Burton T. (et. al.) Wind energy Handbook

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the grid-loss case is liable to become the critical one as regards out-of-plane bending

moments, unless the tip deployment time can be reduced sufﬁciently.

The ‘Normal turbulence model’ speciﬁed for load case 1.1 includes random

variations of both the longitudinal wind velocity component about the 10 min mean

and the lateral component about a zero mean. Both components are taken to be

Gaussian distributed, with the standard deviation (m/s) of the longitudinal compo-

nent of turbul ence given by



¼ 0:18(

15 þ

hub

)(7:8)

for a Class A site and the standard component of the lateral component of turbulence

taken as 0:8

. The design load case is then the set of conditions existing over at least

one rotation cycle that produces the extreme value of the loading under evaluation.

Utilizing the probability distribution of the longitudinal wind velocity component

about the 10 min mean in combination with a Weibull distribution of 10 min mean

wind speeds on the one hand, and the probability distribution of the lateral wind

velocity component on the other, it is possible to establish, for wind speed ‘bins’

corresponding to different values of the longitudinal wind speed component, the

maximum yaw angle that would occur for at least one rotation cycle over the

machine design life. For each case, the out-of-plane bending moment at 12 m radius

is calculated (allowing for shaft tilt), enabling the critical case to be identiﬁed. It is

seen from Table 7.1 that the combination of 40.4 m/s wind speed and 278 yaw angle

is the most severe, producing a moment of 130 kNm, which is 10 percent larger

than the moment produced by the worst of the deterministic load cases (load case

1.3). Note that the 40.4 m/s wind speed here is the resultant of a longitudinal

velocity component, assumed parallel to the shaft axis in plan, of 36 m/s and a

lateral component of 18.3 m/s. Thus the yaw error arises from an additional lateral

component which increases the total wind speed, in contrast to load cases 1.3 and

1.8 where the wind merely changes direction.

The derivation of the extreme 12 m radius out-of-plane bending moment for the

‘Normal turbulence model’ load case described above is conservative on three

counts, because no allowance is made for the following:

• lack of correlation of the wind over the outer 40 percent of the blade,

• limitation on maximum wind speed seen during operation by high wind cut-out,

• limitation on maximum yaw angle by yaw control.

The alleviation of extreme loadings by high wind cut-out and yaw control depend

on the averaging times applied to the wind speed and direction signals by the

control system.

Extreme loading during operation: pitch-regulated machines

The charact erization of extreme operational loadings on pitch-regulated machines

is inevitably more complicated than for stall-regulated machines, although at the

BLADES 395

same time it should be more accura te because of the avoidance of uncertainties

associated with stall. It is instructive to focus comparisons on the blade bending

moment about the weak axis at 60 percent radius once again. This time it is referred

to as the ﬂapwise bending moment rather than the out-of-plane (of rotation)

moment because of blade pitching.

Figure 7.10 presents the variation of 60 percent radius ﬂapwise bend ing moment

with short-term mean wind speed at several yaw angles for a 500 kW, 40 m

diameter pitch-regulated machine ﬁtted with TR blades and rotating at 33 r.p.m.

The rated speed, V

, is 12 m/s and other parameters, including the wind shear

exponent, are the same as in the stall-regulated example above. The ﬁgure only

shows the bending moments resulting from slow variations in wind speed, i.e.,

those which can be followed by the pitch control system, so moments arising from

faster wind speed ﬂuctuations must be added to obtain the total. The curves are

very different in shape from those obtained for the stall-regulated machine. The

12 m radius ﬂapwise bending moment reach es a peak at rated wind speed, and

then drops off sharply, becoming negative by about 24 m/s in the case of zero yaw

and zero wind shear. This is because the blade has pitched to such an extent that

the outboard section of the blade is providing a braking torque to counteract the

increased torque from the inboard section. At high wind speeds and yaw angles,

large negative bending moments are developed, which approach the magnitude of

the peak positive moment at rated speed. Note that the bending moment reduces

with negative yaw angle at zero azimuth, instead of increasing as it does for stall-

regulated operation. This is because blade pitching renders angle of attack, which is

reduced under these conditions, more critical than relative velocity. Plots of the

-80

-60

-40

-20

0 5 10 15 20 25 30 35 40 45

Wind speed (m/s)

12 m radius flapwise bending moment (kNm)

Shear exponent = 0.2

Rotational speed = 33 r.p.m.

