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?