薄壁管数控弯曲成形过程失稳起皱及成形极限的研究
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摘要
薄壁管数控弯曲精密成形技术是管弯曲成形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易发生失稳起皱的复杂非稳态物理过程。特别对于大口径、薄壁管小半径弯曲成形过程，失稳起皱成为稳定成形的瓶颈问题。因此失稳起皱及成形极限是这一先进加工技术研究与发展中迫切需要解决的关键问题。为此，本文采用有限元数值模拟和理论解析及实验研究相结合的方法，对该过程中的失稳起皱及成形极限进行了深入系统的研究，取得了如下成果：
(1)改进了薄壁管数控弯曲起皱数值预测系统TBWS-3D：修正了薄壁管数控弯曲成形失稳起皱预测模型，使预测结果更加准确：改善了绝对-相对自由度壳单元边界条件的处理方法，使有限元模拟结果更符合实际；针对不同情况，丰富了弯曲过程中摩擦和压块侧推速度等边界条件的处理方法，使得系统深入地研究成形参数对失稳起皱的影响成为可能；将面向对象技术引入有限元程序的编制，基于VC++平台开发了有限元起皱预测系统TBWS-3D，从而可以方便地嵌入起皱预测等成形质量控制模块，并易于实现上述提出的改进算法。
(2)采用改进的起皱数值预测系统TBWS-3D，系统深入地研究并揭示了薄壁管数控弯曲成形过程中成形参数对失稳起皱的影响规律。从而为成形过程参数优化及成形极限的确定奠定坚实的理论基础。
(3)摩擦和模具间隙对失稳起皱的影响规律表明：随着管坯与防皱块及管坯与芯棒间摩擦系数的增大，起皱因子有减小，有利于防止起皱的发生；随着管坯与弯曲模及管坯与压块间摩擦系数的提高，起皱因子增大，但幅度并不大，对管坯起皱的影响较小；随着管坯与防皱块间隙的增大，起皱因子逐渐增大；当模具间隙大于0.5mm时，失稳起皱趋势急剧增大。即管坯与防皱块间隙对管坯失稳起皱的影响很大。
(4)影响失稳起皱的主要因素有：相对管径、弯曲半径、硬化指数、芯棒的伸出长度、管坯与防皱块间摩擦、管坯与芯棒间摩擦、管坯与防皱块间隙等。基于虚拟正交试验，获得成形参数对失稳起皱影响的显著性大小依次为：相对管径、弯曲半径、硬化指数、管坯与防皱块间隙、管坯与防皱块间摩擦、管坯与
西北工业大学硕士学位论文
芯棒间摩擦、管材与弯曲模摩擦等。
(5)结合薄壁管数控弯曲过程的成形特点，定义了基于失稳起皱的薄壁管数
控弯曲成形极限的概念;基于起皱预测系统TBWS一3D，提出了成形极限的搜索
算法，得到了不同工艺参数下的成形极限，建立了初步的成形极限库:通过成
形参数对失稳起皱影响规律的研究，获得了提高成形极限的方法;在此基础上
提出了基于成形极限与数值模拟的参数确定与优化方案，使薄壁管数控弯曲过
程成形的参数快速确定与优化成为可能。最后对今后的进一步研究方向进行了
探讨。
本研究对提高薄壁弯管制品的质量、缩短产品开发周期、降低生产成本、
充分发挥数控弯管设备的优势，从而实现薄壁管数控弯曲精密成形具有重要意
义，同时也丰富了薄壁件塑性成形失稳起皱理论。
NC precision bending process of thin-walled tube is showing an inevitable tendency to improve and develop tube bending process into advanced plastic forming technology. However, it is a complex astable process with coupling interactive multi-factor effects and wrinkling phenomenon as a compress instability often occurring , when the process parameters are inappropriate, especially for tubes with large diameter and thin wall-thickness. Thus, the wrinkling and forming limit have become one difficult and key problem urgently to be resolved in the R&D of the process. In this dissertation, a systematical and thorough investigation on the wrinkling and the forming limit of the process has been carried out by using rigid-plastic FEM simulation combining with analytical and experiment methods. The main achievements of the project made are as following:
(1) Some of the key techniques related to the 3D rigid-plastic FEM simulation and wrinkling prediction of thin-walled tube NC bending process have been studied and improved methods and algorithms have been proposed: The instability predicting model has been improved which make prediction results more precise. Shell element with absolute-relative degree of freedom and corresponding setting method of velocity boundary conditions make the simulation results more efficiently and more accurately. Frictions on four areas in the forming process and side pushing velocity have been added in to the finite element equations, which makes FEM model more correspond the reality. Based on OOP ( Object-Oriented Programming ) theory, one numerical wrinkling prediction system TBWS-3D for visual NC Tube Bending have been reconstructed successfully with VC++. The validity of system has been verified by experimentation and comparison with data in the literature.
