板料冲压成形及回弹有限元数值模拟分析研究
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摘要
板料冲压成形是一种先进、优质、高产、低消耗、低成本的加工工艺方法，在众多生产领域中得到广泛的应用。同时，板料冲压成形是一个同时包括几何非线性、材料非线性和边界条件非线性等问题的复杂的弹塑性大变形力学过程。因此对于复杂的冲压成形件，仅靠工程师的经验公式设计出来的模具往往不能满足产品的技术要求。
随着计算机技术的迅速发展，设计师开始采用计算机模拟技术来指导模具的设计。大量实践证明，有限元法是进行冲压成形过程计算机仿真最合适的数值模拟方法，合理的使用有限元数值模拟技术可以显著地提高模具设计质量，缩短模具设计周期。本文即是通过有限元数值模拟方法对某汽车冲压成形件进行冲压成形及回弹过程的数值模拟试验，研究一些关键参数对成形过程及回弹结果的影响规律。
在冲压成形数值模拟部分主要研究了拉延筋形状及布置形式、坯料初始形状、网格单元属性、坯料与模具及压边圈之间摩擦系数、网格自适应技术对成形结果的影响，并得出这些关键因素对成形结果的影响规律。
回弹是在实际生产中引起冲压件尺寸不合格的主要因素之一，回弹计算结果的准确性和收敛性也一直是回弹数值模拟的难点。本文详细介绍了运用LS-DYNA软件进行回弹模拟的全部过程，通过数值模拟试验分析了模具间隙、板料厚度及坯料初始网格数量对回弹量大小的影响，得到了这三个因素对最终回弹结果的影响规律。
The sheet metal forming is an advanced, high quality, efficient, lowconsumption and low cost manufacture technology. It has been widely appliedin all kinds of mechanical industry. At the same time, sheet metal formingis a complicated elastic and plastic mechanical process which includesnon-liner problem of material models, boundary condition, element algorithmand contact handling methods etc. So when faced complicated accessories, thedie designed by the engineer only through traditional experience and formulassometimes can not reach the technical demand of products.
With the development of computer technology, engineers begin to usecomputer simulation technology to aid the tool's design. Lots of practicesprove that finite element method is the best way to simulate the process ofsheet metal forming. Using the technology of CAE can remarkably improves thequality and shortens the cycle of die design. In this paper, numericalsimulations of sheet metal stamping and springback process about an automobilepanel are investigated and the rules of some selected processing parametersare found through comparatively deep study.
On the section of stamping simulation, the infection to the result aboutthe distribution of drawbead, the original sharp of the blank, the attributeof the meshing element, the friction coefficient between the blank and thedie, the techno]ogy of adaptive meshing are mainly investigated. The effectingrules of these processing parameters above are found.
The phenomenon of Springback is one of the main effects for the geometryof the stamping parts. The accuracy and the convergence of the simulation arealso the key points for the springback. In this paper, the whole process abouthow to deal with springback problem using the software of LS-DYNA is introducedin detail. And the infection to springback result about the clearance betweenthe up-die and the low-die, the thickness of the blank and the demand amountof the meshing element for the blank are analyzed through computer simulationtest. At last, the effecting rules of these processing factors to thespringback result are found.
随着计算机技术的迅速发展，设计师开始采用计算机模拟技术来指导模具的设计。大量实践证明，有限元法是进行冲压成形过程计算机仿真最合适的数值模拟方法，合理的使用有限元数值模拟技术可以显著地提高模具设计质量，缩短模具设计周期。本文即是通过有限元数值模拟方法对某汽车冲压成形件进行冲压成形及回弹过程的数值模拟试验，研究一些关键参数对成形过程及回弹结果的影响规律。
在冲压成形数值模拟部分主要研究了拉延筋形状及布置形式、坯料初始形状、网格单元属性、坯料与模具及压边圈之间摩擦系数、网格自适应技术对成形结果的影响，并得出这些关键因素对成形结果的影响规律。
回弹是在实际生产中引起冲压件尺寸不合格的主要因素之一，回弹计算结果的准确性和收敛性也一直是回弹数值模拟的难点。本文详细介绍了运用LS-DYNA软件进行回弹模拟的全部过程，通过数值模拟试验分析了模具间隙、板料厚度及坯料初始网格数量对回弹量大小的影响，得到了这三个因素对最终回弹结果的影响规律。
The sheet metal forming is an advanced, high quality, efficient, lowconsumption and low cost manufacture technology. It has been widely appliedin all kinds of mechanical industry. At the same time, sheet metal formingis a complicated elastic and plastic mechanical process which includesnon-liner problem of material models, boundary condition, element algorithmand contact handling methods etc. So when faced complicated accessories, thedie designed by the engineer only through traditional experience and formulassometimes can not reach the technical demand of products.
