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DESIGN OF AN ACTIVE HELICOPTER CONTROL 

EXPERIMENT AT THE PRINCETON ROTORCRAFT 

DYNAMICS LABORATORY 

Andrew M. Marraffa 

R. M. McKillip, Jr. 

Department of Mechanical and Aerospace Engineering 

Princeton University 

Princeton, NJ 08544-5263 

Principal Investigator: R. M. McKillip, Jr. 

Technical Repon No. 1861T 

NASA Ames Research Center Grant No. NAG 2-415 

Experimental Studies in System Identification 

of Helicopter Rotor Dynamics 

NASA Technical Officer for this Grant: S. Jacklin 

INTERIM REPORT 

Covering the period January 1988-May 1989 

May 1989 

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Design - of an Active Helicopter Control Experiment at the Princeton 

Rotorcraft Dvnamics Laboratorv 

ABSTRACT 

In an effort to develop an active control technique for reducing 

helicopter vibrations stemming from the main rotor system, a helicopter 

model was designed and tested at the Princeton Rotorcraft Dynamics 

Laboratory (PRDL). A description of this facility, including its latest data 

acquisition upgrade, are given. The design procedures for the test model 

and its Froude scaled rotor system are also discussed. 

The approach for performing active control in this paper is based on 

the idea that rotor states can be identified by instrumenting the rotor 

blades. Using this knowledge then, Individual Blade Control (IBC) or 

Higher Harmonic Control (HHC) pitch input commands may be used to 

impact on rotor dynamics in such a way as to reduce rotor vibrations. 

This paper discusses an instrumentation configuration utilizing 

miniature accelerometers to measure and estimate first and second 

out-of-plane bending mode positions and velocities. To verify this 

technique, the model was tested in the PRDL. Resulting data were used 

to estimates rotor states as well as flap and bending coefficients, 

procedures €or which are discussed. \ 

Overall results show that a cost- and time-effective method for 

building a useful test model for future active control experiments was 

developed. With some fine-tuning or slight adjustments in sensor 

configuration, prospects for obtaining good state estimates look 

promising. 

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LIST OF FIGURES 

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Fig. 1.1 

Fig. 2.1 

Fig. 2.2 

Fig. 3.1 

Fig. 3.2 a 

Fig. 3.2 b 

Fig. 3.3 

Fig. 3.4 

Fig. 3.5 

Fig. 3.6 

Fig. 3.7 a 

Fig. 3.7 b 

Fig. 3.7 c 

Fig. 3.8 a 

Fig. 3.8 b 

Fig. 3.8 c 

Fig. 3.8 d 

Fig. 3.8 e 

Fig. 3.9 

Fig. 3.10 

Fig. 4.1 a 

Fig. 4.1 b 

Fig. 5.1 

Fig. 5.2 

Fig. 5.3 

Rotor blade reaction forces at hinge. 

Description of the Princeton Rotorcraft Dynamics Lab. 

Data acquisition functional diagram. 

Helicopter test model arrangement. 

Rotor blade and holder arrangement (side view). 

Rotor blade and holder arrangement (top view). 

Typical transfer function. 

Cambell diagram of rotor blade properties. 

Blade accelerometer dynamics. 

Impact test locations. 

Transfer functions for positions 10 through 7. 

Transfer functions for positions 6 through 4. 

Transfer functions for positions 3 through 1. 

Coherence functions for positions 10 and 9. 

Coherence functions for positions 8 and 7. 

Coherence functions for positions 6 and 5. 

Coherence functions for positions 4 and 3. 

Coherence functions for positions 2 and 1. 

1st and 2nd bending modeshape data with 5th-order 

polynomial fits. 

Accelerometer position layout in a rotor blade. 

Model-strain gauge balance adapter setup (side view). 

Model-strain gauge balance adapter setup (rear view). 

One per rev ramp signal. 

One per rev clock. 

Forward flight velocity (tachometer output). 

Fig. 5.4 Reference blade pitch angle (el). 

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PRECEDING PAGE BLANK NOT FILMED 
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Fig. 5.5 

Fig. 5.6 

Fig. 5.7 

Fig. 5.8 

Fig. 5.9 

Fig. 5.10 

Fig. 5.11 

Fig. 5.12 

Fig. 5.13 

Fig. 5.14 

Fig. 5.15 

Fig. 5.16 

Fig. 5.17 

Fig. 5.18 

Fig. 5.19 

Fig. 5.20 

Fig. 5.21 

Fig. 5.22 

Fig. 5.23 

Fig. 5.24 

Fig. 5.25 

Fig. 5.26 

Fig. 5.27 

Fig. 5.28 

Fig. 5.29 

Fig. 5.30 

Fig. 5.31 

Fig. 5.32 

Second blade pitch angle (e,). 

Third blade pitch angle (e,). 

Tip accelerometer response (acc. 6, out-of-plane). 

Accelerometer 4 response (out-of-plane). 

Accelerometer 3 response (out-of-plane). 

Root accelerometer response (acc. I, out-of-plane). 

Accelerometer 5 response (lead-lag). 

Accelerometer 2 response (lead-lag). 

Aerodynamic x-force. 

Aerodynamic y-force. 

Aerodynamic z-force. 

Aerodynamic Roll moment. 

Aerodynamic Pitch moment. 

Aerodynamic Yaw moment. 

Pre-filtered accelerometer output from acc. 1. 

Pre-filtered accelerometer output from acc. 3. 

Pre-filtered accelerometer output from acc. 4. 

Pre-filtered accelerometer output from acc. 6. 

First mode displacement estimate. 

First mode velocity estimate. 

First mode acceleration measurements. 

Second mode displacement estimate. 

Second mode velocity estimate. 

Second mode acceleration measurements. 

Non-dimensional flap spring coefficient. 

Non-dimensional flap damping coefficient. 

Non-dimensional first mode pitch forcing coefficient. 

Non-dimensional second bending mode spring coefficient. 

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Fig. 5.33 Non-dimensional second bending mode damping 

coefficient. 

Non-dimensional second bending mode pitch forcing 

coefficient. 

Fig. 5.34 

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LIST OF SYMBOLS 

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Vi 

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X 

Xd 

Y 

Yd 

Xk 

Yk 

... 

... 

... 

... 

... 

... 

... 

... 

... 

... 

... 

... 

... 

... 

... 

... 

... 

... 

... 

2-dimensional lift coefficient curve slope 

non-rotating beam frequency coefficient for nth mode 

number of rotor blades 

blade chord 

offset of flap hinge or point of fixity from rotation axis 

second mode 

ith modal position 

ith modal velocity 

ith modal acceleration 

mass per unit length of beam at root 

non-dimensional nth accelerometer location on blade 

system input 

system output 

measurement noise 

external disturbances 

sting balance voltage outputs 

differenced voltage outputs 

six degree of freedom vector of model states 

differenced force and moment inputs 

... 

... 

... longitudinal cyclic 

... lateral cyclic 

... Power coefficient 

... Torque coefficient 

x-force component of kth blade 

y-force component of kth blade 

VI 
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... 

... 

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... 

e.. 

Mjj,n(t) ... 

Mel(t) ... 

Mg(t) ... 

Mg/n(t> ... 

Me2(t) ... 

N ... 

P ... 

R ... 

Rlk ... 

R2k ... 

R3k ... 

U(f) ... 

t 

Thrust coefficient 

bending stiffness of beam at root 

F-test value 

power spectrum of u 

cross-spectrum between u(t) and v(t) 

sting balance calibration matrix 

frequency response function 

blade inertia 

Southwell coefficient for the nth mode 

zero-offset Southwell coefficient 

offset correction factor to KO, 

model roll moment, rotor length (R) 

model pitch moment, blade mass, modal sensitivity 

matrix 

flap spring coefficient 

flap damping coefficient 

flap pitch forcing Coefficient 

second mode spring coefficient 

second mode damping coefficient 

second mode pitch forcing coefficient 

model yaw moment 

Power 

rotor radius 

rotating frame radial force component on kth blade 

rotating frame tangential force component on kth blade 

rotating frame vertical force component on kth blade 

Fourier transform of u(t) 

VI1 

t 

0 
U*(f) ... 

V(f) ... 

Vni ... 

X ... 

Y ... 

complex conjugate of U(D 

Fourier transform of v(t) 

variance for ni parameters 

x-force acting on model 

y-force acting on model 

first mode shape function 

second mode shape function 

z-force acting on model 

z-force component of kth blade 

0 

Zk ... 

first mode 

blade lock number 

P ... 

Y ... 

coherence function between x and y 

... ith mode shape function vi 

a 1.. pitch angle of kth blade 'k 

... '0 collective pitch command 

air density at sea level 

solidity 

non-rotating natural frequency of the nth mode 

0 P ... 

d ... 

6lN& ... 

0 

% ... rotating natural frequency of the nth mode 

R ... rotor speed (Hz) 

... azimuth angle of kth blade vk 0 

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TABLE OF CONTENTS 

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Chapter 1 Introduction 

1.1 Motivation 

1.2 Background 

1.3 Thesis objectives 

Chapter 2 The Princeton Rotorcraft Dynamics Laboratory 

2.1 The facility 

2.2 The data acquisition system 

2.3 Data collection and manipulation software 

Chapter 3 Design of the test model 

3.1 Design objectives 

3.2 Designing the model 

3.2.1 Choosing the helicopter kit 

3.2.2 The rotor blades 

3.2.3 Powering the model 

3.2.4 The servo actuators 

3.2.5 Additional model modifications 

3.3 Sensor configuration and instrumentation 

3.3.1 Accelerometer signal content 

3.3.2 Blade accelerometer installation 

Chapter 4 Experimental procedure 

4.1 Test preparation 

4.2 Test procedure 

Chapter 5 Results and conclusions 

5.1 Resulting data and post-processing 

5.2 Conclusions 

References 

Appendix 

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14 

15 

16 

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27 

29 

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55 

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CHAPTER 1 

Introduction 

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1.1 Motivation 

For many years research has been going on in an effort to reduce 

vibrations in helicopters. There are three main sources of vibrations, 

and they can be placed in three categories, low, medium, and high 

frequency [l]. The highest frequency vibrations are caused mainly by the 

drive train. The medium frequency source is primarily the tail rotor 

which typically spins about five times as fast as the main rotor. The 

lowest frequency vibrations stem almost exclusively from the main 

rotor, and it is because of their low frequency that they are the most 

pronounced and destructive ones. These vibrations not only cause 

discomfort for pilots and passengers, but are also responsible for 

shortening the useful life of many components in the rotor system as 

well as in the fuselage of the helicopter. They lessen performance and in 

some instances are the limiting factor in achieving top flight speeds. 

