GEOMETRIC MODELING OF CONJUGATED SURFACES BY THE NORMAL METHOD

Abstract

The paper proposes geometric modeling of a trapezoidal cutter using the normal method, for the practical use of machining parts that have a spatially complex surface that is closely associated with the formation of mutually enveloping conjugated surfaces.

         In modern airplanes, rockets, ships, metal cutting machines, parts of very complex shapes are often used. Since the surface of the machining part and the cutting tool is conjugated, each of these surfaces can be represented as an envelope with respect to the second movable surface.

Scientists have been trying for a long time to optimize the process by creating universal graphic tools, which, in fact, is a graphical representation of the parameters of kinematic pairs, changing one of which leads to a change in the other, opens up the possibility of obtaining shapes of parts with predetermined parameters.

The theory of envelope surfaces was further developed in matters of profiling of a cutting tool. Concerning the design of a cutting tool by the graphoanalytic method of profiling, it follows that from graphical constructions at any stage of design, it is easy to switch to calculation by the analytical method, if necessary, checking or accurately determining the parameters.

Graphic methods allow you to visualize the process of obtaining a tool profile, give an analysis of the influence of each parameter on the profile and design dimensions, where it is easy to identify profiling errors of complex curved profiles. For accurate design, it is necessary to carry out quite a number of geometric constructions, which is accompanied by the introduction of completely objective errors, which can be avoided and also requires substantial creative preparation, which this article is devoted to.

Keywords: modeling of conjugated surfaces, method of normals, gear wheels, cutting tool, trapezoidal milling cutter.