IMPROVE Aerodynamic Quality System Dynamic Analyses of Wind Tunnel Model

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SYSTEM

DYNAMIC

ANALYSIS TO IMPROVE

OF A WIND

TUNNEL

MODEL

WITH

APPLICATIONS

AERODYNAMIC

DATA

QUALITY

A Dissertation Division of Research of the University in partial requiremems DOCTOR

submitted

to the Studies

and Advanced of Cincinnati of the of

fulfillment

for the degree OF PHILOSOPHY

in the Department Industrial, of the College

of Mechanical, Engineering of Engineering

and Nuclear

1997 by Ralph B.S.M.E., M.S.M.E., David Buehrle of Akron of Cincinnati 1985 1988

University University

Committee

Chair:

Randall

J. Allemang,

Ph.D.

SYSTEM

DYNAMIC

ANALYSIS TO IMPROVE

OF A WIND

TUNNEL

MODEL

WITH

APPLICATIONS

AERODYNAMIC

DATA

QUALITY

ABSTRACT The research aerodynamic required pressures, to unsteady angular investigates data. During the effect wind of wind tunnel tunnel model system to obtain balance model dynamics lift and forces system on measured drag and data, the

tests designed steady-state

aerodynamic and model

measurements attitude. and The

are the

moments,

However, inertial

the wind tunnel loads which force result

can be subjected translations model and attitude of of a

aerodynamic rotations.

in oscillatory and data inertial taken

steady-state by filtering goals

balance

measurements high model model

are obtained vibrations. dynamics

and averaging of this research steady-state

during

conditions the effects and develop

The main

are to characterize aerodynamic data

system

on the measured

correction are

technique

to compensate dynamic inputs. dynamic

for dynamically response of the

induced model modal

errors. system

Equations subjected

of motion to arbitrary to study the the model NASA This high

formulated

for the and inertial

aerodynamic effects

The resulting response the

model

is examined data.

of the model of motion or angle Research

system

on the aerodynamic effect of dynamics that is used

In particular, inertial at the the world. during

equations attitude, Langley activity levels

are used of attack, Center and

to describe measurement other wind model

on the routinely

system tunnel attitude

facilities sensor

throughout response

was prompted of model

by the inertial while

observed Facility

vibration

testing

in the National

Transonic

at the NASA

Langley ResearchCenter.The inertial attitude sensorcannotdistinguish betweenthe gravitationalacceleration andcentrifugalaccelerationsssociated a with wind tunnelmodel systemvibration, which resultsin a model attitudemeasurement biaserror. Bias errors over an orderof magnitudegreaterthanthe requireddeviceaccuracywerefound in the inertial model attitude measurementsuring dynamic testing of two model systems. d Basedon a theoreticalmodal approach, methodusing measured a vibration amplitudes and measured calculatedmodal characteristics f the model systemis developedto or o correct for dynamic bias errors in the model attitudemeasurements.The correction methodis verified throughdynamicresponse testsontwo modelsystems andactualwind tunneltestdata.

ACKNOWLEDGMENTS I wish to thank Dr. Dave grateful advice my adviser, Dr. Randall Rost, J. Allemang, for their and my graduate and support. review committee,

Brown,

and Dr. Robert P. Young, program.

guidance

! am especially and his A. Foss, F. Mrs. finite

to Dr. Clarence during this research F. Hunter,

Jr. for his technical I thank my NASA

review

of this document Mr. Richard

supervisors, H. Lucy, ! would

Dr. William Fernald, Genevieve element Bridget, work "Modal

Dr. William

S. Lassiter,

Mr. Melvin studies.

and Mr. William

for their encouragement Dixon modeling Joseph of the area. NASA Finally,

during

my Ph.D.

also like to thank in the and

Langley I would

Research

Center

for assistance Barbara, during

like to thank

my wife,

children, This entitled

and Blaine, under for AOA

for their patience the NASA Bias Errors".

and understanding program, RTR

my studies.

was

completed

research

274-00-95-01,

Correction

TABLE 1.0 INTRODUCTION 1.1 Introduction 1.2 Problem 1.3 Literature 1.4 Solution 2.0 EFFECTS Description Review Approach DYNAMICS

OF CONTENTS

I 2 11 16 ON AERODYNAMIC DATA 18 19 Forces 19

OF MODEL

2.1 Introduction 2.2 Force Balance Measurements of Balance

2.3 Transformation 3.0 THEORETICAL 3.1 Introduction

FORMULATION 25 25 28 28 29 30 30 31 31 34 35

3.2 Dynamic 3.2.1 3.2.2 3.2.3

Equations Lagrange's Kinetic Potential

of Motion Equations

Energy Energy Dissipation Forces of Motion Function

3.2.4 Energy

3.2.5 Generalized 3.2.6 Equations 3.3 Modal 3.4 Analysis Model

Simplified

3.4.1 Two Degree

of Freedom

Example

2.4.2Extension Multiple Degreeof Freedom to System 4.0 MODEL ATTITUDE BIAS ERRORCORRECTION 4.1 Introduction 4.2 Modal Correction Theory 4.3 Modal CorrectionImplementation 5.0 EXPERIMENTAL VERIFICATION 5.1 Introduction 5.2 Wind-Off DynamicResponseests T 5.2.1 TestSetupandProcedure 5.2.2 Commercial ransportModelTestResults T 5.2.3 High Speed TransportModel TestResults 5.3 High Speed TransportModelWind TunnelTests 5.3.1 TestSetupin Wind Tunnel 5.3.2 DynamicResponse estsin Wind Tunnel T 5.3.3 Wind TunnelTestResults 6.0 CONCLUDINGREMARKS 7.0 REFERENCES APPENDIXA: Effect of Aerodynamic Forces ModalCharacteristics on

42

44 45 55

59 59 59 64 72 84 84 86 90 98 102 105

LIST OF FIGURES Figure 1.1 Figure1.2 Figure1.3 Figure1.4 Figure2.1 Figure2.2 Figure3.1 Figure3.2 Figure3.3 Figure3.4 Figure3.5 Figure4.1 Figure4.2 Figure4.3 Figure4.4 Figure5.1 Figure5.2 Figure5.3 Figure5.4 Figure5.5 Figure5.6
National Schematic Effect Wind Transonic of wind Facility tunnel model model support system. attitude cavity. axes. for Cta=0.05. measurement. system. 4 5 9 10 20 23 26 36 37 38 41 47 53 54 57 6O 62 65 66 mean AOA 68 mean AOA 69

of vibration tunnel model forces

on inertial

model

instrumentation and model

Aerodynamic Influence Reference

coordinate

of angle of attack coordinate

error on drag coefficient

systems. 9.0 Hz vibration 9.2 Hz vibration mode. mode.

Sting bending Sting bending Two degree Mode shapes

in yaw plane, in pitch plane, of freedom

model. of freedom at natural system. system. method. bay. in the yaw plane. mode. mode. example. frequency of 0_y.

for two degree of model of model of model

Harmonic

motion

Yaw plane mode Pitch plane mode Flowchart

of modal

correction assembly

Test setup in model Shaker attachment

for excitation

Sting bending Model yawing

in yaw plane, on balance, AOA,

10.3 Hz vibration 14.4 Hz vibration

Measured versus

mean

estimated

bias, and corrected input at 10.3 Hz. bias, and corrected input at 14.4 Hz.

yaw moment

for sinusoidal estimated

Measured versus

mean AOA,

yaw moment

for sinusoidal

iii

Figure5.7 Measured meanAOA, estimated bias,andcorrected meanAOA versuspitch momentfor sinusoidalnput at 11.2Hz. i Figure5.8 Measured meanAOA, estimated bias,andcorrected meanAOA versuspitch momentfor sinusoidalnput at 16.2Hz. i Figure5.9 Stingbendingin yawplane,9.0 Hz vibrationmode. Figure5.10 Model yawingon balance, 9.8Hz vibrationmode. 2 Figure5.11 InertialAOA measurement, acceleration, yaw andyaw moment versustime for 9.0Hz sinusoidalinputin yawplane. Figure5.12 InertialAOA measurement, yawacceleration, andyaw moment versustime for 29.8Hz sinusoidalinputin yawplane. Figure5.13 Measured meanAOA, estimated bias,andcorrected meanAOA versusyaw momentfor sinusoidalnputat 9.0Hz. i Figure5.14 Measured meanAOA, estimated bias,andcorrected meanAOA versuspitch momentfor sinusoidalnput at9.2 Hz. i

70

71 74 75

76 77

79

80

AOA andestimated biaserrorfor 9.2 Hz sinusoidal Figure5.15 (Top) Measured excitationin pitchwith 0.25Hz modulation.(Bottom) Corresponding 82 measured balance pitch moment. Figure5.16 (Top)Measured AOA andestimated biaserror for randomexcitation in pitch. (Bottom)Corresponding easured m balance pitch moment. 83 Figure5.17 Measured andcorrected meanangle-ofattackfor sinusoidal excitationat7.3 Hz. andcorrected AOA for sinusoidal xcitationat e Figure5.18 (Top) Measured 7.3 Hz with 0.5 Hz modulation. Bottom)Corresponding ( balance yaw moment. 88

89

Figure5.19 Angle-of-Attack(AOA) for first sixty-fourseconds a wind tunnel of 91 teston a high speed transportmodel. Figure5.20 (Top)Time domainresponse theAOA measured of with the servoaccelerometer sensor ndthe corrected a AOA afterremovalof the dynamicallyinducedbiaserror. (Bottom) Correspondingime t domainmeasurement yawmoment. of

93

iv

of with theservoFigure5.21 (Top) Time domainresponse theAOA measured accelerometer sensor ndthecorrected a AOA after removal of the
dynamically induced domain measurement bias error. (Bottom) of yaw moment. Corresponding time 94

Figure5.22

(Top) Time domain response of the AOA measured with the servoaccelerometer sensor and the corrected AOA after removal of the dynamically induced domain measurement bias error. (Bottom) of yaw moment. Corresponding time 95

Figure5.23

(Top) Time domain response of the AOA measured with the servoaccelerometer sensor and the corrected AOA after removal of the dynamically domain induced bias error. (Bottom) Corresponding time 96 measurement of yaw moment.

v

LIST OF TABLES Table5.1 Table5.2 Table5.3 Table5.4 Table5.5
Modal Modal Modal Parameters Parameters Parameters of Wind of Wind Intervals Transport Transport Transport model Model Model Worst Natural Mode Case Loading Frequency Radius Conditions Comparison for Commercial for High Speed Transport Transport Transport Model Model Model in Test Section 64 72 86 90 for One Second Data 97 107 108 109

for High Speed Tunnel Tunnel Results Results

Summary Summary Acquisition

AppendixA Table1 AppendixA Table2 AppendixA Table3

Comparison

vi

LIST aB(t) acceleration centrifugal

OF SYMBOLS

bias error estimate acceleration normal tangential longitudinal signal acceleration acceleration acceleration device

a c

an(t) at(t) ax(t) A fil

time dependent time dependent time dependent filtered AOA

from inertial

Ar

peak acceleration time dependent

for r th mode unfiltered AOA signal

Aunf (t)
cij CO

damping

coefficients

drag coefficient force coefficient for degree of freedom i

CFi CC

lift coefficient slope of lift coefficient versus angle of attack

CM

pitching-moment moment coefficient

coefficient for degree of freedom i

CM i

ccr
dcg/bc

correlation distance distance

coefficient from model

for least square mass center

fit of mode

r balance center

of gravity

to model

dF/bc di D

from point of force application length corresponding function

to model

balance i

center

characteristic energy

to degree

of freedom

dissipation

vii

f, FA
F
c

natural

frequency

of r th mode

in Hertz

axial force centrifugal force

FD FL FN
g i

drag force lift force normal force

gravitational scalar inertia stiffness bending index about

constant

the y-axis

for a reference

at the model

balance

center

influence stiffness stiffness of included coefficients mass of lumped of degrees coordinate

coefficients

kr
m

torsional number inertia model number number modal

modes

m_j
mm

n

masses

used to represent

the wind tunnel model

model

system

N p_ Pry qi

of freedom for mode ry r

in the analytical

amplitude
.th

for mode

generalized of

coordinate
i th

derivative

generalized

coordinate

with respect

to time

q_

dynamic

pressure

viii

ai

non-conservative generalized generalized current mode

generalized

applied

force (or moment) degree

associated i

with qi

an OMi
?-

aerodynamic aerodynamic number

force for translation moment for translation

of freedom

degree

of freedom

i

rp ry S Si T t U
Vr(t)

designates designates reference reference kinetic

pitch plane mode yaw plane mode area of the model area for degree of freedom i

energy

of the system

time in seconds potential energy of the system velocity for mode wind velocity displacement for r th mode r for rth mode

time dependent peak velocity free-stream

v,
V=

Yr(t)

time dependent peak displacement

rr
o_
O_

for rth mode undeflected sting and inertial coordinates

pitch rotation model estimate difference model effective attitude attitude,

angle between

or angle of attack attitude with bias error correction

6
A

of model

E

error of r th vibration mode

Pr

radius

ix

COl.

circular

frequency

of rth mode

d dt derivative with respect to time

_r It]

modal matrix

damping

for mode

r

of damping

coefficients

[-,.]
[_ [_ (q}

identity

matrix

matrix matrix vector subset

of stiffness of inertia

coefficients coefficients coordinates coordinates forces forces transformed to modal space representing rigid model

of generalized of generalized of generalized of generalized of modal

{Q}
{Q'}

vector vector vector

(p} {_,}_ [_]

coordinates modal modal vector matrix for mode r

mass normalized mass normalized

diagonal

matrix

of natural

frequency

squared

[_]

modal,

or eigenvector

matrix

diagonalized

damping

matrix

(x,y,z)
(xs, Ys, zs) (x_o, Y_o, z_o)
(XBi, yBi, ZBi)

inertial

coordinate

system system system relative to the inertial mass coordinate system

undeflected origin body

sting coordinate

of sting coordinate axis coordinate

system

for ith concentrated

x

(Xi, yi,

Zi)

position rotation

of ith body coordinate of ith body coordinate

axes relative axes relative

to sting axes to sting axes

13)

LIST AOA BPF Angle of Attack filter of gravity model

OF ACRONYMS

bandpass

c.g.

mass center finite Hertz lowpass National element

FEM Hz LPF NTF

filter Transonic Facility

xi

Chapter

1

INTRODUCTION 1.1 Introduction Model vibrations are a significant [1], model and support problem vibrations stings, when testing in high pressure model to foul, wind tunnels. integrity,

As discussed overload force

by Young balances

can jeopardize cause models

structural affect

aerodynamic

data, and often limit test envelopes.

