## 1 Introduction  
The mine hoisting system, whose safety and stability directly influence both productivity and personnel safety, plays a pivotal role in mine production. As depicted in Figure 1, the core components of the mine hoisting system include the rigid guide, roller cage shoe, and hoisting container. The roller cage shoe is affixed to the hoisting container and moves vertically along the rigid guide. During the operation of the mine hoisting system, some factors such as the failure of the rigid guide and disturbances from internal and external airflow can lead to adverse working conditions, and thereby intensify complex collisions between the rigid cage shoe and rigid guide, subsequently exacerbating the corresponding deformation damage. Consequently, a new roller cage shoe equipped with features that can absorb the vibration of the hoisting container should be proposed. Conventional lifting system vessels are usually equipped with four sets of roller cage shoes which play the roles of guiding and buffering, and each set consists of three pieces. They are distributed and fixed at both the left and right sides and both the upper and lower ends of the container. The traditional elastic roller cage shoe structure, as illustrated in Figure 2, comprises four main components, including the disc springs, base, rocker arm, and polyurethane roller. The roller is connected to the rocker arm via the drive shaft, which can make the rocker's arm pivot around the base and simultaneously compress the disc springs. Therefore, horizontal buffering forces will be generated when lateral impacts are imposed on the roller in the lifting process. Due to the existence of the disc springs and its friction damping, the horizontal vibration of the container can be suppressed to a certain extent. However, this type of guide device lacks the function of damping adjustment with which the horizontal vibration of the container can be greatly reduced. The present paper is devoted to designing a new roller cage shoe with a magnetorheological damper to realize a reduction in the horizontal vibration of the mine hoisting container. In recent years, some researchers have investigated reductions in transverse vibration in mine hoisting systems. [PERSON] et al. [1] studied the lateral response of a moving hoisting transporter in a cable-guided system. They developed a nonlinear dynamic model and compared it with simulation results. The analyses included vibration responses under different initial conditions, and some suggestions were provided to reduce vibration and improve the system stability. [PERSON] et al. [2] introduced a semi-active control scheme to address horizontal vibrations in mine hoisting systems by employing a fuzzy skyhook damping strategy in tandem with magnetorheological fluid dampers. In the present mine hoisting system, there is a noticeable emphasis on investigating the vibration characteristics  
Figure 1: Mine hoisting systems. (**a**) main view; (**b**) top view; (**c**) actual picture. Figure 2: Conventional roller cage shoe. and control of mine hoisting. [PERSON] et al. [3] based a constant deceleration compensation device on the original brakes, and it was verified through experiments and simulations that the device can realize constant deceleration in a very short time. However, there has been relatively limited exploration of vibration control devices. The majority of conventional roller cage shoes rely on passive vibration-damping methods, such as disc springs and hydraulics [4]. The present guide device unfortunately exhibits drawbacks such as a slow response, a limited damping capacity, and susceptibility to structural failure. Given the system's vulnerability to both internal and external disturbances, it is prone to generating substantial vibration impacts. In more severe instances, it can culminate in rope breakage and catastrophic falling accidents. In the elevator hoisting system, which is similar to the mine hoisting system, the study of transverse vibration and vibration control devices is more in-depth.