###### Abstract  
To improve the accuracy of a flexible support system (FSS) used for optical mirror processing, the influence of air content in the working medium and ambient temperature change on the FSS is analyzed and studied. First, the disturbance model of the FSS and single support cylinder affected by different air contents in the working medium and ambient temperature is established, and the mapping relationship between the influencing factors and the affected factors is analyzed. Then, the effects of ambient temperature change on volume, support height, and support pressure for different air contents are simulated and analyzed separately. The results of the simulation obtained show that when the working medium is mixed with different volume fractions of air and the ambient temperature changes, upper and lower chamber volumes, support rigidity, and support height of the support cylinder are also changed. Finally, an experimental study of pressure changes in the upper and lower chambers, support height, and support rigidity changes at different ambient temperatures and air contents are carried out. By measuring the support height, support pressure, and support rigidity error, the effectiveness of the established mathematical disturbance model of FSS is further verified. It not only provides a theoretical basis for improving the support accuracy of the FSS but also provides a foundation for the application of the FSS in the processing stage of large optical mirrors. optical mirror processing; flexible support system; dynamic disturbance; elastic modulus; error analysis +
Footnote †: journal: Applied Sciences  
**C10**: [PERSON]. accuracy of the optical mirror processing system, in addition to improving the motion accuracy and repeated positioning accuracy of the processing robot, the performance parameters of the support system are the main factors that determine the precision of the optical mirror surface. Traditional optical mirror support systems mostly offer base support, mechanical whiffle-tree support, and endless belt support [8]. They can meet the rigid requirements of an optical mirror support system, but due to the non-adjustability of the support stiffness, it is difficult or even impossible to unload the impact load produced by the tool in the process of machining. It may damage the surface of the optical mirror to be processed, especially for large, lightweight, and thin mirrors [9; 10]. It may crush the mirror surface, resulting in a large amount of manpower and material resources. In the research of an optical mirror flexible support system (FSS), some scholars used pneumatic support, hydraulic support, or other forms of FSS for the postural adjustment and error correction of optical mirrors and achieved good results. To improve the fabrication efficiency and testing accuracy of the meter-scale, [PERSON] et al. designed and manufactured dozens of hydraulic support units and tested them through a 4 m SiC mirror, which proved the high accuracy of the designed support system [11]. To release the thermal stress of the optical primary mirror, [PERSON] et al. proposed a novel kinematic flexure mount composed of three identical chains and analyzed the stiffness characteristics of its structure [12]. [PERSON] et al. designed a new type of three-leaf flexible structure based on the principle of spring, and optimized the size parameters of the flexible structure through the finite element analysis method [13]. In order to achieve accurate surface shape and optical axis stability of a large aperture lens in a ground-based telescope system that is subject to various load cases, [PERSON] et al. proposed a novel lens support with a multi-point flexible support structure and optimized the support structure based on low-order modes and system accuracy [14]. The above scholars have conducted a lot of research on the support system of optical mirrors.