Effect of interfacial contact forces in radial contact wire strand

A new mathematical model has been developed to predict the behaviour of a stranded cable assembly under the influence of interfacial radial contact forces and radial contraction of the core. A single layered cable assembly with six helical wires and a straight cylindrical core, all made with the same material, Steel has been chosen to explain this phenomenon when the assembly is under the influence of core–wire radial contact. An attempt is made in this paper to model the strand with a radial (core–wire) contact and deduce its equations of equilibrium. Numerical analysis of strand force, twisting moment, strand stiffness, contact force and contact stresses is carriedout based on the equilibrium of thin rods, and the results are compared with the earlier research work. The importance of the inclusion of interfacial forces at the contact locations and their associated effects of axial and twist slip of the helical wires on the core, is highlighted. The behaviour of the stranded cable assembly due to the contact force in the radial direction and its associated effects on the axial strain of the core due to Poisson’s effect is one more additional feature incorporated in the present work.     

Statically indeterminate contacts in axially loaded wire strand

This paper is concerned with the analysis of simple wire strands made from one layer of circular wires helically wrapped around a circular straight core wire. The undeformed configuration is the special case in which each of the surrounding helical wires touches its two adjacent neighbouring helical wires as well as touching the core wire. This forms a statically indeterminate contact problem. A simple finite element model is developed to analyse this situation. Numerical results show that contacts can occur simultaneously at all possible contact points when the strand is subjected to extension with both ends fixed against rotation.     

Response of a wire rope strand to axial and torsional loads: Asymptotic modeling of the effect of interwire contact deformations

The refined discrete mathematical model of a simple helical wire rope strand is developed. The effect of the transverse contraction of the wire strand through Poisson’s ratio and also through local contact deformations (wire flattening) has been studied in detail. In order to express the interwire contact deformation in terms of the parameters describing the strand deformation, we formulate a two-dimensional model interwire contact problem. The interwire contact interaction is treated as a frictionless unilateral plain strain problem. The nonlinear model interwire contact problem has been solved by the method of matched asymptotic expansions. The constitutive equations for a helical wire rope strand, which take into account both the Poisson’s ratio effect and the effect of contact deformation, are obtained in a closed form.     

A Theoretical Study on Nonlinear Bending of Wires

The nonlinear bending of thin wires is a challenging topic in several applications where the final geometry of the wire after bending and springback has to be known. Typical examples are tyre manufacturing, helical spring design, spectacles frames. In order to develop analytical models able to set bending parameters for a required final shape of the wire, both account material behaviour (during the loading and unloading phases with springback effect) and geometrical nonlinearity have to be considered. In the case of plates bending, many analytical and numerical models are available in the literature, offering an accurate solution to this problem. However, the bending of thin wires could still be the subject of discussion and research. In this paper a new analytical model was developed, starting from the models available in the literature, in order to provide the designer with a simple model to predict the final shape of a wire by using mathematical codes. The model allows to predict with a higher level of accuracy the final shape of wires having different cross-sections after nonlinear bending. Since Bernoulli’s hypothesis is assumed, the model can be used in all the applications where the material behaviour of the wire guarantees that plane cross sections of the wire will remain plane after rotation due to bending, with negligible errors from the engineering point of view.     

基于SWT方法的钢绞线索微动疲劳特性分析

为得到钢绞线索丝间接触区的应力场分布并预测微动疲劳裂纹萌生位置和微动疲劳寿命,本文利用参数化方法建立了精细化的钢绞线拉索有限元模型,包括整索模型和不同层丝间接触区域的局部精细化子模型．分析了钢绞线索在两种交变荷载工况下的应力场变化情况,并基于多轴疲劳SWT(Smith-Watson-Topper)临界平面法进行了疲劳特性分析和疲劳寿命预测．主要结论如下：钢绞线索内接触区边缘处的微动幅值较大,中心处几乎没有相对滑动,微动疲劳的初始裂纹萌生点位于接触区域边缘;经不同区域子模型分析比较,在轴向循环荷载作用下,外层钢丝的接触区域比内层钢丝更易发生微动疲劳损伤;在横向位移循环荷载作用下,同层钢丝因位置角度不同而产生了较大的疲劳特性差异,且相比轴向循环拉伸,该工况下最不利单丝的微动疲劳寿命更低;与非接触区域相比,接触区的疲劳寿命大幅降低,微动现象对钢绞线索的抗疲劳性能有明显降低作用．     

Analytical procedure for modelling recursively and wire by wire stranded ropes subjected to traction and torsion loads

The aim of this article is to introduce a new theoretical procedure for modelling wire ropes subjected simultaneously to tensile and torsional loads. The procedure is based upon the beam assumption and takes account wire by wire of the double helical wires on the basis of general thin rod theory developed by [Love, A., 1944. Mathematical Theory of Elasticity. Dover Publications, New York]. The proposed kinematics are based on the assumption that wires are un-lubricated and therefore that no relative sliding between adjacent wires happens.     

