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基于经典的间隙单齿轮副非线性动力学模型,采用伪不动点追踪法研究了齿轮系统共存的周期解,采用胞映射方法研究了各共存周期解的全局稳定性。结果发现,在考查参数下,齿轮系统存在3种不同形怎的周期运动,即分别是周期1解(0.634 6,0.062 5)、周期2解(-0.141 4,-0.150 5)和周期4解(-0.2053,-0.151 8)。其中,周期1解不具备长期运动稳定性;周期2解的吸引域面积较大且连续,具有较高的局部稳定性;周期4解的吸引域不连续,运动的初值稳定性较差。
Based on the classical nonlinear dynamic model of single gap gear pair, the quasi-fixed point tracking method is used to study the periodic solution of the coexistence of gear systems. The global stability of the coexistence periodic solutions is studied by using the cell mapping method. The results show that there are three kinds of periodic motions of the gear system under the test parameters: cycle 1 solution (0.634 6,0.062 5), cycle 2 solution (-0.141 4, -0.150 5) and cycle 4 solution (-0.2053, -0.151 8). Among them, the solution of period 1 does not have the long-term stability of motion; the solution of period 2 has larger and continuous attracting area with higher local stability; the solution of period 4 has discontinuous attracting domain and the stability of the initial value of motion is poor.