(2) By using improved wrinkling system TBWS-3D, a systematical and thorough investigation into influence of forming parameters on wrinkling onset has been carried out and influence laws are obtained, which may be helpful to the parameters design and determination of forming limit.
(3) Influence law of friction factor and clearance between tube and die on wrinkling initiation is obtained. The results show: with the friction factors between tube and mandrel and the one between tube and wiper die turn bigger, the wrinkling factor may become lower to some extent. With the other friction factors between tube
and pushing die, as well as between tube and bend die increase, the wrinkling factor rises a little. Namely the friction factor between these dies have little influence on the wrinkling onset, when clearance between tube and wiper die rises, the wrinkling factor increases; the wrinkling factor increases sharply, when clearance is larger than 0.5mm.
(4) The main parameters are gained: relative diameter, bending radius, hardening exponent, mandrel extension length, friction factor between tube and wiper die, friction factor between tube and mandrel, clearance between tube and wiper die. Based on a virtual orthogonal experiment, information regarding the relative importance of every processing variables for wrinkling onset has been investigated. The results are listed according to relative importance for wrinkling: relative diameter, relative bending radius, hardening exponent, clearance between tube and wiper die, friction factor between tube and wiper die, friction factor between tube and mandrel, friction factor between tube and bend die.
(5) According to analysis of forming characteristics of thin-walled tube bending, concept of forming limit for the process has been put forward. A searching algorithm of forming limit by using developed FEM wrinkling system TBWS-3D as virtual experiment has been brought forward. Employing the algorithm, wrinkling limit under various process conditions can be obtained conveniently and quickly, and one primary forming limit data base has been established. Influence law of main forming parameters on wrinkling limit has been investigated thoroughly. Thus measures to improve the wrinkling limi
(1)改进了薄壁管数控弯曲起皱数值预测系统TBWS-3D：修正了薄壁管数控弯曲成形失稳起皱预测模型，使预测结果更加准确：改善了绝对-相对自由度壳单元边界条件的处理方法，使有限元模拟结果更符合实际；针对不同情况，丰富了弯曲过程中摩擦和压块侧推速度等边界条件的处理方法，使得系统深入地研究成形参数对失稳起皱的影响成为可能；将面向对象技术引入有限元程序的编制，基于VC++平台开发了有限元起皱预测系统TBWS-3D，从而可以方便地嵌入起皱预测等成形质量控制模块，并易于实现上述提出的改进算法。
(2)采用改进的起皱数值预测系统TBWS-3D，系统深入地研究并揭示了薄壁管数控弯曲成形过程中成形参数对失稳起皱的影响规律。从而为成形过程参数优化及成形极限的确定奠定坚实的理论基础。
(3)摩擦和模具间隙对失稳起皱的影响规律表明：随着管坯与防皱块及管坯与芯棒间摩擦系数的增大，起皱因子有减小，有利于防止起皱的发生；随着管坯与弯曲模及管坯与压块间摩擦系数的提高，起皱因子增大，但幅度并不大，对管坯起皱的影响较小；随着管坯与防皱块间隙的增大，起皱因子逐渐增大；当模具间隙大于0.5mm时，失稳起皱趋势急剧增大。即管坯与防皱块间隙对管坯失稳起皱的影响很大。
(4)影响失稳起皱的主要因素有：相对管径、弯曲半径、硬化指数、芯棒的伸出长度、管坯与防皱块间摩擦、管坯与芯棒间摩擦、管坯与防皱块间隙等。基于虚拟正交试验，获得成形参数对失稳起皱影响的显著性大小依次为：相对管径、弯曲半径、硬化指数、管坯与防皱块间隙、管坯与防皱块间摩擦、管坯与
西北工业大学硕士学位论文
芯棒间摩擦、管材与弯曲模摩擦等。
(5)结合薄壁管数控弯曲过程的成形特点，定义了基于失稳起皱的薄壁管数
控弯曲成形极限的概念;基于起皱预测系统TBWS一3D，提出了成形极限的搜索
算法，得到了不同工艺参数下的成形极限，建立了初步的成形极限库:通过成
形参数对失稳起皱影响规律的研究，获得了提高成形极限的方法;在此基础上
提出了基于成形极限与数值模拟的参数确定与优化方案，使薄壁管数控弯曲过
程成形的参数快速确定与优化成为可能。最后对今后的进一步研究方向进行了
探讨。
本研究对提高薄壁弯管制品的质量、缩短产品开发周期、降低生产成本、
充分发挥数控弯管设备的优势，从而实现薄壁管数控弯曲精密成形具有重要意
义，同时也丰富了薄壁件塑性成形失稳起皱理论。
