Contact Strength Analysis Of Involute Beveloid Spur Gear

Beveloid gear is a general form of involute gear,and its modification coefficient changes continuously along the direction of gear axis,which can realize parallel shaft,intersecting shaft and staggered shaft transmission.Because the working tooth surface of the beveloid gear is an involute spiral surface,it can mesh with different types of involute gears in different working environments to meet the working requirements under this environment.beveloid gear can also achieve precision transm ission through axial movement when working,so it has obvious advantages and wide application prospects in some precision transmission fields with strict requirements for backlash.As a new type of gear,the research on strength calculation and life predic tion of beveloid gear is not yet mature.Therefore,this article takes parallel axis beveloid gears as the research object,based on the fractal contact theory,cumulative damage theory,gear meshing principle,fatigue life theory and Hertz contact theory,this paper studies the related parameters,tooth surface equation,meshing efficiency,mathematical model,gear pair contact strength,fatigue life and fatigue damage of the beveloid gear.The research content of this article is as follows:(1)Considering the influence of tooth width and pitch cone angle of beveloid gear,the restriction conditions of undercutting,addendum sharpening,gear interference and no backlash meshing condition of beveloid gear are deduced.Based on the The principles of taking shape and surface equation of beveloid gear,establish an accurate mathematical model.Based on the calculation model of the meshing efficiency of spur gears and helical gears,the calculation formula of average meshing efficiency of beveloid gear is deduced.The influence of different parameters on gear meshing efficiency is analyzed,which provides a theoretical basis for the design of beveloid gear.(2)Based on Hertz contact theory and considering the geometric structure of beveloid gear,the calculation method of contact ratio,curvature radius,normal load,contact line length,contact ratio coefficient,tooth form angle coefficient and pitch cone angle coefficient of beveloid gear is determined.The improved Hertz contact model of beveloid gear is established,and the influence of different pitch cone angle,tooth number,modulus and pressure angle on the contact stress of beveloid gear is studied.(3)Based on the fractal contact theory,which analyzes the deformation form of the asperity on the contact surface,and the modified distribution function of the asperity on the tooth surface of the beveloid gear is established by introducing the contact coefficient of the tooth surface.The formula for calculating the contact coefficient of beveloid gear is derived and its rationality is verified.Based on the fractal contact theory and Hertz contact theory,a fractal contact model of beveloid gear is established,which comprehensively considers the parameters such as rough surface morphology,material properties and elastic deformation of contact points.The effects of fractal dimension,friction factor on the real contact area of tooth surface are studied.The maximum contact stress of gear pair is compared and analyzed by using fractal contact model,Hertz contact model and improved Hertz contact model.(4)Establish a dynamic model of parallel axis beveloid gear pairs,The dynamic stress cloud diagram of gear operation is obtained by simulation analysis.The dynamic contact stress of beveloid gear in meshin g process is taken as the load spectrum of fatigue analysis.Based on the S-N curve of material 20 Cr Ni Mo,the fatigue life of parallel shaft variable tooth thickness spur gear pair is calculated.The changes of fatigue life and fatigue damage of gear pair under different material survival rates are analyzed,which provides theoretical reference for engineering application.The research results show that the limiting conditions of the addendum modification factor,the improved Hertz contact model and the fr actal contact model proposed in this paper are feasible,which play an important role in selection of the addendum modification factor of the beveloid gear,the improvement of the transmission performance of the gear pair and the extension of the service l ife,this paper provide a theoretical basis for the practical application and development of the beveloid gear.