НОВІ МАТЕМАТИЧНІ МОДЕЛІ КОЕФІЦІЄНТУ УПОРУ І КОЕФІЦІЄНТУ МОМЕНТУ НА ВАЛУ ГРЕБНОГО ГВИНТА СУДНА

Abstract

Solving the problems of course stabilization of the ship, dynamic positioning, the ship divergence dynamics, the construction of effective simulators and autopilots are not possible without the use of adequate mathematical models of the dynamics of the ship. The presence of the latter is also a necessary condition for studying various ship maneuvers, in particular, such as circulation, Kempf zigzag, slowing down, acceleration, etc. Improving control methods, including trends towards full autonomy of ships, necessitates constant improvement of mathematical models of the ship's propulsion complex. The general mathematical model of ship dynamics includes mathematical models of inertial and non-inertial forces acting on the ship. The latter include, in particular, hydrodynamic forces on the hull, forces caused by the operation of the ship's rudders and propellers, aerodynamic forces acting on the ship's hull, and forces caused by the ship's sailing rig. Mathematical models for non-inertial forces have an empirical multilevel character, include mathematical models of various quantities and parameters, and are built on the basis of experimental data processing or methods of computational hydrodynamics. Therefore, the improvement and refinement of each such model leads to the improvement of the mathematical model as a whole and is an important scientific and actual practical task. An important task is also to bring the specified mathematical models to a form that is convenient for use. In this work, new adequate, easy-to-use, mathematical models of the thrust coefficient of the propeller and the torque coefficient on the propeller shaft were obtained using regression analysis methods, and their excellent consistency with known mathematical models was shown on specific examples. For the main types of commercial vessels, the numerical values of the coefficients of the models are given, and the values of the propeller advance ratio of the zero thrust and zero torque on the propeller shaft are determined. This made it possible to obtain the condition of normal accident-free operation of the propulsion complex of the ship, which must be satisfied by the speed of the ship and the frequency of rotation of the propeller shaft, at different values of the drift angle and angular speed. Keywords: mathematical models, ship propellers, propeller thrust coefficients, propeller shaft torque coefficients.