ROLLING OF A DEVELOPABLE HELICOID OF THE SCREW LINE ALONG ITS BENDING

Abstract

A very common helical surface in various mechanisms is a straight closed helicoid or screw conoid, known in the technical field as a screw. Considering the wide application of screws, there are various methods of their production (winding, rolling, stamping, stretching flat rings welded together on a shaft). Since the surface of the screw conoid is nondevelopable, the flat ring is an approximate sweep of the screw, since an exact sweep does not exist. During the formation of the turn of a screw conoid from a flat ring, plastic deformations occur in it, caused by the transformation of a developable surface into a nondevelopable one. 
 It is known from differential geometry that any screw surface can be bent into a surface of revolution. For a screw conoid, such surface is a catenoid. The paper presents parametric equations for the continuous bending of a catenoid into a screw conoid. It is proposed to replace the compartment of the catenoid, which corresponds to the given compartment of one turn of the conoid, with a truncated cone. The sweep of this cone in the form of a flat ring can be considered a blank for forming the surface of a conoid. A comparative analysis of the sizes of the ring obtained by the proposed method with the sizes that can be obtained according to the formulas of the reference literature were made. Although there are differences, but they are practically insignificant.
 As a result of the study of the continuous bending of a catenoid into a screw conoid, an improvement of the process of such bending is proposed. In one of the existing methods of forming a screw from flat rings, several rings in the form of a sector are proposed to be welded together and then stretched to obtain a screw with the same number of turns. Welded rings are put on the shaft, one end is fixed to it (for example, by welding), and the other is stretched to the desired size. With this method, the twisting of the workpiece around the axis of the shaft is not taken into account. It is necessary to bend truncated cones from separate sectors, weld them together, and only then stretch them. In this case, the twist angle is already embedded in the workpiece in the form of welded cones.