Torque in mooring chain. Part 1: Background and theory

Chain in both its forms - common (or stud-less) and stud-link - has many engineering applications. It is widely used as a component in the moorings of offshore floating systems, where its ruggedness and corrosion resistance make it an attractive choice. Chain exhibits some interesting behaviour in that when straight and subject to an axial load it does not twist or generate any torque, but if twisted or loaded when in a twisted condition it behaves in a highly non-linear manner, with the torque dependent upon the level of twist and axial load. Clearly an understanding of the way in which chains may behave and interact with other mooring components (such as wire rope, which also exhibits coupling between axial load and generated torque) when they are in service is essential. However, the sizes of chain that are in use in offshore moorings (typical bar diameters are 75 mm and greater) are too large to allow easy testing. This paper, which is in two parts, aims to address the issues and considerations relevant to torque in mooring chain. The first part introduces a frictionless theory that predicts the resultant torques and 'lift' in the links as non-dimensionalized functions of the angle of twist. Fortran code is presented in an Appendix, which allows the reader to make use of the analysis. The second part of the paper presents results from experimental work on both stud-less (41 mm) and stud-link (20.5 and 56 mm) chains. Torsional data are presented in both 'constant twist' and 'constant load' forms, as well as considering the lift between the links.

Torque in mooring chain. Part 2: Experimental investigation

Chain is a commonly used component in offshore moorings where its ruggedness and corrosion resistance make it an attractive choice. Another attractive property is that a straight chain is inherently torque balanced. Having said this, if a chain is loaded in a twisted condition, or twisted when under load, it exhibits highly non-linear torsional behaviour. The consequences of this behaviour can cause handling difficulties or may compromise the integrity of the mooring system, and care must be taken to avoid problems for both the chain and any components to which it is connected. Even with knowledge of the potential problems, there will always be occasions where, despite the utmost care, twist is unavoidable. Thus it is important for the engineer to be able to determine the effects. A frictionless theory has been developed in Part 1 of the paper that may be used to predict the resultant torques and movement or 'lift' in the links as non-dimensional functions of the angle of twist. The present part of the paper describes a series of experiments undertaken on both studless and stud-link chain to allow comparison of this theoretical model with experimental data. Results are presented for the torsional response and link lift for 'constant twist' and 'constant load' type tests on chains of three different link sizes.

Predictive computed-torque control of a PUMA 560 manipulator robot

This paper describes the integration of constrained predictive control and computed-torque control, and its application on a six degree-of-freedom PUMA 560 manipulator arm. The real-time implementation was based on SIMULINK, with the predictive controller and the computed-torque control law implemented in the C programming language. The constrained predictive controller solved a quadratic programming problem at every sampling interval, which was as short as 10 ms, using a prediction horizon of 150 steps and an 18th order state space model.

Assessing wind profile effects on the global atmospheric torque

The impact of a new approach to the evaluation of surface gravity wave drag (GWD) is assessed. This approach uses linear theory, but incorporates the effects of wind profile shear and curvature, by means of a second-order WKB approximation. While the theory predicts the possibility of either drag enhancement or reduction, depending on the wind profile, results obtained with the ERA-40 reanalysis data clearly indicate the predominance of local drag enhancement. However, the global impact of shear on the atmospheric axial GWD torque comes mostly from regions with predominantly easterly flow, contributing to a slight reduction of the bias found in different studies of the global angular momentum budget. The relative correction due to shear on linear GWD is found not to depend too strongly on the levels chosen for the computation of the low-level wind derivatives.