1. No category

rlr >vJ-l.r- z z1 3
T H E D Y N A M T C B E H A V I O U R O F T H E S T A L L _ R E G U L A T E DN I B E A W I N D
T U R B I N E . I ' I E A S U R E M E N T SA N D A M O D E L I ' O R S T A L L - I N D U C E D V I B R A T I O N S
P . L u n d s a g e r, ; . 1 . P e t e r s e n , a n d S . F r a n d s e n
Abstract.
The report
is
in
two parts.
rn the first
part
the pre-
rininary
m e a s u r e m e n ts y s t e n u s e d i s d e s c r i b e d , a n d a s u r v e y o f
the measurements inade until
the end of i,iarch 1980 is given. Res u l t s a r e p r e s e n t e d c o n c e r n e d w i t h t h e m e a s u r e m e n t , so f t o w e r
eigenfrequencies,
eigenfrequen'bies of
the stationary
rotor
The findings
and
of both f lapwise and edgewise bending mornents.
are compared with the design assumptions, ancl the
agreenent is
found to be good. rn the second part
the ch.lracteristics
occurrence of
Vibrations
stall-induced
with
one cegree of
first
blade vibrations
is
the
possible
investigated.
flapping
eigenfrequency are reported and a
freedon moder with velocity-dependent load is pre-
sented. Calculated
results
are shown with
with measuredcharacteristics.
stay systen is
agree reasonably well
A possible modification
of the
suggested.
EDB diSCTiPtOTS:
C O I 4 P U T E RC A L C U L A T I O N S ; D Y N A J . , I ] CL O A D S ; E I G E N -
F R E Q U E N C Y ; F A T I G U E ; F R E Q U E N C YR E S P O N S E T E S T I N G ,
IjECHAN]CAL VIBRATIONS; ii.OTOrRSS
r TRESSESI TURBINE BLADEST V/IND TURBINES.
RISO BIBLIOTEK
U D C6 2 1 . 5 4 8 : 5 3 4
s 1 0 0 0 2s 7 4 9 3 2 9
]ilililililililililililil
ililililililili
ililrl
N o v e m b e r 19 B 1
Riso National
Laboratory , DK 4000
Roskilde,
Dennark
The work described
in this report was made under contract
with
the wind power program of the ministry
of energy and the electric utilities
of Denmark
rsBN B7-550-0815-1
ISSN O4IB-6435
Riso Repro 7982
CONTENTS
Page
PART T:
P R E L I M I N A R Y R E S U L T S F R O M B L A D E LOAD MEASUREMENTS
FOR THE NIBE A WIND TURBINE
I.
T H E P R E L I M I N A R Y M E A S U R E M E N TS Y S T E M
2.
SURVEY OF MEASUREMENT
L2
3.
RESULTS
L4
3.1.
Locations of sensors on the rotor
L4
3.2.
Determination of
the tower eigenfrequency
L4
3.3.
Determination of
frequencies of the stationary
rotor
2I
3 . 4 . F l a p w i s e b e n d i n g m o m e n t sd u r i n g o p e r a t i o n
25
3.5. Stresses in the trunnion and shaft
29
3.6. Driving
m o m e n t sd u r i n g o p e r a t i o n
3.7 . Stresses due to gravity
forces
,
38
^ ?
40
IJJ-DLU)DI.\JL\
4.I.
The preliminary
m e a s u r e m e n ts y s t e m
4.2. The results
Minimizing
40
A Note
the
abount
Material
Wind Turbine
Rotor Lay-out
Fatigue Problem,
by Helge Petersen
PART II:
40
40
REFERENCES
APPENDIX A:
30
37
3.8. Deflection of the blade
T.
.
43
FLAPWISE BLADE VIBRATIONS IN THE NIBE A WTND
T U R B I N E A T H I G H W I N D S P E E D S . M E A S U R E M E N T S ,A P O S S ] B L E
EXPLANATION OF THE PHENOMENONAND THE SUGGESTION OF A
MOD]FICATION
OF THE STAY SYSTEI\I
1.
INTRODUCTION
2.
M E A S U R E M E N T SM A D E A P R ] L
4B
I9BO
4B
Page
MODEL FOR STALL INDUCED
3 . SINGLE DEGREE OF .b-REEDOM
VIBRATIONS
57
4.
RESULTS CALCULATED FOR A DUTY CONDITION
62
5.
EVALUATIONS OF MEASURED RESULTS
65
6.
CONCLUSIONS
66
REFERENCES
70
f
PART I:
PREL]MINARY RESULTS FROI,I BLADE LOAD MEASUREMtrNTSFOR
THE NIBE A WIND TURBINE
r - _
presented
Paper
with
special
April
2lth
at
4th
respect
to
and 22Lh,
Preliminary
Expert
Results
"Rotor
Meeting
Fatique
Design
Blade
Problems"
Technology
in
Stockholm
1980.
from
Blade
Load Measurements
for
the
Nibe
Wind Turbine
oy
Per
Riso
Lundsager
and Helge
National
Laboratory,
The Nlbe
erected
'Arr wind
turbine
is
Power Program
and the
the
The wind
and is
Denmark
two wind
one of
the
of
Ministry
turbines
by the
Wind
near
Petersen
town
Electric
Nibe
turbine
equipped
in
Utilities
Jutland,
has a diameter
with
the
of
of
Commerce
Denmark
Denmark.
of
an asynchronous
40 metres,
generator
a height
of
of
630 kW.
45 m
"A"
i.l _
THE PRELTMINARY MEASUREMENT
SYSTEM
The preliminary
a number
of
measurement
system
operationar-
parameter
wri-ter
and an xy-pl0tter.
A total
meters
are
available
Table
ted
the
brush
to
located
the
adjacent
turbine-
available
on the
made by
of
the
current
(cf.
writer
six
to
wrlter
the
Tn additi-on
at
rotor
the
patch
shaft-
changing
totar
signals
are
of
the
bottom
qauqe
at
rotor
shown in
of
rotor
a time
Fig.
the
r.r.
being
a patch
the
slip
hub.
Drop resistances
Range
rings
are
A diagram
indicated.
hannel
of
channer_s are
combinations
rotor
connec_
panel
tower
through
channel
in
connectlngr
channer- brush
operationarpara_
channe]s
in
the
by
a slx
twelve
through
connections
is
to
a time
three
changes
system
0f
strain
panel
cable
sensors
1.I),
at
arr
was established
on
Conversion
volt
Wind Speed aE-EB;
Rel. Wind Directlon
0 - 2. 5
5
Blade pitch
angle
0 - 2. 2
6
Rotor
torsue
0-4.5
0/180 kNm
RPM Generator
0 - 8 .s
Force a. pitch
regulation
0/2250 vpm
40v+0 kNm
180v+0 vpm
0 - 4. 4
0/9L
10
Force b. pitch
regulation
36.4v+0 bar
0 - 4. 4
11
Nacelle
0 - 4. 4
L2
Active
13
Reactive
L4
15
A
t
9
shaft
position
power
0-2.0
power
0/9L
bar
-L80/L80 deg
-I20/l-200 kw
0/500 kVar
Current
a-2.0
0/40 Amp
Voltage
0-5.0
0/25 kv
top
0-1.0
O/2.45 m/s
top
0-1.0
0/2.45 m/s
Rotor
channel
1
16
Rotor
channel
2
2
Rotor
channel
3
WE
bar
0-s.0
1
NS
-180/+180 deg
-20/+L5
deg
Acc NS tower
Acc WE tower
List
of
sensors
144v-180 deg
L6v-20
deg
36.4v+0 bar
162v-180 deg
660v-I20 kW
100v+0 kVar
20v+0
5v+o
Amp
kV
2.45v+0 m/s
2 .45v+0 m/ s
E-_
- 9
a
rU
3
r, o
bf " i
o 3 q
318,i
t!
U
2
6
6
\9
lb
(- v )2
, o L2
? U
J - )
fr6
FEu,
rt
ll
X
o
t)3c-.ry-
llj
)
.HEg.
a
ur
t!
.J
I
d
r{r
tu
P
?
