Electromechanical simulation and test of rotating systems with ...

N94- 35905 ELECTROMECHANICAL SYSTEMS

WITH

SIMULATION MAGNETIC

ACTUATOR

AND TEST

BEARING

ACTIVE

OF ROTATING

OR PIEZOELECTRIC

VIBRATION

__.,

CONTROL

..J

//?// Alan B. Palazzolo, Department

Punan Tang,

Chaesil

of Mechanical

Engineering,

College

Albert

F. Kascak*,

Gerald

Kim, Daniel

Manchala

Texas

Station,

A&M University

TX

Brown, Gerald Montague'* NASA Lewis Cleveland,

* U.S. Army

at Lewis,

and Tim Barrett

and Eliseo

DiRusso

OH ** Sverdrup

at Lewis

Steve Klusman GMC Allison

Gas Turbine

Indianapolis,

Reng

IN

Rong

Lin

A.C. Compressor Appleton,

WI

ABSTRACT

This paper

contains

for rotating machinery are discussed.

a summary - active

of the experience

vibration

control.

of the authors Piezoelectric

in the field of electromechanical

and magnetic

bearing

actuator

modeling based

control

INTRODUCTION

The stability years.

analysis

More recently

rotor or rotor-bearing analysis

of conventionally attention

has been

installations

supported focused

rotating

machinery

on the stability

with active vibration

control

has been treated

analysis systems.

extensively

of magnetically Assembling

supported the model

for many flexible for this

has four basic steps:

P.,_%_..._.-_._. INTENTi_AJ_LY BLANK

467

(a)

Form the passive mass, stiffness, damping model from the shaft and disc geometry and from the flow, fluid and geometric properties of bearings and seals; Obtain transfer fimction representation of all frequency dependent components in the

(b)

feedback

loop of the control

system.

This typically

(c)

digital signal processors and actuators; Assembly (coupling) of the frequency dependent

(d)

bearing-seal system model in (a); Solution of the characteristic equation inspection

of the eigenvatues

includes

component

of the closed

to investigate

sensors,

power amplifiers,

representations

loop system

in (b) with tile passive

for the eigenvalues

rotor-

and

stability.

111a previous paper [1], the authors demonstrated how step (b) could be accomplished by curve fitting the component's frequency response to that of a 2nd order low pass electrical filter. This approach provided a 2nd order linear differential equation representation of the component which could be very easily coupled to the rotor system extract

model

to accomplish

the eigenvalues

Maslen component

and Bielk

task (c). Task (d) was then performed

from the finite element [2] presented

with a generically

an approach

defined

and Kirk [3] presented

closed

for coupling

transfer

method avoids the problems encountered stability problem, namely non-collocated Ramesh

formulated

function,

utilizing

the QR algorithm

to

loop model.

a frequency

to a standard

dependent,

finite element

feedback

loop

rotor system model.

This

in transfer matrix based approaches to solving the closed loop sensor-actuators and frequency dependent feedback components.

a comparison

between

their F.E. approach

to electromechanical

system

(ES) modeling and a transfer matrix based approach. Their results show good agreement between tile methods; however, no analytical treatment of their F.E. approach was provided. Ku and Chen [4] present F.E. based method approach

appears

sol ved repeatedly

for stability

evaluation

of ES models and demonstrate

very accurate

but it may be somewhat

while

guesses

'lhis manuscript this application.

analysis

making

provides Theory

a review

at the natural

of the author's

inefficient

it on our industrial

in that the eigenvalue

modeling's

problem

a The

must be

frequencies. experience

in electromechanical

and test results are given, along with a chronologically

of tile current

pump model.

system modeling

based description

for

of tile

methodology.

DISCUSSION

The test and theoretical Thc test rig employed actuators, unbalance equation

amplifiers response

feedback

This simulation response functions curve fit frequency

468 ii

for piezoelectric

actuator

in Figure

active vibration

1. The theoretical

control

results

are given in reference

in that paper

assume

[5].

ideal

and controllers which do not exhibit phase lag or amplitude roll off. Typical predicted curves for various derivative feedback gains are shown in Figure 2. The governing

for this system

pure derivative

results

in that study is shown

only represents gain (linear

approach

pure proportional

dependence

was improved

feedback

gain (constant

of gain on frequency,

in reference

[1] where

gain, zero phase lag) and

90 ° phase lead).

the actuator

and amplifier's

frequency

were represented by 2nd order low pass filters. Figures 3 and 4 show the measured and response functions of a piezoelectric actuator. The curved fit representation represents 2nd

order differential chanical

equations

model.

