The Study On Time-varying Mesh Stiffness Calculation And Crack Identification Of Cracked Gear

Time-varying mesh stiffness(TVMS)is an important parameter of the gear system and leads to the generation of internal excitation,which is produced by the periodic and alternating meshing of the teeth.Fatigue crack,tooth profile modification,etc.will have an impact on TVMS.It is an important method to identify and diagnose the defect of the gears by calculating the TVMS of the defective gears and substituting into the gear system model,and then simulating the effect of defects on system responses.This paper mainly studies the TVMS of modified gear and cracked gear under different conditions,with the aim of providing guidance for the identification of gear crack defects and the optimization of tooth profile.Fatigue crack propagation along the radial direction of the gear will have great impact on the stiffness of the gear body.The previous TVMS algorithms have not considered or only considered a part of the gear body deformation,which will produce a large error for calculating TVMS of the radial cracked gear.This paper presents an improved potential energy method for calculating TVMS in which more gear body deformation is considered.The finite element method is used to prove that the improved algorithm has higher accuracy.The vibration model of the single-stage standard cylindrical gear system is established by using the obtained TVMS and the statistical indicators sensitive to the radial crack propagation are simulated,which is designed to provide theoretical basis for identification and diagnosis of radial crack.The results show that the kurtosis of residual signal is sentive to the crack length.At last,the gear dynamic verification experiment is carried out and the results are in good agreement with the simulation,which also proves the effectiveness of the improved stiffness algorithm.The vibration and shock at the time of gear engagement is usually considered to be an important cause of the crack.A hyperbolic tooth profile which smooths transition with the unmodified tooth profile is proposed for the first time in order to reduce the vibration and suppress the occurrence of the crack.The modified results are evaluated from the perspective of TVMS.The TVMS of the gear with the hyperbolic modified tooth profile is studied in the case of both perfect and cracked,and compared with the involute and other modification profiles.The results show that,regardless of whether the gear is perfect,the TVMS fluctuation of the gears with the hyperbolic modified profile is the minimum in the case of single and double teeth alternation.The contact stress of different tooth profile gears is calculated and compared by ANSYS software,and the hyperbolic profile is also the minimal.Therefore,the gear with the hyperbolic modified profile results the minimal vibration and shock,and has a certain inhibitory effect on the generation of fatigue crack and the resulting TVMS change,it also has good contact performance.The problem of gear TVMS with dynamic crack is studied.For gears made of tough materials such as metal or alloy,crack arrest is a common phenomenon that occurs during crack propagation,i.e.it will automatically terminate shortly after propagation tiny size.This paper defined this dynamic crack as the short time crack(STC)and study its influences on TVMS.The modeling method of STC is studied and an improved algorithm model of TVMS is proposed.The existing crack length before the short time propagation(STP)is taken into consideration.Then,the TVMS and its components(bending stiffness and shear stiffness)are studied.The results show that the change trend of TVMS caused by STC is similar to that of crack propagation model,and the stiffness variation caused by the same length STC decreases with the existing crack length increases.In the identification of gear crack defects,due to the deviation of the vibration experiment operation,the error in the data acquisition and processing process and the errors caused by various contingencies and randomness will result in a certain degree of uncertainty in the identification.The model parameters in the traditional identification method are fixed values;the fault tolerance mechanism is poor and can not deal with these uncertainties.For this,the generalized interval BP neural network(GBPNN)is applied to the crack length identification for the first time to make up for the insufficient of traditional identification methods.The crack susceptibility index such as the kurtosis and so on is obtained by simulation based on TVMS is constructed as the characteristic quantity of crack identification.The results are compared with those of BPNN and PNN,which shows that the correctness of GBPNN model is the highest.This means that the GBPNN model can well deal with the uncertainty of crack length identification.