为揭示对称式三辊矫圆原理，优化矫圆策略，对三辊矫圆工艺进行理论解析和试验研究。基于平面曲梁纯弯曲弹复方程，采用双线性简单随动强化模型，通过数学归纳法建立往复弯曲弹复曲率方程和弹复曲率统一方程。理论解析结果表明：管坯周向不同初始曲率的管壁微段在矫圆加载过程中经历多次往复弯曲湮灭了初始曲率的差异，最终使各管壁微段弹复后曲率统一。通过几何关系，建立上辊压下量、弯曲曲率半径和弹区比的定量关系，进而可实现上辊压下量的预测。三辊矫圆试验验证了对称式三辊矫圆原理。试验结果表明：随着弹区比减小，残余椭圆度逐渐减小，当弹区比接近40%时，残余椭圆度接近0.3%，远小于美国石油管道协会API 5L的规定。同时验证了在小变形范围内，残余椭圆度与初始椭圆度关系不大。
In order to reveal the mechanism of the symmetrical three-roller setting round process and optimize the setting round strategy, the theoretical analysis and experimental research of the three-roller setting round process are carried out. The springback equation of small curvature plane pure bending about curve beam is a base, the bilinear simple kinematic hardening model is used, and the springback curvature equation and the unified springback curvature equation of reciprocating bending are established by the mathematical induction method. Theoretical analysis results show that the difference of initial curvature can be eliminated and the curvature values are unified through every micro-pipe-wall of the pipe with different initial curvature experiences multiple times of reciprocating bending. The quantitative relationship between the upper roller reduction, bending radius and elastic area ratio is established by the geometric relation, nominal curvature, wall thickness, and mechanical properties. The mechanism of the symmetrical three-roller setting round process is verified by three-roller setting round experiments. The experiment results show that with the decrease of the elastic area ratio the residual ovality decreases gradually. When the elastic area ratio is close to 40%, the residual ovality can be close to 0.3%, which is far less than the requirement of API 5L. It is verified that there is little relationship between residual ovality and initial ovality in the small deformation range.
[1] KARRECH A,SWIBI A. Analytical model for the expansion of tubes under tension[J]. Journal of Materials Processing Technology,2010,210:356-362.
[2] REN Q,ZOU T X,LI D Y,et al. Numerical study on the X80 UOE pipe forming process[J]. Journal of Materials Processing Technology,2015,215:264-277.
[3] 殷璟,赵军,屈晓阳,等. 大型管件扩径矫圆弹复分析[J]. 机械工程学报,2011,47(12):32-42. YIN Jing,ZHAO Jun,QU Xiaoyang,et al. Springback analysis of expanding and setting round for large diameter pipe[J]. Journal of Mechanical Engineering,2011,47(12):32-42.
[4] 殷璟,赵军,孙红磊,等. 大型管件的模压式精确缩径矫圆[J]. 光学精密工程,2011(9):2072-2078. YIN Jing,ZHAO Jun,SUN Honglei,et al. Precise compression and setting round by mould for large pipes[J]. Optics and Precision Engineering,2011(9):2072-2078.
[5] 潘鑫,陈鹏,钱勇,等. 大口径直缝焊管整圆定径工艺过程的数值模拟[J]. 钢管,2009(5):70-73. PAN Xin,CHEN Peng,QIAN Yong,et al. Numerical simulation of rounding-sizing process of large-sized straight welded pipe[J]. Steel Pipe,2009(5):70-73.
[6] 王关荣. 压力容器整圆模的设计和应用[J]. 压力容器,1991(6):40-44. WANG Guanrong. The design and application of rounding moulds for pressure vessels[J]. Pressure Vessel Technology,1991(6):40-44.
[7] 贺幼良,乔进先,贾春德. 焊管整圆工艺研究[J]. 焊管,1998(3):22-24,63. HE Youliang,QIAO Jinxian,JIA Chunde. Research on the rounding size process for welded pipe[J]. Welded pipe and Tube,1998(3):22-24,63.
[8] ZHAO J,ZHAN P P,MA R,et al. Control strategy of over-bending setting round for pipe-end of large pipes by mould press type method[J]. Transactions of Nonferrous Metals Society of China,2012,22:S329-S334.
[9] ZHAO J,ZHAN P P,MA R,et al. Quantitative prediction of reduction in large pipe setting round process[J]. Chinese Journal of Mechanical Engineering,2013,26(4):722-729.
[10] ZHAO J,ZHAN P P,MA R,et al. Prediction and control of springback in setting round process for pipe-end of large pipe[J]. International Journal of Pressure Vessels and Piping,2014,116:56-64.
[11] 展培培,赵军,李平,等. 大型管件管端过弯矫圆三步法控制策略[J]. 材料科学与工艺,2014(2):97-103. ZHAN Peipei,ZHAO Jun,LI Ping,et al. Three steps control strategy of over-bending setting round for pipe-end of large pipes[J]. Materials Science and Technology,2014(2):97-103.
[12] 展培培. 大型管件管端过弯矫圆及智能化控制技术研究[D]. 秦皇岛:燕山大学,2013. ZHAN Peipei. Study on over-bending setting round process for pip-end of large pipes and intelligent control technology[D]. Qinhuangdao:Yanshan University,2013.
[13] FENG Z K,CHAMPLIAUD H. Investigation of non-kinematic conical roll bending process with conical rolls[J]. Simulation Modelling Practice and Theory, 2012,27:65-75.
[14] FU Z M,TIAN X L,CHEN W,et al. Analytical modeling and numerical simulation for three-roll bending forming of sheet metal[J]. International Journal of Advanced Manufacturing Technology,2013,69:1639-1647.
[15] CHUDASAMA M,RAVAL H. Bending force prediction for dynamic roll-bending during 3-roller conical bending process[J]. Journal of Materials Processing Technology,2014,16:284-295.
[16] 邢娇娇. 三辊矫圆工艺研究[D]. 秦皇岛:燕山大学,2014. XING Jiaojiao. Research on the setting roundness process by three rollers[D]. Qinhuangdao:Yanshan University,2014.
[17] 崔甫. 矫直原理与矫直机械[M]. 2版. 北京:冶金工业出版社,2007. CUI Fu. Straightening theory and straightening machine[M]. 2nd ed. Beijing:Metallurgical Industry Press,2007.
[18] ZHAO J,YU G C,MA R. A mechanical model of symmetrical three-roller setting round process:the static bending stage[J]. Journal of Materials Processing Technology,2016,231:501-512.
[19] ZHAO J,YIN J,MA R,et al. Springback equation of small curvature plane bending[J]. Science China-Technological Sciences,2011,54:2386-2396.
[20] 李钊,周晓军,徐云,等. 大口径钢管圆度测量喷标系统设计与误差补偿研究[J]. 农业机械学报,2013(9):272-278. LI Zhao,ZHOU Xiaojun,XU Yun,et al. Error compensation and design of roundness measurement and stenciling system for large diameter steel pipe[J]. Transactions of the Chinese Society for Agricultural Machinery,2013(9):272-278.
[21] ANSI/API Specification 5L,Forty-foruth Edition,ISO 3183:2007,Specification for line pipe[S]. Washington DC:ANSI/API Specification 5L,2009.
