Study On Parametric Roll And Its Rudder Stabilization Based On Unified Seakeeping And Maneuvering Model

The International Maritime (IMO) has being dedicated in the development of secondgeneration intact stability criteria. This paper presents a model for the simulation andstabilization of parametric roll considering ship sea-keeping, maneuvering andcontrol in regular head seas. In the real-time simulation, the frequency-domainpotential terms calculated by strip theory are transferred to time-domain, and therestoring forces and wave exciting forces (FK force) are calculated non-linearlythrough pressure integration on instantaneous wetted surfaces. Meanwhile,maneuvering motion is calculated based on the MMG Model. Finally the seakeepingand maneuvering model are combined together in the same coordinate based on theUnified Theory. The so-called6-DOF unified model can be applied to investigatethe influence of maneuvering motion, propeller and rudder on parametric roll. Themodel is also validated through the comparison with experiment.Based on the6-DOF model, a simplified3DOF model is applied to simulateparametric roll motion of three containerships with different main particulars.Results show that wave steepness and block coefficient cause GM variation which isimportant for the occurrence of parametric roll. And ship speed, roll moment ofinertia and GM height change the relationship between encounter frequency and rollnatural frequency which is also important for the occurrence of parametric roll. Then,through the comparison between the6-DOF unified model and the3-DOFsimplified model, it is found that time-varying ship speed causes smaller maximumroll amplitude than constant ship speed.Parametric roll in random seas is also investigated based on the6-DOF unifiedmodel. The influence of significant wave height is investigated. Accordingly theprobabilistic property of parametric roll in random seas is also discussed. Finallybased on the6-DOF unified model, rudder is applied to stabilize parametric rollwhile keeping the ship’s course simultaneously. The controller is designed using traditional PID method. Results show that rudder roll stabilization using PD controlscheme can prevent parametric roll from happening. Moreover, early controllertrigger-on time can get a better roll reduction rate with smaller rudder angle.Meanwhile, it is found that even at low ship speed rudder roll stabilization can alsobecome effective in parametric roll reduction, which is different from the notion intraditional rudder roll stabilization.