齿轮传动共轭曲线原理  

The Principle of Conjugate Curves for Gear Transmission

作　　者：陈兵奎[1] 梁栋[1] 高艳娥[1] 

机构地区：[1]重庆大学机械传动国家重点实验室,重庆400044

出　　处：《机械工程学报》2014年第1期130-136,共7页Journal of Mechanical Engineering

基　　金：国家科技支撑计划资助项目(2013BAF01B04)

摘　　要：在定义曲线连续相切接触的基础上,提出共轭曲线的概念,给出曲线共轭接触的基本条件。建立共轭曲线的基本理论:计算任意接触角方向的法矢量;论证曲线共轭啮合的充要条件,同时建立曲线沿给定接触角方向的啮合方程;推导共轭曲线及啮合线的通用表达式。分析研究典型曲线——圆柱螺旋线的共轭曲线及其接触性质,揭示不同接触角条件下共轭曲线的啮合关系,并且讨论齿面曲线共轭啮合的特点。研究表明该原理具有一定的通用性可适用于多种齿轮传动类型,同时共轭曲线接触的特点及选择的灵活性能够实现齿轮共轭啮合的最优设计。研究结果为齿轮齿面的构建提供了新方法,并为进一步研究共轭曲线齿轮啮合理论奠定了基础。The concept of conjugate curves is put forward based on the definition of continuous and tangent contact, and the basic conditions of conjugation contact between a pair of conjugate curves are given. The fundamental principle of conjugate curves for gear transmission is provided： The normal vector to arbitrary direction of contact angle is calculated; the meshing equation is derived and the necessary and sufficient conditions of conjugation meshing for these curves are demonstrated simultaneously; the corresponding conjugated curve can be identified and line of action is also deduced with this method. A general conjugation model is therefore established according to the aforementioned theory and the result is demonstrated with parallel axis gearing as well as cylindrical helix. The geometric properties of conjugation in arbitrary contact angle direction are revealed and the characteristics of meshing motion of conjugate curves are discussed. The versatility of the principle and the outstanding contact features become obvious with treating any gear transmission. The freedom of selecting contact curve suggests the possibility of optimal conjugation design. The results provide a new method for the generation of gear tooth profile and lay a solid foundation for the further study of the gear meshing theory of conjugate curves.

关 键 词：共轭曲线 接触角 啮合方程 圆柱螺旋线 齿轮最优设计 

分 类 号：TH132[机械工程—机械制造及自动化]