线面对构齿轮啮合原理

根据曲线和曲面两种几何元素的接触特点,提出了线面对构齿轮啮合原理。定义了线面接触与线面啮合的概念,给出了线面啮合运动三要素;建立了线面啮合基本理论,得到与已知曲面相啮合的共轭曲线方程的通用表达式;通过在曲线每一点处的法平面上建立截面齿廓,进而构建连续曲面。以平行轴内啮合渐开线齿轮为例,通过在渐开线内齿轮齿面上选取接触曲线,构建新的线面啮合齿轮副,分析了线面啮合齿轮啮合过程的一般规律。研究结果表明,根据线面啮合原理,通过选取合适的几何参数,可以构建出一对正确啮合的点接触齿轮。该原理为齿轮齿面构建提供了新方法。

Principle of Geometric Elements Constructed Tooth Pairs with Curve-surface Mesh

According to the contact characteristics of curve and surface, the principle of geometric elements constructed tooth pairs with curve-surface mesh for gear transmissions was put forward. The concepts of curve-surface contact and curve-surface mesh were provided and three key elements for curve-surface mesh were given. The fundamental principle of curve-surface mesh was presented. The corresponding conjugated curve was also deduced. By establishing a cross section profile on normal plane of every point of the curve, the tooth surface was constructed. Taking an internal helical gear of parallel-axis as an example, a new gear pair with curve-surface mesh was established by selecting a contact path on the internal helical gear and the general law for the mesh processes of the gear pair was analyzed. The results reveal that based on the principle of curve-surface mesh, a gear pair with point contact may be obtained by choosing appropriate design parameters. The principle of curve-surface mesh provides a method for the generation of tooth surfaces.