Approaches to the structural analysis of wind turbine blade designs are reviewed. Specifications and materials data are discussed along with the analysis of vibrations, loads, stresses, and failure modes

Spera, D. A.

English

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STRUCTURAL ANALYSIS CONSIDERATIONS
FOR WIND TURBINE BLADES
David A. Spera
NASA Lewis Research Center
Cleveland, Ohio
SUMMARY
Items which should be considered in the structural analysis
of a proposed blade design are briefly reviewed. These items
include the specifications, materials data, and the analysis of
vibrations, loads, stresses, and failure modes. The review is
limited to the general nature of the approaches used and results
achieved.
INTRODUCTION
Wind turbine blades are being designed in a variety of con-
figurations and are being manufactured from a variety of mate-
rials. It is the task of the structural analyst to verify that
a particular design satisfies all requirements concerning struc-
tural integrity. These requirements include freedom from fail-
ure mechanisms such as fatigue, buckling, yielding and fracture,
and limitations on deflection, wear, and corrosion. The purpose
of this paper is to briefly review the items which should be
considered when planning the structural analysis of a wind tur-
bine blade. These items include specifications, materials data,
and the analysis of vibrations, loads, stresses, and failure
modes. Specialized methods for performing these analyses will
not be discussed in this review, but rather the general nature
of the approach and the results.
Among the many critical components in a wind turbine sys-
tem, the blades are usually considered to be the most difficult
to design. Typically, wind turbine blades are long flexible
rotating airfoils which continuously sustain cyclic and transient
loads. They must operate efficiently at off-design conditions
because of the variability of wind speed and direction. As flex-
ible airfoils, they are subject to aeroelastic and mechanical
instabilities. However, the most difficult design requirements
are those which are inherent in all wind energy systems. These
are the requirements for all-weather operation, long service
life, and low cost. In spite of these difficulties, reliable and
economical wind turbine blades can be built, provided that the
design is verified by structural analysis of the scope described
i_ this paper.
For convenience, the activities of design and analysis are
treated here as being separate and distinct. In reality, they
are closely connected and iterative at the detail level. Refer-
ences 1 and 2 provide additional background information to illus-
trate this iterative process.
211
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SPECIFICATIONS
Specifications are the set of requirements which do not
change as iterations of structural design and analysis take place.
In general, specifications restrict the designer and establish
fixed allowable conditions or "criteria" for the analyst. Thus,
blade specifications must be clearly defined and should be no
broader in scope than is necessary to insure that the blade is
compatible with the rest of the wind turbine system. The speci-
fications of interest to the structural analyst can be grouped
conveniently into the following five categories: (i) performance;(2) site; (3) geometry; (4) loading; and (5) reliability.
Performance specifications define requirements on rotor
power, annual energy output, rotor speed, and wind speeds for cut-
in, rated, and cut-out operations. Site specifications would in-
clude the annual average wind speed, the cumulative distribution
of wind speeds during the year, the roughness of the terrain,
wind turbulence, wind shear, the elevation of the site, tempera-
ture extremes, and the seismic zone. Further information on per-
formance and site characteristics can be found in reference 3.
Geometry specifications establish requirements for compati-
bility between the blade and the other components of the wind tur-
bine system. These specifications include requirements on the
size of the blade, its aerodynamic profile, definition of inter-
faces such as hub connection, total blade weight, allowable
ranges for blade natural frequencies, and allowable deflections.
Loading specifications define sets of operating conditions
which constitute the required design load cases. Often, the
structural analyst will add other cases which are found to be
more severe. Tables I and II indicate the scope of design load
cases currently defined for large horizontal-axis wind turbines.
Table I lists the 21 load conditions and additional stability
conditions defined for the 2.5 MW DOE/NASA Mod-2 wind turbine
system now being designed by the Boeing Engineering and Construc-
tion Company (ref. 4). Table II presents the operating conditions
for i0 load cases considered during the design of the 3.0 MW
GROWIAN wind turbine currently being designed by the M.A.N. firm
for the West German government.
Reliability specifications are closely connected with the
loading specifications since they establish lifetimes and failure
modes which must be considered for each load case. They also
define other possible requirements such as lightning and corro-
sion protection and fail-safe design.
MATERIALS DATA
Documentation on the materials of construction is an impor-
tant item which is shared by the structural designer and analyst.
212
This documentation generally includes the following information:
1. Selection criteria, the specific materials in the design.
. Physical properties, such as specific gravity, thermal
expansion coefficient, and corrosion resistance.
