A simple and robust method for spiral bevel gear generation and tooth contact analysis

A simple and robust method to simulate spiral bevel gears generating and meshing processes is proposed. In a first part, a mathematical model of universal hypoid tooth surfaces generator is formulated. It is based on Fong’s approach. The model takes into account all the kinematic motions of common CNC machine tools dedicated to hypoid gears machining. It is general enough to enable the simulation of various hypoid gears cutting methods such as face-hobbing, face-milling, plunge cutting and bevel-worm-shaped-hobbing processes. In this paper, only developments related to face-milled spiral bevel gear generation are presented. We show that the results obtained are in good agreement with those of certified software. In a second part, a simple and numerically stable algorithm is proposed for unloaded tooth contact analysis. The simulation method is based on a discretization of one of the two tooth flank surfaces in contact and a specific projection of the points on the opposite flank. It gives a good approximation of the contact pattern location. The accuracy of the contact point locations and computing time is directly dependent on the mesh density. However, this approach enables obtaining in a very short time sufficiently accurate results to meet the needs of designers, particularly in the preliminary stages of design. The relative displacements of the gears can be taken into consideration. The robustness of the proposed computing process and the adjustable accuracy of the results are the two main advantages of the presented approaches.