Cable Shape Research Articles

Statics of elastic cables under 3D point forces

The catenary problem for elastic cables is extended to the case of uniformly distributed loads and point forces however oriented in space. The equilibrium equation is written in vector form and its solution, i.e. the deformed shape of the elastic cable, is obtained in closed form for the cases of uniformly distributed load, one point force and many point forces. The formulation is suitable to solve straightforwardly cable structure problems, as shown in the numerical applications.

Study on Main Cable-Shaped of Long-Span Suspension Bridge

The main cable is made of PPWS. Its large displacement and nonlinear mechanical properties are shown by their own elastic deformation and its geometry changes affecting the system balance. To get the real main cable-shaped of long-span suspension bridge, based on the finite element method, the element stiffness matrix was derived, which displacement field was same to the element shape. Then through the horizontal and vertical direction equilibrium equations were solved, the relationship between main cable shape and the system parameters was obtained. The calculation method was compiled to MATLAB 7.0 programs, and applied to ascertain the main cable-shaped of one long-span suspension bridge. When the paper calculated result was contrasted with the design value, it could be concluded that: the main cable-shaped of long-span suspension bridge could be accurately obtained by the paper method, and the method was convenient for compiling.

A Haptic-Based Approach for Cable Design and Routing in Industrial Complex Products

Cable design and routing is a time-consuming and costly process for industrial complex products, traditionally it is finished by experienced engineers through soft lead or aluminum wire fitting in physical models, or by automatic or semi-automatic computing method in CAD system, but both with little success. In this paper, a new haptic-based interactive method is proposed. After rigid product models are loaded from CAD system, a geometry modeling method is used to represent cable shape, a physics modeling method for calculating cable deformation, and a haptic modeling method for interaction and force feedback. In this prototyping system, the user can define cable position and path, change its shape and size, and then simulate the design and routing process with haptic to feel the touch, collision and force feedback.

Suspension Bridge Profiles

SummaryThe standard model of a uniform roadbed suspended from a weightless cable constrains the cable to a parabolic shape. What if the roadbed is not uniformly loaded? We characterize the shape of the suspension cable in this case, and show that, among other possibilities, a catenary may arise. Additional properties of such suspension profiles are discussed, and the work of a seventeenth century Jesuit savant makes a cameo appearance.

3-D Sensing for Flexible Linear Object Alignment in Robot Cell Production System

We have constructed 3-D sensing system for alignment of connector-fitted cables as flexible linear objects which used to be difficult to be automated at the production sites. In the system an industrial robot has a 3-D sensor and a monocular camera mounted at the hand. 3-D sensor, using space encoding method, allows the robot to make high-precision measurements of the order of sub-millimeters, but emphasis is placed on precision at the expense of fields of view. In addition, active sensing methods such as the space encoding method is hard to take measurements for black cables, as well as it has some difficulties with measurements of semitransparent plastic connectors depending on view-points. To cope with those problems, our system is such that the monocular camera on the robot is moved for motion stereo to take measurements on cable shapes; connector’s poses are coarsely estimated from the measurement results; and such view-points as will ensure stable measurements are computed by space encoding method to take precision measurements of connectors. Technical features of the system could be summarized as follows: 1) Determination of view-points to measure connectors, based on measurements of cable shapes, requires no more than two measurements, without repeated searches, to grab semitransparent plastic connectors. 2) Performance of stereo correspondence for plain or black cables, which tends to result in a failure with the aids of no more than irradiated slit patterns and epipolar constraints, has been improved through sequential correspondence inmotion image sequence and its stability evaluations. At the operation tests in the validation system, the robot is assigned a task to assemble the cables into industrial servo amplifiers available on the market, in which automatic alignment of 200 connector-fitted cables has successfully been accomplished in succession to confirm constant performance of the system.

