## 1 Introduction  
In order to realize the goal of \"carbon peaking and carbon neutrality\", the construction of a new type of power system has become the main direction of China's energy structure transformation [1; 2; 3; 4]. However, the randomness, intermittency, and volatility of renewable energy generation, such as that from wind power and photovoltaic power, pose challenges when integrating large-scale renewable energy into the power system. This results in issues like insufficient power consumption and resource waste [5]. Compared with wind power and photovoltaic power generation methods, gravity energy storage technology has the advantages of large application scale, high conversion efficiency, low cost, long service life, not being affected by the environment, long energy storage time, and no self-discharge. It can realize stable and controllable conversion between gravitational potential energy and electric energy by lifting and lowering heavy loads cyclically through a hoisting system [6], which is suitable for grid peaking and realizing day and night transfer of electric energy, and is of great significance for maintaining the stability of a high proportion of renewable energy power systems [7]. A vertical shaft gravity energy storage system (Figure 1) mainly includes a weight block, a hoisting system, an energy conversion system, and a power grid connection system. The hoisting system realizes the reciprocal lifting and lowering of weights in a wide range of transport distances for energy storage and release. At the same time, the energy conversion system achieves the mutual conversion of mechanical energy and electric energy, and then the electrical energy is integrated into the power grid. The hoisting system is the core component of the gravity energy storage system, and its lifting capacity and lifting speed seriously restrict its capacity, energy conversion efficiency, and operational safety and reliability. Therefore, the design of a friction hoisting system for gravity energy storage system is crucial. In the process of energy storage, the permanent magnet motor drives the friction wheel to rotate, and the friction between the steel wire rope and the friction lining on the friction wheel drives the loaded cage and the unloaded cage to rise and fall alternately. When the loaded cage is hoisted to the wellhead for unloading, the unloaded cage is lowered to the bottom of the mine for loading. Then, the loaded cage is hoisted again by friction to the wellhead for unloading, while the original loaded cage becomes empty and is lowered to the bottom of the mine for the next loading. In the process of energy release, the loaded cage is lowered under the motor assistance and the action of gravity, and the friction between the steel wire rope and the friction lining on the friction wheel drives the friction wheel to rotate. When the loaded cage is lowered to the bottom of the mine for unloading, the unloaded cage is hoisted to the wellhead for loading. Subsequently, the loaded cage is again lowered to the bottom of the mine for unloading under the motor assistance and the action of gravity, while the original loaded cage becomes empty and raised to the wellhead for the next loading. The gravity energy storage system is still in the preliminary research stage at home and abroad. Research teams in Europe and the United States have carried out in-depth exploration in the mechanical structure innovation of the hoisting system, such as the use of advanced materials and manufacturing processes to design high-strength and lightweight  
Figure 1: Working principle of gravity energy storage system. 1—Ground; 2—derrick; 3—sheave wheel; 4—hoisting rope; 5—canister road; 6—lifting container; 7—balance rope; 8—friction wheel; 9—machine-side converter; 10—grid-side converter; 11—transformer; 12—power grid. hoisting parts to reduce energy loss.