碰摩转子-轴承系统的随机分岔与混沌特性分析
|
摘要
为研究碰摩转子的随机分岔及混沌特性,建立了白噪声下碰摩转子-轴承系统的动力学方程。利用数值积分法对方程求解,以最大Lyapunov指数为指标,并结合分岔图、轴心轨迹、Poincare映射分析了转子系统的非线性特性。结果表明,在拟周期及邻近周期解和转速较大的一定区间,随机扰动对转子有显著的影响;转子转速较大时,随机扰动的强度越大,其影响越明显,并且随机扰动对转子非线性响应具有一定的抑制作用。
A dynamic differential equation of a rub-impact rotor-bearing system under white noise excitation was built to investigate the stochastic bifurcation and chaos behavior of the system. Through numerical integration,the solution to the equation was obtained. The nonlinear characteristics of the system were analyzed. With the help of the largest Lyapunov exponents,bifurcation diagrams,orbit maps and Poincare maps. It was indicated that the effect of the random disturbance on the response of the rotor is significant if the response of the rotor system is a quasi-periodic solution or a nearly periodic one or within a bigger rotation speed zone; the greater the random disturbance the more significant the influence when the rotation speed is bigger; the random disturbance has a certain suppression action on the nonlinear response of the rotor system.
A dynamic differential equation of a rub-impact rotor-bearing system under white noise excitation was built to investigate the stochastic bifurcation and chaos behavior of the system. Through numerical integration,the solution to the equation was obtained. The nonlinear characteristics of the system were analyzed. With the help of the largest Lyapunov exponents,bifurcation diagrams,orbit maps and Poincare maps. It was indicated that the effect of the random disturbance on the response of the rotor is significant if the response of the rotor system is a quasi-periodic solution or a nearly periodic one or within a bigger rotation speed zone; the greater the random disturbance the more significant the influence when the rotation speed is bigger; the random disturbance has a certain suppression action on the nonlinear response of the rotor system.
引文
[1]Cao J Y,Ma C B,Jiang Z D,et al.Nonlinear dynamic analysis of fractional order rub-impact rotor system[J].Communications in Nonlinear Science and Numerical Simulation,2011,16(3):1443-1463.
[2]Khanlo H M,Ghayour M,Ziaei-Rad S.Chaotic vibration analysis of rotating,flexible,continuous shaft-disk system with a rub-impact between the disk and the stator[J].Communications in Nonlinear Science and Numerical Simulation,2011,16(1):566-582.
[3]沈小要,贾九红,赵玫.具有初始弯曲的不平衡转子碰摩条件的研究[J].振动与冲击,2007,26(9):11-13,33.SHEN Xiao-yao,JIA Jiu-hong,ZHAO Mei.Rubbing condition analysis of an unbalance rotor system with initial permanent deflection[J].Journal of Vibration and Shock,2007,26(9):11-13,33.
[4]祝长生,陈拥军,朱位秋.不平衡线性转子-轴承系统的非平稳地震激励响应分析[J].计算力学学报,2006,23(3):285-289.ZHU Chang-sheng,CHEN Yong-jun,ZHU Wei-qiu.Response analysis on linear imbalanced rotor-bearing system under nonstationary random seismic excitation[J].Chinese Journal of Computational Mechanics,2006,23(3):285-289.
[5]Younga T H,Shiaub T N,Kuoa Z H.Dynamic stability of rotor-bearing systems subjected to random axial forces[J].Journal of Sound and Vibration,2007,305(3):467-480.
[6]苏长青,张义民.质量慢变转子系统碰摩的可靠性分析[J].东北大学学报(自然科学版),2008,29(11):1605-1608.SU Chang-qing,ZHANG Yi-min.Reliability analysis of slowly variable mass rotor system with rubbing[J].Journal of Northeastern University(Natural Science),2008,29(11):1605-1608.
[7]张楠,刘占生,姜兴渭.高速转子轴承系统碰摩故障仿真研究[J].振动与冲击,2010,29(9):77-81,243.ZHANG Nan,LIU Zhan-sheng,JIANG Xing-wei.Simulation study on rub-impact fault of high-speed rotor-bearing system[J].Journal of Vibration and Shock,2010,29(9):77-81,243.