NC precision bending process of thin-walled tube is showing an inevitable tendency to improve and develop tube bending process into advanced plastic forming technology. However, it is a complex astable process with coupling interactive multi-factor effects and wrinkling phenomenon as a compress instability often occurring , when the process parameters are inappropriate, especially for tubes with large diameter and thin wall-thickness. Thus, the wrinkling and forming limit have become one difficult and key problem urgently to be resolved in the R&D of the process. In this dissertation, a systematical and thorough investigation on the wrinkling and the forming limit of the process has been carried out by using rigid-plastic FEM simulation combining with analytical and experiment methods. The main achievements of the project made are as following:
(1) Some of the key techniques related to the 3D rigid-plastic FEM simulation and wrinkling prediction of thin-walled tube NC bending process have been studied and improved methods and algorithms have been proposed: The instability predicting model has been improved which make prediction results more precise. Shell element with absolute-relative degree of freedom and corresponding setting method of velocity boundary conditions make the simulation results more efficiently and more accurately. Frictions on four areas in the forming process and side pushing velocity have been added in to the finite element equations, which makes FEM model more correspond the reality. Based on OOP ( Object-Oriented Programming ) theory, one numerical wrinkling prediction system TBWS-3D for visual NC Tube Bending have been reconstructed successfully with VC++. The validity of system has been verified by experimentation and comparison with data in the literature.
(2) By using improved wrinkling system TBWS-3D, a systematical and thorough investigation into influence of forming parameters on wrinkling onset has been carried out and influence laws are obtained, which may be helpful to the parameters design and determination of forming limit.
(3) Influence law of friction factor and clearance between tube and die on wrinkling initiation is obtained. The results show: with the friction factors between tube and mandrel and the one between tube and wiper die turn bigger, the wrinkling factor may become lower to some extent. With the other friction factors between tube
and pushing die, as well as between tube and bend die increase, the wrinkling factor rises a little. Namely the friction factor between these dies have little influence on the wrinkling onset, when clearance between tube and wiper die rises, the wrinkling factor increases; the wrinkling factor increases sharply, when clearance is larger than 0.5mm.
(4) The main parameters are gained: relative diameter, bending radius, hardening exponent, mandrel extension length, friction factor between tube and wiper die, friction factor between tube and mandrel, clearance between tube and wiper die. Based on a virtual orthogonal experiment, information regarding the relative importance of every processing variables for wrinkling onset has been investigated. The results are listed according to relative importance for wrinkling: relative diameter, relative bending radius, hardening exponent, clearance between tube and wiper die, friction factor between tube and wiper die, friction factor between tube and mandrel, friction factor between tube and bend die.
