# Multi-Objective Parameter Optimization of Flexible Support System of Optical Mirror
## 5 Conclusions  
An FSS with adjustable stiffness and unloading impact of the tool on the mirror surface to be processed is designed to improve the processing precision of optical mirrors. The movement resistance of the support cylinder is established to study the axial movement resistance of the FSS. The main factors affecting the movement resistance are the deformation resistance of the BBR and RD. To minimize the motion resistance of the support cylinder and improve its force output consistency, a multi-object parameters deformation resistance model of BBR and RD is established and its structural parameters optimized. The established model is simulated and analyzed in ANSYS. The force required to deform the BBR by 1 mm in the positive or negative \(Y\)-direction, force required to deform it by 0.5 mm in the positive \(X\)-direction, deformation caused by the application of a force of 1 N in the positive or negative \(Y\)-direction, and deformation caused by the application of a force of 10 N in the positive \(X\)-direction are calculated separately. In addition, the forces required by the RDs with different hardness values under different deformations are calculated by simulation. The simulation results are analyzed to obtain the optimal parameters for the BBR and RD that satisfy the performance requirements of the FSS.  
A pressure test of the FSS, an internal resistance measurement experiment, and a force output consistency experiment are conducted to determine the effect of the BBR and RD optimized by multi-objective parameters on the performance parameters of the FSS. The experimental results show that the actual measurement and simulation analysis of the deformation of the RD and BBR require essentially an equal force. In addition, the maximum and minimum force output of the support shaft is less than the design limit of 1 N. The optimized design of the FSS satisfies the adjustable support stiffness while effectively reducing the movement resistance and improving the force output consistency. This provides a theoretical basis for its application in the field of high-precision optical processing. The designed FSS can also be applied to the attitude adjustment of large optical mirrors, and similar engineering fields with high accuracy requirements are also the application object of this study.  
Based on the results of this paper, the cooperative work between the FSS and the optical mirror machining robot can be applied to the whole process of optical mirror machining. The response of the support system in the dynamic environment is analyzed, in order to optimize the overall performance and further improve the surface accuracy of the optical mirror.  
Conceptualization, Z.J. and G.C.; methodology, Z.J.; software, Z.J.; validation, G.C., S.X. and D.Y.; formal analysis, Y.P.; investigation, S.X.; resources, G.C.; data curation, S.X.; writing--original draft preparation, Z.J.; writing--review and editing, Z.J.; visualization, G.C.; supervision, G.C.; project administration, G.C.; funding acquisition, G.C. All authors have read and agreed to the published version of the manuscript.  
Financial support for this work, provided by the Priority Academic Program Development of Jiangsu Higher Education Institutions and the National Natural Science Foundation of China (Grant No. 91648105), are gratefully acknowledged.  
This study does not involve humans or animals.  
The simulation and experimental data used to support the findings.  
The authors declare that there are no conflict of interest regarding the publication of this paper.