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.

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In the present paper methodology of computer aided geometric modeling of formation of workpieces with periodic teeth machined with centroid enveloping method is developed without involving complex mathematical apparatus. During its application, as opposed to already known methods, simultaneous modeling of two objects of formation – wraparound and removed contents – takes place. Analysis of configurations of solid models of cutaway layers and respective removed content volumes allows a design engineer to intentionally set the optimal values of tool advance parameter and number of passes. The key point of the present paper is to establish logical connection between geometric computer simulation of removed contents in CAD environment and analysis of chip formation in the process of cutting using ANSYS software. In the present paper AutoCAD 3D simulations rendering of cutaway layers is shown along with the corresponding realistic simulation of chips, created using metal cutting process finite element analysis software. Due to substantial difficulties of cutting process 3D simulation, it is considered reasonable to perform computer simulation of cutaway layers geometry generation on the first stage of problem solving. This will allow us to choose the optimal cutting parameters and consequently speed up the cutting process simulation.