多齿根裂纹对齿轮传动时变啮合刚度的影响

时变啮合刚度是影响齿轮传动振动特性的重要参数,常用于基于振动的齿轮传动裂纹诊断。为深入研究齿轮裂纹诊断问题,旨在研究齿根裂纹对齿轮传动装置时变啮合刚度的影响。首先,基于齿轮所受转矩和啮合齿轮转角变形量,推导出齿轮传动装置的时变啮合刚度理论模型。然后,以渐开线标准直齿圆柱齿轮为对象,建立含齿根裂纹齿轮传动副有限元模型,提出基于有限元方法的齿轮传动时变啮合刚度计算方法。最后,通过数值算例讨论了一个啮合周期内齿根裂纹对单对轮齿啮合和两对轮齿啮合时啮合刚度的影响。结果表明,两对轮齿啮合时,双裂纹参与啮合不仅降低啮合刚度,而且远大于单裂纹对啮合刚度的影响;与单裂纹参与啮合相比,随着双裂纹的裂纹深度增加,啮合刚度的下降率增大;增加裂纹深度时,两对轮齿啮合时啮合刚度峰值与单裂纹单对齿啮合时啮合刚度峰值的差距缩小;组合裂纹参数下两对轮齿啮合时,因为轮齿参与啮合顺序不同,裂纹深度对齿轮啮合刚度的影响明显不同。研究结论可为基于振动特性的含多裂纹的齿轮传动裂纹诊断提供理论支撑。

Impacts of Multiple Tooth Root Cracks on Time-Varying Mesh Stiffness of Gear Drive

Time-varying mesh stiffness is one of the important parameters to the dynamic perfomances of the gear drive. It is often used in the crack diagnosis of gear drive by vibration analyssis. In order to understand the crack diagnosis issues of the gear transmission set, the goal is to examine the impacts of tooth root cracks on the time-varying mesh stiffness of the gear transmission set in the present study. Firstly, based on the torque acted on the drive gear and the angular deformation of the drive gear and the driven gear, a theoretical model of time-varying mesh stiffness for the gear drive pair was derived. Subsequently, a cylindrical standard spur gear drive pair was used as the study object, and the finite element model of gear transmission system with tooth root cracks was developed. Thereafter, a calculation method of time-varying mesh stiffness of the gear drive system by finite element method was proposed. Static analysis was used to determine the time-varying mesh stiffness of the gear drive pair within one mesh period having different crack parameters. Case studies were carried out for the time-varying mesh stiffness of the gear drive system with double tooth root cracks. The effects of single crack and double cracks on the time-varying mesh stiffness of the gear drive pair were compared in the end. Results indicate that tooth root cracks decrease the time-varying mesh stiffness of gear drive. When double of toothes are meshing, the effects of double tooth root cracks on the time-varying mesh stiffness is more obvious than that of single crack on the time-varying mesh stiffness. Compared with the single crack, the increase of crack depth increase the decrease ratio of the time-varying mesh stiffness for double cracks. When double toothes are meshing, the increase of crack depth decreases the difference of the peak value of time-varying mesh stiffness of gear drive pair having double toothes root cracks and having single tooth crack. For double cracks with different crack depth, the impacts of cracks on the time-varying mesh stiffness of gear drive pair is different, because the meshing order for the different tooth is different. The conclusion could provide a theoretical support to the crack diagnosis of gear drive set having multi cracks by vibation characteristic.