The National Langley

Transonic Center

Facility which

[2] , NTF,

is a transonic

wind

tunnel

located

at NASA number foot. Severe began support in the of

Research

has the capability pressure

for testing

models

at Reynolds

up to 140 million The NTF

at Mach

1 and dynamic with

up to 7000

pounds

per square

is a cryogenic have

facility been

operating

temperatures

as low as -290°F. since the tunnel and model uncertainty The

model operation

vibrations in 1984.

encountered 3 through a 1993

on a number 6 document wind

of models studies test,

References

of model increased vibration.

vibrations model

in the facility. data

During

tunnel

attitude

was observed

for periods

of high model shaker input model

response

the onboard airflow, These

instrumentation

to electrodynamic

to the model systems errors inertial

without

tunnel

"wind-off", wind-off

was examined tests the found

for two transport model vibration accuracy

[7, 8] at the NTF. over an order of

dynamic than

induced for the

magnitude measurements.

greater

required

model

attitude

This research investigates theeffectof wind tunnelmodelsystemdynamicson measured aerodynamic data. The objective is to improve the aerodynamic data quality during conditions of high model vibrations. The equationsof motion are developedusing Lagrange's equationsfor the generalized problemof a cantilevered wind tunnel model. This was the first time a systemdynamicanalysisapproachwas usedto examinethe effects of model vibrations on the aerodynamic data. The modal solution of the

equations motion providesvaluableinsight into the underlyingphysicsand provides of the basisfor the proposed "modalcorrectionmethod"for dynamicallyinducederrorsin wind tunnel model attitudemeasurements. he proposedcorrection methodusesthe T modalpropertiesof themodelsystem minimizethe numberof transducers to requiredfor implementation. This is critical due to limited interior model spaceand thermal considerationsassociated with cryogenicwind tunnels where heated instrumentation packages required.The methodwas the first time domain techniquedevelopedto are compensate multiple modesin both the pitch andyaw planesof the model system. for The ability to correct in the time domain is necessitatedy the random natureof the b measuredmodel dynamic responseand the increasedemphasison correlating time dependent changes modelattitudewith aerodynamic in loads.

1.2

Problem

Description of wind cylinder, tunnel referred tests are conducted to as a "sting", with a model which supported on the end of a or is

The majority long tapered movable

is cantilevered

from an arc sector support system

vertical

strut-type

of support.

A schematic

of the NTF model

2

shownin Figure 1.1. Pitch attitudeof the modelis adjustedby rotationof the arc sector. The arcsectorsystemis designed suchthatthecenterof rotationof thearc sectoris at the model,so that changing modelpitch angledoesnot translate modelto a different the the position relative to the wind tunnel test section. Roll attitude of the model can be adjustedby rotationof the sting. A six componentforce balanceis usedas the single point of attachment etweenthe modeland supportsting as shownin Figure 1.2. In b order to achievethe desiredmeasurement accuracyon three force and three moment aerodynamic load components, balanceis designed be flexible ascomparedto the the to sting. The flexibility of the balance resultsin vibrationmodescharacterized y the model b vibratingasa rigid bodyon a spring(forcebalance)n pitch, yaw androll. Thesemodes i are typically lightly dampedand often excitedduring wind tunnel testing [6]. Other primarylow frequency vibrationmodesareassociated ith stingbendingin thepitch and w yaw planes,where most of the bending deformationoccursover the small diameter portionof the stingnearthemodel.

This dissertationwill focuson the "pitch-pause"9] wind tunneltest techniquesincethe [ supportingwind tunnel test datawere acquiredusing this techniqueat the NTF. The pitch-pause technique a commontestmethodusedto obtainaerodynamic is loadsdatain continuousflow, closedcircuit wind tunnels. In the pitch-pause technique,the model is movedto a prescribedangleof attackwith respectto the velocity vector,the transient responses reallowedto decay,andthenthe forcebalance,pressure, ndangleof attack a a data are measured.At the NTF, the data measurement period is one second. The

3

Bearings

Sting Fixed fairing Model Roll drive

Arc sector Locking pin -_ Shell Crosshead Insulation

Hydraulic cylinder

Figure

1.1

National

Transonic

Facility

model

support

system.

Balance moment center Model attach point Y
X

AOA package

Balance g sin(z

Balance/sting joint

Figure

1.2

Schematic

of wind

tunnel

model

system.

5

procedure Increasing times (less

is then repeated emphasis time on

for a series tunnel for

of model

attitudes, is pushing to

which

is referred towards the

to as a polar. shorter on test the

on wind point

productivity

facilities decay) and

transient

dynamics

effect

aerodynamic

data accuracy

must be evaluated.

During

wind

tunnel

tests, leading

free stream to unsteady

turbulence forces low-pass

produce

fluctuations

in dynamic balance to obtain

pressure and angle "steadyfor the to be and the response the the In

and flow angularity of attack state"

on the model. filtered

The force

measurements attitude, variation

are typically aerodynamic

and averaged data [10].

model

force

and moment component

It is not unusual force data

peak-to-peak

of the dynamic

of the

"steady-state"

50% or more of the true mean. resulting due to model the vibration

In Reference

[11], the unsteadiness that,

of the airflow vibration

is discussed.

It is noted the

if the model to

flow

unsteadiness of interest methods for Aerospace Quality and

is excessive, may

ability

accurately [11]

measure approaches tunnel.

aerodynamic problem

quantities

be compromised.

Mabey

by examining Group Flow

to reduce Research Data

the flow unsteadiness and Development Requirements"

in the wind (AGARD) [12],

the Advisory "Wind accuracy vibrations pitching Tunnel

report one

entitled data and and

Accuracy

of the

issues

is the measurement and support

of, and correction systems. Accuracy

for, aeroelastic requirements regime

deformations

of models moment ;

[12] for lift, drag, are:

for transport Drag In order

type aircraft

in the high speed ;

Lift Coefficient coefficient free-stream

AC L = 0.01 AC M =0.001.

Coefficient to maintain

AC D = 0.0001 the required

Pitching-moment the tunnel

accuracy,

6

conditions must be repeatablewithin the following boundaries: Tunnel total and stagnationpressure, P= 0.1%;Model angleof attack, Ao_ = A
AM = 0.001. of 1 drag long-range As an example, for conditions near a maximum the payload 0.01°; and Mach Number: an increase 1% for the

lift to drag ratio, by approximately

count

(AC D = 0.0001)

will decrease aircraft.

mission

of a large transport

The

predominant in wind

instrumentation tunnel testing

used at NASA

to measure Langley

model Research

attitude Center

or angle and wind

of attack tunnels 13. 1.2. with The The the

(AOA)

throughout inertial AOA

the world package uses

is the servo is shown a servo

accelerometer installed

device

described

in Reference in Figure parallel provides

AOA package

in the nose of a test model with its sensitive axis

accelerometer For quasi-static

longitudinal attitude a range During dynamic

axis of the model.

conditions,

this sensor

a model

measurement of +20 °. wind

with respect

to the local gravity

field to an accuracy to an acceleration

of _+0.01 ° over of 175 micro-g's.

An increment testing,

of 0.01 ° corresponds the model flows mounted

tunnel

at the

end

of the

sting

experiences attitude

oscillations

due to unsteady

that result

in a bias error in the model

measurement.

Young response study with

et. al [7] conducted to a simulated

an experimental dynamic environment

study

on the inertial

model The

attitude

sensor

in 1993 is due

at the NTF. to centrifugal harmonic

experimental associated is shown

[7] clearly model

established

that AOA

bias error mode

forces this

vibration.

For a single

in simple

motion,

7

schematically Figure 1.3.TheAOA package in moveson a circular arc abouta centerof
rotation be treated outward divided model device vibration multiple that is mode similar from the dependent. For a single mode, the motion The of the AOA package will can act

to that center arm.

of a simple of rotation During

pendulum. and be equal dynamic

centrifugal

acceleration velocity acceleration

to the

tangential

squared due to

by the radius vibration accuracy mode vibration

wind-off

tests, centrifugal of magnitude was found

created of 0.01

a bias error degree. The

over an order The bias error

greater

than the desired on the

to be dependent of the problem

and amplitude. modes

study revealed involving

the complexity

when

were present

both pitch and yaw motions.

Although

the Reference dynamics exists

7 study was conducted is not unique model

at the NTF, tunnel

the AOA

measurement wind device in the (i.e.

error tunnels. in the inertial

due to model The problem presence model

to this wind is being

or to cryogenic by an inertial of error dynamics

anytime

attitude

measured The

of significant attitude

model

system

vibrations.

amount system

measurement system)

is dependent

on the model to quantify

will vary tests.

for each model

and is very difficult

during

actual

wind tunnel

Space used model

limitations to implement

in wind tunnel a correction cavity sensor

models

require

that the number This 1.4.

of additional

transducers tunnel such must as be

be minimized. shown in Figure

is illustrated

by the wind facility,

instrumentation special AOA

Also,

in a cryogenic The

the NTF, placed

packages to maintain

[13] are required. the sensors

instrumentation accurate and

in a heated

package

and obtain

calibrated

oI.

_.,

AOA package
(o r

Y
_d

ac

X

PF

Mode center of rotation

X
I

___/
I I I I

g a, I
I I I I I I

Figure

1.3

Effect

of vibration

on inertial

model

attitude

measurement.

C_ O

c_

o

_

o

LT_

measurements placed outside

at extreme of the heated due

temperatures instrumentation

(-290°F). package

Past experience has revealed

with problems loss.

accelerometers ranging The from

sensitivity temperatures requirements inertial

shifts

to temperatures limited placing output affects

variations interior

to complete model space,

signal and

extreme accuracy of the

conditions, necessitate sensor not only

stringent for correction The if

the additional heated inertial axial

transducers instrumentation AOA device

necessary package. but can,

AOA

in the the

centrifugal are

acceleration sufficiently of dynamics dissertation.

amplitudes

high, affect the desired on pressure

force or drag measurement can be a factor but

accuracy. addressed

The effect in this

measurements

is not

1.3

Literature

Review of wind Uselton tunnel model system dynamics were restricted vibrations to a planar on measured rigid body Lagrange's Again, that

Previous problem. dynamic motion equations

analyses Burt and stability

[14] examined The equations using Newton's of motion

the effects of motion second law.

of sting

derivatives. plane

were derived Billingsley

for model [15] uses

in the pitch to derive

the equations

for a cantilevered plane.

sting-model

system.

the derivation model mounted includes dynamics yaw

is restricted vibration angle pitch

to motion

in the pitch

Young

et. al [7] have pitch angle

shown

can result of attack yaw

in an error device. plane

in the

measured

for a modelis required that

inertial both

Therefore,

an analytical evaluate

model the

and

dynamics data.

to better

effects

of model

on the measured

aerodynamic

11

The first correctiontechnique model vibrationinducederrorsin inertial wind tunnel for modelattitudemeasurements wasdeveloped 1984by PeiterFuijkschotof theNational in AerospaceLaboratory in the Netherlands[16]. This time domain technique was developedfor one vibration modein eachthe yaw and pitch plane. Two additional accelerometers areusedto measure tangentialaccelerations ueto the yaw andpitch the d motion of the model. The tangentialaccelerations integratedto obtain velocity, are squared,and divided by a scalefactor to compensate the effective radius of the for vibrationmode. This signalis thenadded theunfilteredAOA outputto cancelthe bias to term.Themoderadiusin theyaw andpitch planeis determined tuning a potentiometer by while manuallyexciting the model in the yaw and pitch plane,respectively. A major drawbackis that this techniquedoesnot address casewheremultiple yaw andpitch the modesarepresent.

Renewedinterest in the effects of model vibrations on the measuredaerodynamic quantities was prompted by the 1993 study of Young et. al. [7]. Prior to this

investigation, nly a singlemodein themodelpitch andyawplaneswasconsidered.This o studyshowedthepotentialfor multiplemodes eachplaneto participate. Several ecent in r studieshavebeenconducted atNASA LangleyResearch Centerto examinethe effectsof model vibration on model attitudemeasurement devices[7, 8, 17, 18]. In addition,

analysis of the vibration effects on gravity sensinginclinometers is underway by Fuijkschot[19,20] of theNationalAerospace Laboratoryin the Netherlands.

12

Frequencydomaincorrectiontechniques havebeenproposedby Young et. al [7] and Tchenget. al [18]. The correctionmethodof Young et. al is derivedusing an average displacement f the model throughone cycle of vibration. This methodrequiresthe o measurement the naturalfrequencies of andcorresponding eakacceleration p magnitudes from the frequencyspectra the yaw andpitch accelerations.Young proposes of that the requiredscalefactor,effectiveradius,bedetermined empiricallyduring wind-off ground vibration tests.The correctionmethodof Tcheng[18] requiresthe measurement the of natural frequenciesfrom the frequencyspectraof the tangentialaccelerations and the second harmoniccomponents from thefrequency spectrum the unfilteredAOA signal. of This techniqueis difficult to implementdueto the participationof multiple modesand the required data accuracyto measuresmall magnitudesat the second harmonic frequency.Both techniques aveimplementation h problemsdueto the requiredfrequency domain signalprocessingof randomwind tunnel test dataover short (1 second)data acquisitionperiods.

Another method under development y Tripp [8] usestime and frequencydomain b analysesto estimateand correct for the dynamic bias error. The proposedtime and frequencydomainbiaserror correctionalgorithmis basedon the bias term for a single yawmodebeingrepresentedy thesquare the velocitydividedby the moderadius. A b of sensitivecorrelationtest betweentime seriesis providedby the cross spectraldensity coherence function. Correlated spectral omponents c commonto boththe unfilteredAOA signalandsquare the dynamicyaw or pitch measurement of appearin the crossspectral density coherencefunction. Other spectralcomponentscommonto the auto spectra

13

which arenot phasecoherent,i.e. unsynchronized, tendto be removedfrom the cross spectrumby averagingand canceled normalization,and do not appearin the cross by spectralcoherence function. The coherence functionandcrossspectrumthus providea meansof detecting andquantifyingAOA biaserrorsdueto angularoscillation. The cross spectraldensitycoherence functionis examinedfor spectralcorrelationwithin the AOA passband and the corresponding modal frequencies identified. The modal radius are corresponding eachnaturalfrequency estimated a leastsquares of the integralto is by fit squared yaw (or pitch) measurement the dynamicAOA output.This requiresa longer to datarecordinitially (>_10 seconds)o obtain a goodestimateof the moderadius. This t moderadiusis thenusedas a constantfor the remainderof the datapoints. A bandpass filter aboutthemodalfrequency usedto isolatea particularmode. The resultingsignal is is thennumericallyintegratedandsquared anddividedby the scalarmoderadiusto give the biaserror associated with a particularmode. The correctAOA output is thenfound by subtractingoff the contributionsfrom all of the modesshown to have spectral correlationandlow-passfiltering the result. In wind-off dynamictests[8], this method had implementation problemsdueto significantlow frequencyrandomdisturbances in the integral-squaredaw (or pitch) measurements y which wereabsentin the AOA time series.

