Topography measurement of gear tooth flanks with CMM and evaluation of pitch deviations with the new definition

The purpose of this research is to derive the meaningful parameters and the new procedure of measurement of tooth flank topography to evaluate the individual gear accuracy objectively. The tooth flank topography is measured using a Coordinate Measuring Machine (CMM) and characterized as the curved surface. The parameters for global tooth flank topography are obtained from the 3-dimensional measured deviations of tooth flanks with profile modification, crowning and manufacturing errors. The idea of separation of tooth flank topography into three global form deviations, that is, the 0th, the 1st and the 2nd order form deviations, and the residuals is proposed. For the first step, a new definition of the pitch deviation as the 0th order form is proposed. The pitch deviation is calculated with multiple deviations of a tooth flank. According to this new definition, a pitch error should be expressed by a unit of the angle, also by a unit of the length, and it can be calculated from the measured conventional deviations. As an example, actual bevel gear flanks have been measured with a CMM with the new measuring procedure and the new pitch deviation is calculated. The results have shown the validity of the new pitch deviation as the 0th order form deviations. It is clarified that the new definition is very useful to evaluate the pitch deviation of gears. Even in the case of bevel gears, the new pitch value is expressed by only one numerical widely available for many different types of gears.