A simple and robust method for spiral bevel gear generation and tooth contact analysis
Résumé
A simple and robust method to simulate spiral bevel gears generating and meshing processes is proposed. First, a mathematical model of universal hypoid tooth surfaces generator is formulated, based on Fong’s approach and taking into account all the kinematic motions of common CNC machine tools dedicated to hypoid gears generation. This model is general enough to allow the simulation of various hypoid gears cutting methods such as facehobbing, face-milling, plunge cutting and bevel-worm-shapedhobbing processes. In this paper, only developments related to facemilled spiral bevel gear generation are presented. It is shown that the results obtained are in good agreement with those of certified software. A simple and numerically stable algorithm is then proposed for unloaded tooth contact analysis. The simulation method is based on a discretization of one of the two conjugated tooth flank surfaces, and a specific projection of the different nodes of this discretization on the other flank. The contact path location can be easily approximated using this method. The accuracy of the location of contact is directly dependent on the mesh density. Although improving the accuracy requires an increase in computation time, this method allows 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.