Trushkov G. Geometric modeling of the surfaces of multiple-thread milling cutter

The object of the study is the process of simulating conjugate curvilinear surfaces with point and linear contact. The purpose of the study is geometric modeling, based on the theory of spatial parametric kinematic screw, conjugate curvilinear surfaces with point and linear contact (on the example of a multi-turning worm cutter), which eliminates interference and contributes to the increase of productivity and quality of processing of a wide class of products, limited by complex curvilinear surfaces. The implementation of the tasks set in the work is based on the system analysis, the kinematic method of studying spatial links, the methods of analytical geometry in the plane and space, differential geometry, the theory of the kinematic screw and modern computer technologies. The research paper presents a theoretical justification and developed algorithms for the formation of conjugate curvilinear surfaces with a point and linear contact regarding the simulation of a multiple-feed worm milling cutter. A geometrical-kinematic method and geometrical toolkit for modeling multiple-threaded worm milling cutters are proposed. The theory and methods of curvilinear-projection modeling of space, namely, the spatial parametric kinematic screw for formation of analytical description of screw surfaces, have been used, which made it possible to reduce the recording of equations to a parametric form, to algorithmize the geometric modeling of the initial surface of a cutting tool, to simplify algorithm-program realization of the received results, to increase accuracy and the productivity of product processing in accordance with modern requirements. The algorithm of geometric modeling of the conjugate screw surfaces based on the kinematic screw according to machining on numerically controlled machine tools is improved. A direct and inverse problem of geometric modeling was developed for determining the surface of a worm cutter with several measures based on the theory of spatial parametric kinematic screw. The use of the obtained method is advisable in the manufacture of a cutting tool in mechanical engineering, characterized by complex curvilinear surfaces of products, with increased accuracy, reliability and performance. The results of the work were introduced into the work of the Military Academy (Odessa).