Meshing Stiffness Calculation And Load Contact Analysis Of Spur Bevel Gears

In the meshing process of gear transmission,the internal nonlinear excitation is one of the important factors leading to the early failure of gear,the modeling and calculation method of the internal nonlinear excitation are the indispensable theoretical basis for the study of high precision gear transmission system.Internal excitation mainly includes stiffness excitation,error excitation and meshing impact excitation.The stiffness excitation is generated by the time-varying meshing stiffness which varies with the meshing period.It is precisely because of the time-varying,that the parameter vibration state of the gear transmission system is caused.Therefore,the study of the calculation method of meshing stiffness and the analysis of gear dynamics are of great significance and engineering value to the optimal design of gear transmission system.Spur bevel gears are widely used in transmission devices in vehicle differential,machine tools and other industrial fields.Therefore,this paper takes straight bevel gear as the research object and calculates its meshing stiffness and analyzes its loading contact.However,it is difficult to accurately and quickly calculate the meshing stiffness of straight bevel gear by using the traditional material mechanics method because of the particularity of its tooth profile,let alone to accurately obtain the modified meshing stiffness of straight bevel gear.Therefore,the key to solve the problem is to establish an accurate analytical model for the time-varying meshing stiffness of straight bevel gears and modified straight bevel gears.In this paper,two new models and methods for calculating the meshing stiffness of spur bevel gears,"equivalent spur gear" and "cumulative integral",are proposed based on the idea of equivalent tooth profile and "micro-element",combined with the principle of energy equivalence and deformation coordination.Aiming at the problem that there is no accurate algorithm for calculating the meshing stiffness of modified straight bevel gears,an accurate calculation model and a new algorithm for modified straight bevel gears were proposed based on the meshing principle of gears,Hertz contact theory,energy equivalence and deformation coordination principle.The main research work includes:1.For the calculation of single tooth meshing stiffness of spur bevel gear,considering that the tooth profiles are not equivalent at different sections along the lengthwise direction of the tooth,in order to simplify the tooth profile reasonably,the integrated use of the equivalent tooth shape and "micro-element" as well as the energy equivalence principle,respectively is proposed based on equivalent spur gears and based on the elementary ideas of two kinds of single tooth meshing stiffness analytical model.2.In view of the calculation problem of the comprehensive meshing stiffness of straight bevel gears,based on the single tooth meshing stiffness and deformation coordination principle,the analytical calculation model of the comprehensive meshing stiffness of straight bevel gears was further derived by supplemental deformation coordination equation.3.A fast analytical method was proposed to calculate the meshing stiffness of straight bevel gears after modification.Firstly,based on the discrete data points of the tooth surface,the equation of the tooth surface was obtained by using the B-Spline surface construction method.Then,based on the tooth contact analysis,the contact trace of the whole tooth surface was solved by the gear meshing principle.Then,based on the Hertz contact theory and principle of energy equivalence,an analytical calculation model of single tooth meshing stiffness is proposed.4.To solve the problem of calculating the comprehensive meshing stiffness of modified straight bevel gears,based on the single tooth meshing stiffness and the principle of deformation coordination,a time-varying analytical calculation model for the meshing stiffness of modified straight bevel gears was further proposed by supplemental deformation coordination equation.5.3D modeling of straight bevel gear and modified straight bevel gear is carried out by using 3D software,and mesh division software is used to divide the mesh,and finally the finite element analysis software is used to analyze it.The single tooth meshing stiffness curve and the comprehensive meshing stiffness curve are extracted,and the results are taken as the standard to verify the effectiveness of the analytical algorithm.The comparison of the calculation results shows that the method presented in this paper can effectively construct the calculation model of meshing stiffness of involute straight cone teeth and modified straight bevel gears.