高阶变性椭圆齿轮的研究与设计

Study and Design on High-Order Deformed Elliptic Gears

在综合研究高阶椭圆和变性椭圆生成机理的基础上,提出了一种新型非圆齿轮形式——高阶变性椭圆齿轮.采用数学推导与数值计算相结合的方法,建立了以高阶变性椭圆为基础的椭圆族数学模型,提出了最小传动比位置偏移率的概念,以表征周期内传动比曲线的不对称性.研究了在以高阶变性椭圆为节曲线的齿轮传动副中,主动轮与从动轮的转角关系、传动比关系、曲率半径及弧长计算等问题,得到了设计高阶变性椭圆齿轮所需各种参数的求解方法,采用这些方法并结合实际情况,即可设计出满足要求的高阶变性椭圆齿轮副.该设计方法对于普通椭圆齿轮的设计计算也同样适用,因此统一了各种椭圆齿轮的设计过程.

Synthesized the creating mechanism of high-order ellipse and deformed ellipse, a new non-circular gear form named high-order deformed elliptic gear is put forward, where analytical deducing and numerical calculation are combined to establish the mathematical model of ellipse family on the basis of high-order deformed ellipse. To express the asymmetry of transmission ratio in one period, the concept of excursion ratio of minimum transmission ratio position is introduced. Some features, such as rotation angle relation, transmission ratio, curvature radius, arc length calculation etc., are investigated in high-order deformed elliptic gear pairs. The calculating methods of each parameter are adopted comprehensively to design high-order elliptic gears to meet the individual engineering requirements. This design method is naturally suitable for common elliptic gears.