Hillyard Magnetic Bearing

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Joint Advanced Student School

2006

Jeff Hillyard

Technische Universitt Mnchen

Magnetic Bearings


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OverviewMagnetic Bearings

Introduction

Magnetism Review

Active Magnetic Bearings Passive Magnetic Bearings

Industry Applications


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IntroductionMagnetic Bearing Types

Active/passive magnetic bearings electrically controlled

no control system

Radial/axial magnetic bearings


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IntroductionMotivations

Advantages of magnetic bearings: contact-free

no lubricant

(no) maintenance tolerable against heat, cold, vacuum, chemicals

low losses

very high rotational speeds

Disadvantages: complexity

high initial cost

Minimum Equipment for AMB

Source: Betschon


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IntroductionSurvey of Magnetic Bearings

Source: Schweitzer


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MagnetismMagnetic Field

north polesouth pole

magneticfield line

iron filings

Pole Transition


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MagnetismMagnetic Field

Magnetic field, H, is found around a magnet or a currentcarrying body.

r

iH

2

idsH

(for onecurrent loop)

H

i

dsds


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MagnetismMagnetic Flux Density

B = magnetic flux density

= magnetic permeability

H = magnetic field

HB

r 00= permeability of free space

r= relative permeability

1

1

diamagnetic

paramagnetic

ferromagnetic

r

niH

2

multiple loopsof wire, n

1

Meissner-Ochsenfeld Effect


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MagnetismB-H Diagram

H

B

area within loop representshysteresis loss

magnetic saturation

Ferromagnetic: a material that can be magnetized

HB

Coercivity, Hc

Remanence, Br


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MagnetismLorentz Force

f = force

Q = electric charge

E = electric fieldV = velocity of charge Q

B = magnetic flux density

BvEQf


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Simplification:

BvQf

Source: MIT Physics Dept. website

BvEQf


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Further simplification:

Bif

BvQf

force perpendicular to flux!

f

i

B

Analogous Wire


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MagnetismReluctance Force

VBHdVU

21

The energy in a magnetic field withlinear materials is given by:

Force resulting from a difference between magnetic

permeabilities in the presence of a magnetic field.

force perpendicular to surface!

2

2

ABf

U = energy

V = volume

l

Uf


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Aa

slFe 2


V

BHdVU

2

1

Basic equation:

sAHBVHBU aaaaaaa 22

1

2

1

Energy contained within airgap:


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Evaluating the magnetic circuit for a simple system:

nisHHlHds aFeFe 2

NIniB

sB

lr

Fe 00

2

sl

NIB

r

Fe 2

0

aaFeFe ABAB

BBBaFe

Assumption:

Aa

slFe 2


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Principle of virtual displacement:

0

BHa

aa

a ABHl

Uf

cos2

2

0 a

rFe

Asl

nif

2

2

s

ikf

0

quadratic!

inversely quadratic!


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Active Magnetic BearingsElements of System

Electromagnet

Rotor

Sensor Controller

Amplifier


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Active Magnetic BearingsForce Behavior

Distance

fs

Force

Distance

fm

Force

2

1~

sx

Magnetic Force Spring Force

xs

xs


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Active Magnetic BearingsForce Linearization

Magnetic Force Spring Force

fsfm2

1~

sx

xs

xs

mg

0x

mg

0x


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Operating Point (constant current)

xs

fm

xkf s

x

0x

f

xkf siism m

0,

x

Redefining distance:

0xxx s

ks= force-displacement factor


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ikf ixxim s

0,im

fm

im0i

2

~ mi

mg

fm

im0i

ikf i

i

0iii m

ki= force-current factor

Operating Point (constant position)


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Linearized equation:

00

,,, xximiism smffixf

ikf ixxim s

0,

x

im

xkf siism m

0,

0iii m

0xxx s

ikxkixf is ,

Not valid for:

- rotor-bearing contact

- magnetic saturation

- small currents


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Active Magnetic BearingsClosed Control Loop

Open Loop Equation: Basic System

ikxkixf is ,

Controller function?

- Provide force,f

Controller signals?

- Input: position,x

- Output: current, i

i = i(x)

x

i

x

Artifical damping and stiffness:

xdkxf x

k d


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Solving for controller function:Basic System

xdkxikxk is

x

i

x

To model position of rotor:

i

s

k

xdxkkxi

xmf Just like for the spring system!


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System characteristics:

with

02 kdm

x(t)

ttCe

j

2

2

4m

d

m

k

m

d

2

General solution for position:

tCetx t cos

Eigenfrequency:

mk 220


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Controller Abilities:1) k, d can be varied in controller

2) air gap can be varied in controller

3) specify position for different loads4) rotor balancing, vibrations, monitoring...