(5) According to analysis of forming characteristics of thin-walled tube bending, concept of forming limit for the process has been put forward. A searching algorithm of forming limit by using developed FEM wrinkling system TBWS-3D as virtual experiment has been brought forward. Employing the algorithm, wrinkling limit under various process conditions can be obtained conveniently and quickly, and one primary forming limit data base has been established. Influence law of main forming parameters on wrinkling limit has been investigated thoroughly. Thus measures to improve the wrinkling limi
引文
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66 S. I. Oh. Finite Element Analysis of Metal Forming Processes with Arbitrary Shaped Dies. Int. J. Mech. Sci., 1982, 24:479～487
67 Q.C. Yang, Z. Qi and S. N. Qu. Studies on Finite Element Simulation Techniques of Metal Forming Processes. in: Z. R. Wang and He Yuxin eds. Advanced Technology of Plasticity-Proceedings of the Fourth ICTP. Beijing, Int. Acadc. Publishers, 1993, 2:1077～1081
68 范建文．复合挤压的的数值模拟及缺陷预测．西北工业大学博士学位论文，1998
69 赵国群，阮雪榆．轴对称锻造过程金属流动规律的有限元模拟．模具技术，1991，(5)：1～8
70 刘庆斌．模拟技术和人工神经网络在锻造过程中的应用．西北工业大学博士学位论文，1996
71 卫原平．金属塑性成形过程的有限元数值模拟．上海交通大学博士学位论文，
1995
72 詹梅．面向带阻尼台叶片精锻过程的三维有限元数值模拟研究．西北工业大学博士学位论文，2000
73 S. Kobayashi, S. I. Oh and T. Altan. Metal Forming and the Finite Element Method. New York Oxford: Oxford University Press, 1989
74 P. Forde, W. Torgeir etal. Application of Numerical Simulation in the Bending of Aluminum-alloy Profiles. J. of Mats. Proc. Tech., 1996(58): 274～285
75 胡福泰．异型管材与型材无模弯曲工艺理论及实验研究．东北重型机械学院博士学位论文：1995
76 J. B. Yang, B.H. Jeon, and S. I. Oh. The Tube Bending Technology of a Hydroforming Process for an Automotive Part. J. of Mats. Proc. Tech.,2001(111):175～181
77 L.H. Han, S.Y. He, Y.P. Wang, etc. Limit Moment of Local Wall Thinning in Pipe Under Bending. Int. J. of Press. Vess. Piping, 1999:539～542
78 D. Boussaa, V. Dang and K. Labb(?), P. Tang. Finite Pure Bending of Curved Pipes. Comput. Struct., 1996, 60(6): 1003～1012
79 R.D. Cook. Axisymmetric Finite Element Analysis for Pure Moment Loading of Curved Beams and Pipe Bends. Comput. Struct., 1989, 33(2):483～487
80 S.C. Tang, C. C. Chun, K. S. Yeung. Collapse of Long, Noncircular, Cylindrical Shells under Pure Bending. Comput. Struct., 1985, 21 (6): 1345～1353
81 吕丽萍，有限元法及其在锻压工程中的应用．西安：西北工业大学出版社，1989
82 陈如欣，胡忠民．塑性有限元法及其在金属成形中的应用．重庆：重庆大学出版社，1989
83 王勖成，邵敏．有限单元法基本原理与数值方法．北京：清华大学出版社，1998
84 汪大年．金属塑性成形原理．北京：机械工业出版社，1995
85 王祖唐，关廷栋，肖景容等．金属塑性成形理论．北京：机械工业出版社，1989
86 N. Kanok, R. L.Taylor and T. J. R.Hughes. A Large Deformation Forming for Shell Analysis by the Finite Element Method. Computers & Structures, 1981(13):
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87 薛明德，王和慧．闪蒸罐的应力分析与强度评定．压力容器，1999(3)：24～29
88 林艳，杨合．一种可应用于板壳成形过程模拟的绝对-相对自由度壳单元．机械科学与技术，2003(1)：121～123
89 刘鸿文．板壳理论．杭州：浙江大学出版社，1987
90 胡世光．板料冷压成形原理．北京：国防工业出版社，1979
91 钱能．C++程序设计教程．北京：清华大学出版社，1999
92 王同海．管材塑性加工技术，北京：机械工业出版社，1998
93 孙志超．管轴压精密成形过程中无模约束自由变形规律的研究．西北工业大学硕士学位论文，2000
94 孙志超，杨合，蔡旺，林艳．一种确定管材塑性本构关系的反算法．重型机械，2000(3)：43～46
95 吴诗惇．冲压工艺学．西安：西北工业大学出版社，1987
96 周新宇，贾德伟，李杰．运用试验设计法实现金属成形商用模拟软件的参数优化．机电产品开发与创新，2002(4)：13～15
