Time Varying Meshing Stiffness Analysis Of Cracked Spiral Bevel Gears Based On Modified Finite Element Method

Spiral bevel gear is widely used in construction machinery,transportation,aerospace and other fields because of its high transmission efficiency,stable transmission and high load-bearing capacity.It is the core component of gear transmission system.Spiral bevel gear often bears significant alternating load in the process of transmission,which is easy to induce tooth crack fault and threaten operation safety and service life.It is a common fault that spiral bevel gear needs to be monitored and prevented.The generation of cracks will lead to the change of many factors in the meshing process,and the time-varying and nonlinear characteristics of time-varying meshing stiffness are the bridge between gear crack failure and gear dynamics.Accurate calculation of time-varying meshing stiffness is the premise of dynamic analysis of spiral bevel gears.In the existing methods for calculating the time-varying meshing stiffness of spiral bevel gears,the non-working face meshing leads to the unstable fluctuation of the meshing stiffness,and the crack is simplified to an equal width linear crack which is different from the actual crack.In view of the above problems,taking the cracked spiral bevel gear as the research object,the main work is as follows:1.According to the equivalent gear principle of spiral bevel gear,the parametric solid modeling is realized,and the simplified model of finite element loaded contact analysis of spiral bevel gear is established,and the accuracy of the model is verified by contact spots.The results show that the ratios of tooth width and tooth height are 85.94%and 40.75%respectively.The proportion of tooth width and tooth height of the simulated contact spot is 87.40%and 41.98%respectively,and the simulation results are close to the experimental results.2.In order to solve the problem of unstable fluctuation of time-varying meshing stiffness of spiral bevel gear in typical finite element method,a modified finite element method is proposed to calculate the comprehensive time-varying meshing stiffness of spiral bevel gear in normal state and crack state.The calculation accuracy of finite element method is improved.The results show that the average comprehensive meshing stiffness of the modified finite element method is basically consistent with that of the typical method,and the unstable fluctuation of the time-varying meshing stiffness of the modified method is obviously reduced.3.Three kinds of parabolic path crack definition methods in accordance with the working conditions of spiral bevel gears are put forward,and the variation rules of time-varying meshing stiffness under different parameters are summarized.The results show that the amplitude of the average comprehensive meshing stiffness decreases when the crack exists,the average comprehensive meshing stiffness decreases with the decrease of the crack angle,and the average comprehensive meshing stiffness decreases with the increase of crack tip depth and crack width.Among the three kinds of path cracks,q₀>h path crack is least affected by crack angle,crack tip depth and crack width parameters.Among the three parameters of crack angle,crack tip depth and crack width,the crack tip depth has the greatest influence on the average comprehensive meshing stiffness of spiral bevel gears.4.The effectiveness of the modified finite element method is verified by the experimental meshing frequency.The validity of the variation law of time-varying meshing stiffness of cracked teeth is verified by simulating the amplitude trend of meshing stiffness and the time domain characteristic amplitude of simulated and experimental vibration signals.The conclusions are as follows:the meshing frequency of the simulated meshing stiffness is the same as that of the experimental vibration signal,and the variation trend of the time domain characteristic amplitude of the simulated vibration signal is the same as that of the experimental vibration signal.The crack fault will cause the decrease of the time-varying meshing stiffness and increase the amplitude of the peak factor,pulse factor and margin factor.With the increase of the crack degree,the amplitude of the time-varying meshing stiffness increases,and the time-domain characteristic amplitude reflecting the impact of the system also increases.