Nonlinearity analysis based algorithm for indentifying machine settings in the tooth flank topography correction for hypoid gears

In the tooth flank topography correction technique for design and manufacture of hypoid gears, there is always a fundamental issue that instable numerical solution for determining the corresponding machine settings with modification variation. The main reason lies in the strong nonlinearity of objective correction model which mainly includes the coupling influence of machine settings and the ill-conditioning of Jacobian matrix. In this paper, a novel nonlinear least square algorithm is proposed for tooth flank topography correction. An accurate correction model and its objective function are established considering the residual ease-off. With synthesis and analysis of typical algorithms, such as the generalized inversion (GI), the singular value decomposition (SVD) and the Levenberg-Marquardt (L-M), the nonlinearity problem is investigated. And then a trust region algorithm with double Dogleg step is descrined to solve the established objective model. where, there are two key points concerning i) the control of iteration step with double Dogleg method and ii) the update strategy of trust region radius. Finally, practical numerical instance can verify the high precision and efficiency of the proposed algorithm, as well as computational robustness.