An applied explicit mathematical model of conical drill point geometry without flank rubbing

Abstract

Conical point drills are often used for making holes. In drill design, three drill point parameters, namely, drill point angle (or semi-point angle), chisel edge angle, and lip clearance angle, are specified. Geometrically, the conical point geometry is generated by two symmetric and oblique cones intersecting at the end of drill land. Thus, the drill point has to be designed in detail, which is to calculate the cone location and orientation parameters so that the drill point parameter values are equal to the specifications. Unfortunately, the previously proposed methods of drill point detailed design cannot be implemented in cutting tools companies, because one set of drill point parameter specifications can correspond to many sets of cone parameters which determine different drill point shapes. Moreover, the heel clearance flanks of some drills could rub stock material at the hole bottom while drilling, resulting in a large amount of force and heat, tool breakage, and severe wear. Drills with flank rubbing are invalid. However, the previous researches and applied industrial software cannot eliminate flank rubbing. To address the above problems, a practical and explicit mathematical model of conical drill point geometry without flank rubbing is established in this work. This work derives close-formed equations of the cone parameters and establishes a new criterion of flank rubbing detection. It can efficiently and consistently compute the cone parameters and detect flank rubbing for a valid drill point design. This explicit mathematical model is verified, and an approach to conical point detailed design is applied on two twist drills in the authors’ company. The differences between the drill point parameter values in the ground drill and the drill design parameter specifications are within an acceptable tolerance. Thus, the proposed method can be directly used in drill design and manufacturing in the tooling industry.