| Gears are widely used as transmission components in modern mechanical equipment,especially in some precision equipment.How to reduce vibration and noise is an issue that must be considered when designing gear systems.Gear displacement and modification can improve the stability of gear operation so as to reduce vibration and noise and extend the operational life of the gear.This paper focuses on speed-increasing gears.considering factors such as gear profile shifted,gear modification,eccentricity,time-varying meshing stiffness and time-varying friction,the gear-bearing-rotor bending and torsional coupling nonlinear dynamic model is established based on the concentrated mass method and the vibration differential equations of the gear system are derived from the Lagrangian equations,therefore the dynamic characteristics of the gear pair are obtained by solving the vibration differential equations of the system using the LUNGE-KUTA numerical integration method.The main research content of this article is as follows:(1)Deriving and calculating the time-varying mesh stiffness of profile shifted gears based on the principle of potential energy,analyzing the influence of different profile shifted coefficients on the time-varying mesh stiffness of gears;investigating the influence of gear profile shifted on the dynamic characteristics of gear train;studying the changes of dynamic characteristics of profile shifted gear transmission systems under the application of different input torques.The research has shown that gear profile shifted can advance or delay gear meshing.It provides a relevant foundation for the selection of gear profile shifted coefficients.(2)The time-varying meshing stiffness of modification gears is derived and solved,and the changes of the time-varying meshing stiffness of gears under the action of different modification parameters are analyzed;the changes of dynamic characteristics under the action of different modification amounts and modification lengths are investigated respectively;the change of dynamic characteristics under the action of gear eccentricity is studied.The research has shown that gear modification can effectively change the sudden change in gear time-varying mesh stiffness when alternating single and double teeth;gear eccentricity is more sensitive to low frequencies.It provides a foundation for the selection of modification parameters in gear design.(3)The time-varying mesh stiffness of profile shifted gears with gear modification is calculated,and the changes of the time-varying mesh stiffness of gears under the interaction of gear profile shifted and modification are investigated;the influences of gear profile shifted on the dynamic characteristics of the modified gear train and the effects of gear modification on the dynamic characteristics of the profile shifted gear system are discussed respectively.The research shows that tooth profile modification has a greater influence on the meshing characteristics of profile shifted gears.(4)The time-varying friction coefficient of gears is derived and calculated,and the effects of rotational speed and roughness on the time-varying friction coefficient of gears are studied;the time-varying mesh stiffness of gears taking into account constant friction,as well as time-varying friction,is derived and solved based on the energy method;the changes of dynamic characteristics of gear transmission systems under the action of constant friction and time-varying friction are studied respectively;compared the dynamic characteristics of profile shifted gears considering tooth profile modification with standard gears.It is shown that the gear stiffness transitions smoothly at the pitch position when the time-varying friction coefficient is taken into account,and a comparison of the dynamic characteristics before and after the correction,it is found that the gear runs more smoothly after the correction. |