Y
2
rI
e
o
.J
cL
o
ir
I
I
I
I
l,-
z
T
c!
t:
CI
I
:)
C/,
Ht
I
I
I
n -{
a 1v
a t u
u
lx
I
I
63.cJ
39"
r
P
o
)
I
a
,j ut l
s
x
ul
I
uJ
'+r,3
lr
r - J
{
llr
EE
Fiqure
1.1
d
10
Fis.
r-2
shows the rotor
channels avai-1abfe. sections numbered
on mod A bfades instrumented for
A1 to A4 are sections
measuring
bending
moments (indicated
by S) or strains
(indi_
cated by r).
T
S
strain
section
force
Section
at
blade tip
Fiqure
The xy-plotter
and 1s
is
therefore
and electric
every
hal-f
simple
ive
effects
voltages.
i
I
I
T
I
I
I
I
minute-
having
scatter
of
usuarly
power
manner
RC-links
intended
of
the
the
give
to
a preliminary
permanently
coupred
channels
in
a mode where
rn
to
simulate
order
channel-s
a time
the
I.2
constant
points
RC-links
are
is
the
plotter
the
ro0
Due to
had to
be
s.
the
speed
a pornt
plotter
the
curve
wlnd
prots
it
to
approx.
avoided.
to
time-averaginq
connected
of
power
Thus,
vortage
calibrated
in
a
throuoh
excess_
divider
by known
I.
1 1
t l
-
The Brush
writer
known voltages.
have
not
been
in
the
based
results
based
writer
least
the
zero
of
is
10-20
brush
people
For
to
procedures
writer
of
the
presentation
is
signal
during
L.2.
ref.
readings
is
resolve
the
the
rotor
conciucted
calibration
been
frequenci-es
adopted
preliminary
channels
as part
The accuracy
estimated
are
very
simple:
of
the
the
of
be
to
5-L5'a.
correctly
up
writer
is
accomplished
rotor
channels
in
of
zero
Coordinatj-on
of
the
performed
by
is
turbine
from
parameter
value,
rotor
Reconnecting
on the
readjustment
as described
obtained
1.1)
for
including
no problems.
the
for
have
panel
the
the
a known absolute
poses
factors
the
patch
turbine
operati-onal
channe]s,
the
the
turbine
signals
the
using
including
operating
curves
that
chart
to
the
(ref.
in
instead
applying
Hz.
gauge preamplifiers.
operation
of
by
parameter
factors
tests
able
calibrated
context,'
conversj-on
described
Reconnecting
30 minutes
this
Conversion
and sensitivities
minutes.
been
operational
operators
on strip
The measurement
to
the
program
the
in
on laboratory
The Brush
at
by
system.
measurement
to
calibrated
determination
measurement
are
Otherwi-se
given
constants
have
sentivities
so that
detail
channer
as the
a slow
is
average
revolution
hub
settings
in
a few
takes
of
of
less
the
the
telephone
with
contact
voltage
interpreting
not
the
case
in
refs.
1.3
the
at
are
corresponds
the
for
and 1.4.
referred
to
max and min
the
start
resulting
the
of
rotor
rn
the
this
a zero
val-ues
than
strain
measuremenEs with
zero
signals
of
resetting
naceI1e.
signals
This
in
the
the
channels
of
turbine.
the
-
12
SURVEY OF MEASUREMENTS
Following
the
campaiqns
have
ment
the
system
been
has
Deparment
Denmark,
this
rn
installation
ref -
made as per
been
of
used
Fruid
2-r-
and running-in
by
primo
Riso
Mechanics
Some resur-ts
of
April
the
from
system
lgBO.
Nationar_
of
the
The measure_
Laboratory
Technicar
ref .
2.r
four
and by
universrty
are
incfuded
in
presentation.
Tabl-e 2-r
are
indlcated'
indicated'
were
the
The rotor
During
recorded
and partly
response
campaigns
each
partllr
the
]isted
channel
campaiqn
as aids
as preriminary
of
are
turbine.
in
and thei-r
combinations
a variety
the
of
primary
avail-able
operatlonal
commissioning
of
checks on the calculations
,able
2.2 shows the rotor
the
of
alms
are
also
parameters
turbine
the
channel_
combinations.
The results
records
and conclusions
made during
these
:-n this
four
presentation
campaj_gns.
are based on
r
13
Campaign
Purpose
Rotor
Date
Channel
No
combination
3 0 .l . B 0
r3.2.80
First
indication
blade
loads
Check of
blade
pitch
tower
resonance
Investigation
z t-26-z-6u
anqle
of out-of-plane
regulation
blade
of
on blade
influence
Tab1e 2.I
Rotor
List
Investigation
campaigns Jan.-Mar.
of
Rotor
channels
of
loads
(ref.2.
and power production
5-6. 3.B0
pitch
blade
Ioads.
l9B0
available
channel
combination
Out-of-plane
all
bending
moments
at
station
A2 for
bending
moments
at
station
AI
in-plane
stay.
3 bl-ades
plane
Out-of
for
2 blades.
Force
in
fn-plane
all
Table
2.2
one
bending
station
moment for
I
Al
for
3 blades
In-plane
bending
adj acent
in-plane
Rotor
moments at
channels
stays
available
blade" Forces
in
f)
-ql
-
3.
1 A
RESULTS
The results
tiation
that
the
given
shown in
have
all
Location
with
it
is
the
r.i.
rn
brade
,in a chosen
on the
root
of
shaft.
The shaft
at
in
the
plane
and one strut
3'4
3 ' 5 of
this
giving
the
papertensile
whlch
B
ratj'ons
by recording
identifying
the
The struts
forces
are
used in
the
in
372rA that
time,
on
per-
extractinq
a tube
and
Fig.
3.3
supported
3.2
of
shows the
foll0wino
give
flapwise
paper.
The
moments used
moments shown in
al-so equlpped
struts
the
this
bendino
mounted
by two
shown in
Fict.
on
together
The figure
and 3.4
bending
3.2
by a bearing,
are
A of
trunnion
with
strain
in
section
oauqes
_qection 3.5.
enfre
has
wind-induced
the
supported
flapwise
as chordwi-se
eigenfrequency
of
shown in
resul-ts
give
Determinati_on
The tower
shown,
plugged
and the
out-of-p1ane.
Sections
in
section
as well
is
gauges 1n section
used
in
blade
is
end of
for
The strain
moments
sectiotr
the
sections
gauges
of
outer
The trunnion
house
strain
period
are
rotor.
the
a bearinqr
bending
instrumen_
some results
an FFT analyzer
packard
a Hewlett
is
in
sections.
3.2
by the
by means of
sensors
mounted.
inst::r'rmented
recorded
simultaneously.
of
rotor
are
section
The analyzer
3 ' 1 shows the
which
section
analysis
frequencies
Figure
Fig.
paner.
an actua1
J . l
this
been obtained
patch
forms
in
been determined
vibrations
accelerations
resonance
point.
during
of
the
by recording
the
tower
upstart
top
of
accer-e_
as werf
the
mill_
as
and
I-*__
\
\
\
s
'i*"
\
\
A
A
t_
_1
The glass-fibre
wing
mounted
Fiqure
I
on the
3. I
trunnion
;&I
Sadius Sooo
/390
$
N
--Jlju
(@j@)
\
\ 8
\
\'{
n
L9
@
Section A
Trunnion
Section
Shaft
Fioure
3.2
B
tr-__
-
Figure
3.3
shows time
(WE) acceleration
the
tops
are
vibrations
as
for
of
both
(NS) and west-east
north-south
recorded
with the
components
j
n
d
u
c
e
d
,
are wind
and by measuring
indicated
found
tracks
1'l
the
in
the
figure,
frequencies
NS and WE directlons,
of
stopped
the
L.29
rotor.
time
Thus
between
Hz and 1.34
Hz
respectively.
1 . 3 4H z i i
5.25 sec
L.
j
I
.
|
Fiqure 3.3
Figure
3.4 shows corresponding
sequence. As indicated
RPMon the generator
in the
shaft,
shaft or 0.45 Hz. At this
3 .0.45 = 1.35 Hz.
Figure
3.5 shows the
time tracks
figure
during
a start-stop
a resonance occurs
corresponding
to
at
1215
27 RpM on the
rotor
speed the btade passage frequency
calculated
varues
designer in October 1978. The calculated
by the measurements, considering
the
as given
value
accuracy
by the
tower
L.28 Hz is
1evel
of
is
this
confirmed
preli-
minary instrumentation.
