Research On Meshing Characteristics And Vibration Reduction By Tooth Modifications Of The Planetary Gear Systems

Planetary gear transmission system has the advantages of large bearing capacity,large transmission ratio and high transmission efficiency.It is widely used in high-speed low-power or low-speed large-torque equipments,such as geared turbofan(GTF)engines,wind turbines,industrial robots,medical testing equipments and other related machinery.The time-varying mesh stiffness of gear pair causes the internal excitation of transmission system,which is one of the main vibration sources of mechanical equipments.In this paper,based on the potential energy method in elasticity,the accuracy of mesh stiffness calculation of planetary gear with involute profile is improved,and considering the effects of tooth modifications,an accurate time-varying mesh stiffness calculation model of planetary gear is established and verified by the comparison of various methods.Introducing the precise time-varying mesh stiffness into the dynamic model of planetary gear transmission system and taking the ring flexibility into account by the finite element method,the influence of tooth modifications and ring flexibility on the vibration response of the system is analyzed.It provides theoretical basis for the modification design of precision gear mechanism.The main research contents and conclusions of this paper are as follows:(1)Based on the potential energy method in elasticity,considering the effects of gear ring deformation and extended tooth contact of planetary gear pair,an improved mesh stiffness calculation model of planetary gear with involute profile is developed.The effectiveness of the improved model is verified by two-dimensional finite element method,literature comparison and KISSsoft software.The research results show that the improved mesh stiffness model has higher calculation accuracy and related to finite element method,has higher calculation efficiency;the extended tooth contact phenomenon of the internal mesh gear pair is more obvious than that of the external mesh gear pair.(2)Considering the coupling effects of tooth profile modification and lead crowning relief,a mesh stiffness model is established based on the slice method.The effectiveness of the model is verified by three-dimensional finite element method and KISSsoft software.Based on the proposed mesh stiffness model,the influences of different modification methods and parameters on the time-varying mesh stiffness of planetary gears are analyzed,and the optimal modification parameters are optimized by genetic algorithm and other optimization methods.The research results show that the tooth profile modification reduces the fluctuation of mesh stiffness;the lead crowning relief makes the load distribution more uniform,and the load and contact stress concentrate to the center of the tooth surface.The combine of these two modification methods is beneficial to the smooth operation of the gear system,and offset the impact of elastic deformation,manufacturing and installation error.(3)Based on lumped mass method,the motion components of the system are modeled as mass points,each particle contains 6 degrees of freedom,and the connection between them is modeled as spring and damping.The accurate time-varying mesh stiffness is introduced to establish the bending-torsion-axis-pendulum coupling dynamic model of planetary gear system.The natural characteristics and dynamic responses of the system are predicted and the influences of time-varying mesh stiffness,modification methods and parameters on the vibration characteristics of the system are analyzed.The research results show that gear modifications have important effects for the vibration characteristics of the system and the optimization method of modification parameters proposed in this paper can reduce the vibration response of gear system,especially for high-speed gear transmission,while unreasonable modification will aggravate the vibration of the system.(4)Based on the finite element method,the results of solving the natural characteristics of the gear ring by different beam element models are compared with experiment result;the gear ring is simulated by curved beam element,and other components are simulated by mass points.The rigid-flexible coupling model of planetary gear system is established,and the influence of the flexibility of gear ring on the dynamic characteristics of planetary gear is analyzed.The research results show that the curved beam element adopted in this paper has a high calculation accuracy.The flexibility of the gear ring affects the resonance frequency and amplitude of the system,so that the resonance speed tends to decrease,which leads to the shift of the resonance peak.