MODELING OF CONJUGATED CURVED SURFACES ON THE BASIS OF A KINEMATIC SCREW

Abstract

Modeling of mating curved surfaces for practical use in the design of mechanical engineering products based on a parametric kinematic screw. In mechanical engineering, when modeling conjugate curved surfaces of kinematic pairs, trochoid graphs and electronic modeling installations were used, they had low accuracy and productivity. It is proposed to optimize the process of creating universal graphic tools, where there is, in fact, a graphic representation of the parameters of kinematic conjugate curved surfaces, a change in one of which leads to a change in others, opens up the possibility of obtaining the shapes of parts with predetermined parameters. It should include wishes to expand the capabilities of the propeller diagram [1], taking into account the real picture of the kinematics in the design, which, when the distance between the axes of the propellers changes, would give a real idea of the change in the geometry of the contact surface at each point of the instantaneous movement of the wheels.

The kinematic screw has proven itself well for the formation of conjugate ruled surfaces [3], therefore, geometric 3d-modeling of the kinematic parametric screw diagram for the formation of conjugate curved surfaces has become an urgent problem. The technique of 3d-modeling of the kinematic screw diagram is based on the theorems of Professor A.M. Podkorytova [4]. Modeling of mating curved surfaces on the basis of a parametric kinematic screw means that from graphic constructions at any stage of design, you can easily go to the calculation by an analytical method, if you need to check or accurately determine the parameters. It will allow you to visually represent the process of obtaining conjugate curvilinear kinematic pairs, to analyze the influence of each parameter on the profile and its structural dimensions, you can identify errors in the profiling of conjugate curved surfaces where to avoid them, which is what this article is about.