The application of the pseudospectral method to the analysis of helical springs of arbitrary shape

Abstract

The pseudospectral method is applied to the static analysis of helical springs of arbitrary shape. The displacements and the rotations are approximated by series expansions of Chebyshev polynomials. The entire domain is considered as a single element and the governing equations are collocated to yield the system of algebraic equations. The boundary conditions are considered as the constraints, and the set of equations is condensed so that the number of degrees of freedom of the problem matches the total number of the expansion coefficients. Displacements and rotations are computed for noncylindrical helical springs as well as cylindrical helical springs, and parameters that affect the convergence of the solution are discussed.