新型环面渐开线齿轮齿面生成和几何特性研究

Study on Tooth Surface Generation and Geometrical Characteristics of Novel Torus-involute Gears

环面渐开线齿轮是一种对安装误差不敏感,无须修形就具有良好啮合性能,并且加工便捷的新型齿轮。根据环面渐开线齿轮的加工原理,从产形齿条的齿面方程出发,推导了凸环面渐开线齿轮和凹环面渐开线齿轮的完整齿面方程;利用MATLAB编程计算出环面渐开线齿轮齿面上点的三维坐标值,生成了精确齿面,并在Pro/E中建立了齿轮的实体模型;基于齿面数学模型,通过计算仿真对环面渐开线齿轮的根切与尖化现象进行了分析,获得了环面渐开线齿轮的根切界限曲线、尖化初始点以及不发生根切与尖化现象的最大齿宽;根据已生成的齿面进行有安装误差条件下的齿轮接触分析,证明了环面渐开线齿轮对安装误差不敏感。

Novel torus-inwolute gears are unsensitive to installation errors and have a good meshing performance without tooth modification, which are easy to machine. According to the processing principles of torus-involute gears, the tooth surface equations of the working tooth surface, the fillet surface and the tooth root surface of the convex torus-involute gear and concave torus-involute gear were derived from the tooth surface equations of the virtul rack cutter. The complete and precise tooth surfaces of torus-involute gears were generated via three dimensional coordinates of points on the tooth surface in MATLAB and the solid models were established in Pro/E. Based on the mathematical model of tooth surface, the phenomena of tooth undercutting and tooth pointing of torus-involute gears were analyzed through numerical simulation. The limit curves of tooth undercutting, the begin- ning points of tooth pointing and the maximum tooth width of torus-involute gears were obtained. According to the generated tooth surface, the tooth contact analysis with installation errors were performed to demonstrate the advantages of insensitive to installation errors.