Discrete solid modeling of the standard twist-drill

Services of technological process planning need to forecast axis deviations of the holes obtained by drilling operationally. For this purpose, it is necessary to calculate drill bending caused by cutting and fixing forces during stating of drilling. The finite element method (FEM) is the most widespread method for calculating drill bending. FEM taken separately or in conjunction with the SPH method used for simulation the workpiece machining process provides the most accurate estimates of drill walking. In this regard, there is a need to generate finite element meshes that accurately correspond to the geometry of drilling tools. The analytical geometric models of cutting tools previously described in the publications either use spline approximation, or model solutions are based on iterative approaches. The presented paper proposes an accurate calculation of the surfaces and edges of standard twist drills based on algebra of sets and voxel modeling. The paper presents mathematical relations for describing major flanks obtained during tool grinding in the form of flat surface, cylindrical, conical (two types of sharpening) and screw surfaces. These relations in combination with the relations for helical chip grooves, tooth backs and lands of margin early published by the author make it possible to develop geometric models of almost all standard twist drills. Further automatic conversion of the calculated voxels into finite elements provides an opportunity to perform the necessary calculations of drill bending and to evaluate the location of the machined holes of the parts. The obtained relations have been used to develop computer programs for modeling of various types of drills, including drills with all the types of major flanks indicated above, with one and two lands of margin, with different types of lands of margin sharpening. Thus, the universality of the presented model of standard drills and its sufficiency for finite element meshes generation has been proved.