The signal level of the accelerometers
(^'10.1 v) was too smal1 for the FFT anaryzer, and therefore the
eigenfrequency could not be determined by the frequency anaryzer
which was available.
-*-*r
-
Ecl:ar=rrr< coN-rr:oLE
1B
R B H / 3 18 / 1 0 0 1
Fiqure
3.4
19
Sag nr
8 . H o j l u n d R a s m u s s e n , r A d g i v e n d ec i v i l i n g e n i o r e r
1+ g a
Udarb.
Dato
S-Y
Mode shapes (max. amplitude = 1.000)
node
no
1
000
-684
000
000
-395
2
BB4
-221
968
926
z3v
3
752
266
835
897
811
4
627
645
112
963
1000
5
508
892
599
824
831
6
398
1000
494
780
7
299
978
397
733
413
-95
B
212
Bs6
307
581
-53s
9
139
662
224
627
-7 BB
10
BO
438
148
570
-800
11
36
222
79
510
-580
12
+
2B
5
438
-106
13
0
U
0
335
0
Frequencies
bendi ng
tor sion
Figure 3.5
bend i ng
l0 -78. --
-f'-
- 2 4
:
l
L
o
"F{
H
rtl
A
v
Figure
3.6
I- 2 1
?
Determination of
?
the
blades
and releasing
nion
(section
Secs were
AII
3.6
from
the
it.
A in
recorded
three
other
uencies of
by pulling
was bent
The signals
Figure
from
3.2)
and analyxed.
blades
rotor
the stationar
of
by a series
were determined
The frequencies
one of
fre
the
the
tip
strain
were successively
which
the
towards
tower
gauges on the
was used, and the
A typical
in
tests
record
exited
first
is
blade
trun15
10 to
shown in
as well
Fig
as
blades.
Figure 3.7 shows a typical output from the FFt analyzer' fn the
2.3 HZ, three peaks are appearent, and a fourth one
range 1.g
may be identifYed
above 3 Hz.
^/
LHz
2 H z
3 H Z
4 H z
:fr
Flgures
3.8a
3 . B c s h o w s p l o t s o f calcul_ated
eigenmodes for the
stationary
rotor,
r e f . 3 . 1 , T a b l e 3.1 indricates
the corresponding
eigenfrequencies
according to the Iatest cal_culatlons
together with
the eigenfrequencies
determj_ned on the basis
of a series of 1g runs
with the FFT analyzer.
Mode
Calculated
Measured
Hz
'l
Hz
t _ .9 9
1.95 t
2
1.99
3
2.12
2 . r 2 1 o .0 4
2 . 2 4 1 o .0 3
4
?
Table
3.1
??
Rotor
3.44 t
eigenfrequenc
0.04 RMS
0 .0 3
ies
I
I
\
\
I
t
Mode I
Fiqure
3. Ba
It-
- 2 3
Mode 2
Figure
3 .8b
'r\
Mode 3
Fisure
3.8c
2.I2 Hz
Figure 3.9a
Flapwise
Chordwise
6.37 Hz
Figure
t
F_
3.9c
3.33 Hz
Fiqure 3.9b
Flapwise
Chordwise
-
The fourtlr
Fig.
ei-genmode shown in
excited
phase
blade.
fag
of
At
one bl-ade
indicating
3.4.
almost
3.10
feature
is
initiated.
a normal
23 kNm the
level
140 kNm. This
about
normal
condition
experienced
turbine
over
attempts
to
from
Fig.
excited
the
two
time
has
blade
that
indicating
the
at
The
the
from
others
are
by
appears
operation
l-ow wind
speed.
A ,
stop
sequence
44 kNm and an amplitude
pitching
of
This
low wind
blades
the
to
of
to
d,uring
load
This
during
the
stalled
at
hioh
to
of
connect
and fails-to
not
does
cycle
to
this
condition.
dynamic
to
the
Therefore
It
amplification.
causes
of
130 kNm may
]ow
from
a stop
than
bending
flapwise
for
severe
level
partly
already
peak
the
However,
average
the
is
13 m,/s is
approx.
occur.
blade
as the
3.10)
from
a stop
ru 95 kNm corresponds
(Fig.
be more
3.10
Fig.
stop
be caused by
winds
of
level
average
peak
the
shown that
where
a stop
from
winds.
Figure
3.L2
taken from
shows records
the
the pronounced
flapwise
rise
in
to
similar
sensors
level
at
during
those
section
the
in
Fig.
B,Fig-
stop
a
the
each time
occurs
is
the
5 secs.
approx.
stop.
a peak
95 kNm with
about
of
section
The dominant
when the
maximum C"-values
each
3.I1,
2
phase,
in
grid.
It
a
mode
indicated
moments at
the
a period
ih
signal
flapwise
to
due to
start
val-ues.
1 the
occurrj-ng
rises
during
once
measured
by
approx.
of
through
gradually
stop
stalled
is
at
peak
From an average
approx.
the
stop
pronounced
the
the
the
secs
moments during
of
blade.
predominant.
now is
shows records
a single
blades,
while
stationary
bending
3.2,during
Fig.
l0
the
to
for
is
other
two
approx.
mode I
that
Flapwj-se
Figure
After
3.6
indicated
the
180 deg to
is
Fig.
of
time
the
L0% of
within
are
track
predominant.
2 is
is
time
calculated,
3.9b,
frequencies
The uppermost
corresponds
eigenfrequency
calculated
cafculated
z)
3.I0,
3.2.
sequence
but
Again
from
1ow
From a leve]
speed is seen, but the peak is not so pronounced.
to tu
rises
of n,24 kNm the level
of 'r,30 kNm and an amplitude
a maximum of 'v 110 kNm.
88 kNm with
the
+ - f ; - - . + + + + r . i r ;i{. ; l , t ; , i - , ,i + + - + l , i . , l ; _ l i ; i
i t i , , i l i . ; r l r t i i l l i l l,r if i l L
r " l " ' l : i , ' l , l r r " l t i: l l
ffififfi
:
10C Rd Tcrir 3
:
l
t,
I
6 A o
Fiqure
3.10
I
--
i r l r t l r l , i l i l l i . , i - i ; i t l i r i l i l l i l , l i i - l i l i i ,i i , li ], -l l
i- |
|
i
|
|
I
I
I
li'ilir"lillLliliirlr,l*,i'l'li.'l
Bending moment at R = B. 1
111 t
_Erqur-e_3 .11
19 kNm
1
i,i',
,*]--J*
---l-,zi:r-i-Tr
,
: : i : : . : l : :
;.i.r.
*
l
i
I
r ! : : 1 .i:
I
i :
::::::;::t:i.:
r,T|r;FlfiTirtii:iL.rJTili'f
,_iTf.,fij
-
29
3.13
Figure
due
tions
ponding
to
due to
moments
coning
of
angle
moments at
the
kNm due to
aerodynamic
the
the
levels
95 kNm and
during
stop,
the
forces
in
to
corresponds
This
obtained.
I.04
BB kNm,
are
respectively,
between
3.13. Thus the
been based are
force
centrifugal
A and B,
ratio
the
L47 kNm and I4l
moments
station
the
uppermost Fig.
the design has
on the
dicated
tions
on which
through
acting
of
corres-
and the
By adding
A and B to
measured
respectively,
(below).
blade
stations
forces
centrifugal
the
moment distribu-
(above)
load
aerodynamic
a triangular
bending
flapwise
calculated
shows the
values
the
predic=
computational
confirmed
in-
by
the
measurements.
shows the
3.14
Figure
due to
moments
bending
Department
by the
statistics
the
By referring
the
within
are
cycles
corresponding
Figs.
3.10
which
are
ponding
within
do not
far
3.5.
shaft
the
The observed
given
design
the
of
in
the
the
peak
of
steel
bearing,
the
zero
for
3.I2
3.I4
radius
cycles
I Moment of
inertia
,
A , R -
B m
e , R - 7.2 m
Table
3.2.
one
radius
3'108
I'I08-
for
The peaks
of
tu 400 kI*,
6'10t,
up to
corres-
measurements
so
trunnion
station
shaft
at
station
A Fig.
moment d u r i n g
corresponding
stresses
Eccentricity
3.1 3, and
in
Fiq.
