二次曲面钻头几何角度的统一模型

以麻花钻前后刀面的数学模型为基础，建立了二次曲面后刀面麻花钻各几何要素的平面像图；应用平面表像法，将麻花钻上复杂的空间角度计算问题转化为平面上的非欧距离和非欧夹角的计算问题，从而大大简化了计算分析的难度；建立了麻花钻切削角度与结构和刃磨参数关系的统一计算模型，为麻花钻的结构和刃磨参数的分析和优化设计提供了一种新的建模方法。

A Universal Model for Cutting Angles of Drills with Quadratic Flank Faces

Based on the mathematical models of the flute surface and the flank of the twist drill with quadratic flank faces, its relevant planes and lines were mapped on a projection plane. With this planar displaying method, the calculation of angles between 3- dimmensionally situated lines and planes of the drill was transformed to the calculation of non-Euclidean distances and angles on a plane in 2-D space, and thus greatly simplified. A universal model for calculating cutting angles from structural and grinding parameters is developed, resulting in a new modelling method for optimization of structural and grinding parameters.