section l i f t - c u r v e slope
SYMBOLS.
section l i f t - c u r v e slope a radians lateral component of blade cyclic feathering motion, *1 thrust coefficient CT C blade chord, in.
virtual hinge o f f s e t , i n .
e V mass moment of i n e r t i a about v i r t u a l hinge, slug-ft2 Southwell c o e f f i c i e n t f o r f i r s t flapwise mode e f f e c t i v e spring s t i f f n e s s a t v i r t u a l flapping hinge, in-lb/radian KVF e f f e c t i v e spring s t i f f n e s s at v i r t u a l l a g hinge, in-lb/radian KvL longitudinal component of r o t o r hub moment, in-lb M A lateral component of r o t o r hub moment, in-lb MB blade chordwise bending moment, in-lb
Mc
moment about v i r t u a l l a g hinge, in-lb EavL t i p Mach number 4 i P blade weight moment about root end, in-lb M, a i r c r a f t r o l l i n g angular velocity, radians/sec P a i r c r a f t pitching angular velocity, radians/sec R blade radius, in.
t time, sec velocity along f l i g h t path, mph V simulated f u l l - s c a l e velocity along f l i g h t path, mph Vs i m blade first-mode flapwise deformation, r o t a t i n g , in.
WIR I ~ X r a t i o of blade element radius t o blade radius amplitude of blade first harmonic flapping angle with respect t o shaft axis, radians amplification f a c t o r l a g response coefficient blade Lock number blade b c k number, based on v i r t u a l lag hinge, pacd/Iv damping coefficient i n first mode load f a c t o r blade collective pitch angle, radians first harmonic cyclic blade pitch, radians t o t a l blade t w i s t , radian rotor t i p speed r a t i o , V/RR blade first chordwise mode natural frequency, rotating, radian/sec blade first chordwise mode natural frequency, nonrotating, radian/sec nondimensional o f f s e t of v i r t u a l hinge density of atmosphere, slugs/ft 3 blade first mass moment about v i r t u a l hinge, slug-ft azimuth phase angle of first harmonic blade flapping angle, degree azimuth phase angle of first harmonic blade cyclic feathering, degree azimuth phase angle of cyclic control input, degree blade azimuth position, degree r o t o r rotational speed, .radians/sec normal operating rotor rotational speed, radians/sec blade f i r s t flapwise mode natural frequency, rotating, radians/sec .
%R blade f i r s t flapwise mode natural frequency, nonrotating, radians/sec WlS GENERAL CRARACTERISTICS O F HINGEU3SS ROTOR The hingeless rotor i s sometimes referred t o as a "rigid" rotor system.
While t h i s terminology focuses a t t e n t i o n on t h e primary difference between hingeless and a r t i c u l a t e d rotors, it must be recognized t h a t , i n f a c t , it i s t h e use of f l e x i b i l i t y t h a t i s t h e key t o t h e successful u t i l i z a t i o n o f t h e hingeless-rotor concept. From t h e standpoint of s t r u c t u r a l loads and dynamics, the hingeless r o t o r represents a fundamental change from dealing with t h e a r t i c - ulated blade dynamic response i n the rigid-body pendulum mode t o dealing with t h e cantilever blade dynamic response i n t h e first bending mode. Certainly a rigorous treatment of e i t h e r configuration would d e a l with higher order bending modes, but it i s the nature of t h e first-mode response c h a r a c t e r i s t i c s that determines the fundamental differences i n t h e two r o t o r systems.
Blade Flapping Response A comparison of hinged and cantilever blade first-mode natural frequencies as a function of r o t o r speed i s shown i n figure 1. A curve of t h e first-mode n a t u r a l frequency i n t h e flapwise degree of freedom, as a function of r o t o r r o t a t i o n a l speed, i s given f o r each of t h r e e uniform blade configurations: (1) zero-offset hinged blade, (2) conventional o f f s e t hinged blade, and ( 3 ) a t y p i c a l cantilever blade. Also shown are t h e first-mode shapes f o r t h e three configurations. The frequencies and mode shapes shown i n figure 1 were obtained from reference 1. While t h e mode shapes f o r t h e hinged rigid-body modes a r e not influenced by r o t a t i o n a l speed, t h e cantilever mode i s a l t e r e d somewhat by cen- trifugal stiffening, which reduces the curvature over t h e outboard portion of t h e blade.
From the standpoint of r o t o r control and response, t h e predominating force inputs a r e occurring a t once-per-rotor revolution. A t y p i c a l source of such once-per-revolution force inputs i s t h e aerodynamic force r e s u l t i n g from r o t o r The governing equation of motion f o r t h e flapping degree of cyclic control.
freedom response t o cyclic control input i n hovering f l i g h t is:
$1 PI, s t a t i c
- = rl
81 81
h, s t a t i c
( 3 )
@e,l = tan' 1
Substitution of t h e natural frequencies am and mode shapes wm a t normal operating r o t o r speed from figure 1 i n t o the above equations w i l l give the r e l a t i v e response characteristics of the hinged and cantilever blades.
Assuming the blades a r e i d e n t i c a l i n uniform mass d i s t r i b u t i o n and aerodynamic characteristics, the r e l a t i v e response characteristics a r e shown i n figure 2.
The three-blade configurations are being forced at a frequency a t o r s l i g h t l y above t h e i r n a t u r a l frequency and t h e r e s u l t s indicate t h a t the r e l a t i v e ampli- tude responses of the three blades are very nearly t h e same. Therefore, the cantilever r o t o r blade deforms l i k e a hinged blade and i s f a r from being a s t r u c t u r a l l y "rigid" blade.
