The Use of Descriptive Geometry Methods for Graphical Study of the Parameters of the Cutting Part of a Spiral Drill

The article presents examples of practical application of descriptive geometry methods for solving engineering problems of determining and studying the parameters of the cutting part of a spiral drill. The necessity of graphical constructions is noted, which is due to the fact that it is impossible to measure the rear angle by a direct measurement method using a universal measuring instrument due to the complex geometric shape of the measuring object. The analysis of the geometric shape of the working part of the spiral drill, which includes the main rear conical surface of the drill tooth, the front screw surface of the drill groove, the cylindrical surface of the tooth back, the main and transverse cutting edges are presented. Using the double contact theorem, a projection of the tooth profile of a spiral drill is constructed on a plane parallel to the drill axis with a given profile projection on a plane perpendicular to the drill axis. The tooth profile is determined by the lines of intersection of the conical surface with the cylindrical surface and with the helical surface of the drill groove. The shape of the drill groove is considered to be set. Projections of the transverse cutting edge of the drill are constructed as lines of intersection of two conical surfaces with intersecting axes. The problem is solved using a bundle of auxiliary planes. The tendency of an increase in the angle of inclination of the transverse cutting edge to the drill axis with a decrease in the distance between the intersecting axes of conical surfaces is shown. Graphically, at an arbitrary point of the drill blade, the value of one of the main geometric parameters of the drill - the rear angle is determined. It is shown that the closer the point of the blade is to the center of the drill, the greater the value of the rear angle. The constructions are made in the 2D Compass-Graph design system. The paper used alternative methods for solving geometric problems, which, unlike traditional ones, provide a simpler and more visual graphical solution.