Abstract
Planetary gears are widely used in automobiles, helicopters, heavy machinery, etc., due to the high speed reductions in compact spaces; however, the gear fault and early damage induced by the vibration of planetary gears remains a key concern. The time-varying parameters have a vital influence on dynamic performance and reliability of the gearbox. An analytical model is proposed to investigate the effect of gear tooth crack on the gear mesh stiffness, and then the dynamical model of the planetary gears with time-varying parameters is established. The natural characteristics of the transmission system are calculated, and the dynamic responses of transmission components, as well as dynamic meshing force of each pair of gear are investigated based on varying internal excitations induced by time-varying parameters and tooth root crack. The effects of gear tooth root crack size on the planetary gear dynamics are simulated, and the mapping rules between damage degree and gear dynamics are revealed. In order to verify the theoretical model and simulation results, the planetary gear test rig was built by assembling faulty and healthy gear separately. The failure mechanism and dynamic characteristics of the planetary gears with tooth root crack are clarified by comparing the analytical results and experimental data.
Highlights
Planetary transmissions are an important form of mechanical transmission
Due to the influence of time-varying parameters, the planetary gear system always has the problem of nonlinear dynamics and excessive vibration. e planetary transmission system has a high failure rate, and the root crack is one of the most important forms of gear failure, due to complicated internal structure and large load during operation
Mathematical modeling and analysis are important methods to solve the nonlinear dynamics of planetary gear transmission systems. e control of nonlinear dynamic systems is a widely recognized challenging issue
Summary
Planetary transmissions are an important form of mechanical transmission. Because of its advantages of high transmission ratio, high bearing capacity, and compact structure, it is widely used in complex mechanical equipment such as aerospace, wind power generation equipment, and mining machinery. E dynamic model of a gear transmission system with tooth root crack was established by using the lumped parameter method, and the dynamic equation was solved to obtain the dynamic response. Zhou [11] considered the time-varying stiffness of rolling bearings, established the coupled dynamics model of MWclass wind turbine gear transmission system by using the lumped parameter method, obtained the inherent characteristics of the transmission system, and solved the dynamics of each bearing contact stress, but it does not consider the influence of the centrifugal force of the roller on the bearing stiffness. E influence of crack failure on the dynamic characteristics of the gear is explored, which provides a more detailed mathematical method for the fault diagnosis and vibration control of the planetary gear transmission system. Where G is the gyromatrix; Km is the meshing stiffness matrix; Kω is the centripetal stiffness matrix; x is the generalized displacement matrix of the system; M is the generalized mass matrix of the system; Kb is the bearing support stiffness matrix; Km is the meshing stiffness matrix; T is the external load of the system; and F is the internal excitation
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