两空间耦合下齿轮传动系统多稳态特性研究

通过将系统参数定义为参数变量, 构成参数空间,研究齿轮传动系统在参数空间和状态空间耦合下的非线性全局动力学特性,以及多参数、多初值和多稳态行为之间的关联特性.首先设计了一个两空间耦合下非线性系统多稳态行为的计算和辨识方法.其次,基于该方法并结合相图、Poincaré映射图、分岔图、最大Lyapunov指数、吸引域等,研究齿轮传动系统在不同参数平面上多稳态行为的存在区域和分布特性,以及多稳态行为在状态平面上的分布特性,揭示了参数平面和状态平面上系统可能隐藏的多稳态行为和分岔,并分析了多稳态行为的形成机理. 结果发现,两空间耦合下系统在参数平面上存在大量多稳态行为并呈"带状"分布, 状态平面上多稳态行为出现两种不同的侵蚀现象, 即内部侵蚀和边界侵蚀.分岔点或分岔曲线对初值的敏感性导致多稳态行为的出现.当齿侧间隙和误差波动在较小的范围内变化时,系统全局动力学特性受间隙和误差扰动的影响较小,受啮合频率的影响较大.两空间耦合下系统全局动力学特性变得丰富和复杂. 

RESEARCH ON MULTI-STABILITY CHARACTERISTICS OF GEAR TRANSMISSION SYSTEM WITH TWO-SPACE COUPLING1)

By defining the system parameters as parameter variables and forming the parameter space, the nonlinear global dynamics of the gear transmission system under the coupling of parameter space and state space are studied in detail in this work. The correlative relationship between multiple parameters, multiple initial values and multiple stable behaviors is also obtained. Firstly, a method for calculating and identifying the multi-stable behavior of a nonlinear system under the coupling of two spaces is designed. Secondly, based on the designed method and combined with phase diagram, Poincaré map, bifurcation diagram, top Lyapunov exponent and basin of attraction, the existence and distribution of multi-stable behavior for the gear transmission system in different parameter planes are investigated numerically to better understand the motion mechanism of the system. In addition, the distribution characteristic of multi-stable behavior in the state plane is also studied on the base of the cell-to-cell mapping method. The multi-stable behavior and bifurcation that may be hidden in the parametric plane and the state plane are fully revealed. The formation mechanism of multi-stable behavior is analyzed as well. The results show that there are a large number of multiple stable behaviors which are banded distribution in the parametric planes of the gear system under the coupling of two spaces. Two different erosion phenomena, such as internal erosion and boundary erosion, are clearly observed in the state plane. The sensitivity of bifurcation points or bifurcation curves to initial values leads to the occurrence of multi-stable behavior. When the amplitude of backlash or error fluctuation changes in a small range, the global dynamic characteristics of the gear system are less affected by the backlash or error disturbance. However, the global dynamic characteristics are greatly affected by the meshing frequency. Global dynamic characteristics of the gear system become rich and complex under two-space coupling.