An overview of a mechanical rotor control design is presented. Operation at constant RPM and rapid response are obtained by using blade pitch moments for both sensing control need and blade pitch actuation. The basic concept, static or equilibrium design, and dynamic analysis are briefly presented

Currin, H.

English

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NQRJH WIN l) _4K W 'PASSIVE' CONTROL SYSTEM DESIGN
Hush Currin
Foehn consultinl
Box 51Z3
Klamath Falls, OR G7S01
i
The control system described here is Part of a
SWECS desisn done for North Mind Power Co. under
= a RocKwell/DOE contract. The machine, as now
conFisured is a 10 meter, down wind, HAMT rated
at 6KW B 8uls, It is a line interface unit using
a direct drive synorcnous alternator. The rotor
is a t_o bladed, teeterins systee with delta
z three and uses solid laminated wood blades. The
syst_Free yewins on a euyed wooden Pole tower.
An o_er_iew o¢ a Mechanical rotor control desisn is Presented. OPeration at constant
RPH and rapid response are obtained by usins blade Pitch moments For both sensins
_n_rol need and blade Pitch actuation. The basic concept, static or equilibriu_
deslsn, and dynamic analysis are briefly presented.
ansle at each wind speed. The rotor POWer
output, beans dependant on wind speed and Pitch
angle, is determined by this Ho Function.
Fisure ] also shows the blade center of sravity
offset Frou the rotor axis. This aires a
Positive (+8) eitchine MoMent due to rotor
ansular velocity which results in sensitivity to
rotor opersPeed.
The Point ocntroI is an all mechanical system
which re,Ponds to blade aerodynamic loads and
RPH. Po_er and load controTisacoomPIished
S th_oug_ [1rode eitohins in the direction of
Feather with shot down beans Full Feather.
9tartire copes froe an inboard blade twist.
CONCEPT
The coF_trol systee concept is to choose blade
Pitch _nsle in response to blade Pitch Moment.
The blades ape then sensors transmittins control
information, and also suPPlying control actuation
Force, via blade Pitch Moment. Pitch moment,
throuah Placement of the Pitch axis, is made
sensitive to aerodynamic and centrifugal forces.
-- This c_ntrol can thus be used with a rotor
opera'ins atconstant, synchronous/ReH while
still prcpldins Protection asainst overseeed
conditions.
Fisure 1 shows the PitCh axis Placement at one
radial station. Aerodynaetc Lift, the
-- eredQu_nant blade Force, will create a PitChing
aoment throush offset Xa. Equilibrium is
obtained by aPelyina the control moment Hc. For
a gipe_ _ind speed there is one equilibrium Pitch
angle 8, For exsaPle, assume S is increased from
an equilibrium POSition, then the airfoil angle
of attack will decrease, reducins the coefficient
of l|#_ and thus Lift Force. The aerodynamic
moment is now less then the control Moment which
actuates a blade Pitch, decreasins B, until
equilibrium is again reached. This aerodynamic
restorins Force _aintaios equilibrium.
For constant RP_ operation a choose in wind
speed _ill mope the systea to a new equilibrium
Pitch _ngle. The Predominant effect of an
in_rease in wind speed is an increase in ansle of
attac_ _hich increases the lift coefficient and
Li_t f_rce. This difference between aerodynamic
and control MoMents will tend to increase the
Pitch _nsle until a new equilibrium Point is
reaohe_.
The control eolent Rc is a Function of Pitch
ansle _nd will determine the equilibrium Pitch
STATIC DESIGN
Static Design of this control systeminPolves s
trade-off between rotor secmetry, control moment
characteristics, desired POWer curve, and
resultins unloaded equilibrium ovsrsPeed. Fisure
2 represents the Final seometric layout of the
rotor.
To eualuate this analytically a Blade Element
Theory For aerodynamic Forces (Per 1) is combined
with a simple field _ody model for rotational
effects. A Plot For constant rotor RPH is maven
in Fisure 3. Here the Pitch aoMent, or
equilibrium control _oeent, is siusn as a
Function of Pitch angle For constant _ind speeds
sn_ rotor POWer outputs. Flsure 4 Presents the
same tyPe of PlOt For zero Power output,
remresentins the unloaded control response.
Equilibrium Performance is determined by these
Plots, With control moment siren as i Function
of PitCh ansle the resoltins Power, unloaded RPH,
and blade Pitch are defined as Functions of _ind
speed. Assuaed control Moment curves are
Presented in Fisures 3 and 4 as dotted lines.
Trade-oFFs to obtain desireeble static
Performance characteristics involve adjusting
rotor aeoeetry, control moment Function, and
associated structure. Since t_ese involve
constraints such as manufacturability and
