NASA CR-175026

Under Distribution Limitation

Until December 31, 1987

ANALYSIS AND TEST EVALUATION OF THE DYNAMIC

RESPONSE AND STABILITY OF THREE ADVANCED

TURBOPROP MODELS AT LOW FORWARD SPEED

By

Arthur F. Smith

HAMILTON STANDARD DIVISION

UNITED TECHNOLOGIES CORPORATION

WINDSOR LOCKS, CONNECTICUT 06096

December, 1985

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135

Contract NAS3-22755

3. RacJ/_ient's C_tewg No,

$. RepOrt Date

December, 1985

1. Report No. _ 2. Government Accmion No.

l

NASA CR- 175026

4. Title end Subtitle

Analysis and Test Evaluation of the Dynamic Response

and Stability of Three Advanced Turboprop Models at

Low Forward Speed

7. Author(s)

Arthur F. Smith*

9. Performing OrganiZltion Name end Address

Hamilton Standard

United Technologies Corp.

Windsor Locks, CT. 06096

12. Sponsoring Agency Name and Address

National Aeronautics & Space

Administration

Wn_hlno'tc_n: ]_ C_ 2(_R4fi

15. Supplementlry Notes

6. Performing OrojItllZatiOn Code

8. Performing Organization ReDort No.

HSER 11055

10. Work Unit No.

11. Contract or Grant No.

NAS3-22755

13. Type of Report and Period Covered

Cont rector Report

14. SOo_llorJ_ Agency Code

Final Report, Project Technical Monitor, O. Mehmed, NASA Lewis Research Center, Cleveland, Ohio 44135

*Now with: Hirock Corporation, 1 Main Road, Granville, MA 01034

16. Abstrac_

Results of wind tunnel tests at low forward speed for blade dynamic response and stability of three

62.2 cm (24.5 in) diameter models of the Prop-Fan, advanced turboprop, are presented. Measurements

of dynamic response were made with the rotors mounted on an isolated nacelle, with varying tilt for

non-uniform inflow. Low speed stall flutter tests were conducted at Mach numbers from 0.0 to 0.35.

Measurements are compared with predictions made using beam analysis methods for the model _ th straight I

blades, and finite element analysis methods for the models with swept blades. Measured stall flutter stress I

boundaries are compared to Eigen-solution flutter boundaries. ]

Calculated 1P stress response agrees favorably with experiment. Predicted stall flutter boundaries correlate

well with measured high stress re_ons.

Stall flutter is significantly reduced by increased blade sweep. Susceptibility to stall flutter decreases rapidly

with forward speed.

7 Key Words {Suggested bv Author(s})

Advanced Turboprop

Prop-Fan

Energy Efficient

Structural Response

Stall Flutter

IF="

19. Security Cfassif.(of this rel_rtl

Unclassified

18. Distribution Statement

_til December 31, 1987

I20. Security Classif (of this page} [ 21 No, of Pages

I"

Unclassified I 106

22. Price"

• For sale by the Nahonat Techmcal Informahon Service, SprDnsf,eld V,rg=n13 22161

NASA-C-168 (Rev I0-75)

i!i[

FOREWORD

This work was accomplished under contract NAS3-22755 For the NASA-Lewls

Research Center in Cleveland, Ohio. Mr. Oral Mehmed was the technical monlfor for the contract.

All of the testing reported herein was performed by NASA-Lewis personnel in

the lO x lO wind tunnel at NASA-Lewls. The data were reduced, analyzed and

reported by personnel from Hamilton Standard, a dlvlsion of United

Technologles Corporation.

The data reduction was performed by Mr. Donald J. Marshall. The analysls and

reporting was performed by Mr. Arthur F. Smith. Mr. Bennett M. Brooks was

the Hamilton Standard Project Manager.

iii/iv

Section

l.O

2.0

3.0

4.0

5.0

6.0

7.0

TABLE OF CONTENTS

ABSTRACT ..............................................

FOREWORD ..............................................

TABLE OF CONTENTS .....................................

SUMMARY ...............................................

SYMBOLS AND ABBREVIATIONS .............................

INTRODUCTION ..........................................

DESCRIPTION OF EXPERIMENTAL PROGRAM ...................

2.1 Test Models .....................................

2.2 Wind Tunnel Facility ............................

2.3 Propeller Test Rig ..............................

2.4 Model Instrumentation ...........................

2.5 Test Procedures ..................................

2.6 Operating Conditions ............................

2.7 Data Reduction ..................................

ANALYTICAL TECHNIQUES .................................

3.1 Approach ........................................

3.2 Aerodynamic Loads ...............................

3.3 Critical Speed Analysls (Beam Models) ...........

3.4 Critical Speed Analysls (Flnlte Element Models) ,,

3.5 IP Analysis (Isolated Nacelle/Beam Blade Model) ..

3.6 IP Analysis (Isolated Nacelle/Finlte Element

Blade Model) .................................

3.7 Aeroelastic Stall Flutter Stability Analysls ....

3.8 Analytlcal Descript|on and Operating Conditions ..

3.9 Analytlcal Results ..............................

TEST DATA EVALUATION AND COMPARISON WITH CALCULATIONS ..

4.1 Stall Flutter ...................................

4.2 Modal Response Frequencies ......................

4.3 Angular Flow Dynamic Response ...................

4.4 Reverse Thrust ..................................

CONCLUSIONS ...........................................

RECOMMENDATIONS .......................................

REFERENCES ............................................

TABLES ................................................

FIGURES ...............................................

v/vi

i

iii

vii

ix

9

12

12

13

15

15

19

2O

23

25

27

29

31

37

SUMMARY

Stall flutter and dynamic response tests were conducted in the 3 x 3 meter

<lO x I0 ft) wind tunnel at the NASA-Lewls Research Center on three Prop-Fan

models, in an isolated nacelle installation. These models are designated the

SR-2, SR-3 and SR-5, with the blades characterized by Increaslng sweep, From

the unswept (straight) SR-2 blade to the highly swept SR-5 blade. The tests

were conducted over flight speed range of 0.0 to 0.35 Mach number, as well as

a large range of blade angles and rotational speeds (RPM), Including areas of

deep stall. Limlted testing was conducted for reverse thrust operation. Also, testing was performed with the rotor axls tilted relative to the tunnel

airstream to provide angular inflow to the rotor, for many operating conditions. Blade vibratory stress measurements were recorded For all operating

conditions. Extensive analysis of these data was performed.

Perhaps the most significant result of the stall flutter testing Is that the

blades with increased sweep had larger operating regions than the less swept

blades and responded with less stress under stalled vibratory conditions.

The unswept SR-2 model was the most susceptible to stall flutter, responding

with the highest stresses. The moderately swept SR-3 and the highly swept

SR-5 models remained stable at increasingly higher blade angles and RPM's

than the SR-2, and also responded with lower stresses, it was observed that

stressing was significantly reduced with the introduction of forward flight

speed, for all of the blade models. As expected, all three models encountered high stresslng at the highest blade angles and rotational speeds, which

at some conditions was indicative of a forced excitation response due to vortex shedding, or buffeting. Also, high stressing was observed at some reverse thrust (negative or very low blade angle) conditions for the SR-3 and

SR-5 models.

Stall flutter calculations were made using a recently developed flutter analysis method that can determine the stability of thln, highly swept blades,

such as those used on Prop-Fans. The calculated onset of stall flutter is

defined to be at operating conditions for which blade damping goes to zero.

Negative damplng indicates an unstable condition.

Flutter predictions for the three Prop-Fan models were made and compared to

test data. Flutter boundaries were determined from the test data, based on

the occurrence of steeply rising stresses with increasing blade angle or rotor RPM, since damplng was not measured. The calculations show negatlve

damping occurring at generally the same operating conditions for which high

stresses were encountered during test. Very good agreement was seen for the

SR-2 and SR-3 models, with less agreement for the SR-5 model which gave only

weak flutter Indications during test. However, the experlmenta] trend which

showed stability to increase with blade sweep was well predicted. The theory

predicted that stall flutter will occur primarily In the torslonal mode for

all three models. This agreed with the SR-2 test data, but not with SR-3 and

SR-5 measurements.

vii
Measured blade stress trends for angular inflow operatlng conditions followed

well established trends associated with conventional turboprops. Blade

stress Increased linearly with rotor tilt angle and consisted almost entirely

of IP response. Stress sensitivity (stress divided by excitatlon factor) increased with increasing blade angle and RPM, and decreased with increasing

Mach number.

Correlation between tested and predicted Campbell diagram modal frequencies

was excellent for the important lower modes, for all blade models. This indicates the validity of the structural prediction models.

Increased blade sweep significantly reduced both angular inflow (IP) and

critical speed stress responses.

Analytical predictions of IP blade stress correlate well with measured test

data.

viii
Cp

D

EF

F

_F

K

m

N

N_

n

P.

r

Q

SHP

R

Veq

VT

_.75

_REF

P

o

SYMBOLS AND ABBREVIATIONS

Power coefficient : 2_Qlpn2D s

Prop-Fan Diameter, m

Excitation Factor = _(Vr/644.8) z (p/po)

Centrifugal Force - Newtons

Incremental Force - Newtons

Stiffness, kg/m

Mass per unit length, kg/m

Rotatlonal speed, RPM

Normalized blade chord

Rotational speed, revolutions/second

Normalized load

Blade radial station, m

Prop-Fan Torque, Newton - m

Shaft horsepower

Prop-Fan Radius = D/2, m

Equivalent air speed = V_v/-p/po, knots

True airspeed, knots

Blade angle at 3/4 radius, degrees

Reference blade angle, degrees

Air density (kglm _) : 1.2250

Sea level ambient air density (kg/m _)

Stress, kPa

Prop-Fan shaft tilt, degrees

ix
SYMBOLS AND ABBREVIATIONS (Continued)

Frequency, Hz

_o Natural frequency, Hz

IP Frequency = one per propeller revolutlon, Hz

nP Frequency = n per propeller revolution, Hz

SI units of measurement used throughout unless specified otherwise.

X
l.O INTRODUCTION

The occurrence of fuel shortages, Increased fuel cost and the threat of future worsening conditions for alr transportation has caused NASA to sponsor

studies of new, more efficlent, aircraft and propulslon systems. One of the

promising concepts established by these studies is the advanced high speed

turboprop, or Prop-Fan. Thls propulslon system differs from existing turboprops. The Prop-Fan has greater solidity than a turboprop, achieved by more

blades of larger chord. The turboprop has straight blades with relatively

thick alrfoll sections; the Prop-Fan has swept back blades with thin airfoil

sections to enhance performance and reduce noise. The turboprop cruises at

no more than 0.65 Mach number; the Prop-Fan Is designed to cruise at 0.7 to

O.B Math number. The diameter of the Prop-Fan Is about 40 to 50% smaller

than that of the turboprop. For maximum performance the Prop-Fan makes use

of advanced core engines of the klnd being used in modern turbofan engines.

Performance Is also enhanced by use of a spinner and nacelle aerodynamically

contoured to reduce compressibility losses by retarding the high velocity

flow through the root sections of the Prop-Fan blades.

Utilizing predicted and measured aerodynamic performance data, welght estimates, and noise projections, several Government sponsored studies by both

engine and airframe manufacturers have concluded that a fuel savings of approximately 20 to 40_ depending on operating Mach number should be achieved

by a Prop-Fan aircraft, as compared wlth a hlgh bypass ratio turbofan aircraft. Hlth these encouraging results, a research technology effort has been

instituted to establish the design criteria For this new propulslon system.

A major objective In the development of Prop-Fan configurations is to insure

the structural integrity of the rotor. Since the Prop-Fan Is such a significant departure from conventional propellers, with its highly swept, thin

blades, the structural demands are substantial. The high speed operation of

highly swept blades imparts large forces to the limited materlal Inherent to

the thln airfoil sections needed for efficient performance. It Is imperative

that the rotor be able to absorb the aerodynamic loads at all operatlng conditlons, as well as the centrifugal loads assoclated with Its unique shape

and construction. The steady-state dynamlc response of the blades must be

low and flutter instabilities must be avoided, for safe operation.

