Математичний опис конструювання витків розгортного гелікоїда за заданими конструктивними параметрами

The object of this study is a helical sweeping surface or a helicoid torso and the process of its design according to predefined structural parameters. Helical surfaces are widely used in engineering practice. They have become widespread in devices for transporting various materials, as well as in agricultural machinery. The problem is that when they are manufactured, the technique of their formation from the point of view of analytical description is not always taken into account. Helical surfaces can be linear and nonlinear. Linear surfaces, or helicoids, are formed by the helical motion of a straight-line generatrix around an axis, and the generatrix can intersect it or be coincident. If the straight-line generatrix intersects the axis at a right angle, then the helicoid will be a helical conoid, which is very common in technology under the name of a screw. Certain conditions are imposed on the helical motion of the straight-line generatrix of a helicoid torso. Its main advantage among other helicoids is the possibility of constructing an exact sweep. All other helicoids cannot be swept. For their manufacture, an approximate sweep is found, which is deformed into the desired shape. At the same time, the energy intensity of the process of deformation of this sweep into the finished product increases due to overcoming significant plastic deformations. As a result of this research, dependences were established that make it possible to construct a set of helicoid torsos that pass through the predefined helical line. The results are based on the differential characteristics of the surface. These are their distinctive features from known results, according to which only one helicoid torso corresponds to the predefined helical line. This paper shows the practical application of the helicoid torso as a supporting turn of the narrowing screw of a forage harvester with a radius of R=0.25 m of the outer edge and r=0.125 m of the inner one