Synthesis of hypoid gear surface topography by a nonlinear least squares approach

This paper outlines a systematic methodology for finding the machine setting corrections required to obtain a predesigned ease-off surface in spiral bevel and hypoid gear teeth. The problem is given a nonlinear least squares formulation which, however, is highly prone to numerical instabilities. The Levenberg– Marquardt algorithm with a trust region strategy turned out to be quite effective and robust to obtain feasible solutions. The proposed method was tested on lengthwise crowning, profile crowning and spiral angle correction. In all cases, the goal was achieved with very high accuracy, in a few iterations and, remarkably, with different sets of machine parameters.