Algorithm for geometrical and metrological characterization of gears with low module and high number of teeth: low-cost gears

Abstract

In the specific case of low-cost gears, and also in some general cases, the use of expensive instruments such as gear measuring machines may not be appropriated during their verification. In the scientific literature there are many works that allow the development of mathematical models capable of establishing the geometric elements of spur gears, necessary for the determination of deviations in circular pith according to what is included in the ISO 1328-1:2013 standard. In this work, the verification of gears from the adjustment and measurement of their flanks treating them as ellipse arcs is presented as an alternative to classic verification. Most of the software implemented in the coordinate measuring machines and the vision machines, has detection and adjustment algorithms of ellipse arcs. However, it is not so common the availability of gear analysis software, and in any case, it would require the payment of expensive additional licenses. The authors present an alternative way in which, from the elliptical arc adjusted to the flank of the tooth, it is possible to determine the fundamental parameters of the gear (tooth thickness, circular pitch and profile form deviation). Naturally, it is necessary to determine under what circumstances (module, number of teeth, gear quality) the approach of the tooth flank by an ellipse is feasible.