拖拉机行星齿轮箱故障响应特性动力学仿真及验证

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

针对目前农业机械设备少有从振动机理方面研究行星减速轮系的故障特性,且缺乏对不同故障程度下系统故障特性的研究等问题,该文以拖拉机传动系统中的行星齿轮减速箱为研究对象,建立了行星轮系动力学模型,考虑了其在运行时振动传递路径时变效应对振动信号的影响;推导了行星轮故障下的啮合刚度变化表达式,并引入故障因子,得到了不同故障程度下的啮合刚度;采用变步长的Runge-Kutta方法求解行星轮系动力学模型,分析得到了行星轮分别出现裂纹及断齿故障时系统响应的频谱特性。模型分析结果表明,由于振动传递路径时变效应对响应信号的调制作用,行星轮系频谱中的啮合频率及其倍频附近出现了以行星架转频为调制频率的边频带;当行星轮出现裂纹或断齿故障时,啮合频率及其倍频附近不仅出现了以行星架转频为调制频率的边频带,同时还会出现以行星轮故障频率为调制频率的边频,且断齿故障状态下的边带幅值较裂纹故障下更加明显。最后将试验信号与模型信号进行对比分析,分析发现,试验与模型响应信号对应频率的最大相对误差分别为4.65%和2.32%,决定系数R2分别为0.999 6和0.999 8,所得试验结果与模型结果基本一致,验证了所建立模型的准确性。该文可为农机设备中行星轮系的故障机理及系统健康监测研究提供参考。

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 kfm±mfp±nfc(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.