中文摘要：

根据多股螺旋弹簧钢丝中心曲线和弹簧中心曲线的缠绕关系，建立了基于微分几何学的单股钢丝中心曲线的几何方程，并推导了曲线方程曲率和挠率等参数的表达式。采用MATLAB软件，以压缩弹簧和拉伸弹簧为例，对钢索拧角参数取值相同和取值不同的两种情况下曲率和挠率的变化过程和规律进行了分析。结果表明，曲率的差异影响多股螺旋弹簧的应力应变，钢索拧角取值影响多股螺旋弹簧的刚度。

英文摘要：

The geometric equations were put forward on a single--wire in the stranded wire helical springs based on the winding relationship between the center curve of the wire and of the springs, the differential equations of curvature and torsion etc. were derived as well. Taking the compression springs and extension springs as instances to analyze the changes of curvature and torsion of the single --wire both in the same and different values of twisting angle of the strand by software MATLAB. The results show that the difference of curvature effects on the stress--strain ability of the stranded wire helical springs, and the value of the twisting angle of the stranded effects on the stiffness of the stranded wire springs. The results can give more thought and basis on elastic--plastic and performance of the stranded wire helical springs.