Over the years, many different active control methods have been 

used for tackling this vibrations problem. Probably the most successful 

approach so far has been the use of higher harmonic control (HHC) [ZI. 

In this method, various points on the fuselage, often including the pilots 

seat, are instrumented with vibration sensors. These are to detect 

vibrations introduced to the fuselage by the rotor system via its shaft. 

Then, based on these measurements, high frequency blade pitch 

commands are input to the rotor system. 

Although HHC 

reducing vibrations, a 

methods have demonstrated good results 

different, more direct technique is suggested 

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this paper, and is directly responsible for the experiment described 

subsequently. The objective is to skip difficult dynamic modeling 

processes and to identify rotor states directly by instrumenting them. 

This process would tackle the vibrations problem at its root, and by using 

individual blade control (IBC) based on rotor state knowledge, could 

conceivably correct it there. 

The experiment which was directly motivated by these facts is 

described in this paper. 

1.2 Background 

Vibrations of the helicopter fuselage are the response to oscillatory 

forces acting at the roots of the rotor blades. These are transmitted 

through the shaft to the non-rotating frame. The periodic forces occur at 

l/rev and nb/rev frequencies, where b is the number of rotor blades and 

n any positive integer. This phenomenon can be explained analytically 

b41. 

The resulting forces acting on each blade hinge can be represented as 

in figure 1.1 by R1, R2, and R3. If Y were the azimuth angle of the zeroth 

(reference) blade, then Yk=Y+(2nk)/b would be that of the kth blade. 

The corresponding components acting in the non-rotating frame would 

then be: 

xk= -Rlk COSwk) + R2k Sinwk) 

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Z 

Fig. 1.1 Rotor blade reaction forces at hinge 

Assuming steady flight conditions, Rlk, R2k, and R3k would be periodic 

and could be represented by Fourier expansions. Looking then at the 

overall X, Y, and Z forces transmitted through the shaft, they would take 

the forms of summations over the number of blades of the above 

equations with the R's in terms of their Fourier series. It can be shown 

mathematically [4] that by simplifying these expressions, in the resulting 

series, all harmonic terms cancel except those which are integer 

multiples of b. 

This fact played an important role in this experiment. A three 

bladed rotor was designed which would have that 3/rev excitation. 

Rotor blades were then designed with second out-of-plane natural 

bending modes close to this excitation frequency. This was desirable for 

future experiments. The ability to suppress vibration would be much 

easier to show if large vibrations were present. Thus, a major task was 

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created, to make a rotor blade with just such characteristics, as well as 

insure similarity between the three blades. A process for making the 

subject rotor blades was developed and the resulting specimen were 

tested for modal properties. The frequency ratios were found to be 3.4 

and 1.3 for second and first out-of-plane bending modes, respectively. 

Thus, a test operating condition of 8 Hz (480 RPM) was chosen for the 

model at which both the first and second natural modes were in close 

neighborhood of the 1 /rev and 3/rev forcings. 

As mentioned earlier, IBC was to be implemented to control rotor 

states in future experiments. This type of control is possible through the 

use of a conventional swashplate setup in the case of a three bladed 

rotor. If the rotor azimuth angIe were known throughout operation, 

then analog sin" and COSY functions could be produced and combined 

with desired individual blade pitch angles 01,02, and 03 according to [6] 

as: 

Thus collective and cyclic commands would be the result and could be 

input through conventional actuators to the rotor system. As will be 

seen, this was accomplished using a l/rev sensor combined with analog 

circuitry. 

Using this background information along with other design 

features, this experiment was conceived. A model was built and tested 

in the Princeton Rotorcraft Dynamics laboratory with certain objectives 

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in mind. 

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1.3 Thesis objectives 

In order to be able to show in the future that a closed-loop 

controller, by using rotor state knowledge, could impact on rotor 

dynamics and achieve vibration reduction, a model had to be built and 

tested. This was necessary to perform system identification and to verify 

that a rotor state estimator could actually yield realistic results based on 

the instrumented blade configuration. 

Thus, the main objectives of this experiment were to build a usable 

model with correct scaling factors, and to test it in the Princeton 

Rotorcraft Dynamics Laboratory, which is also described. The model was 

to have Froude scaled rotor blades, one of which was instrumented with 

six accelerometers. These were used to estimate first and second out of 

plane bending modal position and velocity as well as first lag modal 

position and velocity. 

The final step was to do a dynamic test of the fully instrumented 

model on the track. This required additional support electronics all of 

which are also described in this paper. Actual data and post-processed 

results showing rotor states as well as parameter estimates are presented. 

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CHAPTER 2 

The Princeton Rotorcraft Dynamics Laboratory 

2.1 The Facility 

In the mid 1950’~~ the Princeton Dynamic Model Track (PDMT) was 

built for the purpose of investigating aerodynamic characteristics of 

V/STOL aircraft at slow forward velocities and near hover using 

powered Froude scaled models. The PDMT which has since been 

upgraded with a new data system is today known as the Princeton 

Rotorcraft Dynamics Laboratory (PRDL). It consists of a 750 foot long 

metal building with an approximately 30x30 foot cross-section, as 

described in figure 2.1. Along one side of the building runs a monorail 

track, on which a hydraulically driven carriage rests. The carriage is 

supplied with three-phase power which it picks up via brushes along 

one of two sets of four rails spanning the length of the track. This source 

may be tapped in the form of 400 cycle power at 115 volts AC. It is used 

by the drive system as well as any necessary on-board experiment 

support electronics. In order to allow mounting of large, heavy models 

near the center of the test section, the drive system was located on the 

near wall side of the track to counterbalance the model weight. Thus, 

the system is capable of carrying models weighing up to 60 pounds and 

spanning up to 8 feet in diameter at speeds approaching 30 feet/second. 

There are two modes of operation at the PRDL. In the dynamic 

testing mode, models can be mounted on a ball bearing gimbal support. 

Using this setup, any undesirable degrees of freedom of the model may 

be constrained, while desirable ones may be left unconstrained allowing 

small translational freedom with respect to the carriage. While the 

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model is actually moving inside the carriage reference frame, its motions 

can be measured. Originally, an on-board analog computer could use 

these feed-back signals to accurately position the carriage with respect to 

the model. The carriage's dynamic performance is sufficient for 

following the model in the Froude time scale [5]. Combining this 

arrangement with the capability for precise position and velocity 

measurements provides a complete system for system identification 

[6]. During static testing, which will be implemented for this 

experiment, a model is rigidly mounted on a six-component strain 

gauge balance constraining all degrees of freedom in the carriage frame. 

The forces and moments acting on it are then measured during an 

experimental run at specified conditions. The steel boom to which the 

strain gauge balance is attached may be rotated to provide any angle of 

attack for the model. It may also be interchanged with another boom 

allowing models to be mounted and tested in ground effect. 

At various points along the track, light bulbs can be installed to act 

as light switches to activate or deactivate several functions. For example, 

near the end of the track, a light switch disengages the hydraulic drive 

system and brakes the carriage. Then it throws it in reverse and retrieves 

it at high velocity until another switch is encountered several feet before 

the control room is reached. This switch again brakes the carriage and 

allows a controller to hit a mechanical stop switch. A light switch can 

also be used to activate smoke release for flow visualization 

experiments. 

The main advantages of the PRDL are low power requirements 

during operation of the track, ability to control the models' flight 

velocities very precisely, and the removal of all wall boundary layer 

effects on the test subjects. Of course, the main disadvantages include 

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30 ft 

dulic drive / / 

,model / 

rack / 

30 ft 

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Fig. 2.1 Description of the PRDL 

the fact that the carriage must be retrieved after each experimental run, 

thus disallowing continuous testing as may take place in wind tunnels. 

Also, in order to be able 'to look at data in real time, it must be 

telemetered from the moving reference frame to the control room. 

2.2 The Data Acquisition System 

One of the major upgrades that have taken place within the past 

two years is the data acquisition system. When the PRDL was originally 

built, there was no necessity for very high data sampling rates, since 

V/STOL aircraft flight dynamics happen on a relatively slow scale. Thus, 

the original data acquisition system had fairly low bandwidth. It was, 

however, capable of real-time data monitoring via strip chart recorders. 

After the telemetry system broke down, data was recorded during 

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experimental runs on magnetic tape on the moving carriage. At the end 

of each testing period, the tape had to be removed from the carriage and 

the information on it read into a computer for post processing. This 

system did not allow for real-time data monitoring. 

Today, however, to make use of the PRDL facility for active 

helicopter control experiments such as the one described in this paper, 

greater demands are put on the data acquisition system. Signals from the 

instrumented blades must be sampled at high rates in order to obtain 

accurate rotor state profiles. The rotor in this experiment will be 

spinning at approximately 5 Hz during test conditions. Thus for samples 

on the order of 100 per revolution, a sampling rate of approximately 500 

Hz would be necessary. Also, being able to monitor certain channels in 

real time could be very helpful in evaluating experimental runs on line, 

leading to more time efficient research. This is a not necessary but 

desirable characteristic to have. 

Being faced with these new demands, a decision was reached to 

completely replace the old data acquisition system. A functional diagram 

of the new system is described in figure 2.2. It is based on the AYDIN 

VECTOR PDS-700 commutator and PAD-400 decommutator, both of 

which are fully documented [9,10]. The PDS-700 unit is capable of 

simultaneously sampling 44 channels at 1000 Hz each. 32 of these are 

high-level single-ended analog inputs while the other 12 are low-level 

strain gauge inputs. The commutator converts the 44 signals to 10 bit 

words corresponding to a voltage range between -5 and +5 volts. These 

words comprise a serial bit stream to the beginning of which two 

synchronization words are added. The result is a 46 word frame. This 

serial bit stream is then scaled to TI'L voltage levels and fed into the 

American Laser Systems ALS-85 optical open-air transmitter [8]. This 

unit is mounted close to the supporting rail to minimize any vibratory 

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noise or misalignment effects. The highly directional optical signal is 

shot along the track while the carriage is moving and received by the 

ALS-85 receiver which is mounted at one end of the track. (An almost 

true monorail combined with accurate aligning sight glasses on each 

unit allow this type of system to work.) Next, the signal is sent via coax 

cable to the control room and into the PAD-400 decommutator box. 