conceptual deslsn they don't lead to explicit
evaluation.
hERDELASTIC
The torsional stiffness of this blade-hub
system is inherently very low heine Predominantl_
Frc_ the aerodynamic restorine force Mentioned
earlier, Because of this the rotor is suscePtable
to aeroelastio instabilities.
Modes _hich involve in-plane motions shouldn't
be excited d_e to the high natural frequencies in
this desree of Freedom, Followins this
reasonins, Problems of sround resonance and whirl
modes aren't anticipated, h teeterins s_stem
with Free yaw is not Prone to these Problems
(ref 2).
265
https://ntrs.nasa.gov/search.jsp?R=19820015838 2020-03-21T17:04:22+00:00Z
This leaves Pitch/flap instabilities which •re
of concern. By studying the rotor Mode shapes
and noting pitch deflections are concentrated •t
the pitch axis • single blade analysis can be
Justified.
Out-of-plane vibration modes can be classified
into two groups as either invo!vins or not
involving teeter. Figure 5 shows the first Four
out-of-plane mode shapes for a teetering rotor.
The first and third (5•, 5c) involve • teetering
motion ,ith the Flap deflections of each blade
opPoOltte. Conversely, the second and third (5b,
5d) involve no teetering deflection and have
identical Flap deflections. Control pitch
deflections, due to mechanical requirements of
the pitch linkage, change the pitch angles of
each blade by the Same amount.
Pitch/Flap instabilities involve an
aerodynamic coupling of the •bore control pitch
and out-of-plane deflections. The •bore then
,ould require instabilities involving teeter
motians to have • different mode shape for each
blade. A |80 degree phase shift in Pitch/Flap
deflections ,ould have to occur. For this reason
instabilities which involve a teetering motion
are not anticipated. Other Pitch/flap
instabilities which involve cantilever
deflections are however possible.
Note that Pitch deflections due to • delta 3
angle, being directly coupled to teeter motions,
are not independant degrees of Freedom. This
delta 3 effect ,ill Further stabilize Modes which
involve teeter motions (ref 3,4).
Three simple analytic models have been used to
investigate Pitch/flap •eroelasic stability. All
involve rigid body, equivalent hinge
representations, The first being • "classic"
Form derived from the helicopter industry. It
incorporates 8uasi-Steadx, Theodorsen,
aerodynamics with constant chord and t,ist {Per
_,B). The second uses the same formulation but
assumes steady state aerodynamics. Figure G
shows a representation of the first t,o models.
The third model uses steady state aerodynamics
but includes soveril geometric improvements over
the first two. It includes twist and taper along
with hinge offsets to better approxiaate
geometric control characteristics. This model
was derived For time domain investigations of
control response. Figure 7 represents this
model.
Each of these analytic models can be presented
in matrix form as:
_' M_ M_J[_] M_ M_jLeJ LM_ M_Lej
The stability derivatives, here the matrix
elements, •re given in Table I for each of
the theoretical models. A numerical eigen value
approach was used to solve the unforced equations
for stability information.
A pitch/Flap instability .as predicted in each
case. An attempt has been made to understand the
parameters involved .ith this instability and
eliminate it. In doing so sole understanding of
the system and the models used has been gained.
U•riouu parameters were chansed to determine
.hioh have a significant effect on this
instability. This resulted in three parameters
being Flap natural Frequency, RPN, and pitch
damping. RPN is determined by the static desian
and .as KePt as small •s reasonable. This leaves
Flap n•tur•1 Frequency and Pitch daiplns For
adjustment. F/sure 8 shows stability plots for
each of the three an•lyrical models. These are
calculated for running RPH and she, Flap natural
Frequency versus Pitch d•mping. The three agree
in gener•l, predicting the instability, but
differ quantitatively.
The flap natural frequency can be adjusted
but, without • change in blade sructure, this
Parameter o•n ndL be viried enough to stabilize
the system. Since pltoh deflections are
concentrated at the pitch axis daMPiflu can be
added. This solution ,as adopted although a
damper, being mechanical, can Fail and allow the
system to become unstable. A vibration shut down
is required. For reliability, dampers ire Placed
at the Pitch shape to •void linkage ,ear and
fatigue. Although havlns • iiflli•l llPact, Pitch
damping ,ill slow gust response.
Some insight can be gained •bout the three