In t h e case of t h e phase response of the three blade types, it can be seen i n figure 2 t h a t the cantilever blade phase response i s quite different from that of t h e hinged blades. The hinged blades have phase-angle response equal t o o r close t o 90 degrees. However, the flapping deformation of the cantilever blade l a g s the force input by only 60 t o 70 degrees. It should be noted t h a t the cantilever blade phase l a g i s f a r f r o m that of a t r u l y r i g i d r o t o r which would have a phase l a g of zero degrees. Due t o the difference i n phase-angle response t h e control phasing must be retarded from the conventional 90 degrees t o t h e order of 60 degrees. This "retardation," indicated on figure 2, must * be incorporated i n t o t h e cantilever r o t o r control system i n order t o eliminate large, undesirable cross-coupling i n r o t o r response t o lateral and longitudinal control inputs.
Another area where t h e reduced phase-angle response of t h e hingeless r o t o r requires attention i s i n regard t o r o t o r p i t c h and r o l l angular-velocity damping. Here again, the force inputs t o t h e blade associated with r o t o r angu- l a r velocity i n p i t c h and roll originate from once-per-rotor-revolution gyro- scopic and aerodynamic sources. The result i s that t h e basic hingeless-rotor i s a l s o cross coupled i n t h e lateral and longitudinal angular-velocity response directions. I n other words, a longitudinal (pitching) angular velocity pro- duces a l a t e r a l rotor moment as w e l l as t h e d i r e c t longitudinal r o t o r damping moment.
Analytical Methods In order t o treat t h e control and damping response of t h e hingeless-rotor system i n a r e l a t i v e l y simplified manner and t o u t i l i z e conventional r o t o r analysis, the cantilever blade can be replaced by an equivalent o f f s e t hinge blade, which i s considered as a r i g i d body, with spring r e s t r a i n t a t t h e hinge as shown i n f i g u r e 3 . The equivalence i s derived and described i n reference 2.
The equivalent o f f s e t blade i s established on t h e b a s i s of t h e cantilever blade mode shape, nonrotating natural frequency, and r o t a t i n g natural frequency. The equivalent o f f s e t i s established t o give t h e approximate bending-mode shape and Southwell coefficient, o r frequency rise factor, of the cantilever blade. The equivalent o f f s e t i n nondimensional form i s given by I n order t o provide complete dynamic equivalence some hinge spring r e s t r a i n t i s required and t h e spring constant i s such as t o give a nonrotating hinged-blade natural frequency qS equal t o t h a t of t h e nonrotating canti- lever blade. The spring constant i s given by This spring r e s t r a i n t a t t h e hinge w i l l be representative of t h e l e v e l of can- tilever s t r u c t u r a l s t i f f n e s s . For a typical case t h e contribution of t h i s s t r u c t u r a l stiffness t o t h e t o t a l r o t a t i n g blade s t i f f n e s s i s about 5 percent of t h e t o t a l . In other words, t h e centrifugal force f i e l d s t i l l provides t h e even f o r t h e cantilever system. There- major portion of' flapwise stiffening, fore, f o r the flapwise degree of freedom, t h e c a n t i l e v e r blade deformations and t h e influence of centrifugal force on t h e deformed blade a r e e s s e n t i a l l y the same as f o r a conventional o f f s e t hinge blade.
However, it i s necessary t o include t h e hinge spring i n t h e equivalent blade treatment so t h a t t h e I cantilever blade mode shape, flapping angles, n a t u r a l frequencies, blade response phase angles, and root bending moments can be simulated properly.
I With t h e equivalent o f f s e t and spring r e s t r a i n t established on the basis , of the cantilever blade first-mode characteristics, the cantilever blade root moments and effective flapping angles can be calculated using conventional l I hinged-rotor analysis. The first harmonic blade root moments and phase angles calculated using the equivalent o f f s e t blade and spring r e s t r a i n t w i l l be equal I I t o the first harmonic cantilever blade root moments and phase angles. This equivalence i s a l s o derived i n reference 2.
I
In general, the cantilever blade flapping response w i l l result i n effec- 1 t i v e blade flapping angles p1 which are very nearly equal t o those of conven- t i o n a l offset hinged blades. I n contrast t o the s i m i l a r i t y i n the amplitude a most significant difference between the hinged and canti- of blade motion, lever blade i s the magnitude of the moments transmitted t o the rotor shaft.
The effective offset and spring r e s t r a i n t of the cantilever blade serve t o develop large moments a t the rotor hub. The magnitude of these moments a r e of an order-of-magnitude greater than those normally associated with hinged-rotor systems.
, I Rotor Moment Characteristics The control-moment and angliLar-velocity damping-moment characteristics of
'
a hingeless-rotor system can be calculated using the concept of an equivalent hinged blade with an 8- t o 12-percent offset and with spring r e s t r a i n t a t the hinge.
The conventional o f f s e t hinged-blade flapping equations can be used with suitable modifications t o account f o r the hinge spring r e s t r a i n t .
The results of sample calculations are shown i n figures 4 and 5 f o r an
The longitudinal and l a t e r a l hub equivalent offset value of 10 percent.
moments, i n nondimensional form, are presented f o r a range of blade Lock num- ber and blade nonrotating first-mode natural-frequency r a t i o , "IS/". Current cantilever blade designs have a nonrotating flapwise frequency r a t i o of CDJS~" on t h e order of 0.2.
Figure 4 indicates that the d i r e c t longitudinal moment per degree of lat- eral blade cyclic feathering input is accompanied by l a t e r a l , o r cross coupled, moment. For a given value of qs/!i'l the amount of cross coupling varies with blade h c k nmiber 7 due t o t h e a f f e c t of aerodynamic damping on phase response. This indicates that there w i l l be variations i n control-moment Figure 5 presents d i r e c t response associated with large changes i n a l t i t u d e .
