Dynamics of a marine lash system with a flexible link

Abstract

Admiral Makarov National University of Shipbuilding, MykolaivНациональный университет кораблестроения имени адмирала Макарова, г. Николаев abstract. In connection with increase in operating depths and expansion of the scope of use of marine lash systems (MLS), it is urgent to improve the theory and methods of designing their flexible links (FL) and refine the existing calculation methods. The existing calculation and design methods are either simplistic and do not take into account the actual loads and the nature of loading of the MLS FL or are rather complicated and cumbersome for design and construction kits and require considerable timing for their implementation. The mathematical model of the MLS dynamics includes not only the FL equations, but also the equations of dynamics of the tugboat and the towed UV. Their movement determines the boundary conditions at the FL nodes with the numbers i = 0 and i = N. The FL node with the number i = 0 is fixed to the tugboat, and the FL node with the number i = N is fixed to the UV. Dynamics of the tugboat and that of the towed UV differ only in their parameters, thus, the equations of their dynamics have the same form. Let us assume that the tugboat and the UV are absolutely rigid rods. Their position in space is determined by the coordinates of their center of mass (х i , y i , z i ), the course angle (φ k i ), the trim angle (φ d i ) and the roll angle (φ kr i ). The length of the rods (L i ) is equal to the length of the tugboat or the UV. The position of the center of mass is determined by the distance from the stern (L ki ) to it. Based on the developed mathematical model, there has been determined a system of equations that describes the FL element dynamics as the result of impact of external forces and reactions of stretching, bending and turning. An algorithm for simulating the FL dynamics is obtained, which makes it possible to perform calculation of the dynamics of the MLS FL and further proceed to development of a computer program describing the MLS dynamics. Keywords: marine lash system (MLS) dynamics; marine lash system (MLS); flexible links (FL); tugboat; underwater vehicle (SV); algorithm of the marine lash system (MLS) dynamics; computer program.Аннотация. На основе разработанной математической модели определена система уравнений, описывающая динамику элемента ГС в результате действия на неё внешних сил и реакций растяжения, изгиба и поворо-та. Получен алгоритм моделирования динамики ГС, позволяющий выполнять расчёты динамики ГС МПС и в дальнейшем перейти к разработке компьютерной программы, которая описывает динамику МПС. Ключевые слова: динамика морской привязной системы; морская привязная система; гибкая связь; судно-носитель; подводный аппарат; алгоритм динамики морской привязной системы; компьютерная программа.Анотація. Розроблено алгоритм динаміки морської прив'язної системи (МПС), який дає можливість викону-вати розрахунки динаміки гнучкого зв'язку (ГЗ), судна-носія і буксируваного підводного апарата, а на його основі створити комп'ютерну програму...

Construction of a mathematical model to describe the dynamics of marine technical systems with elastic links in order to improve the process of their design

“…We tested the mathematical model of the tethered system and the calculation algorithm based on the examples of a stationary towing mode of three types of tethered systems. The results of our modeling are consistent with the calculations given in [12,13,15,16].…”

“…This principle is taken into consideration if the Courant-Friedrichs-Levy condition is met, which determines the stability of the iterative computational process by formulae (45) and (47). According to the condition by Courant-Friedrichs-Levy [13] / ,…”

Improving the designing of marine tethered systems using the principles of shipbuilding 4.0

“…The limitation of this study is the complexity of the mathematical apparatus used to develop an MM for the description of the dynamics of MTS with FL [5,7,10]. This study should be advanced towards further improvement of MM, SW, and SMC.…”

“…The derived MM to describe the dynamics of MTS FL and MTS with FL [7] have allowed the development of SMC, which makes it possible, in the design process:…”