As part of the continuing studies of Prop-Fan structural stability and blade

dynamic response, static and low speed stall flutter tests, and angular inflow tests were conducted on the SR-2 B-bladed, SR-3 B-bladed, and SR-5 lObladed model Prop-Fan configurations. These tests were conducted during

December 1981 and February 1982 at the NASA - Lewis Research Center.

Hamilton Standard, under contract, analyzed the data acquired durlng these

tests.
This report summarizesthe results of this stability and dynamic response Investigation. Included are trends of the measuredblade stress test data with

operating conditions for the three models. Total vibratory stress, modal vibratory stress and blade stress frequency spectra were analyzed. In additlon, stall flutter stability boundaries and IP dynamic responses were calculated for comparison to test results. The comparisons were used to evaluate

the accuracy of the prediction methods and to recommendImprovementsto increase their effectiveness as Prop-Fan des|gn tools.

2
2.0 DESCRIPTION OF EXPERIMENTAL PROGRAM

The tests described in this report were conducted on three Prop-Fan model

configurations, mounted on an isolated nacelle, in the NASA-Lewls Research

Center 3 x 3 m (lO x lO ft) wind tunnel. Two types of tests were combined

in thls study. One test was performed to determine the stall flutter

characteristics of the turboprops at static conditions and at low speeds (up

to 0.35 Mach number). The second test was performed to determine the effects

on dynamic response of rotor tilt relative to the airstream at low speeds (up

to 0.35 Mach number).

2.1 Test Models

Each of the three Prop-Fan models is nominally 62.2 cm (24.5 in) in diameter. The Prop-Fan concept incorporates thin airfoils and swept blades to

achieve hlgh aerodynamlc efficiency with low noise generation. Table 2-I is

a summary of some of the Prop-Fan overall design parameters. The model

blades are designated SR-2, SR-3 and SR-5, which have respectively increasing

tip sweep, as seen in Figure 2-I. The blades and hub for each of the three

models were designed and built by Hamilton Standard.

Figure 2-2 shows some of the characteristics used to describe the model

blades. Shown are the geometric twist angle, section thickness ratio, chord

to diameter ratio, aerodynamlc sweep and geometric sweep. The aerodynamic

sweep is measured using the local air velocity vector, to account for the

flow around the spinner and rotational speed. The geometric sweep is the

angle between the tangent to the blade mldchord locus and the stacking

(pitch-change) axis. The aerodynamic sweep is considered the more important

parameter because it describes the movement of each blade section relative to

the air.

2.2 Nind Tunnel Facility.

The three model Prop-Fans were installed in the NASA-Lewis 3 x 3 m

(lO x 10 foot) Supersonic Wind Tunnel. This tunnel is described in Reference

I, and is designed for supersonic testing at Mach numbers from 2.0 to 3.5,

but can also be operated for subsonic testing. In the present tests, the

Mach range was from 0.0 to 0.35. Conditions in the test section are close to

standard sea level conditions. The test section is 12.19 m (40 ft) long and

has a cross section of 3.05 x 3.05 m (lO x lO ft). The test section has two

flexible side walls used as a nozzle for adjusting the flow in the supersonic

mode. This nozzle was set at the full open position for the subsonic tests,

and a set of flow control doors on the downstream end of the test section

were used to regulate the tunnel Mach number.
2.3 Propeller Test Rig

Figure 2-3 shows the SR-3 model Prop-Fan blade installed in the wind tunnel

test section at NASA-Lewis. The Propeller Test Rig (PTR) is strut-mounted

from the ceiling in the tunnel test section with the angle-of-attack (shaft

tilt) remotely variable between -2° to +15 °. A cutaway view of the PTR is

presented in Figure 2-4. The model is driven by a three-stage air turbine

utilizing high pressure air at 3.1 x IOb newton/m z (450 psi) and heated

to 366°K (660°R). The turbine is capable of delivering nearly 634 kw (850

hp) to the Prop-Fan model.

A rotating balance which is part of the PTR can be used to measure rotor

torque and thrust. Rotor torque only was measured during thls test.

2.4 Model Instrumentation

Foil strain gages mounted on the cambered (suction) surfaces of selected

blades for each Prop-Fan configuration were used to measure dynamic stresses

due to blade vibration.

The blade strain gages were located at polnts of maximum modal and IP stresses, based on calculations. These calculations were made at the blade natural

vibratory response frequencies, using a beam analysis for the SR-2 model and

finite element methods for the SR-3 and SR-5 models. Figure 2-I shows the

relative locations of a full set of strain gages for each model blade. Single element gages were used to measure bending stresses and dual element

gages were used to measure shear stresses due to torsion. A full set of

gages was applied to opposite blades on each model, while other selected

blades were instrumented with either a shear gage, or a shear and a bending

gage. These gages were used to determine the relative phasing of strain gage

signals between blades. Table 2-11 describes the gage locatlons and functions in more detail. The gage designations correspond to the gage number as

shown in Figure 2-I.

The number of strain gage slgnals that were measured was limited by the

number of channels available on a rotary transformer device used to transmit

electrical signals from the rotor to the fixed system. The strain gage

signals, as well as a once-per-revolution (pipper) signal from the rotor,

were recorded on FM magnetic tape for later processing.

2.5 Test Procedures

The tunnel was brought up to speed with the Prop-Fan unpowered. The windmilling rotational speed was dependent on the blade pitch angle setting,

which was manually set before tunnel startup. The model rotational speed, at

this fixed pitch blade angle and fixed tunnel Math number, was incrementally

increased by increasing the power to the rotor. This was done until an operating limit, such as a blade stress limit, rotational speed limitl rig power

limit or vibration limit was reached. The maxlmum allowable rotational speed

was 9000 RPM. This was repeated for different shaft tilt angles. The whole

process was repeated for different Mach nvmbers.
The tunnel had to be shut down In order to change the blade pitch angle

(ground adjustable). An Inclinometer was used to set the blade pitch angle

(reference blade angle) at the reference locatlon prior to tunnel start up.

The reference location was 0.78 R for the SR-2 and SR-3 and 0.73 R for the

SR-5. A blade/hub collective pitch arrangement allowed a slngle blade to be

used for thls procedure.

2.6 Test Conditions

The Conditions for these wlnd tunnel tests were primarily sea level condltions, i.e. (sea level density and temperature). The parameters that were

variable for the test were Mach number, Prop-Fan shaft tilt angle, blade angle and rotor RPM. All of these parameters were remotely controllable from

the control room except blade angle. A schedule of the blade angles tested

can be found In Table 2-III. The RPM range tested was between 2000 and 9000

RPM In 500 RPM Increments, and the Mach numbers used are also included in the

table. Figures 2-5 through 2-7 show the test envelopes for the SR-2, SR-3

and SR-5 Prop-Fan models. These envelopes show the boundaries of the actual

test and include the limits encountered, defined by hlgh stresses, wlndm111-

Ing RPM, maximum RPM and the maximum power avallable. Also shown are the

boundaries of the test envelope for the 15 degree tilt conditions. One set

of boundaries Is shown for each Mach number.

2.7 Data Reduction

The magnet|c tapes which were recorded at NASA-LeRC were processed at

Hamilton Standard. The analog tapes were analyzed by obtaining total vlbratory stress using peak stress converters and recording the signals on strip

charts. As a second step, the outpu_ from the magnetic tape was processed

using an electronlc real time analyzer to produce narrow band spectral analyses. This Information was then stored on tape for a permanent record of

each case run. The data were then transmitted to a high speed digital computer for processing. At this point, a computer program was used to determine the amplitude of spectral peaks and the associated frequencies. These

were then tabulated and printed according to case number and conditlon.

Automatic plot routines were developed that produce Campbell dlagrams and

curves of vlbratory stress vs. RPM for each blade angle. These Items are

discussed further in the section on test data evaluation.

5/6

3.0 ANALYTICAL TECHNIQUES

3.1 Approach

The IP response theoretlcal prediction analysis and the stabllity theoretical

prediction analysis used for this project embody different approaches. Both

methods, however, require the use of alrload computations In order to determine the blade excitations and force derivatives. The stability analysis also requires modal calculations for the mode shapes and frequencies used in

the eigen solutions. Flgure 3-I is a flow chart that shows theprogresslon

of methods that are used for the computation of stability and IP response.

The blade definition and operating conditions are used as input for the alrloads analyses and the frequency and modes programs, and are also used to set

up the grids for the finite element analyses. Two airloads analyses were

used, one designated as HSIH045 which uses Goldstein type calculations for

the Induced flow (see Ref. 2), and the other which uses a skewed prescribed

wake method (see Ref. 3) for the Induced part of the flow, known as HS/H337.

Table 3-I lists the methods and the computer designation of the various analyses dlscussed In this report.

The next step in the process is to define the blade geometry and its position

In space. This includes deflnlng the grid for the finite element methods.

These definitlons are then used to determlne the modal characteristlcs for

the stabllity analyses.

The blade modal characteristics for the SR-2 blade were determined using the

Hamilton Standard beam analysls programs HS/H025 (bending modes) and HS/H027

(torslonal modes). The width, sweep, and offset characterlstics of the SR-3

and SR-5 blades are such that a simple beam analysls was not adequate to represent the complex behavior observed for these blades. Finite element analyses were requlred to model the high degree of coupling between flatwise

bending, edgewise bending, and torsion modes. The general purpose finite element code MSC/NASTRAN, was used to calculate the modal characteristics for

the SR-3 and SR-5 blades.

Blade modal properties were used in the HS/F203 stability analyses. Here,

the modal displacement from the frequency and mode calculatlons are converted

to beam type displacements, where each mode Is described by two translatlons

and a rotation at each blade section belng used. Transformatlons are made

putting the system Into the blade chord coordinate system. Thls is done in

order to use linearlzed aerodynamics and small angle assumptions. The analysls |s an energy balance method that provides blade frequency and damplng

information. The operatlng condition for which the calculated damplng goes

through zero Is considered the point of Flutter onset. Analytical flutter

boundaries for the Prop-Fan blades were established by compillng the operatIng conditions Indicating zero damplng.

7
The SR-2 IP dynamic response analysis was performed using the beam analysis

code, HS/H026 developed at Hamilton. The SR-3 and SR-5 IP dynamic response

analyses were done with the MSC/NASTRAN code using the models developed for

the frequency analyses. The blade excitation loads were obtained from the

aerodynamic program and used as Input to the response analysis, from which

blade stresses and bending moments were obtained. Plots of stress per excitation factor were made. Exc|tation factor Is defined as:

E.F. = _ (Veq1348) 2

where g Is the In?low angle In degrees and Veq is the equivalent velocity

In knots.

3.2 Aerodynamic Loads

A preliminary requirement for the load determination of a Prop-Fan is the

knowledge of the flow velocity variations around the disk. Hamilton Standard

employs a computer analysis, designated HS/H039, that calculates the flowfield around an aircraft Including the fuselage, nacelle and wings. For the

present study however, only the features of the nacelle were Incorporated to

represent the wlnd tunnel configuration. The analysis uses a threedimensional potential ?low representation of the nacelle. Since the nacelle

is at a tilt angle along with the propeller, the cross flow around the nacelle Is accounted for, as well as the spreading of the flow around the

spinner.

The flowfleld, having been determined from the procedure discussed above, is

used as input for either one of two Hamilton Standard strip analysis codes,

designated HS/H045 and HS/337. These codes determine the time variation of

the loads and perform Fourier analyses to get the harmonic components. They

both perform a quasl-static lifting line airfoil analysis, uslng 2D airfoil

section data for lift and drag, at a number of azlmuthal and radial locations, and are often referred to as multlazimuth strip analyses. A Goldsteln

type wake analysis is used in HS/H045, and a skewed wake analysis is used in

HS/H337 to determine induced effects, via an iterative approach. Refinements

have been added to the codes to handle transonic aerodynamics, sweep, compresslblIity effects, and stall. These codes produce the harmonics of the

In-plane and out-of-plane aerodynamic loads at a number of radial locations.

