The general dynamic equations of helical compression springs with circular wire cross section, variable pitch angle, and variable helix radius are derived. The equations are formulated by Hamilton’s principle and a variational method. In contrast to previous studies, the effects of coil flexure bending, variable pitch angle and variable helix radius are taken into account. The general equations are shown to agree with dynamic equations found in literature when the general equations are reduced to simplified forms. For a specific helical spring and static loading, the equations are solved with both the predicted radial expansion and the predicted longitudinal spring compression force in excellent agreement with experimental data.

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