Rope Cross-section Research Articles

Continuity breakageof cableinorthotropic stay rope of rectangular cross-section

Purpose. Construction of an algorithm for determining a stress-strain state of a multi-layer stay rope of a rectangular cross-section with a broken reinforcing fiber. Methods. Analytical solution of an interaction model of parallel fibers connected by elastic material of a stay rope of rectangular cross-section in the event of reinforcing element breakage using methods of mechanics of layered composite materials with soft and hard layers. Findings. An analytical algorithm for determining a stress-strain state of a composite stay rope of rectangular cross-section with a damaged reinforcing fiber is constructed.An analytical method for determining a stress-strain state of a rope with a comprehensive consideration of structure, mechanical properties of components, layout of reinforcing fibers in a cross-section, in a presence of a broken fiber, is developed in a closed form.It is established that load unevenness on fibers is practically independent of the ratio of an amount of fibers and layers in a rope and their total amount, and the ratio of fiber placement spacing in layers and spacing of layers in case of fiber breakage in a stay rope cross-section. Scientific novelty. It is established that load unevenness on fiber does not depend on a ratio of an amount of fibers and amount of layers in a stay rope. Practical significance. The developed algorithm makes it possible to determine the share of tractive capacity loss of a stay rope of rectangular cross-section due to breakage of a reinforcing element. The known value of lost strength makes it possible to establish acceptable conditions for use of a rope of rectangular cross-section. It is advisable to give a rope a shape with less resistance to air pressure by reducing the amount of layers compared to the amount of fibers in layers. Damage to a corner element of cable reinforcement is more dangerous, it leads to a load increase of almost 30 % in the most loaded fiber, while the specified parameter is less than 20 % in case of a breakage of the central fiber.

The influence of flux rope heating models on solar prominence formation

Context. Prominences are cool, dense clouds suspended within the solar corona. Their in situ formation through the levitation-condensation mechanism is a textbook example of the thermal instability, where a slight energy imbalance leads to a runaway process resulting in condensed filamentary structures embedded within the concave-up portions of a flux rope. The detailed interplay between local radiative losses and the global heating of the solar corona is investigated here for prominence-forming flux rope structures. Aims. We begin by exploring the influence of two classes of commonly adopted heating models on the formation behaviour of solar prominences. These models consider either an exponential variation dependent on height alone, or local density and magnetic field conditions. We highlight and address some of the limitations inherent to these early approximations by proposing a new, dynamic 2D flux rope heating model that qualitatively accounts for the 3D topology of the twisted flux rope field. Methods. We performed 2.5D grid-adaptive numerical simulations of prominence formation via the levitation-condensation mechanism. A linear force-free arcade is subjected to shearing and converging motions, leading to the formation of a flux rope containing material that may succumb to thermal instability. The eventual formation and subsequent evolution of prominence condensations was then quantified as a function of the specific background heating prescription adopted. For the simulations that consider the topology of the flux rope, reduced heating was considered within a dynamically evolving ellipse that traces the flux rope cross-section. This ellipse is centred on the flux rope axis and tracked during runtime using an approach based on the instantaneous magnetic field curvature. Results. We find that the nature of the heating model is clearly imprinted on the evolution and morphology of any resulting prominences: one large, low-altitude condensation is obtained for the heating model based on local parameters, while the exponential model leads to the additional formation of smaller blobs throughout the flux rope which then relocate as they tend towards achieving hydrostatic equilibrium. Finally, a study of the condensation process in phase space reveals a non-isobaric evolution with an eventual recovery of uniform pressure balance along flux surfaces.

