The gear-rack systems are essential power transmission devices in rack vehicles. They mainly consist of a three-stage gear transmission system and a gear-rack mechanism. In the track subsystem, the rack is fixed on rail sleepers while a driving gear on each rack vehicle engages with it to provide traction or braking forces. However, due to uneven support stiffness and installation errors, there will inevitably be deviations from theoretical values in tooth pitch at rack joints. These deviations result in time-variation impacts on gear transmission systems through corner contact and ultimately affect the power transmission stability of rack vehicles. To investigate the influence of pitch deviation on the dynamic characteristics of the multi-stage gear transmission system, the contact position, impact velocity, and impact force of the gear-rack engagement process considering corner contact are calculated. Then, a rack vehicle-track coupled dynamic model considering the gear transmission system is presented based on classical vehicle-track coupled dynamic theory. The coupled model incorporates nonlinear time-varying meshing stiffness and rail geometrical irregularity. By using this model, the dynamic responses of gear transmissions under pitch deviation excitations at rack joints. The simulation results show that: (1) in the power transmission path, the load characteristics of the first stage of the transmission system are more sensitive to rack joint impact; (2) compared with the vibration of wheelsets, no significant impacts are observed in gearbox vibration signals in the time domain. This investigation could provide a theoretical basis for analyzing the dynamic characteristics of rack vehicle transmission systems under typical track(rack) system defect excitations while also offering a theoretical foundation for identifying typical track(rack) defects from a dynamic analysis perspective.