## 3 Vibration Behaviors of the Brake Shoe during Emergency Braking
### Vibration Characteristics of the Brake Shoe during Emergency Braking  
The vibration acceleration is used to evaluate vibration characteristics of brake shoe. Figure 5a-c show the obvious vibration along Z direction of the brake shoe (the direction of braking pressure) and unobvious vibrations in other directions, which is consistent \begin{table}
\begin{tabular}{c c c} \hline \hline
**Hoisting Stage** & **Equation Form** & **Fitting Coefficients** \\ \hline \multirow{3}{*}{Acceleration} & \multirow{3}{*}{(5)} & \(a_{0}=-7.438\times 10^{6}\); \(a_{1}=-9.777\times 10^{6}\); \(b_{1}=2.117\times 10^{7}\); \(a_{2}=1.205\times 10^{7}\); \(b_{2}=1.018\times 10^{7}\); \\  & & \(a_{3}=9.083\times 10^{6}\), \(b_{3}=-4.612\times 10^{6}\); \(a_{4}=-4.979\times 10^{5}\), \(b_{4}=-5.407\times 10^{6}\); \(a_{5}=-3.411\times 10^{6}\), \\  & & \(b_{5}=-9.719\times 10^{5}\); \(w=1.353\) \\ \multirow{3}{*}{Constant speed} & \multirow{3}{*}{(6)} & \(a_{1}=7.837\times 10^{6}\), \(b_{1}=0.6227\), \(c_{1}=-0.1956\); \(a_{2}=3.538\times 10^{6}\), \(b_{2}=2.766\), \(c_{2}=-2.755\); \\  & & \(a_{3}=4.36\times 10^{6}\), \(b_{3}=1.278\), \(c_{3}=1.081\); \(a_{4}=1.034\times 10^{6}\), \(b_{4}=3.489\), \(c_{4}=4.363\), \(a_{5}=3.744\times 10^{5}\), \\  & & \(b_{5}=3.853\), \(c_{5}=6.447\) \\ \multirow{3}{*}{Deceleration} & \multirow{3}{*}{(6)} & \(a_{1}=9.48\times 10^{6}\), \(b_{1}=1.279\), \(c_{1}=-0.5925\); \(a_{2}=2.327\times 10^{6}\), \(b_{2}=6.504\), \(c_{2}=3.287\); \\  & & \(a_{3}=9.069\times 10^{6}\), \(b_{3}=3.015\), \(c_{3}=2.71\); \(a_{4}=1.157\times 10^{7}\), \(b_{4}=2.62\), \(c_{4}=0.1908\); \(a_{5}=3.482\times 10^{5}\), \\  & & \(b_{5}=7.563\), \(c_{5}=4.704\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Evolution equations of dynamic torque exerted on the drum and corresponding fitting coefficients during emergency braking in cases of distinct hoisting stages. Figure 4: Evolutions of dynamic torque exerted on the drum during emergency braking. (**a**) Dynamic torque exerted on the drum in cases of different hoisting stages; (**b**) fitting curve of dynamic torque in the acceleration stage of hoisting; (**c**) fitting curve of dynamic torque in the constant speed stage of hoisting. with the evolution characteristics of the fluctuating normal pressure of the brake shoe during emergency braking (Figure 5d) obtained using the self-made friction braking test rig and which validates the dynamic model of the disc brake based on Adams. In order to quantitatively reveal the vibration characteristics of the brake shoe at different locations during emergency braking, brake disc 1 contacts brake shoes 1-6, and brake disc 2 contacts brake shoes 7-12; the inner and outer surfaces of the brake disc correspond to brake shoes \(i\)-2 and \(i\)-1, respectively (Figure 5e). Figure 6 shows that the 12 pairs of brake shoes all present obvious vibration phenomenon along the normal pressure direction between the brake disc and the brake shoe during emergency braking. The vibration accelerations of various brake shoes fluctuate in the range of \(-80\) m/s\({}^{2}\)-80 m/s\({}^{2}\), and tend to be zero at some moments due to stick-slip vibration between the brake disc and the brake shoe. The time-frequency distribution of the brake shoe can be obtained through the STFT transformation of the vibration acceleration of the brake shoe. It can be seen that the low-frequency vibration intensity is larger than the high-frequency vibration intensity in cases of various brake shoes; the maximum vibration frequency is greater than 800 Hz. Figure 7a shows the relatively large vibration intensity of the brake shoe in the vibration frequency range of 0-200 Hz, the sparse vibration distribution but high vibration intensity in the vibration frequency range of 200-400 Hz, and the relatively uniform vibration distribution but relatively low vibration intensity in the vibration frequency range of 400-800 Hz.