A Comparison between Tip Speed Ratios (2, 4, 5) to Obtain ...

A Comparison between Tip Speed Ratios (2, 4, 5) to Obtain

the Fatigue Life of Horizontal Axis Wind Turbine Blades

Aiya Naseer Hussein, Basim Ajel Sadkhan

Mechanical Engineering Department, College Of Engineering, Almustansriyah University, Baghdad, Iraq.

Email Address:

Correspondence should be addressed to Aiya Naseer Hussein [email protected]

Received: 6 May 2021, Revised: 11 May 2021, Accepted: 26 May 2021, Online: 21 Jun 2021

Abstract

The power of the wind is considered the best source of non-pollution renewable energy. The wind turbine blade

is the major and costly part of the wind turbine system. The fatigue phenomena of the blade is a major design

condition to predict the wind turbine blade fatigue life. If the blade fails at serving time, the turbine system will

collapse and the cost will be high. This work aims to estimate the fatigue life for a wind turbine blade with

different tip speed ratios (2, 4, and 5). For obtaining the fatigue life of the blade, the Miner-Palmgren rule and

M-N curve were used. According to the results, at wind velocity (13.85 m/s, 10.96 m/s), it was found that TSR 2

has the highest fatigue life. It was found that three variables depend on each other and the changing in one of

them affects the others. So, the 3-Dimensional plots are useful tools to find the relationship between them.

Visual observation noticed that the damage in the wind turbine was found at the adhesive bounding joint for a

tip speed ratio of 4, and tip speed ratio 2; but, the tip speed ratio of 5 took a long time to fail.

Keywords: Renewable Energy, Fatigue Life, Damage, Tip Speed Ratio

1. Introduction

Wind energy is the fastest energy

technology growing because of its

inexhaustible and renewable source. Wind

energy was developed in the twentieth –

century because the price of oil was a

shock in the 1970s. The development of

wind turbine technology has found a

serious interest in many countries as a

clean source of energy. This technology is

still very new for approximately 25 years,

but the idea of using wind as a source of

energy has existed for centuries. A wind

turbine is a combination of devices and

systems used to extract the kinetic energy

from the wind and convert it into

mechanical energy by using a rotor system

for driving a generator producing electrical

energy, see figure (1). [1-3].

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Figure (1): wind turbine components.

Fatigue is the major mechanism of failure

for constructions beneath a cyclic loading,

which can be considered as an important

design parameter in some applications.

The failure passes in three phases as Crack

initiation, Crack growth, and Fracture of

the structure. Multiple factors can affect

the fatigue of a wind turbine blade as

material, operation speed, wind velocity

distribution, blade length, and the aerofoil.

These factors create seven forms of blade

damage which are an adhesive joint

failure, delamination, adhesive depending,

buckling, split into fibers, cracks in Gel-

coat, and sandwich debonding. [4, 5]

The fatigue phenomena of wind turbine

design were studied and researched with

many methods. (Basim Ajel Sadkhan,

2009) [6] studied the life of the fatigue of

the fiberglass composite blades of wind

turbine according to aerodynamic forces

using TSR (1.5). The air duct system was

used to obtain the experiment data as air

velocity, forces, amplitude moment, and

ultimate moment to estimate the number of

cycles to failure to form an M-N curve

(moment – number of cycle to failure).

The fatigue slope 12 was found as the best

slope to find the fatigue. The M-N

relationship and Palmgren -miner rule

were used to find the damage and fatigue

of the blade. In the experimental program,

fatigue was found at the adhesive joints.

(Amr Mohamed Metwally Ismaiel et al.,

2017) [7] studied the fatigue of full-scale

wind turbine blades by using traditional

theory, as well as probabilistic and

numerical techniques. FAST and M-Life

being utilized for finding the blade's

fatigue life. The fatigue analysis showed

the service life of blade until failure takes-

place. When the rotational speed reaches

36 rpm, the blade lifetime is 17 years, and


when the rotational speed reaches 47, the

blade lifetime is 15.8 years. (Qiang Ma et

al., 2018) [8] studied a simplified load

spectrum. A full-scale test of fatigue is a

successful technique to obtain the behavior

of the blade's fatigue of a wind turbine.

