Influences of Tooth Crack on Dynamic Characteristics of a Multi-Stage Gear Transmission System Considering the Flash Temperature

Abstract The crack failure is prone to happen for the gear teeth under alternating loads. The crack reduces the time-varying meshing stiffness, thus causing changes in the system vibration responses. Moreover, the tooth friction leads to the flash temperature on the tooth surface, and the flash temperature causes the deformation of the tooth profile. The flash temperature stiffness generated by this deformation is an important component of the resultant meshing stiffness, and inevitably influences the dynamic characteristics. Hence, this paper makes an effort to provide a clear understanding of the relationship between the tooth crack and nonlinear dynamics for a multistage gear transmission system considering the flash temperature in a mixed friction state. The time-varying meshing stiffness and flash temperature stiffness are separately calculated using the potential energy method and Hertz's theory, and the torsional dynamic model is established by the lumped mass method for the system with high-speed driving gear crack in the mixed friction state. The influences of the flash temperature and crack on the dynamic behaviors are studied through a bifurcation diagram, frequency spectrum, phase portrait, and Poincare map, and the frequency spectra of numerical simulation and experimental testing are compared. The results indicate that both flash temperature and tooth crack decrease the time-varying meshing stiffness, the flash temperature increases the displacement amplitude of chaotic motion, and the tooth crack enlarges the interval of chaotic motion. Meanwhile, the results provide a suitable meshing frequency, which puts the system in a stable working state. The research provides significant guidance for monitoring the crack fault of multistage gear transmission systems.