Research On Dynamic Similarity Theory And Prediction Method Of Gear Transmission System Under Error Distortion

Gear transmission system is widely used in aviation,military and marine fields.Vibration and noise reduction of the system has always been an important research topic in the engineering field.The operating condition of gear transmission system is developing towards high-speed and heavy load,which is of great significance to the prediction of dynamic characteristics,performance evaluation and structural parameter optimization of the system.In addition to the analytical method and finite element method,the physical test method is indispensable for the comprehensive study of the dynamic characteristics of gear transmission system.According to its application and function,the size of gear transmission system is as low as a few millimeters and as large as a few meters.Especially for large and super large gear transmission systems,there are some problems,such as long processing cycle,high manufacturing cost and difficult to control the test process.Therefore,based on the similarity theory,the scale model is used to replace the prototype for the test,which provides an effective and convenient research means for the performance prediction,structural parameter optimization and vibration suppression of the prototype gear transmission system.Based on the mass equivalent method,the model of each toothed component in the gear transmission system is simplified,and the modeling of each equivalent shaft segment and component is completed by node finite element method and spatial beam element.The factors such as bearing stiffness,time-varying meshing stiffness and meshing error are incorporated into the dynamic model.Through the gear meshing relationship obtained by analysis and derivation,the coupling between each shaft system is completed,and the dynamic models of parallel shaft gear transmission system and planetary gear transmission system are established.It lays a foundation for the subsequent calculation of system dynamic characteristics,derivation and verification of similarity relationship.According to the hierarchical idea of complex system,the gear transmission system is split "from top to bottom",and the similarity relationship is deduced and analyzed "from bottom to top" combined with the similarity theory of complex system.The unified vector unit method is proposed to solve the problem that the matrix similarity ratio in the dynamic equation cannot be solved directly,and the similarity ratio of mass,stiffness and damping matrix between prototype and scale model is obtained.The similarity relations of parallel shaft gear transmission system and planetary gear transmission system are deduced by equation analysis method.Based on the dynamic model of gear transmission system,the natural characteristics and vibration response of scale model and prototype are calculated respectively,and the correctness of similarity relationship is verified.Considering the machining error in the dynamic equation of gear transmission system,the similarity relationship between static displacement and dynamic response is deduced by equation analysis method.In order to solve the problem of error distortion of scale model,the concept of peak to peak similarity ratio of vibration response and the modification method of distortion model are proposed.The calculation results of the dynamic model show that the prediction accuracy of the vibration response curve of the distortion scale model is improved after the load modification method and the similarity ratio modification method.The transmission error tests of scale model and prototype are completed.Through the comparison and analysis of transmission error response curve,the effectiveness of similarity ratio modification method is verified.According to the calculation formulas of load sharing coefficient of dynamic model and test model,the corresponding similarity ratio of load sharing coefficient is deduced respectively.Through the scale model and the dynamic model of the prototype,the load sharing coefficient of the prototype gear transmission system under different working conditions and different structural flexibility is predicted and the similarity relationship is verified.The sensitivity of load sharing coefficient to different errors is analyzed and compared,and the conclusion that the position error has a relatively large influence on the load sharing coefficient is obtained.The load modification method and similarity ratio modification method are proposed to deal with the problem of position error distortion,and the effectiveness of the two modification methods is verified by the dynamic model.Based on the similarity theory and load sharing test,the load sharing performance of the prototype planetary gear transmission system under similar working conditions is predicted and analyzed.In short,using the similar model to study the dynamic characteristics of the gear transmission system,on the one hand,it can study the variation law of the vibration response and realize the prediction of the prototype vibration response of the system.On the other hand,it can develop and verify the vibration and noise reduction technology of the gear transmission system,and provide an optimization scheme and platform for the design of the gear transmission system.Therefore,the research of this paper has important engineering and academic value.