在考虑齿面摩擦、时变啮合刚度、传递误差和质量偏心的情况下,利用集中质量法及牛顿定律建立了齿轮传动系统非线性振动微分方程。通过时变啮合刚度仿真了齿根裂纹故障,进而建立了具有齿根裂纹的非线性动力学故障模型。该模型在计算摩擦力时,考虑了载荷在啮合区的动态分配以及利用齿轮副的检验标准与公差值来确定齿轮副的传递误差。模型数值解的结果与故障特征的规律相符,为频谱机理的分析及故障特征的提取提供了有力的理论依据。
A non-linear dynamic model for gear transmission system is proposed, with lumped mass method and Newton's law, considering surface friction, gear mesh stiffness, transmission error and mass eccentricity. Gear tooth crack is simulated by time-varying mesh stiffness, thus the non-linear dynamic model becomes a fault model. The dynamic distribution of load in the mesh area is taken into consideration in calculating the friction force. Transmission error of the model is determined by checking standard and tolerance of pair gear. The numerical solution of the fault model matches the rule of fault character, so the presented fault model offers theoretical basis for extracting the fault characteristic frequency and the frequency spectrum.