These become the input for the beam or finite element structural dynamic

analyses.

3.3 Critical Speed Analysis (Beam Models)

The Hamilton Standard beam analysis program HS/H025 gives the natural frequencies, mode shapes, and modal masses for the bending modes of a straight

blade acting under the influence of a centrifugal field. Another program,

HS/H02?, gives the same informatlon for the torsional modes. These decks are

limited to the analysis of long, slender, i.e. beam-like, Isotropic blades.

The accuracy of the codes have been verified over a number of years with correlation of predicted and measured frequencies for many propeller blades.

Critical speeds are determlned from a Campbell diagram using the HS/H025 and

HS/H02? calculated frequencies.
3.4 Critical Speed Analysis (Flnite Element Models)

Due to the sweep, offset, and large chords of the SR-3 and SR-5 blades, the

beam analyses are not adequate to obtain reasonable approximations of the ha- -

tural frequencies and the highly coupled mode shapes. Any number of finite

element codes could be used to model the blades. For purposes of this contract, the natural frequencies were calculated uslng the MSC/NASTRAN code

(see Ref. 4).

Finite element grlds were set up to analyze the bending and centrlfugal

stresses of the solid blades. The non-linear capabilities of MSC/NASTRAN

were used to update the steady load position to the final dlsplaced blade

posltlon. The vibratory mode shapes and vibratory modal Information are determlned about this displaced position. Figure 3-2 shows In schematic form

the grid set-up used for the Prop-Fan models. Triangular elements were used

In general. However, quadrilateral elements were used on the outer portion

of the SR-S, In an attempt to eliminate the bias of the triangular elements

In the highly swept tlp region.

3.5 IP Analysis (Isolated Nacelle/Beam Blade Model)

A computer code was developed at Hamilton Standard (HS/H026) for the analysis

of beam-like blades, (e.g. SR-2) where only IP response is anticipated.

Aerodynamic IP loads, such as those calculated by the HS/H045 code, and the

blade structural properties are used as Inputs to the code, which performs an

iterative soIutlon for the blade vibrato[y displacements and stresses. A direct approach to the solution of the equations of motion Is used, where the

effects of the centrifugal field are taken Into account. The effects of differential stiffness and modificatlons In loading, due to the displacement,

are taken Into account by iterative techniques.

3.6 IP Analysis (Isolated Nacelle/Finite Element Blade Model)

As in the determination of critical speeds for the SR-3 and SR-5 blades, it

was found that a finite element analysis Is required to represent the IP response of these wide, swept blades. There is too much coupling between flatwise, edgewise, and torsional modes to allow the use of a beam representation. For these IP analyses the MSC/NASTRAN code was used. Flnite element

models were generated by using quadrilateral (CQUAD4) elements. Figure 3-3

shows a flow chart which outlines the procedure used in the calculation of ]P

vibratory stresses. Note that the Incluslon of higher order vibrations could

easily be Incorporated Into this procedure.

Aero Loads - Based on previous analyses, it was possible to estimate the

steady untwist of the blade at speed. From thls estimate of untwist and the

initlal shape of the blade, a static (zero RPM) position of the blade can be

determined, so that the blade angle at speed (Initial plus untwist) closely

matches the blade angle (B.,s) predicted from the HS/H045 aerodynamic analysls, for the particular operating condltlon under consideratlon.
The calculated aerodynamic loads, centers of pressure, and B.75 are used by

the preprocessor code (HS/F194) to distribute the harmonic loads on the flnIre element grids. The centers of pressure versus span are assumed to be independent of azimuth: They are calculated from the alrload analysis with

steady state, zero In-flow angle. The aero loads are expressed in terms of

In-plane and out-of-plane components. The HS/F194 code converts these to

components parallel and normal to any given blade section. The assumptlon is

made that the load parallel to the blade chord (drag) is uniform across the

blade. The normal loads (lift) are distributed using an analytlcal

expression:

P, = A(Nc)8(l-(N¢)°'2s) 2

where Ncts the normalized chordwise position and A and B are chosen to

match the total load and center of pressure desired. Figure 3-4, shows typical samples of thls distribution function.

Steady State Position - Before the IP dynamic response analysls could be performed, it was necessary to do an analysis to determine the steady state posItion and stiffness of the blade. Because of the non-llnear effects of prestress (centrifugal stiffening) and large displacements, It Is desirable to

perform a non-linear analysis of the blade under the influence of centrifugal

loading. This portion of the analysis was done using rigid format 64, a geometric non-llnear static analysis in MSC/NASTRAN. The solution technique employs a Newton-Raphson Iterative scheme to converge on a displaced shape

which satlsfies the equations of equilibrium. This Is a more rigorous approach than the prevlously used differential stiffness solution (rigid format

4 In COSMIC/NASTRAN). The iteration is done at full RPM. Rigid format 64 in

MSC/NASTRAN does account for the centrifugal effects including an update of

the load vector with displacement.

It was found during the course of the iterative procedure, that slngularlties

often occurred in the structural stiffness matrix, associated with the lack

of plate element stiffness about its own normal. This is a feature of the

NASTRAN plate elements. Removal of the singularitles can be accomplished by

fixing or tying affected degrees of freedom to neighboring nodes (SPCS or

MPCS in NASTRAN terminology). It was also found that there exists a procedure within NASTRAN whereby the user may add artificial stiffness to the diagonal of the assembled stlffness matrix. The solution still converges to

the correct answer even with an erroneous stiffness matrix. This is a feature of the Newton-Raphson iterative scheme employed. A further feature is

that the final solution is a function only of the elemental stiffness matrix

and not the assembled global stiffness matrix. Both these fixes were employed during the analyses.

Upon completion of the iteration using rigid format 64 of MSCINASTRAN, the

Incremental stiffness matrix is saved on magnetic tape. The Incremental

stiffness matrix is the stiffness matrix which Is used to examine small (linear) perturbations about the steady state deflected position. It Includes

10.
the basic elemental structural stiffness and the differential stiffness representlng the additional stiffness due to the fact that the blade is |n a

centrlfugal fleld. However, the matrix output from NASTRAN does not recognize that the magnitudes of the load vectors on the model's mass polnts

change as the points v_brate about the steady state position. This effect

can be explained as follows.

Consider an element of mass under the influence of a centrlfugal field.

There Is a radial force acting on this mass equal to mr_ 2, where 'r' Is

the radlus from the center of rotation. If the mass Is a11owed to deflect

outward, then there will be an Increase In the centrifugal force due to the

Increase in radius;

aF , m 2 ar.

Since the Increment in force Is In the same direction as the dlsplacement

(instead of a restoring force), it Is equlvalent to a negative stiffness,

thus;

Krad_a_ : -_Fl_r = -m_ z.

It can also be shown that the same effect Is present In the tangential direction, hence;

Ktangent i al : -- IT_'_2 •

The Incluslon of these terms In the stiffness matrix is necessary to produce

accurate results. Since the new terms are proportional to the mass matrix,

just as the inertia terms are in a vibratlons problem, it is clear that their

Importance depends upon the relationship between the frequency of vibratlon

and the rotatlonal speed. The lower the frequency of vibratlon, the more important these terms are. At hlgh frequencies the Inertia terms dominate and

the negative in-plane stiffness terms are less important. This negative inplane stiffness matrix Is added to the incremental stiffness matrlx generated

by MSC/NASTRAN. It is actually added using a program modification (DMAP alter) in r|gld format 64, before the stiffness matrix Is written to magnetic

tape.

Because the stiffness matrix generated from the steady state analysls is

based on the shape of the blade after deformatlon, it was found necessary to

save the steady dlsplacements. These displacements are added to the original

gr_d point poslt_on and these 'updated' grid cards are used for the dynamic

analysis. They could also be used for an elgenvalue analysls. The updated

grid cards are checked to ver|fy that the steady state position Is near the

desired operating condOr|on (_.e. correct 8.75).

Load Distribution - With the calculated dynamlc aero loads and centers of

pressure as input, the HS/F194 code is used to distribute the loads on the

finite element model. This is done In the same manner as for the steady

loads, except that the loads are written to different NASTRAN bulk data cards

(DAREA instead of FORCE) because the loads are harmonlc.

II
Using the updated grid cards, the aero loads, and the stiffness matrix saved

on tape, the dynamic analysis is performed using rigid format 26 in

MSC/NASTRAN, Direct Frequency Response. Alternately, the Modal Frequency Response analysis could be used (Rigid Format 30). Note that DMAP alters are

required to read the stiffness matrix from tape and effectively replace

the stiffness matrix, which would not otherwise have the differential or negative In-plane stiffness effects.

Upon completion of the NASTRAN dynamic analysis the elemental stresses are

saved for postprocesslng. A computer program has been written which reads

the elemental stresses, interpolates for stress at any position and calculates strains for comparison to test. Apparent stress is calculated as the

strain in a given direction times Young's modulus. It is to be noted that

this postprocessor accounts for the straln gage thickness by increasing the

bending, but not membrane strain, to correspond to a 1ocatlon at a distance

from the neutral axls which is Increased by the gage thickness.

3.7 AeroelastIc Stall Flutter Stability Analysis

The stability of the model Prop-Fan blades was investigated using the HS/F203

stability analysis. This analysis is discussed in detail in Reference 5.

For modeling the structure, the mode shapes, frequencies and modal masses are

obtained from the results of a finite element analysis run at a particular

flow condition. The data are transformed from the finite element coordinate

system to the HS/F203 coordinate system using the HS/F214 transformation analysis. The blade Is divided into a series of discrete aerodynamic panels

with constant properties. Each panel is defined with a plunglng and pitching

motion about a reference axls along the chord specified by the mode shape

displacement definition.

The unsteady aerodynamics are derived from an analysis that was done by

Steinman, described in Reference 6. The steady state aerodynamic forces are

derived from the results of Hamilton Standard Goldstein performance analysis

HS/H444. Only steady-state lift curve slopes are used, as obtained from

HS/H444 for the particular operating condition, and are formulated uslng

strip theory. The solution is determined uslng an eigen solution, or an energy method, where an energy balance is maintained between the energy supplied by the air forces and the straln energy within the structure. The output of this analysis is in the form of response frequency and blade damping.

The onset of flutter is determined to be at the point where the damping goes

from positive to negative, passing through zero.

3.8 Operating Conditions for Analysis

Some of the operating conditions and ranges of conditions for use with the

analysis are shown in Table 3-11. Three specific cases were run for each of

the models for the response calculations, and are numbered one through nlne.

Each case includes a complete run through the flowfield analysis, the multiazimuth analysis including the induced flow calculatlons and the response analyses, finite element or beam type. Some of the independent parameters

12
listed are RPM, Mach number, and shaft horsepower. The blade angle at the

75% radius is a dependent variable and has been made to account for the variation In e]astlc deflection due to the centrifuga] and steady alrloads. This

angle Is the result of iteration to a set horsepower, because later correlations become more meaningful when comparing horsepower. This angle was also

the angle used for the finite element response calculation with the appropriate deflected shape.

Also included in this table are the operating conditions used for the stability calculations. Two blade angle settings and three RPM's were used for

each of the two swept Prop-Fans, the SR-3 and SR-5, to get the frequencies

and modes from the finite element method. A range of blade angles at 5 degree intervals was used for the SR-2 blade, since a beam analysis is used to

determine the frequencies and mode shapes for straight blades, and it requires a small amount of computer time. The modal frequencies were interpolated between the two blade angles used for the finite element runs on the

SR-3 and SR-5. The values of Math number, blade angle, and rotational speed

used In the stability analysis are given for all blades.

3.9 Analytical Results

The calculated natural frequencies resultlng from structural analyses are a

measure of how well the blade modal properties are represented. The natural

frequencies for the SR-2 model Prop-Fan were calculated using HS/H025 and

HS/H027. The results are shown in Figure 3-5. The critical speeds for the

SR-3 and SR-5 model Prop-Fan are shown in Figures 3-6 .and 3-7. The natural

frequencies for the SR-3 and SR-5 model blades were computed using the

MSC/NASTRAN code. Comparison to test results will be made in a later section.

