A Study on Cylindrical Coil Spring Deflection and Stress Done Using Analytical and Numerical Methods

SUMMARY In this study, a linear cylindrical coil spring under axial quasi-static point load is considered. Two types of coil springs with a circular cross-section, i.e. straight and inclined, are clearly distinguished and analysed. The straight cross-section implies parallelism with respect to the vertical axis of the spring. The inclined cross-section considers the perpendicularity with respect to the tangent of the spring helix curve. Several new closed-form spring deflection and stress correction factors are proposed which constitutes the main contribution of this manuscript. The obtained results are based on the basic theory of strength of materials, the theory of elasticity, and linear finite element analysis. The novel correction factors prove to be very accurate compared to the parametric numerical analyses performed and the results obtained from the literature. The accuracy of the proposed corrections is especially evident when considering very large pitch angles in combination with small spring indices, i.e. thick and steep coil springs. The direct engineering applicability of the obtained results is highlighted.