齿根疲劳裂纹扩展致传动系统振动异常特征的仿真研究

Simulation analysis on characteristics of abnormal vibration of gear system caused by tooth root fatigue crack propagation

为研究齿轮啮合过程中齿根疲劳裂纹扩展与齿轮传动系统振动特性之间的关系,建立了含齿根裂纹的齿轮对接触分析有限元模型,模拟了齿根裂纹的扩展过程。通过提取有限元分析结果中的啮合齿面节点位移和接触力信息,求得齿轮时变啮合刚度,进而得到齿轮啮合刚度随齿根疲劳裂纹扩展的退化规律;将该刚度变量代入8自由度齿轮振动系统的运动微分方程动力学模型中,进一步研究齿根裂纹扩展与传动系统振动之间的关联性。仿真结果表明:当齿轮单个轮齿含齿根裂纹时,该轮齿啮合振动时域信号异常的范围为单齿-双齿-单齿三个连续区间,其中双齿啮合区间振动冲击响应最为明显。随着齿根裂纹的扩展,该齿时域振动信号振幅显著增大;频域内的振动信号中各倍频的峰值基本不变,高频区域最先出现边频带,并且边频带向低频区域扩展,且幅值也逐渐增大。该研究结果可以为裂纹故障识别检测提供一定的理论依据。

In order to study the relationship between gear root fatigue crack propagation and the vibration characteristics of gear transmission system during gear meshing process,a finite element model of gear pair contact analysis containing gear root crack was established to simulate the propagation process of gear root crack.By extracting the joint displacement and contact force information of the meshing tooth surface from the finite element analysis results,the time-varying meshing stiffness of gear was obtained,and then degeneration rule of gear meshing stiffness with gear root crack propagation was gained.The stiffness variable was substituted into the dynamic model of motion differential equation of 8-degree-offreedom gear vibration system for further study on the relevance between gear root crack propagation and vibration in transmission system.The simulation results show that when the single tooth of the gear has a tooth root crack,the range of time domain signal anomaly of meshing vibration of the tooth is three continuous intervals of single-double-single tooth,where the vibration-impact response in the double-tooth meshing interval is most obvious.With the propagation of gear root crack,the amplitude of vibration signal in the tooth time domain significantly increases;the peak value of each frequency multiplication in the vibration signal within the frequency domain is basically unchanged,and the sideband in the high frequency region first appears.Then,it expands to the low frequency region and the sideband amplitude also gradually increases.The research results can provide a certain theoretical basis for crack fault identification and detection.