?
stop,
Fig.
3.10, is
C, are given
are shown in
3. 2 .
Station
radius.
42 kNm. These
life.
are
zero
assumptions.
and the
bending
Fig.
speed
flapwise
zero
to
of
Thus these
life.
operational
I40 kNm, and the
approx.
TabIe
values
in the trunnion
Stresses
The dimensions
of
to
contradict
to
operational
the
42% of
referred
the
< I% of
to
shown in
values
to
and 3.I2
referred
364 kNm and an amplitude
of
values
for
to
wind
the
Mechanics
loads
Fi-gures 3.10
of
from
calculated
Fluid
of
aerodynamic
values
an average
obtains
spectrum
design
I Stress
,-o-4 *4
z
^ I5
0 14
91
3 IO
0 16
72
t q
L
-
At
stati-on
C the
the
centrrfugal
st -
52-3
3.6
Drivinq
Figure
for
stress
force.
whlch
one blade
a normal
st'op
entirely
dominant
when the
generator
trace
for
the
(cf.
train
Figure
3.17
in
blades
all
enlarged
main
ref.
at
clearly
lndicates
gravity
in
at
shows the
Fig.
3.19
for
3.16
pointing
period
just
radius
torque
in
the
the
gravity
forces
are
stop
is
0. 75.
grid.
the
due to
others.
although
Hz is
excited
The peaks
slack
these
into
traces
the
fourth
in
the
of
on the
Dower
shaft.
is
forces
By comparison
of
the
3.I
(t
trace
of
probably
later
Fis.
shown in
in
3.4
M3IA2
one month
From Fig.
wel-I
to
3.18,
the
due to
3.r7
the
10 kN and 16 kN are
respectively,
corresponds
the
Table
the
value
shown
shaft.
corresponds
wel-l- with
sj-nus-
moment distributi-on
horizontal.
and backwards,
This
basically
3.2) .
whj-ch corresponds
again
efficiency
Fig.
moments
shown 21, tj_mes
the
trace
most
in-plane
driving
mode of
each period.
abnormar
gauge on the
stop.
the
are
oscillations
bl_ade (cf .
blade
of
The traces
by the
predicted
forward
agrees
the
undramatic,
3.1) of .r, 3.4
moment M3lA2 being
bottom
tensile
B m, which
190 kW the
power is
to
read,
the
before
72 kNm. This
shows that
the
the
two
when the
struts
of
the
addition
40 kNm is
From Fig.
at
B,
particular
forces
amplitude
for
durinq
some mechani-car- probrem,
that
3.19
3.2,
struts
are
more detail
cusp has developed
Figure
torque
Fiq.
in-plane
from
dj-sconnected
B,
adjacent
a normal
superposed
cusps
of
two
station
is
to
shows regular
bearing
moment at
Table
station
fn
which
operation
The figure
shaft
Hz in-p]ane).
this
350-4oo trrx/m2.
mode (mode 4 of
shows in
but
is
2.L).
compared
oidal,
stress
i-n the
and that
in-plane
is
driving
sequence.
first
the
tension
moments during
forces
by a tensile
stress
due to
n g trlN/m2. The material
is
yield
shows the
and the
superposed
This
the
bendinq
3.16
is
30
to
torque
with
power
to
found
during
a driving
a rotor
shaft
train
recorded
of
torque
for
electric
and generator
the
a short
force
76 kNm recorded
the
in
at
3 kN
of
the
power
this
- 31
F - rl
I
I
u
ti
ll
rd
C)
!
o .tJ
0 )
i
i
o -( ) i ' i '
d
A
t r
t v ?
ah
:
Rel-ative
bendinq
flapwise
due to
Ioad
axiallyr
distributed
Radius,
m
moment
aerodynamic
dssurn€d to
as a trianol-e.
Fiqure
3. 12
be
--
- 3 2
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;'i
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l.::..:J.-:ij,:.i
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i:i:l
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Fiqure
3.14
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:l.i
: : : :: 1 . . i . , '
: - ' . : li ' : i ' . :
--+--r,-_
-
- 33
(*
| /r*hnton
) dian elers
\ ou/e, 282 mn
I inner 2/o mm
\
\
Shaf/ diam32oo/254omm
-r
x'.1-
0O
tl
-\
k
\
-
Beari4g
\
N
sr. 52-3
I'
R.
Figure 3.15
iJind
SE
r-s ,9 , B
5 mm/s
Normal-
J
rt/s.
Corrected:
B, B m/s
LUU
---:-_--
20 mV/div
K3A1 stay
forward
50 mV,/div
10 kN
ii31A2 Yellow
blade
shaft
-5U
-: -1-i 56
rllV,zOlV
:
!
k3A2 stay backward
:
Figure 3.16
50 mVldiv
l
t
I
q"--r
m
:
i/ ]\T
:
i
t
'
fuA.
\$q .::"-98-
lahlut*
I'igure 3.17
25 mmls
-"-
T r - n
i\JA
4
Stay force
'
..:
I
L"IJ I AZ
Driving
moment
Iigqe_3-:!_
37
P
tl-.1
o
."'l
s
Lt
()
(l)+r
rn
(U
0)
Bending
rrl
from gravity
moment
blade,
on a horizontal
c5t
kNm
*o
F
z
90
P
ci
()
u
bt
.rl
n
()
rn
/o
8
/
0
Radius, m
F_'iqure l_. 19
It
be noted
shoutd
ing
in
the
This
forces.
tensile
tive
house
This
of
mom.ent in
3.7.
driving
Stresses
The bending
ding to
rig.
superposed
MN./m' at
due to
stress
Fig.
gravity
moment in
3.19.
be
could
the
maximum power.
the
reason
3.16
seems to
bearing
a radiaL
for
the
load
which
abnorma]
posi-
are
there
be stickwas
trace
3-18.
forces
due to
trunnion
The stress
from
the
carries
the
Fig.
of
stays
that
means
and therefore
unintentional.
the
both
in
that
is
gravity
is
correspondingly
t
moment is
the
driv'i"ng
of
37 kNm accor-
24 ItlN,/m2.The
order
of
14
33
3.8.
Deflections
3.20
Figure
by the
out
3.2.
power
lated
at
a pure
in
Department
at
case
the
blade
2.
of
rotor
pondingly
in
curve
The coning
effect
by
for
blade
Ole
a duty
The deflected
I
and for
reduces
deflection
Gunneskov,
609 kW, the
is
-4o.
blade
redueed
Axial
shaft
angle
maximum axial
and the
calculated
is
the
of
Engineering,
tip
radial
curve
blade
shows a cal-culation
The load
the
the
of
Riso,
ref.
for
whlch
maximum power
cafcu-
condition
shapes
are
a bl-ade with
the
carried
tip
shown for
cone
deflection
bending moment in the steel
4 0 o / oa s s h o w n i n f i q .
3.2I.
shaft
angle
by
is
60
25 %
corres-
bending moment
IkNm]
. - . : -. . . - _
' : .
l4aximum
o
Radial
@
Inc1.
conditions
blade
coning effect
!n
t
-
stay
supporting
point
R a di u s
iml
I
Turbular
Fiqure
i
I
t
steel
3 .21
beam
- 3 9
'
NIBE
I
DefIec t ions
WINDMILL A
'-- :': :
Rad i us
Operating conditions
a t m a x i m u mp o w e r :
or= 3.5 tud/=, u = 14 m/s
Aerodynamic and centrifugal
load without
coninq
offonf
Do. with coninq effect.
F-t
:*-,
Ll
A J X O
O J O U )
+ ) - o c
u,+(-'-i
:
:
E
rd
- fro
: -,: -_
: ---
Sta;z supporting
...- point
. C J
o
. r l
--. :.
c)
G)
.lJ
(.f)
, ___ lr
(d
: F , l
:..!c
--r E-{
:
1,0
Def 1ection
Fiqure 3.20
t ml
-
-
4.
A n
= U
DISCUSSION
4.1.
The preliminary
measurement system.
This
ad hoc measurement system was relatively
easily established.;
the main problem was the influence
of the measurement system on
some of
After
the
channels
separating
the
turbiners
microcomputer.
the
system from the computer by amptifiers
have been no problems in the recording of operational
there
parameters.
by noise
The recording
of
the rotor
caused by the long cables
occasionally
but
shared with
caused the strain
absorbing
radio
gauge preamplifiers
on the preamplifier
modifications
channels has been hampered
instal-l-ation
siEnals.
