Improved analytical model for cylindrical compression springs not ground considering end behavior of end coils

In a context of increased competition, companies are looking to optimize all the components of their systems. They use compression springs with constant pitch for their linear force/length relationship. However, it appears that the classic formula determining the global load-length of the spring is not always accurate enough. It does not consider the effects of the spring's ends, which can induce non-linear behaviour at the beginning of compression and thus propagate an error over the full load-length estimated. The paper investigates the entire behaviour of a cylindrical compression spring, not ground, using analytical, simulation and experimental approaches in order to help engineers design compression springs with greater accuracy. It is built with an analytical finite element method, considering all the geometry and force components of the spring. As a result, the global load-length of compression springs can be calculated with more accuracy. Moreover, it is now possible to determine the effective tri-linear load-length relation of compression springs not ground and thus to enlarge the operating range commonly defined by standards. This study is the first that enables the behaviour to be calculated quickly, by saving time on dimensioning optimisation and on the manufacturing process of compression springs not ground.