Optimized dimensioning of helical compression springs

Helical compression springs are known for their linear force-length relation. However, it is often observed that not ground springs admit a very different mechanical behavior than expected due to the spatial behavior of the end coils. Their behavior is neglected by the standard formula determining the global stiffness of the spring, resulting in errors. Spring makers and customers currently use the standard formulations to design springs. This practice significantly affects the complex spring making process. Operators must experimentally retrieve the desired stiffness by modifying machine inputs, leading to the simultaneous loss of both tuning time and raw materials. The proposed robust and reliable optimization algorithm considers the manufacturing uncertainties and the material variabilities and proposes a target spring design that ensures the highest probability of meeting all constraints. It integrates modern equations for the principal outputs of spring sizing, which are significantly more precise than standard equations, and tends to propose a spring with the lowest possible mass. The algorithm has been successfully confronted with industrial applications. As result, the proposed solution spring sizing is significantly more reliable and robust than the most commonly used software in the spring industry.