Design optimization of a flexure spring used in small-sized ultra-precise optical instrument

Small-sized ultra-precise optical devices require compact compliant ortho-planar springs (COPS) aka. flexure springs, for precise, frictionless linear motion which depends highly on the design. A self-developed arm-hinge-linked design, named "Panto-style" flexure spring was optimized by selecting 5 design parameters (thickness: t, hinge width: W, arm length 1 and 2: L₁ and L₂, arm angle: Ө) and constructing sets of design of experiments (DOEs). Signal-to-noise ratio (SNR) and response surface model (RSM) regression were obtained in terms of axial deformation. The highest response from the main effects plot was the thickness (t), followed by hinge width (W). The angle of the arm (Ө), was considered a non-relevant parameter. The parameters optimization was implemented with constraint input and output. Kinetostatic performances (axial/radial deformations, and stress) were predicted, validated, and compared (RSM, KNN, FE simulations, and experiments) using the optimized design. The average value of KNN and RSM (KNN + RSM) increased the accuracy of axial deformation value compared to RSM alone. To conclude, RSM design parameter optimization followed by KNN + RSM has successfully predicted the output results (axial/radial deformation and stress) confirmed both numerically and experimentally.