A Study On Simulation Of Spatial Structure And Mechanical Behavior Of Wire Rope

Round wire rope is a complex assembly structure formed by a large number of helical wires.When wires lie in the same direction as the strands lie in a rope the rope is in lang lay and when they lie in the opposite direction to that of the strands the rope is in ordinary lay.Wire rope can therefore be produced as various combinations of lang or ordinary,called alternate lay.Wires which arc wound around a central straight wire produce a straight strand.The outer wires in this strand are all single helices.These strands are then wound around a central straight strand these outer strands will also have a single helical form,however,the remaining wires in these outer strands each take on the form of a double helix.Research findings on mathematical geometric model has been developed in differential geometry Frenet frame method.This method is an effective way to describe the mathematical geometric model of double helix,but not intuitive enough and the expression of triple or above helix is very complex.The research contents are as follows:Firstly,the mathematical geometric model of center curves of wires which rope is deformed into three especial shapes have been establish in POE method,based on the study on the mathematical geometric model of single helix,Lie group,Lie algebra,screw theory and forward kinematics.The mathematical method of center curves of wires which rope is deformed into general curve have been made in differential geometry.Secondly,accoring to the kont theory,the quantitative analysis of ordinary lay and lang lay are given.The polynomials show that lang lay and ordinary lay are not equivalent.The sum of writhing number and twist number is conserved,which satisfies the White-Fuller formula.When wire rope deforms,there is a geometric invariant between single helix and double helix.This invariant is considered as correlation factors 9)and the influence of 9)as an integer on the performance of wire rope is discussed in this thesis.Thirdly,taking the right-hand lang lay as an example,based on the forward kinematics,the Jacobian of double helix of wire rope structure is given.In a rope lay length,when double helix's projection in - plane is closed,the condition of correlation factors is discussed.The correlation factors 9)must be an integer is proved.Fourthly,according to the mathematical geometric model of wire rope structure,the anlysis of strain of the 39 M strand under tensile loads is further implemented in a finite element program.Comparisons have been made between the finite element program results and experimental data.Good agreement is shown.