Fault response characteristics of tractor planetary gearbox based on dynamical simulation and its validation

Abstract: The planetary gear set as a new and efficient type of transmission is more and more widely used in many agricultural machinery. The working conditions and environment of agricultural machinery are complex and harsh. Hence the gear cracked, tooth broken and other failures often happen in planetary gearbox. It results that the whole equipment is not stable and cannot meet the farming requirements. More seriously, it can lead the whole equipment to downtime, and lead significant losses to agricultural production in busy seasons. Therefore, it is very important to establish the dynamic model of the planetary gear system and to study the vibration response characteristics based on the fault. And it is of great significance to study the fault mechanism and health monitoring of the planetary gear set in agricultural machinery. Most studies reported in current literature on planetary gearboxes of agricultural machinery have few results based on the vibration mechanism. And most of the dynamics models based on planetary gear system are under health conditions; in addition, they are founded on many assumptions. Even if the dynamics models of planetary gearbox are established under fault conditions, few of them are focused on the studies of fault characteristics under different fault degrees, and the time-varying effects of transmission paths are ignored in these models. Aiming at these shortcomings, this paper took the tractor planetary gearbox as the research object, and a dynamic model of planetary gear sets was established. The model considered the static transmission error, the backlash and the time-varying meshing stiffness of the meshing gear pairs. Furthermore, due to the revolution of planet gears, the transmission path between the meshing points and the sensors is time-varying periodically. The time-varying paths have a modulation effect that can't be ignored on the response signal, which is called the time-varying effects of transmission paths. Thus the time-varying effects of transmission paths at runtime were considered in the model, which was expressed with Hanning function. The Fourier series was used to express the time-varying meshing stiffness, so the problem of the stiffness mutation due to the piecewise function was avoided to some extent. Then the time-varying meshing stiffness under the planetary gear fault conditions was calculated, and the meshing stiffness expression under different gear fault degrees was deduced by introducing fault factor. When the fault factor is equal to 0, it is under heath conditions; when equal to 1, it is under serious failure conditions such as tooth broken; and when the fault factor is in between, it is under minor fault conditions such as gear cracked. The established dynamics model of planetary gearbox system was solved with Runge-Kutta method of variable step size. Using the dynamic model, the fault response characteristics under the conditions of the planetary gears cracked and broken were obtained. The characteristics are that the sidebands appear at the frequency location of (where k, m and n are integers, and fm, fp and fc are the meshing frequency, the planet gears' characteristic frequency and the rotating frequency of the planet carrier respectively) in the Fourier spectrum with the localized damage of planet gears, and the peak of spectrum under planetary gears broken is more obvious than under planetary gears cracked. Finally, the simulation signals were compared with the test vibration signals captured from a planetary gearbox fault diagnosis test rig. The test result shows that the vibration signals are modulated by the planet gears' characteristic frequency and the rotating frequency of the planet carrier under the condition of the planet gear fault. Although most of the parameters in the model were optimized, there are also some gaps with the actual situation inevitably. However the spectrum characteristics can basically reflect the actual fault state, and the simulation results and the test results are basically the same. Consequently the comparison showed that the maximum relative errors were 4.65% and 2.32%, and determination coefficients were 0.999 6 and 0.999 8, which verifies the validity of the established model. The model provides a theory basis for health monitoring and fault diagnosis of planetary gearboxes in agricultural equipment.