Вестник МГТУ. 2018, №4.

Пашенцев С. В. Моделирование циклических реверсивных движений судна... УДК 519.8:[629.543.017.3:629.5.035.5] S. V. Pashentsev Modelling cyclic reverse movements of the vessel using modified Lammeren's curves of screw action In our national practice, the screw action curves are traditionally used either for positive values of the screw speed n and the vessel's velocity v, or when one of these characteristics of the movement is negative. Consequently, the used curves of the screw action do not allow to create computer simulators for testing specific maneuvering tasks with reversible moves. The purpose of the work is to study the opportunities of mathematical modelling of the vessel's reverse movements, when the propeller advance of the fixed pitch screw is constantly changing. In foreign sources, really universal Lammeren's curves of screw action can be found. The specificity of these curves is that the introduction to them is performed not due to the pitch ratio itself, but due to the angle в of the direction incident to the propeller blade. This angle is determined by using tangent tg( P ) = v/(0.7 nnD), and it is sensitive to the change of sign o f both the ship's velocity v and the revolution speed n . Therefore, these curves are presented as functions of the angle в in the range of angles 0 ° -360 ° . These curves are obtained and described by Lammeren as the results of processing experimental data concerning the thrust and the screw torque and are approximated by Fourier series, in which 20 terms are kept. These curves can be used as universal ones. This allows to integrate a system o f two equations: the motion of the vessel and the rotation of the screw with arbitrary signs of these movements' direction by means of MathCad. By setting the law regulating the speed of the ship engine, it is possible to simulate arbitrary maneuvers of the vessel with any change of direction. The considered approach to modeling has been tested in the paper and implemented in the interface control for vessel maneuvering within the computer simulator. Key words: reverse propulsion, mathematical modelling, the curves of screw action, Lammeren's curves of screw action. Introduction Over the years screw action curves have been used for solving problems connected first of all with the ship's propulsion. In these calculations the ship's velocity and the screw speed are positive, and the advance ratio does not change its sign. Therefore, only the action curve in the first quadrant has been used where "advance ratio is thrust and torque ratios". In modern conditions, when the hydrocarbon production is carried out offshore, the problem of maneuvering vessels with changing the direction of screw rotation and reversing has become extremely acute. This is a characteristic of maneuvering tankers at the oil loading terminals or during dynamic positioning of drill ships at the drilling site. It should be noted that the screw action curves which have been used in Russian research might be named semi-universal. For this particular reason such modified advance ratios as "Lavrentiev advance ratio" ,/ Л and "Hoffman advance ratio" J have been introduced [1]: J = v A ( v A ) 2 + ( nD ) 2 J r = nD . ( v A ) + ( nD ) The former one solves the problems of changing the sign of ship's velocity, the latter deals with changing the sign of screw speed. And even though the advance ratio curves are plotted for them, they do not solve the problem of arbitrary combinations of the ship's velocity and screw rotation signs. The main objective of this research is the development and improvement of computer simulator programmes which allow to practice maneuvering of the above types. Accordingly, the purpose of this work is investigating the perspectives of mathematical modelling of vessel's reverse movement with constant changing the advance ratio of a fixed pitch screw. In foreign sources [2], Lammeren's action curves are mentioned as the result of systematic B-series screws tests in Wageningen Ship Model Basin (the Netherlands). The specificity of these curves is that the introduction to them is performed not due to the pitch ratio itself, but the angle в of the direction of the flow running onto the blade. This angle is determined by using tangent tg( e ) = v/(0.7nnD). It is sensitive to the change of the sign of both the ship's velocity v and the revolution speed n, if the inverse tangent is calculated taking into account the quadrant o f its solution. Therefore, these curves are presented as functions of angle в in the range of angles 0 ° -360 ° . They are obtained and described by Lammeren as the results of processing experimental data concerning the thrust and the screw torque and are approximated by Fourier series with 20 terms. These curves can be used as universal ones, which allows to integrate a system of two equations - the motion of the vessel and the rotation of the screw with arbitrary signs of the direction of these movements - by means of the MathCad package. By setting the law regulating the speed of the ship's engine, it is possible to simulate arbitrary maneuvers of the vessel with the direction change of the vessel's movement and screw rotation. Further, this approach to modelling implemented in the interface maneuver control of a computer simulator has been developed. 566