2025 Volume 2025 Issue 70 Pages 43-50
Various types of springs are frequently used as machine parts. The main purpose of springs is to utilize their elasticity, and analysis of the relationship between load and deformation is a fundamental and important issue in industry. Commonly used spring shapes include coil springs, spiral springs, and thin leaf springs. Apart from common shapes, there are many other springs. Flexible and elastic materials such as polymeric materials exhibit unexpectedly large deformations even under small loads. It is impossible to analyze the deformation behavior accurately by using the conventional small linear deformation theory, and a strict analysis by using nonlinear theory is required. In the meantime, it is necessary to create a model suitable to analyze a large deformation for various supporting conditions. Some analyses have been already done on a cantilever, a post-buckled beam, a three-point bending and a four-point bending of simply supported beams. In these analyzed examples, the beams were generally straight. In this paper, the large deformation behavior of C-type springs (e.g., retaining rings and piston rings) with various opening angles and curvatures in the initial state is analyzed by using nonlinear large deformation theory. Analytical solutions based on elliptic integrals are obtained for several typical deformation amounts when compressive or tensile load is applied horizontally to the tip of a spring. Furthermore, in order to confirm the applicability of the derived theoretical solutions, large deformation experiments are carried out and comparisons are made with the theoretical results.
