲成形过程的变形特点，获得了以下的主要结果：(1)两种管坯材料的整体变形、等效应变场分布、塑性变形区分布、塑性变形能与
西北工业大学博士学位论文
起皱能比值随弯曲角度的变化规律及大小基本一致;而两者切向应力场分布随
弯曲角度的变化规律一致，只是不锈钢管所受的切向应力值大于铝合金管所受
的切向应力。(2)管数控弯曲成形过程中应力和应变中性层的内移现象不显著。
(3)在成形的初始阶段管坯所受的最大切向压应力不断增加;但当最大切向压应
力超过一定值后，管坯进入稳定变形阶段，最大切向压应力只在很小的范围内
波动。(4)在变形初期管坯塑性变形区不断扩展;管坯进入稳定变形阶段以后，
各变形阶段塑性区形状及尺寸基本保持一致，而已变形部分不断发生卸载。(5)
塑性变形能与起皱能的比值随着管弯曲成形过程的进行是不断波动变化的，但
存在一个最大值。
应用所开发的起皱预测系统，对由失稳起皱所决定的管坯最小弯曲半径一成
形极限进行了数值模拟研究，揭示了不同成形参数对管坯最小弯曲半径的影响
规律:(1)当芯棒伸出长度足够时，弯曲半径对管坯失稳起皱的影响不大;而
当芯棒长度不足时，随着弯曲半径的减小管坯发生起皱的趋势增加。芯棒伸出
量的增加可提高管坯基于失稳起皱的成形极限;当芯棒伸出量足够时，即使得
管坯弯曲时的压缩塑性变形区完全受到刚性芯棒的约束，其它成形参数不影响
管坯的最小弯曲半径。(2)随着管径的增加，由起皱所决定的管坯最小弯曲半
径成线性增长。(3)加工速度的变化对管坯成形极限的影响不大。(4)随着硬
化指数值由小变大，管坯的最小弯曲半径先减后增。(5)应力强度系数的变化
不影响管坯最小弯曲半径。(6)摩擦系数的变化将使得管坯最小弯曲半径在一
定的范围内波动。
Precision forming process of thin-walled tube NC bending is showing an inexorable tendency to improve and develop tube-bending process into advanced plastic forming technology. However, it is a complex process with coupling; interactive multi-factor effects and the possibility of wrinkling initiation. Particularly, the development of aviation and aerospace requires bent parts much thinner in wall-thickness, larger in tube radius, smaller in bending radius and more precise in the forming process. The prediction and control of wrinkling have thus become a difficult and key problem urgent to be resolved in the research and development of the process. Consequently, a numerical method for predicting the wrinkling onset during the tube bending process, which combines the rigid-plastic FEM with energy criteria, is proposed in the paper. The method can predict the wrinkling phenomena quantitatively, thus achieving optimal processing parameters with less needed experiments. The main achievements of the project are as following:
According to the practical NC tube bending process, a reasonable FEM model has been set up and the key techniques of 3D rigid-plastic FEM have been studied in the paper. A shell element with relative and absolute degree of freedom is put forward so that the velocity boundary conditions can be considered by setting "1" or large number in the finite element equations; cubic factor method is applied to calculate the deceleration factor in the FEM iteration which can increase the computation efficiency while ensuring the convergence.
Mathematic description of the winkling wave initiated on the compressed wall of tube during the bending process is established. Prediction criteria for the wrinkling onset is derived based on the theory of thin-walled shell bending and minimum
energy principal; then how to combine the criteria with the FEM simulation system to make the numerical prediction of wrinkling into reality is also resolved in the paper.
A numerical wrinkling prediction system TBWS-3D is developed for the NC thin-walled bending process. It includes modules for the description of die cavity, auto-meshing of tube being, treatments for dynamic boundary condition and friction condition, rigid-plastic FEM analysis, visualization of deformed tube and field variables and prediction of the wrinkling initial. The system can be used to both predict the wrinkling phenomena and analyze the bending process.
The analysis of the bending process of aluminum and stainless tube has been carried out by the numerical system and the simulation results include: (1) the deformation, distribution of equivalent strain and plastic zone and variation of the ration of plastic forming energy and wrinkling energy of aluminum tube are same as those of stainless tube; the variation of stress distribution along the bending direction of these two tubes with bending angle is identical even though the stress of stainless tube is larger than that of aluminum tube. (2) the internal shift of the stress and strain neutrolayer is not noticeable for the bending process is a rotate bending process with booster. (3) the stress along the bending direction increases at the initial forming stage; the forming process comes into a stable process after the maximum compression stress along the bending direction exceeds some value and the stress just varies in a small scale. (4) the plastic forming area extends at the initial forming stage, while the area remains the same at the stable forming stage and the bended part of the tube being unloads continuously. (5) the ratio of plastic forming energy and wrinkling energy of the compressed part of the tube fluctuates and has a maximum value during the forming process.
