钢管定减径过程的理论计算研究及有限元模拟分析
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摘要
定（减）径是热轧无缝钢管生产中的精轧工序，其工艺水平的高低直接关系到成品的质量和成材率，无缝钢管定减径成形工艺由以前的经验分析到定量分析，这是现代科学技术发展的必然趋势。
钢管减径时存在明显的金属横向流动和宽展，在研究减径过程中轧件内部应力及变形分布的基础上，采用工程计算法求解轧制过程的变形力，能够正确选择压力加工设备和轧辊的结构及强度；分析减径变形时金属流动的规律，可以寻求荒管的形状尺寸与加工后成品管的形状尺寸的关系，因此对其进行研究对于制定合理的轧管工艺具有重要的意义。
本文具体研究方法为：以冷尺寸为φ219×6.55的荒管经12架微张力减径机组减径后，达到φ194×6.80的成品管的过程为研究对象，利用经典的金属轧制变形理论和弹塑性有限元理论对减径过程进行分析研究。在此基础上，采用工程法计算了各机架钢管壁厚值和轧制力的大小；利用ANSYS/LS-DYNA大型有限元分析软件，对减径过程变形区金属的三维流动过程进行了直观、适时、定量的有限元仿真模拟；通过实验（壁厚）验证了工程法计算结果，并结合现场实际建立出回归模型。
通过对钢管定减径过程的理论计算研究和有限元模拟分析，计算出的壁厚变化值与端头实验数据接近，因为壁厚精度（特别是端头）直接关系到轧管成材率的高低，故工程计算法对端头壁厚控制及热轧壁厚控制线的制定有较大的实用意义；用有限元模拟得到的变形区的应力应变分布状态，以及轧制力和壁厚的变化规律，与实际生产中钢管的变形结果基本一致，能够很好的解释横向壁厚不均现象，故用三维弹塑性有限元分析钢管定减径过程是有效的；通过实验对影响壁厚变化的主要因素作数学回归，建立起简便实用的壁厚回归模型，对于现场生产有着重要的指导作用和使用价值。
综合运用以上三种方法对定减径过程进行深入的研究，能帮助我们确定最佳工艺参数，缩短新品种开发周期，对提高无缝钢管的产量、质量及成材率有着重要的科学意义。
As the finishing step in hot rolling of seamless steel tube, reducing technology decides the end product rate and quality. It is the development trend of steel tube reducing technology to go through from empirical analysis to quantitative analysis as every modern science and technology.
There is obvious metal flow in tube reducing. Based on the calculation of rolling pressure after study on strain and stress distribution, it can help to make proper choice of rolling mills, profile and strength of rollers; dimensional relationship between raw tube and its end product can be determined by analysis on the law of metal flow in reducing deformation, so it's worth of studying for working out a reasonable tube reducing technology.
Rolling process of raw tubes reduced by 12 slight stretch reducing mills from 219*6.55 to 194*6.8 were analyzed with classical rolling deformation theory and plastic-elastic FEM. Thus, the wall thickness and rolling pressure of each mill were calculated by engineering method, 3D metal flow is visually simulated by ANSYS/LS-DYNA; the result of engineering calculation is verified by experiment data to establish model.
The experimental data of wall thickness at both ends were approximate to the theoretical values and FEM analysis. As wall thickness has effect on the product rate, engineering calculation is practical to wall thickness control at both ends and arrangement of rolling line; strain and stress distribution, rolling pressure and thickness changing law obtained by FEM matches well with reality and can give good explanation to phenomenon of non-uniform wall thickness, therefore it's effective to use 3D plastic-elastic FEM in analysis of tube reducing process. Practical wall thickness model has been established by regression on major effect factors, and it plays an important and practical role in actual production process.
Further study of reducing process with combination of 3 methods above is helpful in determination of the best processing technology as well as shortening new products developing circle, and it is also significant in enhancement of production, quality and product rate.
