Study On The Fault Excitation And Dynamic Response Characteristics Of Planetary Gear Train With Spalling Defects

High power density transmission system is the key device and system which pressing needed in our national defense,energy,transportation,aerospace and other fields.Due to the advantages of small volume,compact structure,high transmission efficiency,high carrying capacity and high transmission torque,planetary gear trains(PGT)are widely used in modern machinery such as ships,wind power system,transportation and aerospac.Since the gears in the PGT system unsualy work under the bad condition with high speed and heavy load,the frequent failure of the gears in the system has become the key factor that restricting the development of the PGT system to high reliability and long life.Among them,as the most common fault,the spalling defect will seriously affect the normal operation of the PGT system,it may lead to several reliability and safety problems,which can furthurly result in a catastrophic accident.Therefore,developing the research of the spalling fault excitation and vibration response characteristics of the PGT system has important meaning in academic theory and engineering.The complex structure and internal excitation of the PGT system distinguishes it from all other fixed axis gear transmission system,it has many unique vibration characteristics.For example,because of the multi gear pairs participate in engaging and the rotation and revolution of the carrier,the vibration responses of the PGT system are more complex than the conventional fixed axle gear trains.For the planetary gear system,the center gear is engaged with all the planet gears simultaneously,the vibration signals produced by each meshing pair are similar.However,due to the existence of the meshing phase difference,the dynamic vibration responses of some components are suppressed or neutralized under the excitation,one the other hand,the vibration responses of some components are enhanced.Otherwise,taking consideration of the defect of the gear aggravate the difficulty of the dynamic response analysis of the PGT system.Therefore,forced on the thses problems,the main research work on the fault excitation and dynamic response characteristics of a PGT system with spalling defect is carried out in this paper,the main research work is summarized as follows:(1)Based on the position of the root circle center,according to the two conditions: the center of the root circle is inside of the base circle and outside of the base circle,an improved analytic model for evaluating the time varying mesh stiffness is proposed,which accurately considered the potential energy between the root circle and the base circle.Directed against the position of the root circle center,the improved algorithm for the time varying meshing stiffness of the teeth under different parameters is studied.Otherwise,the influence of the torsional moment of the vertical direction on the meshing stiffness caused by the asymmetrical spalling defect is studied.A calculation method of the time varying meshing stiffness,which considered the torsional energy of the spalling tooth surface,is proposed,and the theoretical model for calculating the mesh stiffness of the gear teeth with asymmetrical spalling defect is obtained.(2)Based on lumped parameter method,a dynamic model of the PTG system with the spalling defect is established.With the relation of the meshing phase between different meshing pair,the position of the spalling teeth participate in engaging are deduce.Based on the model,the dynamic responses of the system with different fault excitation positions is simulated.Based on the spectrum diagram of the dynamic results,the characteristic fault frequency under different fault conditions is obtained.The influence of spalling defect size on the vibration response of the system is also analyzed.(3)Considering the time-varying effect of the vibration transmission path and the modulation effect of the spalling defect at different positions on the measured signals,a mathematical analytical model is established based on the Fourier series expansion to study the vibration characteristics of the PGT system under the healthy and spalling condition,which can provide a reasonable explanation for the appearance of some side bands.This mathematical model of signal can be used to determine the location of the additional frequency components caused by the spalling fault on the tooth surface.(4)A test rig for the tooth surface spalling defect of the planetary gear train is built,the spalling defect is seeded into the sun gear,planet gear and ring gear respectively,the test experiment of the dynamic response of the system is carried out.The correctness of the theoretical study is verified by comparing the experimental results and the simulation results.