Tower solar thermal power is a flexible and green power source that is clean, environmentally friendly, stable, and efficient, especially for energy storage and peak shifting. It plays a significant role in the carbon peaking and carbon neutral strategy. The reflective mirrors of heliostats are the core optical components for concentrating solar energy, typically shaped into spherical mirrors or other optically curved surfaces. However, in tower solar thermal power stations, the large scale of heliostats and their varying distances from the central heat absorber require reflective mirrors with different optical focal lengths, usually ranging from 100 m to several kilometers. Manufacturing reflective mirrors with varying focal lengths using traditional thermoforming methods requires numerous molds, resulting in limited flexibility and significantly higher manufacturing costs. This approach is unsuitable for the construction needs of large-scale tower solar power plants. Therefore, it is crucial to explore high-precision, low-cost methods for molding and manufacturing optically curved mirrors for heliostats. This has been an ongoing pursuit within the industry.

In this paper, we focus on the regular pentagon heliostat widely used in engineering. We propose a novel manufacturing approach to form an optical spherical surface by directly jacking up several support bolts on the back of a flat mirror. The optical-mechanical integration analysis method is employed to investigate the influence of key geometric parameters, including the number of support bolt rings N, desired bolt spacing d, target spherical focal length f of the formed surface, and the reflective area of the heliostat, on the optical precision of the formed surface. The influence of gravity load and static wind load on the service optical accuracy of the mirror surface is also examined under the assumption of truss rigidity.

The total slope error S_t of the jacked mold reflective mirrors gradually decreases as the number of bolt rings N increases, but this improvement diminishes with further increases in N. Reducing the bolt spacing d also decreases S_t, with S_t being more sensitive to d when N is larger(Figs. 5 and 6). As the target spherical focal length f increases, the optical precision of the jacked mirror improves, making the influence of N and d on the molding error S_t less significant. For short focal length heliostats with a target focal length f within 100 m, S_t can be controlled within 0.60‒2.60 mrad. In large tower solar thermal power stations, where the target focal length can reach several kilometers, the bolt jacking method achieves very high optical accuracy, e.g., S_t can be controlled to as low as 0.12 mrad when N=5, d=1200 mm, and f=750 m, making it highly suitable for large-scale applications (Fig. 8). The total mold slope error S_t increases with the heliostat’s reflective area, but excellent optical accuracy can still be obtained by increasing the target focal length f or the number of bolt rings N (Fig. 9). When the heliostat's area is 50 m² and the target focal length f=750 m (considering only the mirror’s load-bearing deformation), the gravity load increases the total slope error from 0.15 mrad to approximately 4.00 mrad, with the effect being more significant when N is small or d is large (Figs. 10 and 11). The total slope error of the mirror increases linearly with wind load, but increasing N can reduce this linear slope and improve service optical accuracy. At d=400 mm and N=6, the total mirror slope error varies from 0.543 mrad to 2.022 mrad as the wind load increases from 0 to 250 Pa (20.2 m/s), while at N=8, the error is only 0.587 mrad even under maximum wind load (Figs. 12 and 13).

As the target spherical focal length f increases, the optical accuracy of the jacked mirror improves, with the influence of N and d on the total slope error S_t decreasing. This characteristic is particularly favorable for tower solar thermal power stations, where the focal length of the heliostat mirror can extend to several kilometers. For mirror areas ranging from 50.0 m² to 175.5 m², the total slope error S_t of the mirror with f=50 m and N=10 can be controlled within the range of 0.912‒1.380 mrad. In typical long focal length applications with f=750 m, even with N=5, S_t can be controlled within 0.110‒0.185 mrad. In terms of jacking molding accuracy, the bolt jacking method is applicable across the full span of heliostat sizes, from short to long focal lengths and from small to larger areas. The total slope error of the mirror in service increases linearly with the wind loads, and increasing N or reducing d can improve optical accuracy in service. However, a well-designed arrangement of the support bolts and a robust heliostat support structure are essential prerequisites for maintaining optical accuracy in service.