## 4 Results and Discussion
### Bearing Characteristics of the Canopy  
Canopy is one of the key bearing components of hydraulic support, and its bearing characteristics affect the bearing characteristics of hydraulic support. Therefore, the vertical displacement and stress distribution of the canopy at the most dangerous time are selected, as shown in Figure 11. Due to the symmetrical structure of hydraulic support, the stress distribution above and below the canopy is analyzed with the symmetrical plane of the canopy as the interface. At the same time, the vertical displacement change from the front to the rear of the canopy is examined using the canopy's median line as the sampling line. The sliding instability of the upper immediate roof at the coal wall causes the mean stress of the canopy to be 200 MPa, and the stress concentration is mostly situated at the front column sockets and the rear end of the canopy, as shown in Figure 11a. This is because the support area in front of the canopy is large, resulting in greater pressure on the front column. For this reason, it is necessary to increase the strength of the column sockets and the auxiliary ribbed plate. On the other hand, the displacement of the front end of the canopy is the largest, and the subsidence is 8.7 mm. The subsidence gradually decreases along the length of the canopy, and the overall trend shows a downward trend. The variation in subsidence between the support intervals of the front and rear columns is 1.41 mm. This is because the top coal is not fractured, and the support of the front and rear columns ensures the canopy's support state, but the highly stressed zone of the top coal is positioned at the back end of the canopy. The rear end of the canopy will be subjected to local dynamic stress as a result of repetitive contact and collision between the top coal and the canopy, resulting in bending deformation. The bending deformation at the back end of the canopy is also shown in Figure 1a. To prevent bending at the rear end of the canopy from disrupting the attitude control of the canopy, it is also important to ensure that there is no interference between the back end of the canopy and the caving shield. Additionally, the support area at the back end of the canopy should also be reinforced. As shown in Figure 11b, under the rotary instability of the upper immediate roof at the coal wall, the mean stress of the canopy is 480 MPa. The stress between the front and rear columns is large and distributed regularly, and the maximum stress appears in the front column sockets. The displacement of the front end of the canopy is the largest, and the subsidence is 139 mm. Compared with other types of instability, the subsidence angle of the canopy is the largest when the upper immediate roof is unstable at the coal wall. This is because in the process of rotary instability, the top coal is subjected to a large impact dynamic load, and the lower top coal is squeezed and constrained to appear more broken, resulting in a large amount of crushed coal concentrated in the front end of the canopy. The canopy has a significant subsidence angle due to the support it receives from the front and back columns, and the column sockets are especially prone to experiencing stress concentrations due to their location. Therefore, in order to avoid the decrease of the support capacity caused by the uneven bearing of the canopy after the large crushing of the top coal, box-like structures and reinforcing ribs can be set between the column socket and the canopy to ensure that the canopy can better bear impact dynamic load, and the stress distribution of the column sockets is more uniform. As shown in Figure 11c, the mean canopy stress under rotating instability of the top immediate roof during roof cutting is 380 MPa. The majority of the stress concentration is situated at the rear end of the canopy, and the edge ribbed plate, particularly the stress at the rear end of the canopy, is near the yield stress.