制作高精度环面蜗轮滚刀是提高蜗杆副啮合质量的重要方法，滚刀的几何结构直接影响蜗轮齿面结构及蜗杆副传动性能，然而通过开制容削槽得到前刀面的传统几何结构设计方法限制了滚刀切削性能及蜗杆副啮合质量的提升。为此，本项目借鉴Coons曲面拟合理论，探索插值于给定边界和跨界切矢的环面蜗轮滚刀几何结构单齿等前角设计方法。首先，通过研究切削刃与蜗轮齿面的作用机理，提出各切削刃沿螺旋线方向的分布方案，研究非连续边界条件下任一点的跨界切矢和前角之间的几何关系，实现等前角前刀面的独立构建；其次，研究滚刀几何结构参数与蜗杆副啮合质量评价参数的多对多映射建模，由定性和定量评价指标指导滚刀几何结构设计；探索多参数耦合作用下滚刀几何结构参数优化求解策略，实现滚刀几何结构参数的优化；最后，借助蜗轮滚切及蜗杆副对啮试验，分析齿面接触区，验证设计方法的合理性。预期研究成果将为复杂刀具的精密制造提供科学方法与实践依据。

Making high-precision hourglass worm gear hobs is an important method to improve the meshing quality of the worm pair. The geometry structure of the hob directly affects the quality of the worm gear tooth surface and the transmission performance of the worm pair. However, the traditional design method of obtaining the rake face by making flutes is difficult to achieve the balance of the cutting performance of the tooth, also limits the guidance of the worm gear meshing quality on the design of the hob geometry. To this end, this project draws on Coons surface fitting theory and explores a new method of independently constructing the rake face that interpolates at a given boundary and cross-boundary tangent. Firstly, by studying the action mechanism of the cutting edge and the worm gear tooth surface, the distribution plan of each cutting edge along the spiral direction is proposed, and the geometric relationship between the cross-boundary tangent vector and the rake angle at any point under a discontinuous boundary condition is studied to achieve the front independent construction of the cutting surface; secondly, the many-to-many mapping modeling of hob geometry structure parameters and worm pair meshing quality evaluation parameters is studied, and the design of the hob geometry structure by qualitative and quantitative evaluation indicators is guided; the optimization strategy of the hob geometry parameters under the multi-parameter coupling effect to realize the optimization of the hob geometry parameters is explored; finally, with the help of the worm gear hobbling and the worm pair engagement test, the tooth surface contact area is analyzed to verify the rationality of the design method. It is expected that the research results will provide scientific methods and practical basis for the precision manufacturing of complex tools.