A novel approach based on a mathematical algorithm and measurement of involute flanks for computing spur gear dimensions with unknown parameters

Abstract Involute gears of all sizes and types are widely utilized in most machinery. Accurate generation of teeth flanks from the nominally required base circle is most vital in gear manufacturing, performance, and inspection. Despite the vital importance of the base circle in actual gear performance, it is not a widely used inspection parameter. Moreover, the size of base circle radius and geometrical center cannot be obtained by direct measurement. In this work, a new mathematical algorithm was developed to evaluate the base circle dimensions by measurement of only the teeth profiles. Measurement of the outer diameter is not required nor is the prior knowledge of any gear dimension such as its module or pressure angle. The evaluated base circle dimensions are then used to compute remaining dominant gear dimensions including its pressure angle. The developed approach was tested on an ideal gear model then applied to the flank points obtained by measurements performed on a Coordinate Measuring Machine (CMM) and by photogrammetry (PG). The experimental results were compared to those measured using a gear roll tester (GRT) and were found to be in very good agreement. The methodology and measurement procedure presented in this work are distinguished by their ability to measure the actual gear dimensions regardless of any tooth modification made to the profile or addendum during manufacturing. This makes the proposed work well-suited for reverse engineering and rapid prototyping reverse calculations.