中文摘要：

为了实现正交面齿轮的加工,采用包络法对正交面齿轮齿廓的几何设计方法和根切条件进行了研究.建立了正交面齿轮的包络过程坐标系,给出了产形面及其齿角方程,推导了面齿轮齿廓和过渡曲面方程,并利用Matlab软件对面齿轮齿廓的几何设计进行了仿真.文中还分析了面齿轮的根切现象,得出了相应的根切条件,通过对根切条件的数值计算获得了根切参数表,并利用最小二乘法对参数表进行统计分析,得到了面齿轮根切几何条件的工程近似方程.最后通过面齿轮加工实验,验证了上述理论计算和工程近似方程的可行性.

英文摘要：

In order to effectively machine an orthogonal face gear, the geometrical design of tooth profile and the undercut condition for the gear are investigated via the enveloping method. In the investigation, first, a coordinates is established to describe the enveloping process of the gear, and the generation of the gear as well as the tooth-angle equation is studied. Next, the equations describing both the tooth profile and the transitional surface are presented. Then, the geometrical design of the tooth profile is simulated by using Matlab software. Moreover, the undercut of the face gear is analyzed and the corresponding undercut conditions are obtained. According to the calculated datum of undercut and the corresponding statistical results obtained via the least square method, an approximate engineering equation of undercut is deduced. The feasibilities of the theoretical calculation and the proposed approximate equation are finally verified by the practical machining of a face gear.