Mechanics model and its equation of wire rope based on elastic thin rod theory

Abstract

In view of the lack of general mechanics model and theoretical formula for force-deformation calculation of wire rope, a novel modeling method for wire rope mechanics model is presented. The mathematical model of wire rope's secondary helix is established using the Frenet frame and differential geometry. On the basis of that geometrical parameters of secondary helical line is derived from the necessary assumptions and geometrical relationship, using elastic thin rod theory of Love to establish an equivalent mechanics model of wire rope, and the equivalent elastic modulus and equivalent shear modulus calculation formulas are deduced. The deformation and elongation of wire rope under known tension can be calculated by the formulas. The force-deformation calculation of actual wire rope is carried out, and the results show that the maximum deviation of elongation is less than 8% compared with the finite element simulation and experimental measurement. Therefore, the correctness and generality of the model are verified, and it has theoretical and practical significance for the application and analysis of wire rope.