含万向铰偏斜轴系的主共振及其稳定性分析

Analysis of principal resonance and stablity of torsional vibration in misaligned shafts driven by universal joint

为了揭示含万向铰偏斜转子系统非线性动力学的基本特征,研究了固有结构偏斜与实际误差偏斜共同作用下含万向铰偏斜轴系的扭转振动问题。首先,推导出偏斜转子系统的弱非线性扭转振动方程,利用多尺度法求得其在主共振情形下的周期解,并给出稳态周期解的幅频特性和相频特性关系式;然后,运用李雅普诺夫第一近似稳定性理论,对系统平衡点进行稳定性研究,得到主共振解振幅与相位随调谐参数变化的稳定区与不稳定区;最后,对偏斜轴系中从动轴一端的一阶近似稳定周期运动进行了分析与仿真。研究结果为进一步的分岔与奇异性分析奠定了基础。

The nonlinear tosional vibration of the rotor system driven by the universal joint was stu- died according to natural structure misalignment and practical error misalignment. Firstly, the equa- tion of weakly nonlinear vibration was derived. Secondly, the periodic solution in the case of principal resonance was obtained by use of the multi-scale method, and the amplitude-frequency characteristics and phase-frequency characteristic curves were presented. Thirdly, the stable regions of the amplitude and phase of the periodic solution were deduced by using Lyapunov＇s approximate stability theory. Fi- nally, the analysis and simulation of the driving shaftrs stable periodic motion of the first approxima- tion were carried out according to the kinetic relation between the driven shaft and the driving shaft. Studies reveal the fundamental characteristics of the nonlinear dynamic on the misaligned shafts, lay- ing the foundations for further bifurcation analysis.