等基圆锥齿轮的齿面曲率分析

以数控加工技术和等基圆曲线齿锥齿轮理论为基础,导出了考虑齿线修形时,仿形加工等基圆锥齿轮的指状铣刀中心轨迹方程;确定了考虑齿廓修形时指状铣刀的廓线方程;导出了铣刀回转曲面的主曲率、主方向和任意方向的法曲率;按共轭曲面理论,由刀具曲面的几何结构和刀具与轮坯的相对运动,确定了被加工齿面的法矢、主方向、主曲率和任意方向的法曲率·为齿面啮合分析、修形设计及强度计算奠定了基础·

Analysis on Tooth Surface Curvature of Equal-Base-Circle Bevel Gear

Equal-base-circle bevel gears can be cut precisely in an economical way, which is of importance to large size bevel gears. Taking tooth trace modification into account, the equation of cutter center trace was derived. To carry out tooth profile modification, the modified cutter profile equation was determined for equal-base-circle bevel gear profiles. According to differential geometry theory, the primary curvature and primary direction and normal curvature in different directions of cutter surface were obtained. Based on the theory of conjugate tooth surface, the primary curvature, primary direction and normal unit vector of gear tooth surface were derived from the geometry structure of cutter surface and the special relative motion between the cutter and tooth blank, which can be used to predetermine the meshing properties. All of these lay a foundation for gearing analysis, modification and strength calculation. The modification design of equal-base-circle bevel gear, which is available to improve meshing quality, can be carried out easily by NC technique.