Here again, and cross-coupled rotor pitching-velocity darnping-moment trends.
the moment response i s cross coupled and strongly influenced by blade Lock num-
ber f o r any given value of mis indicates there w i l l be a l t i t u d e
q s / Q .
e f f e c t s on t h e angular-velocity damping-moment response of the rotor.
cross coupling l i e s i n some form of While t h e solution t o control-moment control input "retardation," the solution t o cross-coupled angular-velocity damping may require careful selection of blade s t i f f n e s s and Lock number or the.
use of some feedback system which i s sensitive t o a i r c r a f t angular velocity.
The rotor control-moment and damping-moment capability indicated i n figures 4
%/a, are an order-of-magnitude and 5, even f o r blades with low values of greater than conventional helicopter r o t o r capability. This increased moment capability was demonstrated during t h e wind-tunnel t e s t s of a f u l l - s c a l e hingeless-rotor helicopter a t the NASA-Ames Research Center. The r e s u l t s of t h i s investigation are presented i n reference 3 . This increased moment capa- b i l i t y suggests t h a t c a r e f u l a t t e n t i o n must be given t o t h e blade root and rotor hub s t r u c t u r a l loads.
FLIGHT INVESTIGATION I n order t o proceed with an exploratory f l i g h t investigation with a hingeless-rotor system, N A S A purchased from B e l l Helicopter Company a duplicate of an existing s e t of experimental hingeless-rotor components. The configura- t i o n w a s i d e n t i c a l t o t h a t of t h e r i g i d hub r o t o r described i n reference 4.
The t e s t a i r c r a f t i s shown i n figure 6.
T e s t Aircraft, Instrumentation and Procedure The basic a i r c r a f t w a s an Army H - l 3 G helicopter. The standard t e e t e r i n g r o t o r and t h e control linkage above t h e swashplate were removed and replaced by t h e experimental three-bladed hingeless-rotor system. The rotor blades were modified H - l 3 H m e t a l blades. The modification consisted of removal of a sec- The resulting r o t o r radius t i o n of blade t i p and adding a 12-pound t i p weight.
w a s l9O inches with t h e m d i f i e d blade mounted on an experimental r o t o r hub, as shown i n figure 7.
The hub was i n t e n t i o n a l l y overdesigned so as t o provide generous margins of safety.
The principal feature of the main r o t o r blade p i t c h control linkage arrangement was t h e phasing used between t h e control inputs a t t h e swashplate This phasing w a s reduced from and the feathering a x i s of t h e r o t o r blades.
the usual 90 degrees t o 62.5 degrees and corresponds t o a control "retardation" of 27.5 degrees. This "retardation" w a s discussed i n general i n t h e first sec- t i o n of t h i s paper, i n connection with c a n t i l e v e r blade response, and w a s i l l u s t r a t e d i n f i g u r e 2. No a r t i f i c i a l s t a b i l i z a t i o n devices were used during the investigation and t h e horizontal s t a b i l i z e r , normally used on t h e H - 1 3 a i r c r a f t , was removed p r i o r t o beginning t h e t e s t program.
Since the principal innovation i n t h e hingeless-rotor-system concept i s the capability t o t r a n s f e r large moments from t h e r o t o r system i n t o t h e hub and r o t o r shaft, a t t e n t i o n w a s focused on t h e measurement of t h e s t r u c t u r a l bending moments i n t h i s area.
The blade root, hub, r o t o r shaft, and control linkages were the primary components selected f o r strain-gage instrumentation.
Flight-test instrumentation w a s a l s o i n s t a l l e d f o r the measurement of t h e nec- These param- essary parameters t o document t h e a i r c r a f t ' s f l y i n g q u a l i t i e s .
e t e r s included a i r c r a f t angular v e l o c i t i e s and control positions.
The test program consisted of 1 4 hours o f operation. During the program, data were obtained f o r various ground and f l i g h t operating conditions. I n gen- eral, the f l i g h t conditions investigated included l e v e l f l i g h t throughout the forward speed range, autorotation, verticaldescents, steep turns i n l e v e l and autorotative f l i g h t , abrupt maneuvers, and slope take-offs and landings.
Control Characteristics While the documentation and analysis of t h e a i r c r a f t flying q u a l i t i e s are treated i n references 5 and 6, a b r i e f mention of the a i r c r a f t ' s control char- a c t e r i s t i c s i s included here i n order t o i l l u s t r a t e the influence of r o t o r dynamics on t h e flying-qualities evaluation. The response of the hingeless- rotor system was very rapid when compared t o the response of t h e typical articulated-rotor system a s i l l u s t r a t e d i n the right-hand portion of figure 8.
Because of the t i g h t response, the p i l o t received e a r l y and c l e a r evidence of t h e angular velocity developed by a given control input. The measured control power and damping values a r e an order-of-magnitude greater than conventional a r t i c u l a t e d rotors. This comparison i s presented i n t h e right-hand portion of This increase i n control power and damping i s a l s o reflected i n the figure 8.
calculated values f o r t h e H-13 hingeless rotor a l s o shown i n figure 8. This calculated control power and damging was obtained using the equivalent-offset flapping blade approach discussed i n t h e first portion of t h i s paper. The new l e v e l of control and response capability led, u l t i m t e l y , t o t h e performnce of more abrupt and more severe maneuvers, hence, d i r e c t l y influencing the s t r u c t u r a l loads experienced.
While t h e overall l e v e l of control power and damping improved s i g n i f i - cantly, t h e presence of cross coupling i n the pitch and r o l l response was noted by the p i l o t and was borne out by the measured response t o purely longitudinal- The measured response t o a longitudinal- and lateral-control step inputs.
control s t e p input and t o a lateral-control step input i s shown i n figure 9.
