Numerical Study of Deformation and Dynamic Characteristics of Ring Spring-Mass System

HUO Yinlei; FENG Yifan

doi:10.19554/j.cnki.1001-3563.2026.01.030

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Packaging Engineering ›› 2026, Vol. 47 ›› Issue (1) : 261-269. DOI: 10.19554/j.cnki.1001-3563.2026.01.030

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Numerical Study of Deformation and Dynamic Characteristics of Ring Spring-Mass System

HUO Yinlei^*, FENG Yifan

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Abstract

The work aims to investigate the nonlinear large deformation characteristics of ring spring buffers through numerical methods, providing theoretical reference for their design and application in buffering or vibration isolation. For the basic elastic system composed of ring spring and mass, based on the Euler-Bernoulli beam theory, the governing equations of large deformation of the ring spring and the motion equations of the mass were derived with the radius and cross-sectional angle of the ring spring as fundamental parameters. Considering the large deformation characteristics of the ring spring, the boundary conditions for the equilibrium equations of the ring spring were provided. Considering the dynamic coupling between the system's equation of motion and the spring's equilibrium equation, a numerical method for two-point boundary value problems was employed to study the system's nonlinear equilibrium characteristics, micro-amplitude vibration behavior around equilibrium points, and shock response performance. The static force-deformation curve, frequency variation curve, and impact acceleration change curve of the system were obtained. The force-deformation curve of the ring spring-mass system exhibited distinct piecewise nonlinear characteristics, with the two nonlinear stages being continuous and transitioning from point contact to line contact between the spring and the support at their junction. The abrupt change in the micro-amplitude vibration frequency of the system based on the equilibrium position, as well as the inflection point in the time-history curve of the system's impact acceleration, further confirmed the piecewise nonlinear behavior of the system. The micro-amplitude vibration frequency displayed a significant low-frequency region, and the impact acceleration response of systems with different masses exhibited a pronounced minimum value. The analysis results of the nonlinear characteristics of the ring spring buffer based on numerical methods show good agreement with the corresponding experimental data, confirming the reliability of this numerical method. The relevant conclusions can provide guidance for its design and application in buffering or vibration isolation.

Key words

ring spring / large deformation / low-frequency vibration isolation / buffering performance

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HUO Yinlei, FENG Yifan. Numerical Study of Deformation and Dynamic Characteristics of Ring Spring-Mass System[J]. Packaging Engineering. 2026, 47(1): 261-269 https://doi.org/10.19554/j.cnki.1001-3563.2026.01.030

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