This
to oscillate,
have removed
these oscillations.
- and still
The system has served
ing
preliminary
data
used by interested
permitting
validity
wilL
early
of
ideally
of
suit,ed
beyond the
while
not
Therefore
on the mod B turbj-ne.
than
because it
frequency
5-15?.
is
range of
the amplitudes
of
However, the protter
standing
calculations.
better
obtainit may be
a minjmum of instructions,
thus
turbine behavior and of the
assessments of
the design
as a means of
way. This means that
a versatile
persons with
be estabrished
accuracy
in
serves
a similar
The penalty
The Brush protter
able
to resolve
interest.
the records
in
is
is
an
not
frequencies
far
the wj-nd turbines,
are limited
has proved reasonabry
system
to about
reliable
5 cm.
while
several months in an unheated room j_n
to record up to 6 channel-s
the turbine
tower, and its ability
simultaneously
has proved val_uable.
4.2.
unattended
for
The results
The measurement results
values.
However, they
investigated
The most
a]so
good agreement with
show some anomarj-es that
the predicted
shourd be
further.
pronounced
mod A wind
are in
turbine
characteristics
as they
appear
of
the
stayed,
from
the
measurements
sta1l-requlated
are:
a
-
41
are
Gravity
forces
forces.
As indicated
very
important
For the
role
out-of-plane
clearly
in
in
the
FigkeePing
loads
it
most dominant in-plane
3. 19 the
the
is
in-plane
resulting
characteristic
PlaY a
blade moment low.
struts
for
a turbine
that during a normal
as the mod A turbine
coefficients
Ftop sequence the blade passes through hiqh lift
This means that the blade is exposed to
condition.
to a stalled
loads of the same magnitude as those at high wind speeds '
which
is
regulated
dFE
- 4 2
References
l.l:
V. Askeqaard, C. Dyrbye, S. Gravesen:
"Laboratory Tests on Gedser Wind Turbiners
Research Laboratory,
Structural
Technical
P. Nielsen:
"Measurj-ng Program for
Proc.
University
1977.
of Denmark. Report S 28/7 7 Nov.
I.2z
Blades".
Two Windmills
at Nibe,
Denmark'.
IEA Expert Meeting on LS-WEC's.
September 26-27, L979, Boone, North Carolina,
1.3:
P. Lundsager, C.J. Christensen, S. Frandsen:
"The Measurements on the Gedser Wind Turbine I977-I979".
The Wind Power Program of
the Electric
1.4:
USA.
Utilities
the Ministry
of
Commerce and
of Denmark, November L979.
P. Lundsager, C.J. Christensen, S. Frandsen, S.A. Jensen:
"Analvsis
of Data from the Gedser Wind Turbine Measurements
L977-I979".
The Wind Power Program of
the Electric
2.Iz
Commerce and
in Denmark, May 1980.
Utilities
pe Nibem@ll€
(Measurements
27th
of
on Nibe
1980.
and 28th,
Department
of
Fl-uid
A,
den 27.
og 28.
Wind Turbine
rn
Danish).
Mechanics,
mod.
februar
A,
AFM Notat
February
vK-62-800325.
Technical
the
1980"
University
Denmark.
P. Lundsager, O. Gunneskov:
"Stati.c deflection
and eigenfrequency
wind
turbine
Riso-M-2199,
3.22
of
B. Maribo Pedersen:
"M&linger
3.1:
the Ministry
rotors.
Nov.
O. Gunneskov, P.
"Static
Deflection
Wind Turbine
Risa-M-2200,
of
the
Nibe
of
the
Nibe
Background".
L979.
Lundsager:
and Eigenfrequency
Rotors.
(to
Theoretical
analysis
Analysis
appear) .
Analysis
and Results.
A.
Appendix
A Note
about
Fatigue
Lay-out
Rotor
rurbine
Material
the
Minimizing
Petersen
divisj-on
of
the
shown in
turbines
of
feature
An obvious
the
wind
Problem
Helge
by
4'1
Fig.
order
in
blade
AI.,
produces
which
a blade
are
to
pitch
conventional
problems
design
it.
in
The two
Nibe
is
wind
respect'
this
,-i:\
-'-l'.
B
A
Fiqure
For the mod A the
-\
blade
is
A.1.
divided
in
an outer
and an inner
part,theouterbtadepartisstructually''Shrunk''tobeableto
inner blade
pass through the bearing at the end of the fixed
For mod B the whole blade
blade root and this limits
is
carried
the
by a large
structural
Two other sorutions are shown in Fig.
'
n2gtt and Concept " 50" , respectivily
bearing
blade
part'
at the
diameter'
A.2 and A.3,
named concept
I
- 44
I
I
I
Wind
I
Concept
t t2 9 t l
Diameter 29 m
Generator 250
I
rI rr' iv^ ur 1r- g^
I
a
J - I. z
KW
r- 4 5
'l
\
I
I
I
I
t_
-t-r
,V]
\;n-
I
)
V
I
-I-Jr
t l f
I r l
\li
ut
\
I
I
I
I
I
\
\
tt,
I
I
I
I
I
,
I
I
I
I
\
\
\
\
\
\
\
Concept
' r5 0 ' t
Diameter 50 m
Power 1000 kW
Fioure
A.3.
-:E:.+--
- 4 5
The wind
turbine
However,
the
struts
outside
of
placed
is
hinged
the
to
blade
The wind
lever
in
the
A.2,
are
hinged
the
hub.
structure
turbine
structure
Fig.
to
the
blade
structure,
Still
the
not
is
shown in
fixed
Concept
to
blade
the
A.3,
blade,
has strutted
the
and the
interrupted
Fig.
"28",
hinge
root
can pitch
of
the
blade
this
way
and bearlnq.
"50",
hub and surrounded
being
9Oo. In
by a shaft
Concept
bl-ades.
has
a canti-
by the
hollow
I
I
blade.
This
As for
tj-on
the
of
hub.
zero
pitch
all-ows the blade to
tt29tt the bending
Concept
at
the
fn
the
it
is
to
withstand
less
outer
the
bearing
carrying
outer
difficult
the
bearing
to
fatique
around
the
and increases
design
loads.
carrying
member.
from
posi-
I
moment decreases
end of the
member of rr50rr the
at
the
a fixed
carrying
the
member towards
bendi-ng moment is
towards
structure
the
hub.
strong
However,
enough
I
47
PART II:
FLAPWISE BLADE VIBRATIONS IN THE NIBE A W]ND TURBINE
A T H I G H W I N D S P E E D S . M E A S U R E M E N T S ,A P O S S I B L E E X P L A NATION OF THE PHENOMENONAND THE SUGGESTION OF A
MODIFICATION OF THE STAY SYSTEM
J
-t-r-r-
- 4 8
1.
Introduction
A preliminary
obtain
measuring
checks on the design
behavj-our of
the
commissioning.
A series
pitch
angle
series
power,
has been reported
During
the
the
turbine
using
oscillatj-ons
ing
2 Hz of
the
(Refs.
eigenfrequency
strip
charts
possible
If
tl:e
explanation
this
first
test
run are
rigid
is
of
strong
a frequency
third
m/s,
flap-
correspond.-
fundamental
should
blades.
shown in
the mechanism that
prove
t.hat st.all-regulated
relatively
run with
the range r2-L6
periods
system,
to the
test
flapwise
3 and 4) .
of
explanation
conciude
system
from
At wind speeds in
were observed at
the
to maximum
2.
1980 a 24-hour
measuring
wise blade
to
Ref.
25i-h,of April
preriminary
the
in
of measurements, durj-ng whj-ch the
at wj-nd. speeds close
in
was started.
to
and to monitor the
Nibe wind Turbine 1tA" during
of measurements has been reported
was varied
24Lh to
in order
assumptions
stall-regurated
Ref . L, and a separate
brade
system has been established
A modificat.ion
of
remedy should
note with
drives
to be correctr
wind turbines
shown as a possible
this
a
the phenomenon.
w€ would
ought
to have
the Nibe ,A, stay
the
phenomenon prove
to be serious.