This figure i s i n the form of p l o t s of a i r c r a f t pitching angular velocity versus r o l l i n g angular velocity resulting from u n i t step inputs i n the longi- t u d i n a l d i r e c t i o n and i n t h e l a t e r a l direction. The curves may be viewed as representations of v a r i a t i o n i n magnitude and direction of t h e resultant air- c r a f t angular velocity following t h e control step inputs. A s previously men- tioned, t h e i n s t a l l e d control retardation was 27.5 degrees. Also shown on the figure, f o r comparison purposes, a r e t h e calculated response curves based on the r e s u l t s of the equivalent-offset blade analysis and t h e coupled pitch and r o l l equations of motion f o r t h e a i r c r a f t .
The most significant points t o be noted here are (1) the difference i n t h e phasing between i n i t i a l angular-velocity response and final steady-state angular-velocity direction and (2) the dropoff i n t h e f i n a l measured roll angular-velocity response. The shift i n response phase w a s due t o cross cou- p l i n g during the maneuvers and the s h i f t w a s p a r t i c u l a r l y objectionable t o the p i l o t , especially i n t h e r o l l maneuvers. The large reduction i n the f i n a l r o l l angular v e l o c i t y indicated by the measured data i n figure 9, i s a t t r i b u t e d t o a strong dihedral effect, which was not included i n the calculated curves. The calculated response curves, including 27.5 degrees control retardation, compare reasonably well with the measured results. The calculated curves, without con- t r o l retardation included, indicate that very undesirable response characteris- t i c s would be expected.
The r e s u l t s of t h i s investigation suggest t h e need f o r careful attention during the detailed design of a hingeless-rotor system so a s t o minimize the e f f e c t s of cross coupling. This w i l l involve careful selection of blade s t i f f n e s s , Lock number, control retardation and t h e possible use of an angular-velocity feedback system.
Structural Loads The objective of the s t r u c t u r a l loads portion of t h i s investigation w a s t o sample a l l the p r a c t i c a l ground and f l i g h t operating conditions i n an e f f o r t t o identify those conditions which require most immediate and detailed study. The rotor system possessed control capability of s u f f i c i e n t l y large magnitude t o cause concern over the large-amplitude cyclic loadings that could be induced i n the primary structure of the a i r c r a f t . The following discussion t r e a t s some of the more significant r e s u l t s of the s t r u c t u r a l loads investigation.
Ground operation.- The ground-operation investigation was limited t o observing the trends i n the rotor-blade and rotor-shaft bending moments. Due t o the fact t h a t the rotor shaft was designed f o r use with a teetering rotor system, t h e allowable cyclic bending-moment amplitude w a s established a t 1500 foot-pounds on the basis of rotor-shaft fatigue t e s t data. Inasmuch as the hingeless-rotor system had the capability of producing hub moments on the order of 1200 foot-pounds per degree of cyclic control input, extreme care had t o be exercised by the p i l o t t o keep the cyclic s t i c k centered during ground run-up and l i f t - o f f . It w a s necessary f o r the p i l o t t o anticipate t h e cyclic t r i m position during t r a n s i t i o n from the ground t o $he airborne condition i n order t o avoid large transients i n rotor-shaft cyclic bending moment.
Structural loads trends were observed during slope take-offs and landings.
It was determined t h a t the best control technique t o minimize cyclic bending moments i n the rotor system w a s t o apply almost full collective control p r i o r t o bringing the a i r c r a f t t o a l e v e l a t t i t u d e with cyclic control. The reverse control sequence was used i n slope landings. In addition t o p i l o t technique, there a r e a number of available approaches toward t h e reduction of the rotor shaft bending moments, such a s reducing gear tread width, but it w i l l require specific design attention.
Flight loads.- The i n - f l i g h t s t r u c t u r a l loads encountered are considered
i n two categories - first, those measured i n l e v e l f l i g h t and, second, the
loads measured i n maneuver f l i g h t .
Level f l i g h t : The level-flight s t r u c t u r a l loads i n primary rotor compo- nents a r e summarized i n figure 10.
Although t h e t e s t rotor was fabricated from standard articulated components (except f o r the hub i t s e l f ) , the measured loads experienced i n l e v e l f l i g h t throughout the speed range were not above the design "fatigue l i m i t " f o r these components. "Fatigue l i m i t " I S defined a s the cyclic load amplitude which r e s u l t s i n a fatigue l i f e equal t o lo8 cycles.
I *Manewer f l i g h t : During the t e s t program, structural. loads were monitored carefully a s the f l i g h t envelope w a s expanded i n order t o assure safety of f l i g h t . In general, the high loadings were not of a c r i t i c a l nature, and the I increase i n load l e v e l with severity of the maneuver was certainly not unex- pected, especially with regard t o rotor shaft and blade flapwise bending moments. The s t r u c t u r a l loading of most concern was the "in-plane," o r chord-
I
w i s e bending moments induced i n the r o t o r blades. The amplitude of the rotor blade chordwise cyclic bending moment was very sensitive t o maneuvers i n which high a i r c r a f t angular v e l o c i t i e s were developed.
I n some instances the ampli- ~ tude of t h i s loading expanded well beyond the s t r u c t u r a l fatigue l i m i t , during
I
p i t c h and r o l l maneuvers that w e r e w e l l within t h e control capability of the a i r c r a f t .
The buildup of cyclic chordwise blade bending moment with a i r c r a f t angular velocity occurred i n pitch and roll maneuvers throughout the forward speed This is i l l u s t r a t e d i n figures 1 1 and 12, where sample time h i s t o r i e s range.
mast bending moments are presented f o r a hovering maneuver and of the blade and a maneuver a t a forward speed of 70 knots.
