Mechanics and Industry 2 Cylindrical extension springs have been commonly exploited in mechanical systems for years and their behavior could be considered as well identified. Nevertheless, it appears that the influence of the loops on the global stiffness is not yet taken into account properly. Moreover, it would be of key interest to analyze how initial tension in extension springs influences the beginning of the load-length curve. The paper investigates these topics using analytical, simulation and experimental approaches in order to help engineers design extension springs with greater accuracy. As a result, the stiffness of the loops has been analytically defined. It enables to calculate the global stiffness of extension springs with more accuracy and it is now possible to determine the effective beginning of the linear load-length relation of extension springs and thus to enlarge the operating range commonly defined by standards. Moreover, until now manufacturers had to define by a try and error process the axial pitch of the body of extension springs in order to obtain the required initial tension. Our study enables for the first time to calculate quickly this key parameter saving time on the manufacturing process of extension springs. KeywordsExtension springs/spring design/springs/initial tension.

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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.