| Gear transmission system is extensively applied to transportation,aerospace,shipbuilding,energy and other industries.Vibration,shock and noise will occur during the meshing process because of the manufacture error,installation error,tooth profile error and tooth deformation.Therefore,it is of great theoretical value and important engineering significance to establish the coupled nonlinear dynamic model of the helical gear transmission system.This paper put forward the general coupled nonlinear excitation analytical calculation model of helical gear according to the helical gear meshing stiffness and the coupling mechanism of error excitations.Based on this model,the influence of tooth profile modification,tooth profile error and axial modification on meshing stiffness and transmission error of helical gears is researched.Then taking the high speed railway traction gear transmission system as the research object,the overall finite element model of helical gear transmission system is established.Considering the effect of time-varying meshing stiffness,transmission error,time-varying impulse excitation,torsional excitation,tooth end relief drum,the inherent characteristics and vibration response of high speed railway traction gear transmission system are studied.The main contents are as follows:(1)Improved a calculation method for meshing line position and length of the helical gear,which avoid solving the complex equations and greatly improved the calculation efficiency.Based on the calculation method for meshing line position and length of the helical gear,the stiffness excitation and errors excitation coupled nonlinear analytical calculation model of helical gear is presented which considers the coupling relationship of stiffness and errors.The average meshing stiffness of helical gears is research and compared with the calculated results by the aviation industry standard.The research results shows that the nonlinear coupling model of helical gear presented in this paper is of great accuracy and reliability.Based on this model,the influence of tooth profile modification,tooth profile error and axial modification on meshing stiffness and transmission error of helical gears is researched.The research results can provide theoretical basis for helical gear modification.(2)Based on the generalized finite element method,the helical gear transmission system is divided into different type of element,the shaft element,the gear meshing unit,the bearing unit and the lumped mass element and the stiffness matrix and mass matrix of each type of element are established.The influence on the inherent characteristics of the gear transmission system is analyzed by respectively using Euler beam,Timoshenko beam and Euler beam element considering shear deformation,and the effect of the number of nodes on the inherent characteristics is studied.Taking the high speed railway traction gear transmission system as the research object,the overall finite element high-speed rail traction gear transmission system model is established which is adopted to research the inherent characteristics of the coupling of the flexural,torsional and pendulum of the high speed railway traction gear transmission system.The influence of gear meshing stiffness,bearing stiffness and other parameters on the natural frequency of the system is obtained.(3)The calculation of stiffness and error excitations of high-speed railway traction gear system according to the helical gear coupling nonlinear model presented in this paper is introduced into the dynamics mode of high speed railway traction gear transmission system.The dynamic response characteristics of high speed railway traction gear system under stable and variable speed conditions are studied.The calculation of the meshing impact excitation of helical gears is presented,the research results shows that the internal excitation of the gear is the coupling of the stiffness,the error and the impulse.The vibration response of the gear system is studied when the internal excitation and the rotational excitation are considered.Considering the tooth end relief drum,the high speed railway traction gear transmission system vibration response is researched with the same modification amount,the change of the modification length and the same modification length,the change of the modification amount and the optimum modification amount of gear pair is obtained by taking the optimal vibration acceleration as the optimization objective.(4)Experimental platform of high-speed railway traction gear transmission system is established for researching the vibration response of the system under different conditions.The time course of vibration acceleration at different measuring points are obtained,and the experimental results are compared with the theoretical results,which shows that the rationality of the dynamic model of the gear transmission system is verified. |
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