Investigation On The Vibration Characterisitics Of Spur Gears With Tooth Crack

As the most widely used type of gear transmission system,cylindrical spur gears are prone to generate crack failure during service.Previous studies have shown that crack failure has a significant impact on the vibration characteristics of spur gears.It is necessary to analyze the relationship between crack failure and dynamic behavior of a transmission system and to clarify the quantitative relationship between degree of failure and dynamic characteristics of transmission system in order to ensure the operation safety of the gear transmission system.In view of this,this paper takes cylindrical spur gear as the research object to study the vibration characteristics of transmission system with crack failure.Firstly,taking the time-varying meshing stiffness,backlash,bending and torsion effect of the rotor and the flexibility of the box support into account,and comprehensively considering the coupling relationship among the gears,the rotor,the bearing and the box,a rigid-flexible coupling non-linear dynamic model of a 12-degree-of-freedom cylindrical spur gear transmission system is established.The dynamic equation of this kind of transmission system is solved by Runge-Kutta method to obtain the steady-state response of the system.The analysis shows that the relative dynamic displacement of gear pair along the line of action has the largest amplitude at the first-order meshing frequency,while the vibration displacements of gears and bearings has the largest amplitudes at the third-order meshing frequency.The relevant results provide a mechanical basis for vibration suppression of the gear transmission system.Secondly,based on the potential energy method,the time-varying meshing stiffness of spur gear pairs with root crack and reference circle crack failure is deduced and the percentage of crack depth is proposed as an index to characterize the degree of crack failure.On the basis of this,the effects of root crack and reference circle crack failure on the time-varying meshing stiffness of gears are further compared and the differences between them are analyzed.The non-linear dynamic model of spur gear transmission system with crack failure is established by combining the meshing stiffness model with gear crack failure with the established non-linear dynamic model of gears,and the influence of crack failure on the dynamic characteristics of transmission system is investigated.The results show that the degree of failure caused by root crack is greater than that caused by reference circle crack under the same percentage of crack depth.In addition,the failure mechanism of crack failure is further analyzed.Dimensionless indexes such as kurtosis,margin factor,peak factor and pulse factor are introduced as criteria for judging the degree of failure,which provides a reference for early alarming of failure of gear system.Finally,the parallel axial gear box failure experiment with crack failure is carried out on the power transmission simulation system test bench(DDS).The experimental results show that the measured data are basically consistent with the simulation calculation,which verifies the correctness of the nonlinear dynamic model and the description method of crack failure established in this paper.This research can provide theoretical basis for on-line monitoring and failure diagnosis of gear transmission system,and has certain engineering application value.