After the needto compensate multiple vibrationmodeswas demonstrated NASA for at Langley ResearchCenter [7,8,17], Fuijkshot extendedhis time domain correction techniqueto compensate multiple modes[19, 20] using Euclideankinematicsof a for

14

solid body. This work was done in parallel with the proposedtime domain "modal correctionmethod"that is the subjectof this dissertation.For a given planeof motion, Fuijkshotproposes measuring both therotationalrateandthe velocityof the rigid model anddeterminingthe correctiontermfrom the productof the two signals. The rotational rateandvelocity signalsfor the yaw (or pitch) planewill containthe contributionsfor all modesacting in that plane. The radius for eachof the modeswill not need to be determined explicitly. The correctiontermsfor the pitch andyawplanesarethen added to the unfilteredAOA signalprior to filtering. The methodis currentlyunderevaluation andhasbeenverified for sinusoidaltests[20]. The velocitycan be determinedthrough integration of an accelerometer ignal. In application,the rotational rate has been s obtainedby integratingthe differencefrom two linear accelerometers ttachedto the a model fuselage,oriented in the yaw (or pitch) plane, divided by the accelerometer separationdistance. This assumeshe accelerometersre connectedby a rigid model t a fuselage. This correction techniquerequiresfour additional transducers order to in determinethe rotational rate and velocity in the pitch and yaw planes. The limited interior spacein modelsandextremetemperature environments somewind tunnels, in where heated instrumentationpackagesare required, may prohibit this number of transducers.This methoddoesnot providea meansof checkingthe rigid-body model assumptions ponwhichit is based. u

In general,the proposed time domaincorrections provideseveraladvantages. First, time domainsignalprocessing be appliedto the randomwind tunnel test data acquired can

15

over short data samplingperiods. Secondly,the inertial AOA packageoutput can be correctedfor the dynamicallyinducederrorsto give an accuratetime domain model attitude signal. The measurement time varying signalsand analysisof this data is of becoming a more significant requirementfor subsonic and transonic experimental researchers[21]. he measurement instantaneous T of andaverage valuesof modelattitude andcorrelationwith measured modelloadsis gainingincreased interest.

1.4 The

Solution research

Approach is divided into the following four areas: examination of the effects model; tunnel development model attitude of

models

dynamics

on aerodynamic for model vibration

data; development induced verification. errors

of a theoretical in inertial wind

of a correction measurements;

and experimental

In Chapter dynamics introduced propagation

2, the significance on the measured

of the problem drag forces force and

is shown

by examining drag vibration

the effects coefficient.

of model Errors The forces

corresponding with model

by the centrifugal

associated during

are quantified. of the measured

of the angle of attack body

errors

the transformation

from the model

axes to the wind axes is also examined.

In Chapter system describes are

3, the governing derived

equations form

of motion using

for a cantilevered equations. of motion

wind This

tunnel

model

in discrete

Lagrange's The equations

formulation using a

both pitch and yaw plane dynamics.

are solved

16

modal analysisapproach obtain the generalized, odal,solution. Basedon observed to m behaviorof wind tunnelmodelsystems,heproblemis simplified. t

In Chapter4, the theoreticalmodelis usedto developa time domaincorrectionmethod for model vibrationinducederrorsin inertial wind tunnel model attitudemeasurements. The implementationof the proposed"modal correctionmethod" using digital signal processing techniques alsodescribed. is

In Chapter5, the modalcorrectionmethodis verifiedthrougha combinationof wind-off dynamictestson two transportmodel systems and wind tunnel test data. The modal correctionmethodis appliedto wind-off model dynamicresponsedata for sinusoidal, modulatedsinusoidalandrandomshakerinputsin the pitch andyaw plane. In addition, the modal correctionmethodis applied to measured dynamic responsedata recorded duringwind tunneltestingof a transportmodelin theNTF.

In Chapter6, the research resultsare summarized andrecommendations future work for aredescribed.

17

Chapter EFFECTS OF MODEL DYNAMICS

2 ON AERODYNAMIC DATA

2.1

Introduction tunnel data acquisition, over unsteady a time flow and Steinle and Stanewsky [ 12] recommend out the that samples of dynamic However, by as of

For wind data

be taken and

interval

sufficient the the

to average desired centrifugal wind tunnel that

effects

response discussed vibration For

to establish Young [17],

confidence

interval. created

by Buehrle results

acceleration model the

model

in a bias error model offset

in the inertial response, which greater

attitude inertial

measurement. angle of attack

wind-off

sinusoidal has a mean

it is shown cannot

measurement Errors possible

be removed

by filtering device accuracy

or averaging. of 0.01 ° are

over an order of magnitude [7, 8].

than the required

In this quantified.

chapter,

the

effect effect

of model

vibration

on

the

force

balance

measurements

is of

The direct forces

of the vibration Typically, balance which

induced the forces

centrifugal

force on the accuracy are measured that is fixed force

the measured internally model. using

is examined. strain-gage

and moments system drag

by an to the

mounted This data

has a coordinate the desired

is transformed model process attitude.

to obtain The

lift and

components error during

the measured

propagation

of the model

attitude

the transformation

is also examined.

18

2.2

Force

Balance

Measurements induced centrifugal force forces result in errors being introduced into the

Model balance

vibration forces.

The centrifugal

F can be written
C

Fc = mma c where m m is the model mass and a C is the total centrifugal on the model will be small. acceleration.

(2.1) It is anticipated

that the centrifugal a centrifugal degrees, acceleration pounds. dynamics,

force acting

For the servo attitude This

accelerometer, error of 0.1

acceleration is

of .00175 the

g's corresponds required device centrifugal tunnel

to a model accuracy. force

which

10 times

same

centrifugal 150 model

will result

in only a 0.26 pound pressure wind

for a model

weighing

For the high dynamic this would result

tests that produce

significant accuracy.

in a drag coefficient

error less than the required

2.3

Transformation significant attitude.

of Balance

Forces forces may occur due to errors attitude error in the measured drag force in the

A more model

error in the measured

The propagation by Owen

of the model The

into the measured forces

was described model body

et. al. [22].

strain

gage balance and transformed Figure

are measured

axes, which

are fixed to the model, model attitude.

to the lift and drag force the relevant the forces and

components coordinate measured defined direction.

using the measured axes. relative The axial

2.1 shows force,

force,

FA, and

normal

FN, are

balance force,

forces FD, are flow two

to the body to the wind model

axes, (XB, ZB). The axes, (x ,z), which _, defines

lift force, have one

FL, and drag axis parallel

relative The

to the the

measured

attitude,

the transformation

between

19

F'ltFN
direction ZB ¢ _rz L_ FA

Figure

2.1

Aerodynamic

forces

and model

coordinate

axes.

20

coordinate

systems.
F L = F N cos(Or

The lift and drag forces
) - F A sin(or )

can be written (2.2a) (2.2b) can be written (2.3a) (2.3b) attitude error, e, are defined by the

FD = F a cos(ct ) + F N sin(or ) If the model attitude has an error, E, the lift and drag forces

FL = F N cos(o_ + _ ) - Fa sin(or + E ) Fo = F a cos(or The errors differences + E ) + FN sin(oc + Iz ) due to the model

in the lift and drag forces of Equations 2.2 and 2.3.

AF L = FN (cos0x AF D = FA (cos(or Expanding

+ E ) - cos(o_ )) - FA (sin(o_ + E ) - sin(or )) + _ ) - cos(o_ )) + FN (sin(or + e ) - sin(o_ )) expressions and applying small angle assumptions

(2.4a) (2.4b) for e, (2.5a) (2.5b)

the trigonometric

AF L = -e (F N sin(or )+ FA cos(o_ )) AF D = _ ( FN cos(or ) - Fa sin(cx )) Substituting from Equation 2.2 for the terms in parentheses results in

AF L = -EF o AF D = eE L The aerodynamic forces are expressed in coefficient form as

(2.6a) (2.6b)

CL -

EL

and

C D -

FD

(2.7)

q_S where pressure, CL is the coefficient

q_S of lift, is the coefficient of drag, q_ is the dynamic

CD

and S is the reference

area of the model.

21

RewritingEquation2.6 in coefficientform gives
AC L = -EC D (2.8a) (2.8b)

ZXCD ECL =

As discussed

in Chapter aircraft

1, the accuracy in the high

requirements speed regime

[12] for lift and drag measurements are: Lift Coefficient, near AC L = 0.01 ; of

for transport-type Drag drag Coefficient, is significantly will

AC D = 0.0001. less than more

Except

for conditions

zero lift, the coefficient Therefore, the error

the coefficient with regard

of lift [23].

in drag accuracy. attitude,

coefficient Assuming gives

be

critical

to its required as a linear

measurement of model

the lift coefficient

can be represented

function

C L = CL_ O_+ Cons tan t

(2.9)

where results

CLa is the slope of Equation

of the lift coefficient

versus

model

attitude

plot.

Substituting

the

2.9 into Equation

2.8b gives

AC D = 180 e ( CLa °t + Constan rt where ot and E are expressed

t) The slope of the lift coefficient versus

(2.10) model [23].

in degrees.

attitude plot for several Using the most versus

characteristic lower,

wing shapes value

range from 0.05 to 0.1 per degree degree, of model the error attitude

conservative, model

of CLa = 0.05per for several values 2.10

in drag error in

coefficient Figure 2.2.

attitude

is plotted

For this plot, the constant term

term in Equation however,

is set to zero. trends

For a non-

zero constant with those

the lines will be shifted,

the basic

will be consistent

shown.

22

0.0025 .... .... 0.002 ...... AOA Error = 0.20 AOA Error = 0.15 AOA Error = 0.10
J ,i J I,g f ,i" °i¢J I .I °_° I .I _' .I" o''" ° .° ..o-" °'° ° '°I° ,f ,I f

- -- AOA Error = 0.05 Error = 0.01

--AOA 0.0015

.e
u

°f j° •J j°

J°

iE
0

0.001
jJ

J

C3
f J J ._ .-°°

j°

0.0005

0 0 2 4 6 (Degrees) 8 10 12

Angle of Attack

Figure

2.2 Influence

of angle of attack

error on drag coefficient

for CLo _=0.05.

23

As can be seen from Figure propagation equivalent error of the errors to those drag measured coefficient

2.2, significant in the model in wind-off that

errors attitude dynamic

in drag coefficient measurement.

can occur Model

due to the errors in an

attitude result the

tests (E>0.1 o) [7, 8] would of magnitude greater than

in the

is an order

required

accuracy

at high angles

of attack.

24

Chapter THEORETICAL

3

FORMULATION

3.1 Introduction In this chapter, derived generalized convenient using the equations Lagrange's of motion Equations approach The resulting Based for a cantilevered [24for 26]. The the wind tunnel model system provides are a

Lagrange equations

method

systematic coordinate

energy system.

defining equations

of motion

in any in terms system model

of motion

are formulated of the model simplified 4.

of the generalized, during provides wind tunnel

modal, tests,

coordinates. the analytical

on observed

behavior

model

is simplified. correction method

This

the basis for development

of the modal

in Chapter

3.2

Dynamic

Equations model

of Motion will be used the planar to represent analysis the wind of Billingsley system. tunnel [15] model and its support both pitch

A lumped system.

mass This

work

extends

to include

and yaw dynamics

of the sting-balance-model

In order coordinate inertial system center model

to represent systems are

the

model

system in Figure

during 3.1. parallel

pitch-pause The coordinate

wind

tunnel

testing,

three

defined

system direction.

(x, y, z) is the The coordinate at the arc sector portion of the is

coordinate

system

with the x-axis

to the wind

(xs, ys, z_) is fixed to the undeflected of rotation. support Recall from Chapter

sting axis and has its origin is the movable

1, that the arc sector adjustment

system

that provides

the pitch

for the model.

The arc sector

25

° ,,,,I

X

N

designed angle section.

such that its center not translate

of rotation

is at the model, position

so that changing relative

the model tunnel

pitch test (xs0, axes of the

does

the model system

to a different

to the wind

The coordinate

(x_, Ys, z_) can be defined coordinate system

by the location angle (_).

of its origin The body

ys0, Zs0) relative (xBi, yBi, zBi) are body axes

to the inertial fixed

and the pitch mass.

to the ith concentrated mass relative

The position

and orientation sting axes

for the ith concentrated
(Xi,

to the undeflected
_i).

are defined

by the translations

Yi,

Zi)

and rotations

(7i, oq,

In the pitch-pause (eq) and paused

method to establish

of wind tunnel "steady-state"

testing,

the model

is pitched in:

to a desired

angle

conditions.

This results

Xs0 = J's0 = Zs0 = _s = 0 where the "o" denotes the motion the derivative with respect to time. The time varying

(3.1) components (Ti, oq, of

representing _i) relative

of the ith mass sting.

are the translations

(xi, yi, zi) and rotations describing

to the undeflected

The generalized system

coordinates

the motion

the cantilevered

sting-balance-model

can be written:

{q}

={Xl

Yl

Zl

T1

°_ 1

_1

...

Xn

Yn

Zn

'_n

°_n

_n} T

(3.2)

where The

n is the number rotation angles

of lumped (7i, _,

masses

used to represent by inertial small terms and

the wind aerodynamic

tunnel

model

system.

13i) induced derivations, order

loading (i.e.,

are small. sin(o_ )----o_;

Therefore,

in the subsequent

angle

approximations

cos(o_ ) = 1) can be used and higher

can be neglected.

27

3.2.1

Lagrange's

Equations Lagrange's _U _qi for i=l ..... N Equations [26] can be written as:

For a lumped

mass model, _D
_qi

d ( _T "_ _T -_--j-_-+--+--=Qil [_qi_qi where: D = energy n = number

(3.3)

dissipation of lumped

function masses used to represent of freedom the wind tunnel model system

N = 6*n = number qi = ith generalized
t_i = derivative

of degrees coordinate

of ith generalized generalized of the system of the system

coordinate applied

with respect

to time associated with qi

Qi = non-conservative

force (or moment)

T = kinetic U = potential

energy energy

3.2.2

Kinetic

Energy of the system can be written [26]:

The kinetic

energy
1 NN

T

=

"_i_=l

_. mijqiqj J=l

(3.4)

where inertia

the

mij

are

inertia

coefficients. and

For small the kinetic

oscillations energy

about

the equilibrium, of {q} only.

the The

coefficients

are constants

is a function

mass

matrix _T
_=0

is symmetric,

i.e., mij=mji . Since

the kinetic

energy

is not a function

of {q},

(3.5)

3qi

28

Taking

the derivative coordinate N Y_ mijitj
j=l

of the kinetic gives:

energy

with respect

to the time

derivative

of the ith

generalized OT

_
Oqi

(3.6)

The time derivative

of Equation

3.6 is:

.-_tt(,-_qi )= jE=lmiSl j

(3.7)

3.2.3

Potential

Energy wind tunnel system. energy model, the potential energy is equal to the strain energy stiffness energy by

For the cantilevered stored Fung

in the sting-model [27]. The as:
NN

A detailed can

derivation

of the strain of the

is given

potential

be written

in terms

influence

coefficients

U

_--

2 l i_=lj_=l t.lqtq j k
.. .