2. Measurements made 24-25 Aprj_l I980
strip
charts
measuring
the
were taken
the channel-s listed
system as described
Brush writer
1. Wi-ndspeed at
2. Active
of
power
in Ref.
l.
below,
The sensors
using
the
coupled
to
were
58 m height
(kW)
3. Out of use
4. Trunnion
5.
6.
Fig.
moment orange blade
rr
It
rr
rt
yellow
fed
2.L shows the position
rr
rl
of
section
2, where the strain
gauges are praced.
From here the
signal
preamplifiers
amplification
1000x and slip
the bottom of
the
a Brush plotter
with
at
is
turbine
transferrecl
rings
tower
(cf.
via
down to
Fig.
2.2)
- 4 9
On this
Hewlet.t-Packard
frequency
plotter
printout
for
mainly
is
signal
(the
static
the
20e" of
approx.
is
flapwise
fundamental
signal.
the
the
each revolution
recorded on 24 AprLL 1980. For
an upstart
2.4 indicates
Fig.
and wind shear)
forces
oscillation
f requency) . The dynamic anrplitude
average of
high wind speeds. The
(gravity
sinusoidal
moment
of a trunnion
trace
at relatively
by a two hertz
superposed
spectra.
frequency
of a typical
earlier
aS was recorded
(Model 372IA) and an XY-
analyzer
of
shows a record
2.3
Fig.
the
a
was supplemented with
the Brush plotter
occasion
pronounced peak that
has one very
trace
is
therefore, this can scarcely
slow rotation;
j-n the blade. No explanation
of this
a dynamJ-c effect
be called
phenomenon has been found, but a possible one is that the
present
also
channel
is
of
at very
f rom that
deal"t with
trace
with
(above) compared with
to the
precJ-sely adjusted
in
dominant
entirely
trunnion
f lapwise
eigenfrequency
Fig.
is
when the wind speed is
at
where oscillations
spectrum is
Fig.
much like
that
close
During
in the signal
is
Fig.
shown in
the
several
a 2-Hz flapwise
run'
at
the
a time
periods
2.5 below.
24-hour
minutes
oscj-llation,
run where the
to a power producti-on
Lhe blad.es are close
of
peak at
while
and the corresponding
Lo L5 m/s corresponding
a. period
however,
There are short
2 Hz are dominant,
of more than 500 kW, i.e.
condiLion.
L2 m/s.
a sequence of
2.7 illustrates
wind speed is
approx.
24-hour
the
not be
the rotor
of
shows a furLher
a sequence of
of
a record
could
analyzer
shown above,
spectrum
moment spectrum
a normal
2.6
the
be taken with
should
the frequency
signal;
are shown
The spectra
because the frequency
some reservation
to a
corresponding
that
The specLra
axis.
frequency
a linear
(below).
moment signal
to the
spectrum corresponding
frequency
the
2.4
of Fig.
normai- trunnion
is
later.
2.5 reproduces
Fig.
The phenomenon seems to differ
earlier"
not been recorded
has
as this
as large
an offset
although
level,
the signal
cause an offset
to r:adj-o waves; they will
sensitive
to a fully
stalled
Lhe dominant term
having a large
7
.fu
strain
section
force
A+
T
A g A2
I
T
s
AI
s
Section
at
blade tip
/6m
f'rqure z. I
+
Eentng
m)men/
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;'iqurg ?J
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&-
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AlLhough Figs.
amplitude.
2.6 and 2.7 are taken at different
paper speeds the character
are clearly
different
2.8i
figure.
rotor
a normal
In the
is
however,
in
to Fig.
spectrum
is
2.7 is
two figures
shown in
shown below in
the above part
spectrum below the rotational
just
the
from each other.
The spectrum corresponding
Fig.
the signals
of
visible;
the flapwj-se
frequency
fundamental
of
the
of
the
frequencies,
are dominant.
^ n
J I
v.ll4r/
^
Fiq.2.8.
Table 2.L shows a survey of
phenomenon shown in Fig.
amplitudes
d.uring
that
are
signals
of Fig.
is
clearly
associated
significant,ly
normaL operation.
SignaI
fig.
2.7
the
kw
2 . 5
larger
than
2.3 to
the
with
l40ment
middrampl.
f
ampl/stat
I11t 19 kitlm
0.17
L70
67!50
kNm
0.74
2.6
490
92!33
kNm
0.36
2.7
570
9L!40
kNm
0.44
2.1.
Survey of
trunnion
moments.
The
dynamic
amplj-tudes
However,
2.4
Table
2.7.
- 5 1
operation.
normal
same as during
the
maximum moments are
the
so that
lowerr
are correspondingly
averages
static
the
to those
at windspeeds similar
present during the measurement series reported in Ref ' 2, where
the
the phenomenon was not observed. However, at that location
and the degree
lower than on 25 April,
wind speeds were s1ightly
observed
phenomenon is
This
of
turbulence
In
the
gated
as a possible
freedom model for
ree of
1e
One possible
to
a simple
are
they
that
is
vibrations.
stall-induced
possibilit'y,
this
investigate
i.e.
flutter,
stall
oscillationq
stall-induced
the oscillations
of
explanation
caused. by so-called
In order
oscillations.
the
of
explanation
investi-
are
vibrations
stall-j-nduced
sections
following
si
lower.
was markedlY
one degree of
so that the principal
freedom model has been established.r
and compared with
of the phenomenon may be investigated
features
the measured response of
In
this
induced
turbine.
a.
The air
flow
vefocity
v'
is
parallel
this
is
lowest
c.
supposed to have one degree of freeto the rotor plane. The reason for
ej-genmode for
flapwise
load
on the
blade
dependencY
wise
linear
this
way the
is
on the
supposed to rest
a single
on the
blade'
supposed to have a Pieceangle of j-ncidence. In
equation
of motion
term
of
the
incidence
is
computed directly
load
consLant
axis.
rotor
the mechanism is
that
The wind
the
to
dom, perpendicular
are:
homogeneous, and has the
laminar,
movement is
The tip
assumptions
simplifying
The most important
stallwind
of a stall-regulated
tip
a blade
of
oscillations
descri-be
that
are derived
equations
the
chapt,er
turbine.
the
is
I inearized.
d.
The angle
of
speed vrr. The reason
where the
phenomenon is
aerodynamic
factor
for
efficiency
therefore
is
this
is
that
at
from the wind
the power level
the
assumed to be significant,
j-nduction
is small and the axial
correspondingly
small-
L
d!--
-
e.
58
The development
is
based
tip.
for
this
The reason
displacement
deflections
We consider
largest
with
rotation
of
velocity
vector
the
the
the
tip;
or
Conf igurat.ion
the
blade
therefore
not
the
as
the
the
tip
phenomenon
occurs.
3.1.
of blade tip.
that
translational
of
l-oad as well
as shown in Fig.
shows the blad.e tip
x-direction
deflection
that.
whether
a configuration
3 .I.
is
at
determine
Fiq.
The figure
is
on the
moves in
velocity
the positive
v* due to the
the rotor.
The tip is infruenced by the wind speed
Vn, acting j-n t.he positive
y-direction.
The tip has the pitch
angle oo rerative
to the rotor plane, and the relative
wind
rt
is
i'
has the angle
assumed that
the y-direction
movement (i.e.
following
/Vn
0 = l ' "
\tn
The first
stationary
attack
brade defl-ectj-ons
onry,
and by including
assumingi that
relation
of
is
y is
not
o to the
cause the tip
tip
chord.
to move in
the velocity
smarl
v of this
compared. to vrr) the
obtained:
(r)
- J _
V
m
term corresponds
conditions,
due to oscillat,ions.
to
while
Thus,
the angre of
the
attack
second term is
a during
the change in
g
f
- s9
V
-
d
LI
L
V
L
I
-
-
v
The
load
The
tip
na
=
m
m
!
-
o
actj-ng on the blade
is
the description
structural
Eq.
(2) depends on y.
y.
that
This
lj-near
equatj-on
(3)
to
couples
is
coupling
load
shown in
Fiq.
reaListic
the
with
fundamental
based on the
frequency
0J7
6,and the load p(cl), and that due
Thus the linear equation (3) has a load
the
because of
solution
by introducing
linearized
This
Fig . 3.2.
