基于啮合角函数的非圆齿轮齿廓求解及几何特性研究

A Direct-Profile-Design Method for Generating Noncircular Gear Pairs

定义了非圆齿轮的啮合角函数 ,由此 ,建立了非圆齿轮齿廓方程 ,并导出非圆齿轮齿廓曲率半径、齿廓弧长和滑动系数计算公式 ;提出了齿廓根切的条件。啮合角函数决定了非圆齿轮齿廓形状及其几何特性 ,由啮合角函数可直接求解共轭齿廓 ;无需先给定齿廓曲线 ,即可由啮合角函数系统地对齿廓几何特性进行分析。该共轭齿廓的直接求解及几何特性研究甚为简便。

A working pressure angle was defined as a function of an rotation angle of noncircular gears, called the Working-Pressure-Angle (WPA) function. A new method for generating noncircular gear pairs was developed. This method, called the Direct-Profile-Design (DPD) method, is to use WPA functions to obtain the desired profiles of generated pairs. The length of a tooth profile normal between the tooth profile and pitch curve was defined as the normal length of a tooth profile. This length is related to WPA by a first order differential equation. The differential equation ensures one tooth profile to be engaged with the other profile. A formula of the curvature radius of a tooth profile was given. This formula can be used to calculate the curvature radius of a tooth profile directly, when a WPA function for a tooth profile is given. As demonstrated, this new method is applicable to any type of gear pairs including circular or noncircular. In addition, by using this method, it is relatively easier to generate new tooth profiles, to investigate the geometrical and mechanical properties of gear pairs, and to realize the desired geometrical and mechanical properties into the design.