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Linearization:

cos4

1 220

s

iAnf a

cos2

0

2

0

2

0

2

0

xs

ii

xs

iikfff xxx

xss 0xss 0

cos2

2

s

ikf aAnk

2

04

1

magnetic force wasdetermined to be

where

Differential driving mode


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Linearization:

xx

fi

i

ff

x

xx

xx

xx

00

xs

kii

s

kif xx

cos

4cos

43

0

2

0

2

0

0

ik sk

linearized fordifferential drivingmode

Differential driving mode


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Radial Bearing Axial Bearing

Active Magnetic BearingsBearing Geometry


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B circumferential torotor axis

B parallel to rotor axis

- similar to electromotors

- rotor requires lamination

- hysteresis loss low

- lamination avoided

Orientation:

magnet pole pairs are often lined up with the principlecoordinate axes x and y (vertical and horizontal)

control equations are simplified

Active Magnetic BearingsBearing Geometry


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Active Magnetic BearingsSensors

Position Sensor contact-free measure rotating surface

surface quality

homogeneity of surface material various values

Other Sensors speed

current flux density temperature

+ sensor

other concerns:observabilityplacementcost


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Active Magnetic BearingsSensors

Sensorless Bearing- calculate position- less equipment- lower cost

Source: Hoffmann


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Active Magnetic BearingsAmplifier

Converts control signals to control currents.

Analog Amplifier:

- simple structure

- low power applications

P


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Active Magnetic BearingsElectrical Response

There is an inherent delay in the electrical system

inductance

voltage drops: and

velocity within magnetic fieldinduces a voltage

ku= voltage-velocity coefficient

Total voltage drop:


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Active Magnetic BearingsControl Equations of Motion

Block diagram with voltage control:

fxm

xk

dt

diLRiu u

ikxkixf is ),(

Source: Schweitzer


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Active Magnetic BearingsCurrent vs. Voltage Control

Voltage Control:- more accurate model- better stability- low stiffness easier to realize

- voltage amplifier often more convenient- possible to avoid using position sensor

Current Control:- simple control plant description

- simple PD or PID control

Flux Control:- very uncommon


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Active Magnetic BearingsAddressing of Assumptions

Uncertainties in bearing model- leakage flux outside of air gap- air gap is bigger than assumed- iron cross section is non-uniform


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Active Magnetic BearingsTypes of Losses

Air Losses

- air friction divide shaft into sections

Copper Losses (Stator)

- wire resistance Iron Losses (Rotor)

- hysteresis (higher w/ switching amplifier)

- eddy currents

2iRP CuCu


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Active Magnetic BearingsCopper Losses

For differential driving mode:

2

maxmax, 2 iRP CuCu

nAKA dnn

m

nnCu

l

KAPNI

2max,max

An= slot areaKn= bulk factor

= specific resistance

lm= average length of turn

limit of permissible mmf!


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Active Magnetic BearingsRotor Dynamics

Areas of Consideration natural vibrations

forward/backward whirl (natural vibrations)

critical speeds nutation

precession (change in rotation axis)

Source: Wikipedia


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Active Magnetic BearingsRotor Dynamics

rotor touch-down in retainer bearings- maintenance

- sudden system shutoff

- during system shutdownvery difficult to simulate

cylindrical motion conical motion Source: Schweizer


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Active Magnetic BearingsRotor Stresses

Radial

Tangential

2

2

222223

8

1r

r

rrrr aiair

2

2

22222 3133

8

1r

r

rrrr aiait

largest stress is at insideradius of disc with hole!

Source: Schweizer


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Active Magnetic BearingsRotor Stresses

Implications of max stress:max velocity (full disc)!

3

8

max

S

a

rv

s= max tensile strength

Material vmax (m/s)steel 576

brass 376

bronze 434

aluminium 593titanium 695soft ferro. sheets 565

Actual reached speeds (length 600 mm, dia. 45 mm):

s

mv 300max rpm000,120max

Source: Schweizer


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Passive Magnetic BearingsPermanent Magnets

Common Materials:1) neodymium, iron, boron (Nd Fe B)

2) samarium, cobalt, boron

(Sm Co, Sm Co B)3) ferrite

4) aluminium, nickel, cobalt(Al Ni, Al Ni Co)

Relative Sizes

Issues:- material brittleness

- varying space requirements (B-H)

- operating temperatures(equal H at 10 mm)


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at least one degree offreedom unstable!

increase in stiffness withmultiple rings

caution:misalignment!

reluctance bearings:

- non-rotating magnets

- resistance to radial

displacement


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High Potential- economical

- reliable

- practical

already replacing some active magnetic bearings- smaller size equipment and systems

- systems with large air gaps

Source: Boden


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ApplicationsTurbomolecular Pump

cole Polytechnique Fdrale de Lausanne, Switzerland- eliminates complicated lubrication system- high temperature resistance- reduction of pollution

- vibrations, noise, stresses avoided- improved monitoring (unbalances, defects, etc.)

