269 Eddy Current Effects in Spacecraft Mechanisms  

Emilia Wegrzyn*, Claudia Allegranza**, Thomas Adam***, Florian Liebold*** and René Seiler*** 

Abstract  

The mastering of electromagnetic design features  in spacecraft  mechanisms , including desired or  undesir ed effects due to eddy currents , has become a promising area for a model -based design and   development approach.  In this frame, multiphysics type investigations have been performed on a simplified  experimental test set-up and on flight representativ e reaction wheel assemblies . The test results have been  successfully correlate d with  simulation output obtained from basic linearized models up to transient  nonlinear representations of eddy current effects in complex geometries.  The impact of critical parameters  like the electrical conductivity of materials as a function of temperature has been particularly studied . 

Introduction  and Motivation  

Many actuators used in spacecraft  applications are based on electromagnetic  principles for their function  and operation. In this overall context, eddy currents in electromagnetic devices  may have a desired effect,  for instance when creating a resistive torque in speed regulators (or dampers) as used for controlling the  deployment of solar arrays or other spacecraft appendages. I n many other cases  (e.g. reaction wheel  assemblies involving  electric motors) , eddy currents are associated with losses  and/or motion resistance ,  which are normally undesired and to be minimized [1]. However, in comparison to other industrial sectors,  space mechanisms  are often used for very specialized and one- of-a-kind tasks, relying on very few  hardware prototypes and limited testing in the course of their development . Therefore, the understanding  & optimization of electromagnetic design features in their interact ion with other physical effects has become  a very i mportant objective,  which has been the main motivation  for the research presented in this paper .   

Theor etical Framework  

Eddy currents have been subject of theoretical elaborations  and experiments  since the 19th century when  Michael  Faraday and Léon  Foucault were working on this topic . They  may be regarded as loops of electric  current induced within conduct ive materials  by a varying  external magnetic field. When considering a disk  rotating in an air gap between the pole pieces  of a magnet, the resulting torque grow s with the angular  speed of the dis k, which may be approximated by Eq. 1 within a limited speed range [2]: 

𝑇𝑇= 𝜋𝜋 𝑏𝑏 𝑐𝑐2𝑎𝑎2 2∙ �1−𝑟𝑟2 𝑎𝑎2 (𝑟𝑟2−𝑐𝑐2)�∙𝜎𝜎 𝐵𝐵2 𝜔𝜔    (Eq. 1) 

T  … resistive torque due to eddy currents   [Nm]   ω   … angular speed of the disk     [rad/s]   σ   … electrical ( bulk) conductivity of the disk material [S/m]   B   … magnetic flux density (average) in the air gap  [T]  a, b, c, r   … geometric parameters     [m] 

In fact , the resistive torque has been shown to grow linearly (according to Eq. 1) at low speeds  only, levelling  before reaching a maximum at medium speeds and finally decreasing at higher speeds  [2]. 

* Surrey Space Centre, Guildford, United Kingdom   ** ATG Europe, Noordwijk, The Netherlands   *** European Space Agency (ESA/ESTEC), Noordwijk, The Netherlands  

Proceedings of the 45th Aerospace Mechanisms Symposium, NASA Johnson Space Center, 20 20