Mathematical approach to evaluate involute gear profile and helix deviations without using special gear software

摘要

The paper presents mathematical-geometrical approach to evaluate profile and helix deviations of cylindrical involute gear tooth flank without the usage of any specialised gear measurement software. The input data for the evaluation is represented by a set of Cartesian coordinates of surface points (points of contact between the measuring stylus and the measured surface) measured along the profile and flank curves by CAD based tactile gear measurement on coordinate measuring machine. This approach is based on deep study of ISO standards dealing with gear geometry, gear measurement and gear characteristics evaluation. Here, the development of general mathematical model of both helical and spur involute gear tooth flank surfaces is described and geometrical properties of these surfaces (important for corresponding CAD model generation) are mentioned. For practical application, mathematical formulas for calculation of profile and helix deviations from a set of measured points are derived. Due to the purely mathematical approach, no special gear measurement software is necessary for evaluation of profile and helix deviations. The required characteristics of involute gears can be evaluated by means of any general-purpose spreadsheet software. The presented method can be used not only in case of regular involute gear profile and helix inspection but mainly in case of those gear measurement standards that could not be measured as regular gears by commercial software because of unusual shape and design of the standards. (C) 2019 Elsevier Ltd. All rights reserved.