From here the data is sent to a buffer card where an additional six 

channel identifier bits are added to each word. This buffer card performs 

several other functions as well. Two D/A converters and thumbwheels 

allow the operator to choose any two channels and look at them in real 

time on an oscilloscope. A frame clock divide is available to skip chosen 

frames of data. In addition, dip switches corresponding to each channel 

may be used to turn any unused channels off. These options allow 

sampling of data for longer periods of time by not filling the computer 

memory with useless information. From this point, data is sent directly 

into memory of an IBM PC/AT which is equipped with an HSD-16 card 

allowing direct memory access (dma). Using this card, data transfer rates 

of up to 120,000 16-bit words per second may be achieved, well beyond 

the 46,000 words per second requirement imposed by the PAD-400 

decommu t a tor. 

Two sets of red and green LED's on the buffer box constantly display 

the decommutator's major and minor lock status. A green light 

indicates good lock. Data is read into the PC transparent to the central 

processor, such that it may be processed as it is coming in by the 

computer. This allows for real time data validity checks, the results of 

which can be used to adjust any parameters necessary for better results 

on line [81. 

In order to manipulate the incoming data, a high level computer 

language had to be chosen to interface with the HSD-16 1/0 card. The 

10 
analog channels 

12 low-level PDS-700 

gauge channels, commutator 

e 

ALS-85 * optical 

transmitter 

e 

Buffer 

Box 

a 

e PAD-400 coax cable ALS-85 data 

decommutator optical receiver -, 

e 

32 high-level 

optical link 

I I t 1 I Oscilloscope 

16 bit DMA 

words request 7 I HSD-16 1/0 1 

t 1 

Fig. 2.2 Data acquisition functional diagram 

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APL language was picked for this task, since it is very convenient in the 

sense that it can easily be written and edited without cumbersome 

compilation delays and is very handy for data manipulation. APL may 

also call on compiled languages such as C or assembly to perform long 

iterative functions if necessary, by means of additional interface software 

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2.3 Data Collection and Manipulation Software 

Data may be sampled and written in several ways. If relatively few 

channels are to be sampled at slow rates such that only 10,000 or less 

elements will be written during the run, then this first method will 

suffice. While in the APL workspace DMA2APL, the menu driven 

function DMA must be called. Once it is entered, the operator is 

provided with 8 choices, according to which appropriate input data is 

requested by the program. If multiple channels are sampled at high 

rates, memory fills up very fast and much more space may be needed 

than can be provided in the first method. In this case, APL must be 

exited and the program DMA2FILE used. This routine will ask the user 

for the number of channels selected, sampling rate, and length of time 

data will be collected. It is very important that the response to number of 

channels coincides with the dip switches on the buffer box. Before data is 

written, the DMA trigger ( toggle switch on buffer box ) must be hit to 

ensure that it is collected from the beginning of a frame. Once the file is 

filled, the user is asked to provide a file name for the data. In this mode, 

128 k of elements can be obtained at a time. A third method is available 

if sampling rates exceed 500 Hz while every other frame is skipped. In 

this case, data can't be written to memory fast enough and the program 

DMA2PAGE must be used. This program, however, limits the amount 

of data taken to 64 k [71. 

Once data is written, it can be retrieved and processed within the 

APL environment. While in the DMA2APL workspace, the function 

GETCHN is used to get data from the file that was written earlier. When 

called upon, it requests that filename, the channel number, and the 

amount of data points desired. It will then check the top six bits of every 

data element and return with the ones corresponding to the given 

channel number. If more data is requested than was written, GETCHN 

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will return with -1's for excess requests. The function SCOPE is also 

available in the DMA2APL workspace. It is a semi-real time digital 

oscilloscope which can display various channel outputs on the graphics 

screen. In adgition to DMA2APL, there are two other available 

workspaces, PLOTDATA and SPECTRAL. These contain plotting 

routines and spectral analyses tools, respectively. They are fully 

documented in reference 7. 

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CHAPTER 3 

Design of the test model 

3.1 Design objectives 

Several limitations were imposed from the beginning in the design 

of the rotor model. One obvious restriction was that of a size and weight 

limit imposed by the test facility. Rotor span was limited to 8 feet or less 

in diameter and weight to 50 lbs or less. Lack of a full-time professional 

staff forced a different approach from the custom model construction 

techniques used in earlier V/STOL experiments. Thus, a cost and time 

effective method for building a model was sought. Since the objectives 

in this experiment pertain to rotor dynamics, the scaling of the rotor 

system became vital and that of the fuselage relatively unimportant, so 

long as it was scaled in size with respect to the rotor system. Specific 

characteristics of the rotor blades are discussed in subsequent sections. A 

method for instrumenting the rotor blades with sensors which would 

yield accurate rotor state measurements had to be developed. - Also, in 

order to eventually be able to implement adaptive controls on the 

model, it was desired to have the capability of both individual blade 

control (IBC) and higher harmonic control (HHC). 

These described some of the basic objectives to be met by the model 

to be tested in the PRDL. More specific requirements are discussed as 

they were encountered during the actual design phase. 

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3.2 Designing the model 

To satisfy mainly the time and money constraints, an off-the-shelf 

radio control helicopter kit manufactured by Schlueter Inc., West 

Germany, was purchased. This type of kit which is readily available 

today, has reached a level of sophistication unavailable only several 

years ago. It was used as a structural basis for the test model, and is 

shown in figure 3.1 along with major modifications. 

pitch sensor 

potentiometers 

I - 6 11 I II 1 

hollow shaft I I 1- swash plate assemb7 

1 /rev infra-red 

emitter 

main gear 

20 channel 

slip ring 

1 /rev infra-red 

detector 

structural frame 

1 HP DC motor 

Fig. 3.1 Helicopter test model arrangement 

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3.2.1 Choosing the helicopter kit 

The model support frame, as shown in the figure, was provided by 

the helicopter kit, as was the main gear, swashplate assembly, and rotor 

hub. The reason for choosing this model was because of its three-bladed 

rotor hub configuration, as well as its size and weight which were well 

below imposed limits. A three-bladed rotor was necessary to be able to 

use IBC without having to use actuators in the rotating frame. As was 

explained earlier, IBC can be implemented using a conventional 

swashplate setup as long as the rotor system consists of no more than 

three blades. This can physically be explained by the fact that the position 

of the swashplate in space is defined by three independent points. These, 

at any point in time, could conceivably define three independent pitch 

commands corresponding to individual blades. It is for this reason that 

a blade number less than four was chosen. 

The option of a two bladed rotor was also available. The reason it 

wasn't taken was so that HHC could be implemented without interfering 

with pilot inputs. HHC commands are usually input at (b-l)/rev, b/rev, 

and (b+l)/rev frequencies, where b is the number of blades. That means 

for a three bladed system, the lowest frequency closed-loop controls 

would be input at 2/rev. In the case of a two bladed one, however, this 

would occur at l/rev. At that frequency, pilot commands are input, 

resulting in undesirable interferences in the two bladed rotor case. 

3.2.2 The rotor blades 

Since the helicopter kit came with a fiberglass fuselage, the size of 

the model's rotor blades was dictated by the necessity to maintain rotor 

to fuselage scaling. Thus, blades needed to be made which would be 

approximately 2 feet long with a 2 inch chord and display low first and 

16 
e 

a 

e 

e 

a 

second bending mode frequencies ( be relatively soft ). With this in 

mind, a method for making rotor blades, which would assure 

aerodynamic similarity between them, was developed. 

To obtain the necessary softness and flexibility for low frequency 

natural modes, a light weight foam material which could be poured into 

a mold in liquid form, was selected. This type of method, which had 

been used in past experiments, would also insure similarity between 

blades. Following this reasoning, the next step was to make a mold of a 

rotor blade with the following dimensional characteristics: 

1. 2footspan 

2. 2 inch chord 

3. NACA 0012 airfoil 

4. no twist 

5. no taper 

The airfoil section was chosen because it is a standard symmetrical one 

used on vintage helicopters. No taper or twist simplified the process of 

making a mold. Because much time would go into making this mold, it 

was desirable to only have to do it once. This meant making a mold 

which could be used many times over without breaking or wearing. To 

meet these specifications, a rotor blade mold was machined out of two 

3/4 X 3 X 26 inch aluminum slabs using a computerized Bridgeport 

milling machine located in the Jadwin machine shop at Princeton 

University. 

The procedure involved writing a program in Anicam (see 

Appendix) on a minicam computer which was linked to the mill. 

Anicam is a language similar to Basic or Fortran. The program basically 

defined coordinates at the tip and root of one half of the blade. It then 

prompted the milling machine to carve out the material between these 

sets of coordinates, using specified cutting tools, spindle RPM's, and feed 

17 
a 

e 

a 

0 

0 

e 

rates. The procedure of milling was done in steps to assure a smooth 

finished surface and due to the large amount of material which had to be 

removed. Thus, a rough cut, consisting of two steps, which would mill 

to within .01 inches of the final cut, was done first. 14 cuts were made 

with a 1 inch ball mill from the trailing edge to 30% chord, milling from 

root to tip. Then, 6 cuts with a 1/8 inch ball mill were used to rough cut 

from 30% chord to the leading edge. This was necessary because of the 

small radius of curvature in the leading edge. Following the rough 

cutting, a 1 inch and a 1 /16 inch ball mill were used to make 50 finished 

cuts from the trailing edge to 30% chord, and 30 finished cuts from that 

point to the leading edge, respectively. Taking advantage of the 

precision of the computerized Bridgeport, three aligning holes were then 

drilled along one edge of the mold. These were necessary to assure 

perfect aligning of the two mold pieces. Eventually, dowels were pressed 

into one of the halves and the holes enlarged in the other, allowing for a 

perfect fit every time. 

Due to the many cuts performed by the milling machine, the 

process of milling one mold half lasted approximately 2.5 hours. The 

resulting pieces displayed very smooth surfaces, although ridges from 

the cutting procedure were visible. 

