弧线齿面齿轮齿面几何设计及径向齿宽特性

为适应航空领域对面齿轮传动的设计要求，综合弧线齿圆柱齿轮、面齿轮传动的各项优点，提出了弧线齿面齿轮齿面设计并研究了其径向齿宽特性。以端面渐开线齿廓弧线齿圆柱齿轮作为产形齿轮通过包络成形建立面齿轮齿面数学模型；结合齿面方程在MATLAB中进行齿面可视化分析，并通过MATLAB软件的数值计算和CATIA软件的复杂曲面造型实现面齿轮的参数化建模；确立内端根切、外端顶尖对径向有效齿宽的限制条件，计算面齿轮的径向有效齿宽，分析刀具齿轮的齿线圆弧半径和坐标系位置参数对径向有效齿宽的影响。研究表明:当增大齿线的圆弧半径，面齿轮的内径减小，外径、径向有效齿宽均增大；当增大坐标系位置参数，面齿轮的内径、外径均增大，径向有效齿宽减小。 

Geometrical design of tooth surface and characteristics of radial tooth width for face gear with arc tooth

In order to meet the design requirements of face gear transmission in the field of aviation, a type of arc tooth face gear was proposed and its radial effective tooth width characteristics were studied. The involute tooth profile cylindrical gear with arc tooth was used as the generating gear, and the mathematical model of the gear surface was established by envelope forming. Combined with the equation of tooth surface, the tooth surface was visualized in MATLAB, and the parameterized modeling of the gear was realized through the numerical calculation function of the MATLAB software and the complex surface modeling function of the CATIA software. The restrictive conditions of the inner undercut and the outer tip to the radial effective tooth width were established, and the radial effective tooth width of the face gear was calculated. The influences of the arc radius of the tooth line and the position parameters of the coordinate system on the inner radius, the outer radius and the radial effective tooth width were analyzed. Results showed that, when the arc radius of the tooth line was increased, then the inner diameter was decreased, the outer diameter and the radial effective tooth width were increased. When the position parameter of coordinate system was increased, the inner diameter and the outer diameter were increased and the radial effective tooth width was decreased.