With the development of computer technology, engineers begin to usecomputer simulation technology to aid the tool's design. Lots of practicesprove that finite element method is the best way to simulate the process ofsheet metal forming. Using the technology of CAE can remarkably improves thequality and shortens the cycle of die design. In this paper, numericalsimulations of sheet metal stamping and springback process about an automobilepanel are investigated and the rules of some selected processing parametersare found through comparatively deep study.
On the section of stamping simulation, the infection to the result aboutthe distribution of drawbead, the original sharp of the blank, the attributeof the meshing element, the friction coefficient between the blank and thedie, the techno]ogy of adaptive meshing are mainly investigated. The effectingrules of these processing parameters above are found.
The phenomenon of Springback is one of the main effects for the geometryof the stamping parts. The accuracy and the convergence of the simulation arealso the key points for the springback. In this paper, the whole process abouthow to deal with springback problem using the software of LS-DYNA is introducedin detail. And the infection to springback result about the clearance betweenthe up-die and the low-die, the thickness of the blank and the demand amountof the meshing element for the blank are analyzed through computer simulationtest. At last, the effecting rules of these processing factors to thespringback result are found.
引文
1 翁克索夫，W．约翰逊，工藤英明．金属塑性变形理论．北京：机械工业出版社，1992
2 包向军，蒋宏范等．轿车车门内板冲压成形计算机仿真．金属成形工艺，2000(4)：19-20
3 施法中，陈中奎．板料冲压成形过程的计算机仿真．中国机械工程，1998(11)
4 李尚健．金属塑性成形过程模拟．北京：机械工业出版社，1999
5 Gupta, Meek. A brief history of the beginning of the finite element method. International Journal for Numerical Methods in Engineering,1996,39:3761-3774
6 Marcal. A note on the elastic-plastic thick cylinder with internal pressure in the open and closed-end condition. International of Mechanical Sciences. 1967,7(12):841-845
7 Yamada Y. Plastic stress-strain matrix and its application for the solution of elastic plastic problems by the finite element method. International Journal of Mechanical Sciences. 1968,10(5):343-354
8 Hibbitt H D, Marcal, Rice. A finite element formulation for problems of large strain and large displacement. International Journal of Solids Structure. 1970,6(8): 1069-1086
9 Lee, Kobayashi. New solution to rigid plastic deformation problems using a matrix method. Journal of Engineering for Industry. ASME, 1973,95:865-873
10 Oden J T, Bhandari D R, Yagawa G et al. A new approach to the finite element formulation and solution of a class of problems in coupled thermo elastovisco plasticity of solids. Nuclear Engineering and Design. 1973,24(3):420-429
11 Mcmeeking R M, J Rice R. Finite element formulation for problems of large elastic plastic deformation. International Journal of Solids Structure. 1975,11 (5): 601-616
12 Owen D R J, Hinton E. Finite element in plasticity. Pinerige Press Limited, 1980
13 Keeler Stuart P. Circular grid system-a valuable aid for evaluating sheet metal formability. SAE Trans,1968, No. 680092: 371-379
14 P. V. Marcal, I. P. King. Elastic-plastic Analysis of Two-dimensional Systems by the Finite Element Method. International Journal of Mechanical Sciences. Vol. 9, 1967
15 Y. Yamada et al. Plastic Stress-strain Matrix and its Application for the Solution of Elastic-plastic Problems by the Finite Element Method. International Journal of Mechanical Sciences. Vol. 10, 1968.
