Cutting principle and tooth contact analysis of spiral bevel and hypoid gears generated by duplex helical method

Abstract

The duplex helical method is an advanced manufacturing method of face milling spiral bevel and hypoid gears for its characteristics of higher machining efficiency and power dry cutting. In order to reveal the generalized theory of the duplex helical method, the cutting mathematical model on three reference points is established and the basic machine settings of the formate spiral bevel and hypoid gears generated by the duplex helical method are determined with the vector method according to principle of gearing and differential geometry and the relative position and motion among head-cutter, machine and workpiece. Then, the hypoid gear dimensions are modified based on the root angle of the pinion obtained by the midpoint of the point width for the pinion as the reference point. In addition, and a novel method for calculating ease-off is presented utilizing the pinion generating surface instead of its conjugate surface, which can gain the same simulation results and greatly simplify the process of calculation compared to the traditional methods. Finally, a hypoid gear drive 7×43, designed and manufactured using the duplex helical method, is performed and validated, the results of the tooth contact analysis and rolling tests show that the proposed theory of the duplex helical method is correct, and new spiral bevel and hypoid gear software has been developed using the new approach, which provides the theoretical basis and technical support for the promotion of the duplex helical method at home.