Theoretical Analysis on Large Deformation Behaviors of Zigzag- spring Based on the Nonlinear Deformation Theory

Abstract

There are various types of springs that are frequently used as mechanical parts. The main purpose of springs is to utilize their elasticity, and an analysis of the relationship between load and deformation is a basic and important issue. Generally, the spring shapes that are often used include coil springs, spiral springs, and thin leaf springs, but there are many springs with other shapes, such as clips for fastening paper, and industrially, zigzag-springs that support automobile seats. In general, spring materials show unexpectedly large deformation even with a small loading, so it is difficult to analyze the deformation behavior accurately by the conventional small-deformation theory, and a strict nonlinear analysis is required. In the analysis of such large deformation behaviors, cases when the beam is straight have already been analyzed. However, in the initial state, the zigzag-spring has a complicated shape, such as a combination of an arc member and a straight member. Deformation of zigzag-springs has been previously analyzed based on a small deformation linear theory, but large deformation has not been elucidated. For a large deformation analysis, a new modeling is required. Therefore, in this paper, when the tip of the zigzag-spring is fixed by the rotation-fixed end, the large deformation behavior when a compression or tension load is applied in the horizontal direction at the support end is analyzed non-linearly. An analytical solutions using elliptic integrals are given to the typical quantity of deformation, and an experiment is performed to confirm the adaptability of the analytical theory. Finally a comparison with the theoretical calculation is carried out.