Analysis on Motion and Cable Dynamic Tension for An ALT-Tanker System

A two-degree freedom model for an ALT-tanker system is established corresponding to the pitch of the ALT and the surge of the tanker.Tension in the mooring cable between the ALT and the tanker is represented by an unsymmetrical,piecewise-nonlinear function.Wave load on the tower is evaluated by use of the Morison equation.The first order wave load acting on the tanker is calculated by the linear diffraction theory based on the 2-D Helmholtz equation,and the near field approach of Pinkster is used to evaluate the second order drift force.The dynamic equation of motion is established based on the principle of D＇lembert.Dynamic response and cable tension of a mooring system composed of an 88.4 m ALT and a 100000 t grade tanker are calculated.The influence of wave frequency,wave excitation amplitude,wind and current force on ALT-tanker motion and cable tension is discussed.

Rapid Optimization of Tension Distribution for Cable-Driven Parallel Manipulators with Redundant Cables

The solution of tension distributions is infinite for cable-driven parallel manipulators（CDPMs） with redundant cables. A rapid optimization method for determining the optimal tension distribution is presented. The new optimization method is primarily based on the geometry properties of a polyhedron and convex analysis. The computational efficiency of the optimization method is improved by the designed projection algorithm, and a fast algorithm is proposed to determine which two of the lines are intersected at the optimal point. Moreover, a method for avoiding the operating point on the lower tension limit is developed. Simulation experiments are implemented on a six degree-of-freedom（6-DOF） CDPM with eight cables, and the results indicate that the new method is one order of magnitude faster than the standard simplex method. The optimal distribution of tension distribution is thus rapidly established on real-time by the proposed method.

Efficient modeling of cable-pulley system with friction based on arbitrary-Lagrangian-Eulerian approach

In conventional modeling of a cable-pulley system, the cable must be finely meshed with Lagrangian elements for valid contact detections with pulleys, leading to extremely low efficiency. The sliding joint method based on the arbitrary-Lagrangian- Eulerian （ALE） formulation still lacks an efficient cable element, and in particular, modeling of friction between a sliding joint and the cable has not been studied. This paper presents efficient multi-body modeling of a cable-pulley system with friction. A variable- length cable element with a node movable along the cable, which is described with ALE, is developed to mesh the cable. A transitional cable element is then proposed to model the contact part of the cable by fixing its two nodes to the two corresponding locations of the pulley. Friction of the cable-pulley is derived as a simple law of tension decay and embedded in the multi-body system modeling. It is simplified as a generalized friction force acting only on the arc-length coordinate. This approach can use a rough mesh on the cable, and is free of contact detections, thus significantly saving computation time. Several examples are presented to validate the proposed method, and show its effectiveness in real engineering applications.

Dynamic properties analysis of a stay cable-damper system in consideration of design and construction factors

A numerical solution based on the Steffensen stable point iterative method is proposed to resolve the transcendental frequency equation of a stay cable-damper system. The frequency equation, which considers clamped supports and fl exural rigidity of the cable, is intended to investigate the infl uence of the parameters of the cable damper system on its dynamic characteristics. Two factors involved in the design and construction phases, the damping coeffi cient induced by external dampers and the cable tension, are the focus of this study. Their impact on modal frequencies and damping ratios in these two phases of cable-damper systems are investigated by resolving the equation with the proposed solution. It is shown that the damping coeffi cient and cable tension exert more noticeable effects on the modal damping ratios than on the modal frequencies of stay cable-damper systems, and the two factors can serve as design variables in the design phase and as adjustment factors in the construction phase. On the basis of the results, a roadmap for system-level optimal design of stay cable-damper systems that can achieve global optimal vibration suppression for the entire bridge is proposed and discussed.

TIME-DOMAIN RESPONSES OF IMMERSING TUNNEL ELEMENT UNDER WAVE ACTIONS

The time domain responses of the tunnel element under wave actions during its immersion are investigated based on the linear wave diffraction theory. The integral equation is derived by using the time-domain Green function that satisfies the free water surface condition in the finite water depth, and is solved by the boundary element method. The motion equations of the tunnel element are solved by the fourth order Runge-Kutta method. A comparison between the computed and measured results reveals that the numerical model can effectively simulate the motion responses of the tunnel element and the cable tensions when the motions of the tunnel element are within some limit. Taking the tunnel element of 100 m in length, 15 m in width and 10 m in height as an example, the computational results of the motion responses of the tunnel element and the cable tensions in different immersing depths are obtained under different incident wave conditions.

On the dynamics of the gravitational lifting system in the deep sea mining industry

The dynamics of the gravitational lifting system of the deep sea mining industry is demonstrated in this article.A simplified dynamic model is obtained when gravity,buoyancy and drag force are the major concerns.By quantitative analysis,different variables like bucket size,distribution distance,and filling rate are considered to measure their influence on lifting speed and production rate,which ends up with that the most influential factor is the bucket size,and it has a positive correlation with both the two targets:lifting speed and production rate.Due to the breaking strength of the cable wire rope,a feasible design of such a lifting system should take the tension force into consideration.Hence,the feasibility is also examined and a conclusion is summarized that a combination of the bucket size and the distribution distance should be optimized according to the concrete working conditions.