Enhanced Formulae for Determining Both Free Length and Rate of Cylindrical Compression Springs

Cylindrical compression springs have been commonly exploited in mechanical systems for years and their behavior is considered as well identified. Nevertheless, it appears that, even though old research studies suggest correcting the rate formula, the main industrial software dedicated to spring design exploits the uncorrected one. In order to evaluate the accuracy of the analytical formulae for spring behavior, an experimental study was performed, which tried to cover the common design space. This study was done using the two common coil ends: closed and ground ends, and closed and not ground ends. Moreover, the accuracy of the load–length relation was investigated whereas older studies focused only on the spring rate. It appears that the common uncorrected formulae give satisfactory results only when large numbers of coils are involved. We also highlight, for the first time, that it is interesting to correct not only the spring rate but also the free length of the spring.