The dynamics of a flexible Motorised Momentum Exchange Tether (MMET)

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

The rigid-body dynamics of tethers in space

Three fundamental tether motions were considered for payload orbital transfer with tethers: hanging, prograde libration and prograde motorised spin. The symmetrical double-ended motorised spinning tether performed best and was most efficient, improving by two orders of magnitude on the librating tether which in turn improved on the hanging tether by roughly a factor of two. An upper payload using long tethers with a motorised tether on a circular orbit can be transferred from a low to a geostationary Earth orbit by employing relatively high motor torque and a safety factor on the tether strength close to unity. Two common literature results, the constant efficiency index of seven for a hanging tether upper payload release and the maximum efficiency index of fourteen for an upper payload released from a prograde librating tether, were found to be a lower bound and quite readily breached, respectively. Orbit circularisation through tether release was found to be feasible with retrograde librating tethers. When the point of release does not occur along the local vertical then a non-optimum release of the payload was found to severely reduce the performance of payload transfer with tethers. Consequently, a very precise and accurately timed release is important for the success of payload orbital transfer with tethers since missing the point of release by a single degree with a spinning tether, say, can cause the payload to miss its required target. The best design for the outrigger system to provide the necessary resistive torque is to utilise the gravity gradient and tap the outrigger system within the gravitational potential well. In this manner the outrigger tether length can be significantly reduced and the outrigger end masses can be minimised, thus saving valuable launch mass and cost, as well as exposing less tether surface area to the space environment. With current materials the maximum ?V to be expected with a motorised tether is between 600-1400 m/s depending on the tether length and payload mass. The duration of the spin-up lasts approximately between half and a full Earth day but may vary by an hour, say, depending on the initial conditions and orbit eccentricity. Ensuring the motor torque axis remains perpendicular to the orbital plane was found to be vital otherwise the spin-up time is greatly increased. The motorised tether has the ability to shift the datum of a hanging tether, which may have useful applications in Earth monitoring or tethered Interferometry. Out-of-plane initial angular displacements or the motor torque axis not remaining perpendicular to the orbital plane caused the motorised tether to precess. Furthermore, the motion of the motorised tether with a constant motor torque was found to be regular, but quasi-periodic, which implies that the payload cannot be reliably delivered at perigee along the local vertical

A Small-Satellite Demonstrator for Generating Artificial Gravity in Space via a Tethered System

It is well-known that prolonged exposure in humans to a microgravity environment leads to significant loss of bone and muscle mass; this presents a formidable obstacle to human exploration of space, particularly for missions requiring travel times of several months or more, such as a 6 to 9mon th trip to Mars. Artificial gravity may be produced by spinning a spacecraft about its center of mass, but since the g– force generated by rotation is equal to “omega-squared times r” (where omega is its angular velocity and r is the distance from the center of rotation), we have that unless the distance from the center of rotation is several kilometers, the rotation rate required to generate “1 − g” would induce vertigo in the astronauts as they moved about the capsule (e.g. if the distance from the center of rotation is 10 meters, the required rotation rate for 1 − g would be 9.5 rpm). By tethering the crew capsule to an object of nearly equal mass (such as the spent final rocket stage) at a distance of 1 to 2 kilometers, the necessary rotation rate would be sufficiently small as to not cause discomfort for the astronauts. For example, if the distance from the center of rotation is 2 kilometers, the required rotation rate for 1−g would be 0.67 rpm; at 1 kilometer the rate is still only 0.95 rpm. 1 rpm is considered an acceptable spin rate for the human body to withstand for extended periods of time. This paper gives an overview of the Tethered Artificial Gravity (TAG) satellite program, a 2-part program to study the operation and dynamics of an artificial-gravity-generating tethered satellite system. Phase I of the program will culminate in a flight of a model spacecraft in a non-ejected Get-Away-Special (GAS) Canister on the Space Shuttle. It is to be operated under the aegis of the Texas Space Grant Consortium. The purpose of the Phase I flight is to test key components of the system to be flown in Phase II of the program. Phase I will also involve detailed modeling and analysis of the dynamics of the spacecraft to be flown in Phase II of the program; the Phase II spacecraft will be a small, 65 kg, tethered satellite system which will be boosted into low-earth orbit, deployed and then spun-up to produce artificial gravity. In addition to a description of the TAG program, results of parametric studies related to TAG will be presented in this paper

The dynamics of tethers and space-webs

The thesis 'The dynamics of tethers and space-webs' investigates the motion of the Motorized Momentum Exchange Tether (MMET) on an inclined orbit, and while deploying and retracting symmetric payloads. The MMET system is used as a basis for examining the stability of space-webs using a triangular structure of tethers while rotating. The motion of small robots is introduced as they move on the space-web, and their motions are found to influence the behaviour of the structure. Several methods of limiting the destabilising influences of the robots are considered, and are found to stabilise the web in most circumstances. A structured method for describing the rotations of a tether system is outlined, and different rotational systems are compared. This lays the foundation for the further chapters examining MMET dynamics on an inclined orbit and while deploying and recovering the payloads. Lagrange's equations are generated for the three cases, and are solved using standard numerical integration techniques. To emphasise the practical uses of the MMET system, several missions are analysed by using the system as a re-usable launcher for micro-satellite payloads

The dynamics of tethers and space-webs

The thesis 'The dynamics of tethers and space-webs' investigates the motion of the Motorized Momentum Exchange Tether (MMET) on an inclined orbit, and while deploying and retracting symmetric payloads. The MMET system is used as a basis for examining the stability of space-webs using a triangular structure of tethers while rotating. The motion of small robots is introduced as they move on the space-web, and their motions are found to influence the behaviour of the structure. Several methods of limiting the destabilising influences of the robots are considered, and are found to stabilise the web in most circumstances. A structured method for describing the rotations of a tether system is outlined, and different rotational systems are compared. This lays the foundation for the further chapters examining MMET dynamics on an inclined orbit and while deploying and recovering the payloads. Lagrange's equations are generated for the three cases, and are solved using standard numerical integration techniques. To emphasise the practical uses of the MMET system, several missions are analysed by using the system as a re-usable launcher for micro-satellite payloads.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Cosserat Analysis of Microscale Structures

In this thesis, the application of Cosserat mechanics to micro-scale structures is explored. Different structures considered include micro-scale gyroscopes, micro-cantilevers, and clamped-clamped micro-structures. Two-dimensional formulations with nonlinearities up to third order are derived and presented. Different parameterization schemes are used and the equivalence between the obtained results is discussed. Comparisons with prior results available in the literature are made in terms of inertia properties, stiffness properties, and natural frequencies. The present work points to the importance of considering Cosserat mechanics for examining the motions of micro-scale structures that undergo large as well as coupled deformations