The mathematical model for lateral stiffness of variable length conical spring

Abstract

Abstract One form of energy storage in spring is applying a bending moment and converting it into tilt at the head of the spring as strain energy. The relationship between them is the lateral stiffness of the spring. The aim is to find a mathematical equation for the lateral stiffness of the spring and the effect of the length of the spring on the behavior of stiffness. The mathematical model is created according to Castigliano’s second theorem. A simulated model of a conical spring is built using a Solid Work program. The theoretical results are compared with the mathematical model for the same conical spring. Results of both theoretical and simulated models evinced a linear behavior of lateral, while an exponential relationship between the length of the spring and the lateral stiffness is indicated. The difference between theoretical and simulated models is not exceeded 3.2%, which indicates the acceptability of results.