16 胡轶敏，林忠钦等．车身覆盖件冲压成形动态仿真的研究进展．力学进展．2000(2)
17 J. R. Osias etal. Finite Elastic-Plastic Deformation. International Journal of Solids Structure. Vol. 10, 1974
18 Wifi A S. An incremental complete solution of the stretch-forming and deep drawing of a circular blank using a hemispherical punch. International Journal of Mechanical Sciences. 1976, 18 (1): 23-31
19 Kobayashi S, Kim J H. Deformation analysis of axisymmetric sheet metal forming processes by rigid-plastic finite element method. Mechanics of Sheet Metal Forming. New York: Plenum Press. 1978: 341-365
20 N. M. Wang, B. Budiansky, Analysis of Sheet Metal Stamping by a Finite Element Method. Journal Application of Mechanical. Vol.45,1978
21 OH. S I, Kobayashi. Finite element analysis of plane-strain sheet bending. International Journal of Mechanical Sciences. 1980, 22(9): 583-594
22 Tang S C. Computer prediction of the deformed shape of a draw blank during the binder-wrap stage. Journal Application of Metal working. 1980,1 (3):695—712
23 Toh C H, Kobayashi S. Deformation analysis and blank design in square cup drawing. International Journal of Machine Tool Design and Research. 1985, 25(1): 15-32
24 Yang D Y, Kim Y J. A rigid-plastic finite element formulation for the analysis for general deformation of planar anisotropic sheet metals and its application. International Journal of Mechanical Sciences. 1986, 28: 825-840
25 Nakamachi E, Sowerby R. Finite element modeling of the punch stretching of square plates. Journal of Application Mechanical. 1988.5:667-671.
26 Tang S C. Thin shell element simulation of the sheet metal forming process. Nakamachi E. ICPT90. Japan. 1990:1757-1762
27 Honecker A, Mattiason K. Finite element procedures for 3D sheet metal forming simulation. Thompson E G. NUMIFORM'89. Netherlands. 1989. 457-464
28 郑莹等．板料成形数值模拟进展，塑性工程学报．Vol．3 No4 Dec，1996：34-37
29 白金译．LS-DYNA3D理论基础与实例分析．北京：科学出版社，2005
30 赵海鸥．LS-DYNA动力分析指南．北京：兵器工业出版社，2003
31 林忠钦等．车身覆盖件冲压成形仿真．北京：机械工业出版社，2005
32 李裕春，时党勇，赵远．ANSYS10.0／LS-DYNA基础理论与工程实践．北京：中国水利水电出版社，2006
33 胡轶敏．车身覆盖件冲压成形的三维仿真与试验研究．上海交通大学博士学位论文，1999
34 崔令江．汽车覆盖件冲压成形技术．北京：机械工业出版社，2003
35 雷正保．汽车覆盖件冲压成形CAE技术及其工业应用研究．中南大学博士学位论文，2003
36 陈毓勋．板材与型材弯曲回弹控制原理与方法．北京：国防工业出版社，1990，6
37 宋黎，杨坚等．板料弯曲成形的回弹分析与工程控制综述．锻压技术，1996(1)：18-22
38 朱东波，孙琨等．板料成形回弹问题研究新进展．塑性工程学报．2000(1)：11-17
39 徐丙坤．汽车覆盖件冲压成形过程有限元数值模拟技术研究．北京航空航天大学博士论文，2002
40 王勖成，邵敏．有限单元法基本原理和数值方法．北京：清华大学出版社，1997
41 板料成形回弹模拟．张晓静，周贤宾．塑性工程学报．1999(3)：56-62
42 R Hill. Mathematical Theory of Plasticity. Oxford University press, 1966
43 N M Wang, B Budiansky, Analysis of sheet metal stamping by a finite element method. Appl.Mech.Trans. ASME, 1978,45:73-82
44 Mai Huang,James C Gerdeen. Springback of doubly curved developable sheet metal surface-An Overview. SAE, 1994: 718—731
45 Makinouchi, Nakamachi,Onata Wagoner R H. 2nd International Conference on Numerical Simulation of 3-D Sheet Metal Forming Processes (NumiSheet'93). Isehara Japan, 1993
46 Lee J K, Kinzel, Wagoner R H. Proceedings of the 3nd International Conferece on Numerical Simulation of 3-D Sheet Metal Forming Processes-Verification of Simulations with Experiments (NumiSheet'96). Dearborn, Michigan, 1996
47 C Q Du, L Zhang. Springback prediction in sheet forming simulation. ASAE, Trans. Section5,940937:707-717
48 M J Finn,P C Gallbraith. Use of coupled explicit-implicit solver for calculating springback in automotive body panels. J Mater Processing Tech., 1995,50:395-409
49 M Kawka,T Kahita, A Makinouchi. Simulation of multi-step sheet metal forming process by a static explicit FEM code. J Mater Processing Tech., 1998: 54-59