Using this mold, a procedure for making the actual rotor blades was 

devised. A two part polyurethane foam manufactured by the SIG Mfg. 

company was acquired. In order to use this product with the mold, a 

release agent had to be found which would insure the blade's release 

from the mold without braking. After testing several possibilities such 

as glycerin, oils, etc., a paste car wax was chosen for its good release 

characteristics. The procedure for making a rotor blade consisted of 

several steps. First, the mold had to be lined with a very thin, uniform 

layer of release wax. The next step was to mix the two foam components 

18 

e 
e 

e 

e 

0 

e 

a 

e 

a 

one part to one. Initially, 18 ml of each component were mixed together 

resulting in rotor blades weighing approximately 35 grams. However, 

after a 35 gram blade was eventually instrumented, it weighed 

approximately 48 grams. As a result, the two non-instrumented blades 

had to be made heavier to maintain weight balance. This was 

accomplished by mixing 24 ml of each foam component together, 

yielding approximately 48 gram rotor blades ( these figures play an 

important role in achieving Froude scale characteristics ). The mixing 

procedure turned out to be very crucial, as under- or over-mixing 

slightly meant less than maximum expansion. This would result in 

large air bubbles inside the blade, or simply an incomplete blade. A good 

indication that the foam had been mixed the proper amount was when 

small bubbles started to form on the surface of the mixture. This would 

happen within a matter of about one minute ( one nice characteristic of 

the foam was that it didn't require external heat to react as was often the 

case with products used in the past). Once this point was reached, the 

foam was poured uniformly into the mold. It was then quickly closed 

and clamped shut with c-clamps to prevent foam from gushing out the 

sides. To obtain best results the mold was left overnight to allow curing. 

It was found that although the foam hardened in a matter of minutes, it 

was more advantageous to let it cure for 24 hours. This resulted in 

much easier release from the mold. The procedure of retrieving the 

rotor blade necessitated some carefulness. When slowly prying the mold 

open with a screwdriver at specially made slots, attention needed to be 

paid to what the blade was doing inside the mold. On one or two 

occasions a blade was lost because opposite ends were stuck to opposite 

mold pieces, resulting in a break when the mold was opened all the way. 

After a blade was removed successfully, fine grade sandpaper was used to 

smooth the seems which resulted from the molding procedure. 

19 

e 
e 

e 

e 

e 

0 

e 

e 

0 

As was mentioned earlier, the blades' mass was an important 

parameter for scaling purposes. In order to obtain realistic experimental 

data, it was very desirable to have Froude scaled rotor blades. Froude 

scaling is scaling between aerodynamic and inertial forces. The lock 

number ( y) of a rotor blade, defined as 

y=3pacR2/M ,for Ib=MR2/3 

is the ratio of aerodynamic and inertial forces acting on it. Hence, to 

obtain Froude scaled rotor blades, it was necessary for them to have 

realistic lock numbers. Full scale rotors usually have lock numbers 

between 8 and 13, this defining our acceptable range. As the definition of 

y shows, the only freedom to vary once the blade mold was finished lay 

in the mass parameter, M. As a result, the blades weighing 35 and 48 

grams had lock numbers of 11.4 and 8.3, respectively, both falling within 

the acceptable range. 

To adapt the rotor blades to the rotor hub, blade holders were 

machined from aluminum. These were made as to hold the blades with 

friction as well as sets of two bolts. This unit in turn would fit into the 

blade holding slot of the rotor hub and be held in place by the lead-lag 

hinge. Figure 3.2 more clearly demonstrates this. 

With this blade holder, a rotor blade could now be clamped down 

and tested for modal properties. In subsequent sections, it will be shown 

that first and second out of plane bending mode shapes become very 

important. How they were obtained will be discussed. At this point it 

was important to know if the rotor blades possessed low natural 

frequencies for these modes, such that good frequency ratios could be 

20 

. 
0 

'a 

I 

'0 

0 

0 

0 

a 

13 

.. blade holder .. . . 

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

.. .. .. . . I 

ri ft :. 

:: 

.... 

.. 

.... 

.... .... 1% .-.* ----e .* 

rotor hub 

I - f extension 1 .. .. 

9/4 )I lead-lag hinge 

a) sideview 

b) topview 

Fig. 3.2 a,b Side and top 'views of rotor blade and holder arrangement I 

(note: all dimensions in inches) 

obtained at slow rotor speeds. To obtain this information, a blade was 

clamped down horizontally at its holder for impact testing. This type of 

modal analysis technique is thoroughly explained in reference 12. It 

consists of using a force hammer to create impulse force inputs to the 

blade. With a portable PC, the response of a miniature accelerometer, 

attached at the tip of the blade, as well as the hammer input, were 

sampled at 100 Hz. The transfer function between the output and input 

was then calculated and its frequency response plotted. This was done at 

21 

0 
one impact point over several samples and also their average. A typical 

transfer function plot is shown in figure 3.3. 

50 

40 

30 

20 

10 

0 

0 10 20 30 

frequency Hz 

Fig. 3.3 Typical transfer function 

0 

0 

The results showed that for a 48 gram rotor blade, the first and second 

out of plane bending mode natural frequencies ( non-rotating ) were 2.34 

and 15.62 Hz, respectively ( This is where the peaks occurred >. These 

figures could now be used for determining frequency ratios. A method 

for finding rotating natural bending frequencies using non-rotating ones 

is described in detail in reference 13. It consists of augmenting the 

non-rotating frequency by the effected centrifugal stiffening depending 

on rotational speed as : 

where the subscript n signifies the nth mode, R and NR for rotating and 

non-rotating. Kn can be broken down to 

22 
KOn and Kln being referred to as the zero-offset Southwell coefficient 

and offset correction factor for that coefficient. e is the offset of the flap 

hinge or point of fixity from the axis of rotation. UNRn can be 

represented in terms of a nonrotating-beam frequency coefficient an, and 

the mass stiffness of the beam at the root as 

mobeing mass per unit length at the blade root, and L the rotor length. 

For a cantilever beam with uniform mass and stiffness distribution, 

e 

als3.5 and 

a2 z 22.0 

e 

according to [14]. With these coefficients, the experimental results for 

UNR~ and UNR2 could be verified by showing that 

Doing these calculations, results of .69 and .71 were found, being within 

3% of each other. Values for Kol, Ko2, KI~, and Klz were determined 

from sets of plots found in reference 13. They yielded: 

23 
0 

With the offset e equaling .47 feet, 

K1 = K01 + K11 e = 1.56 

K2 = K02 + K12 e = 8.13. 

With these factors known, frequency ratios were determined to be : 

a 

0 

0 

a 

o (1st bending ) / R = 1.28 and 

o (2nd bending) / R = 3.43 at 

R=8Hz. 

A Cambell diagram which shows approximate modal characteristics of 

the tested rotor blade is shown in figure 3.4. 

In summary, important rotor blade and hub characteristics are listed 

1) rotor blade radius : 2 feet 

2) rotor blade chord : 2 inches 

3) airfoil section 

4) o (1st bending) / R 1.3 (R=8 Hz) 

5) o (2nd bending) / R z 3.4 (R=8 Hz) 

6) rotor hub configuration: 

as follows: 

: NACA 0012 

a) 3 blades 

b) lead-lag hinge 

c) no flap hinge 

24 
0 

a 30-1 

a 

0 

a 

0 

3 

c 

f 

& 

d) lag hinge offset : 3.9 inches 

e) e = 5.7 inches 

2nd bending 

mode 

0 12 3 4 5 6 7 8 9 10 

operating frequency R Hz 

Fig. 3.4 Cambell diagram of rotor blade properties 

3.2.3 Powering the model 

With the given rotor system specifications, a power source for 

driving the model needed to be found and adapted to it. A simple 

required power calculation was performed. By conservatively assuming 

. 

a thrust coefficient to solidity ratio ( CT / Q ) of .l, where solidity is 

defined as total blade to disc area ratio or 

25 
CY= 

7c R2 

the thrust coefficient was determined to be 0.008. 

By using the relationships 

a 

e 

e 

CT" '2 

'Q= fi 

c, = CQ 

3 

P = c p( ~XR * ) ( RR ) 

necessary power was determined to be 0.9 HP at 480 RPM. These results 

helped in choosing a motor for driving the model. Because operating 

speed wasn't anticipated to be much more than 8 Hz, a 1.0 HP, 

permanent magnet, DC motor was used. 

This motor was adapted to the helicopter model by attaching a gear 

comparable to the rotor's main gear to its drive shaft. The motor was 

then clamped into position against the helicopter's frame as is shown in 

figure 3.1. 

3.2.4 The servo actuators 

A set of three servo actuators was used for positioning the 

swashplate through pushrod assemblies. Located, as shown in figure 3.1, 

were JRS4051 high speed servos manufactured by JR CIRCUS inc. The 

setup was such that for lateral cyclic the two outside ones were used and 

for longitudinal cyclic, the middle one. Collective commands were 

26 

i 
e 

0 

e 

e 

e 

achieved with all three servos in combination. 

Positioning of these off the shelf radio control (R.C.) actuators was 

accomplished with pulse width modulated (PWM) signals. To be able to 

input collective or cyclic commands, an integrated circuit (IC) card was 

designed. This card was to be carried by a card bus on the carriage. Its job 

was to take cyclic or collective inputs and electronically convert them 

into three individual servo commands, by generating and controlling 

pulses and their widths. Since both pilot as well as closed-loop control 

inputs would eventually go through this unit, it comprised an essential 

part for future experiments. 

To determine these actuators' capabilities, a test was performed. 

Again making use of a portable PC, pitch input commands were 

sampled, sweeping through a range of frequencies. Pitch responses to 

these inputs, measured by pitch sensors, were also sampled. Transfer 

functions from this test revealed that the JR servos were effective up to 

approximately 3 Hz. For future closed-loop experiments attempting to 

reduce rotor vibrations, this would be insufficient. 

3.2.5 Additional model modifications 

Additional modifications to the stock helicopter kit were made in 

support of the rotor experimental program. Sensing each blade's pitch 

angle was a necessity for doing system identification as well as for future 

closed-loop experiments. Thus, for each blade, potentiometers were 

installed on the hub. By using a simple gear drive, pitch angles could be 

measured very accurately by ranging the potentiometers through a 30 

volt differential ( between +/- 15 volts ). 

In order to send signals from the rotating to the nonrotating 

reference frame, a slip ring had to be installed. This assembly had the 

27 
a 

0 

a 

0 

capability of twenty channels, a number limited by the size of the rotor 

shaft. As was noted in figure 3.1, a hollow shaft replaced the original. 

