球面渐开线螺旋锥齿轮建模及其齿面检测

Spherical Involute Spiral Bevel Gear Modeling and Its Tooth Surface Inspection

为了精确高效地建立螺旋锥齿轮模型,以球面渐开线的形成理论为依据,采用MATLAB 2023a软件编写齿面离散点程序,分别获取一对配合的大小齿轮的凹凸齿面离散点坐标。采用UG NX12.0软件对齿面离散点进行曲面拟合,分别建模出大小螺旋锥齿轮各自的单个齿条,并绘制各自齿坯。采用Creo Parametric 9.0对大小螺旋锥齿轮进行装配,运用机构分析模块,实现齿轮的运动仿真。采用3D打印机打印模型,经验证大小齿轮实物的啮合运动顺畅。通过对大小齿面单独建模,对齿面进行测点规划和检测得到齿面的3D打印误差。由数据分析得出齿面的平均误差为0~0.16mm,进一步验证了该模型的有效性。

In order to achieve precise and efficient modeling of spiral bevel gears,based on the theory of spherical involute formation,a tooth surface discrete point program is written using MATLAB 2023a software to separately obtain the coordinates of discrete points on the concave and convex tooth surfaces of a matched pair of large and small gears.The tooth surface discrete points are subjected to surface fitting using UG NX12.0 software,and individual tooth profiles of both the large and small spiral bevel gears are separately modeled,followed by the completion of their respective tooth blanks.The modeling of both large and small spiral bevel gears is accomplished using a series of commands such as mirroring,arraying,stitching,and merging.Subsequently,the large and small spiral bevel gears are assembled using Creo Parametric 9.0,and gear motion simulation is achieved using the mechanism analysis module.To validate the effectiveness of the model established,the model is 3D printed,and it is confirmed that the meshing motion of the physical large and small gears is smooth.By separately modeling the large and small tooth surfaces and planning and inspecting measurement points on the tooth surfaces,the 3D printing error of the tooth surface is obtained.The data analysis reveals that the average error of the tooth surface ranges from 0 to 0.16mm,further confirming the effectiveness of the modeling method.