多间隙二级齿轮非线性振动分岔特性研究

发布时间：2018-04-05 21:12

本文选题：非线性振动　切入点：Hopf分岔　出处：《应用数学和力学》2016年02期

【摘要】：采用集中质量法,建立了多间隙二级齿轮系统的五自由度非线性振动模型.模型考虑了各齿轮副间变刚度、齿侧间隙、支承间隙以及传动误差等非线性因素,推导出系统量纲振动微分方程,并利用分岔图、Poincaré截面图,全面地分析了系统转速、阻尼比对系统分岔特性的影响.结果发现系统在各种非线性因素的综合影响下,表现出丰富复杂的分岔特性.系统随着参数的变化先后出现短周期运动、长周期运动、拟周期运动及混沌运动.在不同阻尼比下,系统随着转速的逐渐减小,由稳定的周期1运动,倍化分岔变为稳定的周期2运动,再经过Hopf分岔变为拟周期运动,通过激变又变为稳定的周期1运动,最终通过Hopf分岔-锁相进入混沌.随着转速的逐渐增大,系统随阻尼比变化的混沌运动范围减小,出现稳定的周期1运动、长周期和拟周期运动,并且长周期和拟周期运动范围逐渐变小而稳定的周期1运动的范围逐渐变大.
[Abstract]:A five-degree-of-freedom nonlinear vibration model for a multi-clearance two-stage gear system is established by means of the lumped mass method.The model takes into account the nonlinear factors such as variable stiffness between gear pairs, tooth side clearance, support clearance and transmission error. The differential equation of system dimensional vibration is derived, and the rotational speed of the system is analyzed comprehensively by using the bifurcation diagram and Poincar 茅 section diagram.The effect of damping ratio on the bifurcation characteristics of the system.The results show that the system exhibits rich and complex bifurcation characteristics under the influence of various nonlinear factors.With the change of parameters, there are short period motion, long period motion, quasi periodic motion and chaotic motion.Under different damping ratios, the system changes from stable period 1 motion, double bifurcation to stable period 2 motion with the gradual decrease of rotational speed, then through Hopf bifurcation to quasi-periodic motion, and then to stable period 1 motion by means of shock change.Finally, Hopf bifurcation-phase locking into chaos.With the increase of rotational speed, the chaotic motion range of the system decreases with the change of damping ratio, and there are stable period 1 motion, long period motion and quasi period motion.And the range of long-period and quasi-periodic motion becomes smaller and the range of stable period 1 motion gradually becomes larger.
【作者单位】：塔里木大学信息工程学院;塔里木大学机械电气化工程学院;
【分类号】：O322

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