On the Identification of Machine Settings for Gear Surface Topography Corrections

In this paper we set out to investigate the performances of some of the algorithms proposed in the gear literature for identifying the machine-settings required to obtain predesigned gear tooth surface topographies, or needed to compensate for flank form deviations of real teeth. For the ease of comparison, the problem is formulated as a nonlinear least-squares minimization, and the most widely employed algorithms are derived as particular cases. The algorithms included in the analysis are: (i) one-step methods; (ii) iterative methods; (iii) iterative methods with step control. The performance index is devised in their ability of returning practical solutions in the presence of: (i) strong model nonlinearities, (ii) ill-conditioning of the sensitivity matrix, (iii) demanding topographic shapes purposely selected. Instrumental here is an original classification of topographic modifications as either “simple” or “complex”, based on the SVD analysis of the sensitivity matrix. On the basis of the numerical tests documented, iterative techniques with step control seem the most convenient, due to reliability and robustness of the solutions produced. The generation process here considered is face-milling of hypoid gears, even though the methodology is general enough to cope with any gear cutting method requiring only some minor technical changes.