Dynamic Characteristics Analysis Of Coupling Faults Of Helical Planetary Gear Pairs

In this paper,based on the slice method and adaptive Lobatto numerical integration theory,the energy method is used to establish the energy expression of the internal and external meshing helical gear contact pairs,and the effects of tooth surface spalling failure and root crack failure on the dynamic meshing stiffness of meshing gear teeth are analyzed.The phase relationship between different faults is established through the phase coupling method,and the similarities and differences of different faults in the time-frequency domain are analyzed and compared.The main contents of this study are as follows:(1)The helical gear is sliced along the axial direction by the slice method,and the slice gear is equivalent to a spur gear.The energy expression of each slice gear is established by the energy method,and the single tooth meshing stiffness of the slice gear is further obtained by integral solution.The boundary relationship between the sliced gears is established.The sliced gears are offset and superimposed,and the total time-varying meshing stiffness of the helical gear is solved.The dynamic meshing stiffness obtained by the theoretical method in this paper is compared with that through finite element simulation and experience.Comparison of the maximum,minimum and average meshing stiffness obtained by the method verifies the accuracy of the theoretical method in this paper;(2)By studying the force state of the helical planetary gear system during the meshing process,the expression of the elastic deformation of the internal and external meshing helical gear pairs in the direction of their meshing line is established.By analyzing the stress of each component of the helical planetary gear system,Establish the vibration balance equation of the system;analyze the dynamic excitation factors such as meshing stiffness,tooth surface error,meshing impact excitation and bearing support stiffness in the gear meshing system,and consider the meshing phases between the three planetary gears and the internal and external teeth.The difference is obtained by solving the steady-state vibration response,and the phase diagram and Poincaré cross-section of each component in the helical-tooth planetary gear train are obtained,and the dynamic load sharing coefficient of the normal gear system is further obtained;(3)Using the central meshing point of the flank of the helical gear as the coordinate system,the dynamic meshing angles at the beginning and end of the peeling are established,and the boundary conditions at the beginning and end of the peeling of the slicing gear are established.The dynamic meshing angle is deduced to obtain the energy expression of each part;the effects of different peeling parameters and shapes on the dynamic meshing stiffness are analyzed and compared,and then the steady-state response of the planetary system is solved using the dynamic meshing stiffness after the tooth surface peeling,and the planet under failure System fault response;The dynamic load-sharing coefficient under different spalling parameters of the tooth surface is analyzed,and the spalling width will aggravate the eccentric load of the system;(4)Using ABAQUS to solve the tooth root stress during helical gear meshing,determine the starting point of crack failure,and further obtain the crack length through the finite element crack propagation module;according to the characteristics of the root crack on the gear cross-sectional area and moment of inertia,the establishment The energy expression with tooth root crack information is compared,the effect of different crack parameters on the meshing stiffness is compared,and the dynamic load sharing coefficient of the planetary gear train under different crack parameters is analyzed.The effect of different crack parameters on the system eccentric load is more obvious;(5)The expressions of the dynamic meshing force based on the rotation angle of the sun gear,which are two kinds of faults that occur on adjacent teeth and non-adjacent teeth,are established respectively for the tooth root crack and the tooth surface spalling,and the speed of the axial torsional vibration when the sun gear fails is discussed.The similarities and differences between the domain curve and the frequency domain curve.In order to more intuitively observe the sideband caused by the impact characteristics of different faults,this paper uses the AR model based on the maximum kurtosis criterion,combined with FFT filtering to obtain only the fault information.The residual signal is analyzed in the frequency domain,and the similarities and differences between the two coupled faults in the time and frequency domain are analyzed and compared,which provides an important theoretical basis for future fault diagnosis and status monitoring.