A Second-Order Solution of Saint-Venant's Problem for an Elastic Pretwisted Bar Using Signorini's Perturbation Method

We use Signorini's expansion to analyse deformations of a straight, prismatic, isotropic, stress free, homogeneous body made of a second-order elastic material and loaded as follows. It is first twisted by an infinitesimal amount and then loaded by applying surface tractions, with nonzero resultant forces and/or moments, only at its end faces. The centroid of one end face is taken to be rigidly clamped. By using a semi-inverse method, the problem is reduced to that of solving two plane elliptic problems involving six arbitrary constants that characterize flexure, bending, extension, and torsion superimposed upon the infinitesimal twist. It is shown that the Clebsch hypothesis is not valid for this problem. A second-order Poisson's effect, not of the Saint-Venant type, and generalized Poynting effects may also occur in these problems. This revised version was published online in August 2006 with corrections to the Cover Date.     

The extension and oscillation of a non-Hooke's law spring

We derive a wave equation for small-amplitude, undamped, extensional oscillation of a spring-mass system consisting of a mass suspended on a spring governed by a quadratic force-extension relationship. We justify this quadratic model using a Taylor series expansion of the general elasticity equations for a helical spring. Transformation of the equation of motion of the spring leads to a separable wave equation with the spacial component being a transformation of Bessel's equation. The model is successful in predicting static extension and period of oscillation of a helical wire spring for which the wave equation based on Hooke's law is inadequate.     

Analytical solutions for bending and flexure of helically reinforced cylinders

There has been a great deal of interest in the problems of modelling cables and ropes. A recent review by Cardou and Jolicoeur [Appl. Mech. Rev. 50 (1997) 1] considers the modelling of a cable which consists of a central core surrounded by one or several helically wound wire layers. One approach has been to consider the deformations of an individual helical wire and to synthesise the model of a cable by using contact conditions between the various wires. Other authors have adopted a continuum approach regarding each layer as a transversely isotropic material whose principal direction is along a helix surrounding the central axis of the cable. In each layer the helix angle is constant so that, when referred to cylindrical polar co-ordinates, the cylinder has a constant stiffness matrix in each layer. The intention in this paper is to use the continuum approach and describe the analytical solutions that govern the simple bending, flexure, or bending under a uniform load, of an anisotropic elastic cylinder consisting of a single material of this type. The extension of this work to a composite cylinder consisting of several concentric layers, surrounding a central core, which are either bonded together or make a frictionless contact, is briefly described.     

PROPAGATION CHARACTERISTICS OF HIGH ORDER LONGITUDINAL MODES IN STEEL STRANDS AND THEIR APPLICATIONS

Propagation characteristics of high order longitudinal modes of ultrasonic guided waves in seven-wire steel strands are investigated theoretically and experimentally. According to these analysis results, proper longitudinal modes are selected for defect detection in steel strands. Dispersion curves for helical and central wires in a 17.80 mm nominal diameter seven-wire steel strand are numerically obtained firstly, and propagation characteristics of high-order longitudinal modes, such as wave structures, attenuation and dispersion, are analyzed. In experiments, the signals of ultrasonic guided wave at different high frequencies are excited and received at one end of a steel strand by using the same single piezoelectric transducer. The identification of longitudinal modes in the received signals is achieved based on short time Fourier transform. Furthermore, appropriate L（0, 5） mode at 2.54 MHz is chosen for detecting an artificial defect in a helical wire of the steel strand. Results show that high order longitudinal modes in a high frequency range with low dispersion and attenuation whose energy propagates mainly in the center of the wires can be used for defect detection in long range steel strands.     

