Development of the mathematical modeling method for dynamics of the flexible tether as an element of the underwater complex

Abstract

a result, these equations are strongly coupled, which has to be taken into account when simulating UCFTs. Due to equations nonlinearity usually it is impossible to find an analytical solution of such a complicated problem, hence numerical methods are employed.The motion of MMOs as of solid bodies in the water flow has been well studied [2,3]. The MMO mathematical models include mathematical models of their hulls, hydrodynamic drags, propulsive complexes, bearing surfaces, and other elements. As a rule, it is possible to develop an MMO mathematical model in the form of ordinary differential equations system, despite complex dependencies between parameters of model elements. This allows applying effective methods of numerical solution of differential equations to the MMO simulation.The flexible tether modeling is a more challenging problem, as the FT is an object with distributed parameters which is described by a system of nonlinear differential equations with partial derivatives. Two approaches were evolved for modeling FT dynamics [4]. These are segmental and lumped-mass-spring (LMS) methods. For the former the FT is modeled as a continuous system and resulting partial differential equations are solved numerically by finite difference or any suitable approximation method. In the LMS approach the cable is modeled as mass points joined together by massless elastic elements of finite length, which makes it possible to express the FT model in the form of ordinary differential equations. All the forces along the cable are assumed to be concentrated at the mass points. IntroductionUnderwater complexes with flexible tethers (UCFT) consist of two types of elements: those with lumped and distributed parameters. The former include marine mobile objects (MMO): surface vessels, submarines, remotely operated vehicles (ROV) and others. The latter include flexible tethers (FT): umbilical cables, towing cables, anchor chains, etc. An example of a two-linked UCFT is shown in Fig. 1 [1]. Fig. 1. Two-linked underwater complex with flexible tethersMathematical modeling is one of the main methods of the UCFT studies. In this regard, the UCFT motion simulators should include corresponding MMO and FT mathematical models. It is known that their motion equations are non-linear and their dynamic behaviors are mutually dependent. As APPLIED MECHANICS DEVELOPMENT OF THE MATHEMATICAL MODELING METHOD FOR DYNAMICS OF THE FLEXIBLE TETHER AS AN ELEMENT OF THE UNDERWATER COMPLEX О . B l i n t s o vPhD, Assistant Professor Department of Information Security Lviv Polytechnic National University S. Bandery str., 12, Lviv, Ukraine, 79000 E-mail: energybox@mail.ruРозроблено метод математичного моделю-вання динаміки гнучкого зв'язку (ГЗ) на основі автоматичного контролю осьового руху його еле-ментів. Синтезовано регулятор відстаней між елементами ГЗ як складова математичної моде-лі. Запропоновано спосіб моделювання ГЗ зі змін-ною довжиною. Показано ефективність розробле-ного методу у порівнянні з методом зосереджених мас та еластичних зв'язків при мо...

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Improvement of the inverse dynamics method for high-precision control of nonlinear objects under conditions of uncertainty

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