Estimation of breakage position in wire rope cross-section by geometrical formulation of wire shape

Estimation of breakage position in wire rope cross-section by geometrical formulation of wire shape

In situ multi-spacecraft and remote imaging observations of the first CME detected by Solar Orbiter and BepiColombo

Context.On 2020 April 19 a coronal mass ejection (CME) was detected in situ by Solar Orbiter at a heliocentric distance of about 0.8 AU. The CME was later observed in situ on April 20 by the Wind and BepiColombo spacecraft whilst BepiColombo was located very close to Earth. This CME presents a good opportunity for a triple radial alignment study, as the spacecraft were separated by less than 5° in longitude. The source of the CME, which was launched on April 15, was an almost entirely isolated streamer blowout. The Solar Terrestrial Relations Observatory (STEREO)-A spacecraft observed the event remotely from −75.1° longitude, which is an exceptionally well suited viewpoint for heliospheric imaging of an Earth directed CME.Aims.The configuration of the four spacecraft has provided an exceptionally clean link between remote imaging and in situ observations of the CME. We have used the in situ observations of the CME at Solar Orbiter, Wind, and BepiColombo and the remote observations of the CME at STEREO-A to determine the global shape of the CME and its evolution as it propagated through the inner heliosphere.Methods.We used three magnetic flux rope models that are based on different assumptions about the flux rope morphology to interpret the large-scale structure of the interplanetary CME (ICME). The 3DCORE model assumes an elliptical cross-section with a fixed aspect-ratio calculated by using the STEREO Heliospheric Imager (HI) observations as a constraint. The other two models are variants of the kinematically-distorted flux rope (KFR) technique, where two flux rope cross-sections are considered: one in a uniform solar wind and another in a solar-minimum-like structured solar wind. Analysis of CME evolution has been complemented by the use of (1) the ELEvoHI model to compare predicted CME arrival times and confirm the connection between the imaging and in situ observations, and (2) the PREDSTORM model, which provides an estimate of theDstindex at Earth using Solar Orbiter magnetometer data as if it were a real–time upstream solar wind monitor.Results.A clear flattening of the CME cross-section has been observed by STEREO-A, and further confirmed by comparing profiles of the flux rope models to the in situ data, where the distorted flux rope cross-section qualitatively agrees most with in situ observations of the magnetic field at Solar Orbiter. Comparing in situ observations of the magnetic field between spacecraft, we find that the dependence of the maximum (mean) magnetic field strength decreases with heliocentric distance asr−1.24 ± 0.50(r−1.12 ± 0.14), which is in disagreement with previous studies. Further assessment of the axial and poloidal magnetic field strength dependencies suggests that the expansion of the CME is likely neither self-similar nor cylindrically symmetric.

Some aspects on quantification of the wear at steel wire ropes

Steel ropes are widely used in material handling machines. The excessive wear of wires is often presented as a type of rope degradation. One of many indicators of the wear is abrasion, corrosion and fatigue cracks. Within this class of rope degradation, the main representation of wear is wire abrasion in the layers of the external wires. This is especially noticeable at the steel ropes which are operating in the drum devices with multilayer winding and in hoists of mining shafts. Over performed work cycles, the estimation of losses in rope cross-section is important for the calculation of the rope capacity. Abrasive wear of external wires is a relatively easy phenomenon to detect with a qualitative interpretation. However, it is a very difficult phenomenon to quantify. The aim of this article is to address this issue. A brief survey of usual methods for rope inspections is given, which can serve as practical guidance for the engineers in this field. With accompanying case study, it presented the advantages of magnetic method in rope inspections oriented towards measuring the changes of wires within the wear assessment.

The influence of the process-induced deformed state on straightness of prestressing strands after manufacture

