УДК 621.9.02 © Galina Nikolcheva, Ivo Likov A MATHEMATICAL MODEL FOR CONICAL – HELICAL DRILL POINT AND GRINDING A new drill point geometry, termed conical-helical is developed. <...> Developed mathematical models of the flank surface and of the drill point geometry of drill sharpening on conicalhelical surface. <...> The relationship between the desired conical-helical drill point geometry and grinding parameters for a conicalhelical drill point grinder are described. <...> Twist drills are described and defined more in 1913 [4] and are among the most widely used cutting tools for machining of holes. <...> Significant increase in demand in recent years made economically holes, as in drilling and in developing and sharpening of drills leads to the use of-complex constructions of tools and different ways of sharpening their flank. <...> In any form of grinding the back surface is a big difference between working angles and the characteristics of drilling. <...> This has led to work on mathematical solutions to study the process of drilling. <...> There is a great difference between running angles and drilling characteristics of the various types of sharpening their rear surface. <...> This has led to work on mathematical solutions to study the process of drilling. <...> Devices with different constructions while sharpening the flank surfaces of the drills occur as part of the following surfaces: planar [1], cylindrical [2, 5], cone [3, 6] or screw [12]. <...> MATHEMATICAL MODEL OF THE CONICALHELICAL DRILL POINT GEOMETRY The drill point geometry is uniquely determined by the configurations of the drill flank and of the flute. <...> The flute profile is designed by the manufacturer. <...> To optimize the geometrical parameters of the drills: receiving a smaller angle of cutting edge ψ, appropriate clearance angle α along the main cutting edge is created a new scheme of sharpening drills in conical-helical surface, which is given in fig. 1. <...> Drill bit is rotated at an angle θ, as a cam with a helical top surface is attached to the axis of the cradle CC1, which interact with the body stops. <...> Sharpening is achieved by rotation around the axis CC1 /1/ as coordinated drill gets coordinated linear motion in the direction of the axis /2/. <...> To create a mathematical model is necessary to know the location of the drill tip and the axis of the drill and the tip of the cone surface. <...> For this purpose should be introduced: the coordinate <...>