The results of the IP vibratory response calculations are shown in Table

3-11I for the three model Prop-Fan blades, SR-2, SR-3 and SR-5. The IP airloads were calculated by either the HS/H045 code or the HS/H337 code, which

use a "Goldstein" type momentum analysls and a "Skewed Nake" analysis,

respectively. The skewed wake analysis was used for the SR-2 and SR-5. In

addition, the Goldsteln wake analysis was used for all blades. The stress

sensitivity was determined using the HS/H025 & HS/H027 beam analyses for the

SR-2 model and the MSC/NASTRAN computer code for the SR-3 and SR-5 models.

Some of the conclusions that can be observed from the calculations shown in

Table 3-1II are; stress per E.F. decreases somewhat with Mach number, stress

per E.F. increases with RPM, the important inboard bending stress per E.F.

(gage No. l) Is highest for the SR-2 and lowest for the SR-3, and stress per

E.F. increases with increasing blade angle. It is also seen that the skewed

wake analysis, used for defining the flowfield induced effects, results in

substantially higher stress than the Go]dsteln analysis.

The stability analysis HS/F203 was run using the modal Information generated

by the HS/H025, HS/H027 and MSC/NASTRAN codes, and the steady static section

lift and moment curve slopes generated by the HS/H444 performance analysis

13.
(see Figure 3-I). Figures 3-8 through 3-10 show the resulting elgen frequencles and damping ratios (damping to critical damping ratio). Sample frequencles and damping plots are shown for the SR-2, SR-3 and SR-5 models, respectlvely. The operating condlt|ons used are for 9000 RPM and 0.35 Mach number. Since the air forces on the blade can act as a spring, the response

frequencles can change with Mach number, blade angle and RPM. These curves

show small var|ations In frequency wlth blade angle. The total damping Is

more significantly affected by the air. For all Prop-Fan modes these predicted curves show that the total damping goes negative In the calculated

third mode, whlch is primarily torsional motion. Thls condition is unstable

and the point at which the damping goes through zero can be used to define

the onset of stall flutter.

Figure 3-11 consists of summary plots of blade angle vs. RPM showing the calculated stall flutter boundaries, i.e. the locus of points where the damping

goes through zero for the SR-2, SR-3 and SR-5 Prop-Fan models at varlous Mach

numbers. These curves show that the stall flutter boundaries occur at higher

blade angles wlth increasing Mach number. At zero Mach number, the higher

the sweep, the higher the blade angle at which stall flutter occurs. In general, increasing the blade sweep tends to diminish the amount of area conrained within the stall flutter boundaries.

14
4.0 TEST DATA EVALUATION AND COMPARISON WITH CALCULATIONS

This test program was conducted to study blade stressing due to stall flutter, buffet and tilted flow loading. The stall flutter data were obtained at

zero degrees shaft tilt while most of the P-order dynamlc response data were

obtained at 15° shaft tilt. The tested operating conditions are shown in

Figures 2-5 through 2-7.

4.1 Stall Flutter and Buffet

Total vibratory stress values were read from strip charts for each steady

state test condition for the six strain gage channels on each model. The

stress was determined from the charts by reading the highest amplitude of the

stress signals that occur two or more times during the data sample period.

This stress is sometimes called the "infrequently repeating peak"*. This total peak stress consists of many frequency components occurring slmultaneously on the bTade.

Stress vs. RPM - The effect of rotational speed and blade angle on the total

stress amplitude for zero forward speed conditions can be observed in Figures

4-I through 4-3. Here, total vibratory stress for the inboard bending gage

is plotted as a function of rotational speed for various reference blade angles. These are given for the SR-2, SR-3 and SR-5 models, respectively. It

is seen that the total stress increases wlth rotational speed, at a rate that

is dependent on the reference blade angle. Also, in Figures 4-2 and 4-3 for

the SR-3 and SR-5 models, the total vibratory stress increases with reference

blade angle up to a blade angle of about 50 degrees, and decreases at higher

angles. Similar trends are observed for other gages but will be shown later

in other types of plots.

The effect of Mach number on the total vibratory stress is shown in Figures

4-4 through 4-9, where the total vibratory stress is presented as a function

of rotational speed for various Mach numbers with zero shaft tilt. Again,

these curves were developed for the inboard bending gage for all the blade

models. Figures 4-4 and 4-5 are for the SR-2 at blade angles of 31.8 and

35.8 degrees, respectively. The high stresses seem to occur predominantly at

zero forward speed conditions, particularly for the higher blade angle. The

stress levels at 0.1 _ach number and above remain at about the same magnitude

for both blade angles.

Figures 4-6 and 4-7 show a slmilar stress picture for the SR-3. Here blade

angles of 36 and 50 degrees are shown, respectively. Stresses for 0.1Mach

number and above are low. Also, at zero forward speed, stresses for the 50

degree blade angle are much higher than those for the 36 degree blade angle.

*The infrequently repeating peak is defined as the maximum stress peak that

repeats itself two or three times during the stress data sample period.

This value will generally be higher than that derived from any time averaged

signal process, such as spectral analysis.

15 r
Figures 4-8 and 4-9 show stress vs. RPM for 50 and 60 degree blade angles for

the SR-5 model blades. Here also, the stress at zero Mach number is much

higher than it is at Forward speed, and the data for the two blade angles

show similar trends.

SR-2 Contour Plots - The above discussion concerns total (peak) vibratory

stresses measured by the inboard gages for each of the three model Prop-Fan

blades. A more complete study of the total stresses can be made using

contour plots of constant vibratory stress as a function of both blade angle

and RPM.

Figures 4-10 and 4-II are iso-stress contour plots for the SR-2 model operating at Mach numbers of 0.0 and 0.I, respectively. Data for four gages are

presented. These are the inboard bending, mld-blade bending, shear and tip

bending gages. These are displayed for blade number l only, since it was

Found during data reduction that all the blades showed similar behavior.

The stresses are very high for the bending gages at a blade angle of 50 degrees for all RPM's. For these gages, at zero Mach number (Figure 4-I0), the

stress contours are parabolic in shape and the stress increases with increasing blade angle and increasing RPM. However, the shear gage shows an entirely different picture. The highest stress shown occurs at 7000 RPM and 36 degrees blade angle. The stress at this point is approximately 62.1MPa (9000

psi).

In Figure 4-II, for 0.I Mach number operation, the bending gages show a similar picture as that seen for the zero forward speed data, but with lower

stresses. The shear gage, however, shows stress contours that behave more

like those for the bending gages.

Figures 4-10 and 4-11 also show the calculated stall flutter boundaries for

the SR-2, as were shown in Figure 3-11 for zero Mach number (static) and O.l

Mach number. The calculated boundary for the static condition includes the

region of high stress gradients with RPM and blade angle seen in the sheaf

gage data. There is less correlation between the calculated boundary and the

test data for the forward speed condition, although the calculation generally

follows the stress increase seen in the data.

SR-2 Spectral Analysis - Time averaged spectral analyses were conducted for

some of these SR-2 test data. Figure 4-12 shows plots of the spectral analyses for zero Mach number operation, and represents the output of the inboard

bending gage, the shear gage and the tip bending gage. These curves are for

operation at 6270 RPM and 39.5 degree blade angle. The bending gages show

predominantly high stress in the second bending mode, while the shear gage

reflects the torsion mode frequency. Note that the modes are acting independently (uncoupled), since they are at different frequencies. The predominance of the second bending mode, indicates that stall flutter is occurring in

this mode, or that possible buffeting is causing the high stresses at the

static condition. A discussion of stall flutter and buffeting is presented

later in this section.

16
Figure 4-13 showsspectral analysis plots for the 0.I Machnumbercase at

8000 RPMand zero inflow angle. Shownare the inboard bending gage, the

shear gage, and the tip bending gage, respectively. The l-P stress seemsto

dominate, which Is not explalned, except that the stresses are relatively low -

and buffeting could account for this response.

SR-3 Results - Figures 4-14 and 4-15 are total stress contours for the SR-3

• model at zero and O.l Mach number, respectively. Stress contours are shown

for inboard bending, tip bending and Shear for blade number 1. The total

stresses shown are much lower, for the SR-3 than were seen for the SR-2, indicating a beneflt of blade sweep. For zero Mach number, the shear gage shows

moderate torsion stress while the Inboard bending and tip bending gages show

high total stresses. A high stress for the Inboard bending gage occurs at

about a 50 degree blade angle above 4000 RPM. The tip bendlng gage has a

local maximum total stress at a 40 degree blade angle and 5000 RPM and another local maximum at 60 degrees and above 7000 RPM.

At a Mach number of 0.1, the high stresses occur at higher RPM's and higher

blade angles than for the static condition. Note that for the forward speed

condition, the maximum shear stresses are of the same magnitude as the bending stresses. The calculated stall flutter boundaries, for both the static

and forward speed cases, correlate well with the regions of stress rise.

This is more clearly seen in the tip gage data than the shear gage data.

Figure 4-16 shows plots of stress spectral analyses for the SR-3 model at a

blade angle of 50 degrees and 4000 RPM at zero Mach number for the inboard

bending gage, the shear gage and the tip bending gage. For the inboard gage,

a response peak occurs at the first bending mode and little else Is seen.

The shear gage shows response stresses lower than 3000 kPa (434 psi). The

tip bending gage shows substantial First mode vibratory stress with some second and fourth mode stress. The placement of the mode frequencies can be extrapolated from the calculated frequencies shown in Figure 3-6.

Spectral plots for another zero Mach number case are shown in Figure 4-17 for

the inboard bending, shear and outboard bending gages, respectively. These

plots are derlved from data taken at a blade angle of 60 degrees and 7500

RPM. Again, the inboard gage shows only first mode stressing while the shear

gages show mostly 4th mode stresses. The tip bendlng shows significant response in a11 modes up to the 5th. This is indicative of broadband aerodynamic excitation that Is a characteristic of a buffeting condition which may

occur at these high blade angles, and is probably not associated with stall

flutter.

The calculated stall flutter boundaries for the SR-3 model, as obtained from

Figure 3-II for zero Mach number and O.l Math number, respectively, are shown

in Figures 4-14 and 4-15. These boundaries are derived from third mode calculations since no stall flutter was calculated for the first and second

modes.

17
SR-5 Results - Figures 4-18 and 4-19 show total stress contours for the SR-5

model Prop-Fan at zero Mach number and O.l Mach number, respectively. Both

curves display total stress contours for the inboard bendlng gage, the shear

gage and the chordwlse bending gage. No stall flutter is apparent on the

curves from the lack of any region of steeply rising stress. Only the chordwise bending gage displays total stresses higher than 68,900 kPa (lO000 psl),

with this occurring at blade angles about 50 degrees above 8000 RPM for zero

Mach number. The SR-5 blade seems to be less susceptible to stall flutter

and buffet than either the SR-2 or SR-3 Prop-Fan model blades, agaln IndIcatIng an advantage of Increased sweep. It is noted that the stress at forward

speed is signiflcantly lower than that measured statically.

The calculated flutter boundaries for the SR-5, shown in Figures 4-18 and

4-19 show flutter occurring only at extreme operating condltlons. This Is

supportive of the' measured test data, since the SR-5 did not give stall flutter indications durlng test.

Spectral plots for the SR-5 blade inboard bending gage, the shear gage and

the chordwise bending gage are shown in Figure 4-20 for a zero Mach number

case at 9000 RPM and a reference blade angle of 40 degrees. Although the

stresses are low, all of the gages responded with many modes to an apparent

broadband excitation. This may Indlcate a buffet condition.

Flutter Summary - Operating conditions produclng blade aeroelastic instability were determined from test measurements to be those which were accompanied

by steeply rising vibratory stresses with a small change of condition. In

general, the measured stresses were seen to rise as the blade angle was increased into the stall region, usually between 30 and 45 degrees. Stress also rose with Increased RPM in this region. This type of aeroelastic instability occurred In one or two blade structural modes, which is indicative of

stall flutter.