[8]Adiletta G,Guido A R,Rossi C.Chaotic motions of a rigid rotor in short journal bearings[J].Nonlinear Dynamics,1996,10(3):251-269.
[9]李振平,闻邦椿.刚性转子-轴承系统的复杂非线性动力学研究[J].振动与冲击,2005,24(3):36-39,4.LI Zhen-ping,WEN Bang-chun.Study on complex nonlinear dynamics of rigid rotor-bearing system[J].Journal of Vibration and Shock,2005,24(3):36-39,4.
[10]郜浩冬,张以都,吴琼,等.汇流传动齿轮-转子-轴承系统非线性动力学分析[J].振动与冲击,2013,32(8):105-113.GAO Hao-dong,ZHANG Yi-du,WU Qiong,et al.Nonlinear dynamic characteristics of a confluence transmission geared rotor bearing system[J].Journal of Vibration and Shock,2013,32(8):105-113.
[2]Khanlo H M,Ghayour M,Ziaei-Rad S.Chaotic vibration analysis of rotating,flexible,continuous shaft-disk system with a rub-impact between the disk and the stator[J].Communications in Nonlinear Science and Numerical Simulation,2011,16(1):566-582.
[3]沈小要,贾九红,赵玫.具有初始弯曲的不平衡转子碰摩条件的研究[J].振动与冲击,2007,26(9):11-13,33.SHEN Xiao-yao,JIA Jiu-hong,ZHAO Mei.Rubbing condition analysis of an unbalance rotor system with initial permanent deflection[J].Journal of Vibration and Shock,2007,26(9):11-13,33.
[4]祝长生,陈拥军,朱位秋.不平衡线性转子-轴承系统的非平稳地震激励响应分析[J].计算力学学报,2006,23(3):285-289.ZHU Chang-sheng,CHEN Yong-jun,ZHU Wei-qiu.Response analysis on linear imbalanced rotor-bearing system under nonstationary random seismic excitation[J].Chinese Journal of Computational Mechanics,2006,23(3):285-289.
[5]Younga T H,Shiaub T N,Kuoa Z H.Dynamic stability of rotor-bearing systems subjected to random axial forces[J].Journal of Sound and Vibration,2007,305(3):467-480.
[6]苏长青,张义民.质量慢变转子系统碰摩的可靠性分析[J].东北大学学报(自然科学版),2008,29(11):1605-1608.SU Chang-qing,ZHANG Yi-min.Reliability analysis of slowly variable mass rotor system with rubbing[J].Journal of Northeastern University(Natural Science),2008,29(11):1605-1608.
[7]张楠,刘占生,姜兴渭.高速转子轴承系统碰摩故障仿真研究[J].振动与冲击,2010,29(9):77-81,243.ZHANG Nan,LIU Zhan-sheng,JIANG Xing-wei.Simulation study on rub-impact fault of high-speed rotor-bearing system[J].Journal of Vibration and Shock,2010,29(9):77-81,243.
[8]Adiletta G,Guido A R,Rossi C.Chaotic motions of a rigid rotor in short journal bearings[J].Nonlinear Dynamics,1996,10(3):251-269.
[9]李振平,闻邦椿.刚性转子-轴承系统的复杂非线性动力学研究[J].振动与冲击,2005,24(3):36-39,4.LI Zhen-ping,WEN Bang-chun.Study on complex nonlinear dynamics of rigid rotor-bearing system[J].Journal of Vibration and Shock,2005,24(3):36-39,4.
[10]郜浩冬,张以都,吴琼,等.汇流传动齿轮-转子-轴承系统非线性动力学分析[J].振动与冲击,2013,32(8):105-113.GAO Hao-dong,ZHANG Yi-du,WU Qiong,et al.Nonlinear dynamic characteristics of a confluence transmission geared rotor bearing system[J].Journal of Vibration and Shock,2013,32(8):105-113.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心