The r e l a t i v e magnitudes of t h e and mast bending moments a r e not presented t o scale i n chordwise, flapwise, these figures. The s w l e loads measurements presented i n figure 1 1 are f o r I the hovering maneuver where t h e p i l o t executed a longitudinal control step dis- placement and recovery. During the period of maximum pitching angular veloc- i t y , the buildup of t h e cyclic chordwise bending moment reaches a m a x i m I amplitude which is above t h e s t r u c t u r a l fatigue l i m i t of the blade. The oscil- I l a t o r y flapwise bending moments increased i n amplitude during t h e recovery maneuver, but do not show the degree of s e n s i t i v i t y t o the maneuver exhibited by the chordwise bending moment. The mast moments during the i n i t i a l portion I of t h e maneuver do not build up due t o the application of a control moment because the i n i t i a l control moment cancels a moment due t o minor center-of- gravity o f f s e t . during the recovery, where the control moment and I However, I the o f f s e t center-of-gravity moment add, the cyclic mast moments reach a maxi- mum during maximum angular acceleration.
The s i t u a t i o n a t a forward speed of 70 knots i s shown i n figure 12. Again the chordwise bending moment shows the large buildup with a i r c r a f t angular Continuous operation velocity and again above the s t r u c t u r a l fatigue llmit.
at t h i s load l e v e l would r e s u l t i n a 10-hour fatigue l i f e f o r t h i s rotor blade.
I n contrast t o the loads measured i n hovering and the 70-knot maneuver condi- t i o n s a r e the loads measured during a maneuver performed i n autorotation. I n t h i s s i t u a t i o n there w a s a complete lack of chordwise cyclic bending-moment buildup, even though an angular velocity of 0.4 rad/sec was obtained. This autorotation case involved low blade coning and reduced blade flapwise cyclic bending moments .
From the standpoint of s t r u c t u r a l loads, the s e n s i t i v i t y of the blade cyclic chordwise bending-moment amplitude t o maneuvers w a s t h e primary concern Therefore, the principal goal of the analytical i n the flight investigation.
work of t h i s investigation was t o establish the relationship between rapid a i r c r a f t maneuvers and the high-amplitude chordwise bending moments.
ANALYSIS OF MANEWER LOADS A theoretical analysis of the oscillatory chordwise bending moments during maneuver conditions was performed using an extension of the equivalent offset hinged-blade analysis.
In this case the equivalent offset and hinge spring restraint were determined for the lagging degree of freedom and the moment equation about the virtual lag hinge was derived for the maneuvering conditions.
A s a result of an assumption of identical first bending mode shapes for the flapwise and lagging degree of freedom the effective lag hinge offset is iden- tical to the flapping hinge offset and the lag hinge spring constant is:
(9)
KVL = % V l S The results of this analysis indicate that, for a given configuration, the blade oscillatory chordwise bending moment buildup during maneuvers is primarily dependent upon the amplitude and phase relation between blade flapping deformation p 1 and blade cyclic feathering motion 8 1 as follows: where An example of how the flapping deformations and feathering motions combine to give large-amplitude chordwise bending moments is illustrated in figure 13.
This figure is a polar plot of the recovery portion of the pitch maneuver in
hover shown in figure 11. The polar plot shows the p 1 , el, %,1 situation
at the time of maximum nose-down pitching angular velocity or approximately the
19th revolution in figure 11. The pl, el, and Q,l values presented in
figure 13 have been nondimensionalized by dividing by their respective maximum values during the maneuver, and the resulting values are indicated by the .
symbols in the figure. The blade flapwise bending moments, and therefore the flapwise deformations ply are occurring in the azimuth region of 270 degrees.
These lateral flapping deformations result in maximum flapping velocities in the vicinity of zero degrees azimuth. These flapping velocities, in turn, induce blade cyclic chordwise moments primarily as a result of Coriolis effects.
The maximum blade feathering motion required to perform the recovery maneu- 8,- ver occurs at an azimuth of approximately 320 degrees.
The calculated values of blade chordwise moment, a l s o in a nondimensional form, are shown in figure 13 by the heavy dashed lines. The direct aerodynamic induced chordwise moment is in-phase with the feathering motion and the Coriolis induced chordwise moment is in-phase with the flapping velocity, which is 90 degrees ahead of the flapping deformation. The resultant calculated chord- wise moment, also shown in figure 13, compares reasonably well with the meas- ured maximum chordwise moment amplitude and phase angle.
A detailed comparison of calculated and measured chordwise bending-moment amplitude and phase-angle time histories was performed for the hovering maneu- ver and the 7O-knot maneuver case of figure 12. The difference between the maximum measured and calculated chordwise moment amplitude was approximately 15 percent of the maximum measured amplitude. The agreement obtained in these comparisons indicates that the equivalent offset method is adequate for first- order estimates of the more significant structural loading problems of the hingeless-rotor system. Examination of the autorotation case indicated that the theory would predict low-cyclic chordwise moments in the maneuver, which is in agreement with the measured results.
A s noted in equation (lo), the amplitude of the blade chordwise bending
qL, and this
moment is proportional to blade chordwise structural stiffness offers a means of alleviating the chord load sensitivity to maneuvers by reducing the blade chordwise stiffness.
DYNAMIC MODEL INVESTIGATION A s part of the hingeless-rotor research program, Langley has taken part in a cooperative effort involving U . S . Army, Lockheed Aircraft, and NASA. This program has involved the design, construction, and wind-tunnel testing of a 1/3-scale hingeless-rotor helicopter model, which was aeroelastically scaled.
The model rotor was 1 0 feet in diameter. The program proceeded in three phases.
The first-phase testing was done in Langley 30-foot by &-foot full-scale tun- nel and the second- and third-phase testing was done in the Langley 16-foot The results and analysis of the testing are pub- transonic dynamics tunnel.
lished in references 7 and 8 .
