GEOMETRIC MODELING OF CONJUGATE CONVOLUTE HELICOIDS

Abstract

The paper proposes geometric modeling of convolute helicoids on the basis of a parametric kinematic screw, for practical use in the design of a cutting tool having a spatially complex surface closely related to the formation of mutually enveloping mating surfaces. The helical surfaces formed by the helical movement of a straight line are referred to as ruled surfaces and are called helicoid. Among them, a straight helicoid, oblique or Archimedes are distinguished, involute and convolute helicoids. All of them are widely used in technology. For example, straight and oblique helicoids are used in the design of lead screws for machine tools, hand presses, jacks, etc., having turns of a rectangular or trapezoidal profile. Involute and convolute helicoids are used in the design of worms, screws, screw cutting tools. Since the surfaces of the workpiece and the cutting tool are mating, each of these surfaces can be represented as bypass with respect to the second movable surface. Geometric scientists have long been trying to optimize the process by creating universal graphic methods for designing cutting tools, where there is, in fact, a graphic representation of the parameters of kinematic pairs, changing one of which leads to a change in others and opens up the possibility of obtaining the shapes of parts with predetermined parameters. At the present stage of the rapid development of complex designs of machines and apparatus, with the complex interaction of their parts, the methods of descriptive geometry are widely used in solving various complex technical problems. One of the most common methods for shaping the surfaces of a cutting tool is geometric modeling of conjugate convolute helicoids, which makes it possible to determine the conjugate surfaces of systems of complex movements, to analyze the influence of each parameter on the profile and structural dimensions, and it is easy to detect errors in profiling complex profiles.Keywords: modeling of mating surfaces, parametric kinematic screw, cutting tool, convolute helicoid.