Numerical Simulation Of Tooth Root Crack Propagation And Calculation Of The Time-varying Meshing Stiffness Of Gear Pair

Gear transmission system is widely used in the field of mechanical transmission because of its high transmission efficiency,compact design structure,reliable operation and smooth operation and it's one of vital part in wind turbine generator.However,the related statistics show that the shutdown time which caused by the transmission chain fault accounts for approximately twenty percent in the total outrage time of the wind turbine.Among them,gearbox failure caused by gear failure is up to sixty percent,and tooth fracture is the most important failure mode.In order to improve the reliability and service life of the gear,it is necessary to analyze the crack propagation characteristics of the gear tooth root.The study and analysis of the relationship between the crack propagation characteristics and the dynamic characteristics of the gear is of great engineering significance for the state monitoring and early diagnosis of the gear box.In this paper,the involute cylindrical gears are taken as the research object.The stress analysis of the healthy gear pair was carried out to determine the starting point of the initial crack.Under the linear elastic fracture mechanics frame,the crack propagation path of the tooth root is simulated on the basis of the finite element analysis software ABAQUS.At the same time,combining the vibration theory and the basic knowledge of the gear dynamics,the influence of the tooth root crack depth on the time-varying meshing stiffness of the gear pair is studied.By comparing and analyzing the theoretical calculation results and finite element simulation results,the effect of tooth root crack propagation on the time-varying meshing stiffness of the gear pair was studied.The specific contents of this paper are as follows:First,the parametric equation of gear tooth profile and tooth root curve is derived.the coordinates of every point on the involute and the root curve are calculated and the program code is written,so the finite element model of involute cylindrical gear is created.Using this model,the stress of a pair of healthy gear tooth root is obtained in ABAQUS.In the result,the node position of the maximum principal stress at the root of pinion is found and will be regard as the starting point of the fatigue crack.Secondly,the finite element model of gear is divided into crack block and non crack block and prefabricating initial crack at the position of the maximum principal stress node in the crackblock.Remeshing the crack block element and binding the crack block and the non-crack block element by MPC.Extracting the stress intensity factor in the results to calculate the crack propagation angle with the maximum circumferential stress criterion.After assuming the increment,the new crack is produced.By remeshing and repeated the above steps,the propagation path can be simulated and the residual life can be calculated according to the Paris formula.The influence of the initial crack length and the crack angle so as the external load on the crack propagation path and the residual life are discussed.Then,according to the energy method and the definition of gear meshing stiffness,the time-varying meshing stiffness of healthy gear pair is solved by MATLAB theory numerical method and finite element method.Comparing the calculation results,the accuracy of the finite element analysis method is verified,which provides the basis for calculating the gear pair meshing stiffness when the crack propagation path is taken into account.Finally,the influence of the tooth root crack depth on the time-varying meshing stiffness is considered,and the influence of the degree of different crack faults on the gear meshing stiffness is derived.The finite element method is used to analyze the influence of the crack propagation behavior of the tooth root on the time varying meshing stiffness of the gear pair.