针对简化弹簧模型和非线性动态油膜力模型皆不利于交叉刚度对碰摩转子动力学影响分析的问题，建立了基于非对称直接刚度和交叉刚度的Jeffcott转子动力学模型。结合打靶法和Floquet理论研究了转子交叉耦合刚度对转子系统运动稳定性的影响规律。创新性地引入了“碰摩能”新参量对碰摩故障进行量化表征，在此基础上分析了不同交叉刚度下转静件间隙的变化对转子碰摩程度的影响。分析结果表明，在不同“碰摩能”的情况下，转子系统交叉刚度的变化可诱发周期-1运动，再经擦边分岔突变为混沌和经Neimark-Sacker分岔渐变为混沌，正向涡动经跨临界分岔演化为反向涡动；交叉刚度较大时，增大转静件间隙反而会加重转静子碰摩的程度。
Abstract
Aiming at the problem of the simplified spring model and nonlinear dynamic oil film force model being not conducive to analyzing effects of cross stiffness on rubbing rotor dynamics, a Jeffcott rotor dynamic model based on asymmetric direct stiffness and cross stiffness was established.Combining the shooting method and Floquet theory was used to study influence laws of rotor cross coupled stiffness on rotor system motion stability.A new parameter “rubbing energy” was introduced to characterize quantitatively the rotor rubbing fault, and analyze effects of rotor-stator clearance on rubbing degree of rotor with different cross stiffnesses.The results showed that in cases of different rubbing energy, the change of cross stiffness of rotor system can induce period-1 motion, and then through side-wiping bifurcation suddenly transit to chaos or through Neimark-Sacker bifurcation gradually transit to chaos; the forward whirl through trans-critical bifurcation evolves to reverse whirl; when the cross stiffness is larger, increasing rotor-stator clearance can aggravate the rubbing degree between rotor and stator.
关键词
转子碰摩故障 /
交叉刚度 /
转子动力学 /
碰摩能
{{custom_keyword}} /
Key words
rotor rubbing fault /
cross-stiffness /
rotor dynamics /
rubbing energy
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
［1］WANG W M, LI Q H, GAO J J, et al.An identification method for damping ratio in rotor systems［J］.Mechanical Systems and Signal Processing, 2016, 68/69: 536-554.
［2］MA H, ZHAO Q B, ZHAO X Y, et al.Dynamic characteristics analysis of a rotor-stator system under different rubbing forms［J］.Applied Mathematical Modelling, 2015, 39(8): 2392-2408.
［3］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.
ZHANG Nan, LIU Zhansheng, JIANG Xingwei.Simulation study on rub-impact fault of high-speed rotor-bearing system［J］.Journal of Vibration and Shock, 2010, 29(9): 77-81.
［4］CHILDS D W.Rub-induced parametric excitation in rotors［J］.Journal of Mechanical Design, 1979, 101(4): 640-644.
［5］李东.转子系统若干故障问题的非线性及可靠性分析［D］.沈阳: 东北大学, 2008.
［6］李东, 袁惠群, 吴立明.弹性支承双跨碰摩故障转子系统非线性特性［J］.振动、测试与诊断, 2009, 29(4): 414-418.
LI Dong, YUAN Huiqun, WU Liming.Study on nonlinear characteristic of elastically-supported two-span rotor system with rub-impact fault［J］.Journal of Vibration, Measurement and Diagnosis, 2009, 29(4): 414-418.
［7］刘杨, 李炎臻, 石拓, 等.转子-滑动轴承系统不对中-碰摩耦合故障分析［J］.机械工程学报, 2016, 52(13): 79-86.
LIU Yang, LI Yanzhen, SHI Tuo, et al.Study on misalignment-rubbing coupling fault of rotor system supported by oil film force［J］.Journal of Mechanical Engineering, 2016, 52(13): 79-86.
［8］刘杨, 李炎臻, 太兴宇, 等.转子-滑动轴承系统松动-碰摩耦合故障分析［J］.振动工程学报, 2016, 29(3): 549-554.
LIU Yang, LI Yanzhen, TAI Xingyu, et al.Characteristic analysis of looseness-rubbing coupling fault of rotor-sliding-bearing system［J］.Journal of Vibration Engineering, 2016, 29(3): 549-554.
［9］钟一谔，何衍宗，王正.转子动力学［M］.北京: 清华大学出版社, 1987.
［10］CHANG-JIAN C W, CHEN C K.Chaos and bifurcation of a flexible rub-impact rotor supported by oil film bearings with nonlinear suspension［J］.Mechanism and Machine Theory, 2007, 42(3): 312-333.
［11］CHANG-JIAN C W, CHEN C K.Chaos of rub-impact rotor supported by bearings with nonlinear suspension［J］.Tribology International, 2009, 42(3): 426-439.
［12］XIANG L, GAO X Y, HU A J.Nonlinear dynamics of an asymmetric rotor-bearing system with coupling faults of crack and rub-impact under oil-film forces［J］.Nonlinear Dynamics, 2016, 86(2): 1057-1067.
［13］VARNEY P, GREEN I.Nonlinear phenomena, bifurcations, and routes to chaos in an asymmetrically supported rotor-stator contact system［J］.Journal of Sound and Vibration, 2015, 336:207-226.
［14］KAASPETERSEN C.Computation of quasi-periodic solutions of forced dissipative systems［J］.Journal of Computational Physics, 1985, 58(3): 395-408.
［15］胡海岩.应用非线性动力学［M］.北京: 航空工业出版社, 2000.
［16］HU H Y.Detection of grazing orbits and incident bifurcations of a forced continou, piecewise-linear oscillator［J］.Journal of Sound and Vibration, 1995, 187(3): 485-493.
［17］SIMPSON D J W, MEISS J D.Neimark-Sacker bifurcations in planar, piecewise-smooth, continuous maps［J］.Siam Journal on Applied Dynamical Systems, 2008, 7(3): 795-824.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
PDF(2871 KB)
