Assembly-induced nonuniform deformation prediction and control method for circular flange connectors with spacers in an optical lens support structure

Widely utilized in engineering, circular flange connections are typically secured by multiple bolts, but always result in nonuniform deformations that significantly impact the system shape and position accuracies. Numerous scholars have studied the deformation characteristics under various structures, external loads, bolt preloads, and tightening sequences in classical rough mechanical systems, but there is a lack of research regarding a high-precision optical system. In optical systems, nonuniform deformation of the support structure can be transmitted to the lens, causing astigmatic aberrations and affecting imaging accuracy. In the optical lens support structure as a circular flange connector, spacers need to be introduced to adjust the gap between two parts for controlling the optical path. These spacers tend to be more flexible than the support structures, thereby significantly affecting assembly-induced nonuniform deformations. However, the influence of spacers has been overlooked in previous works and thus needs to be investigated. In this paper, the effects of spacer parameters and bolt tightening sequences on the assembly-induced nonuniform deformation are investigated by the finite element method, which is verified experimentally, and an empirical formula is proposed to predict the nonuniform assembly-induced deformation based on the FEM results. According to the prediction results, a method for controlling the assembly-induced nonuniform deformation by optimizing the bolt preload distribution is proposed. The influence rules can guide the optimization of spacers and the bolt tightening process. The prediction and control method can effectively predict and reduce the assembly-induced nonuniform deformation of the circular flange with a spacer, reducing the aberration caused by the assembly and improving the accuracy of high-precision optical systems.