The main difficulty of this test is the way

to design its load. The traditional methods

for determining the load of test are

intricate and take a long period to process.

For that, an easy technique is used to

convert the blade's loads into the load of

test. Beam theory being employed for

obtaining the relation among the blade

stress, strain, and bending moment.

Assuming the concentration of stress and

the relation between stress and strain, the

M-N curves (Exerted Moment - No. of

cycles to failure) are described. The rule of

Miner is used to calculate the equivalent

damage. The computed outcomes error

between such technique and the

conventional technique is near to (5%),

and one can use this method for the test of

fatigue and to enhance the effectiveness of

the design of the load test. (C. Muyan and

D. Coker, 2020) [9] investigated the static

and fatigue analysis of a (5 m) RUZGEM

composite blade of a wind turbine without

and with a defect. When the defect of

debonding is presented at the side of

pressure, the blade will fail beyond a

loading of (69%), and the zone of defect,

where the debonding is applied, will be the

failure crack propagation laminate failure

region. The outcomes of fatigue expected

that the blade with no defect possesses the

required no. of cycles to failure, while the

blade failed after 85% of loading.

2. Methodology

2.1. Tip Speed Ratio (TSR)

TSR is defined as the relationship between

rotational speed and wind velocity. The

definition of “fast turbines” refers to

turbines with a high optimum TSR, while

the term “slow turbines” refers to turbines

with a low optimum TSR. [10]

In the design of the wind turbine blade, at

first, select a TSR. Usually, the TSR relies

on profile type and blades number. A

different number of blades could be chosen

for various speed ratios. The number of

blades is chosen as a function of design

TSR according to the table (1). In this

study, the number of blades was chosen (6,

4, and 3) according to TSR (2, 4, and 5).

Figure (2): shows the three types of rotors.

The wind turbine blade was made from

composite material as fiberglass and

polyester with 3mm thickness.

Table (1): The relation between TSR and the number of blades. [11]

TSR Number of blades

1 12-36

1.5 6-18

2 4-12

3 3-6

4 2-4

5-8 2-3

8-15 1-2


Figure (2): The Model of the Rotor.

2.2. Load Spectrum Method and

Palmgren-Miner Rule

The load spectrum technique objective is

to derive a fatigue test of an analogous

impairment, which depends completely

upon the Design-Load spectrum method.

The geometry of the blade and the fatigue

characteristics of material aren't important.

Without affecting the conditions of the

test, the test material may deviate from the

intended design. This method stays at the

load range; for that, the stresses are not

important. Therefore, instead of the (S - N)

curve, the (M - N) curve (Applied Moment

– Number of Cycles to Failure) will be

used for the blade failure. [12] This curve

is defined by the following equation:

Ma=Mu* Nf(-1

m⁄ ) (1)

The damage related to every curve can be

studied via implementing Palmgren-

Miner's rule. The fatigure failure is

happened when the damage reach 1.

𝐃𝐚𝐦𝐚𝐠𝐞 = ∑𝐧𝐢

𝐍𝐢

𝐣𝐢=𝟏

(2)

To compute the number of cycles for

loading (i) the following equation is used:

ni = rpm * T (3)

The amplitude moment was found

according to the equation (4) which was

found according to the aerodynamic

analysis presented in [6]

Ma = F * ( L

3 + rR ) (4)

Where:

Ma = amplitude moment (N.m)

Mu = ultimate moment

Nf = number of cycle to failure.

m = fatigue slope.

ni = number of cycle for loading (i).

T = time of operation.

rpm = speed of the rotor.

F= force acts on the blade

L= length of the blade.

r = radius of the rotor.

3. Experiment procedure

3.1. The test rig

A full-size model testing is expensive and

requires a large foundation for the

modified model. For that, a prototype was

made for studying the fatigue life of the

wind turbine blade. Figure (3) shows the

test rig. The experiment test rig was used

to measure wind turbine speed according

to different wind velocities. It contains few

components as listed below:

1) Inverter (regulator or speed

controller) type LS-M100 (2hp, 200-240 v,

1Ф, 1-50Hz).


2) Air Generator type GAMAK

(2800rpm, 1.1KW, 220V, 50Hz) with four

blades at 40°.

3) Anemometer type (MT-4615).

4) Duct.

5) Wind Turbine made of blades, hub,

bearings, and shaft.

