| One of the main causes of gear transmission failure is gear fatigue tooth crack fatigue cracking and gear tooth fracture.Studying the correlation between tooth root fatigue crack growth and gear meshing vibration characteristics helps to identify the root fatigue crack early by the analysis of gear system vibration signal.In this paper,under the framework of linear elastic fracture mechanics,the tooth root crack propagation path is simulated based on the finite element analysis software ABAQUS.Taking the gear system with tooth root crack as the research object,based on the finite element model of the gear pair with tooth root crack,the deformation law of the gear meshing stiffness with the tooth root fatigue crack propagation is established,and the relationship is substituted into eight-free dynamic differential model of the differential equation of the gear vibration system,the correlation between the root crack propagation and the vibration of the transmission system is further studied.The anomalous characteristics of the vibration signals corresponding to cracks of different lengths are analyzed,and the law between crack propagation and vibration signal changes is summarized.Part of the research content of this paper is based on national international science and technology cooperation project(scheme number S2014ZR0245).The main research work is as follows:Firstly,UG 3D modeling software is used to model a meshing standard spur gear in a parameterized way,which is imported to ABAQUS to establish the gear pair contact analysis finite element model.The maximum bending stress point of the root is determined by static analysis as the crack initiation point.In the HyperMesh software,the tooth root region of the healthy gear finite element mesh model is segmented out of the crack block and the initial crack is prefabricated.The re-divided crack-containing mesh model is introduced into ABAQUS to calculate the stress intensity factor,and the maximum circumferential positive stress theory of fracture mechanics is substituted to calculate the expansion angle.After the crack propagation amount is assumed,the crack of the expansion step is determined.The crack definition and the grid update are performed on the crack block,and the above steps are repeated to simulate the crack propagation trajectory.The stress intensity factor and the Pairs formula are combined to calculate the fatigue crack growth life.Then,the time-varying meshing stiffness of the healthy gear is calculated by the finite element method.The validity of the stiffness is calculated by the classical energy verification finite element method,and the meshing stiffness of the gear under the tooth root crack expansion with the gear meshing is calculated by the finite element method.In this paper,the contact force and displacement of the meshing flank joints of the finite element model of root length cracks with different lengths are extracted,and the gear meshing deformation variables are calculated.According to the definition of stiffness,the meshing stiffness of different length root cracks is simulated in MATLAB with the angle of rotation.The degradation law of the meshing stiffness with the root crack propagation is summarized.Finally,a dynamic model of the eight-degree-of-freedom gear system is established.The time-varying meshing stiffness of the healthy gear is substituted into the differential equation of the traditional torsional vibration,and the numerical solution is performed in MATLAB to obtain the vibration signal generated by the time-varying meshing excitation.Similarly,the time-varying meshing of the gear with different lengths of the tooth root crack is obtained.The stiffness is substituted into the equation,and the vibration characteristic signal of the gear with tooth root crack is obtained.A comparative analysis of the radial acceleration signals of the healthy gear and the root crack fault gear is performed in the time domain and the frequency domain.The variation of the vibration signal of the gear system with the gear crack propagation in the time domain and frequency domain is studied. |
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