A considerable number of dynamic configurations were tested during the Research information of general interest resulting from the program program.
included structural load and aerodynamic data for the various rotor configura- tions. Rotors tested included those with twisted and untwisted blades; three-, four-, and six-blade rotors; and variations in blade flapwise and chordwise stiffness and stiffness distribution. Each of these configurations was tested through a forward-speed and load-factor g range simulating conventional heli- copter and compound helicopter operation.
Structural Loads Seven rotor configurations were tested in the Langley 30-foot by 60-foot full-scale tunnel. These tests covered a simulated speed range from hovering to 120 miles per hour and load factors up to 2.5g. A photograph of the model The rotor con- installation in the tunnel test section is shown in figure 14.
figurations tested were all 3-bladed and the blades were of wide chord giving a rotor solidity of 0.12. The testing in the full-scale tunnel was done to study a variety of rotor dynamic configurations at low and moderate forward speeds prior to testing selected configurations at high forward speeds in the transonic dynamics tunnel. The model was dynamically scaled in all respects except Mach number and Reynolds number for the initial testing.
Some of the highlights of the structural loads results from the full-scale In part (a) of each figure tunnel testing are shown in figures 1 . 5 , 16, and 17.
curves are shown for three rotor configurations inlg trimmed flight conditions.
One configuration represents conventional blade design with a blade cantilevered from the rotor hub which had a very high chordwise stiffness relative to its flapwise stiffness. The second configuration was the same blade with a reduced chordwise stiffness at the root achieved by using a flexible drag link. The stiffness of the drag link was such that the static deflection of the blade tip under a tip load was equal in both the flapwise and chordwise direction. The third configuration was such that along the entire blade the chordwise struc- tural stiffness was approximately equal to the flapwise blade stiffness.
The variation in oscillatory blade torsional load throughout the speed range is shown in figure l ? ( a ) . The corresponding variation in the magnitude of cyclic flapwise bending moment is shown in figure 1 6 ( a ) . There were no sig- nificant influences of chordwise blade stiffness or stiffness distribution in the case of the torsional and flapwise moments. From the standpoint of struc- tural loads, the most significant result of the testing is shown in figure 17(a) which shows the amplitude of cyclic chordwise moment at the blade root for l g flight over the simulated speed range. A s indicated in the figure, there is a large increase in chordwise cyclic load with increasing speed for the conven- tional blade (that is, for a blade with high chordwise stiffness and low flap- wise stiffness).
By using a flexible drag link at the blade root to reduce the blade chordwise stiffness to match the flapwise stiffness a large reduction in A n even chordwise cyclic loading was obtained over the entire speed range.
greater reduction in the loads was achieved by matching the chordwise stiffness to the flapwise stiffhess along the entire blade.
While the results presented in part (a) of figures 15, 16, and 17 are for
lg flight, the effects of variations in load factor were investigated and the
15, 16, and 17. A s indicated in
results are presented in part (b) of figures figure l 7 ( b ) , large reductions in blade chordwise cyclic bending moments were again obtained with the introduction of chordwise flexibility.
part of t h i s paper ( f i g s . 1 1 and 12). A s indicated i n equation (10) and demon-
The introduction of blade f l e x i b i l i t y as a means of reducing chordwise s t r u c t u r a l loading may o f f e r t h e solution t o t h e problem of high cyclic chord- wise moments experienced i n the flight-test maneuvers mentioned i n the first part of t h i s paper ( f i g s . 1 1 and 12). A s indicated i n equation (10) and demon- s t r a t e d i n the wind-tunnel-test results t h e blade chordwise s t i f f n e s s i s QL a primary f a c t o r i n determining t h e magnitude of t h e chordwise cyclic loading.
Therefore, a reduction i n blade chordwise s t i f f n e s s w i l l r e s u l t i n a reduction i n blade s t r u c t u r a l bending moments. Care must be taken t o achieve t h i s stiff- ness reduction, without s u b s t a n t i a l reduction i n chordwise section modulus, especially i n t h e r o t o r hub region, so that the net r e s u l t is a decrease i n blade stress levels. This can be handled by proper selection o f materials, cross-section configuration, and s t i f f n e s s d i s t r i b u t i o n along the blade. The b e n e f i t s of increased chordwise f l e x i b i l i t y will apply t o both steady f l i g h t conditions and t o manewer conditions since t h e key t o t h e reduced s t r u c t u r a l moments i s t h e centrifugal relieving moments developed on a f l e x i b l e blade.
Additional Wind-Tunnel Tests Following completion of the model tests i n t h e f u l l - s c a l e tunnel a t scaled forward speeds up t o 120 mph, t h e model was t e s t e d i n t h e Langley 16-foot tran- sonic dynamics tunnel. I n these t e s t s the model was reballasted and t e s t e d i n Freon at a density of 0.008 slug-per cubic f o o t and dynamic and aerodynamic The scaling was achieved including Mach nmiber and Reynolds number similitude.
model is shown i n s t a l l e d i n the transonic dynamics tunnel i n figure 18. The basic configuration t e s t e d w a s t h e 3-blade r o t o r with matched root flapwise and chordwise blade stiffness. Aerodynamic and s t r u c t u r a l load data w e r e obtained with simulated forward speeds from 60 t o 240 mph and t i p Mach number up t o 0.91.
Conventional helicopter and compound helicopter modes of operation were sampled and the r e s u l t s a r e presented i n reference 7.
