Introduction
Reliability, i.e., serviceability and structural integrity of rotor blades,
is essential to fulfill the requirements placed on a wind turbine in the
field. Serviceability is of economic interest while integrity is of interest
from a safety point of view. Before a rotor blade design goes into operation,
a full-scale blade test (FST) is required in the certification process to
validate the assumptions made in the design models. Wind turbine rotor blades
are designed and certified according to the current standards and guidelines
(International Electrotechnical Commission). As part of the
certification process, static as well as fatigue loads are applied to the
rotor blade. Static and fatigue loads are usually applied in the two main
directions, i.e., lead–lag and flapwise. Damage-equivalent fatigue test
loads are applied to the rotor blade, but they do not necessarily reflect the
actual load direction, amplitude and mean during its service life.
Although (Det Norske Veritas Germanischer Lloyd Aksjeselskap) accepts combined static full-scale
tests (SFST) rather than pure lead–lag and flapwise, the importance of which is
highlighted in and , this
approach is rarely used for certification tests.
Attempts have been made to improve fatigue full-scale blade testing (FFST)
towards a more realistic scenario by minimizing the overloading, i.e., the
deviation between applied test bending moments and target bending moments as
per the design requirements. For example,
applied an algorithm to optimize the bending moment distribution for
uni-axial, resonant FFST by using additional masses and determining optimal
actuator positions and excitation frequencies. Moreover,
propose a uni-axial multifrequency approach to
replicate the actual spatial damage distribution more realistically. Bi-axial
FFST is an approach that emulates more comprehensive damage along the blade's
circumference . The random-phase bi-axial resonant
excitation has been a focus of research for a number of years
.
Yet another approach is the phase-locked excitation with frequency ratios, e.g.,
of 1 : 1 between the flapwise and lead–lag mode
. The flapwise mode is excited in its
eigenfrequency while the lead–lag mode is forced in the same frequency
. Alternatively, both modes can be excited in
resonance by tuning both eigenfrequencies independently with the concept of
virtual masses .
states that during fatigue testing, the mean loads
applied shall normally be as close as possible to the mean load under the
operating conditions that cause the most severe fatigue damage. The
importance of considering mean loading for the fatigue life evaluation of
fiber-reinforced polymers is described and quantified in
.
According to lead–lag fatigue loading is the design-driving loading for current and future rotor blades.
Therefore, this work focuses on the most sensitive area for the lead–lag load case, i.e., on the trailing-edge bond line in particular.
, and
proposed subcomponent test (SCT) concepts to
investigate the structural performance of trailing-edge bond lines in
particular. showed an alternative SCT method
for investigating the flapwise buckling response of a blade segment.
Within this work, SCT is presented as a means to potentially overcome some of
the drawbacks of FST. The intention of applying SCT is not to overcome the
necessity of FST. The method of SCT, however, has the potential to be
considered as a standard intermediate test before, during or after
certification. By taking the target mean loading and thus the stress ratio
between the minimum and the maximum stress exposure at the trailing edge into
account, the structural evaluation of the blade can be approached more
realistically compared to field simulations. The testing time can be reduced
significantly by means of SCT when considering the case of a particular blade
segment validation, recertification due to a repair or design retrofit
solution.
First, the FST and SCT concepts are described.
Second, on the basis of calculations the benefits of SCT over static and fatigue FST are highlighted.
Comparison of subcomponent with full-scale blade testing
In the following, the benefits and drawbacks of SCT
over static and fatigue full-scale blade testing (FST) are elaborated.
An advantage of SCT over FST is that the number of relatively inexpensive
specimens can be increased to investigate different design variants of a
critical blade detail, for example. Owing to the smaller dimension and
relatively small displacements of an SCT, it is possible to conduct
experiments under environmental conditions, e.g., in climate chambers, and
to better observe the experiment via optical measurement systems, such as
the digital image correlation shown by .
A disadvantage of SCT is that only a segment of the blade is considered for
testing. Furthermore, the design of the boundary conditions of an SCT relies
on detailed models, e.g., for the determination of blade properties of a
cutout segment as explained in .
The focus of the following sections is on the problem of constrained areas
and overloading of blade parts, the load direction in static and fatigue
testing, as well as on the stress ratio at the trailing edge and the
resulting testing time.
Load deviation ΔM between test bending moment and target
bending moment determined for the DTU10MW blade and test setup for static
full-scale test (SFST) in side view (excerpt from
) (a), fatigue full-scale test (FFST) in top
view (b) and blade cutout subcomponent test (SCT) (c). Untested areas are
shown in gray.
