Tooth meshing simulation and analysis based on isometric mapping Ease-off surface

Based on the isometric transformation of Ease-off surface,a method for the meshing simulation analysis of gear tooth was put forward. By using the parameters of curvature and torsion of surface geometry, both the definition on the 2nd order osculating surface and its topologic method were presented. Within the extent of 2nd order differential precise, the osculating surface was close to the original curve surface, making it possible to carry out the geometric analysis instead of the original scattered curve surface. By using the ordinate system transformation, the derivation of meshing equation and the establishment of universal model on generating spiral bevel gears were done respectively. Based on isometric mapping between two tooth meshing surfaces, the solutions to mismatched size of the relative point at surfaces of tooth were made, then the osculating surface of the Ease-off of tooth surface was set-up by means of the topology of original scattered surface using the least square method. Depending on the parameters of the set-up Ease-off osculating surface, the solving methods were presented on behavior parameters of tooth surface meshing such as contact area, contact path and transmission errors by the introduction of the isoheight line and the asymptotic behavior of the tooth surface contact. The results of analysis show that it is able to obtain directly the tooth meshing perfect information of gears by means of one-off constructing Ease-off surface, and increase the topologic precision of curve surface up to 0.1 μm. This presented method is not only more suitable for the reverse engineering and the numerical computing relative to the conventional methods of meshing simulation, but also more convenient for gaining the information of tooth surface contact.