Colloquia

Summary

Radially arranged sheet flexures enable a single rotational degree of freedom but experience high internal stresses even at small rotations. This study shows that modifying the flange shapes (top and bottom edges) can effectively reduce the high stresses. An analytical model using nonlinear stiffness was developed to estimate the critical axial stress, highlighting that bending moments are the primary contributors to the reduced stress at initial rotations. 

ANSYS Workbench was used to model and analyze the stress in the sheet flexures with modified flange shapes. The tapered and bow-tie flange shapes were identified as the most effective shapes for minimizing the maximum stress, with reductions of up to 54% and 65% respectively. A parameter study revealed that the optimal flange shape and corresponding stress reduction are highly dependent on input parameters such as flexure width, thickness, radius and prescribed rotation. The tapered shape performs better for slender flexures, while the bow-tie shape is more effective for wider configurations. 

Design guidelines were developed to assist in replacing the sheet flexures with the tapered or bow-tie flexures. They include a shape decision graph for selecting the optimal flexure type based on dimensionless input parameters W/L, theta, t/L and R/L. These guidelines also incorporate multiple prediction models that enable the estimation of output parameters, without the need for Finite Element Analysis. The prediction models are able to predict maximum stress of the sheet flexure, as well as optimal shape and stress reduction of the tapered and bow-tie flexures with an relative error <20% for 90% of cases compared to Finite Element Analysis.