Frequency and Vibration Characteristics of High-Speed Gear-Rotor-Bearing System with Tooth Root Crack considering Compound Dynamic Backlash

Weiwei Liu,Weiqiang Zhao,Jie Liu

doi:10.1155/2019/1854263

Abstract

Considering the microstructure of tooth surface and the dynamic characteristics of the vibration responses, a compound dynamic backlash model is employed for the gear transmission system. Based on the fractal theory and dynamic center distance, respectively, the dynamic backlash is presented, and the potential energy method is applied to compute the time-varying meshing stiffness, including the healthy gear system and the crack fault gear system. Then, a 16-DOF coupled lateral-torsional gear-rotor-bearing transmission system with the crack fault is established. The fault characteristics in the time-domain waveform and frequency response and statistics data are described. The effect of crack on the time-varying meshing stiffness is analyzed. The vibration response of three backlash models is compared. The dynamic response of the system is explored with the increase in crack depth in detail. The results show that the fault features of countershaft are more obvious. Obvious fluctuations are presented in the time-domain waveform, and sidebands can be found in the frequency domain responses when the tooth root crack appears. The effect of compound dynamic backlash on the system is more obvious than fixed backlash and backlash with changing center distance. The vibration displacement along meshing direction and dynamic meshing force increases with the increase in crack depth. Backlash and variation of center distance show different tendencies with increasing crack depth under different rotational speeds. Amplitude of the sidebands increases with crack depth increasing. The amplitude of multiplication frequency of rotational frequency has an obvious variation with growing crack depth. The sidebands of the multiplication frequency of meshing frequency show more details on the system with complex backlash and crack fault.

Highlights

Considering the microstructure of tooth surface and the dynamic characteristics of the vibration responses, a compound dynamic backlash model is employed for the gear transmission system
Based on the fractal theory and dynamic center distance, respectively, the dynamic backlash is presented, and the potential energy method is applied to compute the timevarying meshing stiffness, including the healthy gear system and the crack fault gear system. en, a 16-DOF coupled lateraltorsional gear-rotor-bearing transmission system with the crack fault is established. e fault characteristics in the timedomain waveform and frequency response and statistics data are described. e effect of crack on the time-varying meshing stiffness is analyzed. e vibration response of three backlash models is compared. e dynamic response of the system is explored with the increase in crack depth in detail. e results show that the fault features of countershaft are more obvious
Obvious fluctuations are presented in the time-domain waveform, and sidebands can be found in the frequency domain responses when the tooth root crack appears. e effect of compound dynamic backlash on the system is more obvious than fixed backlash and backlash with changing center distance. e vibration displacement along meshing direction and dynamic meshing force increases with the increase in crack depth

Summary

Dynamic Model of the Gear-RotorBearing System

Time-Varying Meshing Stiffness for Gears with Tooth Crack. E meshing stiffness model of a gear pair with a tooth root crack was described by Tian in 2004. The compound dynamic backlash model is established considering rough tooth surface and vibration characteristic of the gear system. E microscopic backlash Δb(t), which represents the inherent characteristic of the rough tooth surface, can be determined as [24,25,26]. Vs represents relative sliding velocity of the meshing point M of the tooth pairs, which can be determined as. Vi and vo representing the contact point velocities between the rolling elements and inner/outer rings are given by. E dynamic backlash and time-varying meshing stiffness with crack are included in the system. E gear-rotor-bearing model with strong nonlinear and time-varying characteristics is established. e dynamic backlash and time-varying meshing stiffness with crack are included in the system. e main parameters are shown in Tables 1 and 2

Dynamic Response and Discussion

Conclusion

Findings

Conflicts of Interest