6) Tachometer type (DT-2234C+).

7) Oil.

Figure (3): the test rig.

3.2. Bending Test

The bending test is used to extract the flexibility behavior of the material. The bending

specimen was made according to the materials and dimensions of the blade (230x20x3 mm).

Figure (4) shows the specimen before and after the test. A 3-point bending test was applied to

find the maximum bending load was extracted from this test.

Figure (4): bending specimen before and after the test.


3.3. Fatigue Test

Fatigue test machine type (Avery 7305),

speed 1400 rpm was used for this test as

seen in the figure (5). A reverse bending

test is associated with this machine. The

fatigue specimen was made according to

standard (ASTM D 3479/D 3479M–96)

for flat polymer matrix composite

materials and the manual of the fatigue

machine [13]. Figure (6) shows the

geometries and dimensions of the

specimen. Figure (7) shows the fatigue

specimen before and after the test. The test

was done under variable amplitude

moment. The specimen materials were

made from the same material as the blade.

The number of cycle to failure was found

from the mechanical cycles counter.

Figure (5): fatigue test machine.

Figure (6): dimension of the fatigue specimen.


Figure (7): Fatigue Specimen Before and After the Test.

4. Results

4.1. Bending Test Results

According to equation (1), the applied moment (Ma) was found as a function of the ultimate

moment (Mu) of the blade, and the number of cycles to failure (Nf). The maximum bending

load was found 0.325 KN before the fracture took place. The test device gives the load and

extension as shown in figure (8). The ultimate moment for simply supported beam was found

by equation (5) [14]:

Mu=Fmax*L

4 (5)

Mu = 0.325*103 * 230*10

-3 /4

Mu = 18.6875 N.m

Where:

Fmax = maximum load.

L = length.


Figure (8): the load- extension chart of the bending test.

4.2. M-N Curve and Damage Results

The M-N curve was found according to the equation (1) and the ultimate moment from the

bending test with fatigue slope m=12 according to reference [9]. The M-N curve equation

takes the final form as follows:

Ma = 18.6875 * Nf-0.083333

Where m = 1/0.083333 = 12.

Tables (2), (3), and (4) show the results for three types of TSR.