钢管减径时存在明显的金属横向流动和宽展，在研究减径过程中轧件内部应力及变形分布的基础上，采用工程计算法求解轧制过程的变形力，能够正确选择压力加工设备和轧辊的结构及强度；分析减径变形时金属流动的规律，可以寻求荒管的形状尺寸与加工后成品管的形状尺寸的关系，因此对其进行研究对于制定合理的轧管工艺具有重要的意义。
本文具体研究方法为：以冷尺寸为φ219×6.55的荒管经12架微张力减径机组减径后，达到φ194×6.80的成品管的过程为研究对象，利用经典的金属轧制变形理论和弹塑性有限元理论对减径过程进行分析研究。在此基础上，采用工程法计算了各机架钢管壁厚值和轧制力的大小；利用ANSYS/LS-DYNA大型有限元分析软件，对减径过程变形区金属的三维流动过程进行了直观、适时、定量的有限元仿真模拟；通过实验（壁厚）验证了工程法计算结果，并结合现场实际建立出回归模型。
通过对钢管定减径过程的理论计算研究和有限元模拟分析，计算出的壁厚变化值与端头实验数据接近，因为壁厚精度（特别是端头）直接关系到轧管成材率的高低，故工程计算法对端头壁厚控制及热轧壁厚控制线的制定有较大的实用意义；用有限元模拟得到的变形区的应力应变分布状态，以及轧制力和壁厚的变化规律，与实际生产中钢管的变形结果基本一致，能够很好的解释横向壁厚不均现象，故用三维弹塑性有限元分析钢管定减径过程是有效的；通过实验对影响壁厚变化的主要因素作数学回归，建立起简便实用的壁厚回归模型，对于现场生产有着重要的指导作用和使用价值。
综合运用以上三种方法对定减径过程进行深入的研究，能帮助我们确定最佳工艺参数，缩短新品种开发周期，对提高无缝钢管的产量、质量及成材率有着重要的科学意义。
As the finishing step in hot rolling of seamless steel tube, reducing technology decides the end product rate and quality. It is the development trend of steel tube reducing technology to go through from empirical analysis to quantitative analysis as every modern science and technology.
There is obvious metal flow in tube reducing. Based on the calculation of rolling pressure after study on strain and stress distribution, it can help to make proper choice of rolling mills, profile and strength of rollers; dimensional relationship between raw tube and its end product can be determined by analysis on the law of metal flow in reducing deformation, so it's worth of studying for working out a reasonable tube reducing technology.
Rolling process of raw tubes reduced by 12 slight stretch reducing mills from 219*6.55 to 194*6.8 were analyzed with classical rolling deformation theory and plastic-elastic FEM. Thus, the wall thickness and rolling pressure of each mill were calculated by engineering method, 3D metal flow is visually simulated by ANSYS/LS-DYNA; the result of engineering calculation is verified by experiment data to establish model.
The experimental data of wall thickness at both ends were approximate to the theoretical values and FEM analysis. As wall thickness has effect on the product rate, engineering calculation is practical to wall thickness control at both ends and arrangement of rolling line; strain and stress distribution, rolling pressure and thickness changing law obtained by FEM matches well with reality and can give good explanation to phenomenon of non-uniform wall thickness, therefore it's effective to use 3D plastic-elastic FEM in analysis of tube reducing process. Practical wall thickness model has been established by regression on major effect factors, and it plays an important and practical role in actual production process.
Further study of reducing process with combination of 3 methods above is helpful in determination of the best processing technology as well as shortening new products developing circle, and it is also significant in enhancement of production, quality and product rate.
