Dynamic Modelling And Dynamic Features Analysis Of Spur Gear With Crack-pitting Compound Fault

Due to the advantages of simple structure,convenient maintenance,accurate transmission,strong bearing capacity and long life,the gear has become a very common part in modern industrial equipment and products.However,production accidents caused by gear failure also occur frequently,which causes countless economic losses and even endangers people’s life and property safety.The gear structure is relatively complex,coupled with high speed,heavy load,poor lubrication and other harsh working environment,which greatly increases the probability of gear transmission system failure.Therefore,it is of important engineering practical value to research on the failure of gear system and find out the fault in time so as to avoid the occurrence of accidents.This paper focuses on the spur gear,the time-varying meshing stiffness(TVMS)calculation formula of healthy spur gear is improved by material mechanics model and finite element method,and the time-varying meshing stiffness of single fault gear and crack-pitting compound fault gear with different fault combinations are deduced.Moreover,an 8-degree-of-freedom gear-rotor model is established to further discuss the dynamic response rule of the gears with compound faults,and the mathematical statistical indexes are used to quantify,the main contents of this paper are as follows:(1)Based on the current research basis of time-varying mesh stiffness of healthy spur gears,considering the nonlinear contact force generated by gear meshing and the Hertzian contact stiffness also presents nonlinear characteristics,the original linear contact stiffness is improved.Secondly,the meshing gear tooth pairs share one gear body at the double meshing stage.Based on this,the existing problem of repeated calculation of fillet stiffness is modified,and the accuracy of the method is verified by finite element method.(2)Based on the first point,the calculation models of gear crack and gear pitting are established with 42 teeth as the limit,and the formulas of time varying meshing stiffness of spur gear with crack and gear pitting fault are deduced respectively.The effects of different degrees of cracks(10%,30%,50%,70%)and different degrees of pitting corrosion(slight: 4 pitting corrosion,moderate: 7 pitting corrosion,severe: 14 pitting corrosion)on the time-varying mesh stiffness are compared,the results calculated by the formula are in good agreement with the finite element method.(3)In order to study the crack-pitting compound fault,the calculation model of the crack-pitting compound fault is established.Based on this model,stiffness calculation formulas of 12 kinds of compound faults composed of 4kinds of cracks and 3 kinds of pitting are derived.A compound fault gear model is established in 3D software,and the error between the finite element method and the formula is about 3%,which proved the correctness of the formula and further analyzed the stiffness calculation results.(4)An idealized dynamic model of spur gear system with 8 degrees of freedom is established,and the motion differential equations of the gear rotor system are derived,and then the calculated time-varying meshing stiffness of the compound fault are substituted into the motion equation as internal excitation.MATLAB is used to solve the dynamic response in time domain and frequency domain under compound faults,the displacement and acceleration response results are analyzed in detail and different faults are distinguished and quantified by statistical indexes.