Research On Meshing Theory And Experiments Of Geometric Elements Constructed Bevel Gears With Curve-curve Mesh

As an extremely important key component in manufacturing equipment industry and national defense industry,the transmission performance of gears is affected by many factors such as materials,heat treatment,manufacturing accuracy,lubrication status,and meshing tooth surfaces.Among them,the meshing tooth surface is the direct action surface of movement and power transformation,and its innovation and development have a key influence on the performance of the gear transmission.Traditional involute gears,bevel gears,etc.are all developed on the basis of conjugate surface theory.Although more systematic and comprehensive researches on conjugate surface theory have been established at home and abroad,it is still difficult to meet the increasing demand for high performance in gear transmissions.Therefore,starting from the research of gear geometry,breaking through the limitation of conjugate surface theory,and developing new meshing theory have very important theoretical significance and extensive engineering application background.Points,lines,and planes are the basic elements in nature.The existing theory of surface to surface meshing has been fully explained.Chen Bingkui et al.revealed the meshing relationship of curve to curve and curve to surface from the perspective of the most basic geometric elements,curve and surface,and formally proposed the concept named “Constructed Tooth Pairs”.It can be divided into curve-surface and curve-curve constructed tooth pairs according to the different ways of meshing.This paper takes curve-curve constructed spiral bevel tooth pairs as the research object,and the main research work and results of the paper are as follows:(1)The research on the basic principle of curve-curve constructed bevel gear meshing is carried out.The space coordinate system is established,and the relative motion speed of meshing curve and normal vector of it are studied.The meshing equation,conjugate curve equation and meshing line equation are carried out.Taking the general cone curve as an example,the cone curve,meshing equation and its conjugate curve are deduced.The normal-sectional profiles with circular arc curve are used to construct tooth surface,and the conjugate surface is established.The condition of line contact along the tooth height direction is obtained,namely,the instantaneous forming condition.Later on,the conjugate tooth surface with instantaneous forming characteristics is constructed.(2)Research on the tooth surface construction theory,tooth profile design and modeling method of bevel gears with multi-point contact.The convex tooth surface equation is obtained through the spiral movement of the normal-sectional curve along the conjugate curve based on the meshing principle of conjugate curve.The corresponding concave tooth profile is constructed by the instanteous forming method,and the concave tooth surface is obtained similar to the construction of original tooth surface.The design criterion of multi-point contact bevel surface is discussed.Next the tooth profile parameters are analyzed,and the examples of the cross-sectional tooth profiles are given.The solid modeling process of curve-curve constructed bevel gears is proposed,and the pinion with convex tooth surface is taken as an example,later on the data points of tooth surface derived by Matlab are put into UG for 3D modeling,and finally tooth surface is inspected by P26.(3)Research on the characteristics of the tooth surface of bevel gear with multi-point contact.The normal curvature,the induced normal curvature and the induced geodesic torsion of the bevel gear is studied.The curvature interference conditions of the bevel gear is discussed and the curvature interference free conditions is obtained.The theoretical model for calculating the sliding ratio of tooth surface is proposed.The contact ratio of bevel gears is deduced.(4)Research on the meshing principle and tooth surface characteristics of bevel gears with involute arc tooth profiles.The tooth surface forming principle is analyzed and the curvature radius of the normal-sectional arc profile is discussed.The spherical involute logarithmic spiral bevel gear tooth surface equation is derived,while the meshing equation and the conjugate curve are derived on the geodesic line.The tooth surface is obtained by the method of normal-sectional tooth profile movement.The difference between sliding ratio of the involute arc tooth profile and the spherical involute tooth profile bevel gear is compared and analyzed.The contact ratio,the multi-point contact coefficient and the multi-pair tooth meshing coefficient of double involute arc spiral bevel gears are discussed in detail.Finally,the transmission error of involute arc bevel drive without modification is analyzed.(5)Finite element stress analysis of bevel gear tooth surface constructed by curve-curve mesh.The finite element models of single-point contact,two-point contact,three-point contact and line contact are established.The finite element models corresponding to three kind of distances of the non-contact area between the meshing points have been established.The finite element model with double involute arc tooth profiles is established,and the double involute arc bevels are compared with the multi-point contact bevel gears.(6)Prototype trial and experiment of curve constructed bevel gears.The trial production of the bevel gear prototype is completed on the machining center.The contact area of the bevel gear with multi-point contact and double involute arc is adjusted separately.The installation and debugging processing is compeleted,and the performance test of the bevel gears is carried out,including no-load test,running-in test,efficiency test and lubricating oil temperature variation test.The feasibility of the bevel gear is verified,which lays the foundation for the realization of industrial application.