微分几何在钢丝绳空间建模的应用

Application of differential geometry to space modeling of wire rope

基于微分几何部分基础知识,详细推导出股在钢丝绳中的旋转角、股上任意一点的曲率、股上任意一点的挠率、钢丝绳中任意一点的伏雷内标架以及钢丝绳中股内钢丝周线的计算公式,所得曲率、挠率算式与文献资料完全一致,为用微分几何法解决钢丝绳问题打下基础。

Based on the basic knowledge of differential geometry,the calculation formulas of the rotation angle of the strand in wire rope,the curvature of any point on the strand,the torsion of any point on the strand,the Frenet frame at any point in the wire rope and the circumference of the wire in the strand are derived in detail.The curvature and torsion formulas obtained are in good agreement with the literature data,which lays a foundation for solving wire rope problems by differential geometry method.