多间隙二级齿轮非线性振动分岔特性研究

Nonlinear Vibration Bifurcation Characteristics of Multi-Clearance 2-Stage Gear Systems

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.

A 5-DOF nonlinear vibration model for multi-clearance 2-stage gear systems was established with the lumped-mass method. In viewof transmission errors,time-varying meshing stiffness and multiple gear clearances,the dimensionless dynamic equations for the system were derived. By means of the Poincaré maps and bifurcation diagrams,the bifurcation properties of the system were discussed under the effects of the rotation rate and the damping ratio. Given the various nonlinear factors,the 2-stage gear system exhibits rich and complex bifurcation characteristics. With the changes of the related parameters,the system will be in short-period motion,or long-period motion,or quasi-periodic motion or chaotic motion. For different damping ratios,with the decrease of the rotation rate,the system state changes from stable period-1 motion into stable period-2 motion through period-doubling bifurcation; then the system state changes into quasi-periodic motion through the Hopf bifurcation,in turn changes into stable period-1 motion after a catastrophe; finally the system enters into chaos through the Hopf bifurcation-phase locking. Moreover,with the increase of the rotation rate,the system damping ratio range corresponding to chaotic motions reduces,and the system will be in stable period-1 motion,or long-period motion or quasi-periodic motion,while the damping ratio range corresponding to long-period motion and quasi-periodic motion shortens and that corresponding to period-1 motion lengthens.