Full-line curves are for 0

⬚ azimuth

Dashed lines are for 180

⬚ azimuth

0⬚ yaw,

0⬚

azimuth

0⬚ yaw,

180⬚ azimuth

⫺20⬚ yaw

⫹20⬚ yaw

⫺20⬚ yaw

⫹40⬚ yaw,

180⬚ azimuth

⫺40⬚ yaw,

0⬚ azimuth

Figure 7.10 Variation of 12 m Radius Flapwise Bending Moment with Short-term Mean

Wind Speed at Various Yaw Angles for an Example 40 m Diameter Pitch-regulated Machine

with TR Blades

396

COMPONENT DESIGN

variation of ﬂapwise bending moment with short-term mean wind speed at inboard

blade cross sections are essentially similar to those in Figure 7.10, because moments

are dominated by loadings on the outboards por tion of the blade.

To the extent that the pitch control system can keep pace with the wind speed

transients, the curves in Figure 7.10 can be used to provide an approximate

indication of the extreme bending moment s arising from some of the IEC 61400-1

deterministic load cases. Leaving aside the grid-loss case (where the outcome is

largely determined by rotor inertia and emergency pitching rate), it is seen that the

extreme moments are only about one half of the maxim um value for the stall-

regulated machine.

The spectrum of the longitudinal wind speed ﬂuctuations will contain signiﬁcant

energy at frequencies above the level at which the pitch control system can respon d,

and these have to be considered in the analysis of the ‘Normal turbulence model’

load case. Figure 7.11 illustrates the per turbations in 12 m radius ﬂapwise bending

moment for the above mach ine, as a result of such high frequency wind speed

ﬂuctuations, with respect to a sharp rise above rated wind speed (12 m/s) and

sharp falls below steady winds of 24, 28 and 32 m/s. In the ﬁrst case considered, the

yaw angle is 208 and the azimuth 08, as this conﬁguration yields the largest

positive bending moment at rated wind speed. In the second case, the yaw angle is

408, which exceeds the maximum value predicted over the design life, and

provides an upper bound on the largest negative moment at short-term mean wind

speeds around the cut-out value.

It is apparent from Figure 7.11 that rapid wind speed increases above rated wi nd

speed will produce a signiﬁcant increase in bending moment, but rapid reductions

in wind speed below, say, a 24 m/s steady value will not, as in this case the blade

goes into negative stall. Over the machine lifetim e, the maximum increase in wind

-80

-60

-40

-20

100

0 5 10 15 20 25 30 35 40

Wind speed (m/s)

12 m radius flapwise bending moment (kNm)

⫺20⬚ yaw,

0⬚ azimuth

⫺40⬚ yaw,

0⬚ azimuth

Rotational speed = 33 r.p.m.

Long curves show variation of bending

moment with short-term mean wind speed;

short curves show variation of bending

moment with rapid wind-speed fluctuations

from short-term mean value

Figure 7.11 Effect of Rapid Wind-Speed Fluctuations on 12 m Radius Flapwise Bending

Moment for an Example 40 m Diameter Pitch-regulated Machine with TR Blades

BLADES 397

speed above rated that does not produce a blade pitch response can be estimated

using

max

¼ 

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

=2

(n)

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

2 ln(T)

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

2 ln(T)



¼ (

)

n . =2

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

2 ln(T)

0:5772

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

2 ln(T)