钢丝的微动磨损及其对疲劳断裂行为的影响研究

采用自制的钢丝微动磨损试验机考察了钢丝的微动摩擦磨损性能，随后将经过一定时间微动磨损试验后的钢丝试样在液压伺服疲劳试验机上进行拉一拉疲劳试验，进而探讨了微动摩擦系数和微动磨损深度随微动磨损试验时间和接触载荷的变化关系；并利用扫描电子显微镜分析了试样磨痕和磨屑的表面形貌．结果表明，在较大的微动振幅下，钢丝的微动摩擦系数变化幅度不大，微动磨损深度随微动磨损试验时间和接触载荷的增加而增大；微动磨损试验后钢丝试样的疲劳寿命同磨损深度成反比关系；可以将疲劳断口划分为4个区域，其同钢丝试样的疲劳断裂过程相对应．     

Propagation of a longitudinal pulse in wire ropes under axial loads

Measurements of the velocity of propagation of longitudinal pulses in wire ropes as a function of applied tension are reported. Twelve 3/8-in.-diam cables are investigated which differ in configuration, i.e., number of wires per strand and number of strands, and in the material from which the wires and the core are fabricated. The velocity of longitudinal waves is found to increase with increasing tension, approaching the velocity in a solid steel bar as the applied load is increased toward the failure load of the wire rope. The material from which the wires are fabricated and the number of strands, rather than the number of wires in a strand or its core material, appear to significantly affect the velocity of longitudinal pulses.     

定、变载弯曲疲劳钢丝绳失效机理对比研究

为对比揭示定、变载弯曲疲劳钢丝绳断裂机理及磨损演化特性,运用自制钢丝绳弯曲疲劳试验机开展钢丝绳定载、变载弯曲疲劳试验,通过人工拆股统计法和VW-9000系列高速度数码显微系统对比研究钢丝绳断丝分布、断丝数、断口和磨痕形貌等断裂机理,对比分析钢丝绳未断钢丝和断丝的磨痕尺寸演化特性. 结果表明:与钢丝绳定载弯曲疲劳相比,变载弯曲疲劳钢丝绳断丝出现较晚,芯股、螺旋股外层断丝数分别较多、较少,芯股外层钢丝断口挤压变形较大,芯股各层钢丝断口裂纹扩展区占比较低,芯股和螺旋股的各层钢丝磨痕尺寸总体较小,钢丝绳更易达到报废水平.      

钢丝绳捻制成形接触问题的有限元分析

基于虚功原理建立了钢丝绳捻制成形过程中考虑接触摩擦时的刚度方程,将小球分裂算法用于接触搜索,Augmented Lagrange法用于计算接触力．以钢丝绳一次捻制成形过程为例,分析了摩擦系数和自扭转系数对接触应力和加工应力域变的影响．研究结果表明。摩擦系数对剪应力的影响比对等效应力和等效塑性应变的影响大;考虑摩擦时钢线表面的轴向残余应力计算结果比无摩擦条件下的计算结果更接近实验结果．     

Control of flow past a circular cylinder via a spanwise surface wire: effect of the wire scale

Flow phenomena induced by a single spanwise wire on the surface of a circular cylinder are investigated via a cinema technique of particle image velocimetry (PIV). The primary aim of this investigation is to assess the effect of the wire scale. To this end, consideration is given to wires with different diameters that are 0.5, 1.2, and 2.9% of the cylinder diameter. The Reynolds number has a subcritical value of 10,000. Compared to the thickness of the unperturbed boundary layer developing around the cylinder between 5° and 75° from the forward stagnation point, the former two wires have smaller scales and the latter has a larger scale. Two angular locations of the wire, defined with respect to the forward stagnation point of the cylinder, are found to be critical. When the wire is located at these critical angles, either the most significant extension or the contraction of the time-mean separation bubble occurs in the near wake. These critical angles depend on the wire scale: the smaller the wire, the larger the critical angle. The small-scale and large-scale wires that have diameters of 1.2 and 2.9% of the cylinder diameter induce bistable shear-layer oscillations between different separation modes when placed at their respective critical angles corresponding to maximum extension of the near-wake bubble. These oscillations have irregular time intervals that are much longer than the time scale associated with the classical Kármán instability. Moreover, the large-scale wire can either significantly attenuate or intensify the Kármán mode of vortex shedding at the critical states; in contrast, the small-scale wires do not notably alter the strength of the Kármán instability.     

Effect of a helical wire on mixed convection heat transfer to carbon dioxide in a vertical circular tube at supercritical pressures