引文
[1] 黄庆学，梁爱生. 高精度轧制技术. 冶金工业出版社. 2002. pp19-21
[2] 许云祥. 钢管生产. 冶金工业出版社. 1993. pp150-163
[3] 王廷溥. 轧钢工艺学. 冶金工业出版社.1996. pp443-459
[4] 彭颖红. 金属塑性成形仿真技术. 上海交通大学出版社. 1999. pp1-35
[5] 汪凌云，刘静安. 计算金属成形力学及应用. 重庆大学出版社. 1991. pp8-206
[6] 刘宏民. 三维轧制理论及其应用—模拟轧制过程的条元法. 科学出版社. 1999. pp31-40
[7] 太原重型机器厂设计科. 张力减径机. 机械工业出版社. 1976. pp1-82
[8] 金如崧，李长穆等. 钢管张力减径. 中国工业出版社. 1964. pp113-203
[9] 吕立华.轧制理论基础.重庆大学出版社.1991. pp1-3
[10] 卢于逑，蒋金梅，付晨光.钢管生产工艺学简明教程（初稿）.北京钢铁学院压力加工系. 1985. pp46-76
[11] 王丽君，钟锡汉. 微张力定径机的工艺计算方法. 钢管. 1989. 6. pp26-29
[12] 王廷溥，齐克敏. 金属塑性加工力学—轧制理论与工艺. 冶金工业出版社. 2001. p355
[13] 赵松筠，唐文林. 型钢孔型设计. 冶金工业出版社. 2000. pp279-282
[14] Rockey K C. The finite element method. London: Granada Publishing. 1983. pp56-75
[15] Baker A J. Finite element computational fluid mechanics. New York: Hemisphere Publishing Corporation. 1983. pp80-114
[16] Zienkiewicz O.C. The Finite Element Method. New York: McGraw-Hill. 1977. pp23-35
[17] 俞汉清，陈金德. 金属塑性成形原理. 机械工业出版社. 1999. p260
[18] 颜云辉，谢里阳，韩清凯. 结构分析中的有限单元法及其应用. 东北大学出版社. 2000. pp1-2
[19] Versteeg H K. etc. An introduction to computational fluid dynamics. London: Pearsion Education Limited. 1998. pp13-25
[20] Winterscheidt D.etc., P-version least-squares finite element formulation for two dimensional turbulent incompressible flow, Journal of numerical method fluids Vol. 8. 1987(4). pp32-37
[21] Owen D R J, Hinton E.Finite Element in Plasticity-Theory and Practice. Swansea U. K. Pinerige Press limited. 1980. pp113-140
[22] 乔端，钱仁根. 非线性有限元及其在塑性加工中的应用. 冶金工业出版社. 1990. pp27-35
[23] C.Liu,P.Hartley,C.E.N.Sturgess and G.W.Rowe.Finite-Element Modelling of Cold Rolling of strip.international Journal of Mechanical Science, 1985. 27(7/8). pp531-541
[24] C.Liu,P.Hartley,C.E.N.Sturgess and G.W.Rowe.Simulation of Cold Rolling of strip Using an Elastic-Plastic Finite Element Technique. International Journal of Mechanical Science , 1985, 27(11/12). pp829-839
[25] 刘才，杜风山，连家创. 薄板连轧过程的变形和应力场. 机械工程学报. 1992. 28 (1). pp104-108
[26] C.Liu,P.Hartley,C.E.N.Sturgess and G.W.Rowe. Finite-Element Modelling of Deformation and Spread in Slab Rolling. International Journal of Mechanical Science, 1987, 29(4). pp271-283
[27] 冀文生等. 钢管微张力减径过程中壁厚变化的有限元计算分析和实验研究.钢管. 2001. 30.(1). pp15-20
[28] 刘立忠，刘相华，王国栋. 轧制过程的显式动力有限元模拟. 力学与实践. 2001.23(5). pp34-35
[29] 易日. 使用ANSYS6.1进行结构力学分析. 北京大学出版社. 2002. pp235-380
[30] 李皓月，周田朋，刘相新. ANSYS工程计算应用教程. 中国铁道出版社. 2003. pp53-65
[31] Ruas V. Finite element method for three-dimensional incompressible viscous flow. finite element method in fluid Vol. 8. 1990. pp216-225