This part had to be machined out of a stock piece of steel, as drilling into 

the kit's hardened steel shaft was an impossibility. The procedure for 

machining the new shaft consisted of first drilling a hole into a large 

piece of steel. Then a lathe was used to cut that piece down, maintaining 

the hole as its center. Twenty wires were then installed to conduct 

signals from the rotor hub to the slipring base. How these channels were 

used will be described in subsequent sections. 

Another important modification to the model was the addition of a 

1 /rev sensor. This sensor consisted of an infrared emitter-detector pair, 

mounted as shown in figure 3.1. Aluminum tubes were used for 

alignment as well as light shielding purposes. A small hole was drilled 

through the helicopter's main gear, resulting in a pulse once every 

revolution. This signal was fed into a phase lock loop card which would 

lock on to it. An LED and a beeper were installed to verify this lock. The 

card would then perform various functions with the locked-on signal. 

The l/rev signal was routed to various locations in support of a host of 

timing applications. First, in order to generate the swashplate 

commands for Individual Blade Control inputs, the pulse was used to 

synchronize a sine/cosine function generator as part of the analog 

electronics on the swashplate command mixer card. In addition, the 

pulse drove a ramp generator that was fed into the commutator as an 

additional data channel. This ramp was used as an indicator of lost data 

in the telemetry signal, as the reconstructed signal would indicate 

discrete jumps in signal level for missing stretches of time-sampled data. 

Finally, the pulse was subdivided to provide synchronized sampling 

pulses for future use with carriage-mounted digital feedback control 

applications. 

28 

0 
0 

e 

e 

a 

e 

3.3 Sensor configuration and instrumentation 

As was mentioned in chapter one, the objective in this experiment 

was to build a model whose rotor states could be identified by directly 

instrumenting the rotor blades. To be more specific, first and second out 

of plane bending modal position and velocity of one of the three blades 

were to be determined. To accomplish this, miniature accelerometers 

were used. This type of sensor configuration had been successfully used 

in previous system identification studies of helicopter rotor dynamics [8]. 

In this reference, first out-of-plane bending mode positions and 

velocities were estimated during hover using a rotor blade instrumented 

with two miniature accelerometers. This experiment demonstrated the 

advantages of accelerometer sensors over conventional strain gauges. In 

this type of application, strain gauges would encounter serious problems. 

When differentiating electronic position signals from the gauge, any 

spiky noise would spell disaster. This kind of problem is avoided by 

using accelerometers and electronically integrating to obtain velocity and 

position estimates. 

e 

3.3.1 Accelerometer signal content 

e 

Planted inside the rotor blade, the accelerometers would measure 

components of out-of-plane inertial as well as centrifugal acceleration. 

Figure 3.5 shows the sensor geometry. According to this setup, the 

accelerometers yield: 

e 

29 

e 
e 

l 

I 

sensitive ; axis 

I 

0 

Fig. 3.5 Blade accelerometer dynamics 

representing the out-of-plane inertial and centrifugal acceleration 

components along the accelerometer's sensitive axis. If the deflection of 

the rotor blades were represented in terms of a modal expansion: 

then each accelerometer content would be: 

0 

n representing the number of modes considered in the expansion (151. 

Being interested in only the first two out of plane modes, a set of four 

accelerometers needed to be installed. Their signal contents can be 

represented as follows: 

30 

e 
e 

e 

e 

e 

e 

4 

where rl represents mode shape, p first bending mode position, b first 

mode acceleration, g and g second mode position and acceleration, and ri 

the spanwise position of the ith accelerometer. Thus, knowing the mode 

shapes of the first two out of plane bending modes, this 4x4 matrix 

(referred to as modal sensitivity matrix) could be inverted and post 

multiplied by the four accelerometer signals ( It becomes evident here 

that because each sensor output actually comprises two components, 

twice as many sensors as desired modes are necessary to obtain an 

invertible matrix. For this reason, four accelerometers were used ). This 

would result in first and second bending modal position and acceleration 

measurements. With this information, a kinematic observer, structured 

to avoid difficult dynamic modeling tasks, could be implemented. As 

described in detail in reference 16, the equations of motion can be written 

as: 

31 

e 
0 

y(t)=[ 1 0 0 0 ] 0 0 1 0 

where w represents external disturbances. These equations basically say 

that modal position is the double integral of modal acceleration. Being 

that modal position measurements were available, the observation 

equations 

Bo> +[I O](Y1(')) 

g(t> 0 1 v+t> 

0 

0 

0 

e 

where v is measurement noise, could be included in a Kalman-filter type 

observer. This would yield a net result of integrating the acceleration 

information to obtain modal positions and velocities. The actual modal 

position measurements would be used for displacement error feedback 

to drive position and velocity estimation errors to zero [16]. 

3.3.2 Blade accelerometer installation 

Having now structured the sensor arrangement, the task of 

instrumenting a rotor blade arose. Placement of the accelerometers 

became an important issue. The criterion for placing the sensors was the 

necessity to obtain accurate measurements. This would be achieved only 

if the modal matrix mentioned earlier were as invertible as possible. A 

measure of invertibility is given by the matrix's condition number. This 

was a parameter which could be varied as a function of placement of the 

accelerometers. However, to find optimum sensor positions, first the 

first and second bending mode shapes and their derivatives had to be 

determined and inserted into the modal matrix. 

The mode shapes were determined using the previously mentioned 

32 
e 

e 

0 

e 

mode shape analysis technique [12]. Again, an impact hammer was used 

to impart impulse forces along a rotor blade, clamped down at its holder 

in the horizontal direction. The response of an accelerometer mounted 

as shown in figure 3.6 along with the input force were first sent through 

a low pass filter with a cutoff frequency of 25 Hz before being sampled. 

This was necessary to filter out unwanted high frequency information 

and, in the process, increase data quality. A portable IBM PC then 

sampled the data at 100 Hz. Using this data, frequency response 

functions H(f) were determined for each impact test as: 

where G,,(f) = U*(f) V(f), cross-spectrum between u(t) and v(t) 

U(f) = Fourier transform of system input u(t) 

V(f) = Fourier transform of system output v(t) 

GJf) = U*(f) U(f), power spectrum of u(t) 

U+ = complex conjugate of U(f) 

This was done eight times at each of 10 impact locations distributed as in 

figure 3.6. 

1/4 in chord line 

Fig 3.6 Impact test locations 

For each of these sets of eight tests, transfer functions were averaged and 

plotted in the frequency domain. The results are summarized in figures 

33 
3.7 a through c. 

e 

e 

0 

a 

n 

a 

a 

\ 

i 

Y 

r 

al 

0 

C 

m 

a - c 

E 

60 

1 

40 

30 

20 

10 

0 

. 

0 10 20 30 

fmquency Hz 

Fig 3.7a Transfer functions for posl0 through pos7 

60 

40 

20 

0 

0 10 20 30 

fmquency Hz 

Fig. 3.7b Transfer functions for pos6 through pod 

e 

34 
e 

e 

e 

e 

e 

e 

e 

e 

120 1 

100 II A 

UJ 

UJ 

E 

\ 

u v0 

D 

E 

P, 

a - c 

E 

0 10 20 30 

frequency Ht 

Fig. 3.7~ Transfer functions for pos3 through posl 

Again one can see that the first and second bending modes for each 

impact point occur at identical natural frequencies, 2.34 and 15.62 Hz 

respectively. To assure that these averaged transfer functions were 

comprised of good data, the coherence functions between the eight tests 

at each impact position defined as 

were determined. The coherence function is a measure of the 

contamination of two signals by noise and nonlinear effects. Thus, a 

value of 1 indicates a perfect linear system correlation between the two 

channels, while one of 0 shows no correlation. Figures 3.8a through e 

show the results. Although coherence is poor in some of the figures 

over various frequencies, all impact tests show coherences close to 1 in 

35 
a 

a 

a 

0) 

0 

E 

0) 

t 

0 

0 

2 

0 10 20 30 

frequency Hz 

Fig. 3.8a Coherence function for posl0 and pos9 

a 

0 

0) 

0 

c 

9, 

c 

0 

0 

2? 

1 .o 

0.8 

0.6 

0.4 

0.2 

0.0 ! 1 1 

0 10 20 30 

frequency Hz 

Fie. 3.8b Coherences for pos8 and pos7 

p0d0 

p059 

p058 

p057 -... 

36 
e 

0 

0, 

u 

E 

Q, 

t 

0 

0 

t! 

1 .o 

0.8 

0.6 

0.4 

0.2 

0.0 

0 10 20 30 

frequency Ht 

Fig. 3.8~ Coherence functions for pos6 and pos5 

1 .o 

0.8 

0.6 

0.4 

0.2 1 

0 10 20 30 

frequency Hz 

Fig. 3.8d Coherences for pod and pos3 

p056 

YI.... p055 " .. 

37 

e 
e 

pos2 

-7". posl 

e 

0.8 

ai 0.6 

0 

c 

a 

0 

0 

E 

0.4 

0.2 

0.0 

e 

e 

0 

0 10 20 30 

fmquency Ht 

Fig. 3.8e Coherence functions for pos2 and posl 

the neighborhoods of resonant frequencies. This leads one to have a 

certain degree of confidence in the test data, since these points contained 

all the relevant information. The natural bending frequencies were 

already determined from this data. Next, first and second bending mode 

shapes were to be obtained. 

The mode shape information lay in the magnitudes of the transfer 

functions at their resonance peaks. This was extracted and plotted versus 

corresponding nondimensionalized rotor blade position. Polynomials 

were then fit to these data to represent the mode shapes analytically. The 

results are shown in figure 3.9. To determine what order polynomial to 

fit the data with such that best presentation of the mode shapes would be 

obtained, an F-test was performed on the data. According to [17], when 

going to the next higher order polynomial, and F becomes less than 4.7 

in this case, then that step up in order does not significantly improve the 

38 
e 

0 

e 

0 

e 

0.0 0.2 0.4 0.6 0.8 1 .o 

nondlmenslonal rotor span 

Fig. 3.9 1st and 2nd bending mode shape data 

with 5th-order polynomial fits 

polynomial fit error. The value F is defined as: 

2nd mode 

1 st mode 

Vn -Vn N -n2 

F= 1 2x 

Vn 2"2-"1 

2 v ni = C(error for n parameters 

ni = polynomial order + 1 

N = number of data points 

The test revealed that for the first mode, a 3rd-order polynomial was 

sufficient and for the second, a 4th-order. Going to the next higher order 

polynomial in either case yielded F values of .15 and .06 for first and 

second modes, respectively (The polynomials which were eventually 

used, however, were of order 5, reason being that additional software for 

39 
0 

e 

a 

e 

0 

optimally placing sensors ran into convergence problems with inputs of 

lower than 5th-order). 

