Abstract: Face gear is different from any other conventional gear in that the tooth shape Angle gradually changes along the tooth width. The small pressure Angle at the inner diameter end leads to the root cutting at the inner diameter end, while the large pressure Angle at the outer diameter end leads to the cusping of the tooth tip, so the design of the tooth width is limited. Influenced by the understanding of conventional gear tooth shape, many students and researchers have difficulty in understanding the tooth shape characteristics of face gear. In order to make students understand the tooth surface characteristics of face gear more intuitively in the process of teaching and scientific research, this paper conducts in-depth analysis and research from the meshing principle and the process of space tooth surface development, and clearly shows the reasons for the change of tooth shape angle. In this paper, based on the tooth surface equation and meshing principle of face gear, the calculation formula of meshing angle at different positions of face gear is derived, and the characteristics of tooth shape at two sections are introduced in the form of drawing. Finally, an example and the result of pressure angle calculation are given, and the difference between face gear and bevel gear is analyzed.

Key words: Face gear transmission; Tooth surface equations; Meshing principle; Tooth shape angle; Calculation formula; Rotation axis

摘要： 面齿轮不同于其他常规齿轮，其特点是齿形角沿齿宽方向逐渐变化。内径端压力角较 小导致了内径端容易发生根切，而外径端齿面压力角大，则容易发生齿顶变尖现象，因此， 齿宽设计受到限制。受对常规齿轮齿形认识的影响，不少学生和研究者难以理解面齿轮的这 种齿形特点。为了在教学和科研过程中让学生更加直观地理解面齿轮的齿面特点，论文从啮 合原理和空间齿面展成过程入手进行了深入分析和研究，清楚地展现了其齿形角变化的原因。 基于面齿轮的齿面方程、啮合原理，推导得出了面齿轮不同位置处啮合角的计算公式，并以 作图形式介绍了两个截面处的齿形特点。最后给出了一个算例和压力角计算结果，并分析了 其与锥齿轮的不同。

关键词: 面齿轮传动；齿面方程；啮合原理；啮合角；计算公式；回转轴线