Constrained areas and overloading
Load frames diminish tested areas because they constrain the structure
(Fig. a). The longitudinal dimension of the
constrained area at a load clamp is assumed to be ±75 % of the
local blade chord length . Critical cross sections should
not be within constrained areas. Owing to the multilinear moment
distribution in the static test, the critical areas are necessarily in under-
or overloaded areas (Fig. a). Thus, due to the
setup of an FST, these areas are subjected to a load deviation, which means a
lower or a higher test loading Mtest compared to the target load
envelope Mtarget:
ΔM=MtestMtarget.
In the fatigue FST, the constrained area is reduced to solely one load clamp,
which increases the area for this test
(Fig. b). The load deviation ΔM,
however, can be even higher for the blade (overloading by up to 20 %)
although mass tuning is conducted. Overloading occurs along all tested areas
because the shape of the target moment distribution cannot be fully
replicated by the test moment distribution. That is, parts of the blade can
be damaged far beyond their fatigue life before all relevant areas reach
their target damage.
In an SCT, the constrained areas are determined by means of a method similar
to that used in FST (Fig. c). This implies that
a reasonable length of the specimen should be chosen to replicate, for
example, a realistic buckling response. The overloading in the tested areas,
however, is close to zero, since the bending moment can be adjusted by
specially designed boundary conditions .
Moreover, in an SCT the cross section of interest can be tested up to its
final fatigue limit state compared to an FST, where other, highly overloaded
blade areas may limit the damage that is required to reach the final
fatigue limit state at the cross section of interest.
Load envelopes in terms of moment vectors determined from
aeroservoelastic simulations for several cross sections of a 34 m
blade and certification test loads contrasted with strength and stability
resistance of the whole blade's cross sections from 0 to
100 % blade length (lB) in terms of the root bending moment
(excerpt from ). The two moment vectors
represent the critical load directions at 35 and
50 % lB.
Load direction in static testing
When designing a static FST, the usual procedure is to use a worst-case
load envelope of each cross section along the blade span
(Fig. ) to create the target loads. From these
envelopes at least two load directions are extracted for the static load
case. Either the pure lead–lag or flapwise load cases (PTS, STP, LTT and
TTL as explained in Fig. ) or any combination of these
load directions can be chosen for the tests. Considering the stress exposure
(Eq. ) of the critical area of interest of each cross section
individually, however, the load direction leading to the critical stress
exposure is not necessarily identical to the overall full-scale loading
directions.
In Fig. the load envelopes at different
cross sections along the blade are plotted against the strength and stability
resistance envelope of all cross sections, i.e., the whole blade.
Furthermore, the load direction with the critical stress exposure is
highlighted by way of example for two different cross sections at 35 %
blade length (lB) and 50 % lB, where the critical
load directions are a combination of PTS plus LTT and STP plus LTT,
respectively.
Theoretically, the load envelopes should be compared to the resistance
envelopes at each particular cross section to determine the most critical
load directions. The determination of the resistances for each cross section
is only possible via analysis of a blade segment or subcomponent cutout
from the full blade subjected to the load envelope determined from
aeroservoelastic simulations.
SCT allows for the flexible adjustment of these critical loading
configurations for particular blade segments on an individual basis.
Load direction in fatigue testing
With regard to the load direction, the uni-axial, resonant FFST is constrained
to the static blade dead load (suction-side points towards the strong floor)
superimposed with the dynamic inertia loads of the mode shape of the blade.
According to , the mean loads applied during FFST shall be
as close as possible to the mean load at the operating conditions that cause
the most severe fatigue damage.
Since no load directions other than the first and second modal shapes, i.e., lead–lag and flap, are possible, the only degree of freedom during uni-axial,
resonant FST is the direction of the gravity load due to the pitching
position of the blade.
The loads for FFST and field calculations are elaborated by way of example
using the DTU10MW reference turbine with respect to the
loading of the trailing-edge bond line. A simplified load calculation was
conducted comprising the superposition of the quasistatic mean flapwise
aerodynamic load for 10 wind speed bins plus the lead–lag gravity load due
to the rotor revolution as a function of the blade pitch angle.
A beam model implemented in ANSYS APDL (ANalysis SYStem Parametric Design Language) was assembled with a
fully populated cross section stiffness matrix determined by the BEam Cross
Section Analysis Software, BECAS . The blade parameterization and
input generation were conducted using workflows from the FUSED-Wind framework
. The BEM-based aerodynamic rotor simulator
CCBlade was used and populated with airfoil polars
determined by Rfoil, an extension of Xfoil including
rotational effects .
The lead–lag load cycles were determined on the basis of wind speed
distribution and the rotor revolution as well as the design life of 20 years.
Furthermore, damage-equivalent loads were determined following
using an S–N exponent of m=10, which is a
typical value for a glass-fiber-reinforced epoxy
and ultimate loads as of
.
