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应用微分几何的曲线曲面论定理,基于课题组已成功研发的直齿非圆锥齿轮的三维齿廓,对螺旋非圆锥齿轮齿面节线的构建原理进行了研究。基于映射法构建了螺旋非圆锥齿轮齿面节线的数学模型,依据密切面的思想及算法,完成了螺旋非圆锥小齿轮实体模型的构建。应用包络原理,完成了螺旋非圆锥大齿轮实体模型的构建。运动学仿真结果验证了算法及模型的正确性。研究成果为变传动比限滑差速器非圆锥齿轮设计及其啮合理论的完善及创新提供了理论和技术支撑。
Based on the theorem of curve and surface theory based on differential geometry, the construction principle of pitch tooth nodules of helical non-bevel gears is studied based on the three-dimensional tooth profile of straight-tooth non-bevel gears which the research group has successfully developed. Based on the mapping method, the mathematical model of the pitch line of helical non-bevel gear was constructed. Based on the idea and algorithm of the close plane, the solid non-conical pinion model was constructed. Applying the envelope principle, the construction of solid model of non-conical screw gear is completed. Kinematic simulation results verify the correctness of the algorithm and model. The research results provide theoretical and technical support for the improvement and innovation of non-bevel gear design and meshing theory of variable ratio slip limited differential transmission.