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Global Dynamic Characteristic of nonlinear torsional vibration System under Harmonically Excitation

Chinese Journal of Mechanical Engineering 2009年第1期22卷 132-139页

作者： SHI Peiming LIU Bin HOU Dongxiao Institute of Electrical Engineering Yanshan University Qinhuangdao 066004 China

torsional vibration generally causes serious instability and damage problems in many rotating machinery parts. The global dynamic characteristic of nonlinear torsional vibration system with nonlinear rigidity and nonlinear friction force is investigated. On the basis of the generalized dissipation Lagrange＇s equation, the dynamics equation of nonlinear torsional vibration system is deduced. The bifurcation and chaotic motion in the system subjected to an external harmonic excitation is studied by theoretical analysis and numerical simulation. The stability of unperturbed system is analyzed by using the stability theory of equilibrium positions of Hamiltonian systems. The criterion of existence of chaos phenomena under a periodic perturbation is given by means of Melnikov＇s method. It is shown that the existence of homoclinic and heteroclinic orbits in the unperturbed system implies chaos arising from breaking of homoclinic or heteroclinic orbits under perturbation. The validity of the result is checked numerically. Periodic doubling bifurcation route to chaos, quasi-periodic route to chaos, intermittency route to chaos are found to occur due to the amplitude varying in some range. The evolution of system dynamic responses is demonstrated in detail by Poincare maps and bifurcation diagrams when the system undergoes a sequence of periodic doubling or quasi-periodic bifurcations to chaos. The conclusion can provide reference for deeply researching the dynamic behavior of mechanical drive systems.

关键词： nonlinear torsional vibration dynamics behavior bifurcation chaos Melnikov's method

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Comparative research of nonlinear torsional vibration in the drive system with clearances

Comparative research of nonlinear torsional vibration in the...

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第十五届全国非线性振动暨第十二届全国非线性动力学和运动稳定性学术会议

作者： GAO Chong-yi DU Guo-jun LI Jian-xiong Key Laboratory of Mechanics Reliability for Heavy Equipment and Large Structure of Hebei Yanshan University Department of Automation Institute of Electrical EngineeringYanshan University

Considering causes of design,installation and wear,the drive system shows different clearances in a heavy plate *** oscillator has repeated impacts in clearance when biting impact or rolling slippage occurs,and the relative amplitude will be increased largely,which is the major factor of most system *** on the 5000 mm heavy plate mill,the torsional vibration models of biting impact and rolling slippage are established *** using the numerical method,the torque amplification factors of biting impact or rolling slippage are calculated,moreover the numerical computation results of dynamic response with clearances and comparative analysis of torsional vibration responses are obtained between different *** with the engineering practice,the influences of different position and size of clearance on torque amplification factors are *** results may provide an important theoretical reference to control and analyze the torsional vibration of this kind of rolling mill.

关键词： biting impact,rolling slippage clearances nonlinear torsional vibration torque amplification factor

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