Status: suboptimal design overheating at load (> 550C) increase life span optimize fill factor reduce cost simplify manufacturing


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ApplicationsFlywheel (97)

New Energy and Industrial Technology Development Organization(NEDO)Japans Ministry of International Trade and Industry (MITI)

T=J2speed has larger influence than mass (better energy density)

fiber-reinforced plastics for high strength

fracture into small pieces upon failure above ground combination of superconductor and permanent magnet bearings (hsys= 84%)


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ApplicationsFlywheel (97)

Current Development Goals (NEDO)

increase load force

reduce amount load force decrease with time (magnetic flux creep)

reduce rotational loss

increase size of bearings for larger systems


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ApplicationsMaglev Trains

Maglev = Magnetic Levitation

150 mm levitation over guideway trackundisturbed from small obstacles (snow, debris, etc.)

typical ave. speed of 350 km/h (max 500 km/h)what if? Paris-Moscow in 7 hr 10 min (2495 km)!

stator: track, rotor: magnets on train

Source: DiscoveryChannel.com


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ApplicationsMaglev Trainsx

Maglev in Shanghai

- complete in 2004

- airport to financial district (30 km)

- worlds fastest maglev in commercial operation (501 km/h)- service speed of 430 km/h

Source: www.monorails.org


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ApplicationsMaglev Trains

Noise Reduction

by FrequencyNoise Reduction

by Speed

Source: Moon


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Magnetic BearingsReferences

1. Betschon, F. Design Principles of Integrated Magnetic Bearings, Diss. ETH. Nr. 13643, ETHZrich, 2000.

2. Boden, K. & Fremerey, J.K. Industrial Realization of the SYSTEM KFA-JLICH PermanentMagnet Bearing Lines, Proceedings of MAG 92 Magnetic Bearings, Magnetic Drives and DryGas Seals Conference & Exhibition. Lancaster: Technomic Publishing, 1998.

3. Electricity and Magnetism. Hyperphysics. Georgia State University, Dept. of Physics andAstronomy. 1 Apr. 2006 .

4. Fremery, J.K. Permanentmagnetische Lager. Forshungszentrum Jlich, ZentralabteilungTechnologie, 2000.

5. Hoffmann, K.J. Integrierte aktive Magnetlager, Diss. TU Darmstadt. Herdecke: GCA-Verlag 1999.

6. Lsch, F. Identification and Automated Controller Design for Active Magnetic Bearing Systems,Diss. ETH. Nr. 14474, ETH Zrich, 2002.

7. Maglev Monorails of the World: Shanghai, China. The Monorail Society Website. 1 Apr. 2006.

8. Maglev Train Explained, DiscoveryChannel.ca. Bell Globemedia 2005.

9. Magnetic Bearings & High Speed Motors, S2M. 1 Apr. 2006 .


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Magnetic BearingsReferences

10. Moon, F.C. Superconducting Levitation: Applications to Bearings and Magnetic Transportation.New York: John Wiley & Sons, 1994.

11. Research and Development for Superconducting Bearing Technology for Flywheel ElectricEnergy Storage System. New Energy and Industrial Technology Development Organization(NEDO). 1 Apr. 2006.

12. Schwall, R. Power SystemsOther Applications: Flywheels. Power Applications ofSuperconductivity in Japan and Germany. WTEC Hyper-Librarian 1997.

13. Schweizer, G., Bleuler, H., & Traxler, A.Active Magnetic Bearings: Basics, Properties andApplications of Active Magnetic Bearings. Zrich: Hochschulverlag AG an der ETH, 1994.

14. Widbro, L. Magnetic Bearings Come of Age. Revolve Magnetic Bearings Inc. 2004.MachineDesign.com. 1 Apr. 2006

.

15. Wikipedia contributors (2006). Hysteresis. Wikipedia, The Free Encyclopedia. April 1, 2006.

16. Wikipedia contributors (2006). Magnetic field. Wikipedia, The Free Encyclopedia. April 1, 2006.


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Questions?


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ApplicationsCrystal Growing System

Hillyard Magnetic Bearing

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