CONSTRUCTION OF AN OPEN HELICOID COIL FROM A FLAT BILLET

In technology, a very common helical surface is a straight closed helicoid, known as a screw. Its formation takes place by the spiral movement of the horizontal segment upwards in such a way that one of its ends crosses a vertical straight line - the axis of the auger. For an open helicoid, the formation of its surface is similar. The difference is that the segment is transient in relation to the axis and is at a constant distance from it. The smaller this distance, the smaller the difference between the surfaces. In both cases, rectilinear generators are perpendicular to the axis. It is known from differential geometry that any helical surface can be bent into a surface of revolution. It is this fact that is taken as the basis for the calculation of a flat blank for the manufacture of an open helicoid coil. Its surface is non-expanded, so the workpiece must be found in such a way as to minimize plastic deformations when forming the surface from a flat workpiece. The article presents parametric equations that describe the continuous bending of the turn of an open helicoid into the compartment of a single-cavity hyperboloid of rotation. Continuous bending can be imagined as a gradual deformation of a helicoid turn by decreasing its pitch. The surface is deformed, remaining helical and ultimately turning into a hyperboloid. Its meridian is the corresponding section of the hyperbola. It is proposed to approximate the section of the hyperboloid by a truncated cone. This approximation will be more accurate in the section of the hyperbola where it asymptotically approaches the line segment. After choosing a cone, its dimensions are determined and its exact sweep is built, since the cone is a sweep surface. The sweep is built in the form of a flat ring with a cut sector and will be a flat blank for forming an open helicoid turn from it. The surface of the turn of an open helicoid can be most accurately obtained by stamping the resulting blank. For low-volume production of the helical surface of an open helicoid, flat rings can be welded together and stretched along the shaft with simultaneous twisting around its axis. The accuracy of the obtained surface will depend on the accuracy of the approximation of the section of the hyperboloid of rotation by a truncated cone.