有界窄带激励柴油机轴系扭振系统主参数共振

Primary Parametric Resonance of Shafting Torsional Vibration System of the Diesel Engine Subjected to Narrow-band Random Excitation

研究柴油机轴系扭振强非线性系统在有界窄带激励下的主参数共振响应和稳定性问题。应用改进多尺度法得到在有界窄带随机激励下柴油机轴系扭振系统的幅频响应方程,导出系统的Ito随机微分方程。通过矩法得到系统随机均方响应的近似表达式,分析各个参数对柴油机轴系扭振系统主参数共振均方值的影响。结果表明,主参数共振稳态解稳定的充分必要条件与系统二阶矩稳定的充分必要条件是一样的;随着阻尼值的增大,系统主参数共振振幅的均方值减小;随着曲轴扭转刚度的减小,系统主参数共振的均方响应曲线的斜率增大;随着随机扰动强度的增大,系统时间响应曲线和相图变化微小。

The primary parameters resonance and stability problems of strong nonlinear torsional vibration of the diesel engine shafting system under narrow- band excitation are investigated. The frequency response equation of the system is obtained based on the modified multi-scale method and the corresponding Ito stochastic differential equation is derived. By means of the moment method, the approximate expression of the mean-square response of the system is obtained and the influence of the system parameters on the mean square value of the primary parametric resonance is analyzed. The results show that the sufficient and necessary conditions for the stability of primary parametric resonance are the same as those of the second order moment stability. With the increase of the damping, the mean square value of the resonant amplitude of the primary parameters of the system decreases; With the decrease of the torsional stiffness of the crankshaft, the slope of the mean square response curve of the system increases; Along with the increase of the random disturbance intensity, the time response curve and the phase diagram of the system only have small changes.