Dynamic Modeling of a Three Degree of Freedom Reaction Sphere
Byron, Joshua Michael
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This thesis presents a method to simulate the dynamics of a three degree of freedom, electromagnetically suspended Northrop Grumman Corporation Reaction Sphere (NGCRS) in MATLAB Simulink® by computing the magnetic force and torque relations offline, using COMSOL® Multiphysics. The goal of the thesis is firstly to demonstrate through Finite Element Magnetic Modeling (FEM) that magnetic field interactions between a stator levitation electromagnet (EM) and the rotor permanent magnets (PM) are limited to a single EM-PM pair and that all other PMs can be considered decoupled from the EM. Secondly, this thesis aims to demonstrate that a set of generalized magnetic force and torque relations can be derived for single EM-PM pair using a COMSOL Multiphysics®. The NGCRS geometry was selected for analysis due to its relative simplicity and design maturity. The NGCRS consists of a stator which houses eight EMs and a rotor with 12 PMs. The NGCRS stator was modified to include six additional EMs to levitate the rotor within the stator and reject external disturbances. The levitation EMs were designed to ensure magnetic field interactions were restricted to a single EM-PM pair for any given rotor orientation and for varying excitation currents. The rotor was modified to be made of iron material and copper inserts were added to decouple the PM fields from the iron, allowing the principle of superposition to be utilized. The geometric and kinematic relations of the NGCRS were derived and then implemented in a COMSOL Multiphysics® model. Simulations were performed to predict the forces and torques between a single levitation EM, rotor PM, and the iron rotor for varying coil excitation currents of 0.5 to 5.0 amperes in 0.5 amp increments and for angular distances of 0 degrees to 31.717 degrees in one-degree increments. Regression analysis is utilized to obtain relations for the forces and torques. Then a series of coordinate transformations are applied to obtain the forces and torques for any orientation of the levitation EM-PM pair. These relations and coordinate transformations are programmed into a dynamic model developed in MATLAB Simulink®.