Having obtained mode shape functions, accelerometer placements 

along the rotor blade could now be optimized. This was accomplished by 

optimizing the modal matrix's condition number varying '1, 1-2, '3, and 

r4, the sensor positions. The condition number of a matrix A in a system 

such as 

Ax=b 

is defined as the ratio of largest to smallest singular value of A. It can be 

shown that these singular values are the positive square roots of the 

eigenvalues of ( A AT ). To obtain most reliable results from the 

accelerometer signals, this condition number had to be minimized [15]. 

Software to perform this optimization was written and utilized. Mode 

shape information was input into this program as 5th-order polynomial 

coefficients. The first and second mode shape functions as plotted in 

figure 3.9 were: 

e 

Ymodel(X) = .0335 X2 + 3.925 X3 - 4.914 & + 1.903 X5 

Ymde2(x) = -11.878 x2 + 16.261 ~3 + 2.934 >P - 6.360 ~5 

a 

The accelerometers themselves introduced a constraint in terms of their 

own placement in the blade. Each sensor was equipped with a 

temperature compensator which was located 18 inches from the sensor 

itself. One non-standard accelerometer, however, with its temperature 

compensator located 23 inches from the sensing point, was obtained. 

From the optimization routine, it was found that one sensor should be 

located as close to the blade tip as possible. Thus, this accelerometer was 

40 
e 

0 

e 

0 

m 

planted closest to the tip. A layout of all the sensor placements resulting 

from the optimization routine is shown in figure 3.10. 

lead-lag 

hinge 

d 14.3 in t 4 .. 

19.9 in 

Fig. 3.10 Accelerometer position layout in a rotor blade 

In addition to the four out of plane bending sensors, two lead-lag ones 

were also incorporated in the rotor blade. Their placement was not as 

vital as that of the out of plane sensors. This was due to the fact that 

only rigid lead-lag motion was to be detected. 

Having determined where to place the miniature accelerometers to 

obtain best possible measurement results, the physical instrumentation 

stage was reached. First, a fresh blade was made and left stuck in one half 

of the mold. This would allow easier handling while instrumenting. 

The exposed half of the blade was then sanded down until only its 

bottom half remained. This was necessary in order to obtain a smooth 

finished product, as will become evident. Next, the cavities for each 

accelerometer as well as the channels for the wiring were cut into the 

blade half making sure not to puncture through the bottom surface. 

This surface's smoothness was to be preserved as it would be the top of 

the rotor blade. Each sensor was then wrapped in aluminum foil. The 

purpose for this was to allow easy removal from the blade if the necessity 

41 

l 

e 
a 

e 

e 

arose. Following this, the accelerometers were carefully placed in 

position, facing up for out of plane and sideways for lead-lag. Since 30 

wires had to come out of the mold, a small groove was milled into the 

other mold half at the root end. Care had to be taken in choosing which 

end of the blade to make the root or tip when implanting the sensors. 

This would determine which surface would become the top and bottom 

of the rotor blade. It was desirable to make the untouched surface of the 

blade ( the surface stuck to the mold half ) the low dynamic pressure 

surface since this was likely to be the smoother of the two. Once the 

sensors were in place, the mold was prepared to be shut. Half of the 

usual amount of liquid foam was mixed and poured over the 

instrumented half. The mold was shut, clamped, and left over night. 

When the blade was finally removed, and seams were sanded off, a 

smooth finished product was obtained. The specimen weighed 48 grams 

prompting the making of heavier non-instrumented blades to maintain 

rotor balance. 

e 

42 

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0 

l 

l 

e 

CHAPTER 4 

Experimental procedure 

4.1 Test preparation 

Several tasks needed to be completed before testing could begin. 

The six-component strain-gauged sting balance had to be calibrated, 

procedures for which can be found in reference 7. To accurately identify 

forces and moments on the model, the 6x6 matrix relating voltage 

signals to the six degrees of freedom had to be constructed such that: 

0 

where y = [ X L M Z Y N IT , x the corresponding voltage signals, 

and H the 6x6 calibration matrix. This was accomplished by calibrating 

each degree of freedom and keeping track of every input and output 

during this procedure. Then, taking the differenced force and moment 

inputs and voltage outputs, 

over all samples, a least squares estimate of H was to be found by: 

This procedure was done, however a small problem was encountered. 

After having taken calibration data for the first five degrees of freedom, 

43 
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0 

e 

a 

it was realized that the channel carrying the yawing moment had been 

switched off the entire time. Due to time constraints and data channel 

priorities established for these tests, it was decided to sacrifice its accuracy. 

However, the entire H matrix could still be constructed using calibration 

data from the last degree of freedom, where the yaw channel was turned 

on. This was accomplished as follows. In the matrix equation 

B and C were determined with the last set of calibration data by: 

e 

The Hsx5 matrix was determined by neglecting any yaw coupling as: 

a 

a 

0 

using data from the first five degree of freedom calibrations. Knowing, 

at this point, Hsx5/ B, and C, a least squares expression for A was 

determined utilizing the yaw calibration data: 

1 

where (M) = C- [yyaw - B xs] 

Thus a complete H matrix was constructed the result being: 

44 
0 

0 

0 

a 

0 

.031 3.34E-4 L33E-4 -208E-4 2 80E-3 5.75E-3 

185E-5 .122 261E-4 L29E-3 5. 61E- 3 ,013 

-2.35E-3 Z81E-4 .308 -4 68E- 3 -3.59E-3 -.OB 

188E-4 406E-5 l.31E-4 .lo8 -2.35E-3 - 4 21E-3 H= 

-2.56~4 a76~-5 242~-3 -3.71~4 .i40 .371 

- .323 .507 .lo3 - .111 - .350 .115 

How this effected the results will be discussed in chapter 5. The balance 

was capable of measuring forces much larger than the ones it would 

experience from the small model in this experiment. Thus, the gains in 

the commutator box were set to their maximum values, resulting in 

maximum sensitivity. 

A fiberglass fuselage which came with the helicopter kit was added 

to the model. To mount the helicopter on the sting balance, an adapter 

had to be machined. This piece had to bolt into the model frame and 

attach to an already existing balance holder. The final mounting 

arrangement is best described by figures 4.la and b. 

Once the strain gauge balance was mounted on the carriage boom, 

and the model on the balance, the pitch sensors had to be calibrated. 

These sensors were actually potentiometers, the voltage across which 

was ranged between -15 and +15 volts. This provided ample sensitivity. 

The fact that the commutator box only accepted signals within -5 and +5 

volts didn't pose a problem since only a small portion of the pots' total 

throw was being used. The potentiometers were easily adjusted such 

that pitch amplitudes between -5 and +20 degrees would produce outputs 

falling within that range. Using a digital inclinometer, calibration 

curves had already been generated prior to mounting the model. Thus, 

only zeros and a small set of test points for each sensor needed to be 

found. These would verify the calibration curve slopes and provide 

45 
e 

e 

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0 

e 

0 

land ing 

Fig. 4.la Modelsrain gauge adapter setup (sideview) 

@m I \ 

Fig. 4.lb Rearview of the adapter 

reference points in case of shifts in the curves. 

The digital inclinometer, which was accurate *to within 0.1 degrees, 

served two additional purposes. First, it was used to adjust pitch links 

between the swashplate and pitch arms. This would assure tracking 

between the blades. In addition, the inclinometer was used to statically 

trim the rotor. In other words, the servo actuators were set such that at 

no control input, each blade was at zero angle of attack. Since the 

experiments to follow were to be open-loop, the low bandwidth actuators 

described earlier were satisfactory. The only necessary inputs to the 

model were to be random pitch commands. Thus, the easiest way to 

obtain them was to use a servo-compatible off-the-shelf radio control 

transmitter/receiver pair. This radio was equipped with trim tabs which 

46 

1 

e 
e 

e 

e 

e 

e 

e 

were set for static trim. 

To transport the sensor signals from the rotor system to the 

nonrotating reference frame, their wire leads had to be connected to the 

slip ring assembly connectors. Each accelerometer had four wires, two 

signal and two excitation voltages. Each pitch sensor had three leads, 

one signal and two excitation voltages. Since the slip ring assembly was 

limited to only twenty channels, the excitation voltages on both the 

potentiometers and accelerometers were made common among each set. 

This resulted in nineteen channels being used. The other end of the slip 

ring hooked up to a 25 pin connector. A wire carried the signals from 

here to the data bus on the carriage. At this point, the accelerometer 

signals were picked up by a set of amplifier balances which provided 10 

volts of excitation per unit. The pitch sensor excitations were provided 

by onboard power supplies. Pitch signals were then fed directly into 

channels 7, 8, and 9 of the PDS-700 commutator. To allow lower 

sampling rates by electing to skip selected data frames (see chapter 21, a 

longer sample period could be achieved. This, however, required the 

accelerometer signals to be prefiltered to smooth them out and get rid of 

unwanted higher frequency information. Thus, the six accelerometer 

outputs were first fed through a variable cutoff frequency filter box ( with 

fcutoff set at 25 Hz 1, before being sent to channels 10 through 15 of the 

commutator. 

Other vital information was provided by the l/rev pulse and the 

ramp function, which were sent over channels 2 and 3, respectively. The 

output of a tachometer, located at the top of the monorail, was fed into 

channel 16. This device had previously been calibrated. To obtain 

accurate carriage position information, a position sensor was also used. 

It consisted of an infrared 

bottom of the carriage, facing 

emitter/detector pair mounted near the 

the near wall; Reflective tape which would 

47 
0 

e 

0 

e 

e 

a 

0 

trigger the sensor was attached at the same level on every support post 

along the track. The resulting data from this setup were pulses at exactly 

every ten feet of carriage travel. This signal was then scaled to TTL 

levels and fed into channel 17 of the PDS-700 unit. 

4.2 Test procedure 

With all vital sensors hooked up and ready, the data sampling stage 

was nearing. First, the dip switches corresponding to channels to be 

sampled on the buffer box were turned on. With the data acquisition 

system powered, as well as the card bus and sensors ( carriage plugged 

into wall socket ), the model rotor was powered up. This was achieved 

with a variac located in the control room. It was connected to two rails 

running the length of the track. As was mentioned in chapter 2, there 

were two sets of four rails, the lower of which used to power the carriage. 

