## 5 Discussions  
### Time Histories of High-Speed Links  
Based on numerical simulation, it is found that the torque time-histories of the high-speed links are affected not much by the position of the payload on girders, but much by the magnitude of the payload, the maximum braking capacity of the brakes and the time interval when the braking capacity of the brake increases from zero to its maximum values. As shown in Figure 9, the torque peaks and maximum torque range occur when the crane is under the rated load or in no-load condition; in the third phase of the braking process, the amplitudes of the high frequency components of \(T_{\text{S3}}\) increase obviously when the crane is in no-load condition. This result, namely the maximum braking time of the lifting mechanism and the maximum braking distance of a payload are determined by the process of lowering a rated payload at full speed, is consistent with rigid dynamic analysis. Figure 8: Time histories of rope load and bending moment acting on the most unfavourable cross sections of girders in scenarios A and B. (**a**) Rope force at scenario A; (**b**) Bending moment in the most unfavourable cross section of the girder at scenario A; (**c**) Rope force at scenario B; (**d**) Bending moment in the most unfavourable cross section of the girder at scenario B. The effects of \(M_{\rm blim}\) and \(t_{\rm ba}\) on the torques of the high-speed links are shown in Figure 10. The yellow lines are about the histories of torques in the basic scenarios. For example, the larger \(M_{\rm blim}\) and the shorter \(t_{\rm ba}\), the shorter the braking time of the lifting mechanism; the larger \(M_{\rm blim}\) and the shorter \(t_{\rm ba}\), the higher peak torques and torque ranges; the larger \(M_{\rm blim}\), the larger amplitudes of the high frequency components of \(T_{\rm s3}\) in the beginning of the third phase; the shorter \(t_{\rm ba}\), the larger the amplitudes of the high frequency components of all torques in the beginning of the second phases. Besides, \(M_{\rm blim}\) and \(t_{\rm ba}\) will also influence the friction moment contributed to by each brake after completion of braking (Figure 11). Without doubt, the lower initial speed of lifting mechanism shortens the braking time, but the initial speed may not affect the peaks and ranges of torques acting on the high-speed links. As long as \(M_{\rm bs}\) has reached its maximum value when braking ends, the peak torques and the torque ranges are almost the same as those under \(n_{0}=\pm n_{\rm e}\). Otherwise, the peak and range of torques decrease as shown in Figure 12. In addition, from Figure 12a-c, when the initial lifting speed is lower and the payload is bigger, a phenomenon is observed that at first the lifting mechanism is decelerated to zero speed by the payload, then accelerated in the opposite rotating direction till the braking torque is applied, finally stopped by the mechanical brake. This phenomenon can also be seen in practice. As for the dual-brake configuration, the greatest advantage is its redundancy function, that is, the safety of payload, equipment and workers around the payload is expected to be ensured if anyone of the two brakes fails to work. However, when only one brake works during braking of a lowering rated payload at full speed, the friction work of the mechanical brake and the braking distance of the payload would be several times higher than those when both brakes work (Figure 13a,b). This implies that a higher requirement for the thermal capacity of the brake should be taken into account to implement this function of the dual-brake scheme. Figure 9: Effect of payload magnitude on time histories of torques acting on the high-speed links.