准双曲面齿轮几何设计新方法

A New Method for the Geometrical Design of Hypoid Gear

介绍了一种准双曲面齿轮几何设计方法。通过准双曲面齿轮副的节锥几何关系,建立了包含7个节锥参数并由4个方程构成的节锥参数基本方程组。采用这组方程,以大轮的节锥角和节圆半径以及小轮的螺旋角这3个参数为自由变量,以准双曲面齿轮副的偏置角为中间变量,用数值求解方法能够非常方便可靠地确定节锥几何参数。在不考虑顶隙的情况下,小齿轮的顶锥与大齿轮的根锥相切,小齿轮的根锥与大齿轮的顶锥相切,应用准双曲面齿轮副的节锥几何关系来确定小齿轮的顶锥角、根锥角、顶锥顶点和根锥顶点到齿轮副轴线交错点的距离等几何结构参数,推导和提供了相应的几何结构参数设计计算公式。通过实例验证了该方法的有效性。

A method for the geometrical design of hypoid gears was introduced. A set of fundamental equations that consist of four formulae and contain seven pitch parameters were established through the pitch cone geometrical relationship of a pair of hypoid gears. With the equations, the pitch parameters can be determined easily and unfailingly by taking the pitch angle and pitch radius of the wheel and the spiral angle of the pinion as design variables and the offset angle as an iterating variable. Under the condition of no consideration of the bottom clearance, the pinion tip cone is tangent to the wheel root cone and the pinion root cone is tangent to the wheel tip cone. By means of the pitch cone geometrical relationship of a pair of hypoid gears, the geometrical structure parameters can be determined, such as root angle and tip angle of the pinion, the distances between the cross point of the gear pair axes and the apexes of the tip cone and the root cone of the pinion. The corresponding formulae for the geometrical structure parameter design were presented. A numerical example was given for demonstrating this method.