Design of Planar Nonlinear Springs for Prescribed Load-Displacement Functions

Nonlinear springs can simplify and improve the performance of a variety of devices, including prosthetics, MEMS, and vehicle suspensions. Each nonlinear spring application has unique load-displacement specifications that do not correspond to one general spring design. This limits the use of nonlinear springs and thus compromises the performance of these applications. This paper presents a generalized methodology, including topology, size, and shape optimization, for creating nonlinear springs with prescribed load-displacement functions. The methodology includes a new parametric model that represents nonlinear springs as a single-plane, ‘fractal’-like network of splines. The parametric model and the objective function are incorporated into a genetic algorithm optimization scheme. Nonlinear finite element analysis evaluates the large displacements of each spring design. Three nonlinear spring examples, each having uniquely prescribed load-displacement functions including a “J”-shaped, an “S”-shaped, and a constant-force function, generate designs that demonstrate the methodology’s effectiveness in designing nonlinear springs.