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E Reaction Wheel Design (LW, WF)E.1 Role of RWA (LW)E.2 RequirementsE.3 Wheel Design (WF)E.3.1 Material SelectionE.3.2 Basic GeometryE.3.3 Governing ModelE.3.4 Structural IntegrityE.3.5 Vendor InformationE.4 Motor Selection (LW)E.4.1 Determination of Required TorqueE.4.2 Motor ComparisonsE.4.3 Motor SelectionE.4.4 Determination of Required PowerE.4.5 Vendor InformationEMFFORCE OPS MANUAL Space Systems Product Development-Spring 2003 E Reaction Wheel Design (LW, WF) E.1 Role of RWA (LW) The spin-up process requires equating the centripetal force on a vehicle with the electromagnetic force generated by the magnets. This process is depicted in Figure E.1-A and in Figure E.1-B. Figure E.1-A shows the initial configuration of the dipoles. Although the finalized design of the system uses two large, coreless electromagnets, the electromagnets are represented here as effective dipoles. The dipoles begin perpendicular to each other. Figure E.1-A: Initial Dipole Configuration Figure E.1-B depicts the two dipoles as they begin to spin up. As soon as a current is applied to the electromagnets, forces and moments are induced in the dipoles. The moments are due to the perpendicular geometry of the system at this point. These moments must be counteracted by applied torque from the RWA. The dipoles initially move in the directions of their respective net forces. As they begin to move, the applied torque from the RWA is decreased to induce centripetal motion of the system. As centripetal force increases, the applied torque continuously decreases, allowing the rotating dipoles to slowly align along the same axis. At the point where the dipoles are perfectly aligned and the centripetal force is equal to the total magnetic force, no more applied torque is necessary. At this point, the system is in steady-state rotation Figure E.1-B shows the process of spin-up. Massachusetts Institute of Technology 1 Dept of Aeronautics and AstronauticsEMFFORCE OPS MANUAL Space Systems Product Development-Spring 2003 Figure E.1-B: Spin-up Configuration The RWA consists of a flywheel and a motor. The motor powers the flywheel and must provide the necessary torque to balance the moments that are produced by the electromagnets. The spinning wheel stores the system’s angular momentum, balancing the system and guiding the system through spin-up to steady-state rotation. The RWA functions on the principle of the conservation of angular momentum. Angular momentum is conserved because the spin-up maneuver is performed entirely using torques and forces that are internal to the system. Therefore, the sum of the angular momentum that accumulates in the wheels on the (in this case) two vehicles is equal and opposite to the angular momentum associated with the spinning of the system about its own center of mass. Massachusetts Institute of Technology 2 Dept of Aeronautics and AstronauticsEMFFORCE OPS MANUAL Space Systems Product Development-Spring 2003 E.2 Requirements • Wheel o As a minimum, the flywheel must store the angular momentum necessary to operate a two-vehicle system in a steady state maneuver. The vehicles will perform the maneuver at a separation distance (between vehicle centers) of two meters and a rotation rate of one rotation per minute. o The flywheel may not be made from an electrically conducting material. The electromagnetic field in which the wheel must operate would induce eddy currents in any wheel made from conducting material. Eddy currents would act as a retarding force against the motion of the wheel and this would hurt the performance of the reaction wheel assembly. o The maximum wheel diameter is limited by the total vehicle size to less than half of a meter. o Due to the material properties of the flywheel the wheel must be capable of storing the necessary angular momentum while operating at a speed below seven thousand rotations per minute. • Motor o The motor in the RWA must provide sufficient torque to accelerate the flywheel in either direction in order to counter moments induced by the electromagnets. Massachusetts Institute of Technology 3 Dept of Aeronautics and AstronauticsEMFFORCE OPS MANUAL Space Systems Product Development-Spring 2003 E.3 Wheel Design (WF) E.3.1 Material Selection The design of the reaction wheel assembly was complicated with the decision from the Electro-magnet team to use hoops of super conducting wire to generate the necessary magnet forces to operate the vehicles. The reaction wheel assembly will be placed inside these hoops and therefore will be operating inside of a magnetic field. Due to problems with eddy currents, which act as strong resisting force to spinning metal wheels inside of a magnetic field, the flywheel cannot be made from any metallic materials. This forced the search for non-metallic materials with a sufficient density and structural rigidity to provide for the angular momentum storage of the vehicles. High-density urethanes appear to be the best solution. These materials provide the density and structural properties necessary to perform as needed and can also be molded into any shape for a relatively low cost. The reaction wheel assembly team has decided to use urethane wheels to be manufactured by Advanced Urethane Solutions because of their ability to meet all of our specifications at a low cost and with a reasonable delivery time. E.3.2 Basic Geometry The flywheel consists of a thick outer ring and thin inner disk. Moment of inertia is dependent on the total mass of material used and the distance of that material from the axis of rotation. The most efficient flywheel design places a majority of the flywheel mass far from the axis of Rotation - the center of the flywheel. Figure E.3-A depicts the basic geometry used as the starting point in the flywheel design. rrwrdiskhringhdisk Figure E.3-A: Basic Geometry of Initial Flywheel Design E.3.3 Governing Model The flywheel on each vehicle must be capable of storing one half of the total angular momentum of the entire system. This is necessary to allow the system to spin up from a static equilibrium into a steady-state rotation, which is a maneuver that will be conducted for this project. The total angular momentum that must be stored in


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