Derivation of parameters of global form deviations for 3-dimensional surfaces in actual manufacturing processes

Characterization of the topography of measured engineering surfaces is discussed. The purpose is to derive the meaningful parameters and the new procedure of measurement of engineering surface topography to evaluate the quality and accuracy objectively. As an example, the tooth flank topography of an actual bevel gear is measured with CMM and is characterized as the curved surface. 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. In addition, the complete parameters for three global form deviations have been derived mathematically. As a result, the parameters for arbitrary global form deviations and the new definition of the pitch error have been obtained. The developed simulation program has calculated the concrete global parameters for the topography with measured and nominal data. The parameters for the tooth flank topography are obtained from the 3-dimensional measured deviations of tooth flanks with profile modification, crowning and manufacturing errors. The results have shown the validity of separation procedure and the derived global parameters. Especially, with respect to the 2nd order form deviations, the parameters, from which we can easily imagine the principal curvature and the anisotropy of global topography, have been obtained. Those global parameters are also useful to characterize not only tooth profile modification and crowning, but also other 3-dimensional measured data, such as freeform surfaces, surfaces with waviness and roughness and so on.