O
one for
curves
3.2.
a tip
curve
3.3.
the piecewise
form is
linear
oi),
a
load.
The load assumption
it
then becomes
(4)
oiloloi+r,
- Pi) / @t*,
dependency on
as can be seen by comparing
where
= (Pi*t
the
l-----
Piecewise
profile,
in Fig.
ni (o) = - i 0 * b i
.i
o.
damping ratio
the
term
of
Zeui+tizy= P(cr)
i+
i.e.
by the
described
movement is
j-s a f unction
tip
and
E**
- 50
=
b.
p
.
- I
I
.
a,'c!,
I
I
a.
+ (2eu *
where
the
the velocit.ies
(6)
(cl-oi) 'vm.
=
Yi
(s)
C!.(O[(C!.,r,
to
cri correspond
(3) we find
Eq.
into
= ar6+b,
* )my * r ' y
limits
(4)
load Eq.
the
By introducing
(5) is
Thus,Eq.
Yi- 1 Y '
range
the velocity
Yi+I'
tfre time
V! ana V! at
(5) has the solution
values
Assuming initial
Eq.
interval
in
valid
Bit
y = y= * Ci"
to,
in
this
(7)
"o" (urrt.-Q),
where
v^
=
(' a . c lr + br . ) / u z
ul ,
ry
R
"i
g + u i /u ^
l-
A
' l -
( v ! - v = 1s g L t o T c o s( o i t o - o i )
].
If
is
a,
for
gi
and
negative
Lras a sufficiently
be negatj-ve,
to
damped but
This
a r c t a n f , 6 o L /t v ! - v = ) - B i ) / u i )
,ito
_
(8)
the
Lf
the
angle
of
attack
Ioad curve
each period
energy is
damping,
in
this
numerical
interval
value
is
not
increasing.
means that
where the
solution
large
Fig.
3.2,
consists
into
blade
enters
cr,pendle
stationary
of
a part
a di-splacement
across
negative
the movement,. and a part
where energy
is
taken
the maximum of
oscillations
with
pattern
with
may occur
in which
damping Bi,
positive
from the movement.
the
where
61
With a load
movement cannot
part
of
shown in Fig.
as that
the
increase
curve with
movement. Therefore,
3.2 the amplitudes
arbitrarily,
positive
of
the
because the damping on the
slope will
the term stall
take
flutter
is
energy from the
not
indicative
of
I
It
l
- f
. +
.
+
I
'
t
l
' f
_J
'qr
c
.\
'
l
- 1
o
; r
; --i
' T
o
o
V1
: f
I
-T--1
i :
I
Li__l
$
a^-2
qr
U
>'
o ^
o -.J
d
F
< -.4
-20
-3?
Fig.
3.3.
4415, that
Aerodynamic
is,
18 m, 2 m from
efficient
when it
8
0
8
Seclpn onqle of ottock, oe, deq
the
tip
coefficients
profile
the blade
Cl versus
tip.
the angle
has some specifi-ed
for
for
the blad.e profile
the Nibe turbines
The curve
A shows the
of attack
o for
roughness close
this
at
NACA
radius
lift
co-
profile,
to the leadj-ng edge.
L---
_-A
- 6 7
the
mechanism
limited
The
which
of
stationary
oscillations
of
amplitude.
equations
solves
the
given
consists
an
shown above
equat,j-on
initial-
movement
is
In
the
into
program
pl.acement
v
(3) that
simulation.
a number
if
the
program
The blad.e
over
tip
and. then
of
rf
oscirlation
dies
in
the
following
the l-oad corresponding
to
way:
down
a static
It
is
dis-
rs
(a)
J
]oad distribution
speed v.
appried
the
5
the wind
wind
is
revolutions
i
, i
p^ = ir)-y^.
-
that
oscillation.
j-s a p p l i e d
load
a FORTRAN IV
velocity,
determine
a stat,ionary
in
and,/or
stepwise
to
the
seen from Eq.
I
by
dispracement
large
develops
coded
motion
descrj-bed
suffici-entry
or
of
are
is
calculated,
on a finite
for
this
the actual
blade
at
a given
wind road d.istribution
may be
element model of
the brade whereby the tip
d.ispracement vj may be found. By means of Eq. (g) the load to
be used in bire dimensionless Eq. (3) may be determined.
If this
is repeat.ed for a number of wind speeds the load curve Fig. 3.2
may be described
at
the degree of
sophistication
that
is
jud.ged
to be necessary.
Cal-culated
rn
this
results
chapter
for
a dut
eond.ition
some results
are shown that are computed using
the model for a pitch angle oo = -4 deg corresponding
to the
setting
at high wind speeds. The wind load. is prescribed. as
described
in Chapter 3 with a wind load distribution
taken from
Ref.
5, and with
described
tip
deflections
computed by the beam model
3. The resurting
wind road is shown in Fig.
in Ref.
4.r.
rn Fig . 4 -2 some results
made for
structural
in
varying
damping is
the model,
with
wind
absorute
some reservation.
general
conclusions
are shown from a seri-es of calculations
speed vrr. The influence
of the ratio
c of
shown. Due to the simplifications
inherent
varues
of
However,
given
below.
the results
it
should
seems reasonable
be taken
to draw the
- 63
With
(i.e.
a smooth load curve
pronounced
oscillations
may occur
stall-induced
stationary
corners),
a curve without
wind speed v3" This wind speed
n
reaches
most probably corresponds to that at which the stall
'
r
A
'
r
turbine.
which j-s 13-15 mrls for the Nibe
the blade tip,
spontaneously
at
When stationary
a large
a well-defined
oscillations
magnitude,
rises
and it
speed. Oscillatj-ons
may occur
is
load
the
Fig.
case for
4.I.
However, this
magnitude
that
is
Most probably,
a limited
of
wind
at wind speeds nelow vfl, which
curve
indicated
with
considerable,
dotted
lines
dj-sturbancies
for
especially
in
of a
the smooth curve.
conditions
these
under realistic
j-n a range of wind. speeds of
periodically
around. vf,, preferably
mutually
gust.
The patterns
different,
in
by a gust,
may be initiated
by another
although
increasing
is
therefore,
extent
oscj-Ilations
with
demands initial
may occur
oscillations
again
the
the dynamj-c amplitude
occur
turbulent
wind.
The
and they may be stopped
shown in Fig.
are expected
2.6 and 2.7,
to be typical
for
this
phenomenon.
Changes j-n the
only
a small
load
curve
determined
oscillations
darnping within
structural
influence
has a large
on the results,
while
The wind
infl-uence.
by the maximum of
realistic
the curve,
the
lirn-its
shape of
speed rf, =""*"
the magnitude
but
have
the
to be
of
the
the curve
seems to depend on the sharpness of the maximum. If
has a jump as indicated. in Fig. 4.I, the phenomenon
may occur
in
in
Fig.
large
4.2.
start,ing
scarcely
take
a significantly
If
the curve
amplitudes
larger
wind speed range as indicated
has a plat.eau at
are required
the maxi:num such
that
the phenomenon will
place.
(.rxro)
{
Fiq.
4.1.
B
) t---.--
Wind load
applied
in
the
mod.el.
L-
-'+--
v =
Lr>
(.) lp.: o.2
(o) afls = o'ls -'--.
(x) eA -- o.\0
{
\
\
tri
b
(Ir)2,3=o.Z
q
\
I
/ / ,
at
\
ot
/{ i! iP
I'/
r1fo'
t
{
'
Ej.q. 4.2.
A gross
est,imate
Results
of
the
tip
measured moment amplitudes
moment at
for
{
{
I
pitclr^ an91e. oo = -4 deg.
deflections
wind
speeds is
to Fig . 3.2 of
Part
r corresponds
of
approx.
to the
The average
100 kNm, which, according
to a tip
d . e ft e c t i o n
of
the
magnitude
40 kNm therefore
order
correspond
may be made as forlows:
high
order
that
0.6 m. The moment amplitude of the magnitude
corresponds to displacement
amplitudes of the
0.25 m, while
of 0.40 m.
Fig.
