On the natural frequencies of helical compression springs

The linearized disturbance equations governing the resonant frequencies of a helical spring subjected to a static axial compressive load are solved numerically using the transfer matrix method for clamped ends and circular cross-section to produce frequency design charts. The effect of varying the number of turns of the spring is investigated, and in the limit of large numbers of turns, our results validate earlier work on the vibration of helical compression springs in which the helix was modeled as an elastic beam with rigidities corresponding to those of unclosed circular rings.