目的 基于数值方法研究环形弹簧缓冲器的非线性大变形特性,为其缓冲或隔振设计与应用提供理论参考。方法 针对环形弹簧-质量组成的基本弹性系统,基于Euler-Bernoulli梁理论,以环形弹簧的半径及截面角为基本参数推导了弹簧的大变形控制方程及质量的运动方程,考虑环形弹簧的大变形特性,给出环形弹簧平衡方程的边界条件。考虑系统运动方程与弹簧的平衡方程的动态耦合,利用两点边值问题的数值解法研究系统的非线性平衡问题、平衡点处的微幅振动特性及冲击响应特性。结果 得到了系统的静态力-变形曲线、频率变化曲线以及冲击加速度变化曲线。环形弹簧-质量系统的力-变形曲线具有明显的分段非线性特性,两非线性阶段连续且在其节点处弹簧与支撑由点接触转变为线接触;系统基于平衡位置的小幅振动频率的突变及系统冲击加速度时程曲线的拐点进一步证明了系统的分段非线性特性;小幅振动频率存在较大的低频区,不同质量系统的冲击加速度响应具有明显的极小值。结论 基于数值方法对环形弹簧缓冲器的非线性特性分析结果与相应试验测得的试验结果吻合性较好,证明了该数值计算方法的可靠性,相关结论可为其缓冲或隔振设计与应用提供指导。
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.
关键词
环形弹簧 /
大变形 /
低频隔振 /
缓冲性能
Key words
ring spring /
large deformation /
low-frequency vibration isolation /
buffering performance
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