基于啮合角函数的非圆齿轮共轭齿廓直接求解

Direct-Profile-Design Method for Generating Noncircular Gear Pairs

定义了非圆齿轮啮合角函数的概念,提出了基于啮合角函数的非圆齿轮共轭齿廓的直接求解方法·建立了齿廓求解的运动几何学模型,给出了齿廓方程,给出了齿廓啮合原理的啮合角函数表达式·该方法,给定啮合角函数,无需坐标变换,可直接求解共轭齿廓,简化了非圆齿轮共轭齿廓的求解·该方法亦适用于圆齿轮齿廓,实现了圆齿轮和非圆齿轮共轭齿廓求解的高度统一·为齿轮传动的设计计算提供了一种有效的新途径·

A working pressure angle was defined as a function of rotating angle of noncircular gears, called WorkingPressureAngle or WPA function. A new method for generating noncircular gear pairs was thus developed and named. DirectProfileDesign (DPD) method, where WPA function is used to obtain the desired tooth 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 relates to WPA by a first order differential equation. The differential equation ensures one tooth profile to be engaged with the other profile. As demonstrated, this new method is applicable to any type of gear pairs including circular or noncircular. In addition, using this method is relatively easier to generate new tooth profiles and investigate the geometrical and mechanical properties of gear pairs, and the desired geometrical and mechanical properties will come true in design.