In order to detect the gear tooth surface wear fault, this paper presents a new fault diagnosis method based on Symlets wavelet family multi-structure element difference morphological denoising and frequency slice wavelet transform (FSWT). Besides considering the gear backlash, time-varying mesh stiffness, gear error and bearing longitudinal response, and low frequency excitation caused by the torque fluctuation, random disturbance of damping gear ratio, gear backlash, excitation frequency, and meshing stiffness are also considered. Dynamics equations of a three degrees of freedom spur gear transmission system with tooth surface wear fault are established according to Newton’s laws. The 4–5 order variable step Runge–Kutta method has been used for solving the equations to get the vibration signal of the system. Then, the proposed method is applied to extract the wear fault signal, which verifies the feasibility and effectiveness of the proposed method.

中文翻译：

---

齿轮齿面磨损失效系统建模与故障辨识

为了检测齿轮齿面磨损故障，提出了一种基于Symlets小波族多结构元差分形态去噪和频率切片小波变换(FSWT)的故障诊断新方法。除了考虑齿轮齿隙、时变啮合刚度、齿轮误差和轴承纵向响应以及转矩波动引起的低频激励外，还考虑了阻尼传动比、齿轮齿隙、激励频率和啮合刚度的随机扰动。根据牛顿定律建立了具有齿面磨损故障的三自由度直齿轮传动系统的动力学方程。4-5 阶变步长 Runge-Kutta 方法已被用于求解方程以获得系统的振动信号。然后，