High-Efficiency Dynamic Modeling of a Helical Spring Element Based on the Geometrically Exact Beam Theory

This paper presents a modeling study of the dynamics of a helical spring element with variable pitch and radius considering both the static stiffness and dynamic response by using the geometrically exact beam theory. The geometrically exact beam theory based on the Euler–Bernoulli beam hypothesis is described, of which the shear deformations are ignored. Unlike the traditional spliced curved beam element method, the helical spring element is described with curvature vector and axial strain by establishing and spline-interpolating a function of the radius, the height, the polar angle, and the torsion angle of the whole spring. In addition, a model smoothing method is developed and applied in the numerical analysis to filter the high-frequency oscillation component of the flexible multibody systems, so as to correct the system dynamic equations and improve the calculation efficiency when solving the static equilibrium of the spring. This study also carries out five numerical trials to validate the above dynamic procedure of the helical spring element. The example of the spring static stiffness design shows that the proposed helical spring procedure enables one to deal with practical engineering applications.