50 Mattiasson, Thilderkvist,Anders Strange. Simulation of Springback in Sheet Metal Forming. Simulation of Materials Processing: Theory Methods and Application, 1995 (6): 115-124
2 包向军，蒋宏范等．轿车车门内板冲压成形计算机仿真．金属成形工艺，2000(4)：19-20
3 施法中，陈中奎．板料冲压成形过程的计算机仿真．中国机械工程，1998(11)
4 李尚健．金属塑性成形过程模拟．北京：机械工业出版社，1999
5 Gupta, Meek. A brief history of the beginning of the finite element method. International Journal for Numerical Methods in Engineering,1996,39:3761-3774
6 Marcal. A note on the elastic-plastic thick cylinder with internal pressure in the open and closed-end condition. International of Mechanical Sciences. 1967,7(12):841-845
7 Yamada Y. Plastic stress-strain matrix and its application for the solution of elastic plastic problems by the finite element method. International Journal of Mechanical Sciences. 1968,10(5):343-354
8 Hibbitt H D, Marcal, Rice. A finite element formulation for problems of large strain and large displacement. International Journal of Solids Structure. 1970,6(8): 1069-1086
9 Lee, Kobayashi. New solution to rigid plastic deformation problems using a matrix method. Journal of Engineering for Industry. ASME, 1973,95:865-873
10 Oden J T, Bhandari D R, Yagawa G et al. A new approach to the finite element formulation and solution of a class of problems in coupled thermo elastovisco plasticity of solids. Nuclear Engineering and Design. 1973,24(3):420-429
11 Mcmeeking R M, J Rice R. Finite element formulation for problems of large elastic plastic deformation. International Journal of Solids Structure. 1975,11 (5): 601-616
12 Owen D R J, Hinton E. Finite element in plasticity. Pinerige Press Limited, 1980
13 Keeler Stuart P. Circular grid system-a valuable aid for evaluating sheet metal formability. SAE Trans,1968, No. 680092: 371-379
14 P. V. Marcal, I. P. King. Elastic-plastic Analysis of Two-dimensional Systems by the Finite Element Method. International Journal of Mechanical Sciences. Vol. 9, 1967
15 Y. Yamada et al. Plastic Stress-strain Matrix and its Application for the Solution of Elastic-plastic Problems by the Finite Element Method. International Journal of Mechanical Sciences. Vol. 10, 1968.
16 胡轶敏，林忠钦等．车身覆盖件冲压成形动态仿真的研究进展．力学进展．2000(2)
17 J. R. Osias etal. Finite Elastic-Plastic Deformation. International Journal of Solids Structure. Vol. 10, 1974
18 Wifi A S. An incremental complete solution of the stretch-forming and deep drawing of a circular blank using a hemispherical punch. International Journal of Mechanical Sciences. 1976, 18 (1): 23-31
19 Kobayashi S, Kim J H. Deformation analysis of axisymmetric sheet metal forming processes by rigid-plastic finite element method. Mechanics of Sheet Metal Forming. New York: Plenum Press. 1978: 341-365
20 N. M. Wang, B. Budiansky, Analysis of Sheet Metal Stamping by a Finite Element Method. Journal Application of Mechanical. Vol.45,1978
21 OH. S I, Kobayashi. Finite element analysis of plane-strain sheet bending. International Journal of Mechanical Sciences. 1980, 22(9): 583-594
22 Tang S C. Computer prediction of the deformed shape of a draw blank during the binder-wrap stage. Journal Application of Metal working. 1980,1 (3):695—712
23 Toh C H, Kobayashi S. Deformation analysis and blank design in square cup drawing. International Journal of Machine Tool Design and Research. 1985, 25(1): 15-32
24 Yang D Y, Kim Y J. A rigid-plastic finite element formulation for the analysis for general deformation of planar anisotropic sheet metals and its application. International Journal of Mechanical Sciences. 1986, 28: 825-840
25 Nakamachi E, Sowerby R. Finite element modeling of the punch stretching of square plates. Journal of Application Mechanical. 1988.5:667-671.
