功率分流齿轮传动参数空间解域界及吸引域全局特性  

Global characteristics of basin of attraction and parameterized solution domain of power-split gear transmission

作　　者：林何 洪灵[2] 刘霞[1,3] 胥光申[1,3] LIN He;HONG Ling;LIU Xia;XU Guang-shen(School of Mechanical and Electrical Engineering,Xi′an Polytechnic University,Xi′an 710048,China;State Key Laboratory for Strength and Vibration of Mechanical Structures,Xi′an Jiaotong University,Xi′an 710049,China;Xi′an Key Laboratory of Modern Intelligent Textile Equipment,Xi′an Polytechnic University,Xi′an 710600,China)

机构地区：[1]西安工程大学机电工程学院,陕西西安710048 [2]西安交通大学机械结构强度与振动国家重点实验室,陕西西安710049 [3]西安工程大学西安市现代智能纺织装备重点实验室,陕西西安710600

出　　处：《振动工程学报》2021年第2期235-242,共8页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(51805402);陕西省自然科学基础研究计划项目(2019JQ-851);陕西省教育厅专项科研计划(18JK0351);西安市现代智能纺织装备重点实验室(2019220614SYS021CG043)。

摘　　要：为揭示齿轮系统动力学全局解域特性,建立了功率分流直齿轮系统非线性振动模型,结合胞映射与区域分解思想构建了主要激振参数下的系统全局解域求解算法。求解了阻尼比分别与综合传动误差、啮合频率和齿侧间隙等参数配置下的平面解域界结构,揭示了两参量解域区内的动态行为潜在趋势,如倍周期分岔序列、混沌窗口带等的迁移演化。借助Lyapunov指数对不同误差幅值下分岔通道结构进行追踪,验证了分岔节点与解域界子域临界点相吻合。数值求解多组阻尼比下的吸引域全局性态,发现混沌吸引域与周期1吸引子吸引域间相互扩张与进退演变激烈,二者胞域边界处系统局部平衡态势异常脆弱;当阻尼比为0.04时吸引域行为相对敏感,多吸引子共存现象突出。其结果可为齿轮系统振动优化及参数全局设计提供参考。In order to investigate the global characteristics of dynamic solutions of gear systems,a nonlinear dynamical model of the power-split spur gear transmission is established,and the calculation algorithm regarding global solutions under main excitation parameters is deduced based on cell mapping method(CMM)as well as domain decomposition method(DDM).Parametric planar solution domains constructed by damping ratio respectively with synthetically transmission error,mesh frequency and backlash are computed,and the potential global evolution behaviors within solution domains are exhibited,such as period-doubling bifurcation cascades,chaotic window zones.The bifurcation routes inside solution domain with respect to varied error magnitudes are tracked by applying largest Lyapunov exponent,which demonstrate that bifurcation nodes are in consistent with the subdomain boundary points presented in parameterized solution domain.By numerically calculating the global behaviors of the basin of attraction under multiple damping ratios,it is shown that mutual expansion and retrogression between the chaotic basin of attraction and the period 1 basin of attraction are remarkably,and the local equilibrium of the cells nearby the boundary is extremely unstable.The basin of attraction is sensitively while the damping ratio reaches 0.04,and multiple attractors coexisting phenomenon exhibits significantly.The result could provide references for vibration optimization or even global design of dynamic parameters for gear system.

关 键 词：机械振动 功率分流传动 胞映射 解域界 吸引域 

分 类 号：TH113.1[机械工程—机械设计及理论] TH132.41