The two rails for powering the model were the lower two of the upper 

set. This power, again, was picked up via sets of brushes. Rotor RPM 

was adjusted using this variac, with a digital RPM readout available in 

the control panel. While the rotor was spinning, each data channel was 

checked at the buffer box with an oscilloscope. This procedure allowed 

better balancing of the accelerometer signals. It also verified that all 

channels were in working order, and tests could begin. 

First, a file of data was written before powering up the rotor. This 

would provide a zero for the strain gauge signals. After providing power 

to the rotor, and 295 RPM were reached, according to the RPM indicator, 

the DMA2FILE program was used to write additional data. Two samples 

were taken at hover with no pitch inputs. Two more sets were taken 

while inputting random cyclic pitch commands. The next step was to 

power up the carriage and do forward flight tests. Carriage power up and 

48 

e 
e 

rn 

0 

operating procedures are explained in reference 7. Four data sets were 

written, two at flight velocities of 5 ft/sec and two at 10 ft/sec. Two 

additional sets were taken during transition from hover to forward 

flight. The forward flight tests at this point required two operators, one 

for carriage control on the track, and the other for data acquisition inside 

the control room. It is a future goal to be able to control both these 

processes from inside the control room. 

After eleven sets of data were successfully written, the first day of 

sampling came to an end. The facility was powered down with the 

exception of the PDS-700 commutator which was to continue providing 

power to the sting balance ( to prevent harmful moisture from 

accumulating on it >. Results from this test are described in the 

following chapter. 

e 

l 

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49 
e 

CHAPTER 5 

Results and conclusions 

a 

5.1 Resulting data and post-processing 

Having made several data runs, enough results were obtained to 

verify the usefulness of the model and facility. Some important test 

conditions can be summarized as: 

1) rotor RPM: 4.05 Hz 

2) forward flight velocity : 5 ft/sec 

3) advance ratio : 0.08 

4) ol(bending) / R = 1.38 

5) %(bending) / R = 4.80 

a 

0 

I 

0 

Figures 5.1 through 5.18 show time histories from the helicopter model 

and its rotor. First, a ramp signal verifies that lock of the data 

transmission link was maintained, yielding good data in that sense (fig. 

5.1). A l/rev clock shows rotor speed to be 4.05 Hz (fig. 5.2). Although 

noisy, the tachometer signal (fig. 5.3) shows approximately 5 ft/sec flight 

velocity. The noise on this signal due to an unknown source occurs at 

about 80 Hz. A possible solution to this problem may be to filter the 

signal before transmitting it. Figures 5.4 through 5.6 show pitch angles 

of each blade. It is important to note that these were input via a radio 

transmitter and just happened to be more negative than positive. This 

fact should be reflected in the measured forces and moments and 

actually is in figure 5.15. Here, the z-force, defined positive in the 

downward direction, is more positive than negative, as expected. 

Comparing the plots, it can be seen that the second and third blades lag 

50 
e 

e 

e 

a 

a 

the reference blade by 1 /3 and 2/3 revolutions, again as expected. Figures 

5.7 through 5.10 are the out of plane accelerometer signals. For reference, 

the accelerometers were numbered 1 through 6, 1 being at the root and 6 

at the tip as shown earlier in figure 3.10. According to this scheme, 

sensors number 2 and 5 corresponded to in-plane measurements. The 

figures show larger accelerations near the tip than the root, expressed in 

g's. This makes sense, as does the fact that the further outboard lead-lag 

sensor response is larger than the inboard one. Figures 5.13 through 5.18 

show the measured forces and moments. Periodicity in each of these 

signals can be attributed to residual rotor unbalance. The high frequency 

noise which is embedded in all the signals is due to an unknown source. 

The roll, pitch and yaw moment responses all show oscillation about an 

average positive value. This is consistent with expected results. When a 

hingeless rotor is subjected to forward velocity, it will tilt back and right 

resulting in hub moments causing positive pitch and roll. Since there 

was no power on the tail rotor, rotor torque reactions imparted a positive 

yawing moment. 

The accelerometer signals could now be used with a kinematic 

observer to estimate rotor states. Figures 5.7 through 5.12 show the raw 

accelerometer responses. Eventhough these signals went through a filter 

before being transmitted, some high frequency noise still managed to slip 

by, as is evident by the signals. Thus, they were filtered again using a 

low-pass filter with a 25 Hz break frequency. Figures 5.19 through 5.22 

show the results of this step on the out of plane accelerometer outputs. 

Using these responses and constructing the modal sensitivity matrix as: 

b 

1 0. 743 0.273 - 7.294 -4.330 

6. 011 2.526 - 11.312 - 18057 

13. 931 7.056 27.904 - 12.763 

20.506 11 810 79.674 2.259 

51 

e 
0 

e 

0 

e 

0 

a 

the measurement vector [ p p g g IT was determined. This was done by 

pre-multiplying the filtered accelerometer responses by the inverse of 

the modal matrix. These measurements could now be used in 

determining first and second bending mode position and velocity 

estimates. Feeding back the error between position measurements and 

estimates to the position and velocity estimates and integrating the 

acceleration measurements, the desired states were propagated. To use 

the position error feedback, feedback gains had to be chosen for all four 

states. In the case of first mode position and velocity, low enough gains 

needed to be used such that higher frequency information in the 

measurements was filtered out. Resulting gains used for these two states 

were 3 and 4, respectively, to set the speed of response of the observer to 

less than 2/rev. In the case of the second mode, this was not necessary. 

Here, the gains used were 30 and 10 for second mode position and 

velocity, respectively. Figures 5.23 and 5.24 show the first mode position 

and velocity estimates. The position estimates are somewhat suspect. 

Realistically, not much more flap position than approximately 0.2 

radians was expected. Adjusting the feedback gains may yield better 

results. Figure 5.25 shows the actual modal acceleration measurements 

which were used in determining the state estimates. The second mode 

position and velocity estimates are shown in figures 5.26 and 5.27. The 

position estimates show more realistic amplitudes, not exceeding 3 

degrees. Again, the second mode acceleration measurements used in 

determining these states are shown in figure 5.28. 

Having knowledge now of p, i/Q, p/Q2, g, g/Q, g/Q2, and 8, where 

p and g represent first and second modes, the flap equation and bending 

equation coefficients from 

a 

52 

? 

e 
0 

0 

e 

e 

0 

could be determined using a recursive weighted least-squares technique 

utilizing a UDUT factorized error covariance matrix. This method, 

which is more thoroughly explained in reference 18, would yield more 

accurate results than a standard least squares fit. Another advantage it 

has over the least squares fit is that it doesn't require large data storage 

which makes it more realizable in application. To determine the 

coefficients mentioned above, they first had to be broken down into their 

constant and harmonic parts, since in forward flight they are not 

constant but periodic. Since additional terms in the flap and bending 

equations due to torsional effects were not modeled, additional periodic 

terms were added( C(t) and D(t) ). Complete flap and bending equations 

can be found in [19]. The individual constant coefficients could then be 

determined using the recursive estimation method. 

The non-dimensional flap spring and damping coefficients as 

shown in the flap equation above, were determined. Figures 5.29 and 

5.30 show the resulting estimates. The spring coefficient was expected to 

be oscillating slightly about a value equaling the first mode frequency 

ratio squared, approximately 1.9. According to reference 19 the damping 

coefficient should be oscillating slightly about a value of approximately 

0.5. The actual results, however show functions oscillating about 4.4 and 

2.0, respectively ( these were the values which the constant parts of the 

coefficients approached ). This may be due to poor state estimates from 

the kinematic observer, or coupling effects on the measurements by 

torsional modes ( the first torsional mode.natura1 frequency was found 

in reference 11 to be approximately 40 Hz 1. The oscillations are also 

53 

i 
e 

e 

e 

much larger than expected. The first mode pitch forcing coefficient as 

shown in figure 5.31 was expected to oscillate about a value of about 0.5 

according to reference 19, but didn't. In this case, the oscillations were 

about a value of approximately 0.1. 

From bending equations in reference 19, non-dimensional second 

mode spring and damping coefficients were expected to oscillate about 

values of approximately 16 and 0.6, respectively. Figures 5.32 and 5.33, 

however, show disagreement with these values. The constant part of the 

estimated spring coefficient settled down at an unrealistic value of about 

-0.4 while that of the damping coefficient approached 0.003, nearly zero. 

Oscillations of the damping coefficient were expected to be between about 

+/- 0.05. Actual results oscillated at larger amplitudes. The second mode 

pitch forcing coefficient was expected to oscillate with an amplitude of 

between approximately +/- 0.01 about a value of approximately 0.5 [19]. 

The actual results oscillate with about double that amplitude about a 

value close to zero, 0.004. 

Although not totally obvious from the figures, almost all the 

constant parts of each estimated coefficient had not actually settled to 

constant values at the end of the estimation routine. Thus, it may be 

possible to increase quality of the results by simply allowing more time 

for the estimates to settle down. 

There are a number of other possible causes for why the resulting 

coefficient estimates didn't agree with theory. The fact that the flap 

position estimates were suspect to begin with is only one. The quality of 

results for this state estimate could possibly be increased by using more 

optimal feedback gains in the kinematic observer. The same goes for the 

other states as well. By not modeling any pitch accelerations due to blade 

lead-lag in the sensor geometry, the actual measurements may become 

suspect. Thus, another solution to the problem may be to include that 

54 

i 
component in the sensor geometry. 

e 

a 

0 

a 

1 

5.2 Conclusions 

Having performed the tasks discussed in this paper, several 

conclusions may be drawn: 

(1) The data acquisition system upgrade at the Princeton 

Rotorcraft Dynamics Laboratory has made high speed data sample rates 

possible as well as real-time data monitoring. These are two essentials 

for performing any type of high frequency active helicopter control 

experiments. 

(2) Froude scaled model rotor blades were made yielding 

frequency ratios of 1.3 and 3.4 for first and second out-of-plane bending 

modes at R = 8 Hz, respectively. Active control experiments in the 

future, however, will likely require a rotor speed of approximately 5 Hz, 

in order to reduce necessary sampling and actuator bandwidths. To 

achieve frequency ratios near 1 and 3 for the two bending modes at lower 

RPM, tip masses or distributed masses could be added to the existing 

blades. Another way to obtain the natural frequencies would be to find a 

new, softer material for making the blades. 

