Black Hawk Helicopter Vibration 

Analysis Due to Main Rotor Damage, 

Directional Constituents of the 

Resultant Vibrations 

by Joseph C. Fries 

ARL-TR-2442 March 2001 

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c 

Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5068 

ARL-TR-2442 March 2001 

Black Hawk Helicopter Vibration 

Analysis Due to Main Rotor Damage, 

Directional Constituents of the 

Resultant Vibrations 

Joseph C. Fries 

Survivability/ Lethality Analysis Directorate, ARL 

. 

Approved for public release; distribution is unlimited. 
Abstract 

Black Hawk helicopter cockpit vibrations due to main rotor damage are presented 

based upon an analysis and computer code originally developed in-house in the Air 

Systems Branch (ASB) of the U.S. Army Research Laboratory (ARL). Ballistic damage is 

simulated by removing various amounts of the outer radius of one blade of the rotor set 

of four blades. This simulated blade damage causes the rotor to be unbalanced 

allowing undesirable vibrations to be transmitted into the fixed-system airframe. This 

work considers the longitudinal, lateral, and vertical cockpit amplitude and phase 

components of the vibrations that make up the total vector vibrations that a cockpit 

occupant would feel. If the vibrations are severe enough, they could lead to attrition of 

the aircraft. This vibration data can be used in conjunction with historical humanvibration-tolerance data for later work toward determining a pilot’s capability to 

function in the helicopter cockpit vibration environment. 

ii 
Contents 

List of Figures 

List of Tables 

1. 

2. 

3. 

4. 

5. 

6. 

Introduction 

Presentation of Fixed-System Vibration Data 

Ranking of the Constituent Vibrations 

Discussion and Results 

Conclusions 

References 

Distribution List 

Report Documentation Page 

11 

15 

. . . 

ln 
INTE~I~NALLY LEFT BLANK. 

iv 
List of Figures 

. 

. 

Figure 1. Cockpit resultant vibrations G’s vs. percent of blade removed.. ......................... 

.2 

Figure 2. l/Rev cockpit constituent vibrations G’s vs. percent of blade removed. .......... .3 

Figure 3. 2/Rev cockpit constituent vibrations G’s vs. percent of blade removed. .......... .4 

Figure 4. 3/Rev cockpit constituent vibrations G’s vs. percent of blade removed. .......... .4 

Figure 5. 4/Rev cockpit constituent vibrations G’s vs. percent of blade removed. .......... -5 

Figure 6. 5/Rev cockpit constituent vibrations G’s vs. percent of blade removed. .......... .5 

V 
INTENTIONALLY LEFT BLANK. 

vi 
List of Tables 

Table 1. Directional vibration constituents.. ............................................................................. 6 

Table 2. Cumulative directional vibration constituents. ........................................................ 6 

Vii 
INTENTIONALLY LEFT BLANK. 

. . . 

vlll 
1. Introduction 

A helicopter-vibration computer code (RTVIBZO) was developed by the author [l] to 

analyze vibrations transmitted into the fixed system by a variety of main rotor-blade 

damages. In this present study, this code is used to investigate Black Hawk helicopter 

cockpit vibrations due to the removal of outer sections of one blade of the rotor set of 

four blades. Such a condition may be the result of ballistic damages. The cockpit 

vibrations are-examined in resultant form for each harmonic from l/Rev (revolution) to 

5/Rev and then in directional constituent cosine and sine form. The harmonic 

component of the vibrations (fixed system) can originate from harmonics in the rotating 

blade system that are either of the same harmonic number as transmitted to the fixed 

system or a rotating harmonic shifted l/Rev above or below the center frequency. 

When the set of rotor blades is undamaged, the blades are called “matched” and cause 

an effect known as “filtering” to occur. Filtering blocks certain frequencies from being 

transmitted from the blades into the fuselage (fixed system). Only blade frequencies 

that are integer multiples of the number of blades can be transmitted from the rotor 

blades to the fuselage. For instance, for the Black Hawk helicopter with four blades 

comprising the main rotor, only 4/Rev, 8/Rev, 12/Rev, etc., vibrations can be 

transmitted. 

However, if one or more blades are damaged thus making them have different physical 

properties from the others, all frequencies are transmitted into the fixed system that 

allows these unwanted frequencies to produce detrimental cockpit vibrations. These can 

cause structural fatigue and pilot-physiological debilitating effects. As an adjunct, 

historical human tolerance to vibration data can be integrated with the vibration data in 

this report to predict the effect on a pilot and his ability to continue to operate the 

aircraft. 

