Transmission Characteristics Of Crossed Beveloid Gear Based On Rack-cutter Modification

The transmission type of crossed beveloid gear is point contact in theory,the slide velocity of tooth surface is large,so the tooth surface is easy to wear and the carrying capacity is low.Through tooth surface design of approximate line contact can increase contact area effectively,and improve the carrying capacity,service life and reliability of crossed beveloid gear pair.But the design condition of approximate line contact is difficult to achieve,and the gear pair with approximate line contact is sensitive to misalignments.For this purpose,from the point of view of tool modification,the tooth surface of beveloid gear is optimization designed in this thesis.Combining hobbing theory,tooth contact analysis(TCA)and dynamic response analysis,the mesh characteristics and dynamics characteristics of beveloid gear is investigated based on parabolic rack-cutter.And compared with beveloid gear processed by standard rack-cutter,the superiority of parabolic rack-cutter is discussed,which can improve the carrying capacity of crossed beveloid gear transmission,reduce the misalignments sensitivity and vibration noise,and has great theoretical significance on the engineering application of beveloid gear.The main contents of this dissertation are shown as follows:(1)The mathematic model of rack-cutter after parabolic modification is developed,and the equation of normal section of modified rack-cutter is derived.Based on hobbing theory,the tooth surface equation of beveloid gear processed by parabolic rack-cutter is deduced.The calculation procedure is written in MATLAB to generate the point set of beveloid gear surface.The solid model of beveloid gear is generated in 3D modeling software Pro/E,then the geometric design of beveloid gear processed by parabolic rack-cutter is conducted and the control requirements to avoid tooth topping and undercutting.And the effect of parabolic modification coefficient on the tooth surface morphology of beveloid gear is researched.(2)Based on space gear engagement theory,the TCA model of crossed beveloid gear is developed,and the effect of parabolic coefficient combinations on the contact path and contact ratio of gear pair is investigated.Considering different geometric design parameters and misalignments,the effect of parabolic rack-cutter on the contact path of crossed beveloid gear pair is discussed.The results show that pinion with positive parabolic modification coefficient and gear with negative parabolic modification coefficient is the best modification combination for beveloid gear pair.The smaller the FPD angle,the gear pair is more sensitive to misalignments and parabolic modification amount.Parabolic modification can reduce the misalignments sensitivity of gear pair effectively.(3)Considering load and system elastic deformation,the finite element mesh models of crossed beveloid gear pair before and after parabolic modification are developed.The effect of parabolic rack-cutter on contact force,transmission error,contact pattern and tooth root stress of beveloid gear pair,under different load,geometric design parameters and misalignments.The results show that parabolic modification can reduce the contact pressure,peak to peak value of transmission error and tooth root stress of pinion,meanwhile,the contact pattern is improved from wave to parallelogram.As the load increases,the contact force,mean and peak to peak value of transmission error,area of contact pattern and tooth root stress all increase before or after parabolic modification.(4)Based on the results of LTCA,the mesh excitation of beveloid gear pair is analyzed,and the time-varing mesh point,line of action(LOA),transmission error and mesh stiffness are derived.Lumped parameter method is used to develop the 14 DOF dynamics model of crossed beveloid gear.The effect of parabolic rack-cutter on dynamics charateristics of crossed beveloid gear pair is investigated,the effects on vibration acceleration,dynamic transmission error and dynamic mesh force are discussed.The results show that parabolic modification can reduce the vibration acceleration of beveloid gear pair,and reduce the amplitude value of dynamic mesh force and dynamic transmission error of beveloid gear pair effectively,especially to the amplitude value of dynamic mesh force and dynamic transmission error at double-frequency.