26 Tang S C. Thin shell element simulation of the sheet metal forming process. Nakamachi E. ICPT90. Japan. 1990:1757-1762
27 Honecker A, Mattiason K. Finite element procedures for 3D sheet metal forming simulation. Thompson E G. NUMIFORM'89. Netherlands. 1989. 457-464
28 郑莹等．板料成形数值模拟进展，塑性工程学报．Vol．3 No4 Dec，1996：34-37
29 白金译．LS-DYNA3D理论基础与实例分析．北京：科学出版社，2005
30 赵海鸥．LS-DYNA动力分析指南．北京：兵器工业出版社，2003
31 林忠钦等．车身覆盖件冲压成形仿真．北京：机械工业出版社，2005
32 李裕春，时党勇，赵远．ANSYS10.0／LS-DYNA基础理论与工程实践．北京：中国水利水电出版社，2006
33 胡轶敏．车身覆盖件冲压成形的三维仿真与试验研究．上海交通大学博士学位论文，1999
34 崔令江．汽车覆盖件冲压成形技术．北京：机械工业出版社，2003
35 雷正保．汽车覆盖件冲压成形CAE技术及其工业应用研究．中南大学博士学位论文，2003
36 陈毓勋．板材与型材弯曲回弹控制原理与方法．北京：国防工业出版社，1990，6
37 宋黎，杨坚等．板料弯曲成形的回弹分析与工程控制综述．锻压技术，1996(1)：18-22
38 朱东波，孙琨等．板料成形回弹问题研究新进展．塑性工程学报．2000(1)：11-17
39 徐丙坤．汽车覆盖件冲压成形过程有限元数值模拟技术研究．北京航空航天大学博士论文，2002
40 王勖成，邵敏．有限单元法基本原理和数值方法．北京：清华大学出版社，1997
41 板料成形回弹模拟．张晓静，周贤宾．塑性工程学报．1999(3)：56-62
42 R Hill. Mathematical Theory of Plasticity. Oxford University press, 1966
43 N M Wang, B Budiansky, Analysis of sheet metal stamping by a finite element method. Appl.Mech.Trans. ASME, 1978,45:73-82
44 Mai Huang,James C Gerdeen. Springback of doubly curved developable sheet metal surface-An Overview. SAE, 1994: 718—731
45 Makinouchi, Nakamachi,Onata Wagoner R H. 2nd International Conference on Numerical Simulation of 3-D Sheet Metal Forming Processes (NumiSheet'93). Isehara Japan, 1993
46 Lee J K, Kinzel, Wagoner R H. Proceedings of the 3nd International Conferece on Numerical Simulation of 3-D Sheet Metal Forming Processes-Verification of Simulations with Experiments (NumiSheet'96). Dearborn, Michigan, 1996
47 C Q Du, L Zhang. Springback prediction in sheet forming simulation. ASAE, Trans. Section5,940937:707-717
48 M J Finn,P C Gallbraith. Use of coupled explicit-implicit solver for calculating springback in automotive body panels. J Mater Processing Tech., 1995,50:395-409
49 M Kawka,T Kahita, A Makinouchi. Simulation of multi-step sheet metal forming process by a static explicit FEM code. J Mater Processing Tech., 1998: 54-59
50 Mattiasson, Thilderkvist,Anders Strange. Simulation of Springback in Sheet Metal Forming. Simulation of Materials Processing: Theory Methods and Application, 1995 (6): 115-124