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

Abstract

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. INDEX TERMS Cable dynamics, finite element method, marine equipment, umbilical cables, underwater cables, underwater drill rig. QINGQING CHANG received the M.S. degree in mechatronic engineering from the Shenyang Institute of Automation (SIA), Chinese Academy of Sciences, Shenyang, China, in 2011. From 2011 to 2014, she worked at the Xuzhou Construction Machinery Group (XCMG) as a Hydraulic Engineer. She then worked at the Caterpillar Technology Research and Development (China) Company, Ltd. (CRDC), from 2014 to 2016, as a Senior Hydraulic Engineer. She is currently working with the Hunan University of Science and Technology. Her current research is in underwater robotics, special hydraulic systems, construction machinery, and industrial automation.

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“…If l 1 varies little then this may be neglected [201]. In some applications cables' lengths vary a lot and this dependence becomes mandatory modeling [116,201,113].…”

“…If l 1 varies little then this may be neglected [201]. In some applications cables' lengths vary a lot and this dependence becomes mandatory modeling [116,201,113]. The Lagrange dynamics as in (1) cannot be applied directly in this case: it is necessary to add a corrective term in the dynamics [191,193], see also [192] for a short historical summary.…”

“…As alluded to above, the mass variation can be neglected if the length variation remains small (or if the cable's mass is much smaller than the hook's and payload's masses). However in some applications it may happen that the cable mass' variation is no longer negligible [113,201,67]. In this case the 2D (or the 3D) single-pendulum or double-pendulum model should reflect this mass variation, by allowing for m 1 = m 1 (l 1 ).…”

“…Cables with variable length: this may be a consequence of cable's longitudinal elasticity, or of winding mechanisms used to add a control input (see section 3.5). This is considered in robotic systems involving cables [116], in tethered systems with long hoisting ropes (marine or space applications [201,113]). In case of winding, this implies considering varying cable's total mass (depending on the length in some way) in the derivation of the dynamical equations, and a variation of the trolley's mass as well (the total mass being kept constant).…”

“…In case of winding, this implies considering varying cable's total mass (depending on the length in some way) in the derivation of the dynamical equations, and a variation of the trolley's mass as well (the total mass being kept constant). If the length variation is very small, or if the cables' total mass is small compared to the hook and payload masses, the cables' mass variation may be neglected, however [201]. This is what is done to obtain (3) as well as its double-pendulum counterpart [32, section 5.4].…”