齿轮滚刀三角面片集模型的建立及分析

Modeling of Triangular Patch Set of Gear Hob

为检验CNC齿轮测量中心中滚刀测量程序的正确性,针对虚拟齿轮测量中心的测量需求,建立了理论准确的齿轮滚刀三角面片集模型.根据滚刀的加工原理.根据滚刀的加工原理,提出了一种滚刀齿面方程的建立方法,以阿基米德滚刀为例,推导了铲背面的方程,求出了理论准确的齿面离散数据点,构建了铲背面的三角面片集模型.研究结果表明:齿轮滚刀铲背面上任一点,都落在以切削刃上对应一点为起点的铲背曲线上,通过求解切削刃和铲背曲线,可求出铲背面上任一点;通过控制各齿面在相接处共用同一组数据点,可实现各三角面片集之间的无缝连接.

In order to test the accuracy of hob measurement in the CNC gear measuring center ,for the requirements of virtual gear measurement center ,a theoretical triangular patch set model of gear hob is established .According to the principle of hobbing ,an establishing method of hob surface equation is proposed .Take the Archimedes hob as an example ,the equations of each shoveling surface are derived , the theoretically accurate discrete points of hob surfaces are solved ,and the triangular patch set model of shoveling surfaces are constructed .The results present ：Every point on shoveling surfaces of gear hob falls on the shoveling curve which startes from a corresponding point on the cutting edge .Any points on shoveling surfaces can be obtained by solving the equations of cutting edges and shoveling curves . Sharing the same set of data points at intersecting line of shoveling surfaces ,the seamless connection between the triangular patches can be realized .