| Under the requirements of lightweight design in aerospace,automotive and other fields,gears are often designed to be with thin webs.These gear bodies are more elastic;therefore,it is of great significance to study the dynamic characteristics for the lightweight design and vibration reduction design of gear system.Therefore,this paper presents a dynamic modeling method of gear system considering the elastic deformation of gear body and rotating shaft,the advantages of the method compared with the lumped parameter method are explained,the influence of elasticity of gear body on dynamic characteristics is discussed,and is applied to the dynamic modeling of two-stage helical gear transmission of an automobile reducer.The main contents and achievements of this paper are as follows:1.A general numerical model of gear rotor is established.According to the theory of multi-body dynamics and the assumption of small displacement and small deformation,a general derivation of kinetic energy expression of the gear rotor considering the elastic deformation of gear body and shaft is proposed.Based on Timoshenko beam theory and Mindlin plate theory,the rotating shaft,gear web and rim are simplified into circular section beam,annular plate and square section curved beam,respectively.The differential quadrature finite element method is used to discretize the substructures.The general numerical models of shaft,sector plate and ring elements are established,and the dynamics model of gear rotor is constructed.The convergence and stability of each element numerical model with the number of elements and nodes are studied.The applicable range of geometric parameters of the elements are given.The correctness of the numerical model of gear rotor is verified by numerical and experimental methods.2.A gear dynamic meshing model considering the elastic deformation of the gear body is established.An analytical method for calculating the meshing stiffness of spur and helical gears is presented.A simplified form that the meshing point moves uniformly along the gear base circle in the meshing process is proposed.The angular coordinates at any time can be obtained from the angular coordinates of the meshing point on the base circle at the initial time,and then the instantaneous vibration displacement can be obtained.Finally,the relative displacement along the meshing line between the meshing points on the driving and driven gears can be obtained.Combined with the time-varying meshing stiffness,the expression of time-varying meshing potential energy in the process of gear meshing is given.The time-varying meshing potential energy and the kinetic energy and strain energy of the gear rotor are brought into the Lagrange equation,and the motion differential equation of the gear transmission system is established.3.The influence of elasticity of gear body on the dynamic characteristics of spur and helical gear transmission systems is studied.The method to determine the coupling modes of the gear system is given.Gear pair composed of four groups of gear rotors with different shaft and gear elasticities are taken as examples,the similarities and differences of modal characteristics and dynamic responses of the dynamic models established by the lumped parameter method,the lumped web method and the proposed method are compared,the advantages of this method are explained,and the structural parameter conditions of the lumped parameter method and the lumped web method reasonably applied to the dynamic modeling of spur and helical gears are given.The dynamic response and dynamic stress of the gear web are calculated and analyzed,and the effects of the thickness and helix angle of the gear web on the dynamic characteristics are studied.The modal and dynamic response characteristics of helical gear transmission are studied,and the coupling mode dominated by the transverse vibration of web is found.The transverse vibration characteristics of the helical gear web and the distribution and variation of the transverse shear stress are summarized.It is pointed out that the periodic movement of the meshing point on the web will cause the periodic change of the transverse shear stress direction of the gear web.4.This method is applied to the dynamic modeling of a two-stage helical gear system.The correctness of the shaft and component models are verified by comparing with the finite element solid model.The modal characteristics of the whole system are studied,and the first several couple frequencies and corresponding modal shapes of the transmission system are given.By comparing with the experimental results,it is found that the numerical results have the same variation trend and magnitude as the experimental results,and the causes of the result deviation are analyzed.The modeling method of cylindrical gear rotor considering the elasticity of gear body and rotating shaft proposed in this paper makes up for the deficiency that the lumped parameter method and the lumped web method cannot model the elastic deformation of gear body,presents the application conditions of the lumped parameter method,and provides an analysis method for the lightweight and vibration reduction design of thin-web gear.88 Figures,21 Tables,126 References... |
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