. Mechanical properties, such as design allowable yield,
ultimate, and fatigue stresses (S-N) curves, elastic
moduli, ductility, and fracture toughness.
, Quality assurance considerations such as procurement
specifications, acceptance tests, process development
tests, and inspection criteria.
Figure 1 illustrates documentation of fatigue allowable
stresses by means of an S-N curve, in this case for a fiberglass/
epoxy composite material. A curve-fit line through the test data
is reduced in stress by one-third, to account for material varia-
bility and other degrading effects. The lettered points indicate
calculated stresses for given load cases, which fall below the
allowable lines, as required for a positive margin of safety.
Extra conservatism is required in establishing fatigue allow-
able stresses for blades if material deterioration by corrosion
and fretting is possible. This is particularly true for wind tur-
bine blades because of the requirement that they operate in an
all-weather environment for many years while being subjected to
continuous cyclic loading.
VIBRATION ANALYSIS
A vibration analysis is conducted to verify that the natural
frequencies of the blade are within allowable ranges, to avoid
amplification of periodic loads. In addition, mode shapes are
defined for each natural frequency for later use in the calcula-
tion of aeroelastic loads. The scope of the vibration analysis
should also include consideration of aerodynamic instabilities
such as classical flutter and divergence.
Vibration mode analysis of structures like blades is usually
conducted by means of finite element models and structural analy-
sis computer codes like NASTRAN. The finite element model may be
very detailed (ref. 6) if many modes are required or quite simple
(ref. 7) if a few modes are sufficient. Results are presented as
frequency tables (table 3, from ref. 6), Campbell diagrams (fig-
ure 2, from ref. 2), and normalized deflection shapes.
LOAD ANALYSIS
The objective of the load analysis is to define the forces
and moments acting on cross-sections of the blade at stations
213
along its span. These forces and moments are technically
"internal" loads which result from "external" load sources such
as the wind, gravity, and inertia. Static, cyclic, and tran-
sient loads must all be calculated in order to evaluate the
structural integrity of the blade. Critical static loads occur
during extreme winds. Cyclic loading occurs continuously during
wind turbine operation as a result of the effects of gravity
and variations in wind speed across the rotor disk. Transient
loads are usually critical during rapid shutdown of the machine.
Specialized computer codes are available to calculate both
external and internal loads in wind turbine blades and in complete
wind turbine systems (Ref. 8). Input to these cases includes
blade mode shapes and natural frequencies (see VIBRATION ANALYSIS),
chord and mass distributions along the blade span, airfoil lift
and drag coefficients, rotor and wind speeds, blade twist and
pitch angles, etc.
The load analysis is the key to determining whether or not a
design meets the specified requirements. The load analysis
approach should be well documented, including the load cases to
be analyzed, the computer codes to be used, supporting information
such as sign conventions and nomenclature, and limitations of
restrictions. The load analysis is often conducted on an
idealized model of the blade, and this model must be documented
as well.
Figures 3 and 4 show typical results of blade load analysis.
Figure 3 (Ref. 2) shows a typical spanwise distribution of
maximum and minimum flatwise (out-of-plane) bending moments which
occur during each rotor revolution at rated conditions. These
loads are the basis of a subsequent fatigue endurance analysis
for this operating condition. Figures 4 (a) and (b) (Ref. 9)
show typical variations in cyclic flatwise and edgewise (in-plane)
moment loads near a blade root, as the wind speed varies. Cyclic
moment is defined as one-half the difference between the maximum
and minimum moments during one rotor revolution. The predicted
lines in Figures 4 (a) and (b) are for levels of load designated
as "mean +i_", which means that approximately 84 percent of the
rotor revolutions at a given wind speed are expected to exhibit
cyclic loads smaller than the prediction and 16 percent would be
larger. Consideration of the statistical variation in blade loads
is required either in each load analysis or in the subsequent
stress analysis.
STRESS ANALYSIS
After loads have been defined at selected blade cross-sections
for each required load case, local stresses can be calculated by
conventional methods. The simplest of these methods considers the
blade to be a beam. This is usually sufficient for the calculation
of spanwise stresses in the surface elements of the blade away from
214
discontinuities. Blades with internal webs and spars are
treated as multi-cell airplane wings (Ref. i0) when shear
stresses are important.