.

(3.8)

where

the stiffness at point

influence

coefficient,

kij, is the force held fixed.

required

at point

(i) due to a unit coefficients function with

deflection

(j) with all other points Taking

The stiffness of the potential

influence energy

are symmetric,

i.e., kij = kji.

the derivative

respect

to the generalized
o_U N

coordinate

( qi ) gives:

_ _., kijq j Oqi j=l

(3.9)

29

3.2.4

Energy

Dissipation viscous

Function damping, [26]. a dissipation function, D, analogous to the potential

For the case of energy function
N

can be defined
N

(3.10)

where the

the damping

coefficients, with

cii, are symmetric, respect to the time

i.e., cij =cii. derivative

Taking of the

the derivative ith generalized

of

dissipation gives: N

function

coordinate OD
_)t)i

- Z co0 j
j=l

(3.11)

3.2.5 The loads

Generalized primary will

Forces forces using are the unsteady a quasi-steady with the translation aerodynamic approximation degrees loads. [15]. The The aerodynamic generalized as: (3.12) pressure and Si is the characteristic of the model attitude. degrees area. The coefficient CFi

generalized be modeled

aerodynamic

forces

associated

of freedom

are modeled

QF i = q_,,SiCF i where, q. is the dynamic linear

will be assumed aerodynamic

and is a function associated

Similarly, of freedom

the generalized are modeled as:

moments

with the rotational

QM

i = q_SidiCM

i

(3.13) length and the coefficient CMi is assumed to be a linear

where function

di

is a characteristic of model attitude.

30

3.2.6 The

Equations equations from

of Motion of motion for the 3.5, 3.7, ith lumped 3.9, 3.11, mass 3.12 and can be obtained 3.13 by substituting 3.3. the

results

Equations

into Equation

In matrix

form this yields: [ M]{/_} + [C]{q} + [K]{q} = {Q} where, (3.14)

{q}

={Xl

Yl

Zl

3'1

°_ 1

Ill

...

Xn

Yn

Zn

"_n

O_n

_n}

T

[C] is a square [K] is a square [M] is a square

matrix matrix matrix

of the damping of the stiffness of the inertia

coefficients, coefficients, coefficients,

cij kij mij

{a}

is a vector

containing

the generalized

forces,

Qi

3.3

Modal

Analysis analysis degree and technique of freedom {q(0)}={q0}. [24, 28] will be used to solve system described The equations modal of motion modes by Equation analysis for the dynamic 3.14 with initial technique is response conditions on the of

The modal the multiple {q(0)}={q0} transformation independent

based

of the coupled set of equations

represented

by Equation

3.14 into an

using the normal

of the system.

In

the

modal

analysis associated

technique,

the

first

step

is to matrices

obtain

the

eigenvalues

and

eigenvectors

with the mass

and stiffness

of the system.

Numerical

31

methodsfor solving the eigenvalue problemarediscussed References 23 and 26. in 21, Another approachis to obtain the eigenvalues and eigenvectors through experimental modalanalysis[29,30]. Oncethe naturalfrequencies ndmodeshapes a areobtained,the solutionto the eigenvalue problemcanbewritten as: [M][_]['032.]= [K][W] where, [W] is themodalor eigenvector atrix m ['032] is a diagonalmatrix of the naturalfrequencies, ,squared _ Normalizingthemodalmatrix with respecto themassmatrixyields: t [_]T [M][_] = ['i. ] [_]T [K][_] = ['03 2.] where,[_] is the mass normalized modalor eigenvector atrix,and m ['I. ] is the identitymatrix (3.16a) (3.16b) (3.15)

The transformation from thegeneralized coordinates, q}, to the modalcoordinates,{p}, { canbewritten:
N

{q(t)}=[_]{p(t)}=

]_ {d_}rPr(t)
r=l

(3.17)

where,

{_ }r is the mass

normalized

modal

vector

for mode

r.

Substituting

Equation

3.17 into Equation

3.14, and premultiplying

by [_]T

yields,

t.Ftdt.l{/,}+ [,02.]{p} =t.F

32

Assuming

the

damping

is a linear

combination the damping

of the matrix.

mass

and

stiffness

matrices,

the

transformation

will also diagonalize

[CI_] [C][cI_] = ['2403. T

]

(3.19)

where

the modal

damping

for mode

r can be written:

_r

-- 20_r

1

{_}T[c]{

_}r

(3.20)

Substituting

Equation

3.19 into 3.18 results

in (3.21)

+
where

]{p} +

]{p}-{Q,}

{Q,}_E_,Ir{Q}

(3.22)

The N independent

equations

corresponding

to Equation

3.21 can be written

as

_0r (t) + 2 4 rO_rP(t)

+ O_2 p(t)

= Qr (t)

,

r=l,2

.....

N

(3.23)

This is the form transformation {q(0)}=

of a single equation [_]{p(0)}

degree

of freedom

system

with viscous

damping.

Using

the

(3.17),

the initial conditions [_]{p(0)}

can be written (3.24)

and {q(0)}=

Premultiplying gives

these

equations

by [_]T[M]

and solving

for the modal

initial

conditions

pr(0)

= {_ }T[M]{q(0)}

and/Sr(0)

= {_ }T[M]{q(0)},

for r=l,2 .... ,N

(3.25)

33

The

solution

to Equation in

3.23 can be obtained

using

the Laplace

transform

method

[24].

This results

pr(t)

=

1--_-i Qr(X )e -_rO3r(t-'_
O_d r 0

) sin0_dr

(t -Z )dx

+e rtl r O cossin dr/ J r d
(3.26) where
(Ddr = O r

_/(1-

_ r2 ) is the damped

natural

frequency

for mode

r.

For a given can be used

set of generalized to solve coordinates, form for the {q}, and

forces modal

and initial

conditions, {p}. from

Equations The Equation and correct

3.22,

3.25

and 3.26 of the is

coordinates, be found

solution 3.17.

in terms The

generalized now

can then

problem vibration

in generalized centrifugal

can be used However,

to estimate the problem

for model

induced

accelerations.

can be simplified

as developed

in the following

section.

3.4 Once

Simplified the natural

Model frequencies system primary and mode shapes based have been obtained, observed the the dynamic during model wind of

the sting-model testing. The

can be simplified dynamic

on behavior affecting

tunnel model angle of the

components pitch axis

wind

tunnel

instrumentation attack device

are in the model has its sensitive

and yaw planes parallel to the

[7, 8].

Since axis

the inertial of the

longitudinal

model,

34

deviceis not sensitiveto roll motionsaboutthis axis. Also, the effectsof axial modeson
the inertial pitch angle of attack device can be removed through filtering. Therefore, only the

and yaw plane motions

will be considered

in subsequent

derivations.

Figures model

3.2

and 3.3

show

measured

mode

shapes

of a high speed mode shapes

commercial demonstrate The lower

transport several frequency

in the National characteristics

Transonic common

Facility

(NTF).

These tested

important modes

to models

in the NTF. by rigid body

(<50 Hz) of the model

system

are characterized

motion

of the model with desired is

on the more flexible sting bending motion

sting-balance in the for the pitch

combination. and yaw

The first two modes plane. In order

are associated the

to achieve the force

measurement relatively used

accuracy flexible

"steady-state" to the model with

aerodynamic and sting. that The

loads, strain the

balance systems

as compared [31]

gage balance loads pitch into

in the NTF

are designed interactions.

flexures

separate

its planar plane the a

components motion rigid-body corresponding

with minimal

This results modes by a

in predominantly of the system. translation y

or yaw

of the model model

for the lower motion can

frequency be defined

For a given or z

mode, with

along

rotation

[3 or t_ (see Figures

3.2 and 3.3).

3.4.1 A

Two Degree degree of

of Freedom freedom

Example example will be used to define The some useful properties of the to an

two

associated two degree

with the planar of freedom

motion

of the "rigid" in Figure

model.

modal

characteristics This is similar

system

shown

3.4 will be examined.

35

>

0

0

N 0

I

°_,,q

0

E_
E
_" •

/
E_ c--

.8

t"l

a

._ I
X

I I I I
N

_h.._ r

0

0

N

._..q

J_
r_

o

E
,/
._,.q

LT._

KT
O_

KB

Balance moment center

Figure

3.4

Two degree

of freedom

model.

38

example

for vehicle

suspension

given

by Thompson moment

[32].

In this example,

the translation the model For small

and rotation motion. angles,

coordinates

at the balance Method, are

center

will be used in defining of motion are derived.

Using

the Lagrange of motion

the equations

the equations

I-mm'mdmcg/bc

-mrn'dcglbc-_Z_+IkBIybc [. 0 J_(iJ

kOT_Z}=fdF/lbc}

f(t)

(3.27)

where, center;

mm is the model dF_

mass,

dcg/bc is the distance

from

the mass center;

center

to the balance about

is the distance center;

from the force to the balance stiffness;

Iy bc is the inertia stiffness;

the balance displacement

kB is the bending

kT is the torsional position; and

z and o_ are the force.

and rotation

from the equilibrium

F(t) is the applied

The

main

interest

is in the

form

of

the

mode

shapes.

The

eigenvalue

problem

corresponding

to Equation

3.27 can be written

0

z

mrn

mrn'dcg/bc_Z

l

(3.28)

Based transport

on

measured model

weight,

physical

dimensions, constants

and

natural

frequencies

of a typical

system,

the following

were determined.

mm=0.3313

pound-secondZ/inch 2

Iy bc= 19.51 inch-pound-second dc_c= 5 inches

kB = 1308 pound/inch kT = 277089 inch-pound

39

Substitutingthesevaluesinto Equation3.28,andsolvingtheeigenvalue problemyields °_1 _9.38Hz;{_}1 1-1"513l
(3.29a)

fl - 2*rt

= [0.0415J

°_2 -26.7Hz" f2 - 2*n

'

{q_}2

l 1"719 l = 10.2955J

(3.29b)

The mode a node this

shapes

are depicted

graphically about ratio which of the gives

in Figure

3.5.

Note that for each mode model rotates.

there

is of

(point

of zero motion) by the

the rigid body translation and

The position

node

is defined

rotation

degrees

of freedom.

Scaling

the modes

to unit rotation

(3.30a) {q_}l :0"0415 l 1 I =

[5.82]

0.2955{-

_2 }

(3.30b)

where shape

the ith mode coefficients

radius, with

Pi, is defined vector

as the ratio of the translation scaled to unit rotation. This

and rotation yields

mode

the modal radius

a physical point on the

interpretation the model mode

of the mode with the positive values

as the distance defined

from the node to the reference x-axis.

direction

by the model

For this example, The radius

radius

are Pl = 36.4 inches, based 5.

and P2 = -5.82 shape.

inches. The effect

by definition

can be positive will be discussed

or negative in Chapter

on the mode

of the sign of the radius

40

Mode

1

_

_

Node

..............

_

-_- x

Mode 2

P2 = -5.82 inch

Z

Figure

3.5

Mode

shapes

for two degree

of freedom

example.

41

3.4.2 The

Extension results of

to Multiple the two

Degree of

of Freedom freedom

System example the planar can be used to simplify of as the the model

degree 3.17.

transformation response

Equation

Recognizing modes, Equation

characteristics

for the lower

frequency

3.17 can be expanded

(3.31)
{q(t)}:[dP]{p(t)}= _.{f) ry }ryPry(t)+ Y,{_ rp }rpPrp(t)+ r_ry _, ,rp {t_ }rPr(t)

The low frequency model. model Letting fuselage,

yaw modes

denoted

by ry are characterized coordinates

by rigid body required

motion

of the the

{q} be the subset yields:

of the generalized

to represent

!o
0
{q}ry = _ry{_f}ryPry (t)

0 - Pry 0 Pry (t) = _.t_ _Bry
ry

(3.32)

ry

0

0
ry

0 0
Pry (t)

1

The coordinates the "rigid" model

shown

represent

the x, y, z, T, or, and

[3 degrees

of freedom

for a point

on

fuselage.

Similarly, model

for the

low frequency by

pitch

plane

modes,

rp , the rigid

body

motion

of the

is approximated

!o
0 Prp(t)= t_a rEp rp -Prp 0 1 0
rp Prp (t) (3.33)

42

For a given mode,the rotationand translationdegreesof freedomin the predominant planeof motionarerelated the moderadius. Themoderadiusis definedasthe ratio of by the translationandrotationmodeshape coefficientsin the predominant laneof motion p with the modalvectorscaledto unit rotation. This simplifiedform of the solution,given by Equations3.32 and3.33, will be usedto developa correctionfor vibration induced errorsin Chapter 4.

43

Chapter MODEL ATTITUDE BIAS

4 ERROR CORRECTION

4.1

Introduction the theoretical for model The model is used to develop induced errors and extends the proposed in inertial time domain wind tunnel procedure "modal model are

In this chapter, correction attitude described. [ 16] domain

method" measurements. The

vibration

modal

correction

theory method

implementation the early modes. work

proposed

modal

correction

of Fuijkschot the first time of vibration in

to compensate correction pitch

for multiple technique

yaw and pitch

vibration

This was modes

developed

to compensate

for multiple

the model data

and yaw planes. periods order

A time domain for the

correction wind [21] balance

is required tunnel involving data. data. the

due to the short This is also of

acquisition in

(1 second) future

random needs

important instantaneous method modal

to meet in model

testing

correlation correction measured

changes

attitude

and force

The modal by using critical

also minimizes properties

the number tunnel

of additional model system.

transducers

required

of the wind space

This is especially

for models conditions

with limited where heated

interior

and in wind packages

tunnels

that have extreme

temperature

instrumentation

are required.

