Study on performance of bended spiral strand with interwire frictional contact

Highlights

• The interwire friction force is automatically achieved with the present model.

• The interwire frictional contact causes an improved bending stiffness of strand.

• A diameter shrinkage of outside wire happens due to the effect of Poisson's ratio.

• The resistance to bending fatigue of strand increases with its lay angle.

Abstract

The present study establishes a solution model of a spiral strand subjected to a bending load, in which the interwire frictional contact and the Poisson's ratio of the wires are considered, and the interwire friction force is automatically achieved. Based on this model, the performance of bended wire rope strand with interwire frictional contact is solved with conjugate gradient method, fast Fourier transform, finite difference method and improved Euler's predictor–corrector method. The effects of the frictional contact, bending load and lay angle on the performance of the bended strand are analyzed. The results show that the consideration of the interwire frictional contact can obtain a larger bending stiffness of the strand compared with a pure bending model. The serious diameter shrinkage of the outside wire due to the effect of Poisson's ratio, the maximum pressure and deformation due to the core-wire contact occur at the furthest part from the curvature center of the bended strand, where the tensile failure and contact fatigue are most likely to happen. Meanwhile, interwire slippage and bending fatigue are liable to happen at the neutral layer. The strand with a large lay angle has a better resistance to bending fatigue but worse tribological properties, compared with a small lay angle strand.

Introduction

A wire rope is often subjected to a bending load once twisted around a drum or sheave, which inevitably leads to contact, friction and slippage between the wires. Owing to the fact that the prolonged interwire friction may cause severe wear and even fracture of wires, an in-depth study on the rope's tribological performance, such as the friction and contact behavior of wires, is necessary for the failure prediction and innovation design of the rope.

Based on the finite element theory, the research by Nawrocki and Labrosse [1] shows that the axial and bending loads mainly cause interwire pivoting and interwire sliding of a spiral strand, respectively. Moreover, at an axial load, the friction between wires has little effect on the performance of the rope. Under a bending load condition, however, the interwire friction cannot be ignored in the rope [2]. Many experimental and theoretical studies on the wire rope subjected to a bending load have been conducted in the past years. Typically, Ridge et al. [3] made a detailed description of the measuring method of the strain of a six strand right-handed Lang's lay wire rope at a cyclic bending load, and gave the variation law of the bending stress. Raoof and Huang [4] studied the free bending characteristics of an axially preloaded spiral strand, and found that the bending stiffness of the strand is affected by the curvature of the strand's axis. Further, the relative movements between the strands and that between the wires in a wire rope bent over a sheave were calculated by Nabijou and Hobbs [5], which provides a reference for the wear analysis of wire ropes. Vennemann et al. [6] made a bending fatigue test on a large diameter steel wire rope, and reported the thermal effect caused by the bending load. A comparison between different analytical formulas estimating the state of stress in the wires of a rope subjected to axial and bending loads was made by Giglio and Manes [7], who found that the bending stiffness and stress of a wire decrease with increasing spiral degree of the wire. Under different end conditions, Chen et al. [8] made comparative tests on three different kinds of wire cables, which are in similar helical structures with wire ropes. Their tests show that the wire bending stiffness is enhanced by increasing the pretension and decreasing the diameter of the cable. In the analytical analysis of the hysteretic bending behavior of a spiral strand, Foti and Martinelli [9] studied the onset of inter-layer slipping in a bended strand by defining the limit domain for the wire sliding. Kim et al. [10] conducted a bending fatigue test of a wire rope, and investigated the effects of the rope diameter and its tensile stress on the fracture strength and fatigue life of the rope, and their work shows that the bending fatigue is a crucial factor shortening the rope's lifetime. In the experimental study on the bending fatigue life of a wire rope, Onur and Imrak [11] measured the heat generated in the loaded ropes, and pointed out that the 6 × 36 WS rope has a longer lifetime compared with the rotation-resistant rope.

Nevertheless, the above-mentioned researchers have not made detailed analyses on the interwire tribological property of the wire rope. Considering the friction between wires and adopting some bending symmetric boundary conditions, Jiang [12] established a concise finite element model of a simple wire strand under a pure bending load, and analyzed the deformation and stress caused by the bending load. Usabiaga and Pagalday [13] also included the interwire friction in their analysis of a multi-strand wire rope. However, their study was conducted based on the assumption that no relative interwire slippage happens and the interwire friction is infinite, which is not applicable to lubricated ropes. Using a hierarchical approach, Inagaki et al. [14] developed a model for the mechanical analyses of cables, with which the multi-order helical structure and frictional effect can be studied. However, they neglected the change in helical radius due to wire deformation, which does not agree with the real situation. In the review on modeling wire ropes, Spak et al. [15] pointed out that the friction force between wires influences the energy dissipation in a rope and should be included in modeling the rope to achieve an accurate solution model of the rope. Ramsey [16] treated the wire in a multilayer rope as a helical rod, and derived the interwire friction of the rope under uniform tensile and twisting loads. The interwire friction force in the bending case, however, was not given. Besides the above studies, finite element analyses on the wire rope with friction were also conducted in literature [17], [18], [19], in which the rope performance considering the interwire friction agrees better with the experimental data, compared with that based on frictionless assumption.

In the wire rope performance analyses considering the interwire friction, however, constant sliding friction coefficient is often employed, which means that the interwire slippage happens at all frictional contact regions between the wires. In fact, on account of the helical structure of the wire rope, not all the frictional contact between wires will bring out an interwire sliding. A static friction may also happen if the tangential friction force is sufficiently small relative to the normal contact force at the interwire contact interface. Therefore, the adoption of a constant sliding friction coefficient is not capable enough to evaluate the interwire tribological behavior of the wire rope precisely. Without setting a constant sliding friction coefficient, LeClair and Costello [20] calculated the distributions of the cross-sectional forces, moments and the line loads along the outside wire centerline of a spiral strand. In their study, the interwire friction was treated as an internal action in the strand and was governed by the equilibrium of the outside wire. Thus both the sliding friction force and the static one in the strand can be obtained simultaneously. However, LeClair and Costello did not consider the interwire contact deformation and the effect of Poisson's ratio that actually exits once the strand is loaded. Since the two influencing factors can lead to changes in the structural parameters of the rope (e.g. the helical radius and lay angle) and further affect the rope performance, they should therefore be considered in the rope's analysis.

With regard to a wire rope winded around a sheave (or a drum), the bending load causing interwire friction and wear is the dominant external action for the rope. Considering the comprehensive effect of the interwire frictional contact deformation and the effect of Poisson's ratio of the wires, the present study establishes a coupling model of a spiral strand subjected to a bending load, in which the interwire friction force is modeled by the use of the equilibrium of the outside wire without the adoption of a constant sliding friction coefficient. Then the model is iteratively solved with the finite difference method and an improved Euler's predictor–corrector method, during which the pressure and deformation due to the frictional contact are simultaneously calculated with the adoption of conjugate gradient method (CGM) and fast Fourier transform (FFT). Based on the numerical solution, the friction and contact behavior between the core and outside wires, the stress and strain of the outside wire are analyzed. Moreover, the effects of the bending load and lay angle on the bending properties of the strand are discussed.