For increased accuracy, finite-element models of the NASTRAN
type are used for the analysis of stress, particularly at critical
joints. Figure 5 (Ref. 2) illustrates the complexity of a finite-
element model of a blade root. Because of this complexity and
the accompanying expense, finite-element modeling is usually
restricted to critical segments of the blade, in order to calculate
joint stresses or to verify buckling margins, for example.
Because of the requirement that wind turbine blades must
function under cyclic loading in an all-weather environment for
many years, special attention must be given to so-called
"secondary" stresses. These are the stresses caused by discon-
tinuities in cross-sections, transverse loads from spars and ribs,
fit-up loads, etc. These stresses can contribute to fatigue
failures and must be considered as primary, not secondary.
Documentation of the stress analysis procedures should include
descriptions of the critical sections to be analyzed, the computer
codes used, cross-sectional dimensions and properties, and appro-
priate stress concentration factors which account for fasteners
and other discontinuities.
FAILURE MODE ANALYSIS
Failure mode analysis is the final step in judging the
structural integrity of a wind turbine blade or of any structural
component. Failure modes which must be considered include fatigue,
buckling, yielding, fracture, deflection, and wear. Theoretically,
the analyst can determine margins of safety by simply comparing
calculated stresses with design allowable stresses (see MATERIALS
DATA). In reality, engineering judgment is required because of
such factors as the statistical nature of the blade loads,
approximations in the stress analysis, and allowances for environ-
mental effects, unless the latter have been included in the design
allowable stresses.
Upon completion of the failure mode analysis, margins of
safety are documented for all sections of the blade, with respect
to each failure mode. Figure 6 illustrates this documentation
for the Mod-2 blade (Ref. 4). The structural analyst then judges
whether or not the requirements of the specifications have been
satisfied and discusses deficiencies, if any. Finally, recommenda-
tions are made concerning any design changes or operational limits.
CONCLUDING REMARKS
The design and analysis of wind turbine blades is still in
a state of development. Nevertheless, valid judgments as to the
215
structural integrity of a proposed blade will continue to depend
on careful consideration of the factors described briefly herein:
the specifications, materials data, vibrations, loads, stresses,
and failure modes• In general, the structural integrity of a
wind turbine blade is judged by the same methods which are
used for many other structures• However, the difficult require-
ments of all-weather operation and very long life under continuous
cycling demand that special consideration be given to secondary
stresses, and that extra conservatism be used in setting fatigue
allowable stresses•
REFERENCES
le Cherritt, A. W.; and Gaidelis, J. A.: 100-kW Metal Wind
Turbine Blade Basic Data, Loads, and Stress Analysis.
NASA CR-134956, 1975.
• Griffee, D. G., Jr.; Gustafson, R. E.; and More, E. R.:
Design, Fabrication, and Test of a Composite Material Wind
Turbine Rotor Blade• DOE/NASA/9773-78/1, NASA CR-135389,
1977.
Be
•
Justus, C. G. : Winds and Wind System Performance.
Institute Press (Philadelphia), 1978.
Franklin
Anon. : Mod-2 Wind Turbine System Concept and Preliminary
Design Report• NASA CR-(to be published).
e Kussman, A.: Wind Rotor Load Conditions• DFVLR,
Inst f. Bau. U. Konst, Stuttgart (no reference available).
• Stahle, C., Jr. : Mod-i WTG Dynamic Analysis. Wind Turbine
Structural Dynamics, DOE Publ. CONF-771148, NASA Conf.
Publ. 2034, 1978, pp. 15-29.
•
.
Sullivan, T. L.: Simplified Modeling for Wind Turbine Modal
Analysis Using NASTRAN. Wind Turbine Structural Dynamics,
DOE Publ. CONF.-771148, NASA Conf. Publ. 2034, 1978,
pp. 31-37•
Spera, D. A.: Comparison of Computer Codes for Calculating
Dynamic Loads in Wind Turbines. DOE/NASA/1028-78/16,
NASA TM-73773, 1977.
• Spera, D. A.; Janetzke, D. C.; and Richards, T. R.: Dynamic
Blade Loading in the ERDA/NASA 100-kW and 200-kW Wind
Turbines• ERDA/NASA/1004-77/2, NASA TM-73711, 1977.
i0. Peery, D. J.: Aircraft Structures.
(New York), 1950, p. 491.
McGraw-Hill Book Co.
216
Q.
No
Q.
No
Q.
