Variable-Length Cable Dynamics of Payout and Reel-in With a Vertically Tethered Underwater Drill Rig

A new dynamic model of the variable-length cable used in a vertically tethered underwater drill rig is presented in this paper, which also includes the dynamics of its fixed-length counterpart. First, the differential equation of the variable-length cable is derived through the theorem of linear momentum, and its finite element formulation is obtained by the Galerkin weighted residual method correspondingly. Second, the implicit time integration formulation is derived by using the Newmark-β algorithm. And then the proposed model is validated by comparing with the experimental data of the fixed-length underwater steel-armored umbilical cable of a work-class Remotely Operated Vehicle (ROV), and the variable-length underwater cables made of nylon and rubber, respectively, and the calculated results show good agreement with the experimental data. Third, the variable-length cable dynamics of payout and reel-in of the underwater drill rig is analyzed under three kinds of sea conditions, i.e., still water, sinusoidal heave, and the actual heave, respectively. Some conclusions are summarized in the end.