传动比对齿轮时变系统拍击门槛转速的影响

建立了具有时变啮合刚度的二级齿轮系统的动力学方程式。由于齿轮副啮合刚度的影响,动力学方程式代表了一个具有时变系数的线性动力系统。用算符分解算法(AOM)得到了系统的近似解析解,并研究了传动比和时变啮合刚度对拍击门槛转速的影响。根据计算结果分析,时变啮合刚度可以导致拍击;齿轮啮合频率等于派生系统的固有频率引起的共振是产生拍击的原因之一;增大从动齿轮的齿数、或者增大传动比,一般情况下,可导致拍击门槛转速下降;增大低阶模态阻尼,能够增大拍击门槛转速。

Influence of Speed Ratio on Rattling Threshold Speed of a Gear System with Time-Varying Meshing Stiffness

The governing equation of a gear system with time-varying meshing stiffness is established. Because of the meshing stiffness of a gear pair, the governing equation denotes a linear dynamic system with periodic time-varying coefficient. A-operator method (AOM) is used to study the influence of the speed ratio and time varying meshing stiffness on rattling threshold speed of the gear system. It is concluded that time-varying meshing stiffness may cause rattle; One of the reasons for the rattle is the resonance caused by meshing frequency when it is equal to the natural frequency of the derived system. If tooth number of the driven gear or speed ratio increases, rattling threshold speed will usually decrease, but in a few cases, it will perhaps increase. If lower mode damping is increased in order to limit the resonance amplitude, the rattle threshold speed will increase.