Additional tests w e r e made using a blade and r o t o r hub design optimized f o r low drag. The blades were of m r e conventional aspect r a t i o and t h e blade flapwise and chordwise s t i f f n e s s were approximately matched along t h e e n t i r e blade. Rotors with 3 , 4, and 6 blades were t e s t e d w i t h r o t o r s o l i d i t i e s of The 3-blade model configuration i s shown 0.06, 0.08, and 0.12, respectively.
i n figure 19. A s i n previous tests, s t r u c t u r a l loads and performance data were obtained f o r a range of load f a c t o r s and forward speeds i n t h e helicopter and unloaded r o t o r mode of operation. The following l i s t i n g represents the m a x i m operating conditions reached with the unloaded r o t o r configurations.
The data obtained i n t h e f i n a l phase of t e s t i n g are presented i n refer- , ence 8. The "optimized" r o t o r design with t h e l o w chordwise s t i f f n e s s blades shows considerable promise from the standpoint of s t r u c t u r a l loads, vibration and performance.
Ground Resonance One of t h e areas which requires careful investigation i n regard t o the reduced chordwise s t i f f n e s s blade design i s t h e ground resonance phenomenon.
Due t o the f a c t t h a t the blade "in-plane" first bending mode natural frequency falls below normal operating rotor speed, a coupling of t h e in-plane blade o s c i l l a t i o n w i t h body p i t c h or roll o s c i l l a t i o n may occur during runup o r This s i t u a t i o n corresponds t o t h e c l a s s i c a l "ground shutdown of the rotor.
resonance" experienced with hinged rotor systems. This coupling can a l s o Occur i n f l i g h t with t h e hingeless-rotor system, due t o t h e f a c t that t h e fuselage has a pitch and roll s t i f f n e s s as a r e s u l t of being spring mounted t o t h e r o t o r through the cantilever action of the blades. This r e s u l t s i n an "air resonance'' phenomenon, which i s equivalent t o t h e c l a s s i c a l ground resonance phenomenon.
A n extensive t h e o r e t i c a l analysis of t h e ground resonance phenomenon f o r the hingeless rotor has been carried out i n reference 9. This analysis included rotor aerodynamics, and t h e results of t h i s work, presented i n reference 10, indicate t h a t the coupled vibration mode can be s t a b i l i z e d without t h e addition of a r t i f i c a l damping. Basically, the studies reported i n references 9 and 10, and other investigations reported i n reference 11, indicate t h a t t h e presence of t h e rotor aerodynamics tends t o s t a b i l i z e the coupled response o f t h e r o t o r and fuselage. The s t a b i l i z i n g influence of aerodynamics results from the f a c t t h a t t h e aerodynamically damped blade flapping degree of freedom i s now cou- pled t o body p i t c h and r o l l degree of freedom through t h e cantilever action of t h e blades. The analyses indicate t h a t , i f t h e aerodynamics i s removed from the system, t h e dynamic response reverts back t o t h e c l a s s i c a l Coleman unstable ground resonance phenomenon.
During t h e t h i r d phase of model t e s t i n g i n t h e transonic dynamics tunnel, limited ground resonance type t e s t i n g w a s conducted i n a i r with t h e model bal- l a s t e d f o r t e s t i n g i n Freon. This resulted i n a dynamic simulation i n which aerodynamic damping forces, r e l a t i v e t o t h e mass and spring forces, were dimin- ished by approximately 60 percent. Under these conditions, cases of unstable "ground resonance" were encountered. I n order t o assure safe operation i n t h e tunnel the body p i t c h and roll frequencies were adjusted t o eliminate resonance when operating i n a i r a t normal r o t o r speed. Operation s t i l l involved passing through a rotor speed a t which body p i t c h n a t u r a l frequency coincided with blade chordwise natural frequency i n t h e nonrotating coordinate system. This situa- t i o n i s indicated i n figure 20 a t t h e i n t e r s e c t i o n of t h e body p i t c h frequency curve and t h e R - V ~ R ) curve.
I n t h e absence of aerodynamics t h i s point theo-
(
r e t i c a l l y corresponds t o a condition of unstable ground resonance. Subsequent operation i n Freon w a s carried out without experiencing unstable ground resonance.
.
.
2 4 thorough study of t h e ground resonance problem was not undertaken during the tunnel program; however, t h i s phenomenon w i l l require further investigation i n order t o conclusively establish whether the reduced chordwise s t i f f n e s s blade configurations can, i n fact, be operated over a wide range of conditions without encountering mechanical i n s t a b i l i t i e s of the ground resonance type.
CURRENT FLIGHT INVESTIGATION A s p a r t of the continuing hingeless rotor program, an XH-5lN helicopter, This a i r c r a f t is equipped with shown i n figure 21, has been purchased by NASA.
a 3-bladed hingeless rotor and represents an a i r c r a f t specifically designed t o u t i l i z e the hingeless rotor system. The a i r c r a f t has been completely instru- mented f o r handling qualities, performance, s t r u c t u r a l loads and dynamics inves- t i g a t i o n s and is being used as a general research vehicle. The new capability of the hingeless rotor system w i l l make it possible t o investigate the influence of increased levels of control power and damping on the handling q u a l i t i e s c r i - t e r i a of reference 12.
A s t r u c t u r a l loads investigation w i l l be conducted concurrently with the handling q u a l i t i e s program. The e a r l y portions of the s t r u c t u r a l loads program w i l l deal with the general nature of the loads encountered i n operation of the a i r c r a f t . L a t e r , specific f l i g h t conditions w i l l be flown t o investigate struc- t u r e s and dynamics problems i n d e t a i l .
