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A new formula that allows the first natural frequency of transverse vibrations of axially loaded steel helical springs to be determined has been presented in the paper. The relationship is easy to use and allows the first natural frequency of spring vibrations to be determined without the necessity of solving analytical or numerical models. According to the Authors’ knowledge, this is the first such formula that allows the first natural transverse vibration frequency to be determined and, consequently, when this frequency becomes zero, it allows the critical axial force or deflection causing the buckling of the spring to be determined. The way of obtaining the described formula is presented in the paper. The results of this formula are compared with those obtained using FEM and experiments. The advantages, drawbacks and limitations of the proposed relationship are also discussed.

A simple formula for predicting the first natural frequency of transverse vibrations of axially loaded helical springs