Dynamic Analysis Of Face Gear Drive And Optimization For Vibration Reduction By Tooth Surface Active Modification

Face gear transmissions are commonly utilized in helicopters,vehicles etc.The transmission system operates in a tough environment with complicated internal and external excitations which are possible to create significant vibration and noise.Thus,the influence of the meshing stiffness,friction,and static transmission error on the dynamic response is investigated by developing the dynamic model of the face gear drive.The vibration reduction optimization of the face gear pair is carried out in conjunction with tooth surface active modification and genetic algorithm(GA)to fulfil the increasingly demanding from the host equipment.The main research contents of this paper are as follows:(1)The theoretical tooth surface of the face gear pair is determined using the engagement theory,and the tooth contact analysis model(TCA)and the loaded tooth contact analysis model(LTCA)are deduced.Considerations for the backlash,friction,static transmission error,and meshing stiffness result in the establishment of a nonlinear dynamic model of the face gear drive and the derivation of the system’s differential equation of motion.(2)The impact of load on the meshing stiffness is addressed,and the meshing sti ffness is computed via LTCA.The influence regulations of the excitations such as meshing stiffness,static transmission error,and friction on the dynamic response of the face gear drive by solving the differential equation of motion.Besides,the effect ratio of the three excitations mentioned above on system vibration is examined.The results demonstrate that the increase of load improves the mean value and the fluctuation amplitude of the meshing stiffness.Decresing the fluctuation amplitude and raising the mean value of the meshing stiffness may assist lessen the vibration of face gear drive.The vibration of face gear drive will grow as the static transmission error and friction coefficient increase.The meshing stiffness has the greatest impact on the system vibration,followed by the static transmission error,friction.(3)The transmission error,the contact path,and the contact ellipse main axis are preset to modify the face gear pair,GA is utilized to calculate the ideal modification parameters based on the modification objective of the minimal root mean square of the vibration acceleration along the meshing line.The geometric contact properties,load-bearing contact characteristics,and dynamic response of the modified system are investigated.The results reveal that the tooth surface active modification can achieve pre-control of the geometric meshing performance of the face gear pair.The fourth-order transmission error is more effective in reducing vibration of the face gear pair than the theoretical and second-order transmission error.The vibration is not only related to the mean meshing stiffness,but it is also heavily influenced by the high-order harmonic amplitude.Within a reasonable range,the suggested contact path inclination angle is in the range of 10.5°～13.5° and extending the length of the contact ellipse main axis is helpful to lower the vibration.(4)The bifurcation characteristics and meshing state of the system with the change of meshing frequency,external load and friction coefficient are studied using bifurcation diagram,time domain,phase plane,frequency spectrum and Poincare section.The findings reveal that increasing the aforementioned parameters causes the system to exhibit single/multi-periodic,quasi-periodic,and chaotic motion.The active modification substantially decreases the region of chaotic motion and increases system stability.With the increase of meshing frequency and friction coefficient,the system exhibits no impact and bilateral impact.Under the change of external load,the system exhibits bilateral impact.The active modification has little effect on the meshing state but reduces the magnitude of the system impact.