(7:9)

where (

)

n . =2

is the standard deviation of wind speed ﬂuctuations above the

pitch response cut-off frequency (assumed to be half the rotational frequency) and

T is the total period of operation in the wind speed band centred on the rated speed

at the yaw angle under consideration. For a 12 m/s rated wind speed, 

2:34 m=s from Equation (7.8) and (

)

n . =2

¼ 2:34(0:4)

0:5

¼ 1:48 m=s. Taking a

wind speed band of 2 m/s and yaw angles between 20 8 and 408, the expression

in square brackets (i.e., the peak factor) comes to 5.5, so that the lifetime ex treme

value of the wind speed increase without pitch response is about 8 m/s. If the wind

speed ﬂuctuations over the outer 8 m of blade are treated as perfectly correlated,

this results in a maximum value of 12 m radius ﬂapwise bending moment of

96 kNm (se e Figure 7.11), which is over 50 percent greater than that occurring in a

steady 12 m/s wind. Thus the extreme ﬂapwise bending moment during operation

occurs at winds around rated rather than around the upper cut-out speed – a

phenomenon which is a normal feature of pitch-regulated machines. Also, the

extreme ﬂapwise bending moment is less than for the similarly rated stall-regulated

machine considere d above.

The relative criticality of the load cases corresponding to extreme turbulent wind

speed ﬂuctuations and the occurrence of the 50 year extreme operating gust during

operation at rated wind speed, which are exempliﬁed by IEC load cases 1.1 and 1.6

respectively, will be determined by pitch control system performance.

Extreme loading at standstill

The derivation of stationar y blade loads is described in Section 5.6. Figure 7.12

shows the out-of-plane bending moment distribution for a TR blade under the

action of a 60 m/s wind, corresponding to the 50 year return extreme 3 s gust

speciﬁed for a Class II wind turbine in IEC 61400-1. A uniform lift coefﬁcient of 1.5

is assumed. Two curves are shown: the lower curve is the quasistatic bending

moment while the upper one incorporates dynamic magniﬁcation due to excitation

of resonant oscillations (see Section 5.6.3).

For comparison purposes, the extreme operational out-of-plane bending moment

(excluding dynamics) for the example stall-regulated machine (load case 1.1, Table

7.1) is also plotted. It is clear that the operational load case is critical over mo st of

the blade length, though only by a small margin. The non-operational bending

398 COMPONENT DESIGN

moment distribution is more highly curved than the opera tional one, so the former

is more likely to govern at the root and the latter to govern outboard.

Extreme non-operational loads tend to govern blade out-of-plan e bending on

pitch-regulated machines, as extreme operational out-of-plane bending moments

are generally signiﬁcantly less than on stall-regula ted machines.

Fatigue loading

The importance of fatigue loading relative to extreme loading is very much a

function of material properties. As the vast majority of blades are manufactur ed

from composite materials with sim ilar fatigue properties, discussion in this sub-

section will be based on these.

As set out in Sections 7.1.6 and 7.1.7, composite materials are characterized by a very

shallow S– N curve i.e., the reciprocal index m in the relation  / N

1=m

for constan t

amplitude, reversed loading (R ¼1) is typically 10 or more. As a result, fatigue

damage can be dominated by the small number of high range stress cycles associated

with unusual wind conditions, rather than by the routine medium range cycles.

The other signiﬁcant property of composite materials is the increase in fatigue

damage with mean stress level, which is usually accounted for by scaling up the

stress amplitude entered in the R ¼1 S– N curve formulation by the factor

1=(1 

 = 

), where 

is the design strength in compression for a compression

mean or in tension for a tension mean. This increases the relative importance of

stress cycles with a high mean.

100

200

300

400

500

600

700

800

0 2 4 6 8 101214161820

Radius (m)

Extreme out-of-plane bending moment (KNm)

Extreme operational out-of-plane bending moment

for 40.4 m/s instantaneous wind speed

and 30⬚ skewed flow angle

excluding dynamic effects

(dotted line)

Rotational speed = 30 r.p.m.

