N叶非圆锥齿轮的设计缺陷分析

Design Defect Analysis of N-Lobed Non-circular Bevel Gear

针对N叶非圆锥齿轮节曲线会产生不连续等问题,提出了一种新的非圆锥齿轮节曲线的设计方法,该方法有效简化了非圆锥齿轮的设计。推导了非圆锥齿轮的节锥与球面的交线方程,以该交线作为非圆锥齿轮的节曲线,以球面渐开线锥齿轮为非圆锥齿轮的产形刀具,建立了刀具的节面与非圆锥齿轮节面的数学模型。依据非圆锥齿轮节面大端曲线的特性,分析了节面曲线产生不连续点的原因及修正方法。研究结果表明,该算法可快速辨识出非圆锥齿轮产生根切和齿顶过切等设计缺陷,且算法准确和有效。

To solve pitch curves of N- Lobed non- circular bevel gear being discontinuous,a novel pitch curve design method for non- circular bevel gear（ NCBG） is presented to simplify design of NCBG. The intersection curve equations between pitch cone surface of non- circular gear and spherical surface are derived,and the intersection curve is taken as pitch curve of NCBGs. The bevel gear with spherical involute is considered as generating cutter of NCBGs tooth profile,and mathematical models between pitch surface of bevel gear cutter and that of NCBGs are established. Based on this model,a machining simulation algorithm is developed. In addition,according to the characteristic of big end curve function of pitch cone surface of NCBGs,the causes of discontinuity and modifying methods of pitch curve of NCBGs are analyzed. The study results show that,the design defects such as undercutting and addendum overcutting of NCBGs can be identified quickly by applying the machining simulation algorithm,and it is exactly and effectively.