At blade angles above 50 degrees, the blade stress response In some cases

changed in character, to a lower level of total stress made up of contributions from many blade structural modes. This behavior Is Indicative of random aerodynamic excitation, known as buffet, which occurs under deep stall

conditions.

Forward speed acts strongly to reduce blade stall and resulting stresses.

The stresses at O.l Mach number and above were considerably below the stresses for static operatlon.

The SR-3 and SR-5 swept blade models generally showed much lower stress levels than the unswept SR-2 blade model. The straight SR-2 model gave robust

flutter indications, while the highly swept SR-5 model gave only weak buffet

indications during test. Increased blade sweep increases the operating region free of high stress rises. Stall flutter for the SR-2 and SR-3 models

occurred in some bendlng modes as well as torsional modes. Responses for the

SR-5 model occurred in many modes, indicating buffet excitatlon.

18
Calculated predictions agreed well with the regions of high stress rise observed during test at zero Machnumber. At forward speed conditions agreement was not as good. Flutter was predicted to be in torsional modesfor all

the blade models, while high stresses were displayed in the bending modesas

well. These results are similar to those found for the zero forward speed

testing of the Prop-Fan models reported in Reference ?.

4.2 Modal Response Frequencies

As previously discussed In Section 4.1, the spectral analyses of time averaged data were taken from many steady state test runs of the SR-2 and SR-5,

and all the test runs of the SR-3 blade model. All of these data were saved

on tape. Methods were developed to pick off the stress peaks and to store

their amplitude values and frequencies. One important use for these data is

the creation of Campbell diagrams, also known as crltical speed plots. Experlmental critlcal speed diagrams are shown in Figures 4-21 through 4-23 for

the SR-2, SR-3 and SR-5 model Prop-Fan configurations. Also shown on these

figures are the calculated blade natural frequencies, discussed earlier.

For the SR-2 model there is good correlation between test data and calculations for the first, third and fourth modes. Some anomalies are noted for

the correlations with the other calculated frequencies. The second calculated mode is flanked by two curves of experlmental data. There is also another

experimental curve just above the third mode but below the fourth. No explanation is offered for thls behavior.

The Campbell dlagram In Figure 4-22 for the SR-3 model shows that there is

excellent correlation between test data and calculations for the first, second and thlrd modes. Agaln, there occurs an experimental mode which doesn't

correlate with calculations and lles between the second and thlrd calculated

modes. This mode is comprised of lower level stresses, so it won't slgniflcantly affect Prop-Fan operation. It is not known whether this is an extra

mode, not predicted by the calculation method, or if the third and fourth

mode frequencles Tare calculated too high.

It should be noted that the SR-3 frequency calculations were done using a

blade angle of 55 degrees (measured at the ?5% radlal station). Two sets of

data from the tests are shown, one for a reference blade angle of 32 degrees

and the other for a reference blade angle of 50 degrees. The data show little difference between the 32 degree and the 50 degree reference blade angles, even though these tests cover different but overlapping RPM ranges.

Thls is probably due to the fact that the blade is operating in stall for

both angles such that there is 1|ttle change in aerodynamic 1oadlng. Also,

in structural terms, centrlfugal restoring moments In torslon (dumbell effects) generally show little change for variations |n blade angle near 45 degrees. It is concluded that data for the 32 degree reference blade angle can

be safely compared to the calculated frequencies at a 55 degree blade angle.

This reasoning Is also used to justify slmilar comparisons for the SR-2 and

SR-5 models, as shown in Figures 4-21 and 4-23.

19
The Campbell diagram showing the SR-5 model tested and calculated vibration

frequencies is given In Figure 4-23. The curves for the SR-5 are slmilar to

those of the SR-3. The first and second experlmental modescorrelate very

well with predictions. However, discrepancies are again seen In the higher

modes. The third through the fifth experimental modesare significantly lower in frequency than the calculated modes.

Summary- Comparisonof measuredand predicted frequencies on the Campbell

diagrams for the SR-2, SR-3 and SR-5 models can be summarized as follows.

Generally, the lower mode frequencies were well predicted by the theoretical

methodology. Thls is important since good frequency correlation is a necessary indicator of the validity of the structural model. Also, most of the

responses observed in test occurred at the lower mode frequencies. Differences between test and theory appear for the higher modes, with these differences appearing to be exaggerated by increased blade sweep. The reasons for

this may be that It Is more difficult to analytically describe the blade

structure to account for sweep. The swept blades may require a finer grid

for the finite element analysis, In order to adequately calculate the response at the higher modes.

4.3 Angular Flow Dynamic Response

Total Stress Measurements L Stress measurements were made for all the model

blades during wind tunnel tests with the Prop-Fan operating with its drlve

shaft tilted relative to the tunnel centerline, to provide angular In-flow to

the rotor. The results are plotted in Figures 4-24 through 4-26 for the

SR-2, SR-3 and the SR-5 model blades, respectively. Here the total stress

per excitation factor is plotted as a function of rotatlonal speed for various blade angles. A separate plot is shown for each Mach number tested.

All these curves are shown for a tilt angle of _ : 15 degrees.

Excitation Factor (E.F.) is a term that Is proportional to Prop-Fan tilt angle and dynamic pressure. It is defined in Sectlon 3.1. E.F. Is a useful

concept for the study of blade stresses because of its linear dependence on

tilt angle. For a uniform, steady inflow to a rotor, theoretically there Is

no aerodynamic excitation to induce a forced response of the blades. If the

rotor shaft is tilted at some angle to this uniform flow, a slnusoidal variation in velocity at the blade wlll occur with a frequency of IP. This will

induce a IP response of the blade that is some function of the mean flow velocity and density (dynamic pressure) and the tilt angle.

A typical spectrum of the inboard bending gage signal, for a tilt angle test

run of the SR-2 model, is shown in Figure 4-27. It is seen from this curve

that the IP r_sponse Is the major contributor to the total stress. The 2P

and other higher order responses may be due to dynamic response magnificatlon

of structural modes by residual higher order aerodynamic excitation from the

nacelle or pylon. Also, resldua] turbulence in the tunnel flow could excite

higher blade modes. Note that this 6000 RPM condition is well above the

2P/Ist mode critlcal speed of about 4500 RPM. Away from critical speeds, the

iota] stress is made up of mostly a IP stress contribution.

20
The varlatlon of total stress with tilt angle Is examlned in Figure 4-28.

These SR-2 test data were taken at 3000 RPM, well below the 2P crossover.

This curve confirms that blade stress Is a linear Function of tilt angle, and

therefore E.F., For constant Flight speed. The stress does not go to zero at -

zero tilt angle, again possibly due to residual tunnel turbulence. There may

also be a small angular error in the physical rotor shaft allgnment to the

tunnel Flow.

For most operation conditlons of interest, that is, away from crltical

speeds, It Is demonstrated that normallzlng blade stress by E,F. is a valid

way to account For the effects of tilt angle and dynamic pressure. In Fact,

thls concept has been in use For many years. Another demonstration of thls

concept for high speed Prop-Fan test data Is given in Reference 8. Note that

stress divided by E.F. is sometlmes known as "stress sensitivity", and these

terms are used interchangably.

The total inboard bending stress per E.F. for the SR-2 Prop-Fan blade Is

shown in Figure 4-24. Stress per E.F. increases with Increasing rotatlonal

speed and blade angle while decreasing wlth Math number. The stress per E.F.

Increases. with blade angle and rotatlonal speed because the blade loading also increases with blade angle and rotational speed. Conversely, the stress

per E.F. decreases with Mach number because the Ioading decreases with Increaslng Mach number For constant blade angle and rotational speed. This

latter effect is due to the reduced section angle of attack accompanying the

Increaslng advance ratio.

Note the flrst curve In Figure 4-24 which shows SR-2 stress sensitivity at

O.l Mach number. Here, the stress/E.F, rises rapidly with RPM and has strong

peaks near 4500 RPM with some smaller peaks near 2500 RPM. From Figure 4-21

we can surmise that these are the 2P and 3P first mode critical speeds. At

the higher Mach numbers, the Prop-Fan windmill RPM is above the 2P crossover

speed. Therefore, data are not available at low speeds. However, the 0.1

and 0.2 Mach number conditions show roughly the same magnitude of additional

stress sensltlv_ty due to the 2P crossover, and it can be assumed that this

behavior can be extrapolated to higher Mach number conditions.

Similar results to those found For the SR-2 model are seen for the SR-3 and

SR-5 in Figures 4-25 and 4-26, respectlvely. Stress sensitlvity Increases

with RPM and blade angle, while decreasing with Mach number. In general, it

is observed that stress sensitivity is reduced as the blade sweep is Increased, with the highest levels seen for the SR-2 and the lowest levels seen

for the SR-5 model. This confirms an advantage of blade sweep In reducing

the dynamic structural response to non-uniform inflow.

The high stress sensitivity peaks due to critical speed response are also

seen for the SR-3 and SR-5 models In Figures 4-25 and 4-26. For both models

the stress peaks are due to 2P/first mode critical speed crossovers. Unlike

the SR-2, however, the magnitude of the additional stress sensitivity for the

SR-3 and SR-5 decreases somewhat with Increasing Mach number. Also, the 2P

response follows the trend of decreasing with Increasing blade sweep. This

indicates that blade sweep is beneficial In reduclng Inflow induced critical

speed response, as well as IP response.

21
IP Stress Measurements Comparison to Predictions - Spectral analyses for all

models were made for a limited number of test cases of the SR-2 and SR-5 models. Spectral analyses were made for all of the SR-3 steady state runs. The

magnitude of the IP vibratory stresses were read from the spectral data,

stored by computer and prlnted in tables. A typical spectrum is shown in

Figure 4-27. The tables will not be presented, but the data are summarized

in Figures 4-29, 4-30 and 4-31, where IP vibratory stress per excitation factor Is p|otted as a function of shaft power, for the SR-2, SR-3, and SR-5,

respectively.

The measured inboard bending stress sensitivity as a function of absorbed

rotor power for the SR-2 Is shown in Figure 4-29 as dashed lines for 6000.RPM

and 8000 RPM. As seen from the data in this figure, stress sensltivity

increases with higher power (higher blade loading) for constant RPM. Also,

the curve for 6000 RPM is higher than the curve for 8000 RPM. Some

calculated points are shown for the skewed wake and Goldsteln calculations as

obtalned from Table 3-111. For 8000 RPM the two calculations bracket the

test data such that the skewed wake results are If% higher than the test data

and the Goldstein calculation results are about I0% lower than the test

data. For the 6000 RPM case.the skewed wake case coincides with the test

data while the Goldsteln calculation Is 16% lower.

Calculations at 8000 RPM only are available for the SR-3, as shown in Figure

4-30. Here the slope of the test data is greater than the slope of the calculations but the magnitudes fall between those for the skewed wake calculations and the Goldstein caIculatlons. The skewed wake is 9% above the test

curve at ll2 kilowatts, and the Goldstein calculation is 22% below the test

curve at 298 kilowatts.

The SR-5 results are similar to those for the SR-3, as seen in Figure 4-31.

At 6000 RPM the Goldstein calculations are 15% lower than the test data. At

8000 RPM the skewed wake calculation is 15% higher than the test results and

the Gol.dsteln calculation is I0% below the test results.

It should be pointed out here that the accuracies quoted for the above correlations are based on measurements of moderate stresses. All of the SR-3 and

SR-5 stresses discussed above are under 25 MPa, or about 3,500 psi. The SR-2

stresses are below 50 MPa (~ 7000 psi). If the increment between the calculated and tested stress were to remain constant, then at high stress the

percentage differences would be smaller, Still, the above correlations indicate that the skewed wake and Goldsteln calculations may be confidently used

to provide estimates of the upper and lower bounds For IP stress.

IP Data Trends - The relative stress levels between the three model configurations are shown in Figure 4-32, where stress sensitivity is plotted as a

function of blade angle at 8000 RPM and 0.28 Mach number. It is seen that

the SR-2 has the highest sensitivity and the SR-5 has the lowest, clearly indicating an advantage of increased blade sweep.