Based on the study of elastic-plastic deformation, the expressions of longitudinal force Nt , bending Mb and torque Mt moments in wire-cross sections subject to the process parameters of rope torsion are obtained: wire tensioning efforts, untwisting and preformation.A technique for determining the technological internal force factors (TIFF) in the rope cross-sections: the longitudinal forces ; bending and torque moments. Being guided by the theorem on unloading and FEM, the external deformed state of the rope unloading from TIFF is studied. The expression of the rope unloading deformations vector as a function of the TIFF vector using the global stiffness matrix of 4×4 rope cross-section corresponding to the elastic deformation is obtained.Based on the bending deformations, an expression was χ and ζ obtained, the parameter h (h is the segment arrow at the chord length of 1 m), which, according to the regulatory standard, characterizes the degree of the rope straightness after manufacture. The connection between the parameters of torsion (tension, untwisting, and preformation) and the parameter h of straightness is established. It is determined that the unstraightness is directly affected only by the deviation from the uniformity of tension. The developed theory allows to determine the permissible deviation from the non-uniformity of tension with the permissible value of the parameter h of straightness. For example, a prestressing strand of a structure 1+6, having a diameter of 6.9 mm is considered to be of high quality according to the standard, if h ≤ 25mm. This value h corresponds to the deviation of the tension of Δκ = 0,8 one of the 6 wires of the layer. With an increase in deviation of tension, h increases almost rectilinearly to Δκ ≃3. With further increase, a loop is Δκ formed – the loss of stability.The obtained theory of the external deformed state of unloading provides further opportunity to study the internal deformed-stress state of the rope wires due to process-induced forces, which opens the prospect of even a deeper study of operational strength and durability of ropes.

Multi-Body Dynamics Simulation of Hoisting Wire Rope and Its Stress Analysis

As a key component of the hoisting system of the crane, the steel wire rope will bear a variety of loading actions such as stretching, bending, vibration and impact in the process of traction hoisting. Therefore, it is important to determinate the dynamic characteristics of the steel wire rope under complex loads and understand the stress-strain state to predict the risk of hoisting operation in advance. This article takes the bridge crane as the engineering background, first, a dynamic model of a steel wire rope lifting system based on ADAMS/Cable was established, and the dynamic stress spectrum of the steel wire rope during the lifting process was calculated and obtained. Secondly, by establishing the geometric model and finite element model of the wire rope, the tensile stress and wire displacement distribution of the wire rope and the contact stress between the wire rope and the pulley and the wires inside the wire rope are analyzed during the lifting process of the crane. The final results show that the instantaneous acceleration of the steel wire rope increases the maximum tensile stress of the steel wire rope by 37% compared with the stable lifting stage at the instant of starting the steel wire rope, causes an increase in the stress amplitude of the wire rope cross section, and the lifting process of the steel wire rope is accompanied by unstable vibration loads. The analysis found that the outermost cross-section of the steel wire rope's outer strand was subjected to the greatest stress, and its local maximum tensile stress amplitude was increased by 56% compared to the stable lifting stage. The contact stress generated by the contact between the steel wire rope and the pulley causes contact wear on the external and internal strands of the steel wire rope, and promotes fatigue fracture of the steel wire rope.

Dynamic contact and slip characteristics of bent hoisting rope in coal mine

Dynamic contact and slip characteristics of bent hoisting rope in coal mine were investigated in this study. Dynamic tensions of hoisting rope bending around friction lining at distinct arc locations were obtained employing hoisting dynamics and friction transmission theories. The finite element model of contacting bent rope and friction lining was established to explore dynamic contact characteristics and relative slip amplitudes between the rope and friction lining, and between contacting strands in the rope, respectively. The results show that dynamic tensions of bent rope at distinct arc locations are related to slip and inactive slip states of rope segments. Higher stress concentrations are present at contacting locations between adjacent strands and between the rope and friction lining at every central angle at any lifting time. An increase of central angle φ causes overall increased equivalent von Mises stress distributions on the rope cross-section and near contacting locations within the slip angle between the rope and friction lining as compared to constant equivalent stress distributions within the inactive slip angle. Relative slips are induced by differences between tensions of bent rope segment at both sides within the slip angle as compared to no relative slip within the inactive slip angle, which is the same in cases of contacting rope and friction lining, and neighboring strands.

