Automated Geometric and Computer-aided Non-Circular Gear Formation Modeling

In non-circular gears of hydromachines used for transit of oil, fuel-oil residue and water, difference takes place not only between gear teeth profiles, but also between lateral profiles of the same tooth. Profiling of such gears requires application of complex mathematical apparatus. The solution to the inverse task of formation is even more complex in this case. This paper proposes a geometrical model of solution to the task of profiling a non-circular gear, the centroid of which consists of interconnected arcs. It is effective in case all the conditions of formation are met. The proposed automated solid computer-aided modeling of the direct and the inverse tasks of formation realized on virtual imitation level allows us not only to acquire the envelope of the profile, but also to observe the possible formation of transition curves and undercuts. It reveals constructive and technological conditions under which they appear, presents an opportunity to conduct the respective research in order to introduce the required corrections into the kinematic scheme of formation, which results in achieving a high-grade solution to the task of profiling. Automated solid modeling of the inverse task of formation allows us to validate the solution to the allocated task and, if necessary, to refine the initial data and therefore exclude the necessity to conduct the expensive full-scale experiments. The results of the study can be used in non-circular gear design in the field of hydromachines used for transit of oil, fuel-oil residue and water.