22
A series of curves shownin Figure 4-33 show IP vibratory stress sensltivity

plotted as a function of Machnumberfor various rotational speeds for the

SR-3model Prop-Fan blades. The data cover a range of reference blade angles

from 24 to 40 degrees. Thesedata are shownfor the inboard bending gage.

It is seen that the vibratory stress sensitivlty Increases with blade angle

and RPM,but decreases with increasing Machnumberfor constant blade angle.

It should be noted that at constant blade angle, the power also decreases

with increasing Machnumber. Therefore, these curves do not show the varlatlon with constant power.

An attempt was made to study the effect of power variation through the use of

the propeller power coefficient. The power coefficient, defined below, is a

non-dimenslonal function of the dynamic pressure due to rotational speed at

the blade tip, and diameter cubed. Everything else being constant, the power

the rotor absorbs is proportional to the tip dynamic pressure and diameter

cubed. Power coefficlent is defined as Cp , 2_Q/pn_D s

where p - air density in slugs/ft 3 Q = rotor torque in ft-lbs

n : rotational speed in revolutions/sec and D , the rotor diameter. Use of

the power coefficient normalizes the effect of size and RPM in the data.

Figure 4-34 shows the result of cross plotting the plots of IP stress sensitivity vs. power coefficient for Mach numbers up to 0.35 and rotationa]

speeds up to 9000 RPM. The resulting curves Indicate the independence of IP

stress sensltivity from Mach number and rotational speed effects. For blades

of similar constructlon, this family of curves can be useful as a design tool

in scaling Prop-Fan blades. Also, they suggest a limit on the power coefficlent allowed for each blade angle, to permit safe operation. The fact that

these curves are independent of Math number indicates that for IP response,

aerodynamic compressibility effects are negligible, at least for the relatively low flight Math numbers considered here. It Is not understood why

there Is a sharp bend in each of these curves.

4.4 Reverse Thrust

One of the operations that a propeller must endure is the reverse thrust condition. Reverse thrust is used on alrcraft generally during landing to

shorten the ground roll, allowing for more efficient ground operations. The

Prop-Fan models were subjected to llmited testlng in this regime, over a

range of operating variables previously discussed. None of the results For

the SR-2 model wlll be discussed, since in the reverse thrust mode no high

stresses were observed, except For some moderate stressing at the first mode

critlcal speed.

Flgure 4-35 shows total vibratory stress For the SR-3 model plotted as a

function of Mach number for various settings of reference blade angle. These

curves are shown for blade number 5 shear gage data. The highest total vibratory stress shown occurs at a reference blade angle of -4.0 degrees, zero

Mach number and 9000 RPM. The next highest stress occurs at a blade angle of

-2.0 degrees for 8000 RPM. Spectral plots are shown In Figure 4-36 for this

case, for the three gages on blade number I. It Is seen that the response,

23
which Is higher in level than that for blade 5, is at the third modenatural

frequency, which is very close to the 5P critical speed. However, it was

observed from oscillograph data at -4 degrees blade angle and 9000 RPM,that

the high stress occurs at a frequency of 675 Hz and not at a P-order. For

someof the high stress points, strip chart data show the stress amplitude

Increasing with time at steady state operating conditions. The indications

are that thls unstable phenomenon is flutter, since the stress amplitude is

divergent and the mode Is coupled with large torsion and bending responses.

SR-5 data are shown In Figures 4-37 and 4-38. Total vibratory stress is

plotted against Mach number for a blade angle of 4.2 degrees and 9000 RPM,

for blade number 6 and blade number l, respectively. Negative blade angle

settings were not possible, due to mechanical interference between the ten

blades, so small positive angles were set for reverse thrust testing. The

data indicate that high stress occurs at zero Mach number and at 0.2 Mach

number. The highest stress for blade ] occurs at Mach= 0.2, and the highest

stress for blade 6 occurs at Mach'zero. The cause of the* differing response

for the two blades is not understood.

Figures 4-39 and 4-40 are spectral plots of SR-5 blade stress at the zero

Mach number and 0.2 Math number conditions, respectively, for a 4.2 degree

reference blade angle at about 8900 RPM. At zero Mach number, the response

is in the second mode and is close to the 2P line (see Figure 4-23). Some of

the high stress may be due to magnification caused by the nearness of the response frequency to the critical speed crossover. At the 0.2 Mach number

condition, the response is in the first mode with other response peaks observed at exactly twice and three times the flrst mode frequency. The greatest response is seen at the shear and chordwise bending gages with significantly high stresses.

This phenomenon may be explained by observing the time history waveforms of

the strain gage signals for this condition. These are shown in the oscillograph records given in Figure 4-41. Generally, flutter responses are sinusoidal, but these are not. It is speculated that this non-sinusoidal behavior is due to the fact that the steady loads on the blade are negative (net

loading on camber side) and may be buckling (oii canning) the blade. If the

vibratory loads push the blade into a buckling conditlon on every cycle, the

waveforms shown in Figure 4-41 could be obtained. The time history traces

shown could produce the Fourier components of 2X and 3X the fundamental frequency, as seen in Figure 4-40. The buckling of the blade is similar to the

bending of a flexible steel carpenter's measuring tape except that the blade

is stabilized by centrifugal loads. It is not known if this possible buckllng Is a result of the flutter, or if this cause-effect relationship is reversed.

24
S.O CONCLUSIONS

As a result of the test and analysis program summarized In thls report,

the following conclusions were obtained regarding the low speed stability -

(stall flutter), angular flow dynamlc response, and reverse thrust response of the SR-2 stralght blade, the SR-3 moderately swept blade and

the SR-5 hlghly swept blade Prop-Fan models:

l ° Blades with increased sweep respond with lower stresses to stall

flutter and buffet.

. Forward speed acts strongly .to reduce blade stall and hence stall

flutter stresses. The blade stresses at O.l Mach number were reduced considerably below the stresses for static operation.

, Comparisons were made between tested stall flutter boundaries, based

on steeply rising stresses with increasing RPM and blade angle, with

calculated boundaries based on zero blade damplng. Good agreement

between test and prediction wa_ indicated for the SR-2 and SR-3 models, with less agreement for the SR-5 model, which did not give

strong flutter indications durlng test.

° Stall flutter was predicted to occur in a torslonal mode for all of

the blade models. During testing, stall flutter was observed for

the SR-2 In torsion, as predicted, whlle for the SR-3 stall flutter

was observed primarily in bending modes.

° During reverse thrust operation, the SR-2 model encountered no high

stresses, while high stresses were observed for the SR-3 and SR-5

models at some operating conditions. The SR-5 data gave evidence

that the high observed stresses were due to flutter.

, Correlation between tested and predicted Campbell diagram modal frequencies was excellent for the Important lower modes, for all the

blade models. Differences between test and theory appear for the

higher modes, with these differences Increasing wlth blade sweep.

, Measured blade stress increased linearly with rotor axis tilt angle. The angular flow stress response, except near critical speeds,

consisted almost entirely of the IP stress contribution.

. Stress sensitivity (stress divided by E.F.) increased with increasing blade angle and RPM at all Mach numbers tested, and decreased

with increasing Mach number.

. Increased blade sweep slgnlficantly reduced both angular inflow (IP)

and critical speed stress responses.

25
10.

II.

Stress sensitlvity vs. power coefficient was found to be |ndependent

of Mach number and RPM, for fixed blade angle, at the low Mach

number condltions examlned. Stress sensitivity was strongly

dependent on power coefficient at low blade angles, and only weakly

dependent on power coefficient at hlgh blade angles.

For Math numbers up to 0.35, the theoretically based IP stress sensltlv|ty calculations agreed very well with measured values. The

skewed wake analysis and the Goldsteln analysis may be confidently

used to provide estimates of the upper and lower bounds for IP

stress, respectively.

26
6.0 RECOMMENDATIONS

I. Stall Flutter

The results from this test program Indicate that stall flutter is

not a problem for the swept blades. However, the model blade designs are of solid metal construction and are considered very

stiff. It is not known how full scale composite blades with lower

relative stlffnesses will behave. Thus, the following recommendations are offered regarding improvement of the stall flutter prediction methods.

a. Non-linear theoretical methods should be developed to predict

blade stress and limit amplitude, rather than the linear methods used which estimate stall flutter onset boundaries based

on damping. It is thought that stall flutter can exist at very

low limit amplitudes and stresses. Therefore, it would be more

useful to compare calculated stresses to measured stresses.

b, Develop and Improve emplrIcal prediction methods and acqulre

Improved test data for unsteady airflow effects. Perform oscillatlng NASA 16 series airfoil tests in a wind tunnel to

study their stalling characteristics. Buffeting as well as

stall flutter conditions should be included in this test program.

C. Continue current unsteady airflow theoretical research into

stall flutter. Extend the effort to include buffeting.

d. Correlate new analyses with existing tests, not necessarily restricted to Prop-Fan tests.

e. Measure rotating blade unsteady pressure distributions in

stalled regions.

2. Angular Flow Response

Efforts should be made to improve the accuracy of the IP response

prediction methods. This should include study of the effects of

varying the induction calculation method, In addition to other aspects of the aerodynamic analysis.

3. Reverse Thrust

Attempts should be made to determine the cause of the reverse thrust

high stresses observed for the swept blades. The initial effort

should include a wind tunnel flow visualization test to determine

the nature of the flow field behavior. This will provide guidance

for future theoretical/empirical analysis studies.

27,/28

7.0 REFERENCES

o Alello, Robert A.; "NASA Lewis lO-by-lO foot Supersonlc Wind Tunnel", NASA TM X-71625, Nov. 1974.

, Goldsteln, S.; "On the Vortex Theory of Screw Propellers", Proceeding of the Royal Soclety of Aviation, Vol. 123, 1929.

. Egolf, T. A. and Landgrebe, H.A.; "A Prescribed Wake Rotor Inflow

and Flowfleld Prediction Analysls - User Manual and Technical Approach", NASA CR-165894, June, 1982.

. MacNeal, R. H.; "The Nastran Theoretlcal Manual" (Level 15.5),

MacNeal - Schwendler Corp., December 1972.

S° Turnberg, J.; "Classical Flutter Stability of Swept Propellers",

Report No. 83-0847 CP, AIAA/ASME/ASCE/AHS 24th Structures, Structural Dynamics and Materials Conference. May 2-4, 1983/Lake Tahoe,

Nevada.

. Stelnman, D. B.; "Aerodynamic Theory of Bridge Osc111ations",

American Society of Civil Engineers, Transactions, Paper No. 2420,

October, 1949.

° Smith, A.F.; "Analysis and Test Evaluatlon of the Dynamlc Stability

of Three Advanced Turboprop Models at Zero Forward Speed", NASA

CR-175025, December 1985.

. Bansal, P., Arseneaux, P., Smith, A., Turnberg, J. and Brooks, B.;

"Analysis and Test Evaluation of the Dynamic Response and Stability

of Three Advanced Turboprop Models", NASA CR-174814, August 1985.

29/30

TABLE 2-1. PROP-FAN MODEL SUMMARY

NO. BLADES

MATERIAL

DIAMETER

3/4 CHORD

AIRFOIL (NACA)

DESIGN C L

A F (TOTAL}

A F (PER BLADE)

SR-2

8

STEEL

24.5 IN

3.57 IN

16 SERIES

0.084

1632

204

SR-3

8

TITANIUM

24,5 IN

4.53 IN

16 SERIES

0.214

1880

235

SR-5

10

TITANIUM

24.5 IN

4.10 IN

16 SERIES

0.271

2100

210

31
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3_
TABLE 2-111. VARIATION OF TEST PARAMETERS FOR THE

NASA-LeRC MODEL PROP-FAN TESTS IN 10 X 10 WIND TUNNEL

MODEL

SR-2

SR-3

SR-5

MACH NO.

(ALL MODELS)

RPM

(ALL MODELS}

TILT ANGLE

(ALL MODELS}

REF. BLADE ANGLE (DEG.)"