No
DISCUSSION
There was much talk about all the available tools, but no discussion of the
most difficult part of the analysis, the fatigue environment over the life
of the machine. What are your thoughts on that?
As you may recall, in the S-N curve that was shown, there were some words
about spectra. The machine does not see just one cyclic load through its
life which gives rise to cyclic stresses of a certain amplitude. It sees a
wide variety of load cycles, and generally what is done is to categorize
those cycles as to their size and the number of times they occur. This then
becomes the load spectrum.
We do not yet have measured load spectrum for wind turbines, as you might
expect would exist for a bomber wing or a fighter aircraft tail section.
Also, we don't as yet have extensive "flight'! spectra. Such data will be
obtained from the Mod-OA and Mod-i tests. However, it is necessary to
account for not only the normal operating conditions, but for all of the
abnormal operating conditions that make up this spectrum.
The cyclic loading is basically a statistical process. If it is measured
on the Mod-O, that doesn't indicate what will happen to another machine.
A better feel may be obtained, but you won't know for sure. Don't you have
to approach the problem in a statistical sense?
Yes. We are doing that in any load calculation. Some type of a probability
of that load occurrence must be assigned. On one of the diagrams which was
shown, the calculated loads were assumed to be the mean load plus one sigma,
or one standard deviation. That is, 84 percent of the cycles at that partic-
ular condition of wind would be expected to fall below that load level.
That will probably vary from machine to machine.
Our experience can help with certain items. For example, the number of
times the machine is started and stopped can be estimated. This is a very
significant load cycle. Also, the response of the Mod-OA machines to gusts
tells us how often gusts of various sizes will occur.
Did the failure of the Mod-O blade occur on the upper or lower surfaces or
on both surfaces?
The cracks which did occur in the root area were first seen on the low pres-
sure side of the blade, which would be the upper side. The blade is highly
twisted, so that is why it is hard to answer that precisely. However,
cracks generally occurred on the low pressure side of the blade first.
217
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EQUIV.
STRESS
RANGE
PSI
• DESIGNPOINTSFOR 150' BLADE
28_
24- _ o
2O
16
12
8
4
0
A
A
B
C
D
E
F
G
120 MPH WIND 7
MAX F_THER RATE
I
MAX UPGUSTAND OVERSPEED (KAMAN)
MAX YAW ERROR
MAX DOWNGUST
RATEDWIND
RMS OF OPERATINGSPECTRUM(BEC/SCI)
_ °_
•E 30 YR
i
t I I I v" LIFE i
104. 105 106 107 108 109
(NASA)
(BEC)
(KAMAN)
LIFE,CYCLES
FIGURE1, - FATIGUEDATA FOR FIBERGLASS/EPOXYCOMPOSITEMATERIAL(TFT).
221
8,0
7.0
6,0
5.0 /
4,o
N FIRST
= 3,0--EDGEWISE
_ 2,O
FIRST
:LATWISE
i,o /,z///
o
0 10 20 30 40 50 60
ROTORSPEED.RPM
FIGURE2, - CAMPBELLDIAGRAM9F UNCOUPLEDFREQUENCIESF9R 62,5 FT,
COMPOSITEWINDTURBINEBLADE,(REF,2).
z
_, 4
J
2
o
"- 0
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,,5 -2
10!
,,\
\
MAXIMUM\
-....
"f _ MIIIMUM
14
0 1 2 3 4 5 6 7 8 x 102
SPANWISESTATION.IN,
FIGURE3, - CALCULATEDFLATWISEMOMENTDISTRIBUTIONIN62,5 FT, COMPOSITE
WIND TURBINEBLADE- LOAD CASE1, (REF,2).
222
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223
FIGURE5, - FINITE ELEMENTMODELOF ROOTSECTIONOF
62,5 FT, COMPOSITEWINDTURBINEBLADE, (REF, 2).
Sta
+0.59 Sta
1550
+0.00 Sta
1320St a
1250
+0.04 Sta
920
BUCKLINGMARGINSOF SAFETY
(1.35 x PEAKLOAD)
+0.01
FATIGUE MARGINSOF SAFEI_P"u
(2 x 108 CYCLES)
Sta
650
+0;05 Sta
360
+0.0_
Sta
+0.00 90 Sta
0
FIGURE6, - ROTORBLADESKIN GAGES- MARGINSOF SAFETYFORTHE
2,5 MWMOD-2 WINDTURBINESYSTEM, (REF, 4),
224


Structural analysis considerations for wind turbine blades

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