Spiral bevel and hypoid gears usually apply the flank modification with point contact to reduce gear running noise and avoid edge contact. This paper proposes the flank modification methodology based on the predetermined contact characteristics without the necessity of the tooth contact analysis. With the given gear member tooth surface, the conjugated pinion tooth surface can be derived by considering the mating gear as the cutter to roll with the work pinion. The center point of tooth-bearing is directly controlled, and the bias angle of the contact point path is designed based on the overlap ratio. Then, the flank modifications along the contact point path and the instantaneous contact lines are determined by the anticipated transmission errors and the elastic deformation as well as the length of the major axis of the contact ellipse. The generated tooth surface is approaching the modified flank by optimization. Additionally, the initial guesses for the optimization, such as the cutter parameters and the machine settings using the face-milling method, are calculated based on the theory of gearing and differential geometry. A numerical example of face-milled hypoid gear generated by the universal cradle-type generator is presented to demonstrate the validity of the proposed flank modification methodology.

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