97 李顺平，杨合．神经网络在塑性加工中的应用．航空制造工程，1998(3)：27～42
98 苑世剑，何祝斌．板料成形性理论评价与深入研究．塑性工程学报，2003(10)：6～11
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64 O.C. Zienkiewicz, Y. C. Lin and G. C. Huang. Error Estimation and Adaptivity in Flow Formulation for Forming Problems. Int. J. Num. Meth. in Eng., 1988, 25(1): 23～42
65 O. C. Zienkiewicz, G. C. Huang and Y. C. Liu. Adaptive FEM Computation of Forming Processes-application to Porous and Non-porous Materials. Int. J. Num. Meth. in Eng.,1990, 30:1527～155
66 S. I. Oh. Finite Element Analysis of Metal Forming Processes with Arbitrary Shaped Dies. Int. J. Mech. Sci., 1982, 24:479～487
67 Q.C. Yang, Z. Qi and S. N. Qu. Studies on Finite Element Simulation Techniques of Metal Forming Processes. in: Z. R. Wang and He Yuxin eds. Advanced Technology of Plasticity-Proceedings of the Fourth ICTP. Beijing, Int. Acadc. Publishers, 1993, 2:1077～1081
68 范建文．复合挤压的的数值模拟及缺陷预测．西北工业大学博士学位论文，1998
69 赵国群，阮雪榆．轴对称锻造过程金属流动规律的有限元模拟．模具技术，1991，(5)：1～8
70 刘庆斌．模拟技术和人工神经网络在锻造过程中的应用．西北工业大学博士学位论文，1996
71 卫原平．金属塑性成形过程的有限元数值模拟．上海交通大学博士学位论文，
1995
72 詹梅．面向带阻尼台叶片精锻过程的三维有限元数值模拟研究．西北工业大学博士学位论文，2000
73 S. Kobayashi, S. I. Oh and T. Altan. Metal Forming and the Finite Element Method. New York Oxford: Oxford University Press, 1989
74 P. Forde, W. Torgeir etal. Application of Numerical Simulation in the Bending of Aluminum-alloy Profiles. J. of Mats. Proc. Tech., 1996(58): 274～285
75 胡福泰．异型管材与型材无模弯曲工艺理论及实验研究．东北重型机械学院博士学位论文：1995
76 J. B. Yang, B.H. Jeon, and S. I. Oh. The Tube Bending Technology of a Hydroforming Process for an Automotive Part. J. of Mats. Proc. Tech.,2001(111):175～181
77 L.H. Han, S.Y. He, Y.P. Wang, etc. Limit Moment of Local Wall Thinning in Pipe Under Bending. Int. J. of Press. Vess. Piping, 1999:539～542
78 D. Boussaa, V. Dang and K. Labb(?), P. Tang. Finite Pure Bending of Curved Pipes. Comput. Struct., 1996, 60(6): 1003～1012
79 R.D. Cook. Axisymmetric Finite Element Analysis for Pure Moment Loading of Curved Beams and Pipe Bends. Comput. Struct., 1989, 33(2):483～487
80 S.C. Tang, C. C. Chun, K. S. Yeung. Collapse of Long, Noncircular, Cylindrical Shells under Pure Bending. Comput. Struct., 1985, 21 (6): 1345～1353
81 吕丽萍，有限元法及其在锻压工程中的应用．西安：西北工业大学出版社，1989
82 陈如欣，胡忠民．塑性有限元法及其在金属成形中的应用．重庆：重庆大学出版社，1989
83 王勖成，邵敏．有限单元法基本原理与数值方法．北京：清华大学出版社，1998
84 汪大年．金属塑性成形原理．北京：机械工业出版社，1995
85 王祖唐，关廷栋，肖景容等．金属塑性成形理论．北京：机械工业出版社，1989
86 N. Kanok, R. L.Taylor and T. J. R.Hughes. A Large Deformation Forming for Shell Analysis by the Finite Element Method. Computers & Structures, 1981(13):
19～30
87 薛明德，王和慧．闪蒸罐的应力分析与强度评定．压力容器，1999(3)：24～29
88 林艳，杨合．一种可应用于板壳成形过程模拟的绝对-相对自由度壳单元．机械科学与技术，2003(1)：121～123
89 刘鸿文．板壳理论．杭州：浙江大学出版社，1987
90 胡世光．板料冷压成形原理．北京：国防工业出版社，1979
91 钱能．C++程序设计教程．北京：清华大学出版社，1999
92 王同海．管材塑性加工技术，北京：机械工业出版社，1998
93 孙志超．管轴压精密成形过程中无模约束自由变形规律的研究．西北工业大学硕士学位论文，2000
94 孙志超，杨合，蔡旺，林艳．一种确定管材塑性本构关系的反算法．重型机械，2000(3)：43～46
95 吴诗惇．冲压工艺学．西安：西北工业大学出版社，1987
96 周新宇，贾德伟，李杰．运用试验设计法实现金属成形商用模拟软件的参数优化．机电产品开发与创新，2002(4)：13～15
97 李顺平，杨合．神经网络在塑性加工中的应用．航空制造工程，1998(3)：27～42
98 苑世剑，何祝斌．板料成形性理论评价与深入研究．塑性工程学报，2003(10)：6～11
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