The greatest damage impact was found at wind speeds around
conditions rated between 11.0 and 15.6 ms-1
(Figs. and ).
found similar results for a 34 m
blade. The relative damage impact peak at around the rated wind speed of an
outboard cross section (Fig. ) protrudes over the
peak of an inboard cross section (Fig. ) because in
outboard regions the influence of aerodynamic loads predominates.
Relative damage of different wind speed bins at 10 % blade length.
Relative damage of different wind speed bins at 70 % blade length.
Moment vectors of lead–lag loading at different wind speed bins and
in a lead–lag fatigue full-scale blade test (LL-FFST) at different pitch
angles at 10 % blade length. A flapwise FFST (F-FFST) and the bounding box
of possible bi-axial FFST scenarios (B-FFST) are shown.
Moment vectors of lead–lag loading at different wind speed bins and
in a lead–lag fatigue full-scale blade test (LL-FFST) at different pitch
angles at 70 % blade length. A flapwise FFST (F-FFST) and the bounding box
of possible bi-axial FFST scenarios (B-FFST) are shown.
Furthermore, uni-axial, resonant, flapwise and lead–lag FFSTs were designed.
To this end, the flapwise and lead–lag target loads were calculated on the
basis of damage-equivalent loads and scaled according to
and to cycle
numbers of respectively 1.0×106 and 3.0×106 using an S–N
exponent of m=10. The test loads were determined on the basis of the
inertia loads caused by the dynamic excitation of the first flapwise and
lead–lag dominated eigenmode extracted from a modal analysis. This load
distribution was superimposed with the gravity loading according to the FFST
setup for different pitch angles θ, where θ=0∘
corresponds to the suction side pointing towards the strong floor and a
negative pitch angle which rotates the leading edge towards the floor.
The minimum and maximum bending moment vectors acting at each wind speed bin
according to field calculations and for three pitched lead–lag FFSTs are
shown for two cross sections at 10 and 70 % blade length
(Figs. and ). From the
angle between the minimum and maximum moment vectors at the inboard cross section
it can be seen that the lead–lag gravity loads dominate. Moreover, bending
moment vectors for the flapwise FFST are superimposed with the lead–lag
FFST. The resulting bounding box represents the extremes of the bending
moment vector in different bi-axial testing scenarios, i.e., random-phase
and phase-locked excitation with different flapwise and lead–lag testing
frequency ratios . The minimum and maximum bending
moment vectors are highlighted for a bi-axial testing scenario that is closest to
the field conditions.
Axial strain along the trailing-edge bond line at different wind
speed bins, lead–lag (LL-FFST) and bi-axial (B-FFST) fatigue full-scale blade
tests at different pitch angles.
Moreover, showed that the quantity of
geometrically nonlinear deformations, e.g., breathing or pumping of
the trailing-edge panel, depends on the load direction. In particular, this
deformation is expected to be most prominent for moment vectors within the
second and fourth quadrants of the cross section coordinate system as shown
in Figs. and .
Pitching the blade in an FFST helps to adjust the mean load direction towards
field load directions for one cross section along the span. In an SCT
setup any of the loading scenarios for the different wind speed bins which
are shown can theoretically be replicated by shifting the load introducing
ball joints while tuning the bending moments ,
leading to a more realistic loading condition in the test.
Using the loading of the most severe wind speeds (11.0,
13.3, 15.7 ms-1), the longitudinal strains in the direction of
the blade span at the trailing-edge bond line were determined for the minimum
and maximum amplitudes (Fig. ). It can be seen that the
trailing-edge bond line is loaded more in compression during an FFST at
θ=0∘ compared to the strains determined from field
load calculations.
Assuming linear elastic material behavior, the stress ratio R can be
expressed as the strain ratio between the minimum and maximum longitudinal
strains:
R=εlminεlmax.
Considering the R of the field load calculation (Fig. ), the
deviation becomes even more prominent towards the tip, where the loading
tends more towards a tension–tension than a tension–compression
loading condition. Pitching the blade in an FFST increases the stress ratio,
but the inclination of the stress ratio distribution is the opposite to that obtained
in field simulations. Thus, in an FFST only the stress ratio of a defined
cross section can be obtained via pitching. As already stated above, in an
SCT the stress ratio can be adjusted according to the cross section of
interest.
Stress ratio R of the axial strain along the trailing-edge bond
line at different wind speed bins, and lead–lag (LL-FFST) and bi-axial
(B-FFST) fatigue full-scale blade tests at different pitch angles.
Stress ratio and testing time
The testing time is compared for the two testing concepts FFST and SCT.
To this end, the loading at the trailing-edge bond line due to FFST is compared to the field calculations.
On the basis of the formulation by , the
internal loading of a material is expressed in terms of stress exposure e
(also referred to as effort), which means an ambient stress σ over the
allowable stress (fracture resistance), which is here the tensile strength
Rt. Thus the stress exposure is generally defined as
e=σRt.