analytical Models From the stability plots in
Figure 8. Note that the First two Models compare
,ell with the only difference due to
• erodynanics. The similarity of these Plots max
be lisle•dins due to the very low torsional
stiffness which tends to slow the actions and
minimize the differences between steady and
8u•si-steady aerodynamics. The steady state
assumption Is the more conservative. The third
model is considerably less stable than the first
t,o. The modeling differences bet,pen these are
the control offsets, taper, twist, and sweep but
it is not Known how much effect each has.
DYNAMIC RESPONSE
To assess dynamic control response the third
model, with its forcing Function, .•s solved in
the time domain. A numerical solution was used
to analytically model several wind gust cases.
Fiaure S sho.s Pitch and fl•p response for •
wind Must of 8 to 24 m/s in one second. This is
Felt to be an extreme suet which would be rarely
encountered. The control sYsteM is responding
within 1/4 second and the greatest out-of-Plane
load, corresponding to the greatest Flap
deflection, occurs at 1/2 second, This response
is Fast enough to relieve major blade loads. The
largest out-of-plane load encountered is near one
fourth the worst case load coming from high wind
shut down conditions.
The rapid response is inherent with this
control system. Translating blade loads into •
control Pitch involves only the Pitch inertia.
266
MOSt contro] systems sense a condition, such as
an RPH change, _hioh involves a Much iarser
inertia, Pitch damping, added For aeroelastio
stability, does slow response time but is a Minor
effect. The Plot presented in Figure S includes
this daMPing,
CONCLUSIONS
AnalySis of the control system is complex but
resutts in a relatiuely simple Mechanical system
with control response rapid enough to relieve
gusts. This comPlexitY is due to the
interdependence of rotor geometry, system loads,
dynaalc response and aeroelastin stability.
The siiP1e aeroi]astio Models used are not in
c|ose agreement. These simple Models are
LtPor%ant in 6HECS design Mhere large comPuter
codes are us.ally not cost effective.
Investigations to deterline the critical
parameters in these Models, and compare results
_ith test data, or the large computer codes
(raP 7), _ould be useful.
ACKNOMLEDGENENT
Recosnitlon is due Ji%o Coleman, North Mind
Po_e_ Co. and Hoody Stoddird, Stoddard Consulting
For oo]aboration in this concept and design.
REFERENCES
1Hil_on,R.E., Lissaian,B.S., "ApPlied
A_rodynaitos oF Hind Poxer Machines', Oregon
State Univ., NTIS P6238594, July 1974.
Sh_,D.T., "EFFects of Tower Notion on the
DynaMic ResPonse of HindliII Rotors', HS
Thes_s, Dept. of Aero. & Astro., HIT, Feb. 1977.
3 Brl_well_ARS, "HelicoPter Dynaaios', Miley &
Sons, 1978.
4 Sto_dard,F.S., "Structural DynaMics,
Szzility and Control oF High Aspect Ratio Hind
Turbines', RocKwell/DOE contract # PF 67025F,
Dee, 1_78.
5 Miller,R.H., Ellis,C,X., "HelicoPter Blade
Uibration & Flutter", Journal of the American
HelicoPter Soc., Ju!y 1956.
B Loexy,R.O., "Reuie_ oF Rotary Hang U/STOL
DY_aaic and Aeroelastio Problems =, AIAA PaPer
69-202, Feb. 1969.
7 SPera,O.A., "Comparison of Computer Codes
For Calculating DynaMic Loads in Mind
Turbines=, NASA-ERDA Structural Dynamics
MorKshoe, Nov. 1977.
** "OeveloeeMent of a 4KX SNECS=, North Hind
Po_er Company, RocKwell DOE contract
#PFQBS01C. (Forthooiins Design RePorts For
Further inForlation).
NOMENCLATURE
- li{t curve slope
c - ch0rd
ca- neff. of lift
J.- dts#t (Fig 2)
c_- _e_Set (Fig 2)
"- I¢/A
Z.- fl_" IOieflt _ inertia
Lr- Piece ooaeet If inertia
i,- IttI_
I_- cr_ss Product of Inertia
m- k!_e HSS
- It=S] radius
- r_di_s
R,- inter blade radius
ec- (:6 radius
v- suet uind velocit_
%- equilibritm uind velocity
* - flap ansi.
_- lock nmaker
e- retch ansle deflection
_o- equilikrtu Pitch onslo
- air density
_,- quarter ©bird/Has. axis
%- qurter cherdlC6 _ffset
_-- rotor SHoIer velccitr
r_- flap natural freqoeonr
_,- eitck oaturel Freqoency
267
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269
From :
Q:
A-
QUESTIONS AND ANSWERS
H. Currin
T.A. Egolf
How does the nonlinearity of the actual unsteady lift response to rapid high angle
of attack variations affect the control system response?
Response should be rapid enough to avoid stall with any "real world" gust (an ad-
vantage of this control). Dynamic stall, if encountered, initially increasing lift
would increase pitch response. Wihtout 8tall, I'd guess unsteady aero would 81ow
response.
270


North Wind 4kW passive control system design

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