4.2 predicts
d.ispracement amptitudes
L
- 65
range
seem to
since
the
on the
velocity
ment
be most
seem to
of
angle
probable
for
occur
of
the maximum;
of
influence
attack,
displace-
the
vibratj-ons
stal1-induced
wind
stall-regulated
the
turbines
blades.
flexible
havinq
on the
based
is
mechanism
sharpness of
the
with
increase
will
the maximum; t'he size
speeds around
wind
of
range
i n a
most probably
a maximum, the vibrationg
is
there
wind- load. has
axial
the
sPeed;
wind
a certain
a maximum at
if
may occur
vibrations
stall-induced
are
on Lhrese calculations
based
The conclusions
of measured results
5. Evaluation
shows the magnitudes
Fig.
5.1
fig.
2.3 and Fig.
of
moments
t.he measured trunnion
2.7 and Table 2.L. The magnitudes are shown
in the so-called
to those predicted computationally
relative
published
in Ref. 4 and originally
"Belastni-nger p& rotorblao'
rotor A'r
in a note AFM VK-22-780108
("Loads on rotor blade, rotor A"). Here the spectrum is converted
Ioad
moments.
to trunnion
It
duty
condition
with
the
load
from those
should
is
cycles
This
in
not
wiII
is
this
T h e steel
as such incl-uded
be considered
therefore
the
assumed that
2? of
approx.
that, are
2.7 have characteristics
found j-n the load spectrum. This
1n the evaluation
t.he spectrum
Lf it
500 kW' agree weII
spectrum.
because t.hey are
and they
approx.
moments of Fig.
The trunnion
d.ifferent
of
aL a power output
the normal
2.3,
moments of Fig.
the trunnion
appears that
able
with
dealt
spectrum,
the
time
be approx.
case the
2L0 m m , r e s p e c t i v e l y r
as loads
Lhe lif etime
spectrum,
to be added to
of
the blades.
2.7 occur
moments of Fig.
in
the nrunlcer of such moment
-operation
106 per year or 3.107 d.uring 30 years.
the corresponding
stresses
trunnion
trunnion
load
the
reason-
of
if
significant
of
in
is
has the
should
outer
so that
are high;
stresses
be evaluated.
and inner
diameters
the cross-sectional
282 mm and
moment of
I-*.
-
--,.+--
- 6 6
inertia
is
smallest
2.r5.10-4
trunnj-on
taken,
leading
)
33 N,/run-. This
a large
rf
to the correspond.ing
judged to reduce the
are
and if
suppress
the
oscillations,
fication
of
by stays
it
therefore
is
are
86 N,/^m2 and
range cannot be considered
cycles.
drasticafly,
small
expected
considered
for
such
lifetime
desirable
to
may be done by means of a modisystem as shown in Fig . 5.2. A point on
the stay
the blades
stresses
stress
results
and the
moments, 131 klrlm and 51 klrlm, respectively,
number of
these
m4. From Tabre 2.L the rargest
near the
it
tip
at
radius
18 m is
connected
to the hub
pointing
forward.
rf this is done, it wirl
seem naturar
at the same time to j-nterconnect
the blades by means of stays
as shown in the figure.
By doing this,
the oscillating
roads
due to gravity
forces may be significantly
red.uced.
6. Conclusion
measurements on the Nibe 'A1' wind turbine
24 and 25 April
1980, using the preriminary
measurement system, flapwise
oscillations
were observed at a frequency of 2 Hz and with
During
significantly
trunnion.
large
amplitud.es of
The oscj-Ilations
power output
NNE; the
was rather
to more than one minute
one possibre
explanation
stall-induced
stationary
tions
using
are givenand that
a simple
this
be expect,ed for
a.
were observed.
is
that
the
oscillations,
show that
ph-enomenon is
and results
the
in
turbulent
from computa-
model of
be the case then the
Nibe 'A,, wind. turbine:
should
caused by
such oscillations
should
The oscillations
especially
500 kw and. above. wind directi-on was
turbulent.
Durations from a few seconds
one degree-of-freedom
The results
if
r5O kNm in the steel
periodically
at wincl speed.s
occurred
13-16 m/s at
air
the order
be expected
a blade
tip
are possible,
forlowing
to occur
wind at a power output
ought
to
period.ically,
above
500 kw.
b.
The observed
amplitudes
immed.iate danger
for
the
fatigue
for
life
of
t5O kl{rn do not
t,he rotors.
should
However,
be considered.
represent
the
any
implicatj-ons
- 6 1
c.
A n extension
1 5 m/s
If
the
oscillations
these
pressed
should
of
the operational
be accompanied by measurements.
prove to be a problem,
by means of a modification
blade
tips
are connected
means of additional
wind speed range above
stays.
of
the
to each other
they may be sup-
stay
system,
and to the
whereby
hub by
L*-
---]-f--
-
58
0o
\
N
\
\s
\
h
\
Tapnomenl,k[VmR
Signal //g. 2.3
Signal ftg. 2.7
Ejs-urs-J--l
t_
- 6 9
\-_
-_._-__
- -"-..-=-
V;nge i s/arls/i//r'ng
Korde
O.Em
; radi us
Ro/orplan
$
q)
V'nge i bremses/i//ing
I'i.gure 5.2
\
qJ
tt
=:-
L-7C
References.
t .
P . L u n d s a g e Lr H . P e t e r s e n .
"Preliminary results from blade load measurements for
Paper presented at 4th expert
N i b e r r A r rw i n d t u r b i n e " .
meeting
"Rotor
fatigue
design problems".
special
Blade Technology with
Stockholm April
respect
the
to
21nd and 22nd
1980.
B.l'laribo Pedersen.
"Melinger pA llibe molle A den 27. og 28. februar
(Measurementson the Nibe A windmill'
february
1980".
27. og 28.
1980. In Danish). AFMnote VK-62-800325, Dept. of F1uid
Mekanik, Techncal University
?
of Denmark.
P.Lundsag€r, O.Gunneskov.
"static
and eigenfrequency analysis
deflection
Nibe wind turbine
rotors.
Theoretical
of
the
background".
Risa-M-2199, November 1979.
I
A
I
H.Peter sen.
"Rotorkonstruktionen
elverkerne".
for
(The rotor
erected by the electric
r
de to Nibe Vindmoller
opfort
af
design for
the two Nibe windmills
utilities.
In Danish)
B.ivlaribo Petersen m.f I
"status for molle A".
,rauau= for windmill A. In Danish)
A F I I n o t e V K - 5 2 - 8 0 0 3 2 5 , D e p t . o f F l u i d t { e k a n ik , T e c h n i c a l
University
of Denmark.
1
R i s s - M -G l
Riss National Laboratory
I col
I
Lnl
a
ntl
I nil
t_l
*
Title
and author(s)
The dynanic
wind
o
&
the
of
staIl-regulated
Depa::tment, or
)epartrnent of
rhysics
and S.Frandsen
H. Petersen'
Sroup' s own registration
number ( s )
pages +
tv
tables
't
illustrations
Abstract
I Copies to
The report
is
in
two parts.
In the first
part
I
the prelirninary measureinent systen used is described, and a survey of the measurementsmade
I
|I
I
t h e e n d o f t ' 4 a r c h1 9 8 0 i s g i v e n ' R e s u l t s
I
"
t
l
m
e
a
s
u
r
e
m
e
n
t
s
t
h
e
r
v
i
t
h
c
o
n
c
e
r
n
e
d
p
r
e
s
e
n
t
e
d
are
torver eigenfrequencies, eigenfrequencies of the
I
of bothl
stationary rotor and the characteristics
until
f lapv;ise bending liroments. The f indings are com- |
I
pared with the design assutnptions' and the agreel
found to be good. In the second part
blade
the possible occurrence of stall-induced
vibrations is investigated. Vibrations with
ments is
flapping
one degree of
eigenfrequency are reported
freedo:n model with
pendent load is presented.
and a
velocity-de-
Calculated
results
are shown v.rith agree reasonabl-y well with
A possible rnodificatio
measured characteristics.
of
group
stall
vibrations.
P.Lundsag€r,
first
19 B 1
A
l4easurements and a model for
i
.l
November
behaviour
turbine.
induced
UALE
the stay sYstem is
suggested.
Risd National
Availa.cle
on request
from Risd Library,
Fors@gsanleg RisO),
Laborabory (Risd Bibliotek),
DK-4000 Roskilde,
Denmark
Telephone: (03) 37 L2 12, ext. 2262. Telex: 43116
I
I