Dynamic Interaction of a Heavy Crane and a Ship in Wave Motion

Abstract

Previous work on the dynamics of vehicle-manipulator systems is extended to offshore ships with heavy cranes. The proposed method is based on a Newton-Euler formulation where the forces of constraint are eliminated using projection matrices based on the method of Kane's equations of motion. This leads to an efficient method for developing the equations of motion of a ship with a heavy crane so that the motion of the crane influences the motion of the ship and vice versa. The calculation of the projection matrices is made efficient and intuitive by observing that the columns of the projection matrices are the screw axes of the joint twists in Plücker coordinates. Wave excitation of the ship is modeled with force RAOs based on established wave spectra. This gives a model that is well suited for design and testing of crane control systems, and for studying the feasibility of demanding crane operations in different weather conditions.The resulting equations of motion have been validated in simulation experiments for a ship with a 3 DOF heavy crane with a payload, where the ship is excited by a JONSWAP wave spectrum using a simple controller based on feedback linearization. The simulations clearly demonstrated that the ship responded in a physically meaningful way to the motion of the crane.

Determination of Reaction Forces of a Deck Crane in Wave Motion Using Screw Theory

“…The implemented vessel model is the same supply vessel model as used in Ref. [9]. The main vessel dimensions are as follows: the length between perpendiculars is 82.5 m, the breadth is 8.0 m, and the draught is 6.0 m. The mass of the vessel is 6362 mT.…”

“…In this section, the mathematical model of a ship moving in waves is presented. This is done by the well-established method where force RAOs are used to calculate the wave forces on the ship and the waves are described with the JONSWAP wave spectrum [9,17]. The JONSWAP wave spectrum describes the distribution of waves in the North Sea and is given by…”

“…This was further developed in Ref. [9], where the partial velocities and the partial angular velocities used in the derivation of Kane's equations of motion were represented by lines in Plücker coordinates [10], and this was demonstrated in the development of the equations of motion for the combined dynamics of a ship and a crane mounted on the ship.…”

“…In this work, we extend the results of Refs. [9,14], first by deriving the equations of motion for a crane and a vessel system including a roll and pitch compensation platform between the ship deck and the crane base. Next, a procedure is developed for the determination of the reaction forces between the crane and the platform and between the platform and the vessel.…”

Kinematics and Dynamics of Flexible Robotic Manipulators Using Dual Screws

“…This was used for rigid mechanisms in [20], [21], and [22], and for flexible systems in [23] and [24]. The fact that a twist is a screw given in Plücker coordinates allows for an alternative formulation in terms of screw theory [25], [26], where the geometrical interpretation of the derivations may be more evident.…”