As a kind of cylindrical spring structured with a helically wound strand, the stranded wire helical springs are widely employed as reset components in engineering fields. The accurate description of the spring geometry is critical for its design, manufacture, and further theoretical and finite element method (FEM) analysis. However, the outside wires of the spring were assumed to be double-helixes in commonly used geometric model without considering the interwire contact interactions, which introduced non-negligible geometric error. To cope with this problem, a deformation-based accurate geometric model considering the interwire contact interactions is presented in this paper. By combining the geometry constraints between wires with the thin rod theory and an elastic–plastic contact model, a novel algorithm is established to determine the interwire contact behaviors and the coordinates of the nodes on the wire centerlines iteratively. The FEM simulations and the experiments are performed to verify the effectiveness of the proposed model. The results show that the accuracy of the proposed model is similar to that of FEM but much higher than that of the commonly used geometric model. The effects of the strand curvature and the outside wire pitch on the spring geometry are analyzed with the presented model as well.

作为一种由螺旋缠绕的股线构成的圆柱弹簧，多股螺旋弹簧被广泛用作工程领域的复位组件。弹簧几何形状的准确描述对于其设计，制造以及进一步的理论和有限元方法（FEM）分析至关重要。然而，在通常的几何模型中，弹簧的外线被假定为双螺旋线，而没有考虑线间的接触相互作用，从而引入了不可忽略的几何误差。为了解决这个问题，本文提出了一种考虑线间接触相互作用的基于变形的精确几何模型。通过利用细杆理论和弹塑性接触模型将线之间的几何约束结合起来，建立了一种新颖的算法来迭代确定导线间接触行为和导线中心线上节点的坐标。进行了有限元模拟和实验，以验证所提出模型的有效性。结果表明，所提模型的精度与有限元法相似，但比常用的几何模型要高得多。所提出的模型也分析了股线曲率和外部钢丝绳节距对弹簧几何形状的影响。结果表明，所提模型的精度与有限元法相似，但比常用的几何模型要高得多。所提出的模型也分析了股线曲率和外部钢丝绳节距对弹簧几何形状的影响。结果表明，所提模型的精度与有限元法相似，但比常用的几何模型要高得多。所提出的模型也分析了股线曲率和外部钢丝绳节距对弹簧几何形状的影响。