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Mathematical modeling of flexible tethers (FT) is an integral part of the study of remotely operated vehicles and underwater complexes in general. In this paper, for the mathematical modeling of the FT dynamics in the flow of liquid, the FT is represented as a set of series-connected elements – solid bodies. The governing equation of the FT element motion is given; it takes into account the external gravity, buoyancy and hydrodynamic drag forces, and internal constraint reaction forces between adjacent elements. The main problem in the inextensible FT modeling is to determine the constraint reaction forces. There has been suggested the method of mathematical modeling of the flexible tether dynamics with automatic control of its elements axial motion (ACEAM). According to the ACEAM method, the flexible tether is represented as a multidimensional automatic control system. The controlled object is the set of the FT elements, the controlled parameters are the distances between adjacent elements, and the controlling parameters are the constraint reaction forces. With the help of the inverse dynamics method, the regulator of the FT elements axial motion is synthesized as a part of the FT mathematical model. The developed regulator provides highly precise control of the distances between the FT elements and, therefore, accurate modeling of the inextensible flexible tether dynamics. The method of the flexible tether simulation considering that its length varies during its operation is suggested. The basis of the method is the dynamic change of the number of the elements being involved in the calculation process, considering the current length of the released part of the FT. Changing the FT length causes additional loads on its inboard and running ends. Taking into account these loads allows accurate simulation of the dynamics of the FT impact on remotely operated vehicles and other components of underwater complexes. The flexible tether motion dynamics is then modeled with the developed method. The modeling results are compared with the method of lumped masses springs. It is established that when the equal precision of the inextensible FT simulation is provided, the suggested method operates about 25 times faster than the method of lumped masses and springs.

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