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 Plucker 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.

Keywords

• Force RAO
• ship-crane modeling
• vehicle-manipulator system
• screw theory
• Kane's equation of motion