Calculation method on shape finding of self-anchored suspension bridge with spatial cables

Based on the spatial model, a reliable and accurate calculation method on the shape finding of self-anchored suspension bridge with spatial cables was studied in this paper. On the principle that the shape of the main cables between hangers is catenary, the iteration method of calculating the shapes of the spatial main cables under the load of hanger forces was deduced. The reasonable position of the saddle was determined according to the shape and the theoretical joint point of the main cables. The shapes of the main cables at completed cable stage were calculated based on the unchanging principle of the zero-stress lengths of the main cables. By using a numerical method combining with the finite element method, one self-anchored suspension bridge with spatial cables was analyzed. The zero-stress length of the main cables, the position of the saddle, and the pre-offsetting of the saddle of the self-anchored suspension bridge were given. The reasonable shapes of the main cables at bridge completion stage and completed cable stage were presented. The results show that the shape-finding calculation method is effective and reliable.

Forward and inverse problems in towed cable hydrodynamics

This paper addresses the problem of reconstructing the velocities of the ocean currents impinging on a towed streamer cable during an offshore seismic survey. This study considers a two-dimensional model describing the motion of a flexible, inextensible cable in the presence of hydrodynamic drag forces in an incompressible fluid. In the first part the forward model is introduced and then solved to yield the cable's velocity, curvature and tension in the knowledge of the towing vessel motion and the hydrodynamic loads applied. In sequence, we formulate the inverse problem of inferring the ocean current velocities from discrete samples of the cable's shape and tension and show that this is rank deficient and ill-posed. In approaching the inverse problem a numerically stable algorithm is adopted based on generalized Tikhonov regularization, in the context of robust differentiation of discrete noisy signals. In order to demonstrate the practical performance of the scheme, some examples of ocean current reconstructions obtained using simulated noisy data are presented.

Motion Stereo including Tracking Stability Analysis for 3-D Cable Reconstruction

We propose a novel approach to the three-dimensional reconstruction of flexible cables for applications in factory automation, such as cable handling and connecter insertion using robotic arms avoiding conflicts among multiple cables. The approach is based on motion stereo with a single vision sensor. To solve the stereo correspondence problem efficiently and effectively, feature-point projection with slit beams and a feature tracking algorithm based on a robust image-matching method is applied. In addition, we define the tracking stability of the feature points in order to reject defective stereo correspondences. Experiments using these methods demonstrate that an arched cable shape can be reconstructed to an accuracy of 1.5%.

NUMERICAL INVESTIGATION OF SEABED INTERACTION IN TIME DOMAIN ANALYSIS OF MOORING CABLES *

In this paper, an efficient two-dimensional finite element model for numerical analysis of mooring cables and seabed interaction has been built. Geometric shape and dynamics of mooring cables are computed in time domain, accounting for the motions of the moored sturcture. In the model, a hybrid beam element is employed to simulate the mooring cable while the seabed is simulated by application of different soil constitutive models. After the elastic and elastic-plastic soil constitutive models have been used for computation, tensions and offsets of mooring cables at fairlead point are also compared accounting for friction effect between cables and seabed. Both transversal and longitudinal behaviors are studied at different water depths.

SHAPE DETERMINING OF A LOADED CABLE VIA TOTAL DISPLACEMENTS

Cable structures are very efficient (in economic aspect) when applied to cover large spans. The cable structure consists of a single cable or a network of cables. The cable attractive feature is the highest ratio of strength to weight amongst other carrying structural elements, usually applied in engineering practice. But a cable is a specific structural element able to response only one type of deforming ‐ tension (flexural rigidity actually vanishes). Therefore, when loaded a cable shapes the form to resist tension only. This adaptation is followed by large nonlinear displacements. Thus, the nature of geometrical nonlinear cable behavior is quitie a different from that of rigid structural elements. Both elements response via small deformations when loaded, but large displacements of a cable are conditioned by its adaptation to loading, and those of rigid structural elements ‐ by actual deformations. One can also note that deformations of a cable are significantly less than those of rigid structural elements, but at the same time actual cable displacements are significantly larger. Thus, the main disadvantage of a cable structure is its response to loading by large displacements caused by asymmetric loading component (usually met in engineering practice, e.g. the design of suspension bridges, coverings of stadium, etc). Therefore stiffness conditions predominate in the actual codified cable design. Having identified governing factors conditioning displacement magnitudes one can introduce the constructional means/solutions assigned to reduce them if required. Therefore the evaluation of cable displacements by a reliable and sufficiently exact method compatible with the calculation of actual engineering structures is under current necessity. When analyzing total displacements the principle of superposition is employed in a special sequence. Total displacement is split into two components: kinematic and elastic. The first component represents cable form shaping the loading, the second one is conditioned by elastic deformations. Any point displacement of an asymmetrically loaded cable can be expressed via its middle span. The developed analytical expressions to evaluate middle span displacements are presented. They enable to identify maximal displacements and their locations. The developed analytical method for total displacements evaluation is tested numerically. The comparative analysis in respect of the influence of various parameters conditioning displacement magnitudes is performed. The displacement evaluation errors, their causality conditioned by the application of approximate‐ widely applied engineering methods, are discussed.

