分度圆裂纹齿轮啮合刚度计算及啮合动态特性分析

Meshing stiffness calculation and meshing dynamic characteristics analysis of gear with graduation circle crack

为了探究分度圆裂纹对齿轮传动系统产生的影响,利用改进能量法计算分度圆裂纹齿轮的啮合刚度,结合动力学模型对齿轮传动系统进行了动态特性分析。首先,将齿轮的齿根圆视为悬臂梁起点,把分度圆裂纹按照其齿廓投影位置分为了3种情况;然后,利用改进能量法理论计算了不同裂纹情况下的齿轮啮合刚度;最后,在啮合刚度的基础上,建立了齿轮系统的六自由度动力学模型,分析了不同裂纹情况下的齿轮系统的动态特性。仿真结果表明:相比于正常齿轮,分度圆裂纹为2.5 mm时,齿轮的啮合刚度最多下降14.3%,传递误差最多升高12.2%,齿间啮合力最多下降3.6%,啮合摩擦力最多下降14.8%;随着裂纹长度增大,齿轮啮合刚度逐渐降低,传递误差随之增大,齿间啮合力和啮合摩擦力逐渐降低。研究结果表明:由于裂纹的影响,齿轮传动系统会受到周期性冲击。

To explore the influence of graduation circle crack on the gear transmission system,the improved energy method was used to calculate the mesh stiffness of the graduation circle crack gear,and the dynamic characteristics of the gear transmission system were analyzed in combination with the dynamic model.Firstly,the tooth root circle of the gear was regarded as the starting point of the cantilever beam,and the graduation circle crack was divided into three cases according to its tooth profile projection position.Then,the gear meshing stiffness under different crack conditions was calculated by using the improved energy method theory.Lastly,based on the mesh stiffness,a dynamic model of six degrees of freedom of the gear system was established,and the dynamic characteristics of the gear system under different crack conditions were analyzed.The simulation results show that,compared with normal gears,when the dividing circle crack is 2.5 mm,the meshing stiffness of the gears decreases by 14.3%,the transmission error increases by 12.2%,the meshing force between teeth decreases by 3.6%and the meshing friction decreases by 14.8%.As the crack length increases,the meshing stiffness of the gear decreases gradually,the transmission error increases,and the meshing force and meshing friction between the teeth decrease gradually.The results show that,due to the influence of cracks,the gear transmission system is subject to periodic impact.