Influence of the function of modification of the initial line profile on the shape of the generating surface of a gear cutting tool

Analytical dependencies, which are the result of the research, are shown; they allow to describe a three-dimensional geometric computer kinematic model of the process of shaping a prototype of a gear cutting tool - a hob cutter. The presented computer model takes into account both the geometric characteristics of the worm gear being designed and the technological characteristics of its manufacturing. The article shows the equivalence of the obtained analytical dependencies of the process of shaping a computer geometric model of the working surface, which describe the generating surfaces of a hob cutter and an equivalent real gear cutting tool, what makes it possible to form its virtual digital equivalent. Obtaining a virtual prototype of a gear cutting tool allows to reduce the cost of designing of a new worm gear. Analytical dependencies for describing a virtual digital prototype of the generating surface of a hob-cutter gear cutting tool are obtained, with the possibility of introducing a profile modification in order to improve the contact of the working surfaces of a cylindrical worm and a worm wheel. The use of a deliberate profile modification makes it possible to introduce into the computer model of a gear cutting tool a profile retraction of the section of its generating surface from the original rectilinear profile, which will entail a modification of the formed working surface of the resulting product and, as a result, will lead to an improvement in the characteristics of the contact zone of the worm gear. The use of a digital prototype of a modified generating surface allows to create a virtual product used in a gear train and makes it possible to study the operation of a worm gear as a whole.