Rotor Design Optimization for a ReactionSphere Actuator
A. BoletisIG VPE Swiss Workshop, 22nd of January 2015Elektromagnetische Felder in der alltäglichen Produktentwicklung
Dr. L. Rossini1, Dr. E. Onillon1, Prof. Dr. Y. Perriard2, S. Mingard3, Dr. A. Boletis3
1Swiss Center for Electronics and Microtechnology, Neuchâtel, Switzerland2Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland3maxon motor ag, Sachseln, Switzerland
Outline
• Introduction
• Rotor design optimization
• Results
• Conclusions
Outline
• Introduction
• Rotor design optimization
• Results
• Conclusions
Application: Spacecraft Attitude Control System
• Example: actuation of the satellite frame
• Stabilizing orientation
• Pointing
Introduction
X0Y0
Z0
ZII
XIIYII
ZI
XIYI
Earth
Satellite
Application: Spacecraft Attitude Control System
• Traditional actuators
• Thrusters
• Reaction wheels
• Control moment gyroscopes
• Reaction wheels
• Minimum of three reaction wheels (no redundancy)
• Actuation: action-reaction principle(the spacecraft frame reacts to the acceleration ordeceleration of the wheels accordingly)
• Stabilization: angular momentum
Introduction
Motivation
• The three axes of the satellite could be controlled by a unique device(reaction sphere)
• Reaction sphere is held in position by magnetic bearings
• Potential reduction of micro-vibrations and improvement of pointing accuracy
Introduction
reaction wheels
reaction sphere
Proposed Reaction Sphere
Introduction
• 3D PM synchronous motor (rotation about any axis):
• 8-pole rotor, 20 ironless-coils stator
• Rotor magnetically levitated (actively)
• Rotor position measured using triangulation sensors
• Rotor orientation measured using linear Hall-effect sensors
8-pole permanentmagnet rotor
20 ironless-coilsstator
(dodecahedron)
Rotor Orientation
Introduction
• Orientation reconstruction algorithm uses linear Hall-sensors information
• Quality of the orientation reconstruction depends on:
• the number of used linear Hall-sensors
• the harmonic content of the rotor magnetic flux density
• Quality of the orientation reconstruction has an effect on:
• the precision of the calculated force and torque constants
• the precision of the generated forces (magnetic levitation) and torques (spacecraftactuation)
Minimize the rotor magnetic flux density distortion with respect to the fundamentalharmonic in order to reduce the number of the Hall-sensors and the complexity of
the reconstruction algorithm
Rotor Requirements
Introduction
• Model agreement
• Rotor requirements
• compatibility with the already produced stator (former project):
Max. rotor mass m 10 kg
Max. rotor outer radius R 90 mm
Min. magnetic flux density over mass BrRMS /m
at a distance for the center of 95.5 mm0.04 T/kg
Model agreement d to be maximized
Min. angular momentum 7.1 Nms
∑ ∑= −=
=N
n
n
nm
mnccd
0
223
( ) ( ) ( )∫ ∫=π π
φθθφθφθ2
0 0sin,,, ddYrBc m
ncrmn
Ideal magnetization
Outline
• Introduction
• Rotor design optimization
• Results
• Conclusions
Rotor Geometry and Design Parameters
Rotor Design Optimization
• 8 bulk permanent magnet poles with truncated spherical shape
• Parallel magnetization
• Back-iron with truncated octahedral shape
• 5 design parameters to be optimized with respect to given requirements
Optimization Process
Rotor Design Optimization
• Analytical approach not feasible due to the highly complex rotor geometry
• Rotor design optimization based on FEM simulations using COMSOLMultiphysics ® (AC/DC Module and Pro/ENGINEER LiveLinkTM)
Pro/ENGINEER ®Pro/ENGINEER ®Parametrized Geometry
COMSOLMultiphysics ®
Pro/E LiveLinkTM
Optimized Geometry
Magnet Shape Optimization
Rotor Design Optimization
• Influence of eccentricity c on model agreement d (linear simulations)
set A: RM + c = 88.5 mm, ~ 6.0 kg magnetsset B: RM + c = 86.0 mm, ~ 5.5 kg magnetsset C: RM + c = 83.5 mm, ~ 5.0 kg magnets
Back-iron Shape Optimization
Rotor Design Optimization
• Non linear magnetic properties of back-ironmaterial (X46Cr13) modeled in COMSOLthrough its B-H curve
• Weight optimization
Back-iron Shape Optimization
Rotor Design Optimization
• Influence on model agreement d and BrRMS /m (non linear simulations)
Back-iron Shape Optimization
Rotor Design Optimization
• Magnetic flux density of the optimized back-iron
Final Rotor
Rotor Design Optimization
• Harmonic content
Final Rotor
Rotor Design Optimization
Requirement Design
Rotor mass m ≤ 10 kg 9.64 kg
Rotor outer radius R ≤ 90 mm 90 mm
Magnetic flux density over mass BrRMS /m
at a distance for the center of 95.5 mm≥ 0.04 T/kg 0.0433 T/kg
Model agreement dto bemaximized
0.9901
Angular momentum ≥ 7.1 Nms7.1 Nms @1’842 rpm
Outline
• Introduction
• Rotor design optimization
• Results
• Conclusions
Rotor
Results
Magnetic Flux Density
Results
• Setup
Magnetic Flux Density
Results
• θ = 55 deg • θ = 65 deg
Magnetic Flux Density
Results
• θ = 75 deg • Mean normalized error w.r.t.fundamental harmonic
Nh = 3 � 7 Hall-sensorsNh = 9 � 41 Hall-sensors
Summary
Results
Reaction Sphere Prototype
Results
Outline
• Introduction
• Second generation rotor design optimization
• Results
• Conclusions
Conclusions
• Design model optimization based on COMSOL Multiphysics ® andPro/Engineer ®
• Model agreement maximized for the given magnet parametrization
• Good correspondence between the simulated and measured values
• Rotor fabrication proven
• Ongoing activities to assess the reaction sphere overall functionality
• closed-loop rotor position and orientation control
Thank you for your attention.
Questions?