Flange design for stress reduction in radially arranged sheet flexures with one rotational degree of freedom

Radially arranged sheet flexures enable a single rotational degree of freedom but experience high internal stresses even at small rotations. This paper 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 56% and 67% 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 has better stress reduction for slender flexures, while the bow-tie shape is more effective for wider configurations. The optimal flange shape is found to be independent of the materials 304SS, Alu 7075-T6, Ti-6Al-4V, ABS, and HDPE.