渐开线环形齿球齿轮传动原理与运动分析

介绍了一种新发明的球齿轮传动--渐开线环形齿球齿轮机构。与传统的Trallffa球齿轮相比,新型球齿轮一是采用了渐开线齿廓,二是轮齿在球面上呈环形连续分布,因而克服了离散齿球齿轮存在传动原理误差和难以加工这两个缺陷。首先介绍了这种新型球齿轮传动及其齿面的形成原理,以及派生出的另外一种新机构--球齿轮齿盘机构;为便于分析研究,对新型球齿轮传动的各部分名词术语进行了定义,然后分析了球齿轮机构的安装方式与结构特点以及球齿轮传动的啮合特点;给出了这种新型球齿轮机构的正确啮合条件和连续传动条件。还推导出这种新型球齿轮的齿面方程和啮合方程,理论结果证明了环形渐开线齿廓的共轭齿廓曲面仍然是环形渐开线曲面。利用方向余弦矩阵法分析了分别固联于主动球齿轮和从动球齿轮上两个动座标架之间的关系,通过旋转变换,分别推导出球齿轮机构和球齿轮齿盘机构的正、逆运动学模型,借助于行星轮系传动比计算方法求出了球齿轮行星传动中行星轮输出轴的偏转角与系杆框架偏转角之间的关系。

RESEARCH ON TRANSMISSION PRINCIPLE AND RINEMATIC ANALYSIS FOR INVOLUT SPHERICAL GEAR

One new kind of invented transmission type of spherical gear called ring involute spherical gear mechanism is introduced. Compared to famous Trallffa spherical gear, one of the two main features of this new spherical gear is its involute tooth profile, the other one is its ring tooth distributed continuously on the surface of sphere. Which makes the gear overcome two disadvantages of Trallffa spherical gear: the principle error and difficulty in manufacturing. The new transmission and the formation principle of the tooth's surface of new spherical gear mechanism are first introduced, then another new mechanism, called disk rack, is introduced, which is derived from spherical gear mechanism, when one of spherical gear's tooth number go to infinite. In order to research conveniently, every part of new spherical gear mechanism is named. In the following part, some problems are discussed, such as the assembly form, the construction characteristics of new mechanism and the correct meshing condition, the continuum transmission condition and so on. Further more, the surface formula of the conjugate teeth profiles is deduced, which proves that the conjugate teeth profiles of ringed involute spherical gear is also one of ringed involute spherical gear. In order to analyze the relationship between two coordinate systems, which is attached respectively to diving spherical gear and driven spherical gear, the method called orientation cosine matrix is utilized. By series rotational transformation, the kinematics model and inverse kinematics model are deduced. Using the method for calculating transmission ratio of planet gear train, the relationship of two oscillating angle between output axis and bracket is found up. Based on the research above, the kinematics graphic simulation of spherical gear mechanism and disk rack are made respectively, the results prove correctness of the kinematics model.