STIFFNESS ANALYSIS OF HELIX SPRING USING EXACT GEOMETRIC BEAM ELEMENT

Based on the exact geometric beam element model, the nonlinear stiffness characteristic of helix spring with circular cross-sections was investigated. The way to choose descriptive variables of spring model was combined with deformation characteristics of slender helix spring, and the spring radius, height, helix polar angle and torsion angle of the cross-section of spring wire were selected as the descriptive variables of helix spring. According to the Bernoulli beam theory, the cross-section coordinate system was established by the centroid curve tangent vector and torsion angle of the cross-section. Spring deformation virtual power equation was built using curvature vector of helix spring which was based on the deformation virtual power of large rotating beam. The deformation virtual power equation of spring was built by using the method of removing high-frequency vibrations in flexible body systems. As validated by numerical examples, the results conformed to the deformation law of spring stiffness. In addition, compared with the classical theory algorithm and the traditional finite element method, the results proved the validity and rationality of the analytical procedure.