Limit–cycle oscillations of a heavy whirling cable subject to aerodynamic drag

In this paper a simple experimental system consisting of a length of cable, fixed to the edge of a rotating disc at its upper end, and free at its lower end or with a point mass (drogue) attached there, is described. This system exhibits a rich variety of bifurcation behaviours as the length of cable, angular speed of the fixed end, mass of the drogue and elasticity of the cable is varied. Bifurcation diagrams for thequasistationaryconfigurations (cable shapes that appear stationary with respect to the rotating reference frame) are described. Linearized stability analyses of these quasistationary balloons are compared with solutions to the full time–dependent equations of motion.It is shown that there is an exchange of stability at the turning points of the quasi–stationary bifurcation curves, and that Hopf bifurcations occur at otherwise undistinguished points of these curves. It is shown that limit–cycle oscillations of the system occur at angular speeds corresponding to points on the bifurcations curves in the neighbourhood of the Hopf bifurcation points. These oscillations have been observed experimentally.

Rain-wind induced vibration of inclined stay cables -Part I: Experimental investigation and physical explanation

The rain-wind induced vibration of stays is a phenomenon discovered recently and not well explained yet. As it is influenced by a wide range of physical parameters (cable size and shape, wind speed, direction and turbulence, rain intensity, material repellency and roughness, cable weight, damping and pre-strain), this peculiar phenomenon is difficult to reproduce in laboratory controlled conditions. A successful wind tunnel experimental campaign, in which some basic physical quantities were measured, allowed an extensive analysis as to identify the parameters of the rain-wind induced excitation. The unsteady pressure field and water thickness around a cable model were measured under rainy-excited conditions. The knowledge of those parameters provided helpful information about the air-flow around the cable and allowed to clarify the physical phenomenon which produces the excitation.

Effect of electromagnetic force on the pressure drop and coupling loss of a cable-in-conduit conductor

In the central solenoid (CS) insert experiment performed with the International Thermonuclear Experimental Reactor CS model coil, significant changes in the pressure drop and coupling losses were observed during coil energization. This phenomenon was quantitatively analyzed from the viewpoint of the deformation of the cable shape in the CS insert conductor due to an electromagnetic force acting on the cable. A new calculation model was proposed to provide the relation between the electromagnetic force and hydraulic characteristics of the conductor. Calculation results indicated that there seemed to be a gap of 1.3 mm between the cable and jacket created by the electromagnetic force when the CS insert was operated at 40 kA and 10 T, which can cause the decrease of the pressure drop by 12% and also the decrease of the local void fraction of the cable from 36.3% to approximately 34%. The latter well explained the increase of coupling losses. A local void fraction of 34.5% is suggested from the calculation in order both to reduce the amount of deformation and to maintain the coupling losses at acceptable level for this type of large current-carrying conductor.

Three-dimensional non-linear coupling and dynamic tension in the large-amplitude free vibrations of arbitrarily sagged cables

This paper presents a model formulation capable of analyzing large-amplitude free vibrations of a suspended cable in three dimensions. The virtual work-energy functional is used to obtain the non-linear equations of three-dimensional motion. The formulation is not restricted to cables having small sag-to-span ratios, and is conveniently applied for the case of a specified end tension. The axial extensibility effect is also included in order to obtain accurate results. Based on a multi-degree-of-freedom model, numerical procedures are implemented to solve both spatial and temporal problems. Various numerical examples of arbitrarily sagged cables with large-amplitude initial conditions are carried out to highlight some outstanding features of cable non-linear dynamics by accounting also for internal resonance phenomena. Non-linear coupling between three- and two-dimensional motions, and non-linear cable tension responses are analyzed. For specific cables, modal transition phenomena taking place during in-plane vibrations and ensuing from occurrence of a dominant internal resonance are observed. When only a single mode is initiated, a higher or lower mode can be accommodated into the responses, making cable spatial shapes hybrid in some time intervals.