Reactor core of a SCWR (supercritical water-cooled reactor) employs a tight lattice in order to efficiently remove heat from nuclear fuels. In the narrow sub-channels of a tight lattice reactor core, a helical wire instead of a complicated conventional spacer has been used as a turbulence generator and a space-keeper between the fuel rods.A series of experiments were performed in order to investigate an effect of a helical wire on heat transfer to upwardly flowing CO₂ in a electrically-heated circular tube with an inner diameter of 6.32 mm, where a helical wire with an outer diameter of 1.3 mm was tightly inserted inside the tube. The tube inner diameter corresponds to the equivalent hydraulic diameter of a sub-channel of a KAERI’s fuel assembly concept. The mass fluxes ranged from 400 to 1200 kg/m² s; the heat fluxes ranged from 30 to 90 kW/m²; and the pressures were 7.75 and 8.12 MPa. The corresponding Reynolds numbers at the test section inlet ranged from 1.8 × 10⁴ to 7.5 × 10⁴. The heat transfer rate reached almost twice the value obtained from the experiment with a plain tube of the same size near the pseudocritical temperature and the effect of a wire was attenuated as the temperature moved away from the pseudocritical temperature. The wall temperature distribution along the span between the contact points was a concave downward parabola. Near the pseudocritical temperature, the wall temperature showed relatively higher values, indicating a stagnant fluid around the wire. On the other hand, the wall temperature at the contact point showed a relatively lower value, indicating a fin function of a wire.     

The influence of the twist of individual fibers in 2D fibered networks

In this work, we propose a model for surfaces made of inextensible fibers that generalizes the existing approach to fibered networks, by taking into account not only the bending resistance of individual fibers, but also their resistance to twist. Assuming that the total energy of the network depends on the shear between the fibers as well as their curvature and twist, we derive the equilibrium equations and discuss an application to a cylindrical shell made of inextensible helical fibers. We discuss the effect of twisting stiffness on the loading–extension curve of the cylinder.     

Velocity derivative skewness in isotropic turbulence and its measurement with hot wires

We investigate the effect of the hot wire resolution on the measurement of the velocity derivative skewness in homogeneous isotropic turbulence. Single- and cross-wire configurations (with different lengths and separations of the wires, and temporal sampling resolution) are considered. Predictions of the attenuation on the basis of a model for the energy spectrum are compared to experimental and numerical data in grid and box turbulence, respectively. It is shown that the model-based correction is accurate for the single wire but not for the cross-wire. In the latter case, the effect of the separation between the wires is opposite to that found in the experiments and simulations. Moreover, the attenuation predicted by the numerical data is in good agreement with that observed in the experiment. For both probe configurations, the sampling resolution has a sizeable attenuation effect, but, for the X-probe, the impact of the separation between the wires is more important. In both cases, the length of the wires has only a minor effect, in the non-dimensional range of wire length investigated. Finally, the present experimental data support the conclusion that the skewness is constant with the Reynolds number, in agreement with Kolmogorov’s 41 theory.

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Quasi-Static Torsion Characterization of Micro-diameter Copper Wires

A method to measure very small torques that subject micro-diameter copper wires to plasticity is developed for quasi-static torsion experiment. Following the concept in the work by Fleck et al. (Acta Metall. Mater. 42:2, 1994), we employed a glass fiber filament as the torque cell. To calculate the small torques applied on the micro-diameter copper wires, an additional rotation sensor is required to measure the rotation of the glass fiber torque cell. The rotation sensor system is attached between the glass fiber and the copper wire specimen. It uses a laser extensometer to gauge the distance between a helical and a horizontal reflection tapes on a foam cylinder, which is calibrated with the angle of rotation. A new set of torsional experimental data for the copper wires with four different diameters, from 16–180 μm, are presented. All copper wires exhibit a typical elastic-plastic response. The torsional properties of these copper wires were not found to be significantly different. The uncertainties of the measurement and analysis are discussed.     

HYDROELASTICITY OF THE KIRCHHOFF ROD: BUCKLING PHENOMENA

We consider the nonlinear coupled hydroelastic problem of a general curved and twisted flexible slender structure (i.e. flexible riser, cable system, fish–farm net system, towed arrays, etc.) embedded in a nonuniform flow field such as the ocean environment; the flow direction is arbitrary, relative to the axis of the slender structure. The motion of the elastic structure is coupled with the hydrodynamic loads acting on the slender structure by the ambient flow field. An important input for such hydroelastic problems is the computation of the hydrodynamic loading per unit length experienced by the slender body. A rigorously derived improvement for the inertial loading per unit length over the commonly used Morison-type semi-empirical force (originally obtained for straight long structures in a uniform stream) is used. The structure is also allowed to undergo small (yet finite) deflections from its original reference central-line, due to a particular model of intrinsic elasticity governed by a corresponding nonlinear PDE, which corresponds to the well-known Kirchhoff rod elastic model. The system of coupled hydroelastic equations is investigated in order to derive analytically the influence of the hydrodynamic loading in a uniform stationary stream on the nonlinear stability of the straight rod. It is found that the presence of an ambient stationary stream decreases the critical parameters (critical twist) of the buckling phenomenon which is known to exist for the same rod when placed in a vacuum. Also revealed is a new type of stability loss, which is affected by viscous effects.