Angle of Twist of a Double-Bent Leaf Flexure under Torsion

This paper describes the rotational displacement of the double-bent leaf flexure subjected to a torsional load. Warping and specifically double partially-restrained warping are considered when the torsion is applied. The warping restraint factor for partially-restrained warping is also considered. Castigliano's theorem is applied to derive the theoretical equations of the angle of twist. The results for the fully restrained, paid ally restrained, and free warping cases a/e compared and verified with finite element analysis (FEA). A sensitivity analysis over the length, width, and thickness is performed and the results are compared with FEA. The errors between the theory result with the warping restraint factor (K = 0.5) and those of FEA are the lowest, below 5%. This suggests that the angle of twist of the double-bent leaf flexure under torsion is accurately predicted by considering double partially-restrained warping.