Furthermore, the materials of a rotor blade, i.e., adhesive, resin and glass
fiber, can be considered to be isotropic. Assuming that a symmetric constant
life diagram is applicable for an isotropic
material , the allowable cycle number to failure
Ni for a given load collective i, with a mean stress exposure
eim=|σim|Rt and a stress exposure
amplitude eia=|σia|Rt, is derived
from
Ni=1-eimeiam.
This means that the cycle number is directly related to the mean stress
exposure, the stress exposure amplitude and to the material-dependent S–N
curve exponent m.
Assuming the same S–N curve exponent m for different stress ratios,
R=eimineimax=eim-eiaeim+eia,
the allowable load cycle number of a load collective of any ratio NiR
and the allowable load cycles NiR=-1 can be expressed as the relation
(Appendix ):
NiRNiR=-1=1-eia1+R1-Rm.
The relation is plotted for different stress exposure amplitudes in Fig. .
Impact of stress ratio on the relation between allowable cycles
using any testing stress ratio and a stress ratio of R=-1
(Eq. )
shown for different stress exposure amplitudes. An S–N curve exponent of
m=10 was used.
The pure testing time in days can be determined using
Ttest=Ntestftest⋅1day86400s,
where Ntest corresponds to the number of test cycles and
ftest to the test frequency.
For a lead–lag FFST of the DTU10MW blade in a pitching position of θ=0∘ and a test frequency equal to the blade's eigenfrequency of
ftest=0.965Hz, a stress ratio of R=-0.9 with an stress
exposure amplitude of ea=0.25 and Ntest=3.0×106 results in a testing time of Ttest≈36days. If the blade is pitched at θ=-20…-40∘, the stress ratio is increased from R=-0.9 to
R=-0.5 and gets closer to stress ratios from field load calculations
(Fig. ). To overcome too high tension strains
(Fig. ), the stress exposure amplitude is decreased to
ea=0.125. Owing to the effect of a higher stress ratio the
testing time can be reduced by 23 % to Ttest≈28days (green dot vs. red dot in Fig. ).
When performing an SCT of a blade segment at 10 % blade length, the
stress ratio of R=-0.9 is close to the field calculations
(Fig. ). For this case, the testing time cannot be reduced by
the testing cycles Ntest but only by an increase in testing
frequency. Assuming a frequency of ftest=1.0…1.5Hz, the testing time is slightly to moderately
reduced to Ttest≈35…23days compared to
an FFST at θ=0∘. When a segment at 70 % blade
length is considered for an SCT with a realistic stress ratio of R=-0.25 from field calculations (Fig. ) and an stress exposure
amplitude of ea=0.25, the test cycles can be further reduced by
47…68% compared to an FFST with a pitch angle
between θ=-20…-40∘ (green square
vs. red dot in Fig. ). Assuming a test frequency between
ftest=1.0…1.5Hz, the testing time
results in Ttest≈11…7days.
Conclusions
The loading conditions of a combined static full-scale blade test (SFST), lead–lag and bi-axial
fatigue full-scale blade test (FFST) were compared to field simulations.
It was demonstrated that SFST does not necessarily cover all critical loading
conditions along the blade length. Blade subcomponent testing (SCT)
allows the flexible adjustment of the load direction for each segment of
interest individually. Thus, the use of SCT could enhance the structural
reliability by covering all relevant loading directions in contrast to
testing the blade solely in its full-scale loading directions.
The simultaneous benefit and drawback of the SCT method is that only one blade segment is considered.
Furthermore, the design of the boundary conditions of an SCT relies on detailed models.
It was calculated that the load directions and the stress ratios at the
trailing-edge bond line along the blade differ significantly in part between
the field and FFST. The load direction and stress ratio of a particular
cross section in an FFST, however, can be arbitrarily adjusted towards the
field load conditions by pitching the blade. The calculation has shown that
the load direction in a bi-axial FFST seems to be closer to the field
load conditions, but it does not affect the stress ratio at the trailing-edge
bond line along the blade, whereas an SCT can be adjusted in any case to
realistically replicate the field conditions. Furthermore, using SCT means
the testing time of one blade segment can be significantly reduced when the
field stress ratio is larger than the stress ratio the blade is subjected to
in FFST.
There are different application scenarios for SCT, e.g., the detailed
exploration of different design variants of a certain blade part under
specific loading (not possible in FST). These experiments can be conducted
within the design phase before or in hand with the certification FST or, in
the case of a design revision, after the certification FST. Although these
benefits of SCT can add value to the design process, SCT is not necessarily
intended to replace FST.
On the basis of the assumptions presented for the damage
calculation, it is shown that the mean stress level plays a substantial role in the fatigue damage calculation.