-14.5 -13.5 -12 -8 -4 12 16 20

24 28 32 36 40 50 60 70

80

-8 -6 -4 -2 0 12 16 20

24 28 32 36 40 50 60 70

80

4.2 5.5 6.0 8.2 12 16 20

24 28 32 36 40 50 60

80

0.0 0.1 0.2 0.28 0.35

2000 TO 9000 RPM, 500 RPM INCREMENTS

0.0 DEG. AND 15.0 DEG.

(AND OTHER SELECTED TILT ANGLES)

70

"REFERENCE BLADE ANGLE(/_REF) TO BLADE ANGLE AT

3/4 RADIUS STATION (#3/4) CONVERSION

/3REF = _3/4 - 0.8 (FOR SR-2 AND SR-3)

/3RE F = /33/4 + 0.5 (FOR SR-5)

33
TABLE 3-1. HAMILTON STANDARD COMPUTER PROGRAMS

DESIGNATION PURPOSE

MSC NASTRAN Finite element analysis used to predict vibratory mode

shapes and frequencies for swept, thin structures.

H025 Beam type analysis used to predict vibratory bending mode

shapes and frequencies.

H026 Beam type analysis used to predict 1-P vibratory response.

H027 Beam type analysis used to predict vibratory torsional mode

shapes and frequencies.

H039 Three-dimensional potential flow field analysis used to

determine the influence of the nacelle on rotor inflow.

H045 Goldstein analysis with azimuthal variations (see H444).

H337 Skewed wake blade aerodynamic loads lifting line analysis,

with vortex wake representation and azimuthal variations.

H444 General Goldstein-type performance strip analysis for

Prop-Fans. Provides power, thrust, section force data and

angles of attack. Section lift and moment slopes are

determined for use in the stall flutter analysis, F203.

F194 Distributes steady or unsteady airloads to finite element

nodes for use in MSC NASTRAN.

F203 Eigen-solution modal stability analysis. Calculates

damping and frequency using unsteady aerodynamics.

F214 Transposes all coordinate system motions into the blade

section coordinate system, in order to take advantage of

small angle assumptions for stability analysis.

tIODES Converts mode shapes from finite element or beam analyses

to form used by the F203 stability analysis.

34
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36
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FIGURE 2-1

\

9.6 IN.

8.9 IN

SR-Z SR-3 SR-5

SR-2, SR-3, AND SR-5 PROP-FAN MODEL BLADES PLANFORM AND GAGE

LOCATION-CAMBER SIDE

37
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38
ORIGINAL F>.,':,= |S

OF POOR QUALITY

FIGURE 2-3. INSTALLATION OF THE SR-3 MODEL PROP-FAN

IN THE NASA LEWIS SUPERSONIC WIND TUNNEL

39
:::.........

FIGURE 2-4. CUTAWAY VIEW OF THE PROPELLER TEST RIG

, 40
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SR3(MSC/NASTRAN)

DIA _--0.622 METERS

SR5 (MSC/NASTRAN)

DIA = 0.622 METERS

CQUAD4

ELEMENTS

CTRIA3

ELEMENTS

THIS MODEL

IS BASED ON THE

PRETWISTED

BESTRAN MODEL

FIGURE 3-2, PROP-FAN ANALYTICAL MODELS USED FOR 1P RESPONSE

PR ED ICT IONS

45
START

STEADY AERO LOADS, / 1 /1P AERO LOADS /

CENTERS OF PRESSURE, / T /AND CENTERS OF /

l. /AND DESIRED OPERATING / L /H045 CODE (SEE /

/BLADE ANGLE FROM HSI /

/H045 CODE (SEE FIG 3-13/ /FIG 3-1) /

DISTRIBUTE LOADS ON

FINITE ELEMENT NODES

• ,, _,

/AND DISPLACEMENTS /

/TO ORIGINAL NODAL //

/POSITIONS /

OUTPUT INCREMENTAL/

AND NEGATIVE IN- /

PLANE STIFFNESS /i

TO MAGNETIC TAPE /--I

FIGURE 3-3.

ESTIMATE BLADE UNTWIST

AT SPEED FROM

PREVIOUS EXPERIENCE

NONLINEAR STATIC ANALYSIS

{RIGID FORMAT 64 MSC/NASTRAN)

1) APPLY STEADY AIR LOADS

2) APPLY CENTRIFUGAL LOADS

BASED WITH A BLADE ANGLE

SET TO UNTWIST TO DESIRED

OPERATING BLADE ANGLE

LINEAR DYNAMIC ANALYSIS

{RIGID FORMAT 26 MSC/NASTRAN)

1) USE STIFFNESS FROM TAPE

2) USE UPDATED GRID CARDS

3) USE 1P AERO LOADS FROM HS/F194

POSTPROCESS STRESSES TO I

OBTAIN STRAINS AND APPARENT

STRESSES AT THE GAGE LOCATIONS J

USE HS/F194 CODE

TO DISTRIBUTE

LOADS ON FINITE

ELEMENT NODES

PROP-FAN MODEL BLADE ANALYSIS-1P DYNAMIC

ANALYSIS USING MSC/NASTRAN

46.
0,8 /

O.Z ,

o

o o.i 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.o

NORMALIZED BLADE CHORD, N

TYPICAL CHORDWISE IP LOAD DISTRIBUTION BASED ON THE ANALYTICAL FUNCTION

PN =' A(Nc)B (!-(Nc)'25)2 WHERE N C IS THE NORMALIZED BLADE CHORD AND A AND B ARE

CHOSEN TO GIVE THE CALCULATED TOTAL LOAD AND TO MATCH THE CALCULATED

CENTER OF PRESSURE.

FIGURE 3-4. SR-3 AND SR-5 MODEL PROP-FAN IP ANALYSES

4T
FREQUENCY (HZ)

1,000 m

800 m

600

400

200

10P 9P 8P 7P

4TH MOOE

6P

5P

3RD MODE 4P

2NO MOOE

3P

1ST MODE

1P

0

0 2,000

FIGURE 3-5.

I I

4,000 6,000 8,000

RPM

SR-2 PROP-FAN MOOEL BLADE

HO25 & HO27 RESULTS

BLADE ANGLE = 55 °

I

10,000

48
FREQUENCY (HZ)

1,000

800

600

400

200

0

0 2,000

FIGURE 3-6.

lOP 9P 8P 7P

/

MODE

:ID MODE

2ND MODE

1ST MODE

6P

5P

4P

3P

2P

1P

I I I I

4,000 6,000 8,000 10,000

RPM

SR-3 PROP-FAN MODEL BLADE

MSC/NASTRAN RESULTS

BLADE ANGLE -- 55 °

49
FREQUENCY (HZ)

1,000 m

800 M

600 m

400

200

lOP 9P 8P 7P

6P

5TH MOOE

4TH MOOE

3RD MODE

5P

4P

2ND MODE 2P

IP

0

0 2,000

FIGURE 3-7.

I

4,000 6,000 8,000

RPM

SR-5 PROP-FAN MODEL BLADE

MSC/NASTRAN RESULTS

BLADE ANGLE = 55 °

I

10,000

50
MACH=0.35

FOURTH MODE

THIRD MODE

ii f l

SECOND MODE

9000 RPM

FREQUENCY RZ

I000

i

800

I

600 --

i

400

F'fRST MODE

Z00 m

o I

-20 0

I I I

20 40 60

_75 " BLADE ANGLE- DEG

J

80

DAMPING RATIO % OF CRITICAL/100

0.08

FIRST MODE

0.04

0.02 SECOND MODE

THIRD MODE

FOURTH MODE

FIGURE 3-8. CALCULATED BLADE FREQUENCIES AND DAMPING RATIO'S FOR THE

SR-2 PROP-FAN MODEL USING THE F203 ANALYSIS

51 ""
1000

800

600

FREQUENCY HZ

400

200

0

-20

9000 RPM MACH = 0.35

FOURTH MODE

i |

SECOND MODE

FIRST MODE

! I ! I

0 20 40 60

_75"BLADE ANGLE- DEG

I

80

0.10

0,08

0.06

DAMPING RATIO %

OF CRITICAL/I O0

0.04

0.02 n

o

-0.0Z

-20

__R_D MOD E

0 20 40 60

_75-BLADE ANGLE- DEG

I

8O

FIGURE 3-9. CALCULATED BLADE FREQUENCIES AND DAMPING RATIOS

FOR THE SR-3 PROP-FAN MODEL USING THE F203 ANALYSIS
FREQUENCY HZ

800

600 m

400

2OO --

0

--20

9000 RPM MACH:0.35

FOURTH MODE

w N i •

THIRD MODE_

SECOND MODE

FIRST MODE

I

I I I

Z0 40 60

_75"BLADE ANGLE-DEG

I

80

DAMPING RATIO % OF CRITICAL/100

0.10 m

FIRST MODE

0.08

0.06

0,04

0.0Z

0

-O.OZ

-20

SECOND MODE

THIRD MODE

FOURTH MODE

i

0 Z0 40

75" BLADE ANGLE- D£G

l I

60 80

FIGURE 3-10. CALCULATED BLADE FREQUENCIES AND DAMPING RATIO'S FOR THE

SR-5 PROP-FAN MODEL USING THE F203 ANALYSIS

53
d _" Z<

?

n,

u1

ow

rmw

.IZ<w0

all

0

w

zu<

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w0w

.i0Z<w

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!i!i!i_

:::::::

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....:

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0

000

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00

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old

0:3

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n,OIw

L_

b.

_4
TOTAL VIBRATION STRESS ±kPa

200,000 _ BLADE ANGLE, DEG

180,000

160,000

140,000

120,000

100,000

80,000

60,000

40,000

20,000

0

I

MACH NO. -- 0.0 I

I

ZERO SHAFT TILT

INBOARD BENDING BGI-1

1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000

ROTATIONAL SPEED, RPM

FIGURE 4-1. SR-2 MODEL BLADE 10 X 10 LOW SPEED

WIND TUNNEL TESTS AT NASA LEWIS

55
TOTAL VIBRATORY STRESS +kPa

140,000 --I_'EF BLADE ANGLE, DEG

120,000

100,000

80,000

60,000

40,000

--!1- 28

•"0- 32

36

.qr,.. 40

-"X'- 5O

m

20,000

0

MACH NO.= 0.0

ZERO SHAFT TILT

INBOARD BENDING BGI-1

1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000

ROTATIONAL SPEED, RPM

FIGURE 4-2. SR-3 MODEL BLADE 10 X10 LOW SPEED WIND TUNNEL

TESTS AT NASA LEWIS

.56
TOTAL VIBRATORY STRESS +kPa

80,000 "_'EF BLADE ANGLE, DEG

-I1- 60.0

'4- 70.0

-.&-- 80.0

60,000

MACH NO. : O.0

ZERO SHAFT TILT

INBOARD BENDING BG 1-1

40,000

20,000

0

1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000

ROTATIONAL SPEED, RPM

FIGURE 4-2. (CONTINUED)

9,000 10,000

5'7
TOTALVIBRATORYSTRESS+kPa

140,000 "-I_'EFBLADE ANGLE, DEG

120,000

100,000

80,000

60,000

40,000

20,000

0

-e" 32.0

-'JIk- 36.0

B _ 40.0

--'X-- 50.0 MACH NO. = 0.0

ZERO SHAFT TILT

INBOARD BENDING BGI-1

.... i , ii ,

1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000

ROTATIONAL SPEED, RPM

FIGURE4-3. SR-5 MODEL BLADE 10X 10 LOW SPEED WIND TUNNEL

TESTS AT NASA LEWIS

.58
TOTALVIBRATORYSTRESS-I'kPa

80,000 "I_'EF BLADE ANGLE, DEG

60,000

40,000

20,000

0

-II- 60.0

•-0- 70.0

• _ BO.0

MACH NO. - 0.0 DEG

ZERO SHAFT TILT

INBOARD BENDING BGI-1

I I I I I I I I I I

1,000 2,000 3,000 4,000 5,000 6,000 "/',000 8,000 9,000 10,OOO

ROTATIONAL SPEED, RPM

FIGURE 4-3, (CONTINUED)

59
TOTAL

VIBRATORY

ST R ESS

± kPa

60000 --

40000 --

20000 --

o I

1000

MACH NO.

x.... x 0.o

"_" 0.1

®-.--® 0.z

--_l 0,28

0.38

BLADE ANGLE = 31.8 DEG ]

ZER0 SHAFT TiLT

INBOARD BENDING BGI-I

I [ I I 1 l 1 I

ZO00 3000 4000 SO00 6000 7000 0000 9000

ROTATIONAL SPEED, RPM

FIGURE 4-4. SR-2 MODEL BLADE 10 X 10 LOW SPEED

WIND TUNNEL TESTS AT NASA LEWIS

6O
TOTAL VIBRATORY STRESS :l:kPa

BLADE ANGLE = 35.5 DEG I

i

ZERO SHAFT TILT I

INBOARD BENDING BG.I-1. ,, I

100,O00

80,000

60,000

40,000

20,000

0

MACH NO.

