旋转刀盘圆弧齿轮成形理论分析及数字化建模研究

Research on the Forming Theory Analysis and Digital Model of Circular Arc Gear Shaped by Rotary Cutter

为得到用于指导加工和仿真计算的圆弧齿轮精确3维模型,根据刀盘与齿轮工件的展成关系,运用空间啮合理论及微分几何知识,推导了圆弧齿轮的齿面方程,证明得到其中截面齿廓为渐开线。对齿面方程中各参数的取值范围进行讨论,给出了定参数下齿轮工件转角φ的计算公式。利用计算机软件实现了旋转刀盘圆弧齿轮的数字化建模,得到了圆弧齿轮的3维数字模型。对比用模拟加工得到的模型,该模型具有更高的建模精度,并根据此模型加工出了工件实体。研究结果可为后续的仿真、实验分析提供基础,并为圆弧齿轮的参数选取及设计应用提供参考。

In order to get a reliable circular arc gear 3D model to guide the manufacturing processing and simulation calculation, according to the development of the cutter and the gear workpiece, using the basic knowledge of spatial meshing theory and differential geometry, the tooth surface equations of rotating cutter circular arc gear was deduced, and the results showed that the profile of the middle section is involute. The range of the parameters was also discussed according to the equation, and the calculation formulas under given parameters of the gear workpiece rotation angle was given. The digital modeling of circular arc gear shaped by rotating cutter was realized and its 3 D model was built by computer software. Compared with the model obtained by simulation machining, this model had a higher modeling precision, and the workpiece was processed according to this model. The research results could provide a reference for the parameter selection and design of the circular arc gear, and could provide the basis for the following simulation and experiment analysis.