Prior to the modal assumption analysis

correction

technique,

the model

attitude

corrections

were based arc with

on the

that the instrumentation of the underlying system

package dynamics.

moved The

on a circular theoretical

no detailed modal

and experimental

44

analysesperformedduring the development f the modal correctiontechniqueprovided o valuableinsight into the dynamicbehaviorof cantilevered wind tunnel model systems. Observation the relevantanimatedmodeshapes of revealedthat the model movedas a rigid body on the more flexible sting-balance combination. The assumptionof rigid body modelmotion is critical to the development multi-modetime domaincorrection of techniques.

4.2

Modal

Correction generalized

Theory forces Unsteady are associated with the "quasi-steady" tunnel results aerodynamic loads random

The primary acting input

on the model. to the model metallic band filter [33].

flow in the wind

in a broadband known the

system. sting-model passing

The input structure,

for this process the damping

is not directly is low and

or measured. acts as a

For the narrow system natural

system

energy

(or responding)

at the natural damped,

frequencies the response mode shape,

of the model motion {_ }r' at a with

If the modes _,

are well separated

and lightly

frequency,

will be described

by the corresponding

residual

effects

of other modes

assumed

negligible.

45

The physicsof the problemcannow be studiedby consideringthe response a single of modeasdepictedin Figure4.1. UsingEquation3.32,theresponse a singleyaw mode for in simpleharmonicmotioncanbewritten
x

0

0
- Pry

Y

*y
= 0 0 0
" ry d_ ry Pry (t)=f_fJry

{_)(t))=

Z

7

0 0 0 1

Pry sin(O3ry t)

(4.1)

where

Pry

is a scalar on the rigid (AOA)

constant fuselage package.

related

to the

amplitude

of motion.

The

reference inertial can

coordinates angle

will be taken The translation

at the location and rotation

of the on-board of the AOA

of attack

package

then be written (4.2)

Yry (t) = Yry sin(O_ry t) 1
_ry (t)= --Pry Yry

(t)

(4.3)

where

Yry is a constant

representing

the amplitude

of motion.

Taking

the derivative

with

respect

to time gives (4.4)

Yry

(t)

= Vry

cos(0lry

t)

where

Vry

=

Yry Olry

1
_ry (t)---Pry

Yry (t)

(4.5)

46

Mode center of

Yry

Pry"

Figure

4.1

Harmonic

motion

of model

at natural

frequency

of t.o_y.

47

The corresponding

tangential

and normal

acceleration

components,

a t and a n , are: (4.6)

at(t)=

Yry (t)=

Ary sin(COryt);

where

Ary =-VryO3ry

Yry2(t) an(t) = _ry (t)Yry (t)--Pry (4.7)

Substituting

for

J'ry

from Equation

4.4 gives 2 (1 + cos(2C0ry t)) 2 Pry (4.8)

Vry
an(t ) ..... ---z---_cos 2 (0_ry t) Pry

Recall with

from Chapter its sensitive normal

1 that the on-board axis parallel to the results

inertial

AOA package axis AOA

uses a servo-accelerometer model. sensing output The a vibration centrifugal

longitudinal in the

of the

induced acceleration

acceleration

package package

coincident

with its sensitive

axis. The AOA

prior to filtering,

Aunf , becomes:

Aun f (t) = g sin e_ + ff ry (t)

_Yry (t)

--

a x (t)

(4.9)

The

first term true

on the right hand attitude, (from

side of the equation to the local

is the gravitational vertical. by the model from flow The

acceleration second term

due is the

to the

model

_, relative Equation ax(t)

centrifugal term

acceleration

4.7) caused , resulting

yaw motion. longitudinal

The third model for the modal

represent

the accelerations, greater than

induced

vibrations AOA

(typically

50 Hz).

In this equation, change in angle

the positive of attack.

output the

package

corresponds

to a positive

Using

48

radiusto relatethe translationandrotationdegrees freedom(Equation4.5) of the rigid of model,the equation canbewritten
Yry2(t) Aunf (t) = g sins Pry ax(t) (4.10)

Expanding

Yry and using the trigonometric

relations

from Equation

4.8 gives

Aun f (t) = g sino_ - Vry2(l+cos(2_ryt)) 2pry

-ax(t

)

(4.11)

This

form

of the equation results

shows

that the centrifugal sensor having

acceleration a constant, bias,

for sinusoidal

model

response component

in the angle of attack the natural can

term and a harmonic and the longitudinal (0.4 Hz cut-off

at twice ax(t), the AOA

frequency.

The harmonic

component

acceleration, frequency)

be removed

by filtering.

Lowpass

filtering

signal yields

Vry 2 Afil = g sinO_ 2 Dry (4.12)

The

filtered

AOA

signal,

Afil, has

a bias

error

due

to model

vibration

that

cannot

be

removed remove

by filtering the bias error,

or averaging. a correction

From method

Equation that

4.12,

it is evident for both

that

in order

to of

compensates

the amplitude

vibration,

Vry,

and the mode

shape,

Pry,

is required.

49

Model pitch vibration causes similar biaserror term, wherethe tangentialvelocity is a actingin thepitch plane. If the vibrationresponse composed multiple yaw andpitch is of modes,the total biaserrorwill be a linear summation theerrorcontributionsfor the m of
modes.

m Vr2
Afi t = gsinot _ r=l 2 Pr acceleration,
m Ar 2

(4.13)

Or, in terms

of the peak

from Equation

4.6,

Afil = gsino_

-

Y_ r=l

2
20) r Pr

(4.14)

The above wind tunnel, dependent modes. appears

discussion

is based

on the case of continuous in nature. This results

sinusoidal

model

motion.

In the

the data is random on the number

in a time varying

bias error that is for those correction

of modes

participating

and the amplitudes bias errors,

of motion

In order

to compensate

for a time varying

a time domain

to be the most suitable.

The proposed given

time domain 4.10.

modal Assuming

correction the model

technique system mode

is based behaves effects.

on the single linearly,

mode

model

by Equation

the total bias error as

will be a linear

superposition

of the individual

This can be written

Aunf(t)=

gsin0_

- _ v2(t------2-ax(t) r=l Pr

(4.15)

50

whereVr(t)

is the velocity mode

(pitch radius.

or yaw plane) For m modes,

at the AOA the bias

location error

for mode

r and

Pr is can be

the corresponding written

estimate,

aB(t),

aB(t)=

_
r=l

v2(t) Pr to the unfiltered AOA output yields

(4.16)

Adding

the bias error estimate

Aunf (t)+

_
r=l

v2(t)
Pr

- gsin0_

-

]_ N
r=m+l

v2(t)
Or

ax(t)

(4.17)

The

longitudinal data

accelerations, in Chapter

ax(t),

can be removed the majority

through

low pass

filtering.

The in the the

experimental pitch effects and yaw of the

5 will show

of the dynamic to six modes. to N)

response Therefore, will be

plane higher

will be concentrated frequency modes

in the first four (denoted attitude by is given

r=m+l by

assumed

negligible.

An estimate

of the true model

LP O_(t) = sin -1

Aunf(t)+ g

Y_ m r=l

v2(t)

Pr

(4.18)

where cut-off

the accelerations frequency

are measured

in g's

and LPF designates

a low pass

filter

with a

of 0.4 Hertz.

In the modal

correction

technique,

natural

frequencies, using analytical

f.or

,

and mode

shapes,

{_ }r must In

first be determined. most cases, a detailed

This can be done analytical model

or experimental Experimental

techniques. modal

is not available.

analysis

51

techniques [29, 30] havebeenusedto determinethe requirednaturalfrequencies,(D r
and mode shapes, {t_ }r' of the cantilevered modes model systems. have Recall from Chapter 3 that

,

the low frequency or yaw and 4.3. rigid body plane

"rigid-model"

of interest design.

predominant

motion

in the pitch in Figures moves mode 4.2 as a shape mode's to the

due to the model-balance mode, the radius square effective as the

This is shown by assuming

graphically the fuselage fuselage A

For a given and using

is estimated linear point

a least an

regression of rotation from the

fit of the (node).

coefficients effective inertial

to determine radius is estimated location

vibration of rotation

distance

mode's

point

AOA

sensor

in the model

fuselage.

The rigid body

assumption

used in the mode

radius

estimation evaluated. coefficient

appears

to be satisfactory of the rigid regression plane

for the low frequency body assumption

(<50 Hz) modes

that are being

The accuracy for the linear fit of

can be assessed mode shape

using the correlation coefficients.

fit of the fuselage mode (see Figure

For a linear by

regression

a yaw

4.2), the line estimate,

Yi, is defined

Yi = axi + b The correlation coefficient [34] is defined ]_x_ n y as

(4.19)

Exy

(4.20)

CC r = I(Y'X2-

(_'x)21]_Y2 (_'Y)2n

n

]

52

Mode center of Undeformed x5
Jr

x4
÷

x2 Y2

rotation--_

_

YT

Y5

Y4

AOA position

Mode radius P

Yi = a*xi + b

Figure

4.2

Yaw plane

mode

of model

system.

53

position

AOA

Mode radius P

--I-

Zl 4.... 3 x2 Xl Mode / center of/ rotation -' x

x5

x4

x

Undeformed z i =a.x i + b

Figure

4.3

Pitch plane

mode of model

system.

54

The correlation no linear Chapter measured

coefficient

is always

between

-1 and +1.

For values strong linear

close linear

to zero,

there

is In

relationship.

For values

near _+1, there is used

is a very

relationship.

5, the correlation fuselage mode

coefficient

to assess

the

regression

fit of the

shape coefficients.

A second tunnel used

assumption

is that the mode This enables of the model of

shapes

do not change estimates

significantly

under

the wind radii to be In were The the

test conditions. for correction A, the using

wind-off attitude

of the mode during the wind

effective tunnel modal model

measurement forces on

testing. radius system.

Appendix evaluated aerodynamic eigensolution aerodynamic Transonic negligible.

effect

aerodynamic model to

measured wind tunnel

a finite

element

of a cantilevered generate prestressed a

forces was forces Facility,

were performed

applied

prestressed loading

model

and For in the

then the

for this on

condition. model

largest National is

measured the predicted

a representative in the modal

transport radius were

shifts

less than

4%, which

4.3

Modal

Correction radius

Implementation and natural correction frequency are obtained is the on-line for each mode measurement of interest, the

Once the effective

next step in the modal AOA model signal, attitude

technique

of the unfiltered Due to the

and the lateral accuracy

and normal

accelerations

at the AOA a range

location.

requirements

( _+0.01 ° over

of +20 ° ), a 16-bit

analog-to

55

digital converteris requiredfor the dataacquisitionsystem. Once the datais acquired, the digitizedmeasurements areprocessedff-line usingMATLAB ®[35]. o

A flow chart of the dataanalysisroutineis shownin Figure4.4. The lateralandnormal acceleration measurements arenumericallyintegrated usingthe trapezoidalrule [36] and scaledto obtain the lateral and normalvelocity, respectively. The velocity signalsare squaredusing array,or elementby element,multiplication. For each lateral mode of interest,a linearphase finite impulseresponse filter is usedto definea passband aboutthe natural frequency. This isolatesthe velocity squaredcomponentsof the individual modes. The filters areappliedin boththe forwardandreverse directionsto obtain zerophasedistortionanddoublethe filter order. This is critical for a time domaincorrection wherethe phaserelationshipof the unfiltered AOA signal and the lateral and normal dynamicresponse mustbemaintained. The squared velocitycomponents eachmode for are divided by their correspondingmode radius and then combined using linear superposition give theestimated to biaserror dueto lateraldynamics.This procedureis then repeatedfor the normal,or pitch, modesto determinethe bias error due to pitch dynamics. The errors due to the lateral and pitch dynamicsare then combinedusing linear superposition yield the total biaserror. The biasestimateis then addedto the to unfiltered AOA and the result is filtered with a 0.4 Hz lowpassfilter as describedby Equation4.18. This givesa corrected time varyingmodelattitudesignalthatcanbe used to determinetheinstantaneous meanangleof attackoverthedataacquisitionperiod. or

56

Start

)

[

mp

_pb_b

i=l,nap

readay, a_, A..f accel, arrays

Vz_-integral(az) Vy_-integral(ay)

]

Vz2_" Vz'* Vy2_.Vy.,Vy Vz

]

apply ban@ass filter to isolate mode effect
Vyi2 (-BPFfy i( vy 2 )

1
estimate ith mode bias
mBy i_-Vyi 2/121yi

!

[

I

()
Figure 4.4 Flowchart of modal correction method. 57

apply bandpass filter to isolate mode effect
Vpi2 4[-BPFfpi(Vp 2)

estimate

ith mode bias
i 2/Ppi

mBpi_-Vp

.%(".%y+.%,p

1
AcC'A.n_Aa

&:fa4"LPFo.4Hz(&:)

AOA(-

asi n(Acr a)* 180/pi

Figure 4.4(continued)

Flowchart

of modal correction

method.

58

Chapter EXPERIMENTAL

5

VERIFICATION

5.1

Introduction the modal correction method model is verified through a combination test data. of windThe modal for

In this chapter, off dynamic correction model shaker applied speed

tests on two transport method is applied induced in the pitch

systems model

and wind

tunnel

to wind-off

dynamic model

response attitude

data to compensate

vibration inputs

errors and

in the inertial yaw plane.

measurement correction tunnel

for defined method is

In addition,

the modal wind

to measured transport model

dynamic

response

data recorded Transonic

during

testing

of a high

in the National

Facility

(NTF).

5.2

Wind-off

Dynamic will describe models

Response

Tests and results correction to the model of wind-off method dynamic is validated response tests on

This section two transport modulated

the test setup The

[7, 8].

modal inputs

for sinusoidal,

sinusoidal

and random

in the pitch

and yaw plane.

5.2.1

Test

Setup dynamic

and Procedure response tests were conducted on two transport models [7, 8] in a

Wind-off model transport cantilever attached

assembly

bay at the National in Figure is positioned sting 5.1.

Transonic The

Facility. mounting

The test setup consists

for the high speed supported model balance. is

is shown sting to that the

of a "rigidly" mechanism. strain The gage

by a pitch-roll-translation a six component

through

59

c_

c_

0

E
°_,.q

E_

,_,.q

Lr_

The model temperature unfiltered, bandwidth package several natural

was instrumented of 160°F. "dynamic", signal. The

with an inertial signal conditioner

AOA

package

[ 13] maintained package

at a constant both an

for the AOA signal,

provides

0 to 300 Hz bandwidth Two miniature yaw and pitch accelerometers motions.

and filtered,

"static",

0 to 0.4 Hz

were installed

on the face of the AOA were installed response at and

to measure locations mode

In addition, and sting

accelerometers

on the model

fuselage

to measure

the dynamic

characteristics.

