Geometric And Computer Modeling of Forming the Gear Wheels with Elliptical Centroid

Abstract

Abstract A fairly simple and accurate methodology of automated forming of the teeth of a wheel with an elliptical centroid is proposed. This methodology is based on computer simulation of the real process of forming and does not require the application of complex mathematical body used in most traditional methods. The key point of the methodology is the proposed solution for determining the instantaneous centers of the cutting tool and the angles of its rotation around these centers. The relative position of the cutting tooth profiles is determined by two arrays of point coordinates: one on the elliptical centroid of the non-circular wheel, the other - on its equidistant curve. Compared to the traditional methods, this methodology is a universal and much more efficient and accurate one, especially for wheels with an elliptical centroid. The proposed automated solid-state computer simulation of the forming allows to obtain not only the envelope part of the profile, but also to observe possible formation of transition curves on it and undercutting, which leads to a qualitative solution of the profiling problem. According to the developed algorithms and programs, a computer model of a non-circular wheel is obtained, on the basis of which a corresponding item used in hydraulic unit pumps is made on a CNC machine.