Spiral Power Springs. Part 1—Theory

This paper is the first of a series of two dealing with spiral power springs (i.e., motor springs or clock springs). A new theoretical treatment is presented which, neglecting friction, predicts the entire torque-turn curve. A key assumption in the model is that the uncaged spring has the shape of a logarithmic spiral, and wide plate theory instead of narrow beam theory is applied to the bending process. The torque-turn curve is divided into two stages. In the first stage, the material in the unpacked inner zone is treated as a hairspring of ever increasing length with the increase in length coming from “peeling away” material from the packed region. In the second stage, it is assumed the packed region of the spring has ceased to exist and the entire length of the spring is “active” with the spring behaving as a hairspring of constant length. Theory is compared against experiment for five commercially manufactured springs. It is shown that the assumption of a logarithmic spiral for the free shape is justified and the theoretical torque-turn curves are in good agreement with those generated experimentally.