Research On The Tooth Surface Construction And Meshing Analysis Of Cross-Axis Bevel Gear Based On Spatial Conjugate Curves

Studying high-performance gear transmission is of great significance to the development of gear transmission,and the construction of tooth surface with excellent contact characteristics is one of the key measures to improve the gear transmission performance.The Gear designed based on the traditional conjugate surface principle is difficult to effectively control the contact path and second-order contact characteristics.With the rapid development of science and technology,a new gear transmission theory has been developed: the conjugate curve meshing theory.Compared with the traditional conjugate surface meshing theory,this theory changes the basic meshing elements of the tooth surface from surface to curve,which provides greater flexibility and diversity in the design of the gear tooth surface,thereby effectively controlling the tooth surface.In this paper,the spatial conjugate curve meshing theory is used to study the tooth surface design and analysis method of the cross-axis conjugate curve bevel gear.According to the tooth surface design and analysis method,the 90 degree interaxial angle conjugate curve gear pairs with conical equal-helical-distant curves is proposed and the design criteria and meshing motion characteristics of gear pairs are studied.Based on the solid model of gear pairs,the tooth loading contact analysis is carried out and the meshing contact and stress distribution are studied.This paper provides theoretical support and design tools for the development of new high-performance cross-axis gear transmission device,which has certain theoretical significance and engineering application prospects.The main research contents of this paper are as follows:(1)Discussd the meshing principle of cross-axis conjugate curve gear pairs.Based on the basic meshing principle of conjugate curve,the meshing equation of cross-axis conjugate curve meshing pairs was derived and the general equation of conjugate curve was established.Then the uniqueness of the spatial conjugate curve was demonstrated and the condition that the spatial conjugate curve can generate the actual tooth profile was demonstrated.(2)According to the meshing principle of conjugate curve and the condition that the spatial conjugate curve can generate the actual tooth profile,the tooth surface design method of the cross-axis conjugate curve bevel gear was studied.Combined with the differential geometry,the tooth surface contact characteristic parameters of the cross-axis conjugate curve bevel gear pairs were studied and the necessary condition of no local interference was deduced.(3)According to the tooth surface design and analysis method of the cross-axis conjugate curve bevel gear,the 90 degree interaxial angle conjugate curve gear pairs with conical equal-helical-distant curves was proposed.Combined with the actual situation of gear transmission,the design criteria of geometric parameters were studied and the design calculation process was given.By using differential geometry,the contact characteristic parameters of the conical equal-helical-distant spiral bevel gear pairs were derived and the curvature range of the gear pairs without local interference was obtained.By using the numerical solution method,the actual tooth surface of the gear pairs we re obtained and the solid model of the gear pairs were established.By using the motion simulation software,the meshing characteristics of the gear pairs were analyzed and the correct meshing trace and contact area were obtained.(4)Based on the solid model of the conical equal-helical-distant spiral bevel gear pairs,the finite element analysis model of the gear pairs were established.By using the finite element method,the gear tooth loading contact analysis of the gear pairs was carried out,the finite element analysis results of the gear pairs was obtained,and the contact trace and stress distribution of the gear pairs were discussed.The finite element simulation results show that the actual contact path is basically in line with the theoretical prediction,which indicates the correctness of the theoretical model.Meanwhile,the amplitude of contact stress and bending stress indicates that the gear pairs has the potential to be used in power transmission.