二齿差摆盘式活齿传动的结构与齿形分析

Structure and Tooth Profile Analysis of the Two-tooth-difference Oscillating-disc Movable Teeth Transmission

摆盘式活齿传动作为一种轴向活齿传动,具有径向尺寸小的突出特点,但其应用受到自身结构复杂及载荷与力偶不平衡等因素的限制。作者通过理论计算、建模仿真、作图分析与控制变量等方法,运用Pro/E与MATLAB等软件,对摆盘式活齿传动进行了结构改进与齿形研究。在摆盘式活齿传动现有研究成果的基础上,通过理论计算推导出了摆盘式活齿传动的二齿差形式及相应的运动方程与齿形方程,设计出两相激波器的新结构;对特征零件端齿轮进行了3维建模并对齿面的曲率分布进行了仿真分析,分别研究了曲率沿分度圆柱面的变化情况及曲率在空间全齿面上的分布情况;通过质点的瞬时圆周运动模型确定了空间全齿面上的齿顶位置,推导出了齿顶处的坐标向量与曲率半径的计算式;研究了平面活齿传动中的顶切现象及原理,由此计算出二齿差摆盘式活齿传动中顶切的边界条件;用控制变量法分别分析了分度圆半径、传动比、振幅及活齿半径等参数对齿形的影响情况,运用相对偏差的概念在同一坐标系中研究各参数对齿形的影响程度的大小。研究发现:二齿差摆盘式活齿传动中端齿轮的实际齿顶点位于分度圆柱面的内部而不在柱面上;4个重要参数的变化如分度圆半径减小、传动比增大、振幅增大、活齿半径增大均将导致齿形收窄变尖并引发顶切,其中前两者的变化实质是改变了齿形的周向分布周期,且影响程度较大,是主要影响因素,而后两者的变化实际上改变了齿形的轴向分布范围。

As an axially movable teeth transmission,oscillating-disc movable teeth transmission has the advantage of small radial dimension,but its application is limited by complicated structure and unbalanced load and force-coupling.In this paper,the theoretical calculation,modeling and simulation,mapping analysis and variable-controlling approach,and softwares such as Pro/E and MATLAB,were used to improve the structure of oscillating-disc movable teeth transmission and analyze its tooth profile.Based on existing research results,through theoretical calculations,the two-tooth-difference form of oscillating-disc movable teeth transmission and its motion equation and tooth profile equation were derived,and the new structure of two-phase surge wheel was designed.By 3D modeling,the curvature distribution of end gear was simulated,the variation along pitch cylinder and the distribution on the spatial tooth surface were analyzed respectively.According to the instantaneous circular motion model,the addendum on the spatial tooth surface was determined,the corresponding formulas of the coordinate vector and the radius of curvature were derived.Referred to the principle of the top cut in the planar movable teeth transmission,the boundary condition of the top cut in the two-tooth-difference oscillating-disc movable teeth transmission was calculated.The influences of parameters such as the radius of the pitch circle,the transmission ratio,the amplitude and the radius of the movable tooth on the tooth profile were analyzed by the variable-controlling approach,and the influence degree of each parameter was studied in the same coordinate system by using the relative deviation as the independent variable.Finally,the actual tooth vertex of end gear was located inside the pitch cylinder instead of on it's surface.Varieties such as the decrease of pitch circle radius,the increases of transmission ratio,amplitude and movable tooth radius,were all found contributing to narrowing the tooth profile and leading to the top cut.The former two parameters actually changed the circumferential distribution of the tooth profile,while the latter two changed the distribution axially instead.