Research On The Accuracy And Parameter Identification Of Involute 2K-V Gear Reducer Under Non-uniform Load Contact

This subject is supported by the National Natural Science Foundation(NO.51275538)and by the foundation project of Shanghai key laboratory of space vehicle institution(SM2014B101).Due to the features of large transmission ratio,small volume,light weight,large stiffness,and low cost,it is suitable for robot,high-quality equipment and other precision transmission systems,and its transmission accuracy is the key performance index that affects the system motion accuracy,stability and system sensitivity.Because of the influence of manufacturing and installation error,the planetary gear pair with 180-degree phase difference in the involute 2K-V reducer has uneven load contact and even disengage in the meshing process as well as the multi-tooth contact effect of the gear pair with small tooth number difference,which will have an important influence on its transmission accuracy and load bearing performance.The manufacturing and installation eccentricity is an important factor affecting the performance of the reducer such as large cycle of tramsmission error and even load contact.Therefore,this paper carries out theoretical and experimental research on accuracy and meshing characteristics of gears of 2K-V reducer with small tooth number difference under eccentric error and uneven load contact as well as multi-tooth contact effect.The main research results are as follows:(1)Considering the eccentricity errors in the gear pair with small tooth number difference in the second stage,an analytic calculation model of the large-period unloaded transmission error of 2K-V reducer was established.On the basis of the analytical model,the influence of the eccentricity error and its initial phase on the unloaded transmission error was analyzed by Monte Carlo method from the perspective of statistics.At the same time,the particle swarm optimization algorithm is used to optimize the initial phase of the transmission error in which the minimum square of transmission error is taken as the objective function.(2)Due to the difficulty to find the solution by traditional fitting method caused by the characteristics of non-differentiable,strong nonlinear,multi-variable parameters as well as multi-local extreme values,this paper proposed an adaptive differential evolution-black hole hybrid algorithm to identify the parameters of transmission error of2K-V reducer.In the identification process,the adaptive differential evolution-black hole hybrid algorithm utilized the advantages of DE/rand/1 and DE/best/2 to generate adaptive variation vectors and black hole algorithm of the diversity of target vectors and improvement of precocity and local convergence,which are common in optimization problems.(3)Aiming at the multi-tooth meshing effect of the gear pair with small tooth number difference under external load torque,an improved analytical calculation model of time-varying meshing stiffness is proposed.On the basis of the above improved analytical model,a novel finite element-analytical hybrid method is proposed to calculate the time varying meshing stiffness of gear pairs with small tooth difference.Finally,a finite element model of multi-tooth meshing for the gear pair with small tooth difference is established and compared with the results of the above two methods.The calculation results of time-varying stiffness of the three methods agree well,which shows that the time-varying meshing stiffness of the gear pair with small tooth number difference increases with the increase of external load moment,and the phenomenon of alternating single and double teeth gradually disappears.(4)The static transmission error of 2K-V gear reducer was calculated by meshing line increment method under the non-uniform load contact condition of the gear pair with small tooth difference.Considering load,speed,time-varying backlash in the non-uniform contact conditions,the nonlinear dynamic model of gear pair with small tooth number difference is proposed,which is solved by the lumped parameter method.The contact characteristics of the gear pair with small tooth difference under different load conditions are analyzed and are verified by the multibody dynamics model in RecurDyn simulation.(5)The transmission accuracy test and analysis of 2K-V reducer are carried out,and the transmission errors under different rotation speed and different initial phase conditions are obtained,and the parameter identification of the reducer eccentricity error and its phase is identified by the adaptive differential evolution-black hole hybrid algorithm.The corresponding transmission error curve from parameters identified are in good agreement with the test transmission error curve in large period whose fitting degree surpass 90% so that the correctness of the theoretical model of transmission error is verified.Based on the test transmission error curve,the discrete backlash measurement and the continuous backlash measurement methods are proposed.