| Summary: | 碩士 === 國立中正大學 === 機械工程學系暨研究所 === 101 === Based on the theory of gearing and differential geometry, mathematical model of hypoid gear is improved with novel pitch cone system equations. There are several pitch cones with varied constraints need to be determined during hypoid gear geometry design and manufacturing phases, for example, standard pitch cones between gear and pinion, manufacturing pitch cones between imaginary generating crown gears and the generated gear or pinion. Conventional pitch cone formula is failed when one of the gear pair is a crown gear (i.e., pitch cone angle is 90o). A novel pitch cone formula is proposed by reexamining the tangency condition between pitch cones of crossed axes. The proposed pitch cone formula is numerically stable and can be easily applied to calculate mating pitch cones even when crown gear is encountered. After pitch cones are determined, the geometry of tooth surface is derived by local synthesis with relative curvatures and relative motion. The machine settings and cutter geometry are derived based on the curvatures of the arbitrarily assigned contact point on the gear tooth surface. The tooth contact pattern and motion error curve can be adjusted by modifying the relative curvatures on the pinion tooth surface. The validation of proposed mathematical model for calculating the machine settings and cutter geometry of hypoid gear and mechanical settings are checked by 3D gear solid modelling and the ease-off topography. Several numerical examples are presented in this thesis to show the validation of the proposed mathematical model.
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