Abstract
This research is focused on the accurate modeling of a tethered deep-sea robot system with variable-length. Since the flexible umbilical cable is influenced by the surface vessel motion, the ocean current and sea states, etc., its transient response will reduce the deep-sea robot’s stability. Thus, dynamic modeling of the elastic umbilical cable is a crucial issue. In this paper, transverse vibration of the tethered deep-sea robot system can be modelled as a one-dimensional distributed parameter system, a class of partial differential equations with nonhomogeneous boundary conditions theoretically. A new numerical scheme with B-spine wavelet on the interval (BSWI) is used to discretize and transform inhomogeneous partial differential equations into a set of ordinary differential equations and to obtain the dynamic response of the tethered deep-sea robot system with different ocean currents. Compared with conventional methods, BSWI finite element with multiresolution analysis principle can approximate the transverse vibration of the flexible umbilical cable better, and handle boundary conditions more easily. Numerical examples of different cases are analyzed in detail by the discussion of an ADAMS model, and simulation results of the ADAMS model also verify that BSWI finite element method has a desirable performance than other methods.
Highlights
A tethered deep-sea robot system, usually composed of a surface vessel, an umbilical cable, and an underwater robot, is used to provide submarine exploration, seabed mineral collection, and offshore oil development, which is ascended and descended by the flexible umbilical cable as Figure 1 [1]
When the ocean current generally flows in one direction, the result of the umbilical cable is different from that produced by periodic disturbance, where the flexible umbilical cable could have spatial shape deformation under the ocean current, and it will cause the phenomenon of severe alternating stress under the high sea state [3,7]
There are three main differences between B-spine wavelet on the interval (BSWI) finite element method and other existing traditional methods: first, it solves the equation directly without converting the non-homogeneous equation into homogeneous partial differential equation; second, the wavelet coefficients can be mapped into physical space by the constructed transformation matrix; the mixed
Summary
A tethered deep-sea robot system, usually composed of a surface vessel, an umbilical cable, and an underwater robot, is used to provide submarine exploration, seabed mineral collection, and offshore oil development, which is ascended and descended by the flexible umbilical cable as Figure 1 [1]. Compared with Galerkin method, FEM has the advantage the C0 type element requires the least zero-order continuously differential interpolation element(i.e., function does notthe need to satisfy theasboundary conditions. Many current research works have been carried out on numerical simulation of the type requires the least one order continuously differential interpolation funct kinematic and dynamic characteristics of the umbilical cable in the tethered deep-sea robot reduceofcomputation cost, the appropriate type selected system the process of underwater operation. There are three main differences between BSWI finite element method and other existing traditional methods: first, it solves the equation directly without converting the non-homogeneous equation into homogeneous partial differential equation; second, the wavelet coefficients can be mapped into physical space by the constructed transformation matrix; the mixed.
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