锥形齿轮滚削齿面的构成理论及参数计算

Hobbing Tooth Flank Generating Theory and Parameters Calculation of Conical Involute Gears

根据齿轮啮合原理中多自由度齿面包络理论,对渐开线锥形齿轮在滚齿加工中,刀具与工件的相对运动及产形齿条的形成机理进行了深入分析,证明了产形齿条的存在,并求解了其齿面形状.通过对齿轮、滚刀和产形齿条三者之间空间几何关系的进一步分析,研究了锥形齿轮的齿面构成理论,求证了由产形齿条包络运动所形成的齿轮渐开螺旋齿面,并推导了齿条和齿轮几何参数的计算公式.研究结果不仅对锥形齿轮的滚齿加工具有重要的理论指导意义,而且对于具有类似运动的其他加工方法也同样适用.

The gear hobbing of conical involute gear is a complex generating motion with doubledegree of freedom. Based on the theory of tooth enveloping for multi-degree of freedom, the relative motion between cutter and gear and the generating mechanism of imaginary rack are analyzed, thus, the existence of imaginary rack is proved, and its tooth shape is obtained. By the aid of the analysis of spatial geometric relationships among gear, hobbing cutter and rack, the tooth generating theory of conical involute gear and the calculation formulae of geometrical parameters are investigated. The results are helpful to hobbing machining of conical involute gears and to the other processing methods that have the similar generating motion.