多因素条件下单级齿轮系统的非线性特性

考虑啮合刚度、齿侧间隙和轴承支撑间隙等因素，运用集中质量法建立了三自由度直齿圆柱齿轮副弯扭耦合非线性振动模型，并据此研究了各参数对齿轮系统非线性振动特性的影响。结果表明：齿侧间隙一定时，随着频率的升高，系统由周期运动通过激变直接进入混沌，然后又由混沌通过激变变为周期运动；在周期运动中，系统经过倍周期分岔,由双周期运动变为四周期运动，然后又通过逆倍周期分岔,由四周期运动变为双周期运动，之后又由双周期运动变为单周期运动；不同的输入转频条件下，间隙变化使系统表现出不同分岔特性，在某些特定频率下，间隙变化只增加系统响应能量变化，并不改变其动力学特性。

Nonlinear Characteristic of Single Stage Gear System under Condition of Multiple Factors

A nonlinear vibration model of three-degree-of-freedom spur gears coupled with transverse and torsion was established by mass centralized method, considering meshing stiffness, gear backlashes and bearing clearances. Parameter influences on the nonlinear vibration characteristics of the gear system were studied. The results show that, with the increase of frequency, the system enters chaos from periodic motion through a catastrophic way, then from the chaos to periodic motions. In periodic motions, the system changes from period 2 to period 4 through a period-doubling bifurcation, then from period 4 to period 2, and then from period 2 to period 1 through a inverse period-doubling bifurcation. For the different input frequencies, the changes of backlash make the system show different bifurcation characteristics. For some specific frequencies, the changes of the backlash only increase the amplitudes of the system response and do not change its dynamic characteristics.