Mathematic modeling of vibration transmission path with discontinuous contact interfaces for gear dynamics in the gear-shaft-bearing-housing system

A twelve-DOF model of gear-shaft-bearing-housing system is developed to study the vibration transmission path characteristics under different internal excitations considering effect of discontinuous contact interfaces. Gear meshing generates vibrations to propagate through the transmission path consisting of gear, shaft, bearing, housing and multiple contact interfaces to reach the external transducer. Effect of contact interfaces between different transmitting components, including that between gear and shaft, inner race and outer race, outer race and housing are characterized using parallel contact stiffness and damping elements. Dynamic responses of transmitting components are analyzed for three internal excitations of single frequency sinusoidal force, dynamic meshing force of both normal and spalled gear tooth. An explicit mathematic model of transmission path function is constructed, which considers effect of transmission path on both amplitude attenuation and frequency structure shift for gear with/without fault. The transmission path function is verified with model predictions, finite element simulation and experiments.