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Loaded transmission error (LTE) is one of the primary sources of gear noise and vibration. While ease-off topography has been shown to be powerful in improving the contact properties of a gear drive, its optimization to minimize LTEs has been an open problem in the gear literature. Through the formulation of an appropriate nonlinear optimization problem, this study proposes a novel methodology to systematically define optimal ease-off topography to simultaneously minimize LTEs and contact pressures, while concurrently confining the loaded contact pattern within a prescribed allowable region on the tooth surface to avoid any edge- or corner-contact condition. Effectiveness of this optimization is presented using a face-milled and a face-hobbed hypoid gear examples. These example analyses reveal particularly promising results that feature both a drastic reduction in LTE and an appreciable decrease in the maximum contact stress. Although the method is employed here for hypoid gears, its intrinsically systematic formulation enables straightforward applicability to any kind of gears. The methodology presented in this work can be a useful aid for gear engineers to determine optimal ease-off topographies without having to rely on time-consuming trial-and-error approaches or on a priori subjective judgments.

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Actual hypoid gear tooth surfaces do deviate from the theoretical ones either globally due to manufacturing errors or locally due to reasons such as tooth surface wear. A practical methodology based on ease-off topography is proposed here for loaded tooth contact analysis of hypoid gears having both local and global deviations. This methodology defines the theoretical pinion and gear tooth surfaces from the machine settings and cutter parameters, and constructs the surfaces of the theoretical ease-off and roll angle to compute for the unloaded contact analysis. This theoretical ease-off topography is modified based on tooth surface deviations and is used to perform a loaded tooth contact analysis according to a semi-analytical method proposed earlier. At the end, two examples, a face-milled hypoid gear set having local deviations and a face-hobbed one having global deviations, are analyzed to demonstrate the effectiveness of the proposed methodology in quantifying the effect of such deviations on the load distribution and the loaded motion transmission error.