The Form of a Spiral Spring in a Free State

This article deals with a spiral spring made of tape material with a rectilinear cross-section. A classic example of the use of this type of spring is mechanical type clockwork and starter mechanisms of internal combustion engines with manual start. If one end of a metal ruler is pinched, and a specific force is applied to the other end, it will bend under the action of the generated moment. The magnitude of the moment depends on the applied force and the ruler’s length. Therefore, the amount of deflection will increase with the increase of these parameters, and the shape of the ruler may take the form of a spiral. After the external load influence is terminated, the ruler will take its initial shape. That is, it will become straight. However, such spiral springs do not exist in practice. In its free state, the spring also has a spiral shape for compact sizes. This article uses the theory of elastic bending of rods for large deflections to determine this form. In addition, the initial curvature of its elastic axis in the free state must be considered for the spring. Simplifying linear bending formulas cannot be used to calculate the shape of the spring. The calculation of the shape of a spiral spring in a free state based on a given final shape with an applied moment is conducted in the article. The nonlinear bending theory is applied using the corresponding differential equations.