齿轮系统动力学分析及计算机仿真

【作者】 朱秋玲；

【导师】 韩致信；

【作者基本信息】 兰州理工大学 ， 机械设计及理论， 2004， 硕士

【摘要】 齿轮传动是最常用的、也是最重要的传动方式之一，它的工作状况极其复杂，不仅载荷、工况等的变化会引入外部激励，而且在齿轮传动过程中，啮合齿对的单、双交替变化导致随时间周期变化的齿对综合啮合刚度，使系统在外载恒定或为零的情况下依然存在动态激励。 本文以渐开线直齿轮为对象，建立了在考虑啮合齿对齿面间的摩擦力的情况下，齿轮传动系统的非线性动力学模型。为了研究时变刚度对系统的影响，本文采用石川法(Ishikawa)求得了齿轮的时变啮合刚度。 采用变步长的Runge-kutta和Gill的数值积分方法，对系统的非线性微分方程进行了求解，经过对系统相应的计算，得到了一对齿啮合时间的齿轮轴心的动态响应曲线。 此外，本文还根据齿轮的啮合原理和坐标的变换公式，求出了齿轮啮合点在误差状态下啮合响应，为研究啮合点齿轮的摩擦力以及运动、振动奠定了基础。更多还原

【Abstract】 Gear transmission is one of the most frequently used and important transmission way. It’s working state is very complicated, because not only the change of loading and operating mode, etc. can introduce outside encourage, but also the alternated change of the odd and even of engaged meshing teeth pairs during the gear transmission can lead to the engaged synthetical stiffness of teeth pairs which periodically vary with the time. As a result, it makes that the system dynamic excitement still exists invariable even when external load is constant or zero.This paper regards involute spur gear as the target, and sets up a nonlinear dynamics model of the system, which consider the frictional force of meshing teeth. In order to study the effect of time-varying stiffness on system dynamic characteristics , the paper carried out the time-varying engaged stiffness by Ishikawa method.In addition, the paper solved the system’s governed nonlinear differential equations by variable step size Runge-kutta and Gill numerical integration methods.as a result , the paper get the dynamics responds of gears axle centers during one tooth meshing.According to the meshing theory and coordinate transformation, the paper get the responds of meshing point on the condition of error meshing also. It is a basis to get the friction force, movement and vibration on the meshing point.更多还原