The RTVIB20 code is documented in U.S. Army Research Laboratory (ARL) report TR-75 

[l] and requires a GWBASIC compiler to execute. Later in 1996, RTVIB20 was updated 

to accommodate a helicopter tied to the ground with springs and dampers and named 

RTVIB21. Such a condition is applicable to helicopter ballistic vulnerability testing. 

For this study, the RTVIB20 computer code was run for a Black Hawk helicopter 

simulation at 25%rpm main rotor speed, 16,260-lb gross weight, 160&n forward speed, 

at a 4,000-ft pressure altitude, on a 95 “F day. 

2. Presentation of Fixed-System Vibration Data 

First, the resultant vibrations are shown in Figure 1 as G’s (gravitational pull) vs. percent 

of the removal of the outer blade section. 
0 

0 10 20 30 40 50 60 

%BladeRemoved 

Figure 1. Cockpit resultant vibrations G’s vs. percent of blade removed. 

There is a predominate 1 /Rev frequency getting through to the cockpit that ordinarily 

would be filtered out for undamaged blades of the set of four, and there is also a 

significant 2/Rev. The higher frequencies have low amplitudes, and it should be noted 

that the $/Rev would be the only frequency transmitted if no damage were present. 

Next, the individual harmonics are viewed one at a time, and the directional cosine and 

sine components are distinguished. In Figure 2, the legend is defined as follows: 

l LNC = Longitudinal Cosine Vibration 

l LNS = Longitudinal Sine Vibration 

l LTC = Lateral Cosine Vibration 

l LTS = Lateral Sine Vibration 

l VTC = Vertical Cosine Vibration 

l VTS = Vertical Sine Vibration 

From Figure 1, it was found that the l/Rev is the biggest resultant vibration, and the 

makeup in Figure 2 shows that the vertical cosine component is the biggest constituent 

followed by the lateral sine. The longitudinal cosine and vertical sine follow next in 

absolute amplitude. In a normal undamaged rotor, none of these l/Rev vibrations 

would occur for a 4-bladed rotor. 

2 
% Blade Removed 

. 

. 

Figure 2. l/Rev cockpit constituent vibrations G’s vs. percent of blade removed. 

Next in order are the 2/Rev vibrations illustrated in Figure 3. In a normal undamaged 

rotor, none of these 2/Rev vibrations would occur for a 4-bladed rotor. 

Next are the S/Rev vibrations illustrated in Figure 4. In a normal undamaged rotor, 

none of these 3/Rev vibrations would occur for a 4-bladed rotor. 

The 4/Rev vibrations are illustrated in Figure 5. Notice that the vibrations for the 

undamaged blade (at 0% blade removed) are not zero. This is significant and points to 

the fact that 4/Rev is an integer number of the blades in the rotor and is not filtered out; 

it is an inherent vibration that always exists. Also notice that the amplitudes of these 

inherent vibrations are relatively low compared to the 1 /Rev that exists when a blade is 

damaged. These are inherent 4/Rev vibrations that are always present in the cockpit for 

a 4-bladed rotor. 

Finally, the 5/Rev vibrations are illustrated in Figure 6. The amplitudes are very small, 

which is as expected for the higher frequencies. Therefore, there is no need to continue 

to list the higher frequencies. None of these vibrations would occur for an undamaged 

4-bladed rotor. 

3 
-0.1 iii~~ii~~““““““““” 

Figure 3. 2/Rev cockpit constituent vibrations G’s vs. percent of blade removed. 

0.08 

0.07 

0.06 

0.05 

0.04 

0.03 

0.02 

0.01 

0 

-0.01 

% Blade Removed 

-+VTC 

- LTC 

LNC 

*LNS 

“VI-S 

- LTS 

-LTS 

-VTS 

LTC 

*w-c 

-LNS 

-LNC 

Figure 4. 3/Rev cockpit constituent vibrations G’s vs. percent of blade removed. 

4 
% Blade Removed 

Figure 5. 4/Rev cockpit constituent vibrations G’s vs. percent of blade removed. 

% Blade Removed 

Figure 6. 5/Rev cockpit constituent vibrations G’s vs. percent of blade removed. 

5 
3. Ranking of the Constituent Vibrations 

In order to make sense of the data, ranking is needed for the constituent vibrations to 

determine which are the dominant vibration directions for each harmonic. Table 1 ranks 

the data with 6 representing the largest amplitude and 1 representing the smallest 

amplitude for each harmonic. 

Table 1. Directional vibration constituents. 

To get an idea which direction occurs most frequently among all the contributors from 

Table 1, a cumulative number can be determined by adding the weighted numbers for 

each direction. This number is calculated and shown in Table 2. 

Table 2. Cumulative directional vibration co.nstituents. 

