<p>This study analyzes the relationship between the gear crack fault in the transmission system of a double-rope winding hoist and the tension characteristics of the steel wire rope in a hoisting system. First, dynamic models of the transmission shaft, planetary gear reducer, and hoisting system are established using the finite element method and the lumped-mass approach. By setting the parameter shape function and coordinate transformation, the coupling interaction between the transmission system and the hoisting system is achieved. Then, a coupled dynamic model of the double-rope winding hoist is established. Second, by building an experimental platform and conducting excitation response experiments, the response results of the wire rope tension difference between the model and the experiment are compared to verify the accuracy of the coupling dynamic model of the hoist. Finally, a mechanical model of the crack at the gear root is established, and the time-varying meshing stiffness under the action of cracks of different lengths is simulated. Through case calculations, the influence of single-tooth crack faults and multitooth crack distributions of the reducer in the transmission system of the double-rope wound hoist on the tension characteristics of the hoisting wire rope is analyzed. Results show that the coupled dynamic model of the double-rope winding hoist can effectively demonstrate the response relationship between the dynamic characteristics of the transmission system and the tension of the steel wire rope in the hoisting system. The response value of the tension difference value of a single rope and the response value of the difference variation value of the tension difference value of a double rope under different crack fault states can effectively determine the influence degree of gear cracks. The maximum response value of the tension difference of a single rope is directly proportional to the number of cracked gear teeth, and it is more remarkable when the cracked gear teeth are dispersed. By contrast, the maximum response difference value of the tension difference value of a double rope reaches its peak when the number of cracked teeth accounts for half of the total number of teeth, and this peak is more prominent under the condition of concentrated distribution of cracked teeth.</p>