Extreme non-operational out-of-plane bending moment

for 60 m/s gust and 1.5 lift coefficient

(lower solid line: quasistatic bending moment,

upper solid: bending moment including dynamic

magnification)

Figure 7.12 Comparison of Extreme Operational and Non-operational Out-of-plane Bend-

ing Moment Distributions for a 40 m Diameter Stall-regulated Machine with TR Blades

BLADES 399

Behaviour of stall-regulated machines in fatigue

For stall-regulated machines, the highe st out-of-plane bending moment ranges and

means normally occur at high wind speeds and yaw angles. This is illustrated in

Figure 7.9, which shows the variation in this moment with wind speed and yaw

angle at 60 per cent radius for a 40 metre diameter machine, based on the three-

dimensional data referred to at the start of Section 7.1.8 above. Note that above rated

wind speed, the bending moment plots level off, so that a given departure of the

lateral wind component from the zero mean, sustained over half a revolution, results

in a larger bending moment ﬂuctuation than a change in the longitudinal com-

ponent of twice this magnitude. For example, if the mean wind speed is

24 m=s, a lateral component of 6 m/s (corresponding to a yaw angle of 148) causes a

bending moment variation of 20 kNm when the blade rotates from 08 to 1808 azimu th,

compared to a variation of 17 kNm as a result of a 6m=s ﬂuctuation in longitudinal

wind speed (which, in any case, could only occur after many blade rotations).

Similar comments apply to vertical wind speed ﬂuctuations, but here there is a

built-in initial tilt angle between the air ﬂow and the shaft axis because of shaft

angle tilt and updraft. Thus bending moment plots derived from three-dimensional

wind simulations above rated are dominated by ﬂuctuations at blade-passing

frequency which bloom and decay as the angle between the air ﬂow and the shaft

axis rises and fall s. Superimposed on these are lower frequency ﬂuctuations caused

by changes in the longitudinal wind speed.

Clearly high wind/high yaw cycles will be a major source of fatigue damage,

although the contribution of cycles at wind speeds below stall may also be

important, because of the more rapid variation of moment with wind speed there,

and the much increased number of cycles.

Thomsen (1998) has investigated for blade root out-of-plane bending on a

1.5 MW, 64 m diameter three-bladed machine, taking a constant turbulence inten-

sity of 15 percent and a S– N curve index of 12. The results, including allowance for

mean stress, are plotted in Figure 7.13 (dotted), and indicate that the damage is

concentrated at wind speeds of 20 m/s and above. The ﬁgure also shows the effect

of adopting a steeper S– N curve (with m ¼ 10) and the IEC Class A turbulence

distribution (with increasing intensities as mean wind speed decreases). In each

case, the relative damage contribution at high wind speeds is reduced, but the

switch to the IEC turbulence distribution causes the more signiﬁcant change.

It should be noted that the relative contributions of different wind speeds to life-

time fatigue damage are also dependent on the shape of the bending moment/wind

speed characteristics. Thus for the machine with the bending moment/wind speed

characteristics at 60 percent radius presented in Figure 7.9, the peak damage occurs

at 10 m/ s, if the IEC Class A turbulence intensity distribution is assumed (see

Figure 7.15).

Behaviour of pitch-regulated machines in fatigue

For pitch-regulated machines, the highest ﬂapwise bending moment ranges occur

at high wind speeds and yaw angles, but the largest mean values occur around

400 COMPONENT DESIGN

rated wind speed. Moreover, blade pitching results in a rapid fall-off in bending

moment with short-term mean wind speed just above rated. This behaviour is

illustrated in Figure 7.10, which shows the variation in ﬂapwise moment with

short-term mean wind speed and yaw angle at 60 percent radius for a 40 m

diameter machine. It transpires that the combination of the steep bending moment/

short-term wind speed characteristic, high mean bending moment and large num-

ber of loading cycles just above rated wind speed results in more fatigue damage at

this wind speed than at higher wind speeds, where the increasing bending moment

ﬂuctuations due to yaw offset are mitigated by reducing mean loads and numbers

of cycles.