Table (2): Results of TSR 2

rpm Vair (m/s) F (N) M (N.m) Nf ni Damage

43 1.24 0.0392 0.012 2.112E+38 928800 4.3986E-33

113 1.74 0.1525 0.0465 1.772E+31 2440800 1.3777E-25

288 2.36 0.3443 0.105 1.008E+27 6220800 6.1694E-21

393 3.24 0.7143 0.2179 1.588E+23 8488800 5.3478E-17

489 3.77 0.9924 0.3027 3.068E+21 10562400 3.4958E-15

594 4.5 1.4435 0.4403 3.42E+19 12830400 3.7866E-13

698 5.2 1.9502 0.5948 9.251E+17 15076800 1.6677E-11

774 5.75 2.3991 0.7317 7.698E+16 16718400 2.3385E-10

882 6.45 3.0353 0.9258 4.577E+15 19051200 4.3958E-09

980 7.25 3.8511 1.1746 2.63E+14 21168000 8.4881E-08

1071 7.94 4.6309 1.4124 2.878E+13 23133600 8.8873E-07

1178 8.87 5.7933 1.767 1.958E+12 25444800 1.3882E-05

1270 9.35 6.4434 1.9652 5.466E+11 27432000 6.4069E-05

1369 10.2 7.6782 2.3418 6.667E+10 29570400 0.0005076

1462 10.96 8.8728 2.7062 1.176E+10 31579200 0.0031935

1560 11.72 10.153 3.0966 2.333E+09 33696000 0.01763503

1651 12.3 11.187 3.4121 728335733 35661600 0.06659816

1755 13.24 12.969 3.9557 123581284 37908000 0.37334364

1856 13.85 14.196 4.3298 41786631 40089600 1.33273183



rpm Vair (m/s) F (N) M (N.m) Nf ni Damage

37 2 0.226 0.0689 1.577E+29 692640 4.3933E-24

54 2.36 0.3443 0.105 1.008E+27 1010880 1.0069E-21

108 3.24 0.7143 0.2179 1.588E+23 2021760 1.2736E-17

227 3.77 0.9924 0.3027 3.068E+21 4249440 1.3977E-15

450 4.5 1.4435 0.4403 3.42E+19 8424000 2.4772E-13

696 5.2 1.9502 0.5948 9.251E+17 13029120 1.4332E-11

870 5.75 2.3991 0.7317 7.698E+16 16286400 2.259E-10

1004 6.45 3.0353 0.9258 4.577E+15 18794880 4.3319E-09

1136 7.25 3.8511 1.1746 2.63E+14 21265920 8.5189E-08

1249 7.94 4.6309 1.4124 2.878E+13 23381280 8.9764E-07

1388 8.87 5.7933 1.767 1.958E+12 25983360 1.4165E-05

1498 9.35 6.4434 1.9652 5.466E+11 28042560 6.547E-05

1604 10.2 7.6782 2.3418 6.667E+10 30026880 0.00051585

1724 10.96 8.8728 2.7062 1.176E+10 32273280 0.00326078

1877 11.72 10.153 3.0966 2.333E+09 35137440 0.01832009

1980 12.3 11.187 3.4121 728335733 37065600 0.0692109

2102 13.24 12.969 3.9557 123581284 39349440 0.38762028

2220 13.85 14.196 4.3298 41786631 41558400 1.38215847



rpm Vair (m/s) F(N) M (N.m) Nf ni Damage

32 2.36 0.3443 0.105 1.008E+27 622080 6.1692E-22

82 3.24 0.7143 0.2179 1.588E+23 1594080 1.0042E-17

168 3.77 0.9924 0.3027 3.068E+21 3265920 1.0744E-15

312 4.5 1.4435 0.4403 3.42E+19 6065280 1.7843E-13

591 5.2 1.9502 0.5948 9.251E+17 11489040 1.2598E-11

791 5.75 2.3991 0.7317 7.698E+16 15377040 2.1235E-10

912 6.45 3.0353 0.9258 4.577E+15 17729280 4.0855E-09

1030 7.25 3.8511 1.1746 2.63E+14 20023200 8.0218E-08

1162 7.94 4.6309 1.4124 2.878E+13 22589280 8.6515E-07

1287 8.87 5.7933 1.767 1.958E+12 25019280 1.3641E-05

1404 9.35 6.4434 1.9652 5.466E+11 27293760 6.3575E-05

1520 10.2 7.6782 2.3418 6.667E+10 29548800 0.00050678

1642 10.96 8.8728 2.7062 1.176E+10 31920480 0.0032217

1764 11.72 10.153 3.0966 2.333E+09 34292160 0.01791874

1881 12.3 11.187 3.4121 728335733 36566640 0.06812449

1992 13.24 12.969 3.9557 123581284 38724480 0.38147679

2103 13.85 14.196 4.3298 41786631 40882320 1.35983564

(a)

Figures (9(a, b, c)) show the M-N curve for the three TSRs. As found from these figures and

tables (2), (3), and (4), TSR 2 as expected has a high fatigue strength as compared with

TSR4, TSR5.


(b)

(c)

Figure (9): M-N curve for ((a) TSR2, (b) TSR4, (c) TSR5).

4.3. 3D Plots

It was found that 3D plots are useful tools

to explain the relationship between three

variables. There are a few remarkable

points has been noticed from the results;

so, 3D plots were used to present them.

The remarkable points are listed as

follows:

1. The increase in wind velocity leads

to an increase in the amplitude moment

effect on the blades. This will reduce the

number of cycle to failure. Figures (10(a,

b, c)) show the relationship between the

wind velocity, amplitude moment, and the

number of cycle to failure of the wind

turbine blade for TSR (2, 4, and 5). For

example; by taking wind velocity of 8 m/s

it was found that the amplitude moment

was 4.6 N.m and the number of cycle to

failure was 2.878*1013

for TSRs 2, 4, 5.

This means that the wind velocity has the

same effect on the wind turbine blade.

2. The increase at the moment leads

to a decrease in the number of cycle to

failure and an increasing in damage.

Figures (11 (a, b, c)) show the relationship

between the amplitude moment, the


number of cycle to failure, and the damage

occurs at the wind turbine blade for TSR

(2, 4, and 5). For example; by taking

amplitude moment 4.3298 N.m the number

of cycle to failure was found 41786631 for

the three TSRs but the damage will be

1.3327, 1.38215, and 1.3598 for TSR 2, 4,

and 5 respectively.

