| This research topic comes from the National Natural Science Foundation of China(9204820005).3K reducer has the advantages of large speed ratio,small volume,etc.,and has a wide range of applications in the fields of national defense equipment,robot,etc.Its accuracy,efficiency and backlash are its important performance indexes.In this paper,the accuracy,backlash and efficiency of a low-speed and heavy-duty 3K planetary reducer are analyzed theoretically and simulated.Eccentricity error caused by machining and installation is the main source of large period transmission error and periodic backlash.Under the condition of variable load,the existence of backlash is the main factor that causes the backside deviation and affects the transmission accuracy.At the same time,transmission efficiency of gear train will also affect the cost and stability of transmission.In this paper,the transmission performance of 3K-I planetary gear is discussed from two aspects of transmission accuracy and transmission efficiency.The main research contents of this paper include:(1)The calculation model of 3K-I planetary gear transmission error and back error under unloaded condition with eccentricity error is proposed.Under no load condition,the mathematical equivalence relation among instantaneous node,transmission ratio error and transmission error is derived by using the analytic model of transmission error.The equivalence relation among the increment of center distance,the circumferential backlash and the backlash is deduced by using the analytical calculation model of the backlash,which provides a theoretical basis for the simulation analysis of the transmission error and the backlash.Monte Carlo method is used to simulate the influence of the initial phase on the transmission error and the reverse assembly.(2)The software Recur Dyn is used for multi-body dynamics simulation.The solid model with eccentricity error of all components is established in the software,and the correctness of the analytical model is verified.The dynamic transmission error of gear under alternating load was simulated,and the model with time-varying backlash was discussed.The relationship between theoretical transmission error,dynamic transmission error and back error was explored for the model under load conditions that varied with rotation frequency and meshing frequency.The results show that the faster the load direction changes,the greater the influence of the time-varying backlash on the dynamic error,the greater the fluctuation of the dynamic error,and the more obvious the impact of the mechanism.(3)By establishing the instantaneous efficiency model of external and internal meshing gear pairs with single pair of teeth,the meshing state of the gear is analyzed in detail,and the forward and reverse driving instantaneous meshing efficiency of single pair of gear transmission is deduced.The instantaneous efficiency diagram is drawn and compared by using MATLAB software programming.The instantaneous efficiency is improved by optimizing the displacement coefficient.(4)For 3K planetary gear mechanism,unit analysis method and substitution method were used to solve the expression formula of overall efficiency,and the expression of instantaneous meshing efficiency of planetary gear mechanism was obtained by replacing the efficiency of K-H mechanism with the instantaneous efficiency of a single pair of gears.Finally,MATALB programming is used to analyze the instantaneous efficiency. |
