Advanced static and dynamic analysis method for helical springs of non-linear geometries

Current design and analysis methods of helical springs are significantly confined to a simple and linear domain. The traditional spring formula is only effective for analyzing helical springs with linear geometric properties like constant coil diameter, unchanged spring pitch and no coil contact. An advanced analytical spring model is proposed in this study to address the non-linear effects of variable coil diameter, spring pitch and coil contact that exist in helical springs of arbitrary shapes. It aims to expand the available spring design and analysis domain to a wider non-linear space. In addition, it is coupled with the modal spring model to explain and predict the dynamic vibrational response of non-linear beehive springs. It is found that the proposed model has an excellent accuracy in estimating mechanical properties of non-linear springs in both static and dynamic conditions by comparing with experimental and FE results. This model may lead to an innovative method for developing innovative tools of spring design and performance analysis that could be beneficial to a wide range of engineering applications.