Direction Cumulative Weight 

LTS 27 

VTS 21 

VTC 21 

LTC 16 

LNC 13 

LNS 7 

From Tables 1 and 2, it can be seen that the lateral and vertical vibrations are dominant, 

but the longitudinal vibrations are relatively unimportant. 

6 
4. Discussion and Results 

From Figure 1, it is seen that the dominant cockpit vibration comes from l/Rev, which is 

the frequency of the main rotor (1 x 258 rpm) followed by the IL/Rev (2 x 258 rpm) in 

amplitude. As the frequency increases, the amplitude of vibration decreases as would 

be expected except if there is no resonance in the system. A separate study would be 

needed to determine how these vibrations might fatigue the structure of the aircraft or 

affect a pilot’s ability to fly the aircraft. 

As the damage of one blade of the rotor set increases by increasingly more of the outer 

blade being removed, the vibrations get worse as would be expected. All of the 

vibrations except the $/Rev go through the origin of the charts because, in the 

undamaged state, the frequencies are filtered out and are not transmitted to the fuselage. 

This is the natural state of the helicopter. The only natural inherent vibration of an 

undamaged helicopter are the 4/Revs. 

Figure 1 shows the cockpit vibration to be above 2 G’s for the high-speed condition with 

half of one blade’s outer portion lost. Further performance analysis would be needed to 

determine the helicopter’s residual capability to survive or the pilot’s capability to 

perform. Helicopter first principles can be found in works by Chopra [2], McCormick 

[3], and Saunders [4]. 

5. Conclusions 

This analysis demonstrates an analytical capability to predict helicopter fixed-system 

vibrations to be used in the survivability estimation of rotary wing aircraft. It uses first 

principles of physics to develop a viable analysis and computer code and can be used in 

conjunction with structural analysis and human-vibration tolerance data to determine 

the performance state of a helicopter after suffering main rotor damage. 

7 
8 
6. References 

1. Fries, J. “Helicopter Forced Response Vibration Analysis RTVIB20.” ARL-TR-75, 

U.S. Army Research Laboratory, Aberdeen Proving Ground, MD, 1992. 

2. Chopra, I. “Notes on Helicopter Dynamics.” University of Maryland, 1992. 

3. McCormick, B. Aerodynamics of V/STOL Flighr. New York, NY: Academic Press, 

Inc., 1967. 

4. Saunders, G. Dynamics of Helicopter Flight. New York, NY: John Wiley and Sons, 

Inc., 1975. 

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED 

March 2001 

I Final, 1992 - 2001 

4. TITLE AND SUBTITLE 

Black Hawk Helicopter Vibration Analysis Due to Main Rotor Damage, lL162618AH80 

Directional Constituents of the Resultant Vibrations 

6. AUTHOR(S) 

Joseph C. Fries 

7. PERFORMING ORGANIZATIONNAME AND ADDRESS 

U.S. &my Research Laboratory 

Al-IN: AMSRL-SL-BD 

Aberdeen Proving Ground, MD 210055068 

B. PERFORMING ORGANIZATION 

REPORT NUMBER 

ART/TR-2442 

9. SPONSORlNGa’MONlTORlNG AGENCY NAMES(S) AND ADDRESS IO.SPONSORINGIMONITORlNG 

AGENCY REPORT NUMBER 

11. SUPPLEMENTARY NOTES 

12a. DlSTRlBUTION/AVAILABlLrrYSTATEMENT 

Approved for public release; distribution is unlimited. 

13. ABSTRACT(Maxlmum 200 words) 

12b. DISTRIBUTION CODE 

Black Hawk helicopter cockpit vibrations due to main rotor damage are presented based upon an analysis and 

computer code originally developed in-house in the Air Systems Branch (ASB) of the U.S. Army Research Laboratory 

(ARL). Ballistic damage is simulated by removing various amounts of the outer radius of one blade of the rotor set of 

four blades. This simulated blade damage causes the rotor to be unbalanced allowing undesirable vibrations to be 

transmitted into the futed-system airframe. This work considers the longitudinal, lateral, and vertical cockpit 

amplitude and phase components of the vibrations that make up the total vector vibrations that a cockpit occupant 

would feel. If the vibrations are severe enough, they could lead to attrition of the aircraft. This vibration data can be 

used in conjunction with historical human-vibration-tolerance data for later work toward determining a pilot’s 

capability to function in the helicopter cockpit vibration environment, 

14. SUBJECTTERMS 

helicopter, vibrations 

115. NUMBER OF PAGES 

I& 

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OF REPORT 

UNCLASSIFIED 

NSN 7540-01-280-5500 

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