0.0

0,2"

I I I I I I I I L I

1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,OOO

ROTATIONAL SPEED, RPM

FIGURE4-5. SR-2 MODEL BLADE 10X 10 LOW SPEED WIND TUNNEL

TESTS AT NASA LEWIS

6I
TOTALVIBRATORYSTRESS::l:kPa

100,0OO m MACH NO.

--m- 0.O

--0- 0.10

m '-'_-- 0.20

80,0OO _ 0.28

--)(-- 0.36

60,000

40,000

BLADE ANGLE = 36 DEG

ZERO SHAFT TILT

INBOARD BENDING BG 1-1

20,000

1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000

ROTATIONAL SPEED, RPM

FIGURE 4-6. SR-3 MODEL BLADE 10 X 10 LOW SPEED WIND

TUNNEL TESTS AT NASA LEWIS

62
TOTAL VIBRATORY STRESS :l:kPa

100,000

--"X"- 0.0 BLADE ANGLE = 50 DEG

0.1 ZERO SHAFT TILT

- INBOARD BENDING BGI-1

60,0O0

40,000

20,0OO

0

0 2,000 4,000 6,000 8,000 10,000

ROTATIONAL SPEED, RPM

FIGURE 4-7. SR-3 MODEL BLADE 10X 10 LOW SPEED WIND TUNNEL

TESTS AT NASA LEWIS

63
TOTAL VIBRATORY STRESS "l'kPa

80,000 "_LADE ANGLE = 50 DEG

60,000

40,000

20,000

0

MACH NO.

•41- 0.0

-e- 0.1

0.2

± d , *

BLADE ANGLE = 50 DEG

ZERO SHAFT TILT

INBOARD BENDING BGI-1

I I ! I I I I I [, I

1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000

ROTATIONAL SPEED, RPM

FIGURE4-8. SR-5 MODEL BLADE 10X 10 LOW SPEED WIND TUNNEL

TESTS AT NASA LEWIS

64
TOTAL VIBRATORY STRESS :l:kPa

140,000 m

120,000

100,000

80,000

60,000

40,000

20,000

0

BLADE ANGLE = 60 DEG

ZERO SHAFT TILT

INBOARD BENDING BGI-1

MACH NO.

0.0

--_- 0.1

0.2

0.28

I I I I I I I I I I

1,O00 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,OOO

ROTATIONAL SPEED, RPM

FIGURE 4-9. SR-5 MODEL BLADE 10 X 10 LOW SPEED

WIND TUNNEL TESTS AT NASA LEWIS

65
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FREOUENCY (HZ)

1,000 --

800

6OO

400

2OO

i

12P 11P lOP 9P_ 8P 7P

• TEST_--31.8 DEG

CALCULATED _ --.SS °

6P

6P

4P

3P

2P

1P

0

0 2,000 4,000 6,000 8,000

ROTATIONAL SPEED, RPM

FIGURE 4- 21. SR-2 MODEL PROP-FAN

MEASURED AND CALCULATED NATURAL

10,000

FREQUENCIEb

77
FREQUENCY (HZ)

1,000

80O

600

400

20O

0

E

12P

• TEST/_ =32.0 ° /

CALCULATED/_.75 =55 °

X TEST/3REF= S0o

0 2,000

BLADE ANGLE = 32 ° MACH = 0.0

11P 10P 9P 8P

I • I J

4,000 6,000 8,000

ROTATIONAL SPEED, RPM

FIGURE 4-22. SR-3 MODEL PROP-FAN

MEASURED AND CALCULATED NATURAL

I

7P

6P

5P

4P

3P

2P

1P

ill | I

10,000

FREQUENCIES

?8
FREOUENCY (HZ)

i BLADE ANGLE = = J

36 o MACH 0.0

12P 11P lOP 9P 8P 7P

1,000

• TEST/3=36 ° DEG

CALCULATED_(_=55 °

6P

800 5P

6OO

4P

400

3P

2P

200

1P

0

0 2,000 4,000 6,000 6,000

ROTATIONAL SPEED, RPM

FIGURE 4-23. SR-5 MODEL PROP-FAN

MEASURED AND CALCULATED NATURAL

I

10,000

FREQUENCIES

79
I'OTAL

STRESS

PER

E.F.

200000

190000

180000

170000

160000

150000

140000

130000

lZoooo

kPa /DEG.

110000

10000

90000

80000

70000

80000

50000

40000

3000(

20001

I0000

0

I000 2000 3000 4000 5000 6000

ROTATIONAL SPEED,RPM

FIGURE 4- 24.SR-2 MODEL BLADE I0 X 10 LOW SPEED

WIND TUNNEL TESTS AT NASA LEWIS

BGI-1

7000 8000 9000 10000

TILT= 15 DEG,

8O
TOTAL

ST R ESS

PER

E.F.

kPa/DEG

150000

140000

130000

120000

110000

100000

90000

80000

70000

60000

50000

40000

30000

20000

10000

0

0

m

m

m

m

m

MACH NO. • 0.20

/_ BLADE

IA// /,o.

I I I I I i I I I I

I000 2000 3000 4000 5000 6000 7000 8000 9000 10000

ROTATIONAL SPEED, RPM

( FIGURE4-24 CONTINUED ) SR-2 MODEL BLADE
TOTAL

ST R ESS

PER

E.F,

kPa/DEG

70000_

60000_

50000 m

40000 m

30000_

20000_

I 0000

0

0

MACH NO. m 0.28

BLADE

A ANGLE

-_ aREF

\ _ 4o.

l i I ! I I I I I I

1000 2000 3000 4000 5000 6000 7000 0000 9000 10000

ROTATIONAL SPEED, RPM

TOTAL

ST R ESS

PER

E.F.

kPa/DEG

40000_

30000_

20000_

10000_

0

0

MACH NO. I" 0.38

BLADE

ANGLE

_REF

40e

A _ 36°

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

ROTATIONAL SPEED, RPM

( FIGURE4-24.CONTINUED ) SR-2 MODEL BLADE

82
TOTAL STRESS PER E.F. kPa/DEG

190,000

180,000

170,000

160,000

150,000

140,000

130,000

120,000

110,000

100,000

90,000

80,000

70,000

60,000

50,000

40,000

30,000

20,000

10,000

0

I

BGI-1 TILT= 15DEG I

MACH NO. - 0.10 ]

BLADE ANGLE

/3REF 40 °

0 2,000 4,000 6,000 8,000 10,000

ROTATIONAL SPEED, RPM

FIGURE 4-25. SR-3 MODEL BLADE 10 X 10 LOW SPEED WIND

TUNNEL TESTS AT NASA LEWIS

83
TOTAL

ST R ESS

PER

E.F.

kPa/DEG

80000

50000

40000

30000_

20000_

10000_

o I

0 I000

MACH NO. _ 0.20

_REF

! I ! I ! I ! I I

2000 3000 4000 5000 6000 7000 8000 9000 10000

ROTATIONAL SPEED, RPM

TOTAL

STRESS

PER

E.F,

I_:_a/DEG

40000

30000

Z0000

I0000

0

m

, I

0 1000

MACH NO.I' 0,Z8

1 I I 1 I 1 1 I I

2000 3000 4000 8000 6000 7000 8000 9000 10000

ROTATIONAL SPEED, RPM

TOTAL

ST R ESS

PER

E.F.

kPa/DEG

50000

4000O

30000

20000

I0000

o

MACH NO. I' 0.35

IOOO

I I__ I I I I I I I

2000 3000 4000 S000 6000 7000 8000 9000 10000

ROTATIONAL SPEED, RPM

FIGURE 4-25. SR-3(CONTINUED)

84
TOT. STRESS/EF

kPaDEG.

10000©--

90000--

80000*---

70000 !

80000

50000

40000_

30000_

20000_

10000

BLADE ANGLE

[] 32.0

0.,._o_._ • 36.0

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I I I i I I I I l

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ROTATIONAL SPEED, RPM

TOT. STR £SS/£F

kPa/DEG.

40000

30000

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10000---

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0

m

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ANGLE

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• 36

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1000 2000 3000 4000 5000 6000 7000 8000 9000 I0000

ROTATIONAL SPEED, RPM

FIGURE 4-26. SR-5 MODEL BLADE 10 X 10 LOW SPEED

WIND TUNNEL TESTS AT NASA LEWIS
TOT STRESS£S/EF KPA/DEG

40000 B

30000

20000

10000

0 .... I

0 1000

MACH NO,=0.28

BLADE

ANGLE

BREF

j_7,. ,,_ .,_ ._ .q..._ .q_ ._,.._,...q 50°

_...._' ,_....... ._. ....... 40°

O-.O-..O-'O-'_:'_ 32o36°

I I I I I I I I I

2000 3000 4000 5000 6000 7000 8000 9000 10000

ROTATIONAL SPEED,RPM

TOT STRESSES/EF KPA/DEG

50000

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30000 m

20000

10000

01

0

I I

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FIGURE 4-26. (CONTINUED)

86
STRESS+kPa

60,000

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20,000

w

o

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SR-2 PROP-FAN TESTS

NASA LEWJS |0X I0 WIND TUNNEL

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BLADE ANGLE:49.7 DEG

ROTATIONAL SPEED,,6000 RPM

INBOARD BENDING BG|-|

2-P

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FREQUENCY, HZ

FIGURE 4-27. SR-2 SPECTRAL PLOT FOR A 15 DEGREE PROPELLER TILT

8?
TOTAL

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80,000

60,000

40,000

20,000

SR-2 PROP-FAN TESTS

NASA LEWIS !0 X !0 WIND TUNNEL

SPEe'D=3000 RPM

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I

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88
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6000 RPM J S _ 0 RPM

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E] SKEWED WAKE CALCULATION

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TEST

I I J 1 I

100 200 300 400 500

SHAFT POWER kW

SR-2 PROP-FAN NASA LEWIS 10 X 10 TESTS IP STRESS CORRELATION

89
I 4,000

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PER EF

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TILT"I 5 =

BGI-I

MACH'0.28

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_, 8000 RPM

.AS

8000RPM- ____ J ''''O 8000 RPM

C]SKEWED WAKE CALCULATION

OGOLDSTE:INICALCULATION

_TEST

I I 1 I I

100 200 300 400 500

SHAFT POWER kW

SR-3 PROP-FAN NASA LEWIS 10 X 10 TESTS 1P STRESS CORRELATION

90
14,000 --

1P STR ESS

PER EF

kPa/oEG

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j j ._ "_ 8000 RPM ,ooo .... ...-

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// Ll /

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A TEST

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! 00 200 300 400 500

SHAFT POWER kW

SR-5 PROP-FAN NASA LEWIS I0 X I0 TESTS _P STRESS CORRELATION

91
1PSTRESSPERE.F.

kPa/DEG

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FIGURE 4-32. MODEL PROP-FAN TESTS AT NASA LEWIS

IN THE 10 X 10 WIND TUNNEL

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94
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97
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FIGURE 4-41 .SR-5 PROP-FAN NASA-LEWIS WIND TUNNEL TESTS

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