[32] Chabard J P.etc. An efficient finite element method for the computation of three dimensional turbulent incompressible flow. finite element method in fluid Vol. 8. 1990. pp245-251
[33] Huo T R, Nakamachi E. 3-D Dynamic Explicit Finite Element Simutation of Sheet Forming. Advanced Technology of Plasticity. 1993, Vol. III. pp1828-1833
[34] Lan, Y. C. and zhang X. Q., Evaluation of Relaxation Schemes for Newton-Raphson Iteration in Regid-Plastic Element Analysis, J. of mater. Process. Techn., 1994, Vol. 41. pp361-373
[35] 洪慧平，康永林.椭圆孔型轧制合金钢方坯三维弹塑性有限元模拟. 北京科技大学学报. 2003. 25(2). pp171-173
[36] Takaaki Iguchi, Owen DRJ, Liu CQ. Analysis of rolling processes by dynamic explicit elastic-plastic finite element method. Processing of the 7th International Conference on Steel Rolling, Chiba, Japan, 1998. pp266-271
[37] 杨节. 轧制过程数学模拟. 冶金工业出版社. 1993. pp200-225
[38] Li Guoji, et al. Spread analysis in rolling by the rigid-plastic finite element method. Numerical Methods in Industrial Forming Processes. Swansea . Pineridge Press, 1982. pp112-159
[39] 喻廷信. 轧制测试技术. 冶金工业出版社. 1994. pp190-212
[40] 王北明. 热轧钢管的质量. 冶金工业出版社. 1987. pp112-151
[41] 刘山等.无缝钢管张减过程平均壁厚控制迭代自学习方法. 钢铁. 2002.37(4). pp28-34
[42] 陈义华.数学模型. 重庆大学出版社.1993. pp22-24
[2] 许云祥. 钢管生产. 冶金工业出版社. 1993. pp150-163
[3] 王廷溥. 轧钢工艺学. 冶金工业出版社.1996. pp443-459
[4] 彭颖红. 金属塑性成形仿真技术. 上海交通大学出版社. 1999. pp1-35
[5] 汪凌云，刘静安. 计算金属成形力学及应用. 重庆大学出版社. 1991. pp8-206
[6] 刘宏民. 三维轧制理论及其应用—模拟轧制过程的条元法. 科学出版社. 1999. pp31-40
[7] 太原重型机器厂设计科. 张力减径机. 机械工业出版社. 1976. pp1-82
[8] 金如崧，李长穆等. 钢管张力减径. 中国工业出版社. 1964. pp113-203
[9] 吕立华.轧制理论基础.重庆大学出版社.1991. pp1-3
[10] 卢于逑，蒋金梅，付晨光.钢管生产工艺学简明教程（初稿）.北京钢铁学院压力加工系. 1985. pp46-76
[11] 王丽君，钟锡汉. 微张力定径机的工艺计算方法. 钢管. 1989. 6. pp26-29
[12] 王廷溥，齐克敏. 金属塑性加工力学—轧制理论与工艺. 冶金工业出版社. 2001. p355
[13] 赵松筠，唐文林. 型钢孔型设计. 冶金工业出版社. 2000. pp279-282
[14] Rockey K C. The finite element method. London: Granada Publishing. 1983. pp56-75
[15] Baker A J. Finite element computational fluid mechanics. New York: Hemisphere Publishing Corporation. 1983. pp80-114
[16] Zienkiewicz O.C. The Finite Element Method. New York: McGraw-Hill. 1977. pp23-35
[17] 俞汉清，陈金德. 金属塑性成形原理. 机械工业出版社. 1999. p260
[18] 颜云辉，谢里阳，韩清凯. 结构分析中的有限单元法及其应用. 东北大学出版社. 2000. pp1-2
[19] Versteeg H K. etc. An introduction to computational fluid dynamics. London: Pearsion Education Limited. 1998. pp13-25
[20] Winterscheidt D.etc., P-version least-squares finite element formulation for two dimensional turbulent incompressible flow, Journal of numerical method fluids Vol. 8. 1987(4). pp32-37
