多间隙弯扭耦合齿轮非线性振动的分岔特性研究

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振动与冲击 ›› 2014, Vol. 33 ›› Issue (19) : 116-122.

论文

多间隙弯扭耦合齿轮非线性振动的分岔特性研究

盛冬平朱如鹏陆凤霞靳广虎

作者信息 +

Bifurcation characteristic study of the transverse-torsional coupled nonlinear gear vibration with multiple-clearances

SHENG Dong-ping ZHU Ru-peng LU Feng-xia JIN Guang-hu

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文章历史 +

摘要

采用集中质量法，建立了齿轮-转子-轴承系统的四自由度的弯扭耦合的非线性振动模型，模型考虑了齿轮副间的时变啮合刚度、齿侧间隙、支承间隙以及综合传递误差等非线性因素；推导出系统的量纲一振动微分方程，采用数值积分方法研究多间隙弯扭耦合齿轮传动的运动随转速、齿侧间隙、支承间隙以及阻尼等参数的分岔特性,同时结合Poincaré截面图，全面系统的分析了转速、啮合阻尼、齿侧间隙以及支承间隙等参数对系统分岔特性的影响。结果发现，在一定的齿侧间隙和啮合阻尼下，随着转速的逐渐增加，系统进入混沌的途径包括激变和拟周期分岔，且随着阻尼系数的增加，系统的分岔和混沌运动被抑制，表现为其混沌区域宽度逐渐降低；在一定的转速和啮合阻尼下，而随着齿侧间隙的逐渐增加，系统会从通过激变进入混沌的途径转变成由倍周期分岔途径进入到混沌，且系统在不同的啮合阻尼下最终锁相为混沌、周期四、周期二和周期一运动；在满足一定的转速和啮合阻尼条件下，随着齿侧间隙的增加，系统可通过倍周期分岔进入并锁定为Naimark-sacker分岔。在满足一定的转速、啮合阻尼和齿侧间隙的条件下，随着支承间隙的增加，系统运动进入狭窄的周期五窗口后锁相为周期一运动，且从系统的控制方程和数值解可以发现支承间隙对系统的运动的影响较弱。

Abstract

Using the mass centralized method, a multiple clearance nonlinear gear-rotor-bearing coupled transverse-torsional vibration model is established and dimensionless equations of the system are derived, and transmission errors, time varying meshing stiffness and gear backlashes are considered in this model. By studying poincaré maps and bifurcation diagrams, the bifurcation properties of the system are obtained. The influence of some bifurcation parameters such as rotation speed, damping coefficient and gear backlashes is analyzed. Under a certain gear backlash and mesh damping and with the increasing of the rotating speed, the way of system entering into chaos is changed from crisis to period doubling bifurcation, and the system phase locked into period-four, period-two and period motion state under different mesh damping coefficient. Under a certain rotation speed and mesh damping, the motion state of the system changes from period doubling bifurcation into Naimark-sacker bifurcation. Under a certain rotation speed and mesh damping and the gear backlash, the system could enter period-five motion and phased locked into period motion rapidly, and judged from the numerical solution, bear rolling clearance has a weak interaction with system motion.

导出引用

盛冬平朱如鹏陆凤霞靳广虎. 多间隙弯扭耦合齿轮非线性振动的分岔特性研究[J]. 振动与冲击, 2014, 33(19): 116-122

SHENG Dong-ping ZHU Ru-peng LU Feng-xia JIN Guang-hu. Bifurcation characteristic study of the transverse-torsional coupled nonlinear gear vibration with multiple-clearances[J]. Journal of Vibration and Shock, 2014, 33(19): 116-122