Оценка несущей способности канатов заливочных кранов на основании данных лабораторных термических испытаний

The article presents an approach to assessing the bearing capacity of the steel ropes of hot metal cranes used at metallurgical enterprises. The rope bearing capacity is assessed based on the data of laboratory thermal tests, which are carried out in two ways. According to the first way, the temperature variation pattern over the rope cross-section is analyzed in subjecting the rope to thermal cycling by means of the contact method with the use of thermocouples and by means of remote measurements using an infrared imager. Recommendations regarding the procedure of carrying out rope temperature measurements under the production cycle field conditions are suggested. The second way implies studying the temperature variation pattern over the rope cross section in subjecting it to a short-term heating, which simulates the burst of flame from the ladle in pouring cast iron into the converter. It has been determined that the temperatures of rope core wires and outer wires of external strands may differ from each other by as much as several hundred degrees. It has been shown that ropes having a denser structure are characterized by better heat transfer between the wires and, as a consequence, feature more uniform temperature distribution over the rope cross-section. An experimental time dependence of the temperature gradient was used for estimating the stresses in wires based on a two-component rod-type analysis scheme. The change in the working rope safety margin under thermal cycling conditions was determined taking into account experimental data on the effect of temperature on the steel strength parameters. It has been shown that the real safety margin of a hot rope is essentially lower than its certified value in the rope delivery state. Possible rope failure cases are analyzed, and the hot rope strength criteria are formulated. A procedure for determining the two-parametric region of the permissible rope operating states on the basis of combined numerical and experimental assessments has been proposed. The suggested procedure makes it possible to determine in advance whether or not safe operation of the rope is possible given the existing technology of pouring cast iron into the converter. A general concept of unsafe operating conditions of hot metal crane ropes is given.

Simplified analysis of the influence of strain localization and asymmetric damage distribution on static damaged polyester rope behavior

In this paper, two factors that govern the response of damaged ropes are numerically examined independently: strain localization and asymmetric damage distribution. These two mechanisms are studied by using two nonlinear mechanical models that account for the strain localization around the failure site due to frictional effects (SLM) and the presence of unbalanced radial contact forces within a rope cross-section due to the asymmetry in damage distribution (ADDM). These models are applied to an available set of static tension tests on asymmetrically damaged, large-scale polyester ropes. The initial damage level of the rope cross-sections and rope diameters varied from 5% to 15% and from 32 mm to 166 mm, respectively. A semi-analytical proof is given to show that SLM and ADDM provide upper and lower bounds, respectively, to the damaged response of the ropes analyzed. Results indicate that, relative to the intact rope, the SLM predicted a reduction in rope capacity similar to the damage level and a maximum reduction in rope deformation capacity equal to 16% for an effective damage level equal to 25%. Conversely, the ADDM predicted a reduction in rope residual strength slightly greater than the damage level and a maximum reduction in deformation capacity equal to 3%.

Damage-Induced Stresses and Remaining Service Life Predictions of Wire Ropes

Wire ropes in marine applications often encounter relatively fast and noticeable wear, a result of the fatigue to which they are exposed coupled with harsh operational conditions. This paper addresses some of the aspects of fatigue damage that occur in wire ropes. Using the finite element method, stress and fatigue analysis of three different design types (6 × 7, 7 × 7, 8 × 7) of wire rope is performed. The size of the wire rope cross-section area is varied in order to simulate the progressive damage of the wires so that consequential stress levels and remaining fatigue life can be numerically predicted. The aim was to provide a better understanding of the mechanical behavior of damaged wire ropes under various conditions, since an appropriate choice of wire rope design could then be made from engineering and economic points of view. Additionally, potential failures can be predicted, resulting in effective maintenance and the avoidance of potential risks of rope failure, especially important regarding economical and safety aspects of transportation in the marine industry.

Assessment of static rope behavior with asymmetric damage distribution

In this paper, a mechanical model is proposed to estimate the static response (stiffness, residual capacity, deformed configuration, strain/strain distribution within cross-section, and deformation capacity) of a rope asymmetrically damaged. In this study, damage corresponds to the complete rupture of one or more rope components in a particular rope cross-section location. In the proposed model, the damaged rope is assumed to behave as a nonlinear beam under biaxial bending and axial load with Bernoulli's kinematic hypothesis. Biaxial bending arises from the unbalanced radial contact forces within rope cross-section, which are related to the initial helical geometry configuration of the rope components, due to the asymmetric damage distribution. An efficient and robust iterative cross-sectional numerical algorithm is implemented to estimate the asymmetric damaged rope capacity curve, stress and strain distributions throughout rope cross-section and rope geometry deformation for a prescribed axial displacement of the rope. The results given by the proposed model are found to be in good agreement with available static tension tests on asymmetrically damaged small-scale (ropes diameter equal to 6mm) polyester ropes and their corresponding 3D finite element (FE) simulations with lower computational cost. Additionally, compared to the solutions obtained by previous analytical models reported in the literature, the range of applicability associated to the degree of damage to rope cross-section (number of broken rope components) is extended.