Figures

which

are assembled

5 and 6 show

with the mechanical

the shape of the measured

model to form a closed

and predicted

unstable

mode

loop electromeshapes

for the

same test rig as shown in Figure 1. Note that the frequency of that instability is approximately 2100-2400 11z. The closed loop model was employed to investigate the effects ofa 4th order low pass filter on stability of the unstable 7.

mode yielding

The authors

[6] improved

representation method

the plots of Real (eigenvalue)

on this approach

of any component

is provided

the transfer

this paper employing

the test rig shown

[71. Figure

the measured

10 shows

by employing

in the feedback

for obtaining

versus feedback

path. The approach

function

in Figures

and curve-fit

a general

gain and cutoff

order transfer is similar

correlation

8 and 9. This test rig was previously function

in Figure

function-state

to [2]; however,

from test data. A theory-test

8th order transfer

frequency

through

variable a systematic

is presented

described the summed

in

in reference proportional

and derivative feedback paths of the digital controller. State space representations of this controller and the power ampli tier were assembled along with a finite element model of the rotor (Figure 9) to predict the stability

bounds

of the coupled

dicted and measured stability results are shown for various the shaft, as explained Actuators sensor

mount

Figure

11 shows a comparison

[7] describes

between

the pre-

feedback gain space. Simulation the back emf induced by vibrations

mounted

a simulation

The rotor model

on a support

structure

study for closed

with some flexibility

loop stability

including

was the same one as employed

effects

in references

and inertia

of its

of actuator

and

[1 ] and [5], and is

depicted in Figure 12. The casing was simulated with 9 node, isoparametric thick shell elements and the actuators and sensors were attached to the flexible casing. Figures 13 and 14 are typical of results shown reference

[7]. Note how one of the three unstable

to casing

does not appear

Figure

! 5 depicts

ifthe

a current

sensor research

modes

shown in Figure

mount is assumed test being

13 for the case of sensor

to be rigid as shown

conducted

by the authors

in Figure

fit transfer

measured

function

and predicted

through stability

the summed bounds

proportional

will be determined

and derivative and published

in

mounted

14.

for predicting

a gas turbine engine simulator. This installation employs a PID based digital controller, modulated power amplifier and a high temperature magnetic bearing. Figure 16 shows curve

of

[6].

are always

flexibility.

system.

boundaries in the proportional-derivative values of a parameter that characterizes

in reference

and sensors

own. Reference

electromechanical

stability

bounds

pulse width the measured

paths of the controller.

for

and The

in the near future.

SUMMARY

This manuscript clectromechanicat were free ofrolloff

summarizes the authors' efforts in the area of active vibration control related-system modeling. Initial efforts employed ideal feedback component characterizations and phase lag. The later research

transfer functions through additional test verifications

the feedback components. ofthe method.

of the authors

utilized

more realistic

models

The future work in this area will concentrate

that

based on on

469

ACKNOWLEDGMENTS

Sincere gratitude is extended the Texas A&M Turbomachinery Allison

Gas Turbine

to the Dynamics Branch at NASA Lewis, the U.S. Army at NASA I,ewis Consortium (TRC) for funding this work. Appreciation is also extended

for their participation

in this NASA/Industry/University

cooperative

and to

work program.

REFERENCES 1.

Lin, Reng Rong and Palazzolo, Rotordynamlc Vol.

.

! 15, April,

Maslen,

.

to Trans. ASME

Ramesh,

"Implementing Journal

K. and Kirk, R.G., "Subharmonic

,

Ku, C.-P.R.

Proceedings

Virginia,

July, pp. 133-142.

Palazzolo,

A.B., et. al,"Test

Machinery," .

5/24-5/27,

470

Method

and Theory

1993, paper

ofActively

c0ntr011ed

Turbines

andPower,

Prediction

for Stability

Symposium

April,

E. and Kascak,

Structure

Models,"

for Turbomachinery

Symposium

Analysis

on Magnetic

Actuator-

and Acoustics,

Flexible

199 I. with

on Magnetic

for Active Bearings,

Active Vibration

Bearings,

Magnetic

Bearing

Alexandria,

Control

of Rotating

Vol. I 13, 199 I, pp. ! 67- ! 75.

A., lnternationaIGas

Turbine

Conference

no. 93-GT-382.

A.B. and Kascak,

no. 93-GT-293

Stability

for Piezoelectric

of Vibrations

A.B., Brown, G., DiRusso,

Barrett, T., Palazzolo, 1993, paper

and Testing

in Discrete

of the Third hffernational

of the Third blternational

,Journal

Tang, P., Pal_zoio, ASME,

.

ASME

Bearing

and Controls,

Resonance

and Chen, t I.M., "An Efficient

System,"

Magnetic

of Dynamics

Active Magnetic Bearings," Proceedings Alexandria, Virginia, July, pp. 113-122. .

Simulation

Actuators;" 7)'arts. AgMEJournalofGas

1993, pp. 324-335.

E.tt. and Bielk,J.R.,

submitted

A.B., "Electromechanical

SyStems with Piezoelectric

A.F., International

Gas Turbine

Conference

ASME,

5/24-5/27,

X

I, /

ho',._e=o.

,

Y

i Figure

Squirrel clge stiffness

2Yf

\

I. Diagram

of test rig with

Piezoelectric

pushers.

OO5 I 131. --.....

I Ou4

....

