图5. 水平位移模式形状（a）影响条的尺寸精度和（b）影响条在水平横模态振型的影响旋转角模式形状上辊的通行证。
图6. 轧机无间隙的复模形状的振幅。（a）第一级（b）第二级（c）第三级（d）第四级
5.结论
在本文中，轧机的空间振动的概念是根据提出并修改后的Riccati-overall传递矩阵法得出。完整的空间振动特性分析及实验以示轧机的空间振动和提出的方法的有效性的存在空间振动分析。下面的结论可以得出：
（1）轧机振动发生在6个自由度，导致空间涉及垂直，水平，轴向，扭转，交叉和行为摇摆振动模式。
（2）基于所述复合模式形状分析，存在无法识别的振动模式涉及水平，交叉和摆动异常行为及其对质量的影响轧制产品都透露出展示空间的需要振动分析的轧机。
（3）对于高刚度轧机，各固有频率大大地增加和两个辊之间的交叉振动是通过结构改进预防。这些优势对轧机进行经营，并具有十分重要的意义更高的轧制速度，提高产品的成品率。
（4）轧制速度的提高，阻尼对轧机的固有频率的影响，效果逐渐明显。
感谢语
作者非常感谢中国教育部编号20111333110001博士的补助基金和评论，以及Prof.Kornel.FEhmann的宝贵意见。
参考文献
Alok, D., 2010. Case study systematic approach for elimination of
vibrations in gapformer wire-section to speed-up the machine. Quarterly Journal of Indian Pulp and Paper Technical Association 4, 151–154.
Guo, K.X., 1983. Vibration Engineer Book. China Machine Press, Beijing, pp. 301–302.
Luo, Z.H., 1989. Guideline of Engineering Vibration. Shanghai Jiaotong University Press, Shanghai, pp. 228–233.
Ni, Z.H., 1986. Mechanics Vibration. Xi’an Jiaotong University Press, Xi’an, pp.124–125.
Nizio, J., 2005. Numerical analysis of the vertical vibrations of rolling mills and their negative effect on the sheet quality. Journal of Materials Processing Technology 162–163, 546–550.
Rui, X.T., 2008. Transfer Matrix Method of Multibody System and its Applications.Science Press, Beijing, pp. 95–98.
Shen, G.X., Li, M., 2009. Statically determinate characteristics of
microdisplacement in a four-high mill. Journal of Material Processing Technology 209,5002–5007.
Shen, G.X., Li, M., Shi, R., 2010. Indeterminacy of the offset mechanism and microscale static determinacy of roll system in four-high mill. Journal of Mechanical Engineering 46, 69–74.
Timoshenko, S.P., 1955. Vibration Problems in Engineering. Van Nostrand, Princeton,NY, pp. 320–323.
Toshifumi, T., 2011. Study on online analysis of transfer function of variable-speed rolling mill motor with shaft torsional vibration systems. IEEJ Transactions on Industry Applications 6, 844–857.
Yan, X.Q., 2008. Research on coupled vertical–torsion vibration of mill-stand of CSP mill. Journal of Vibration, Measurement & Diagnosis 4, 377–381. Yun, I.S., Wilson, W.R.D., 1998. Review of chatter studier in cold rolling. Journal of Machine Tools & Manufacture 38, 1499–1530.
Zhong, J., 2002. Industrial experiments and findings on temper rolling chatter. Journal of Materials Processing Technology 120, 275–280.