Steady-state bifurcations and dynamical stability of a heavy whirling cable acted on by aerodynamic drag

In this article the problem of whirling a heavy flexible cable subject to aerodynamic drag is considered. The top end is moved in a circular path and the bottom end is free. This simple system is found to exhibit remarkably rich bifurcation behaviour as the angular speed, air drag and radius of the circular path are varied. Bifurcation diagrams for the quasi–stationary configurations (cable shapes that appear stationary relative to a reference frame rotating with the same angular speed as the cable) are described. A linearized stability analysis of these quasi–stationary solutions is also described. It is shown that there is an exchange of stability at the turning points of the quasi–stationary bifurcation curves, and a transition to unstable behaviour at sufficiently large angular frequency. There is also unstable behaviour between undistinguished frequencies along the solution branches, the size and number of these regions of instability on each branch increasing as the circular path radius is increased. It is demonstrated that these unstable regions are removed for sufficiently large air drag.

Calculation method of main cable shape of Suspension bridge

Calculation method of main cable shape of Suspension bridge

THE FINITE ELEMENT METHOD FOR HYDROELASTIC INSTABILITY OF UNDERWATER TOWED CYLINDRICAL STRUCTURES

The dynamics of underwater towing of flexible cylindrical structures belongs to the class of fluid–structure interaction problems commonly referred to as “cylinders in axial flow”. The serious concern in such towing operations is the various types of hydroelastic instabilities exhibited by the structure at certain critical tow speeds. In practice, reliable prediction of tow configurations and stability characteristics of such towed systems can lead to optimum deployment of cable scope and control of tow speed. The present investigation is concerned with the development of a comprehensive linear finite element method for the dynamics of the flexible towed cylinder with focus on the stability behaviour. The finite element approximation is derived from a variational statement of the problem based on Hamilton's principle. The various structure- and fluid-related matrices as well as matrices resulting from boundary terms have been derived, resulting in a complex unsymmetric eigenvalue problem. Exhaustive validation and convergence studies show that the comparisons between finite element and analytical results are almost exact. Using the finite element code, the hydroelastic instability of a ship-towed array system has been analyzed. The effect of cable scope and shape of the downstream end on stability have been examined.

Hanging shapes of nonuniform cables

Using a variational approach, I derive the equation governing the equilibrium shape of an inelastic cable with an arbitrary mass distribution hanging freely under uniform gravity except for being supported at both ends. I then develop a parametric solution to this shape equation, giving the coordinates of points on the curve assumed by the cable in terms of the distance along the cable. Using numerical integration to determine values, I plot several examples of the cable’s shape for linearly and exponentially increasing density. I also consider the inverse problem of determining the mass distribution which gives rise to a specified shape. I compare the distributions yielding a semicircle, a parabola, and a catenary.

Neural network system using the multi-layer perceptron technique for the recognition of PD pulse shapes due to cavities and electrical trees

A neural network system, utilizing the multi-layer perceptron approach has been applied to distinguish between power cable insulation partial discharge pulse shapes that are characteristic of cavities and electrical trees. The neural network was found to be capable of recognizing the differences in PD pulses produced by single cavity and electrical tree discharge sources. It also could differentiate between the discharge pulse forms emanating from electrical trees of different lengths; likewise, it was able to recognize changes in the shape of the discharge pulses with time due to aging effects. However, as these recognition capabilities relate only to comparisons of single discharge sources on a one-to-one basis, the application of neural networks to PD pulse shape recognition on actual power cables, where a number of different discharge sources may be discharging simultaneously, is quite premature at this time without more detailed exploratory work on complex discharge patterns. >

Measurements of cable shape in a cross current

In a previous paper, Krail and Brysk (1989), we gave a theory for the curve shape of a streamer in a constant cross current. The curve shape predicted by this theory was compared with the shape of a towed streamer cable determined from a small number of field measurements. The agreement was judged to be fair. At the conclusion of the paper we promised to do a more extensive comparison with field measurements.