垂荡作用下船用转子-轴承系统的动力学特性研究
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摘要
研究了考虑船体垂荡运动时船用转子-轴承系统的动力学特性。首先,在非惯性参考系基于短轴承理论建立了船体垂荡作用下转子-轴承系统的动力学模型,结果显示垂荡作用下船用转子-轴承系统具有几何非线性特性;其次,采用数值方法,分析了系统的分岔图、最大Lyapunov指数、稳态响应、轴心轨迹、Poincaré映射等,并与船体不发生垂荡时的转子系统动力学特性进行比较;最后,研究了垂荡激励幅值对转子-轴承系统非线性动力学特性的影响。结果表明:垂荡运动会显著地影响转子的动力学行为。在转速较低时,系统呈现周期1运动,垂荡对转子的运动特性影响此时占主导作用;随着转速的增加,系统出现准周期、周期2和双Hopf现象,具有周期1、准周期、周期2和混沌运动等复杂动力学特性。
With the ship heaving motion considered,the dynamic behaviors of the marine rotor-bearing system is studied in this paper.First,the dynamic model of the rotor-bearing system under the heaving motion is established based on the short bearing theory in the non-inertial reference system,in which the geometric nonlinearity is found to take place in the marine rotor-bearing system when with the action of heaving motion is taken into account.In addition,the dynamic characteristics,such as the bifurcation diagram,the maximum Lyapunov exponents,the steady state response,the rotor orbit and its Poincarémap are analyzed through numerical method,and the results are compared with those of the rotor-bearing system without heaving motion.Finally,the influence of the amplitude of the heaving excitation on the nonlinear dynamic characteristics of the rotor-bearing system is studied.The results show that the system exhibits a single cycle motion at low rotating speed and the heaving motion effect for this situation is obvious.With the increase of the speed,the phenomena of quasi-periodic,period two and double Hopf bifurcations occur in the system,and its dynamic characteristics present a single cyclic motion,quasi-periodic,period two and chaos etc..
With the ship heaving motion considered,the dynamic behaviors of the marine rotor-bearing system is studied in this paper.First,the dynamic model of the rotor-bearing system under the heaving motion is established based on the short bearing theory in the non-inertial reference system,in which the geometric nonlinearity is found to take place in the marine rotor-bearing system when with the action of heaving motion is taken into account.In addition,the dynamic characteristics,such as the bifurcation diagram,the maximum Lyapunov exponents,the steady state response,the rotor orbit and its Poincarémap are analyzed through numerical method,and the results are compared with those of the rotor-bearing system without heaving motion.Finally,the influence of the amplitude of the heaving excitation on the nonlinear dynamic characteristics of the rotor-bearing system is studied.The results show that the system exhibits a single cycle motion at low rotating speed and the heaving motion effect for this situation is obvious.With the increase of the speed,the phenomena of quasi-periodic,period two and double Hopf bifurcations occur in the system,and its dynamic characteristics present a single cyclic motion,quasi-periodic,period two and chaos etc..
引文
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[2]徐敏,廖明夫,刘佶洲.机动飞行条件下双盘悬臂转子的振动特性[J].航空动力学报,2002,17(1):105-109.Xu Min,Liao Ming-fu,Liu Qi-zhou.The vibration performance of the double-disk cantilever rotor in flight mission[J].Journal of Aerospace Power,2002,17(1):105-109.
[3]林富生,孟光.飞行器内SFD-转子系统的动力学特性研究[J].振动工程学报,2004,17(4):403-407.Lin Fusheng,Meng Guang.Study on the dynamic characteristics of SFD-rotor system in aircrafts[J].Journal of Vibration Engineering,2004,17(4):403-407.
[4]祝长生,陈拥军.机动飞行时航空发动机转子系统的振动特性[J].航空学报,2006,27(5):835-841.Zhu Chang-sheng,Chen Yong-jun.Vibration characteristics of aero engine’s rotor system during maneuvering flight[J].Acta Aeronautica Et Astronautica Sinica,2006,27(5):835-841.
[5]侯磊.机动飞行环境下转子系统的非线性动力学行为研究[D].哈尔滨:哈尔滨工业大学,2015.Hou Lei.Research on nonlinear dynamics of rotor system in manuevering flight[D].Harbin:Harbin Institute of Technology,2015.
[6]刘建华,洪竹.船舶纵横摇耦合运动数学模型研究[J].江苏科技大学学报(自然科学版),2016,30(5):411-416.Liu Jian-hua,Hong Zhu.Mathematical model of ship pitching and rolling coupled motions[J].Journal of Jiangsu University of Science and Technology(Natural Science Edition),2016,30(5):411-416.
[7] Srigrarom S,Chai W S.Effect of pitching and heaving motions of SD8020hydrofoil on thrust and efficiency for swimming propulsion[C].APS Division of Fluid Dynamics Meeting,APS Division of Fluid Dynamics Meeting Abstracts,2013.
[8] Floryan D,Buren T V,Rowley C W,et al.Scaling the propulsive performance of heaving and pitching foils[J].Journal of Fluid Mechanics,2017,822(1):386-397.
[9] Simonsen C D,Otzen J F,Joncquez S,et al.EFD and CFD for KCS heaving and pitching in regular head waves[J].Journal of Marine Science&Technology,2013,18(4):435-459.
[10]Zhang Guanghui,Liu Shupeng,Cao Zhixuan,et al.Analytical model of self-acting journal bearing subjected to base excitation for marine engine system[J].Journal of Engineering for the Maritime Environment,2013,227(2):194-207.
[11]Zhang Guanghui,Liu Shupeng,Ma Ruixian,et al.Nonlinear dynamic characteristics of journal bearingrotor system considering the pitching and rolling motion for marine turbo machinery[J].Journal of Engineering for the Maritime Environment,2015,229(1):95-107.
[12]李明,赵文,何琳.气囊-浮筏耦合船用转子-轴承系统的非线性动力学研究[J].振动工程学报,2015,28(4):618-624.Li Ming,Zhao Wen,He Lin.Nonlinear dynamic behavior of marine rotor-bearing system coupled by air bag-floating[J].Journal of Vibration Engineering,2015,28(4):618-624.
[13]钟一谔,何衍宗,王正,等.转子动力学[M].北京:清华大学出版社,1987:63-68.Zhong Yi-e,He Yan-zong,Wang Zheng,et al..Rotor Dynamics[M].Beijing:Tsinghua University Press,1987:63-68.
[14]刘树鹏.舰船纵横倾作用下转子轴承系统动力学特性研究[D].哈尔滨:哈尔滨工业大学,2011.Liu Shu-peng.Rotor dynamic characteristic of rotor bearing system for ship with vertical and horizontal swinging[D].Harbin:Harbin Institute of Technology,2011.