Correction of a Popular Error in the Optimization Design of Helical Springs

Abstract

Abstract-In the optimized design of helical springs, wire diameter d, mean coil diameter D and number of active coils n as design variables are a prevalent mistake. This paper analyzes and demonstrates this error. When loads F 1 , F 2 and deflections λ 1 , λ 2 are known, the number of active coils n is the dependent variable of wire diameter d and mean coil diameter D in the formula of n. It is known that if some design variables are dependent variables, there must be some equality constraints between them. Almost none of monographs has constrained the number of active coils n by equality constraint as yet. Therefore, in most optimization results of helical springs the number of active coils n is wrong, where value of n is not calculated by the formula of n. The formula of shear stress in spring shows that the wire diameter d and the mean diameter D are independent variables. The wire diameter d and the mean diameter D as design variables are more reasonable in the actual optimization process of helical springs design. Reducing the three design variables to two design variables not only can meet the requirements of the design objective of helical springs but also can significantly improve the efficiency of the helical springs optimization.Index Terms-Helical springs, optimization design, number of active coils n, design variable, dependent variable.