渐开弧面齿轮的形成原理及数学模型

结合传统渐开线齿轮与圆弧齿轮优点,提出一种新型的渐开弧面齿轮传动。定义了渐开弧面齿轮的概念,即分别在主从动齿轮的渐开线齿廓上选取两条相对应啮合的单值曲线,在两条曲线上的任意点分别用凸凹圆弧替代渐开线齿廓形成新的齿廓。根据微分几何基本原理,运用坐标变换法推导渐开弧面齿轮传动的齿面方程。讨论渐开弧面齿轮的中心距可分性,分析表明即使中心距发生改变,只要一对齿轮齿廓能够啮合传动,就仍能保持良好的传动性能。根据实例的具体参数,建立一对渐开弧面齿轮啮合的三维实体模型。研究结果为进一步开展渐开弧面齿轮传动研究提供了理论基础,对后续齿轮的设计、加工等有很大的参考价值。

Generation Principle and Mathematical Models of Involute-circular Gear

A new tooth profile gear,involute-circular gear,is proposed by integrating involute gear’s advantageous edges with circular tooth gear’s advantages in this research.The concept of involute-circular gear is also defined,namely that choosing two single-valued curves which are corresponding engaged from the involute profiles between driving and driven wheels respectively,and replacing involute profile with the convex and concave circular arc separately to form new tooth profile at any point of these curves.According to differential geometry,the equation of tooth surface is established based on method of coordinates transformation.Insensitivity to central distance variation on involute-circular gear is discussed.The analyzed results indicate that the transformation ratio remains still unchanged as long as the gear pair can keep meshing drive,even if central distance generates change.An example of this gearing was presented and calculated,and 3D models of a pair of gears are established.The results offer theoretical supports for further studies on the involute-circular gear and reference value for the design and machining of gear.