A Wire Contact in the Construction of a Steel Rope

A rope is an important, highly effective and one of the oldest transportation systems used in transport by mankind. Nowadays, steel ropes are mainly used for moving loads in mining - coal and ore exploitation, vertical or horizontal transport of persons and goods by cranes, elevators, lifts and cable ways. In many cases steel wire ropes are employed in extreme conditions with respect to the load of the rope: high temperature plants, mining corrosive environments and etc. In terms of labor safety it is necessary to certify each rope people come in contact when working with loads or a rope is used for transportation. It has to be done earlier than a rope is put into operation or on the market. Despite the fact the tests were performed correctly, a rope may not achieve the desired rope life. The great impact on the life of a wire rope has its interaction with a device a rope is deployed on. Interaction of a steel wire rope with a device it is deployed on has a great impact on its life. Durability is also affected by the way a rope is loaded, its maintenance and regular re-examination as well as its construction. Design accuracy is assessed according to strength and deformation properties of wires a rope is made of and a rope cross-section construction is taken in account as well. The important aspect of steel wire rope durability (which can be mostly influenced by a manufacturer) is an appropriate design of diameters and angles of wires winding in accordance with exactly defined conditions of operation. The paper presents models of ropes equally loaded which eliminates the most unfavorable factors affecting their life cycle.

Experimental investigation of pressure fluctuations caused by a vortex rope in a draft tube

In the last years hydro power plants have taken the task of power-frequency control for the electrical grid. Therefore turbines in storage hydro power plants often operate outside their optimum. If Francis-turbines and pump-turbines operate at off-design conditions, a vortex rope in the draft tube can develop. The vortex rope can cause pressure oscillations. In addition to low frequencies caused by the rotation of the vortex rope and the harmonics of these frequencies, pressure fluctuations with higher frequencies can be observed in some operating points too. In this experimental investigation the flow structure and behavior of the vortex rope movement in the draft tube of a model pump-turbine are analyzed. The investigation focuses on the correlation of the pressure fluctuation frequency measured at the draft tube wall with the movement of the vortex rope. The movement of the vortex rope is analyzed by the velocity field in the draft tube which was measured with particle image velocimetry. Additionally, the vortex rope movement has been analyzed with the captures of high-speed-movies from the cavitating vortex rope. Besides the rotation of the vortex rope due to pressure fluctuation with low frequencies the results of the measurement also show a correlation between the rotation of the elliptical or deformed rope cross-section and the higher frequency pressure pulsation. An approximation shows that the frequencies of the pressure fluctuation and the movement of the vortex rope are also connected with the velocity of the flow. Taking into account the size and position of the cavitating vortex core as well as the velocity at the position of the surface of the cavitating vortex core the time-period of the rotation of the vortex core can be approximated. The results show that both, the low frequency pressure fluctuation and the higher frequency pressure fluctuation are correlating with the vortex rope movement. With this estimation, the period of the higher frequency pressure pulsation is approximately a half rotation of the vortex core.

Effect of broken rope components distribution throughout rope cross-section on polyester rope response: Numerical approach

This paper deals with the effects of broken rope components on rope failure axial strain, failure axial load and rope stiffness using 3D finite element (FE) analyses. The analyses are focused on small-scale polyester ropes (ropes diameter equal to 6mm) with different numbers and distributions of broken components throughout rope cross-sections. These small-scale ropes are members of bigger ropes used as deep water mooring systems. For computational purposes, ropes are subjected to extension with both ends fixed against rotation. Numerical simulations show that the reduction of the residual rope strength and the axial strain at the onset of rope failure due to the presence of broken rope components depend on the length of the rope, degree of asymmetry of the rope cross-section and on the number, location throughout rope cross-section (defines type of contact between rope components), and axial distribution of the broken components. Hypotheses associated with a 2D numerical model extended to include the length effect on damaged rope response, which accounts for strain localization around the failure region, are tested by comparisons with 3D FE models results and available experimental data obtained from static tensile tests. The results of this study should serve as a basis to develop more complete numerical models to predict damaged rope response.

