Generalized Synthesis Methodology of Nonlinear Springs for Prescribed Load-Displacement Functions.

Abstract

Compliant mechanisms are monolithic devices that transfer force and motion by exploiting the elasticity of their members. Nonlinear springs are a class of compliant mechanisms that have a defined nonlinear load-displacement function measured at one point on the mechanism. Various applications benefit from nonlinear springs, including medical devices, MEMS, and commercial products designed for user comfort. Since each nonlinear spring application requires a unique load-displacement function, spring configurations must be custom designed. Research in compliant mechanism synthesis has yet to address a generalized method for designing nonlinear springs. This dissertation presents a generalized nonlinear spring synthesis methodology that (i) generates a planar spring design for any prescribed nonlinear load-displacement function, (ii) synthesizes designs having distributed compliance, and (iii) employs a design parameterization conducive to geometric nonlinearities. Key features of the design parameterization include (i) a branching network of compliant beams used for topology synthesis, (ii) curved beams without sudden changes in cross-section, and (iii) boundary conditions that impose both axial and bending loads on the compliant members and enable large rotations while minimizing bending stresses. To generate nonlinear spring designs, the design parameterization is implemented into a genetic algorithm, where potential spring designs are generated and optimized. Each spring design is analyzed by nonlinear finite element analysis and then evaluated by the objective function for its nonlinear response. To improve optimization performance, the objective function is formulated to exploit scaling rules. Four spring examples each having a unique load-displacement function (J-curve, S-curve, constant-force, and linear), demonstrate the methodology’s effectiveness. Two fabricated designs validate the springs’ nonlinear responses, while demonstrating the applicability of nonlinear springs. The synthesis methodology also works for anisotropic spring designs and has been extended to design compliant mechanisms having prescribed velocity profiles at their output. Other developments include scaling rules for springs, guidelines for arranging nonlinear springs in series and parallel, and physical interpretations of springs’ responses. Results indicate that nonlinear load-displacement responses are generated by altering a spring’s axial stiffness while it deforms. This change in axial stiffness is possible by exploiting geometric nonlinearities and boundary conditions.