A High-Efficiency Helical Spring Structure Model for Dynamic Analysis of Flexible Multi-body Systems.

Purpose: Dynamic response of helical spring structures is a focus of attention for dynamic analysis of flexible multi-body system (FMS) involving periodical vibration at high frequencies. In many finite element models, elemental shape functions are adopted to interpolate shapes of the structure with spiral shapes and large curvatures, which would result in a complicated modeling process and enormous degrees of freedom. In view of this, a high-efficiency helical spring structure model for dynamic analysis of FMS is proposed in this paper. Method: The paper presents a high-efficiency helical spring structure model for dynamic analysis of FMS, where helical radius, azimuth angles, height coordinates and torsion angles at one node of each coil are chosen as variables. Strains irrelevant to rigid motions of cross sections and virtual deformation power of the curved beam with geometrical nonlinearity are adopted. And a special shape function that can naturally satisfies the rule of equations of helical curves is constructed to minimize the errors of model for the helical spring. In addition, a model smoothing method is applied to modify the dynamic equation of the spring element, which can improve the computational efficiency obviously. Results: Four examples are considered to evaluate the effectiveness of the proposed spring element. Conclusion: In this paper, the helical spring is modeled as a whole, featuring clear and fewer descriptive variables, facilitating rapid calculation iteration and parametric modular design of the helical spring’s dynamic stiffness in the practical engineering. Additionally, for structures maintaining a regular shape during deformation, characteristic parameters that describe their shape rules are chosen as the descriptive variables. With the help of the specific mathematical relationships between these descriptive parameters and the structure’s shape, a shape function would be obtained that describes strongly geometrically nonlinear structures with minimal model error and fewer degrees of freedom, and this approach is universally applicable, which can be extended to various similar practical modeling applications. [ABSTRACT FROM AUTHOR]