Dynamics Of Helical Gear Flexible Body System Including Support System

New energy electric vehicle reducer is an important part of the vehicle power system,and the dynamic characteristics of the reducer gear transmission system have an important impact on the overall performance of the vehicle.The system has a complex supporting system,including shell supporting rigidity and nonlinear bearing rigidity.The input speed range is large.Under different working conditions,the bearing rigidity is constantly changing,which affects the dynamic characteristics of the gear transmission system.At the same time,the time-varying meshing stiffness of gears is one of the most important internal excitations of gear transmission systems.Therefore,it is necessary to conduct an in-depth analysis of the dynamic characteristics of the reducer gear transmission system,and explore the influence of the housing support stiffness,bearing stiffness and gear time-varying meshing stiffness on the dynamic characteristics of the helical gear flexible body system of the reducer.The main contents of this article are as follows:First of all,considering the influence of lubricating oil film stiffness and roller centrifugal force on bearing stiffness,a stiffness model of high-speed deep groove ball bearing considering elastohydrodynamic lubrication is established.The bearing stiffness model is used to analyze the influence of lubricating oil film stiffness and roller centrifugal force on bearing stiffness at different speeds.The results show that lubricating oil film stiffness and roller centrifugal force will reduce bearing stiffness.As the speed of the bearing increases,the degree of influence on the stiffness of the bearing will also increaseSecondly,based on the slicing principle,the potential energy method is used to calculate the meshing stiffness of the helical gear with a precise tooth profile,combined with the geometric parameters of the shifted gear,to obtain the meshing stiffness of the shifted helical gear in a certain meshing state.The meshing stiffness of multiple meshing positions in a single meshing period is calculated,and the Fourier series is used to fit the gear meshing stiffness,and the time-varying meshing stiffness curve and formula of the modified helical gear are obtained.By comparing with the finite element solution of the time-varying meshing stiffness of the helical gear in the literature,the accuracy of the calculation model of the time-varying meshing stiffness of the modified helical gear is verified,and the influence of the gear helix angle and tooth width on the time-varying meshing stiffness of the gear is analyzed..Finally,a dynamic model of the helical gear flexible body system considering the stiffness of the high-speed bearing,the support stiffness of the housing and the time-varying meshing stiffness of the gear is established.Three-dimensional modeling software,analytical methods,finite element methods and empirical formulas are used to solve the mass,stiffness and damping parameters of the gear transmission system.The dynamic model is solved by the variable step function of the fourth-fifth-order Runge-Kutta method.The calculation results were compared with those of the display kinetic software Ls-Dyna,which verified the accuracy of the kinetic model.The dynamic model is used to analyze the influence of bearing stiffness,shell deformation and gear meshing stiffness on the dynamic characteristics of the gear transmission system under the two working conditions of maximum input torque and maximum input speed.The analysis results show that the bearing lubricating oil film and roller centrifugal force will increase the vibration displacement amplitude of the gear,and the effect will be more obvious at high speed;the gear vibration will be underestimated without considering the box deformation,and the box stiffness will be controlled within the range close to the bearing stiffness The gear vibration can be significantly reduced;the gear displacement reduces the gear transmission accuracy and increases the gear vibration,but the effect is negligible at high speeds.