Determination of the form of a spiral spring in a free state

Abstract

The object of research. This article deals with a spiral spring made of tape material with a rectilinear cross-section.
 Investigated problem. If one end of a metal ruler is pinched, and a certain 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 length of the ruler. Therefore, the amount of deflection will increase with the increase of these parameters, and the shape of the ruler may take the spiral form. After the termination of the external load, the ruler will regain its original shape, that is, it will become straight. However, such spiral springs do not exist in practice. For compact sizes, the spring in its free state also has a spiral shape. In this regard, the purpose of the study is to find the elastic axis of a tape spiral spring in a free state, which under the action of a concentrated force takes a given shape.
 The main scientific results. The shape of the spiral spring in the free state is determined, which under the action of the applied force acquires the desired shape, which does not lead to the occurrence of frictional forces between adjacent coils.
 The area of practical use of research results. Spiral springs are widely used. One example is mechanical clock movements and measuring devices, in which the determination of indicators depends on the applied force that "unwinds" or "twists" the spring.
 Innovative technological product. The paper calculates the elastic axis of a spiral spring in a free state according to its given final shape, taking into account the moment that arises as a result of the applied force at the end of the spring. For this, the nonlinear theory of absolutely elastic bending using the methods of differential geometry of curved lines as a function of the own length of the arc of the spring axis is applied.
 The scope of application of the innovative technological product. The results obtained in the study can be used in the manufacture of spiral springs for various purposes, as well as for the accumulation of potential energy in the absence of other sources