齿轮时变系统的强迫振动

建立了考虑齿轮时变啮合刚度时的二级齿轮系统的动力学模型，用A算符方法推导出了系统的近似解析解，研究了系统对时变啮合刚度、扭矩波动及齿轮误差激励的响应。计算结果表明，A算符方法克服了谐波平衡法的缺陷，可靠性更高；系统响应的频率成分不仅与啮合频率和激励频率有关，还与其组合形式有关；即使激励频率远大于派生系统的固有频率，在实际的物理系统中，由于时变啮合刚度的影响，也可能出现主共振、谐共振和组合共振。

Forced Vibration of Gear System with Time-varying Mesh Stiffness

Dynamic model of two-stage gear system with time-varying mesh stiffness was established. Approximate analytic solution of the system was developed by means of A-operator method (AOM). It was used to investigate the response to time-varying mesh stiffness, torque fluctuation and errors of gear pair. It is shown that A-operator method (AOM) overcomes the filter defaults of harmonic balance method. Therefore it has more reliable numeric results. When the system is inspired by time-varying mesh stiffness, torque fluctuation and errors of gear pair, the frequency components of response are related to the inspiring frequency, and mesh frequency, and to their combined type. Even if inspiring frequency is far from frequency of the derived system, first harmonic, super harmonic and combined harmonic resonance may take place respectively in the normal speed range of an actual gear system, because of time-varying mesh stiffness.