Gear systems are the most useful and essential power transmission systems in the high-speed industry due to their accuracy. It is necessary to make sure that these systems work without defects such as tooth cracks. Therefore, detecting the location and depth of cracks in gear systems is very important. In this research, a new approach is proposed to detect the crack location, and accordingly, some statistical indicators are used to estimate the crack depth in the helical gear tooth. To this end, after explaining the helical gear mesh stiffness and tooth-root crack modeling, the helical gear pair dynamic is modeled. Then, the vibration data of a helical gear system is obtained by an experimental test rig, and the moving average method is undertaken to precisely detect the crack location. The crack depth ratio is estimated using the crest factor, impulse factor, clearance factor, and $S_r$ and $S_{\alpha }$ which are applied to the simulation results and the experimental signal. According to these results, the crest factor, impulse factor, and clearance factor calculated the crack depth ratio with a good agreement, and the indicators $S_r$ and $S_{\alpha }$ estimated it with a more significant error. Also, the average of estimated values is calculated, indicating a better result than each indicator alone.

由于其精度，齿轮系统是高速行业中最有用和必不可少的动力传输系统。有必要确保这些系统正常工作而不会出现牙齿裂纹等缺陷。因此，检测齿轮系统裂纹的位置和深度非常重要。在这项研究中，提出了一种新的裂纹位置检测方法，并相应地使用了一些统计指标来估计斜齿轮齿部的裂纹深度。为此，在解释了斜齿轮啮合刚度和齿根裂纹建模之后，对斜齿轮副动力学进行了建模。然后，通过试验台获得斜齿轮系统的振动数据，采用移动平均法精确检测裂纹位置。使用波峰因子估计裂纹深度比，${秒}_r$ 和 ${秒}_{\alpha }$应用于仿真结果和实验信号。根据这些结果，波峰因数、脉冲因数和间隙因数计算出的裂纹深度比具有良好的一致性，指标${秒}_r$ 和 ${秒}_{\alpha }$估计有更大的误差。此外，还计算了估计值的平均值，表明结果比单独的每个指标都要好。