Degradation of rope properties under increasing monotonic load

This paper describes the development of a computational model to predict the response of synthetic-fiber ropes under both monotonic and cyclic loads. The model addresses the issue of damage to a rope cross-section and its effect on rope response. Isotropic damage is assumed and is therefore characterized by a scalar quantity known as the damage index. The damage index is used to quantify the amount of deterioration that takes place in a damaged rope throughout its loading history. For the current study, data obtained from static tension tests are used to determine the evolution relationship for the damage index. This relationship is based on the stiffness ratio between experimental data and simulation of rope response without any source of damage and is assumed to be described by an exponential equation. Numerical simulations of damaged rope behavior compare well with experimental results.

The true dimensions of interplanetary coronal mass ejections

The majority of observations of Interplanetary Coronal Mass Ejections (ICMEs) are made with a single spacecraft and their properties inferred from a fit to a cylindrically symmetric model. This process produces a single dimension for a magnetic cloud, its radial thickness. If the radius of curvature of an ICME were equal to its half thickness, the shock front driven by the ICME would be at a distance of only about 0.15 times the ICME thickness according to the gas dynamic model, while the observed median thickness is closer to 0.4. The agreement with theory can be improved if the obstacle has two radii of curvature, one corresponding to the rope cross-section and one corresponding to the curvature of the rope axis. This picture is in accord with the popular paradigm of an ICME as a twisted flux rope rooted in the sun. Nevertheless this correction is insufficient to bring full agreement, suggesting ICMEs have yet a third scale size, a cross-flow diameter that may be of the order of four times their radial thickness. This inference is in accord with both indirect evidence in the form of the distribution of impact parameters derived from the cylindrical cross-section model and with direct evidence from the fit of multi-point observations with oval cross-section ropes.

Multiple spacecraft flux rope modeling of the Bastille Day magnetic cloud

The Bastille Day magnetic cloud in July 2000 occurred with NEAR in conjunction with the Earth at a radial distance of 1.76 AU and 1.9° from the Earth‐Sun line. Propagation time from ACE at 0.99 AU to NEAR indicates the cloud did not decelerate significantly between the Earth and 1.76 AU. Using a non‐force‐free, kinematic flux rope model we find the rope contained 130 TWb of magnetic flux, was oriented with clock and cone angles of 50° and 83°, and had a radius of 0.25 AU at ACE. At NEAR its radius had expanded to 0.43 AU. Simultaneous modeling of ACE and NEAR data indicate the axial and poloidal magnetic fields vary as R−1.4 and R−1.2 where R is heliocentric distance. Magnetosheath thicknesses of 0.14 AU and 0.23 AU indicate the rope cross section is elongated normal to the cloud axis and the radial direction.

Magnetic defectoscope with permanent magnets

The paper is intended for the theory of magnetic defectoscope of steel ropes, construction of this equipment and evaluation of measured data. The detector module consists of magnetization head, sensing system and holder with optoelectronic rotary increment encoder. The wavelet transform — a new and promising method for defectoscope signal processing — is presented. It enables to specify the changes of the rope cross-section with an accuracy level better than 0.5%.

Determination of flaws located at different depth levels in the cross-section of steel rope

Signals received from the magnetic testing of steel rope vary depending on the location of the defect in the rope's cross-section. Measurements of the radial and tangential components of the leakage flux performed with a single Hall-effect probe have shown significant variations of the distribution of these components around the rope. The Hall-effect sensor, built in such a way that it measures the average value of the tangential component, indicates stronger and narrower signals from defects positioned closer to the rope's surface. This effect can be used to determine the depth of the flaw's location, which is especially useful in the testing of locked-coil ropes.