共轭曲线齿轮齿面的构建  

Tooth Profile Generation of Conjugate-curve Gears

作　　者：陈兵奎[1] 高艳娥[1] 梁栋[1] 

机构地区：[1]重庆大学机械传动国家重点实验室,重庆400030

出　　处：《机械工程学报》2014年第3期18-24,共7页Journal of Mechanical Engineering

基　　金：国家科技支撑计划资助项目(2013BAF01B04)

摘　　要：在共轭曲线原理的基础上,提出以适当半径的球面沿曲线的指定等距线包络出啮合管的等距包络法,建立共轭曲线齿轮管状齿面的构建理论。推导一对共轭曲线的等距线方程、啮合管方程等,通过截取含有曲线部分的啮合管构建齿轮的啮合齿面,得到具有曲线接触特性的管状齿面;根据啮合管等距距离和等距方向的不同,构建三种不同接触形式的管状齿面:凸凸接触、凸平接触和凸凹接触,其中凸凹接触形式的管状齿面在接触点处的相对曲率半径最大,赫兹接触应力最小。以常用的圆柱螺旋线为例,介绍共轭曲线齿轮齿面构建理论的应用,求解该曲线及其共轭曲线的等距线方程和啮合管方程,并根据运算结果建立精确的共轭曲线齿轮实体模型。The forming theory of the tubular meshing tooth surfaces of conjugate-curve gears is established. An equidistance-envelope method is proposed based on the principle of conjugate curves. The meshing tube is generated by a sphere with an appropriate radius following a given equidistance curve of a given curve; the equations of equidistant curves and meshing tubes of conjugate curves are derived; and the tubular profiles are designed as parts of tubes inheriting all contact characteristics of conjugate curves. Three different contact patterns of tubular tooth profiles, convex-to-convex, convex-to-plane and convex-to-concave, are generated due to the different equidistance and directions. And the convex-to-concave tubular tooth profile has the smallest contact stress at the contact point due to the largest value of the relative curvature radius. An illustration of a cylindrical helix is presented; the equations of equidistance curves and meshing tubs of the conjugate curves are solved; and the models of conjugate-curve gears are set up.

关 键 词：共轭曲线 齿轮啮合 管管状齿面 凸凹接触 圆柱螺旋线 

分 类 号：TH123[机械工程—机械设计及理论]