Dynamics simulation of low tension tethers

This paper presents the development of a mathematical model and computer simulation of an ROV tether operating in low-tension situations. This model makes use of a lumped mass approach in which the ROV tether is considered to be a system of point masses connected by visco-elastic springs. Using this approach, the formulation of the equations of motion for each of the point masses is explicit. The positions and velocities of the point masses at time t are used to calculate the internal and hydrodynamic forces which are, in turn, used to solve for the accelerations. Direct numerical integration is then used to calculate the positions and velocities at a time t+/spl Delta/t. Although this formulation is stable when the tension in the tether disappears, it is necessary to include bending effects in order to generate realistic results for low-tension maneuvers. The present work accomplishes this by first assuming that all sections of the tether have negligible rotational inertia. As a result, the curvature in the tether at any point can be related to the internal bending forces. This relation is then discretized using the Galerkin method of weighted residuals, to allow calculation of the bending forces at the node points. The mathematical model was implemented in C/C++ and was used to model several tether maneuvers. In a static validation test case in which a constant bending moment was applied at the ends of the discretized tether, the model agreed within 4% with the exact analytical solution. To facilitate a qualitative review of the bending model, the modeled tether was harmonically oscillated at one end. This generated slack, coiled sections of tether which showed a strong tendency to uncoil and straighten the tether.