An

experimental function computer. parameters mode

modal data

analysis were

was

performed for point

on force

the

model

systems. and

Frequency to a the fit of and

response personal modal the

acquired

excitation

transferred

The STAR e [36] modal from the measured shape coefficients coefficient

analysis

software

was used to determine A least square the mode radius

frequency was

response used 4).

functions.

fuselage

to estimate

corresponding

correlation

(see Chapter

For the dynamic system through

response a single amplitudes,

tests, point

an electrodynamic force linkage surface

shaker

was

used 5.2.

to excite Due

the model

as shown

in Figure

to the desired wire was The points.

high vibration used in case was

the model attaching

was protected mounting planes block

with tape and safety failed during fuselage used. the

the

glue

the force and

testing. hard

excitation Sine, Packard

applied sine 3566A

in the pitch and band

yaw

at the model input

modulated (HP)

limited signal

random was

shaker used

were

A Hewlett stimulus

dynamic

analyzer

to provide AOA

shaker

and record

the shaker

force input,

model

force balance

outputs,

static

and dynamic

61

_iii!iiiii!iiii

¢)

r_ O

¢)

e_

.,,._

outputs,

and model which Data

accelerations. established

This

system

was used test conditions

to monitor

the model model

yaw and attitude (ADC)

pitch moments measurements. board

the dynamic

for acquiring to Digital

was also recorded computer.

using a 16-bit Analog

Converter

in a personal

The

model

was

set at a prescribed frequencies were

angle identified

of attack using of interest, amplitude

under

static

conditions.

The

model and

system

natural

sine

sweep

excitation forced

in the pitch response peak

yaw planes. conducted pitch

For each natural by controlling

frequency

a sinusoidal to provide The control

test was to peak pitch that

the shaker

input

a defined test variables

or yaw moment for modes

on the model

force balance. pitch

were

moment

that had predominantly yaw motion. for sinusoidal The model excitation

motion,

and yaw moment

for modes

had predominantly amplitude system. levels

attitude

was measured natural

at a series frequency

of moment of the model

at a prescribed

In addition dynamic modulated model

to the response sine and

sinusoidal was

forced for

response modulated and

tests, sine

the

high and

speed

transport excitation.

model The of the

measured

random

random in

excitations actual wind

responses tests.

are more The

representative

dynamics

observed

tunnel

majority

of the modulated frequency to measure in the the

sine tests were conducted pitch model and yaw attitude planes.

with a 0.25 Hz modulation the inertial amplitude AOA levels.

of the first natural package was used

In each case, of moment

for a series

63

5.2.2 During

Commercial

Transport

Model

Test Results transport model had significant the yaw vibrations stimulus for the

wind tunnel tests, the commercial Discrepancies of the AOA concentrated on the model in the device

at 14 Hertz. investigation investigation conducted

aerodynamic

data provided to model

[7] and its sensitivity

vibrations.

The AOA was

on the first four modes. system and the results

An experimental

modal analysis Figures

are tabulated

in Table 5.1.

5.3 and rotation.

5.4 show characteristic The mode Recall radii

yaw plane modes

described

by sting bending

and balance

and corresponding

correlation

coefficients

are also listed

in the table. linear shape

from Chapter

4 that correlation coefficient

coefficients

near +1 indicate

a very strong mode

relationship. coefficients body

The correlation shows

for the least square

fit of the fuselage

the appropriateness for the tabulated

of the linear regression modes.

fit and validates

the rigid

model assumption

Table Modal Mode No. 1 2 3 4 Frequency (Hz) 10.3 11.2 14.4 16.5 Parameters Damping (%) 1.01 1.78 0.46 0.59

5.1 Transport Corr. Coeff. .9998 .9971 -.9973 .9998 Sting Bending-Yaw Sting Bending-Pitch Model Model Plane Plane Model Mode Description

for Commercial Radius (Inch) 38.2 70.5 7.05 12.0

Yaw on Balance Pitch on Balance

64

_r r

0

0
°l,-q

t_

c5

° ,,..q

_0

"0

_

E
e_ _r_ _0 LT_
°_,.q

\
r

0

0
.,-_

I-i
°,,=w

p,

d

,.Q 0 b_

0

N

.,=,_

LI.

For the AOA attack under

investigation, conditions. input

the model Single to provide The test

system frequency a defined variable moment model

was

locked

at near zero

degree

angle

of by on had

static

forced peak was

response to peak

tests were pitch or yaw for

conducted moment that

controlling the model

the shaker force

balance. motion, response

yaw

moment that

modes

predominantly motion. moment The levels.

yaw AOA

and pitch data and

for modes accelerations

had predominantly recorded

pitch

were

for several

This data was transferred technique. output, moment after

to the MATLAB mean of the

® [35] program AOA output, modal 5.8.

for application bias, and are

of the modal corrected shown input,

correction AOA balance

The measured application

estimated

mean versus the

correction Recall in the that mean to the pitch

technique,

in Figures a bias

5.5 through error

for sinusoidal value. AOA After device For this

model of the of +0.01

vibration modal degrees

creates correction

or offset

application accuracy

technique,

the error except

is reduced the second

for all measurements reduction is obtained.

mode.

case, an order

of magnitude

The accuracy accelerometers accelerometer accelerometers obtain the

of the correction adjacent on the located off-axis to or

for the pitch inside the

axis tests may be improved heated AOA early surface modal package.

by locating The pitch A triax

the plane set of

face of the AOA externally accelerations

package

failed upper for the

in the test.

on the fuselage required

was subsequently correction

used technique.

to

67

0.02

0 _""" _- ... ......... • .............. &....-" .... .--''_

_...__..-__. -__..._:...............................
"_m -0.02

g
-0.04

i

-0.06 -- • -- Estimated -0.08 - - _r -- Corrected Bias "X_\ "X_\

°
I 400 800 Yaw Moment I 1200 (Inch-Pounds) I 1600

\
2000

-0.1

Figure

5.5

Measured yaw moment

mean

AOA,

estimated input

bias,

and

corrected Hz.

mean

AOA

versus

for sinusoidal

at 10.3

68

0.02

._.. -0.02
A

.

.................................

. ......

dr ..........

• ...........

• ...........

-0.04 o
D1 O

-0.06

u

,¢
O

e
t,-

,¢ I'" -0.12 I .... 1.... _''" Corrected N°minal +'01° Nominal-.01 ° "_\ "_ _

-0.14

-0.16 1000

, 4000

' 6000 Yaw Moment

' 8000 (Inch-Pounds) 10000 12000

Figure

5.6

Measured

mean AOA,

estimated

bias, and corrected

mean AOA

versus

yaw moment

for sinusoidal

input at 14.4 Hz.

69

0.02

m

I-...... ,-...
..........

...-A ,.: :, - - _- .......... "B
.'_,.=,,. .............................

...........

• ......
_.._

• .....

----e--- •- - _" .... .... -0.04 400

Measured Estimated • Corrected Nominal +.01 o Nominal-.01
J

Bias

°
I I I

800

1200 Pitch Moment

1600 (Inch-Pounds)

2000

2400

Figure

5.7

Measured pitch

mean

AOA,

estimated input

bias,

and

corrected Hz.

mean

AOA

versus

moment

for sinusoidal

at 11.2

70

0.05

'-"--';:-'-0.05

........ -'-

"-"• ,r-'-'---.:---'.'.-.'--::-::-_.'.--;-.-"

o

"_

-0.1

-o.15

i

-0.2 -0.25 - •-0.3

Measured Estimated Bias

_"

,, -,,'_"11 "_
\

- - _- - "Corrected

-0.35

-0.4 4000

I

I

I

I

6000

8000 Pitch Moment

10000 (Inch-Pounds)

12000

14000

Figure

5.8

Measured pitch

mean

AOA,

estimated input

bias,

and

corrected Hz.

mean

AOA

versus

moment

for sinusoidal

at 16.2

71

5.2.3

High Speed

Transport model

Model system

Test Results that experienced to further taken high levels of vibration [6] during on that An

A high speed previous the inertial the primary experimental in Table were 5.2. wind

transport tunnel

tests was selected Measurements excited

investigate during wind 8-10

the effects tunnel

of dynamics indicated Hz [6].

AOA modes

package. being

tests

were at approximately system

Hz and 28-30

modal

analysis

of the model

was conducted coefficients

and the results for the vibration

are listed modes as

The radii and corresponding using a least square linear

correlation regression

estimated

fit of the modal

deformations fit of the fuselage regression fit

described mode validates

in Chapter

4. The correlation shows the

coefficient appropriateness

for the least square of the linear

shape

coefficients

and

the rigid body model

assumption

for the tabulated

modes.

Table 5.2 Modal Mode No. Frequency Parameters Damping of High Speed Radius (Inch) 31.0 30.2 0.18 -1.07 -7.16 Transport Model Mode Description

Corr.

(Hz)
9.0 9.2 20.5 21.7 29.8

(%)
1.32 1.68 2.75 2.70 2.28

Coeff. .9997 .9997 -.9993 .9999 -.9983 Sting Bending-Yaw Sting Bending-Pitch Model Model Model Plane Plane

Yaw on Balance Pitch on Balance Yaw on Balance Bending

with Sting Second 6 34.9 2.59 -7.65 0.9999 Model

Pitch on Balance Bending

with Sting Second

72

It is important vibration error mode

to note that the mode shape. Previously,

radius

may be positive was

or negative

dependent whip"

on the [13] The system of the Hz yaw the point radius is

this bias error

described in the pitch show

as a "sting

and associated

with the first sting bending data presented than previously easily understood

modes

and yaw planes. that the model interpretation 29.8

analyses dynamics

and experimental is more complex is more

in this dissertation assumed.

The physical

sign of the radius modes shown

by examining

the 9.0 Hz and the radius package.

in Figures

5.9 and 5.10. mode

For the case where of the AOA

is negative, A positive

of rotation defined

for the vibration of rotation

is forward

for a point

aft of the AOA package.

The

significance upon

of the sign of the radii is that the bias error may be positive the vibration modes angle mode shown change being excited. This is demonstrated

or negative

dependent

by the response

of the two yaw plane the indicated model

in Figures is negative frequency

5.11 and 5.12. when the

For the 9.0 Hz yaw mode, is being driven angle radius with when value,

model

sinusoidal the shaker shows

excitation system

at the natural is shutoff. positive

and then returns which

to its nominal has a negative driven angle

The 29.8 Hz yaw mode, angle change

an indicated

when the model

is being

with sinusoidal when the shaker trends, that AOA rigid

excitation system however, showed package.

at the natural is shutoff. The

frequency excitation

and then returns system was

to its nominal adequate planes from modes

to show

the

above

only the first mode significant Difficulty shifts

in each the yaw and pitch model attitude

were excited the onboard is attributed

to levels inertial to the

in the indicated the

in driving

higher

frequency

73

r

0

. i,-.q L. . ....q

0

= o.

N

.8
°,,....q

r_

I I I I

>,
0

o

,.o

°,.,_

N

t",l

0

(D

E_
o E
,D

/
l:n r-

0

0

09

Inertial
4.34 .............................................. ............................................ .......................................................................................................................................

AOA

Deg I 4.14i 0 Sec 1.5 .......................... g !_ ........................ ............ i : .......... ! 8 Sec Yaw Acceleration ......

-1.5..................................... i.................................................................................. i .................................... . i.............................................
0 Sec 8 Sec Yaw Moment
3600 ............................................. ............................................ ...................... ...............................................................................................................

In-Lbs

-2400

_: ................. 0 Sec

i............................. 8 Sec

Figure

5.11

Inertial AOA measurement, time for 9.0 Hz sinusoidal

yaw acceleration, input in yaw plane.

and yaw moment

versus

76

0.4 g

-0.4 0 Sec 8 Sec Yaw Moment

2400 .................... i........................................... :................................................................................................................................................ ii
In-Lbs
............ ].......................

-600 0 Sec 8 Sec

Figure

5.12

Inertial

AOA measurement,

yaw acceleration, input in yaw plane.

and yaw moment

versus

time for 29.8 Hz sinusoidal

77

backstop model

support coupled

in the model with the model

assembly support

bay. structure

During

previous

wind

tunnel

tests [6], the yaw moments testing with

resulting

in high dynamic to do dynamic

with energy the model

in the 28-30 installed

Hz band.

This points

out the need

in the tunnel.

The plane these

results

of sinusoidal in Figures

excitation

tests for the first

mode

in each

the

yaw angle

and

pitch

are shown tests.

5.13 and 5.14. The model level, These time domain

was set at a nominal data were acquired

of 0 ° for using where ® [35] was

For a set excitation signal correction was analyzer.

and

stored

the dynamic the modal

data

were transferred in

to a personal in the device.

computer MATLAB

technique,

implemented the bias error

an m-file

language, repeated

used to estimate excitation

in the inertial by the moment

This procedure level.

for several

levels

as defined

amplitude

As shown indicated application

in Figures mean angle

5.13 and 5.14, change

the estimated with

bias error is in good the onboard inertial

agreement AOA

with the After of ° are for

measured method, mode plane.

sensor.

of the modal

correction first

the bias error is reduced yaw plane and from angle results

from a maximum -0.175 ° to-0.006 of attack were values obtained

-0.146 ° to -0.009 ° for the for the first within sinusoidal the mode AOA

in the These of

in the pitch accuracy

corrected

mean

requirement

0.01 °. Similar angles

input tests with the model

set to nominal

of 4.3 ° and 6 °.

78

0.02

__S._
-0.02
A

_-_*.__;_L; -::-._.--._:: _:: ._':----;--.-...

t_

-0.04
0

-0.06
o

-0.08
0

_.e
o} e-

-0.1

-0.12

- • -

-0.14

oreC;%o
Nominal
I

Estimated

Bias

"X_\

.... -0.16 9OO

-.01 o
i I

1800

2700 Yew Moment (Inch-Pounds)

3600

4500

Figure

5.13

Measured yaw moment

mean

AOA,

estimated input

bias,

and corrected

mean

AOA

versus

for sinusoidal

at 9.0 Hz.

79

0.02
m

.......... ,- -_-,_ ......... -0.02

:

;:.,:._.: ._.:_, : :

A

w

-0.04

2
o

-0.06

u m

-0.08 Measu re_ _ \ \

0

-0.1

e
i-

<

-0.12

-O--_--M_amSU:: - - _- - • Corrected

Bias

"_

-0.18 1000

I

I,

I

2000

3000 Pitch Moment (Inch-Pounds)

4000

50O0

Figure

5.14

Measured pitch

mean

AOA,

estimated input

bias,

and

corrected

mean

AOA

versus

moment

for sinusoidal

at 9.2

Hz.

