转子动力学的非线性数值求解

徐小明; 钟万勰

doi:10.3879/j.issn.1000-0887.2015.07.001

转子动力学的非线性数值求解

doi: 10.3879/j.issn.1000-0887.2015.07.001

大连理工大学工程力学系;工业装备结构分析国家重点实验室(大连理工大学),辽宁大连 116024

基金项目: 国家自然科学基金（面上项目）（11472067）

详细信息

作者简介:
徐小明（1986—），男，辽宁东港人，博士生（通讯作者. E-mail: xxm@mail.dlut.edu.cn）;钟万勰（1934—），男，浙江德清人，教授，中科院院士（E-mail: zwoffice@dlut.edu.cn）.

中图分类号: TP391.9;O347.6
计量
- 文章访问数: 1109
- HTML全文浏览量: 42
- PDF下载量: 1235
- 被引次数: 0
出版历程
- 收稿日期: 2015-02-08
- 修回日期: 2015-06-05
- 刊出日期: 2015-07-15

Nonlinear Numerical Simulation of Rotor Dynamics

State Key Laboratory of Structural Analysis for Industrial Equipment(Dalian University of Technology);Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

Funds: The National Natural Science Foundation of China(General Program)（11472067）

摘要

摘要: 将Euler(欧拉)角表示引入转子动力学系统，用以描述转子的非线性旋转运动，并与时间有限元相结合，进而提出了包含非线性因素的转子动力学保辛数值求解方法.以此方法为基础，分析了悬臂梁-圆盘转子系统的涡动行为.数值结果证明该数值解法的有效性与正确性，可用于各种转子系统涡动行为分析.
- 转子动力学 /
- 非线性 /
- 涡动 /
- 陀螺 /
- Euler角
Abstract: A symplectic numerical method using the finite element algorithm in time scheme was proposed for rotor dynamics involving nonlinear factors, in which the Euler angle representation was introduced into the dynamic rotor system for the description of the nonlinear motion of rotation. The swirling motion of the rotor system including the beam-disc combination was analyzed. The numerical results demonstrate the validity and correctness of the proposed method, which can be used for the analysis of swirling motion of rotor systems in various situations.
- rotor dynamics /
- nonlinear /
- swirling motion /
- gyro /
- Euler angle

HTML全文

参考文献(15)

[1]	高亹, 张新江, 张勇. 非线性转子动力学问题研究综述[J]. 东南大学学报, 2002,32(3): 443-451.(GAO Wei, ZHANG Xin-jiang, ZHANG Yong. Review of nonlinear rotor-dynamics[J]. Journal of Southeast University,2002,32(3): 443-451.(in chinese))
[2]	孟光. 转子动力学研究的回顾与展望[J]. 振动工程学报, 2002,15(1): 1-9.(MENG Guang. Retrospect and prospect to the research on rotordynamics[J]. Journal of Vibration Engineering,2002,15(1): 1-9.(in Chinese))
[3]	Rao J S. Rotor Dynamics [M]. John Wiley & Sons Inc, 1983.
[4]	虞烈, 刘恒. 轴承-转子系统动力学[M]. 西安: 西安交通大学出版社, 2000.(YU Lie, LIU Heng.Bearing-Rotor Dynamics [M]. Xi’an: Xi’an Jiaotong University Press, 2000.(in Chinese))
[5]	袁惠清. 转子动力学基础[M]. 北京: 冶金工业出版社, 2013.(YUAN Hui-qing.Rotor Dynamics[M]. Beijing: Metallurgical Industry Press, 2013.(in Chinese))
[6]	张文. 转子动力学理论基础[M]. 北京: 科学出版社, 1990.(ZHANG wen.Basic Theory of Rotor Dynamics [M]. Beijing: Science Press, 1990.(in Chinese))
[7]	张华彪, 陈予恕, 李军. 弹性支承-刚性转子系统同步全周碰摩的分岔响应[J］. 应用数学和力学,2012,33(7): 812-827.(ZHANG Hua-biao, CHEN Yu-shu, LI Jun. Bifurcation on the synchronous full annular rub of a rigid-rotor elastic-support system[J]. Applied Mathematics and Mechanics,2012,33(7): 812-827.(in Chinese))
[8]	李军, 陈予恕. 低压-发电机转子系统弯扭耦合情况下的组合共振研究[J］. 应用数学和力学, 2011,32(8): 895-911.(LI Jun, CHEN Yu-shu. Study on combined resonance of low pressure cylinder-generator rotor system with bending-torsion coupling[J].Applied Mathematics and Mechanics,2011,32(8): 895-911.(in Chinese))
[9]	孙政策, 徐健学, 周桐, 谭宁. 碰摩转子中弯扭耦合作用的影响分析[J］. 应用数学和力学, 2003,24(11): 1163-1169.(SHUN Zheng-ce, XU Jian-xue, ZHOU Tong, TAN Ning. Study on combined resonance of low pressure cylinder-generator rotor system with bending-torsion coupling[J]. Applied Mathematics and Mechanics,2003,24(11): 1163-1169.(in Chinese))
[10]	钟万勰. 应用力学的辛数学方法[M］. 北京: 高等教育出版社, 2006.(ZHONG Wan-xie. Symplectic Method in Applied Mechanics [M］. Beijing: Higher Education Press, 2006.(in Chinese))
[11]	钟万勰, 高强, 彭海军. 经典力学——辛讲[M］. 大连: 大连理工大学出版社, 2013.(ZHONG Wan-xie, GAO Qiang, PENG Hai-jun.Classical Mechanics—Its Symplectic Description [M］. Dalian: Dalian University of Technology Press, 2013.(in Chinese))
[12]	Goldstein H. Classical Mechanics[M]. 2nd ed. San Francisco: Addison Wesley, 1980.
[13]	高强, 钟万勰. 非完整约束动力系统的离散积分方法[J]. 动力学与控制学报, 2012,10(3): 193-198.(GAO Qiang, ZHONG Wan-xie. Numerical algorithms for dynamic system with non-holonomic constrains[J]. Journal of Dynamics and Control,2012,10(3): 193-198.(in Chinese))
[14]	钟万勰, 姚征. 时间有限元与保辛[J]. 机械强度, 2005,27(2): 178-183.(ZHONG Wan-xie, YAO Zheng. Time domain FEM and symplectic conservation[J]. Journal of Mechanical Strength,2005,27(2): 178-183.(in Chinese))
[15]	徐小明, 钟万勰. 刚体动力学的四元数表示及保辛积分[J］. 应用数学和力学, 2014,35(1) : 1-11.(XU Xiao-ming, ZHONG Wan-xie. Symplectic integration of rigid body motion by quaternion parameters[J］.Applied Mathematics and Mechanics,2014,35(1) : 1-11.(in Chinese))