关键词: 齿轮系统, 全局分析, 图胞映射

Abstract: The mathematical model of single degree of freedom gear system with time varying stiffness and clearances is set up. The digraph cell mapping method based on graph theory and generalized cell mapping theory is introduced, and accordingly a digraph cell mapping algorithm for solving nonlinear problems is put forward. The global character of nonlinear gear system is analyzed by using the digraph cell mapping algorithm, and a series of the attractors, the domain of attraction, unstable solutions, and the attractive basin boundaries of the gear system are obtained. The result shows: there are one, three or two stable attractors respectively in the system when  is 0.45, 0.80, or 1.50 and there is also an unstable attraction when  is 1.50. Finally, comparative analysis is carried out by using the phase diagram of the system. Initial points are picked up from different domains of attraction and converge at corresponding stable attractors, thus verifying the effectiveness and credibility of the digraph cell mapping algorithm. Using the result of digraph cell mapping method, a good system response can be obtained by rationally controlling the initial conditions in case of bad parameters.

Key words: Digraph cell mapping, Gear system, Global analysis