80

In order

to obtain

a corrected or average and

time domain values, estimated

angle

of attack

measurement the the

that can be used phase modal relationship correction

for instantaneous between method the

it is important bias error.

to maintain To verify was that

measured

maintains

this phase inputs.

relationship,

the bias error response

examined

for modulated inputs is

sine and random

The measured of actual

for modulated

sine and random

also more representative

wind tunnel

test data.

Figure time

5.15 shows

the measured

angle with

of attack a 0.25

and estimated Hz modulation. angle

bias error Excellent and

as a function agreement estimated

of is bias

for a 9.2 Hz pitch excitation with the difference

obtained error

between

the measured

of attack conducted

being

less than levels

0.005 ° . Modulated

sine tests were

at several

excitation results were

amplitude obtained

for the first mode the measured

in each the y and z axes and predicted

and consistent bias errors

between

angle of attack

for all cases.

In addition, pitch AOA plane sensor

the response

of the AOA Figure

package

for two levels an eight

of random second

excitation

in the

were also examined. response

5.16 shows level random

record The

of the inertial response of

for the highest accelerometer The bias

excitation.

random

measured primarily contribution estimated

by the pitch 9.2 Hz

on the face of the AOA error 5.16. estimate Again, based the

package on only

was composed the angle 9.2 Hz

response. shown

mode and

is also

in Figure

measured

of attack

bias error are in very good agreement.

81

,4
O ..=

O

E
N

cO

I

I

(3O

p:
V7 C4

&
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d

J= C_

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O

"O13_

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r4 E_

£',1

E F:
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&)

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0 <
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0

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5.3

High Speed response

Transport studies

Model were

Wind

Tunnel

Tests transport model installed in for

Dynamic

conducted

on a high speed response

the test section high speed

of the NTF. The dynamic wind tunnel runs.

characteristics

were also recorded

(Mach=0.95)

5.3.1

Test

Setup

in Wind

Tunnel with a re-designed model AOA inertial AOA package that has two servoto measure package is

The model accelerometers the

was instrumented for measuring tangent

and two dynamic axis of the AOA The signal

accelerometers sensors. conditioner signal The

accelerations

to the sensitive temperature

maintained sensors static,

at a constant

of 160°F.

for the

AOA

provide

both an unfiltered, signal.

dynamic,

0 to 300 Hz bandwidth

and a filtered,

0 to 0.4 Hz bandwidth

Initial using

wind-off shaker

dynamic

response

studies

were performed

in the wind in a fixed were at three

tunnel

test section

excitation excitation

of the model tests,

with the arc sector accelerometers motion

position. mounted

For the windexternal to the

off shaker model

six additional model

fuselage

to measure

yaw and pitch

locations.

Data

were

acquired

using

a 16 channel were

digital

data

acquisition

system

with Data

16-bit were

resolution. recorded and static

All dynamic at 200 samples inertial

signals

filtered

to 100 Hz prior Recorded accelerations

to recording. included

per second

per channel.

channels

the dynamic and the six

AOA outputs,

the tangential

in yaw and pitch,

84

force balancecomponents.Datawererecordedfor both the wind-off shakerexcitation testsandthehigh speed wind tunnelruns.

Forthe wind-off shaker xcitationtests,a HewlettPackard e model3566A dynamicsignal analyzerwasusedto providetheshakerstimulusandperformon-linetime andfrequency domainsignalanalysis.The 16channelsignalanalyzerwasusedto monitorand record the shakerforceinput,andtheresponse the six accelerometers of mounted externalto the modelfuselage.

The shakerexcitationtestswereperformedwith the model installedin the test section andthe arc sectorin a fixed position.An electrodynamic shakerwas usedto excitethe model in the yaw planethrougha singlepoint force linkage13 inchesaft of the model nose. Due to schedule constraints,he forcedresponse t testswereconductedin the yaw plane only. The model systemnatural frequencieswere identified using sine sweep excitation. The dynamicandstaticinertial AOA outputs,the tangentialaccelerations in yaw andpitch, andthe six forcebalance components ererecordedfor a seriesof shaker w force amplitudelevels for sinusoidalexcitationat a prescribednaturalfrequencyof the model system. In addition to the sinusoidalforced responsetests, modulatedsine excitationtestswereperformedfor a seriesof shakerforce levels. The modulatedsine excitationsand responses more representative the model dynamicsobservedin are of actualwind tunneltests.

85

For a giventestcondition,time domaindatawereacquired andstoredon the 16-channel dataacquisitionsystem.Thesedataweretransferred a personal omputerwherea to c softwareroutineimplementing themodalcorrectionmethod,written asanM-file in the MATLAB ®[35] language, wasusedto estimate andcorrectfor thebiaserror in the inertial device.

5.3.2

Dynamic

Response modal tunnel

Tests analysis

in Wind

Tunnel for a high speed are listed vibration research model installed was modal radii

An experimental in the NTF wind configured characteristics and

was performed modes

and the dominant than in previous than those

in Table tests,

5.3. The model therefore, The The the mode

differently

wind-off presented

are different correlation

in the previous

section.

corresponding

coefficients

are also listed model assumption.

in the table.

correlation

coefficients

again confirms

the rigid body

Table Modal Mode No. 1 2 3 4 5 6 Parameters Frequency for Survey Damping

5.3 Transport
Corr.

of High Speed Radius (Inch) 37.8 31.8 8.71 -0.93 -3.40 -9.54

Model Mode

in Test Section Description

(Hz)
7.3 9.8 12.1 16.9 17.2 21.1

(%)
0.46 0.28 0.51 1.3 1.0 0.36

Coeff. .9992 .9995 .9995 -.9985 -.9998 -.9994 Sting Bending-Yaw Sting Bending-Pitch Sting/Model Model Model Model Bending Yaw Plane Plane

Pitch on Balance Yaw on Balance Yaw, 2nd Sting

86

The resultsof sinusoidalexcitationtestsfor the first mode(7.3 Hz) in the yaw planeare shownin Figure5.17. This figure showsthe angleof attackmeasured with the primary servo-accelerometer sensorand the correctedangle of attack after removal of the dynamicallyinducedbiaserror. Thesetestswereconducted with themodel at a nominal angle of 6.01° and the arc sectorin a fixed position. After applicationof the modal correctionmethod,the error is reducedfrom a maximumof -0.087 to +0.003 for the ° ° first modein the yawplane. As shownin Figure5.17,the corrected AOA
are within not excited during the AOA accuracy to high enough vibration requirement levels tests. of +/- 0.01 o. The higher significant frequency measurements modes were

to produce

shifts in the AOA

measurements

the wind-off

In addition Figure sensor error. 5.18

to the sinusoidal shows the angle

tests, the bias error was examined of attack of attack measured with

for modulated

sine input.

the primary of the

servo-accelerometer induced bias

and the corrected

angle

after removal

dynamically frequency

This data was obtained The corresponding peak-to-peak correction

for excitation measured value

at the 7.3 Hz natural yaw moment in-lbs. as large

with a 0.5 Hz 5.18 and

modulation. has using a

is also shown Excellent as -0.091°

in Figure

maximum the modal

of 2400

correction being

is obtained to less

method

with errors angle.

reduced

than +/- 0.005 ° from the nominal mode at several excitation response,

Modulated

sine tests were conducted results induced were errors

for the first For this

amplitude correction

levels

and consistent

obtained. results

type of model the mean

for the dynamically

in a shift in

value and a reduction

in the variance

of the signal.

87

6.02

,01

..............................................

"

......

6

_

5.99 5.98

5.97 o
0

5.96

<

5.95 5.94 5.93 5.92 0 400 800 1200 Yaw Moment 1600 (Inch-Pounds) 2000 2400 2800

Figure

5. I 7. Measured

and corrected

angle-of-attack

for sinusoidal

excitation

at 7.3Hz.

88

0 .,= --f_'-r 1

CO

,

CO
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5.3.3

Wind

Tunnel

Test

Results of a test on the high speed T=-254°F) AOA sensor AOA transport model (Mach=0.95, response method. was

The data for the first 64 seconds Q=1800 pounds-per-square-foot, of the primary output of the

were used to evaluate and the proposed is shown pitch angle was in Figure was paused significantly of the energy

the dynamic correction Data

characteristics The filtered

modal 5.19.

primary

analysis

restricted aerodynamic acceleration showed frequency. the modal standard

to the periods data. over the 7.3 The

where pitch

the model

to obtain lower model at the

"steady-state" than the yaw

acceleration period. with

data Hz

analysis response

Analysis additional

yaw 12.1

acceleration Hz natural of and

primarily

Intermittent correction deviation

response method

at other

frequencies

was observed.

Initial

application mean value

included

the modes

in Table

5.3. The AOA 5.4.

over each pause

period

are listed in Table

Table Summary Time Period Measured AOA Mean (Degrees) of Wind

5.4 Tunnel Results Corrected Standard Deviation (Degrees) -3.5403 -2.4764 -1.4392 -0.9121 0.0121 0.0082 0.0088 0.0057 AOA

Measured Standard

AOA

Corrected AOA Mean

(Seconds)

Deviation (Degrees)

(Degrees)

0to

9.25

-3.5664 -2.5094 -1.4803 -0.9308

0.0179 0.0203 0.0248 0.0094

12.5 to 32.5 40.75 56to to 52.5 64

90

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Figures with the

5.20 through primary of the

5.23 show the time domain servo-accelerometer sensor bias error

response and the

of the angle of attack corrected pause angle period.

measured after no

of attack There were

removal optical

dynamically

induced

for each

measurements

to confirm

the corrected

AOA measurements.

Since have For

the response positive a mode radii, with

was trends

primarily consistent radius

at the 7.3 Hz and with the wind-off and fluctuating in a positive significant (Figures

12.1 Hz natural modulated

frequencies,

which

sine test are expected. correction for

a positive errors

amplitude

of motion, value

dynamically variance

induced

will result signal. AOA The signal

shift in the mean reduction

and a reduced observed in

for the corrected time domain

in the variation as compared deviation correction

the corrected primary AOA periods Figures The AOA

5.20-5.23)

to the measured for the corrected method. are shown possible. may aid in The in

and the corresponding indicate successful

reduction

in the standard of the modal

measurement from

application

12.5 to 32.5 seconds

and 40.75

to 52.5 seconds of the amount in the modal important

(part of which of

5.21 and 5.22) of more bias

are the best indicators natural frequencies It is also signal

bias reduction method the low

inclusion the

correction to note that

improving fluctuations model

correction. AOA

frequency in the

in the corrected

may be due in part to oscillatory

changes

pitch attitude.

92

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i

!

!

O4 0 "_f" 0 0
!

,I::1 •

(seeJ6eG)

VOV

[.-, u.. N

0

_

(sq'l-Ul)

luemo_l

MeN
t",l

o

E
&.q

0 o <_

0

0

\ O4 O4 £'_
_ 0

c_ 13 c 0 o 0 0

0

• ,,,,_

"t_ c 0 o

o_,,I

"_

0

E

E
i--

_r..)

<m o'-"

<_
U3
°,,-I

!
"x #,

_0

d
!

'

(seeJ6e(]) VOV

0 0 0 u3

0

0 0 0 u3

0 0 0 0
!

u3

o,,_

_

[-.,_ 0 ,---,

(sql-Ul)

_,uewo_ MeA

t",l

For this test, the data at NTF is typically measured shown in Table mean

acquisition

periods

were longer period.

than normal.

The steady

state data and those

taken

over a 1 second a given

Differences interval intervals

between

the corrected larger than

values 5.4.

over

one second

may be much from

in Table 5.5.

The results between

for one second the measured

16 to 22 seconds AOA mean value

are listed as large

Differences

and corrected intervals.

as -.064 ° are observed

over the selected

one second

Table Summary Time Period of Wind Measured Mean (Degrees) 16 to 17 17 to 18 18 to 19 19 to 20 20 to 21 21 to 22 -2.531 -2.513 -2.508 -2.550 -2.540 -2.511 Tunnel AOA Results

5.5 Second Data Acquisition Difference Measured -Corrected Periods

for One

Corrected Mean

AOA

(Seconds)

(Degrees) -2.473 -2.483 -2.478 -2.486 -2.481 -2.487

(Degrees) -0.058 -0.030 -0.030 -0.064 -0.059 -0.024

97

Chapter CONCLUDING An original system dynamic on analysis approach

6 REMARKS is presented wind tunnel associated to evaluate data. the effects of and

model

vibrations results

measured

aerodynamic

Analytical

experimental cause

show

that centrifugal model systems

accelerations

with model dynamic of magnitude these

vibration response greater errors can

bias errors

in the inertial model

attitude found

measurements.

Wind-off

tests on two transport than the required not be removed of the model

bias errors

over an order

device

accuracy.

An analysis

is presented

that shows

by filtering errors

or averaging.

Equations

are developed

to show

the influence

attitude

on the determination

of the drag coefficient.

A new in the model modes whip" tests

time domain inertial system. model

technique attitude

is developed measurements extends

to correct using previous

for the dynamically measured work modal

induced properties

errors of the

This modal and yaw

technique plane.

to compensate was associated

for multiple with "sting

in the pitch with on two

Previously,

the problem system environment and the

no detailed transport for

analysis models

of the underlying in a laboratory Theoretical into

dynamics.

Dynamic the

response need to are on is

demonstrated modal dynamics. of interest,

compensate presented observed simplified.

multiple

modes.

experimental system modes shows

analyses Based the problem

to provide rigid body

physical model motion

insight

model

for the low frequency model mode, analysis

For a planar

rigid body

that the fuselage of freedom.

motion A mode

can be completely

described

by a translation

and rotation

degree

98

radiusis definedto relatethe translationandrotationdegrees freedomusing analytical of or experimental odeshapes.Analyses m
affected wind significantly by the aerodynamic A correlation are presented loads that show the mode radii are not pressure the

experienced

in a high and

dynamic

tunnel

environment. assumption.

coefficient

is defined

used

to validate

rigid body model

Due wind

to short tunnels,

data

acquisition of the

periods art

and the multi-mode signal processing

random

response are filters

observed required are used using

in to to the

state

digital method modes

techniques Bandpass effects

implement isolate principle unfiltered achieve forward

the modal

correction

in the time domain. and then the mode processes, dynamic response correction a corrected

the effects

of individual

are combined relationship

of superposition. model zero-phase and reverse induced attitude

During signal

the filtering

the phase

of the To the the that

and the model finite The impulse modal

response filters

must be maintained. are applied in both for signal

distortion, directions. bias error

method model

compensates attitude forces time

dynamically

and provides

can be used to correlate

with time varying

changes

in the balance

The

modal

correction actual wind

method tunnel

is verified test data.

through The

a series

of wind-off

dynamic tests device

response show the

tests and method an order

wind-off

dynamic model

response attitude

has the ability of magnitude

to reduce to achieve

the bias error in the inertial the required device

by over

accuracy.