CONCUTDING REevlARKs I n general, the f l i g h t , wind-tunnel and analytical investigations carried out t o date on the hingeless-rotor concept indicate there a r e d e f i n i t e improve- ments t o be gained by proper application of t h e principle. It has been shown that t h e system cannot actually be treated a s a "rigid" structure and, i n f a c t , i n t h e first flapwise mode it deforms much l i k e a hinged system. The improve- ments associated with the hingeless rotor s t e m from i t s simplicity and t h e capa- I n actually u t i l i z i n g the hingeless b i l i t y t o develop large rotor hub moments.
r o t o r design particular attention must be given t o the problems of (1) control and damping cross coupling (2) s t r u c t u r a l loads i n maneuvers, when using high chordwise blade s t i f f n e s s and (3) t h e avoidance of ground resonance type insta- b i l i t i e s , when using blades with low chordwise stiffness.
A s a result of the research conducted t o date, there appear t o be promising avenues open t o cope with the problems t h a t have been identified; however, con- It w i l l also tinuing research i s required t o explore these promising solutions.
be necessary t o expand t h e analytical and experimental investigations i n order t o provide sufficient design c r i t e r i a f o r the successful u t i l i z a t i o n of the ss-rotor system on advanced VTOL a i r c r a f t .
REFERENCES 1. Yntema, R. T.: Simplified Procedures and Charts f o r t h e Rapid Estimation of Bending Frequencies of Rotating Beams.
NACA TN 3459, 1955- 2. Young, D r . M. I.: A Simplified Theory of Hingeless Rotors With Application t o Tandem Helicopters. American Helicopter Society Proceedings of t h e Eighteenth Annual National Forum, Washington, D.C., May 2-4, 1962, PP* 38-45.
3 . McCloud, John L.; and Biggers, James C.: Full-scale Wind-Tunnel Tests Of Nonarticulated Helicopter Rotor. NASA TN D-2392, 1964.
at t h e 4. Cresap, W. L.: Rigid Rotor Development and F l i g h t Tests. Presented IAS 30th Annual Meeting, New York, New York, January 22-25, 1962.
5. Huston, Robert J.; and Tapscott, Robert J.: The Results of Some Wind Tun- n e l and F l i g h t Studies With Helicopters a t NASA. Presented a t New York Academy o f Sciences Conference on V e r t i c a l Take-Off and Landing Aircraft, New York, New York, December 10-12, 1962.
6. Ward, John F.; and Huston, Robert J.: A Summary of Hingeless-Rotor Research Presented a t t h e Twentieth Annual N a t i o n a l Forum of t h e a t NASA-Langley.
American Helicopter Society, Washington, D.C., May 13-15, 1964.
7. Hanson, T. F.: Investigation of E l a s t i c Coupling Phenomena of High-speed U.S. Army - TRECOM Technical Report 63-75. (Sub- Rigid Rotor Systems.
mitted under contract DA 44-177-'IC-929 by Lockheed-California Company, March 1964. ) 8. Hanson, T. F.: Wind Tunnel Tests of an Optimized, Matched-Stiffness Rigid Rotor. (Submitted under con- U.S. A m y - TRECOM Technical Report 64-56.
t r a c t DA 44-177-AMC-78( T) by Lockheed-California Company, November 1964. ) 9. Kanno, J. S.; and Lundgren, S.: Equations of Motion f o r t h e Dynamic Analysis of a Hovering Rotor Including Gyro Control System. Lockheed
California Company, LR 17185, June 1961. (Submitted under U.S. Army -
T m O M contract DA 44-177-TC-828.)
!
10. Kanno, J. S.; and Lundgren, S.: 10-Foot Rigid Rotor Model Basic Data and 1 Results of Hovering Cyclic S t a b i l i t y Analysis. I LR 16997, J u l y 1963.
(Submitted under U.S. Army - TRECOM contract DA 44-177-TC-828.) 1
11. Reed, Wilmer H.: Propeller Whirl F l u t t e r ; A State-of-the-Art Review. Pre- sented a t t h e Symposium on t h e Noise and Loading Actions on Helicopter V/STOL A i r c r a f t and Ground Effect Machines, University of Southampton, England, August 30 - September 3 , 1963.
12. Anon.: Military Specification - General Requirements f o r Helicopter Flying
and Ground Handling Qualities.
MIL-H-850lA, 1961.
i .
? -
x I k -P V -P Q) rn c I I- W
K!
IL .
x I
-
cu
00 * cu
c d 0 4
cu k O
a l
c3
3 'I
dun
-ttm
m
z
I al k H
\ =
r"
Figure 7. - Hingeless-rotor hub and slipring assembly.
pc
cn
cn
n n
w
n k
rq
0 -
' 2 -I c u O O o ( P ~ N 0 o c 0 I.
LL --M n
z
v, n h 0 I I a 3
n
W
U
m
P
a
d bo
w
t
rl a
-
I k
d 8
Fr
a
I I- W
z
z
(3 I -
i 5
Z W
m
W v,
3 LI
W
n
a
-I
m
I-
-
0 0 0
0 0
cu
(D d- 0 00
-
.
b
i
I \ J I
m
(3 W
z
I (3 Z
-
z
- .
a +
f
-
w 2 3
CL: I-
m 5
L z
z
in
i a
Qz LL
z
LL I A Q
a
W
ac
q
I I I I I I I I I I I I I I I
t
-10
0 0 0 M U 4J d PI M
I
U
I
I
U d
e
a
n
l-i P
n
W
a
v)
a
W
E
h I rn d a , a El h a -P k I a [I] a , aJ rl
cu
u . d rl
a
0 a , ul I- .rl
o t
9 - i 5
rl k Q a , a
a
a J rl
s P
w
m m a , FI k k rl c,
cu
\ \ m
a , m
‘5
a k I
“i) :I 2
a0
P
fl 4
P I- / k
0 0
4 J a ,
* d
k
‘ / \ k
>
w
I a , .rl Fr
i i
G
> -
c
$ 3 W
>
.
E : rn E :
E
4 . J I (u NASA-Langley, 19