Sensitivity analysis and optimization design of hypoid gears’ contact pattern to misalignments

Accurate evaluation of the misalignment sensitivity of hypoid gears is a significant foundation for analysis of its dynamics and for the calculation of machining parameters. A tooth contact analysis (TCA) methodology considering four kinds of misalignments is presented to calculate the contact pattern and transmission error. A sensitivity model of contact pattern to misalignments is established to investigate the effects of different alignment errors on meshing performance. By parameterizing the contact pattern, the influences of offset error, angular error, and the axial error of pinion and gear on the direction, shape, and position features of contact pattern are studied. Coefficients of four evaluation indexes to different misalignments are defined respectively, and the minimum sum of the weighted coefficients is utilized to establish a multi-objective comprehensive sensitivity model. Three curvatures of the pitch cone of the pinion are taken as the control variables, and a global selection space is then built within the reasonable range of those curvatures. An improved multi-population genetic algorithm (MPGA) is used to find the optimal set of curvatures to achieve the minimum synthetic sensitivity. TCA results indicate that the offset error and angular error have the greatest influence on the contact pattern. By adopting this methodology appropriately, the sensitivity of the contact pattern to misalignments can be reduced. The contributions of this paper can be summarized as: (1) an accurate parameterized measurement model of the contact pattern; (2) a comprehensive sensitivity model of the contact pattern to misalignments; (3) an optimization framework consisting of a calculation model of the machining parameters, a TCA model considering misalignments, and a misalignment sensitivity evaluation model.