99

Theoreticalandexperimental esultsare presented r that demonstrate needto correct the for dynamicallyinducederrorsin inertial wind tunnelmodel attitudemeasurements. A correctionmethodrequiringfour additionaltransducers asdevelopedandimplemented w at the NationalAerospace Laboratoryin the Netherlands. principal advantage the A of modalcorrectiontechniqueis thatit minimizesthe numberof requiredtransducers (two) using the modal propertiesof the model system. This is especiallycritical for models with limited interior space andin wind tunnelsthathaveextremetemperature conditions where heated instrumentation packages are required. Recently redesigned instrumentationpackages the National TransonicFacility (NTF) provide the two for additionaltransducersequiredfor the modalcorrectionmethod. Currently,facilities in r the UnitedStates havenotimplemented correction. a

Future researchof wind tunnel model systemdynamicsand its effects on measured aerodynamicdata is recommended the following areas: (1) Perform a statistical in analysisto evaluatethe significanceof the magnitudeof the angleof attackcorrection with respectto the measured standard deviation,and small angle assumptionfor high anglesof attack; (2) Performa studyof thecrossaxis sensitivityof the inertial attitude sensor,andthe effectsof modelroll motions; (3) Performa studyof alternatesignal processingmethods,such as modulation techniques,for removing the dynamically inducederrorsin the inertial modelattitudemeasurements;4) Basedon the observed ( rigid body model behavior,performa parametricstudyto evaluatechanges dynamic in response variationsin: massor massdistributionof the model;balancestiffnessand for

100

damping;and sting material properties. This researchwould be aimed at developing designcriteriafor modelsystems thatwould minimize the modeldynamicresponse and move closer to the desired steady-statewind tunnel test conditions. Further

enhancements maybe foundin the useof activevibrationcontrol techniques suppress to the modelvibrations.

101

Chapter

7

REFERENCES

[1] [2]

Young, C. P., Jr.:"Model Wind Tunnels, 1996. Fuller, D.E.: NASA "Guide

Dynamics",

AGARD

Special

Course

on Cryogenic

to Users of the National

Transonic

Facility",

TM-83124, T. W.:

July, 1981. "A Study of the Aeroelastic Transonic Facility", Stability for the Model 1988. of Vibrations of Support

[31

Strganac, System

of the National

AIAA-88-2033, T. W.:

[41

Whitlow, Code",

W., Jr.; Bennet, Transonic AIAA-89-2207,

R. M.; and Strganac, Model 1989.

"Analysis

the National

Facility

Support System

Using a 3-D Aeroelastic

[51

Young, C. P., Jr.; Popernack, T. G., Jr.; Gloss, B.B.: "National Model and Model Support Vibration Problems", AIAA-90-1416, Buehrle, R. D.; Young, C. P., Jr.; Balakrishna, Interaction Model S.; and Kilgore, Between Model Transonic

Transonic 1990. W. A.:

Facility

[6]

"Experimental

Study of Dynamic

Support Structure Facility",

and a High Speed Research AIAA-94-1623, 1994.

in the National

[7]

Young, C. P., Jr.; Buehrle, R. D.; Balakrishna, S.; and Kilgore, W.A.: "Effects Vibration on Inertial Wind-Tunnel Model Attitude Measurement Devices". NASA Technical Memorandum 109083, August, 1994. P.; Finley,

of

[81

Buehrle,

R. D.; Young,

C. P., Jr.; Burner, A. W.; Tripp, J. S.; Tcheng, Response Devices",

T. D.; and Popernack, T. G., Jr.: "Dynamic Wind-Tunnel Model Attitude Measurement Memorandum [9] 109182, February, 1995.

Tests of Inertial and Optical NASA Technical

Pope, A.; and Goin, K. L.: High Speed Wind Sons, Inc., New York, 1965.

Tunnel Testing,

John Wiley

&

[10]

Muhlstein,L. ,Jr.; and Coe, C. F.: "Integration Time Required to Extract Accurate Data from Transonic Wind-Tunnel Tests", Journal of Aircraft, Volume 16, No. 9, pp 620-625, September 1979.

[11]

Mabey, D. G.: "Flow Unsteadiness and Model Vibration in Wind Tunnels at Subsonic and Transonic Speeds", Royal Aircraft Establishment Technical Report 70184, October, 1970.

102

[12]

Steinle, (AGARD)

F. and Stanewsky, Advisory Advisory Report

E.: Group

"Wind

Tunnel

Flow Quality Research 1982.

and Data

Accuracy

Requirements",

for Aerospace

and Development

No. 184, November, Attitude 1992.

[13]

Finley, T., and Tcheng, P.: "Model Research Center", AIAA-92-0763, Burt, G. E., and Uselton, of Dynamic July, 1974. Stability J. C.:

Measurements

at NASA

Langley

[14]

"Effect

of Sting Oscillations AIAA

on the Measurement Paper No. 74-612,

Derivatives

in Pitch and Yaw",

[15]

Billingsley, J. P.: "Sting Dynamics of Wind Tunnel Models", Arnold Development Center Report Number: AEDC-TR-76-41, May, 1976.

Engineering

[16]

Fuijkschot, P. H.: "Use of Servo-Accelerometers for the Measurement of Incidence of Windtunnel Models", National Aerospace Laboratory, The Netherlands, Memorandum AW-84-008, C. P., Jr.; 1984. "Modal Correction Model Method for pp. 1708-1714,

[17]

Buehrle,

R. D.; and Young, Induced Errors

Dynamically

in Wind-Tunnel

Attitude

Measurements",

Proceedings of the 13th International Modal Analysis Nashville, Tennessee, February 13-16, 1995. [18]

Conference,

Tcheng, P.; Tripp, J. S.; and Finley, T. D.; Effects of Yaw and Pitch Motion on Model Attitude Measurements, NASA Technical Memorandum 4641, February 1995.

[19]

Fuijkschot, National

P. H.: Aerospace

"A Correction Laboratory,

Technique

for Gravity

Sensing

Inclinometers", AF-95-004, 1995

The Netherlands,

Memorandum

[20]

Fuijkschot, P. H.: "A Correction Technique for Gravity Sensing InclinometersPhase 2: Proof of Concept", National Aerospace Laboratory, The Netherlands, CR 95458L, 1995. Experimental AIAA Paper Needs To Support 1992. T. A.; "A Dynamic Windtunnel West Applied Aerodynamics:

[21]

Gloss,

Blair, B.; "Future Perspective",

A Transonic [22] Owen,

92-0156,

F. K.; Orngard,

G. M.; McDevitt,

T. K.; and Ambur,

Optical Model Attitude Measurement System", European Transonic GmbH and DFVLR, Cryogenic Technology Meeting, 2nd, Cologne, Germany, [23] Roberson, Mifflin June 28-30, 1988, Paper, C. T.: 21 p. Engineering Fluid Mechanics,

J. A.; and Crowe, 1980.

Houghton

Company,

103

[24]

Meirovitch, p 240-250.

Leonard:

Elements

of Vibration

Analysis,

McGraw-Hill,

Inc.,

1975,

[25]

Wells,

D. A.:

Schaum's

Outline

of Theory Company,

and Problems 1967.

of Lagrangian

Dynamics, [26]

Schaum

Publishing

Tse, F. S.; Morse, Applications, Allyn

I. E.; and Hinkle, and Bacon, Inc.,

R. T.: Mechanical 1978.

Vibrations

Theory

and

[27]

Fung,

Y. C.:

An Introduction & Sons, Inc.,

to the Theory

of Aeroelasticity,

John Wiley [28] Craig,

1955. Dynamics: 1981. An Introduction to Computer Methods,

R. R., Jr.:

Structural Inc.,

John Wiley [29]

& Sons,

Allemang, R. J.; and Brown, D.L.: Chapter 21: Experimental Modal Analysis, Shock and Vibration Handbook, 3rd Edition, McGraw Hill, Inc., 1988. Ewins, 1984 D. J.: Modal Testing: Theory and Practice, Research Studies Press LTD.,

[30]

[31]

Ferris, A.T.: "Cryogenic Wind Tunnel Force Instrumentation", Conference Publication No. 2122, Part II, 1982, pp 299-315. Thomson, W. T.: Vibration Theory and Applications, Prentice-

NASA

[32]

Hall, Inc.,

1965,

pp. 179-182. [33] Davenport, A. G.; and Novak, M.: Chapter 29 Part II: Vibration of Structures Induced by Wind, Shock and Vibration Handbook, 3rd Edition, McGraw Hill, Inc., [34] Alder, 1988. H. L.; and Roessler, E. B.: Introduction to Probability and Statistics,

W. H. Freeman [35] [36] [37] [38] MATLAB Hornbeck, The STAR

and Company, Guide, Numerical

1960. The Math Methods, Spectral Works Inc., August, Publishers, Inc., 1992. Inc., 1996. Corporation, 1989 1975.

Reference R. W.; System

Quantum

User Manual, User's Manual,

Dynamics,

MSC/NASTRAN

The MacNeal-Schwendler

104

Appendix EFFECT OF AERODYNAMIC FORCES

A ON MODAL CHARACTERISTICS

Introduction In this section, wind that the effect of aerodynamic model system forces on the The modal objective significantly of the modal and mode during wind characteristics is to validate under correction effective tunnel model conditions the of a the wind

cantilevered assumption tunnel

tunnel the modal

are examined.

characteristics

do not change assumption frequencies

test conditions. wind-off

This is a fundamental estimates of the natural attitude

method radii to be A as

that enables used finite

for correction element model

of the model (FEM)

measurement

testing. is used including

of a representative characteristics in a recent

cantilevered for several

transport loading

the basis for evaluating the most severe Transonic forces

the modal measured

wind tunnel

test on this model

in the National

Facility

(NTF).

Analytical

Model model of a representative using cantilevered transport model system for the analysis (less model

The finite element NTF was generated The FEM

and analyzed was developed

the MSC/NASTRAN

® [38]

structural

program. than

with the goal of representing that contribute of the wings of beam

the low frequency in the inertial

50 Hertz)

"rigid-fuselage" Detailed fuselage

modes

to the errors

attitude The

measurements.

modeling

was not of interest elements

for this study. material

sting and model

are constructed

with equivalent

105

and cross-section specificgeometricproperties. The force balancewhich connectsthe stingto the fuselagewasmodeledusinga concentrated massequalto the balancemass and rigid bar elements. Springs were usedat the connectionbetweenthe rigid bar elementand the fuselageto represent he balancestiffnesscorresponding the three t to translationandthreerotationdegrees freedom. The balancestiffnesswas determined of from experimentalmeasurements.The wings are modeled as concentratedmasses attached the fuselage to usingrigid bar elements. An additionallumpedmasswas used to represent instrumentation andassociatedardware. h

The primary generalized forcesare the unsteady aerodynamic loads. loads are modeled using a quasi-steadyapproximation [27]. aerodynamic forcesaremodeled as:
QF = q_ × S × C F where, q_ is the dynamic linear and pressure and S is the characteristic of the model as: attitude. area.

The The

aerodynamic generalized

(A.I)

The coefficient the

CF will

be assumed aerodynamic QM where function

is a function are modeled

Similarly,

generalized

moments

= qoo x S × d × C M characteristic attitude. length and the coefficient CM is assumed linear

(A.2) and is a

d is the

of the model

Data from a high-speed this transport model

(Mach

=0.9, q==1800 were used

pounds

per square

foot) wind most

tunnel severe

test of loading

in the NTF

to determine

the four

106

conditions. To add additional conservatism,his data was scaledup to a dynamic t pressure 2700poundsper square of foot. The resultingloadingconditionsare listed in Table 1. Theseforcesandmomentswereappliedto the FEM at a point on the fuselage coincidentwith thebalance momentcenter. Table 1
Transport Worst Load Case 1 2 3 4 Model Conditions Normal Force Pitch Moment Case Loading

Axial Force (Pounds) 69 63 -53 -184

(Pounds) -2271 -491 2688 6035

(Inch-Pounds) 4OOO 3158 1474 632

For

each

of the

four

different model

aerodynamic and then the was

load

cases,

a static was run

analysis for

was

run

to

generate loading baseline

a prestressed condition. set of natural The

eigensolution also

this prestressed to provide a

eigensolution

run for the

no load

case

frequencies

and mode

shapes.

Results

and Conclusions of the analysis was to assess wind constant the effect model of aerodynamic system. radius loading on the modal presented from in a

The purpose characteristics

of a cantilevered an important

tunnel

For the research which

this dissertation, linear regression

is the

modal

is estimated

fit of the fuselage

mode

shape

coefficients.

Therefore,

the comparison

107

criteriaarenaturalfrequencies ndmoderadii.The moderadiusfor the first six analytical a modeswereestimated usingthe methoddescribed Chapter The naturalfrequencies in 4. and mode radii for the different loading conditions are listed in Tables 2 and 3, respectively. The naturalfrequency doesnot shift significantlyfor any of the loading conditions.For the largestaerodynamic forces measured a representative on transport model in the NationalTransonicFacility, the predictedshifts in the modal radiuswere lessthan4%, which is negligible.

Table Natural No Load Mode Frequency (Hz) 9.19 9.23 17.2 17.3 29.5 30.4 * Difference Load Case 1 Frequency (Hz) 9.19 9.23 17.2 17.4 29.5 30.4

2

Transport Model Frequency Comparison Load Case 2 Frequency (Hz) 9.19 9.23 17.2 17.4 29.5 30.4 Load Case 3 Frequency (Hz) 9.20 9.25 17.2 17.4 29.6 30.5 Load Case 4 Frequency (Hz) 9.22 9.30 17.3 17.4 29.7 30.6 Maximum Difference

(%)
1 2 3 4 5 6 Note: 0.3 0.8 0.6 0.6 0.7 0.7

(%) = (fioaa-fnoload '/fnoload * 100

108

Table Transport Mode No Load Mode Radius (Inch) 39.4 39.7 3 4 5 6 Note: 7.68 8.21 -3.67 -3.17 * Difference Load Case Radius (Inch) 39.5 39.8 7.68 8.24 -3.66 -3.18 1 Radius Load Case 2 Radius (Inch) 39.4 39.7 7.67 8.20 -3.67 -3.17

3 Model Comparison Load Case 3 Radius (Inch) 39.6 40.0 7.72 8.28 -3.67 -3.15 * 100 Load Case 4 Radius (Inch) 40.2 41.1 7.87 8.54 -3.64 -3.14 Maximum Difference

(%)*
1.8 3.5 2.5 4.0 -0.8 -0.9

(%) = (Rload-R.olo_)/R.olo.d

109