The nature of the bending moment ﬂuctuations at a mean wind speed just above

rated is shown on Figure 7.14, which is a time history obtained from a three-

dimensional wind speed simulation, for the machine with the bending moment/

short-term mean wind speed characteristics presented in Figure 7.10, (with the

response to high frequency wind speed ﬂuctuations allowed for separately). As

with the case of a stall-regu lated machine operating at high wind speed discussed

above, there are considerable bending mome nt ﬂuctuations at the rotational speed,

but this time they are largely due to spatial variations in longitudinal wind speed

across the disc (i.e., ‘gust slicing’) rather than due to yaw or tilt offset. In addition,

there are large low frequency bending moment ﬂuctuations as a result of short-term

mean wind speed changes – indeed, inspection of the bending moment and short-

term mean wind speed plots reveals an inverse relationship between the two.

The fatigue damage in ﬂapwise bending at 12 m radius arising from operation of

the above machine at different mean wind speeds ignoring dynam ics is plotted out

0 5 10 15 20 25 30

Mean wind speed (m/s)

Percentage contribution per 2 m/s bin

Turbulence

intensity = 15%,

m = 12

Turbulence

intensity = 15%,

m = 10

IEC turbulence

intensity, m = 10

No. of blades = 3

Rotor diameter = 64 m

Rotational speed = 17 r.p.m.

21%

17%

16.10%

Figure 7.13 Relative Contribution to Life-time Fatigue Damage for Different Wind Speeds

for a 1.5 MW Stall-regulated Machine, Including Effect of Mean Load, after Thomsen (1998)

BLADES 401

-10

0 50 100 150 200 250 300

Time (s)

Wind speed (m/s)

Bending moment (kNm)

Rotational speed = 33 r.p.m., Mean wind speed = 14 m/s, Rated speed = 12 m/s

Turbulence intensity = 18.4%, Integral length scale = 73.5 m,

Zero wind shear, Shaft tilt w.r.t. mean flow = 13⬚,

Figure 7.14 Time History of Flapwise Bending Moment at 12 m Radius and Short-term

Mean Wind Speed for 40 m Diameter Pitch-regulated Machine with Three TR Blades, Based

on Three-dimensional Wind Simulation with 14 m/s Mean

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 5 10 15 20 25 30

Mean wind speed (m/s)

Damage number per 2 m/s bin

Rotational speeds: 33 r.p.m. (pitch-regulated)

and 30 r.p.m. (stall-regulated)

IEC Class A turbulence intensity

Zero wind shear, Shaft tilt w.r.t. mean flow = 13⬚

Pitch-regulated machine

Stall-regulated machine

Figure 7.15 Variation of Blade Fatigue Damage in Flapwise Bending at 12 m Radius with

Mean Wind Speed, for Similar 40 m Diameter Pitch- and Stall-regulated Machines, Ignoring

Dynamics

402

COMPONENT DESIGN

on Figure 7.15, and is compared with that for a similar stall-regulated machine

having the same section modulus. The cross section is designed to resist the extreme

bending moment for the stall-regulated machine of 130 kNm. In both cases the S– N

curve index is taken as 10, and the IEC Class A turbulence intensity assumed. It is

apparent that the pitch-regulated machine fatigue damage is concentrated arou nd

rated speed, and that the total damage is an order of magnitude greater than the total

for the stall-regulated machine. As the 12 m radius section modulus to resist the

extreme ﬂapwise moment is likely to be less for the pitch-regulated machine, fatigue

loading is likely to be more critical than indicated by the comparison in the ﬁgure.

