铲齿凸轮理论廓线的设计研究

以铲齿凸轮理论廓线为研究对象，对其设计方法进行了深入研究，提出Hermite型的凸轮回程曲线设计.简要叙述了利用铲齿车床加工齿轮滚刀铲背曲面的基本原理.基于微分几何学和Hermite多项式插值理论，并结合曲线边界条件，给出了三次Hermite型回程曲线的参数方程.结合铲齿凸轮设计实例，比较Archimedes型和Hermite型回程曲线的运动特性曲线，并分析其对加工过程的影响，证明Hermite型曲线的优势.为提高设计效率，用C语言编写铲齿凸轮理论廓线辅助设计程序，并结合开源程序包gnuplot和LaTeX，以曲线图呈现设计结果.

Research on Design of Pitch Profile of Backing off Cam

The method for designing the pitch profile of a cam for a backing off lathe was studied， with the Hermite return curve of the cam designed. The principle of machining the gear hob’s back surface using a backing off lathe was outlined. The parametric equation of cubic Hermite return curve was proposed based on the differential geometry theory and Hermite polynomial interpolation combined with the curve boundary conditions. Taking the design of a backing off cam as an example， the difference between the Archimedes return curve and Hermite one was compared and the influence of different types of return curves on machining process was analyzed， showing that the Hermite curve was better. To increase the design efficiency， the C language was used to program the pitch profile of the cam， and the open source software package gnuplot and LaTeX were used to show the design graph.