An Analytical Model For The Meshing Stiffness Of Helical Gears With Modification And System Vibration Characteristics

Gear transmission has the advantages of stable transmission ratio,high transmission efficiency,compact structure,long service life,wide transmission speed and power,etc.It has been used in energy,transportation,chemical industry,metallurgy,aviation and other fields.It is the most extensive form of mechanical transmission currently used.Compared with spur gears,helical gears have better meshing performance,greater gear ratios,greater load carrying capacity,and lower vibration and noise.However,the meshing stiffness and tooth error of helical gears are three-dimensional space problems.Meshing stiffness calculation method is different from the spur gear considering;the traditional helical gear meshing stiffness calculation method cannot accurately obtain the meshed stiffness of helical gear with modification.Therefore,it is the key to solve the problem to establish a general analytical model of helical gear meshing that considers modification and the helical gear drive system dynamics model.In this paper,a modified turbo-shaft engine dry-type gearbox is taken as the research object.An analytical model for considering helical gear stiffness and error nonlinear coupled excitation and a hybrid dynamic model of the helical gear transmission system are studied.The influence of different modification types,stiffness and error coupling excitation on system vibration response are researched.The main contents are as follows:(1)Using ANSYS APDL parametric modeling,the six-tooth meshing model of helical gears was obtained.The time-varying meshing stiffness was obtained by considering the wheel body deformation or not,and compared with the ISO 6336 standard as a verification for analytical method.(2)A quick calculation method for the contact line of the helical gear is deduced.The nonlinear excitation coupled mechanism between stiffness and error is studied and an analytical model of stiffness is established.The correctness of the analytic model is verified by finite element method and methods in the existing literature.The effects of gear basic parameters,tooth profile modification curve,tip relief,lead crowning and helix angle modification on the single tooth meshing stiffness,overall meshing stiffness,transmission error,and mean squares of stiffness of the helical gear were studied.(3)According to the node finite element method and substructure theory,a hybrid dynamic model of a general helical gear transmission system including a shaft section element,a meshing element,a bearing element and housing element is established.The influence of the flexibility of the box on the inherent characteristics and vibration response of the system is analyzed.The amplitude and frequency curves of the vibration acceleration of the special nodes such as the gear node and the bearing node are studied under the condition of rated working condition and variable speed working condition.Considering the influences of different tip relief parameters,lead crowning parameters on the system vibration response characteristics,appropriate modification parameters of the system are obtained based on the amplitude-frequency response curve of vibration acceleration.(4)Taking a modified turbo-shaft engine dry-type gearbox as the research object,the modification parameters were substituted into the helical gear transmission system.The change law of the contact gear stress after the modification was analyzed from the system perspective,and the experimental platform of the helical gear transmission system was finally established.Vibration signal of the experimental gearbox was obtained,which provide a reference for the helical gear transmission system modification and vibration reduction.