Research On Stiffness Calculation Method And Dynamic Modeling Of Spur Gear With Compound Fault

The failure of gear transmission will directly lead to failure of the gear transmission system and then result in a bad consequence.Therefore,the mechanism and dynamic characteristics of gear failure should be studied to prevent the arising of safety accidents.However,due to the intricate structure of gear transmission system and the alternate meshing that leads to the change of TVMS between single-teeth-pair mesh and double-tooth-pair mesh,which both results in internal excitation that makes the research on its dynamic characteristics difficult.Consequently,it has momentous practical significance and value to optimize the computation method of TVMS of the gear system with composite failure and to build the dynamic modeling of the gear transmission system(normal or unnormal).At first,the TVMS calculation equation of the normal spur gear pair is derived according to the material mechanics and the universal equation of the involute and the transition curve.Then,the TVMS formula of the gear with complex crack fault is derived based on the calculation model of the meshing stiffness of perfect gear,and the effect of the different parameters of multiple cracks on the TVMS of the gear pair is studied in detail.Then,based on the calculation formulas of the TVMS of the normal gear pair,the TVMS computation model of gear pair with composite failure caused by crack and pits is established and the effect of propagation angle of two different cracks on the TVMS is discussed in detail.Finally,a simplified 8 DOF gear system dynamic model considering the time varying parameter is established,and the vibration acceleration response of the perfect gear and gear system with composite fault is obtained by applying simulation block of simulink.The cardinal substance of this paper are as follows:1)Based on the precise involute and transition curve formula,the TVMS of normal gear pair with multiple cracks is computed by application of the theory of material mechanics.The effect of different parameters of multiple cracks on the TVMS of gear system is summarized explicitly.The finite element(FE)model of normal spur gear pair and compound fault gear pair are set up respectively.The results computed by the finite element method(FEM),and then using those FEM calculation to contrast with result obtained by the analytical method(AM)so that the correctness and exactness of the AM can be proved.And the relative errors of the two methods are less than 10% and it can be accepted;2)Based on the meshing stiffness calculation model of healthy gear and the theory of material mechanics,the meshing stiffness calculation formula of compound fault gear including crack and multiple overlapped pits is derived.The relationship among the TVMS of perfect gear,cracked gear,gear with multiple pits and the compound fault gear with crack and pits is discussed in detail.Assuming that the pitting size and the depth and location of the crack remain unchanged,the influence of the different propagation angle of multiple cracks on the meshing stiffness is explained in detail.The FE model of gear pair including crack and pits at the same time is established so that we can get the FE calculation by automatic computation of computer.The FE value obtained at a few mesh points which are the alternate engagement position of single and double teeth pair are selected to compare with the stiffness result of corresponding meshing positions of healthy gears so that the rightness and exactness of the deduced formulas are tested.3)According to existed references we can set up a dynamic model of single-stage spur gear system with 8 DOF considering time-varying parameters of the single-stage gear transmission system that is treated ideally.The vibration acceleration responses of normal gear system and compound fault gear system are solved by applying Simulink toolbox.The vibration acceleration responses of perfect gear system,compound fault gear system with crack and compound fault gear system with crack pitting corrosion are obtained and then the relationship among them is discussed in detail.