Conjugated action and methods for crowning in face-hobbed spiral bevel andhypoid gear drives through the Spirac system

An analytical method for derivation of basic machine-tool settings that allows the conju- gated action in face-hobbed spiral bevel and hypoid gear drives wherein the gear is not generated is proposed. This approach is used as starting point for investigation of further methods of crowning as the one where crowning is achieved through application of a tilt angle. A new approach where crowning is achieved through the application of modified roll between the rotations of the head-cutter and the pinion is proposed. It is based on the application of a two-term Fourier series of a parabolic function to provide a continu- ous and periodic function that is required in a continuous non-indexing process as face- hobbing. The existing and proposed approaches for crowning have been tested by the ap- plication of tooth contact analysis and geometry comparison. The results show that the proposed approach does not yield unloaded transmission errors and allows independent crowning at both tooth sides to get acceptable formations of the bearing contact for both rotational directions. Two numerical examples of design corresponding to a spiral bevel gear drive and a hypoid gear drive are presented as well starting from their basic dataThe authors express their deep gratitude to the Spanish Ministry of Economy, Industry and Competitiveness (MINECO), the Spanish State Research Agency (AEI) and the European Fund for Regional Development (FEDER) for the financial support of research project DPI2017-84677-