考虑齿圈柔性的内啮合齿轮时变啮合刚度计算分析

Calculation and analysis of time-varying meshing stiffness of internal meshing gear considering ring gear flexibility

当前大多数内齿轮啮合刚度都是基于忽略齿圈基体变形的假设计算的,文中应用Weber能量法基于精确的齿廓曲线方程建立内齿轮悬臂梁等效模型,同时基于铁木辛柯(Timoshenko)曲梁理论计算齿圈基体的变形量,并将齿圈变形耦合到齿轮啮合刚度计算中。通过MATLAB GUI编程进行内啮合齿轮时变啮合刚度数值计算,分析了齿圈柔性对啮合变形的影响,研究了齿圈厚度、支撑数量及啮合力位置对啮合刚度的影响。结果表明:齿圈厚度和支撑数量的增加均有利于齿轮副啮合刚度的增大;啮合齿中线位于固定支撑点时,齿圈啮合刚度最大,在靠近支撑中间位置时,啮合刚度最小,齿圈啮合刚度对应于螺栓支撑呈周期性波动。

At present,the meshing stiffness of most internal meshing gears is calculated based on the assumption that the ring gear base's deformation is ignored.In this article,the Weber energy method is used to set up the equivalent model of the in-ternal meshing gear's cantilever beam,according to the curve equation of the accurate tooth profile.At the same time,the Timo-shenko curve beam theory is used to calculate the ring gear base's deformation,and then the deformation is coupled to calculate the meshing gear's meshing stiffness.The MATLAB GUI programming is used for numerical calculation of the internal meshing gear's time-varying meshing stiffness,and the influence of ring gear flexibility on the meshing deformation is explored.In addi-tion,the analysis is conducted on the influence of the ring gear's thickness,the number of supports and the position of the mes-hing force on the meshing stiffness.The results show that both the ring gear's ever-growing thickness and the increasing number of supports are helpful to increase the gear pair's meshing stiffness.When the meshing gear's center line is located at the fixed supporting point,the ring gear's meshing stiffness is the largest;when the meshing gear's center line is close to the middle posi-tion of the supporting point,the meshing stiffness is the smallest;the ring gear's meshing stiffness fluctuates periodically corre-sponding to the bolt support.