## 4 Conclusions  
In this paper, a design method for a multi-rope friction hoisting system of a vertical shaft gravity energy storage system was proposed. A complete set of calculation and selection theories about the structural parameters, the hoisting rope and the tail rope, and static and dynamic analysis of the hoisting system were proposed. In addition, the parameter calculations of the hoisting rope, balance rope, and friction wheel of the friction hoisting system under typical lifting conditions were carried out. The static and dynamic anti-slip capabilities of the friction hoisting system under the typical condition were explored. The design scheme has definite guiding significance for the design of a hoisting system for a gravity energy storage system. Figure 17: Elongation of triangle strand wire rope at different stages: (**a**) heavy-load lifting phase, (**b**) heavy-load lowering phase. Figure 18: Elongation of compacted strand wire rope at different stages: (**a**) heavy-load lifting phase, (**b**) heavy-load lowering phase. The results show that the maximum acceleration/deceleration speed of the compacted strand steel wire rope is 0.75 m/s\({}^{2}\), and the time of lifting/lowering is the shortest, which is 85.7 s. The maximum acceleration/deceleration speed of the triangular strand steel wire rope is the smallest, which is 0.61 m/s\({}^{2}\), and the time of lifting/lowering is the longest, which is 90.7 s.
2. The maximum static tension at the tangent point of the friction wheel in different rope selection schemes was all at the heavy-load end when the right side was the heavy-load end, which was 2756 kN, 2576 kN, and 2797 kN, respectively, and the ratio of static tension was 1.56, 1.62, and 1.55, respectively. The static anti-slip safety coefficient between the hoisting rope and friction lining and the specific pressure between the hoisting rope and friction lining meet the requirements of the Safety Regulations for Coal Mines. 3. The dynamic tension of the hoisting rope at the heavy-load end is positively correlated with the acceleration, and the maximum values are at the acceleration lifting stage and the deceleration lowering stage of the heavy load: 3252.8 kN, 3000 kN, and 3302.6 kN, respectively. At this time, the dynamic tension of the hoisting rope at the light-load end is the lowest: 1696.5 kN, 1551.1 kN, and 1726.6 kN, respectively. The minimum values appear at the deceleration lifting stage and the acceleration lowering stage of the heavy load: 2573.7 kN, 2400.6 kN, and 2614.2 kN, respectively. At this time, the dynamic tension of the hoisting rope at light-load end is the largest: 2132.8 kN, 1900.6 kN, and 2168.1 kN, respectively. 4. The dynamic anti-slip safety coefficient of the hoisting system in the different rope selection schemes is greater than the minimum value of 1.25 stipulated in the Safety Regulations for Metal and Non-Metal Mines. The elastic modulus of the hoisting rope has a great influence on the elongation of the wire rope. Considering that the elongation of the wire rope will cause the cages on both sides to fail to reach the designated parking position at the same time, it is recommended that hoisting ropes with large elastic moduli be used. In future study, we will continue to explore the transmission reliability of the hoisting system under different environments and operating parameters and investigate the impact of different lifting parameters (lifting height, lifting speed, and lifting capacity) on the energy storage efficiency of the gravity energy storage system. Finally, we will comprehensively consider the energy storage efficiency, lifting efficiency, and operating reliability of the gravity energy storage system, and come up with an optimal hoisting scheme. Conceptualization, Q.S. and D.W.; methodology, Q.S., D.W., X.Z., Y.G. and H.W. ; formal analysis, Q.S., D.W., X.Z., Y.G. and H.W. ; investigation, Z.X., Q.D., H.Z., B.W. and C.L. ; data curation, Z.X., Q.D. and H.Z. ; writing--original draft preparation, Q.S., D.W. and Y.G.