(3) Current actuators' bandwidths were too low for active 

control, however, they were sufficient for trimming the rotor and 

providing a means for introducing random pitch inputs into the model. 

For the rotor spinning near 5 Hz, a useful actuator will be expected to be 

able to input +/- 1 degrees of pitch at a minimum of 20 Hz. Thus, the 

search for a more capable actuator will continue. 

(4) Very time- and cost-effective methods for making scaled 

rotor blades and constructing a helicopter test model were developed. 

Lack of a professional full-time staff for making the test articles forced 

55 
e 

this kind of approach. 

(5) Experimental data show that rotor states can be estimated 

using accelerometer mounted rotor blades. Quality of the results may 

possibly be improved through optimal feedback gain computations in 

the kinematic observer or by including pitch acceleration in the sensor 

geometry. Since the point of this experiment was to illustrate the data 

capabilities of the model rotor, lots of fine tuning can be done to the 

process to yield better results. These state estimates could then be used to 

do more accurate system identification using the procedures discussed. 

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NON-DIMENSIONAL SPRING COEFFICIENT 

85 
t 

z 

w 

H 

0 

H 

a 

0 

m 

u) 

. 

a 

H 

lL 

T: 

i? 0 

i 

I 

i 

i 

I 

1 

I 

I- 

> 

*---.+-.+ 

P 

I N 

I 9 tu 0 

NON-DIKEtSIONAL DAKPING COEFFICIENT 

86 
H 

0 

LL 

IH 

n 

ILL 

a 0 

0 0 0 

NON-DIMENSIONAL PITCH FORCING COEFFICIENT 

87 
h 

E 

H 

v1 

1 

i 

H 

Ir. 

< 

I I 

-c) .h 7 + c--* + I 1 0 0 0 

NON-DIHENSIONAL SPRING COEFFICIENT 

88 

H 

x 

I- 

‘L C- 
(u 

TA 

i 

I 

I 

I 

0 

0 

0 

e 

e 

c 

a 

1 

k-- 

(u 

0 

a 

I 

RW-D I KEIZS IONAL DAWI~G COEFFICIE 

89 

NT 
iH 

e 

k- -T 0 I 0 0 

0 

a 

0 0 0 

I 

NON-DIMENSIONAL PITCH FORCING COEFFICIENT 

90 
References 

a 

e 

a 

6) 

Fay, John, The Helicopter; history, piloting and how it flies, David & 

Charles, Inc., North Pomfret, Vt, 1976. 

Shaw, John, Albion, Nicholas, Hanker, Edward J. Jr, and Teal, 

Richard S., Higher Harmonic Control: wind tunnel 

demonstration of fully effective vibratory hub force suppression, 

Journal of the AHS, January, 1989. 

Johnson, Wayne, Helicopter Theory, Princeton University Press, 

1980. 

Bramwell, A. R. S., Helicopter Dynamics, Edward Arnold Ltd, 

London, 91 76. 

Putman, W., Curtiss, H. Jr., and Lapins, M., Low Speed Testing 

Techniques for V/STOL Aircraft in the Princeton Dynamic Model 

Track, Proc., AIAA 17th Aerospace Sciences Meeting, New Orleans, 

La, January, 1979. 

McKillip, Robert M. Jr., Active control rotor model testing at 

Princeton's Rotorcraft Dynamics Laboratory, 2nd International 

Conference on Rotorcraft Basic Research, University of Maryland, 

Md, February, 1988. 

Demko, Michael G., High Speed Data Acquisition for the Princeton 

University Dynamic Model Track, Master's Thesis, MAE 

Department, Princeton University, Princeton, NJ, November, 1987. 

McKillip, Robert M. Jr., Experimental Studies in System 

Identification of Helicopter Rotor Dynamics, 14th European 

Rotorcraft Forum, Milano, Italy, September, 1988. 

Technical Manual, PDS-700-45, manual # M-4247, AYDIN VECTOR, 

31 January, 1985. 

91 
e 

e 

e 

e 

e 

Technical Manual, PAD-400-2, manual # M-4054, AYDIN VECTOR, 

31 January, 1985. 

Hardy, Greg, Analysis and Design Methodology for Aeroelastic 

Model Construction, Senior Independent Work, MAE Department, 

Princeton University, Princeton, NJ, January, 1988. 

Halvorsen, William G., and Brown, David L., Impulse Technique 

for Structural Frequency Response Testing, Cincinnati, Ohio. 

Yntema, Robert T., Simplified Procedures and Charts for the rapid 

Estimation of Bending Frequencies of Rotating Beams, National 

Advisory Committee for Aeronautics Technical Note 3459, Langley 

Aeronautical Laboratory, Langley Field, Va, June, 1955. 

Meirovitch, Leonard, Elements of Vibration Analysis, McGraw-Hill, 

Inc., USA, 1986. 

McKillip, Robert M. Jr., Criteria for Determining the Spanwise 

Position of Flatwise Accelerometers on the Blades of the NASA 

Ames RTR Model Helicopter, January, 1987. 

McKillip, Robert M. Jr., Kinematic Observers for Active Control of 

Helicopter Rotor Vibration, Vertica, Volume 12, No. 1/2, pp. 1-11, 

1988. 

Moroney, M. J., Facts from Figures, Cox & Wyman Ltd., Landon, 

1951. 

Stengel, Robert F., Stochastic Optimal Control, John Wiley & Sons 

Inc., 1986. 

Ham, N. D., Helicopter Blade Flutter, AGARD Report No. 607, 

January, 1973. 

92 
APPENDIX 

93 
SET IS0 ZUP 

NOTE ASSIGN Y-VALUES AT EACH DATA POINT TO VARIABLES USED FOR 

NOTE COMPARISONS LATER ON 

V2=-.12004 

V3=-.11606 

V4=-. 10588 

V5--. 09126 

.V6=-. 07328 

V7=-.05246 

V8--.02896 

V9=-.01614 

V10=-.00252 

.WINDOW XA:< 0 8 > YA:< 0 5 > ZA:< -3 3 > 

V12-. 6 

.V13-. 8 

V14-1.0 

V15-1.2 

V16-1.4 

V17-1.6 

V18-1.8 

v20-2.0 

NOTE ASS 

*v19=1.9 

GN ‘E! iUES T INT START 

NOTE OVER IN .05 IN STEPS UP TO 30 

NG FROM TRAILING EDGE MOVI 

% OF THE AIRFOIL 

NOTE START LOOP FOR FIRST 29 SETS OF POINTS 

n 

J 

NOTE V21 IS THE Y-VALUE ALONG THE CHORD DIRECTION FROM 2 TO 0 

v21-2.0 

v22=20 

NOTE V11 REPRESENTS THE POINT NUMBERS FROM 1 TO 80 

v11-1 

*NOTE v22 IS THE # USED TO CHECK AT WHICH POINT WE ARE 

DO 20 

0 v22=v22-1 

UI’TIL ( V22 < 12 ) 

DO 10 

UNTIL ( V21 < V(V22) ) 

V(23)=V22-10 

V(25)=V22-9 

V(27)-V22+1 

V(26)-((((V(V23)-V(V25))/(V(V22)-V(V27)))*(V2l-V(V27)))+V(V25)) 

V( 24)=V11+80 

P(Vll)-XA:l YA:(V21) ZA:(V26) 

P(V24)=XA:7 YA:(V21) ZA:(V26) 

v11=v11+1 

V21=V21-.05 

a 

0 EKDDO 

ENDDO 

NOTE NOW START THE SAME PROCEDURE FOR THE LAST 30 % OF AIRFOIL 

V1=-. 0249 

V2=-,03788 . V3=-.0523 

V4=-. 0711 

V5=-. 004 

V6=-.09366 

V7--. 1069 

V0=-. 11474 

V9=-.11882 

V10=-.12004 

V11=. 01214 

A- I 

0 
V12-. 025 

aVl3-. 05 

V14=. 1 

V15=. 15 

V16=. 2 

V17-. 3 

V18=. 4 

v19=. 5 

*V20-. 6 

V21-. 6 

v22-20 

Vll-29 

DO 20 

v2 2-v22-1 

DO 12 

0 UNTIL ( V22 < 12 ) 

UNTIL ( V21 < V(V22) ) 

V( 23 )=V22-10 

V(25)-V22-9 

V(27)-V22+1 

V(26)-((((V(V23)-V(V25))/(V(V22)-V(V27)))*(V2l-V(V27)))+V(V25)) 

V(24)=V11+80 

P(Vll)=XA:l YA:(V21) ZA:(V26) 

P(V24)=XA:7 YA:(V21) ZA:(V26) 

Vll-V11+1 

v21-v21-.012 

0 

ENDDO 

0 ENDDO 

P77sXA:l YA:.025 ZA:-.03788 

P157=XA:7 YA:.O25 ZA:-.03788 

P78=XA:1 YA:.01214 ZA:-.0249 

P158=XA:7 YA:.O1214 ZA:-.0249 

P7gnXA:1 YAz.0027 ZA:-.01285 

@P159=XA:7 YA:.OO27 ZA:-.01285 

P80sXA:l YA:O ZA:O 

P160=XA:7 YA:O ZA:O 

NOTE START THE MILLING PROCEDURE 

HOME XA+4 YA+1 ZA+3 

V7-1 

DO 3 

'IF ( V7 = 1 ) 

V6-. 065 

V5-20 

ELSE 

ENDIF 

IF (V7-2) 

@ V6=.01 

V5-20 

ELSE 

ENDIF 

IF ( V7 = 3 ) 

V6-0 

V5-10 

ELSE 

ENDIF 

TOOL #1 D.375 F(V5) 

TOOL #2 D.0625 F(V5) 

IF ( V7 = 1 ) 

ELSE 

D MOUNT #1 

A- 2 
COMP RIGHT 

V1-81 

M10-(V6)IN 

DO 29 

V2-V1-80 

RAPID XA:7 

FEED P(V1) 

0 FEED P(V1) P(V2) 

RAPID ZA:l 

Vl=V1+1 

ENDDO 

COMP OFF 

HOME 

0 ENDIF 

MOUNT #2 

COMP RIGHT 

V3-30 

M10=(V6)IN 

DO 51 

V4 =V3+ 8 0 

RAPID XA:1 

FEED P(V3) 

FEED P(V3) P(V4) 

RAPID ZA:l 

V3-V3+1 

ENDDO 

COMP OFF 

HOME 

V7-V7+1 

ENDDO 

DONE 

.. 

e 

A- 3