## 1 Introduction  
In China, kilometer-deep coal reserves account for 47% of proven coal resources [1]. Mining deep coal resources with a buried depth greater than 1500 m is a major development strategy in China. The hoisting mechanism for a 1.5-km-deep coal mine exhibits characteristics of large inertia and vibration as compared to that of a 1-km-deep coal mine [2; 3; 4]. When safety hazards, such as overspeed and the loss of control of the motor (when the motor continues to provide traction torque when it should be shut down at the end of hoisting), occur in the multi-rope friction hoist of a 1.5-km-deep coal mine [2], emergency braking between the brake disc and the brake shoe, with conditions involving high speed and high specific pressure and vibration [3; 5; 6], easily causes emergency braking tribological behaviors (uneven distributions of thermal stress and friction deterioration) of the brake shoe. Therefore, the failure of emergency braking in the brake shoe greatly affects the braking safety and the reliability of the hoist, and even causes braking impact, rope skidding and overwinding accidents, which causes serious and deadly accidents, such as well destruction in the coal mine and human death. Therefore, it is of great significance to investigate the emergency braking tribological behaviors of a brake shoe under the effects of vibration in order to improve the braking safety and reliability of a 1.5-km-deep coal mine hoist.  
Several scholars have carried out studies on the friction and wear behaviors of brake shoes during emergency braking ignoring vibration. [PERSON] et al. [7] discussed the effect of a temperature rise on the coefficient of friction between the brake disc and the brake shoe. [PERSON] et al. [8] explored the effect of braking pressure on the friction and wear properties of the brake shoe. [PERSON] et al. [9] analyzed the effect of the temperature field distribution on the coefficient of friction and the wear rate of the brake shoe. [PERSON] et al. [10,11] studied the effects of braking parameters on the frictional catastrophe behaviors of the brake shoe. [PERSON] and [PERSON] [12] discussed the effect of the friction material composition on temperature and wear characteristics at the brake shoe surface. [PERSON] et al. [1] explored the effects of initial brake speed, braking specific pressure and brake shoe material on the coefficient of friction of brake shoe material during one-cycle emergency braking. According to the thermo-stress fields and vibration characteristics of a brake shoe during emergency braking ignoring vibration, [PERSON] et al. [9] investigated the temperature field distribution of the brake shoe. [PERSON] et al. [3] studied the effects of hoisting on the equivalent von Mises stress and temperature fields of a brake shoe. [PERSON] et al. [13] explored the effects of braking parameters on thermo-stress fields and flutter characteristics, respectively, without coupling them together. However, emergency braking tribological behaviors (uneven distributions of thermal stress and friction deterioration) of brake shoes under the vibration effect for 1.5-km-deep coal mine hoists have not yet been reported.  
In this study, Section 1 exhibits the performance parameters and emergency braking test method for the brake shoe. In Section 2, the vibration behaviors of the brake shoe during emergency braking are presented. Based on the results presented in Sections 1 and 2, the effect of vibration on the emergency braking tribological behaviors of brake interfaces is investigated in Section 3. In Section 4, the friction deterioration behaviors of the brake shoe during emergency braking are discussed.