3.

(a)

(b)

(c)

Figure (10): The relationship between the wind velocity, amplitude moment, and the number

of cycles to failure for (a) TSR 2, (b) TSR 4, (c) TSR5.


(a)

(b)

(c)

Figure (11): The relationship between the moment, number of cycles to failure, and damage

for (a) TSR 2, (b) TSR 4, (c) TSR 5.


4.4. Damage, Time and Fracture Location

Three, four, and six blades were operated by the test rig at the higher speed in this study,

which is (13.85 m/s) for 12 hours/day. Figure (12) shows that TSR2 has a higher fatigue life

as compared with TSR4, TSR5. The TSR2 fails after 30 days/12 hours; while TSR4 fails 26

days/12 hours and TSR5 fails 27 days/12 hours. Figure (13) shows a comparison between the

three TSRs at wind velocity (10.96 m/s). This velocity was in the range of wind velocity in

Iraq. The damage reaches 1 at 16 years for TSR2, 15 years for TSR5, and 14 years for TSR4.

If the blades rotate at a wind velocity of less than 10.96 m/s, it will have an infinity life.

Figure (12): A comparison between the three TSRs at 13.85 m/s.

Figure (13): A comparison between the three TSRs at 10.96 m/s.

The damage was found at the bounding joints between the ring and the blades as shown in the

figures (14) and (15). The adhesive material was made from the same material as the blades.

Its failure leads to excessive vibration and cyclic loading that acts on the wind turbine. TSR 5

with 3 blades does not fail after 27 days/12 hours. So, the blade takes a long time to fail.


Figure (14): The Failure in 6 Blades Wind Turbine.

Figure (15): The Failure in 4 Blades Wind Turbine.

4.5. Fatigue Results

The five steps increasing loading program (4.5, 5, 5.5, 6, and 6.5). The number of cycles.

Figure (16) shows the block representation and damage results with the amplitude moment of

the test. From the increasing load program, it was noticed that the damage increase by

increasing the load on the specimen. The test gives a damage value of more than one.


Figure (16): Increasing block diagram of fatigue test.

5. Conclusions

Power from wind is considered the best

source of non-pollution renewable energy.

A prototype of the blade was used to find

the effect of the three Tip Speed Ratios on

the fatigue life of wind turbine blades. The

results were obtained for three Tip Speed

Ratios (2, 4, 5) with a different number of

blades (6, 4, 3) respectively. It was

concluded:

1. The behavior of the M-N curve shows

that tip speed ratio TSR2 has high fatigue

strength and fatigue life as compared with

tip speed ratios 4 and 5.

2. The damage increases by increasing

the number of loading cycles after a time.

3. When the wind speed reaches 10.96

m/s, tip speed ratios 2, 4, 5 will fail in 16,

14, 15 years respectively because of the

increase in the rotational speed and

moment and decreases in the number of

cycle to failure.

4. Tip Speed Ratio 2 has been damaged

at 13.85 m/s wind speed after 30 days; but,

Tip Speed Ratio 4, 5 have been damaged

after 26 and 27 days respectively at the

same wind speed.

5. The damage was found at the

bounding joints between the ring and the

blades.

For future work, using vertical axis wind

turbine and other types of blades

manufactured from composite materials

with different tip speed ratios.

6 .Acknowledgment

The authors would like to thank Al-

Mustansiriyah University, College of

Engineering / Mechanical Engineering

Department for academic guidance and

support and the electromechanical

engineering department and the material

engineering department at the university of

technology.

7. References

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2017, Turkey.


[2]. Ferhat kurtulmus, Ali Vardar and Nazmi

Izli “AERODYNAMIC ANALYSES OF

DIFFERENT WIND TURBINE BLADE

PROFILES” journal of applied sciences

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[3]. Gizachew Dereje, and Belete Sirahbizu

(Ph.D.) “Design and Analysis of 2mw

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[4]. Robert M. Jones “Mechanics of

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[13]. Avery 0305, “Users’ Instructions

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[14]. E.J.Hearn. "Mechanics of Materials", vol

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