The influence of processing parameters on the forming limit determined by wrinkling is also researched with the above numerical prediction system. The results are as the following: (1) the bending radius has no effect on the wrinkling if the extension length of mandrel is enough to cover the plastic forming zone, but the te
本文系统深入地研究了薄壁管数控弯曲成形过程三维刚塑性有限元模拟分析中的关键技术问题，提出了有效的算法和处理方法：提出了相对自由度与绝对自由度相结合的壳单元，使得速度边界条件的处理可通过简单、有效的置“1”法或置大数法来实现；采用了三次因式法确定收敛因子，不仅提高了有限元求解过程的计算效率，同时也保证了有限元迭代过程的收敛性。
本文提出了描述薄壁管弯曲过程中失稳起皱波形的数学模型；进而基于薄壳小挠度弯曲理论和最小能量原理建立了预测起皱的能量准则；将预测准则与有限元模拟系统有机结合，可实现对起皱的数值预测。
本文自主开发了薄壁管数控弯曲成形过程的起皱数值预测系统TBWS-3D，包括模具型腔曲面的几何描述、管坯初始网格的自动划分、动态边界条件的处理和摩擦问题的处理、刚塑性有限元模拟分析、变形体几何构形与场变量的显示以及起皱预测等功能。该系统不仅可以实现对成形过程的数值模拟分析，而且可用于对成形过程中失稳起皱现象的数值预测。
采用所开发的薄壁管数控弯曲成形过程起皱数值预测系统深入研究了铝合金和不锈钢薄壁管数控弯曲成形过程的变形特点，获得了以下的主要结果：(1)两种管坯材料的整体变形、等效应变场分布、塑性变形区分布、塑性变形能与
西北工业大学博士学位论文
起皱能比值随弯曲角度的变化规律及大小基本一致;而两者切向应力场分布随
弯曲角度的变化规律一致，只是不锈钢管所受的切向应力值大于铝合金管所受
的切向应力。(2)管数控弯曲成形过程中应力和应变中性层的内移现象不显著。
(3)在成形的初始阶段管坯所受的最大切向压应力不断增加;但当最大切向压应
力超过一定值后，管坯进入稳定变形阶段，最大切向压应力只在很小的范围内
波动。(4)在变形初期管坯塑性变形区不断扩展;管坯进入稳定变形阶段以后，
各变形阶段塑性区形状及尺寸基本保持一致，而已变形部分不断发生卸载。(5)
塑性变形能与起皱能的比值随着管弯曲成形过程的进行是不断波动变化的，但
存在一个最大值。
应用所开发的起皱预测系统，对由失稳起皱所决定的管坯最小弯曲半径一成
形极限进行了数值模拟研究，揭示了不同成形参数对管坯最小弯曲半径的影响
规律:(1)当芯棒伸出长度足够时，弯曲半径对管坯失稳起皱的影响不大;而
当芯棒长度不足时，随着弯曲半径的减小管坯发生起皱的趋势增加。芯棒伸出
量的增加可提高管坯基于失稳起皱的成形极限;当芯棒伸出量足够时，即使得
管坯弯曲时的压缩塑性变形区完全受到刚性芯棒的约束，其它成形参数不影响
管坯的最小弯曲半径。(2)随着管径的增加，由起皱所决定的管坯最小弯曲半
径成线性增长。(3)加工速度的变化对管坯成形极限的影响不大。(4)随着硬
化指数值由小变大，管坯的最小弯曲半径先减后增。(5)应力强度系数的变化
不影响管坯最小弯曲半径。(6)摩擦系数的变化将使得管坯最小弯曲半径在一
定的范围内波动。
Precision forming process of thin-walled tube NC bending is showing an inexorable tendency to improve and develop tube-bending process into advanced plastic forming technology. However, it is a complex process with coupling; interactive multi-factor effects and the possibility of wrinkling initiation. Particularly, the development of aviation and aerospace requires bent parts much thinner in wall-thickness, larger in tube radius, smaller in bending radius and more precise in the forming process. The prediction and control of wrinkling have thus become a difficult and key problem urgent to be resolved in the research and development of the process. Consequently, a numerical method for predicting the wrinkling onset during the tube bending process, which combines the rigid-plastic FEM with energy criteria, is proposed in the paper. The method can predict the wrinkling phenomena quantitatively, thus achieving optimal processing parameters with less needed experiments. The main achievements of the project are as following:
According to the practical NC tube bending process, a reasonable FEM model has been set up and the key techniques of 3D rigid-plastic FEM have been studied in the paper. A shell element with relative and absolute degree of freedom is put forward so that the velocity boundary conditions can be considered by setting "1" or large number in the finite element equations; cubic factor method is applied to calculate the deceleration factor in the FEM iteration which can increase the computation efficiency while ensuring the convergence.
Mathematic description of the winkling wave initiated on the compressed wall of tube during the bending process is established. Prediction criteria for the wrinkling onset is derived based on the theory of thin-walled shell bending and minimum
energy principal; then how to combine the criteria with the FEM simulation system to make the numerical prediction of wrinkling into reality is also resolved in the paper.
A numerical wrinkling prediction system TBWS-3D is developed for the NC thin-walled bending process. It includes modules for the description of die cavity, auto-meshing of tube being, treatments for dynamic boundary condition and friction condition, rigid-plastic FEM analysis, visualization of deformed tube and field variables and prediction of the wrinkling initial. The system can be used to both predict the wrinkling phenomena and analyze the bending process.
The analysis of the bending process of aluminum and stainless tube has been carried out by the numerical system and the simulation results include: (1) the deformation, distribution of equivalent strain and plastic zone and variation of the ration of plastic forming energy and wrinkling energy of aluminum tube are same as those of stainless tube; the variation of stress distribution along the bending direction of these two tubes with bending angle is identical even though the stress of stainless tube is larger than that of aluminum tube. (2) the internal shift of the stress and strain neutrolayer is not noticeable for the bending process is a rotate bending process with booster. (3) the stress along the bending direction increases at the initial forming stage; the forming process comes into a stable process after the maximum compression stress along the bending direction exceeds some value and the stress just varies in a small scale. (4) the plastic forming area extends at the initial forming stage, while the area remains the same at the stable forming stage and the bended part of the tube being unloads continuously. (5) the ratio of plastic forming energy and wrinkling energy of the compressed part of the tube fluctuates and has a maximum value during the forming process.
The influence of processing parameters on the forming limit determined by wrinkling is also researched with the above numerical prediction system. The results are as the following: (1) the bending radius has no effect on the wrinkling if the extension length of mandrel is enough to cover the plastic forming zone, but the te
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