Ismail, Norilmi Amilia
The dynamics of a flexible Motorised Momentum Exchange Tether (MMET).
PhD thesis, University of Glasgow.
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This research presents a more complete flexible model for the Motorised Momentum Exchange Tether (MMET) concept. In order to analyse the vibration aspect of the problem the tether is modelled as a string governed by partial differential equations of motion, with specific static and dynamic boundary conditions and the tether sub-span is flexible and elastic, thereby allowing three dimensional displacements of the motorised tether. The boundary conditions lead to a specific frequency equation and the Eigenvalues from this provide the natural frequencies of the orbiting flexible motorised tether when static, accelerating in spin, and at terminal angular velocity. The rotation matrix is utilized to get the position vectors of the system’s components in an inertial frame. The spatio-temporal coordinates u(x,t), v(x,t) and w(x,t) are transformed to modal coordinates before applying Lagrange’s equations and the pre-selected linear modes are included in generating the equations of motion. The equations of motion contain inertial nonlinearities of cubic order, and these show the potential for intricate intermodal coupling effects.
The study of planar and non-planar motions has been carried out and the differences in the modal responses in both motions between the rigid body and flexible model are highlighted and discussed. The dynamics and stability of the flexible MMET is investigated using the dynamical analysis tools for representing the behaviour of the tether system. The study is also includes the engineering side of the MMET by investigating the power requirements of an electric motor located in the central facility of the Motorised Momentum Exchange Tether (MMET). A simulation was run using a specially written computer program to obtain the required minimum power for a typical duty cycle, and also to study the responses for three different operating conditions; before payload release, torque-off and reverse torques conditions for both the propulsion and outrigger system on both circular and elliptical orbits. The differences in the responses when using rigid body and flexible models of MMET are highlighted and discussed in order to look at the sensitivity of the model to the power budget calculations. The study then continues with a comparative study between the MMET and conventional propulsion systems in terms of the energy used specifically for an Earth-Moon return mission for circular and elliptical orbits.
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