[21] Owen D R J, Hinton E.Finite Element in Plasticity-Theory and Practice. Swansea U. K. Pinerige Press limited. 1980. pp113-140
[22] 乔端，钱仁根. 非线性有限元及其在塑性加工中的应用. 冶金工业出版社. 1990. pp27-35
[23] C.Liu,P.Hartley,C.E.N.Sturgess and G.W.Rowe.Finite-Element Modelling of Cold Rolling of strip.international Journal of Mechanical Science, 1985. 27(7/8). pp531-541
[24] C.Liu,P.Hartley,C.E.N.Sturgess and G.W.Rowe.Simulation of Cold Rolling of strip Using an Elastic-Plastic Finite Element Technique. International Journal of Mechanical Science , 1985, 27(11/12). pp829-839
[25] 刘才，杜风山，连家创. 薄板连轧过程的变形和应力场. 机械工程学报. 1992. 28 (1). pp104-108
[26] C.Liu,P.Hartley,C.E.N.Sturgess and G.W.Rowe. Finite-Element Modelling of Deformation and Spread in Slab Rolling. International Journal of Mechanical Science, 1987, 29(4). pp271-283
[27] 冀文生等. 钢管微张力减径过程中壁厚变化的有限元计算分析和实验研究.钢管. 2001. 30.(1). pp15-20
[28] 刘立忠，刘相华，王国栋. 轧制过程的显式动力有限元模拟. 力学与实践. 2001.23(5). pp34-35
[29] 易日. 使用ANSYS6.1进行结构力学分析. 北京大学出版社. 2002. pp235-380
[30] 李皓月，周田朋，刘相新. ANSYS工程计算应用教程. 中国铁道出版社. 2003. pp53-65
[31] Ruas V. Finite element method for three-dimensional incompressible viscous flow. finite element method in fluid Vol. 8. 1990. pp216-225
[32] Chabard J P.etc. An efficient finite element method for the computation of three dimensional turbulent incompressible flow. finite element method in fluid Vol. 8. 1990. pp245-251
[33] Huo T R, Nakamachi E. 3-D Dynamic Explicit Finite Element Simutation of Sheet Forming. Advanced Technology of Plasticity. 1993, Vol. III. pp1828-1833
[34] Lan, Y. C. and zhang X. Q., Evaluation of Relaxation Schemes for Newton-Raphson Iteration in Regid-Plastic Element Analysis, J. of mater. Process. Techn., 1994, Vol. 41. pp361-373
[35] 洪慧平，康永林.椭圆孔型轧制合金钢方坯三维弹塑性有限元模拟. 北京科技大学学报. 2003. 25(2). pp171-173
[36] Takaaki Iguchi, Owen DRJ, Liu CQ. Analysis of rolling processes by dynamic explicit elastic-plastic finite element method. Processing of the 7th International Conference on Steel Rolling, Chiba, Japan, 1998. pp266-271
[37] 杨节. 轧制过程数学模拟. 冶金工业出版社. 1993. pp200-225
[38] Li Guoji, et al. Spread analysis in rolling by the rigid-plastic finite element method. Numerical Methods in Industrial Forming Processes. Swansea . Pineridge Press, 1982. pp112-159
[39] 喻廷信. 轧制测试技术. 冶金工业出版社. 1994. pp190-212
[40] 王北明. 热轧钢管的质量. 冶金工业出版社. 1987. pp112-151
[41] 刘山等.无缝钢管张减过程平均壁厚控制迭代自学习方法. 钢铁. 2002.37(4). pp28-34
[42] 陈义华.数学模型. 重庆大学出版社.1993. pp22-24