Automated resolution of the spiral torsion spring inverse design problem

Many mechanical applications take advantage of spiral torsion springs due to their robustness, compactness, and simplicity. Brand-new manufacturing methods allow to create spiral springs with unconventional geometries and materials that suit a wider range of uses demanding either linearity or nonlinearity. Designing a spiral torsion spring with a nonlinear desired torque curve may be a great challenge, due to their many degrees-of-freedom (length, width, thickness, arbor, and barrel diameters, etc.) and the complexity of the geometrical and mechanical requirements to ensure their manufacturability, system compatibility, operation safety and reliability; and the solution is never unique. This manuscript proposes and validates an innovative methodology for the resolution of this inverse design problem based on the application of a nonlinear restrained global optimization algorithm. This algorithm is adjusted to converge, out of the infinity of designs that match the desired torque curve and hold all the functional and manufacturing constraints, to a design solution that minimizes strip mass. The methodology is built on a formulation for the calculation of the torque curve of a generalized spiral spring, with or without coiling and with any along-the-length cross-section, already published by the authors.