(:'= (;' (;' (;' (_' G'=

I 5 II} 0 211 28

l /

-\

003

bJ I/I Z O o.

002

t_ t,v

OO1

\

o oo 2000

I

I

3000

4000 POWER

Figure

2. Simulation vs. feedback

I 6000

I 5000

TURBINE

unbalance gain

SPEED

response

coefficients

I 7000

I 8000

(RPM)

at probe

2X or 2Y

in ADFT.

471

i

11F!

.-.

R/

Ave

+ +

I

,

o U.I

_

o

_

Figure

i'_

,,m ,.., .,.IWI: _+ -_.I* 3. Transfer

N

function

+ a.oo,. _,, plot of a typical

1

1 I

i I

I l

! I

1

1

I

t

t

-_..t

i-

pusher.

I FI a/J Jval II Rr - M&'g R+, - 1+_£0 - I, . _n.'O

N

/\ LII

\ (I 0

Figure

472

4. Transfer

_ ik.

_

_I -tlt.t1"

function

=q.O0 I.tZ

ITFI:

plot

of realized

_

electrical

iOOIl.O _ II II

circuit

of pusher

A.

|.11

I j

I I

• I

," _11',

,'

• t.

aI •

',

_]"P'. I1

U

I - | °1

Figure 5. Measured

t,,,'

'I

mode shape of unstable

Figure 6. Predicted

mode at a frequency

mode shape of unstable

of 2100

Hz.

mode at 2400 Hz.

473

4TH ONILPr 150 00

--e--_-

10000

-

CUTOrr

_o .z _ooo -z

fREQ.

R=0.g4T_101fl R=0.:lel'xl0'Cl

C=.3SBxI0-'F

--._.-z • ,- 6ooo _**.z

R=0.T89x 1061"1 R----o..m,,lo.n

-o-

R=O.4T4xl0'C_

,oooo.z

a"

x"

_/._'" ._ ,:_"

5O 00 • ._" It, _I" JD G.

A

000

• _"

O"

_r

.J at -SO00

•

_

.e

t_z3" JL.. _r - I(X) O0

-

-

0 0

.e ..O- -_''°_

_

2'_

-

_3.. _"

_"

_

.

-

-

-

_0

__4.. 4...t.

-

:

75

4,__4.

tOO

tZ5

150

rEr011ACK

Figure

7. Effects

of cutoff

UPPER

frequency

SUPPORT

BEAR_

of 4N ILPF

_

PAiR _

:,l.___k..b__4..

175

20.0

21.5

on the system

instability

onset

N _

I!

FLYWHEel"

HOUSING

,T'_

SENSOR

1

FORCE

_

_

GENERATOR

--- _ -

RMANENT

FLYW_.EL

R_dI'ION /

Figure

474

8. Cryogenic

25O

GAIN (B.)

SEAL

PO_I"ION

I,

-- _- _ -_ _ -_ _- _- _-

Magnetic

_._an_a _

Bearing

Test

Facility

E_ ¢au.

Design.

gain.

0.00?4

stiff, gain

m

FB_

,

L

I

=

l_Power

Figure

9. Block

Diagram

I

I

/umpllfier+Walnel.ic

of rotor

controller

simulation test.

Beefing

and magnetic

Coils

_I

bearing.

_ to.o cx- t.o

=. io.c

1.00 50.

o

_ -5o.o

-

1

m -11_' _w = _

150: -2OO -250 i 10.0

t 100.

l 1000 Frequency

Figure

I0. Measured

and Curve

Fit frequency

IV 8o0o. '1 10000

(Hz)

response

function

for DSP.

475

s;mu|ll Qi l.O

7

Ol

Lion

:

"_ i

480

!

/ /

(Z _ Z40 CI _ - 240

,," I ..

test :

unstable

_ _sf.able

6

E v

5

,3:

m (4 £:

4

O_

3

2'o

3o Damping

_o Cc

5'o

(dim)

Figure I I. Comparison of measured and predicted natural frequencies on the instability threshold.

X _"

sensor

.,-;lle

CmcCq

B*u_m

K_

,%

I

H,I,

im|

Ro¢_r

_-_.

Figure 12. Fourteen mass rotor model and actuator connection. 476

1

I

0

_F

8

:F o

e._

o

0

8 0

|

;!

o

o

o

O

o

o

ol ,iL

o

o _

o ]

ol 0 -lO.O

-|.0

4,0

-4,0

-|.0

°

6.0

_l.O

40

4,0

0.0

10,0

Reml

Figure 13. I/16" casing wall thickness eigenvalue stability graph.

0

o

e.

o

S o I

i;

9 o

o

o

o

°i

o

-,e.e -e.e

.e.o

-,,.e

.a.o

e.e Reel

_.e

4.e

e.o

e.e

,e.e

Figure 14. Uncoupled sensor- (1/I 6" casing). 477

Figure

15. Block diagram of industrial

magnetic

bearing

rotor.

4-

v

2"

Figure

478

16. Comparison

of TAMU simulation

and Measurement

(p:-10 and D:-50).