Research On Crack Propagation Path Of Spur Gear Root And Analysis Of Vibration Mechanical Characteristics Of Crack Fault Tooth

As an important working part of the transmission system,gears have the advantages of high efficiency,compact structure,and stable work.Therefore,they are widely used in aerospace,ships,precision machine tools and other equipment.When the gear teeth bear the fatigue load(meshing force)during the working meshing process,initial fatigue cracks will be induced in the high-stress area of the tooth root.After long-term operation,it will evolve into local defects such as pitting,cracks,and spalling.These faults It will cause gear failure and may cause serious accidents and economic losses.First,the gear transmission system has multiple tooth surface contacts,variable operating conditions,and many interference factors;secondly,during the crack propagation process,the gear structure parameters and the initial state of the crack will affect the crack propagation path.At different stages of crack propagation When the dynamic characteristics have not been fully explained,it is difficult to identify the fault characteristics in time.Therefore,it is urgent to study the crack propagation law and propagation path and its influencing factors,analyze the dynamic characteristics of the gear transmission system with crack failure,which has important theoretical significance and engineering value for the study of crack propagation mechanism and the extraction of vibration characteristics in the propagation stage.Based on the extended finite element method,this paper establishes a cracked gear contact finite element model,studies the influence of different initial parameters and matrix structure parameters on the crack path,constructs a time-varying contact stiffness model at different stages of crack propagation,and combines a 6-DOF gear contact dynamic model,Study the vibration mechanics characteristics of faulty teeth under different crack depth states,and combine with the improved VMD decomposition method to realize the effective extraction of fault features.The main research contents of this paper are as follows:(1)Based on the foundation of elasticity and fracture mechanics,the Westergaard stress function is constructed by the complex variable function method,and the method to overcome the complex nonlinear,discontinuous,and singularity stress field and displacement field at the crack tip is studied.Aiming at the hybrid element formed by the crack tip field,two new extended shape functions and hole structure extended shape functions are added to modify the standard extended finite element method,and the corresponding finite element model of the root crack propagation is established.(2)According to the research status of gear crack propagation law,using the modified finite element model to simulate the relationship between the location of the crack nucleation point and the corresponding positional relationship of the web outer diameter,web hole and nucleation location in the gear base structure on the tooth root crack propagation path Influence law,calculate the stress intensity factor of the crack tip and analyze the influence of different influencing factors on the stress intensity factor of the crack tip.For the special structure of web holes,a new parameter—disturbance influence coefficient is introduced,and the corresponding position relationship between different web holes and nucleation points and the change rule of the new parameters are calculated to study the influence of web holes on the deflection degree of crack propagation path.(3)Based on the premise of vibration mechanism and dynamic basic theory,the improved energy method cantilever beam model is used to study the changing law of gear pair time-varying meshing stiffness under different growth stages of tooth root cracks,and the main influencing factors of the time-varying meshing stiffness of cracked teeth are analyzed.The Runge-Kutta method is used to solve the acceleration response of the gear system at different stages of crack propagation,and the time-domain waveform changes of the fault signal as well as the frequency and amplitude characteristics changes in the spectrogram are analyzed.(4)According to the problem of the non-linear and non-stationary fault signal characteristics of the cracked faulted gear,a fault feature extraction method based on the fusion of adaptive variational modal decomposition(VMD)and singular value decomposition(KSVD)is proposed.The fusion method is used to reduce the noise of the fault collection signal,and automatically optimize and calculate the number of eigenmode components(IMF)of the fault signal,as well as the estimated penalty factor value and initial center frequency of each IMF.Then,the degree of crack failure is reflected by analyzing the characteristics of the spectral amplitude information of each IMF.