New Construction of Reference Frame for Underwater Cable

Abstract

The choice of reference frame applied in a multibody system and finite element method analysis assists in describing the motion of bodies. Two non-collinear vectors are prerequisite for the creation of a local reference frame for three-dimensional cases. The Frenet frame, which is constructed with tangential and normal vectors, is widely used for continuous, differentiable space curves, and the local reference frame for underwater cable systems. However, because underwater cables experience external loads originating from the surrounding environment, it is inappropriate to only treat an underwater cable as a spatial curve. Furthermore, the lumped-mass method involves classical discretized modeling, which is not suitable for continuous, differentiable space curves, and its application complicates the calculation of rotational transformation matrices. This paper proposes a new method for the construction of local reference frames which considers both the cable geometry and external environment. The model of the cable consists of discretized cable elements, of which the orientation of each cable element is described by vectors that describe the local reference frame. Taking advantage of the expression of hydrodynamic drag forces, this paper provides the prerequisite for two non-collinear vectors by replacing the normal vector with one representing the relative velocity of the fluid. The construction of local reference frames is meant to easily express all the loads acting upon a cable. To reveal the advantages of this new local reference frame, we create three classifications for the loads acting upon the cable. Because the axial extension occurs along the orientation of the cable element, the calculation of the first type of loads benefits from the Frenet frame according to the classification. Meanwhile, both the first and second types of loads are expressed easily and accurately with respect to the new local reference frame. Because of the participation of relative fluid velocity in our reference frame, the formulation of the hydrodynamic drag forces can be simplified and its accuracy improved. Moreover, the calculation of the rotational transformation matrix is made less complex and the computational error is reduced. The cable model created by this new reference frame is compared with that based on a Frenet frame and the commercial simulation code ProteusDS. The simulation results show that cable modeling using our novel reference frame is much more stable and accurate than that using a Frenet frame.