Abstract: This study aims to systematically evaluate the mechanical properties of the second-order stiffness suspension spring by combining finite element simulation with experimental validation, with a focus on quantifying its nonlinear characteristics and engineering applicability. A finite element model of the spring was established, on which static strength, static stiffness, modal, stability, elastoplastic and fatigue analyses were carried out in sequence. The results show that under the working load of 7 365 N, the maximum stress of the spring reaches 1 867 MPa with a relative error of 1.22% compared with the theoretical calculation value. The first-order stiffness is 64.49 N/mm and the second-order stiffness is 116.35 N/mm, with the relative errors both less than 5% in comparison with the experimental results. The permanent deformation of the spring is 0.49 mm, accounting for 0.21% of its free height, which is in good agreement with the experimental values (0.5 mm, accounting for 0.212%). Fatigue analysis predicts that the spring can withstand more than 1 million load cycles in the full load range of 340–7 365 N, and this conclusion is verified by bench tests. The analysis method established in this study features a general prediction error of less than 5% for all performance indicators, which can provide a quantitative basis for the design and application of variable stiffness suspension springs.

Key words: second-order stiffness spring; finite element analysis; stability; permanent deformation; analysis of fatigue

摘要： 研究旨在通过有限元仿真与试验验证相结合的方法，系统评估二阶刚度悬架弹簧的力 学性能，重点量化其非线性特征及工程适用性。研究建立了弹簧的有限元模型，依次完成静 强度、静刚度、模态、稳定性、弹塑性及疲劳分析。结果表明，在 7 365 N 工作载荷下，弹 簧最大应力为 1 867 MPa，与理论计算值误差为 1.22%；一阶刚度为 64.49 N/mm，二阶刚度 为 116.35 N/mm，与试验结果误差均小于 5%；永久变形量为 0.49 mm，自由高度占比 0.21%， 与试验值（0.5 mm，占比 0.212%）吻合良好；疲劳分析预测弹簧在全量程 340－7 365 N 载荷 区间可承受超过 100 万次循环，并通过台架试验验证。研究建立的分析方法在各项性能预测 中误差普遍低于 5%，可为变刚度悬架弹簧的设计与应用提供量化依据。

关键词: 二阶刚度弹簧；有限元分析；稳定性；永久变形；疲劳分析