Dynamic suspension modeling of an eddy-current device: an application to Maglev
Abstract
When a magnetic source is simultaneously oscillated and translationally moved above a linear conductive passive guideway such as aluminum, eddy-currents are induced that give rise to a time-varying opposing field in the air-gap. This time-varying opposing field interacts with the source field, creating simultaneously suspension, propulsion or braking and lateral forces that are required for a Maglev system. In this thesis, a two-dimensional (2-D) analytic based steady-state eddy-current model has been derived for the case when an arbitrary magnetic source is oscillated and moved in two directions above a conductive guideway using a spatial Fourier transform technique. The problem is formulated using both the magnetic vector potential, A, and scalar potential, φ.Using this novel A- φ approach the magnetic source needs to be incorporated only into the boundary conditions of the guideway and only the magnitude of the source field along the guideway surface is required in order to compute the forces and power loss. The performance of this analytic based steady-state eddy-current model has been validated by comparing it with a 2-D finite-element model. The magnetic source used for the validation is a radially magnetized Halbach rotor, called an electrodynamic wheel (EDW). The 2-D analytic based transient eddy-current force and power loss equations are derived for the case when an arbitrary magnetic source is moving and oscillating above a conductive guideway. These general equations for force and power loss are derived using a spatial Fourier transform and temporal Laplace transform technique. The derived equations are capable of accounting for step changes in the input parameters, in addition to arbitrary continuous changes in the input conditions. The equations have been validated for both step changes as well as continuous changes in the input conditions using a 2-D transient finite-element model. The dynamics of an EDW Maglev is investigated by using both steady-state and transient eddy-current models. The analytic equations for the self as well as mutual damping and stiffness coefficients of an EDW Maglev are derived using the 2-D analytic steady-state eddy-current force equations. It is shown that the steady-state eddy-current model in which the heave velocity is included in the formulation can accurately predict the dynamic behavior of a 2-degree of freedom EDW Maglev vehicle. The 2-D EDW Maglev vehicle has been built using Matlab/SimMechanicsTM. A 1-degree of freedom pendulum setup of an EDW Maglev has been built in order to investigate the dynamics of an EDW Maglev. The dynamic model of an EDW Maglev has been validated using this pendulum setup. A multi-degree of freedom Maglev vehicle prototype has been constructed using four EDWs. The dynamics of the prototype Maglev has been investigated using the Matlab simulations. This prototype setup will be used to investigate the dynamic behavior of EDW Maglev in the future.