三角股绳索建模及几何特性分析

Modeling method and analysis of geometric characteristic for the triangular strand rope

针对三角股绳索进行建模方法和几何特性研究,基于三角直股内外层中心轨迹的参数方程,以及螺旋股单位矢量矩阵,推导三角股绳索内部钢丝矢量表达式,并通过Pro/E软件构建了三角股绳索实体模型。分析三角股绳索内部螺旋钢丝的曲率和挠率等几何特性。通过对三角股与圆股绳索内部螺旋钢丝几何特性进行对比,结果表明:三角股绳索侧股螺旋钢丝曲率和挠率随着自身旋转角的变化均以360°周期变化,侧股钢丝内侧绳芯的曲率和挠率最大,外侧最小,内层钢丝曲率和挠率大于外层,这些与圆股绳索几何特征一样;三角股绳索侧股螺旋钢丝曲率和挠率大小变化剧烈、且挠率方向发生变化。

Modeling method and geometric characteristics of the triangular strand rope were investigated, and vector expression of double helical wire in the triangular strand rope was deduced based on parameter equations of central trajectories for the single helical triangular rope and unit vector matrix of the helical strand rope. 3D model of the triangular strand rope was depicted by the Pro/E wildfire software. And geometric characteristics of double helical wires were analyzed. The resuhs, by comparison of geo- metric characteristics from round and triangular strand ropes, show that curvature and torsion of the triangular and round strand ropes vary with rotation angles of 360 degree periodically, and the maximums of them occur outside rope core, the minimums oppo- site. And the internal curvature and torsion are greater than the external both for the triangular and round strand rope. But curva- ture and torsion of helical wires in the triangular rope change greatly, especially the direction changes of torsion.