<p>The static and dynamic modeling, analysis, and experimental verification for helical springs with geometric nonlinearity theory are conducted in this study. As a slender curved beam, a helical spring undergoes considerable deformation during service, leading to a nonlinear displacement–strain relationship. Strain evaluation plays a crucial role in the static and dynamic analyses of curved beams with geometric nonlinearity. Moreover, accurately depicting the structure of helical spring is crucial for its finite element modeling. The curvature vector of the beam is defined by comparing the definition of angular velocity. Generalized strains of the beam, including axial deformation and curvatures, are deduced from the virtual power of deformation of the beam, and constitutive equations of the beam corresponding to the curvature vector are provided. The generalized strain expression of the helical spring is derived from geometrically nonlinear beam theory. The displacement field, defined by parameters such as spiral radius, pitch, azimuth, and torsion angle, preserves the spiral deformation pattern under compression or tension. Based on the principle of virtual power, this study derives the static equilibrium and dynamic governing equations for the helical spring element with geometric nonlinearity. The proposed spring element offers the advantages of few variables and high accuracy, as confirmed through comparisons with existing ANSYS models, and its validity is confirmed through experimental verification. Finally, the proposed model is utilized to analyze the static and dynamic stiffness characteristics of helical springs.</p>

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Static and dynamic modeling, analysis, and experimental verification of a helical spring element with geometric nonlinearity theory

  • Jian Zhang,
  • Zhaohui Qi,
  • Gang Wang,
  • Xiqing Zhang,
  • Jing Wang,
  • Wenwen Xu,
  • Yong Shu

摘要

The static and dynamic modeling, analysis, and experimental verification for helical springs with geometric nonlinearity theory are conducted in this study. As a slender curved beam, a helical spring undergoes considerable deformation during service, leading to a nonlinear displacement–strain relationship. Strain evaluation plays a crucial role in the static and dynamic analyses of curved beams with geometric nonlinearity. Moreover, accurately depicting the structure of helical spring is crucial for its finite element modeling. The curvature vector of the beam is defined by comparing the definition of angular velocity. Generalized strains of the beam, including axial deformation and curvatures, are deduced from the virtual power of deformation of the beam, and constitutive equations of the beam corresponding to the curvature vector are provided. The generalized strain expression of the helical spring is derived from geometrically nonlinear beam theory. The displacement field, defined by parameters such as spiral radius, pitch, azimuth, and torsion angle, preserves the spiral deformation pattern under compression or tension. Based on the principle of virtual power, this study derives the static equilibrium and dynamic governing equations for the helical spring element with geometric nonlinearity. The proposed spring element offers the advantages of few variables and high accuracy, as confirmed through comparisons with existing ANSYS models, and its validity is confirmed through experimental verification. Finally, the proposed model is utilized to analyze the static and dynamic stiffness characteristics of helical springs.