Factors affecting fatigue criticality

The relative criticality of fatigue and extreme loading is determined by the material

properties and safety factors adopted, as well as by the loadings themselves. As an

aid to comparison, the fatigue loading can be described in terms of the notional one

cycle equivale nt load, 

eq(n¼1)

, which is deﬁned as the stress range of the single

reverse loading cycle that would cause the same total fatigue damage as the actual

fatigue loading on the basis of the design S– N curve. Then fatigue is critical if



eq(n¼1)

2

. ª



ext



(7:10)

where 

is the stress amplitude given by the reverse loading fatigue design curve

at N ¼ 1, 

ext

is the stress resulting from the extreme loading case, ª

is the load

factor and 

is the design compression stress (which is assumed not to be

governed by buckling considerations). The condition may be rewritten in terms of

characteristic stress values as follows:



eq(n¼1)



ext

. 2ª



(7:11)

or as



eq(n¼1)



ext

. 2:7



with ª

set to 1:35:

As is implicit from the survey of GFRP and wood laminate properties in Sections

7.1.6 and 7.1.7, the value of 

=

can vary between about 1.0 and 1.4. If the

derivations of the characteristic ultimate and fatigue strengths are statistically

similar, the IEC rules indicate that the respective partial mater ials safety factors

should be taken as equal, whereas, as noted in Section 7.1.6, the GL rules for GFRP

imply a value of 1.5 for the ª

=ª

ratio. Thus in principal the parameter

2ª



governing fatigue criticality can take a wide ran ge of values of between 2.7 and

about 6.

BLADES 403

In deriving the fatigue damage plots in Figure 7.15, a mi d-range value of 4 has

been adopted, resulting in total damages of 0.96 and 0.17 for the pitch and stall

regulated machines respectively. However, if, the minimum value of 2.7 were

adopted, corresponding to 

¼ 

and ª

¼ ª

, the fatigue damages would rise

by a factor of 50 for m ¼ 10.

The other important material property governing the criticali ty of fatigue loading

is, of course, the slope index of the log–log S–N curve, m, which affects the value of

the notional one cycle equivale nt load, 

eq(n¼1)

. With the high values applicable to

wood laminates, fatigue is much less likely to govern.

Other sources of variability

There are a number of other sources of variability in fatigue damage calculations,

apart from uncertainty about the material properties themselves, some of wh ich are

detailed below.

(1) IEC 61400-1 provides two alternative stochastic turbulence models – those due

to Von Karman and Kaimal. The Von Karman model is isotropic, whereas in the

Kaimal model, which is more realistic in this respect, the standard deviations of

lateral and vertical turbulences are 80 percent and 50 percent of the longitudinal

turbulence respectively. In the case of stall-regulated machines, where wind

misalignment at high wind speeds is often the main source of fatigue damage,

the choice of turbulence model could clearly have a decisive effect.

(2) When the fatigue assessment is based on simulations of limited duration

(typically 300 to 600 s), the damage is often dominated by a few extreme cycles,

which are subject to signiﬁcant statistical variation from one simulation to

another. Accordingly several simulations at a given mean wind speed are

necessary to obtain an accurate result (Thomsen, 1998).

(3) In allowing for the reduction in fatigue strength due to mean stress. For

example, in Equation (7.7), the mean stress can either be calculated over each

stress range obtained by rainﬂow cycle counting or over the length of the

simulation.

Fatigue due to gravity loading

In-plane fatigue loads arise from gravity loading and ﬂuctuations in the in-plane

aerodynamic loadings, but gravity loadings dominate for machines large enough to

be grid connecte d, rendering the loading calculation relatively straightforward.

In order to compare the approximately constant amplitude in-plane fatigue

loading with the spectrum of out-of-plane fatigue loading, it is convenient to

express bot h as equivalent loads at a speciﬁed number of cycles, n

. Often the 1 Hz

equivalent load is used, in which case the number of cycles, n

, is equal to the

number of seconds in the machine lifetime during which the machine operates. For

404 COMPONENT DESIGN