1 Copyright 2014 by ASME

Study on the Offshore Wind Turbine Installation Equipment with 6 Sets of

Intelligent Legs

Chunxiang Ma* Miaoqi Zheng Jun He Feng Gao$

State Key Laboratory of Mechanical System and Vibration, School of Mechanical and Power Engineering, Shanghai Jiao Tong University, Shanghai, 200240,China.

*cxma@sjtu.edu.cn, zmq7754@sjtu.edu.cn, jhe@sjtu.edu.cn, $fengg@sjtu.edu.cn

AbstractIn this paper, a new type of the offshore wind turbine installation equipment is proposed, which has 6

sets of intelligent legs. Each intelligent leg consists of

two-UPS and one-UP. Based on the theory of the parallel

mechanism, the mechanism of this offshore wind turbine

installation equipment with 6 sets of intelligent legs is constructed. We take a set of the intelligent leg for

analysis and conducted kinematic analysis and dynamic

analysis on the offshore wind turbine installation

equipment. Finally, by studying the fuzzy reliability of the

kinematic accuracy of a branch, the reliability model of

the whole mechanism of the installation equipment

combined with the characteristics of installation process

is established, and the calculation of the fuzzy reliability

of the kinematic accuracy of the whole mechanism is

carried out .

Keywords: Offshore wind turbine , Installation equipment, Kinematic, Dynamic, fuzzy reliability

INTRODUCTION

1 With the coming mature of the wind energy technology,

wind energy has become one of the most important

solutions to energy crisis[1]. By far, offshore wind farms

are the main implementation model for onshore wind

power utilization[2]. The offshore wind energy is also 1.52 times more expensive than onshore because of

construction of foundation installation and maintenance of

offshore wind turbine[3]. Some of Scholars have done a

certain amount of research about the installation of

offshore wind turbine. Zhang[4] introduced three methods:

1.Traditional lifting method ,which installs the base,the tower and the upper facilities of fan and engine in a

sequence. 2.Improved integral lifting method which completes the installation and debugging of the tower and

the upper facilities on land before they are transported to

offshore destination. 3. Installation method for base and

turbine as a whole structure. In this case, the base and the

wind turbine is not separated, but exists as a whole

structure. The whole structure floats on the sea and is

* Corresponding author. Tel.: 86-0 21-34206554 E-mail address: cxma@sjtu.edu.cn (C. Ma).

dragged to the destination by tugboat and fixed there.

Sandy Butterfield [5] studied a floating structure that may

replace driven monopoles or conventional concrete gravity

bases. Further more, the analysis of the pitch, roll and

heave motions of floating wind turbine has been done. But

as A floating structure must provide enough buoyancy to support the weight of the turbine and restrain pitch, roll

and heave motions within acceptable limits, there are still

many technical problems needed to be solved.

The parallel mechanisms have been extensively used in

industry, such as the parallel robots, the parallel earthquake

(a) Offshore wind turbine installation equipment

Fi

Mechanism

Wind turbine

Floating boat

Fig.1 The schematic diagram of offshore wind

turbine installation equipment

Offshore wind turbine

Base platform

Hook hinge

Spherical hinge

Hydraulic cylinder

End effector

(b) Three dimensional model of mechanism

Proceedings of the ASME 2014 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference

IDETC/CIE 2014 August 17-20, 2014, Buffalo, New York, USA

DETC2014-34171

2 Copyright 2014 by ASME

simulators, heavy load Positioner, the parallel machine

tools, parallel link manipulator and so on[6-8]. In this

paper, a new type of the offshore wind turbine installation

equipment is proposed. It has 6 sets of intelligent legs.

Each intelligent leg consists of two- UPS and one-UP. The

mechanism of this offshore wind turbine installation equipment is constructed. The kinematic analysis and

dynamic analysis are carried out. Finally reliability model

of the whole installation equipment combined with the

characteristics of installation process is established, and the

calculation of the fuzzy reliability of the kinematic

accuracy is carried out

MECHANISM OF THE OFFSHORE WIND

TURBINE INSTALLATION EQUIPMENT

Fig.1 shows a new type of the offshore wind turbine

installation equipment. It has 6 sets of intelligent legs.

Each intelligent leg consists of two-UPS and one-UP .The

mechanism of the offshore wind turbine installation

equipment is shown in Fig.2. From Fig.2, it can seen that

the offshore wind turbine installation equipment consists of

twelv-UPS and six-UP. Two-UPS and one-UP construct a

set of the intelligent leg. three universal joints in each intelligent leg distribute in upper platform, which is

treated as moving platform. two spherical joints and one

fixed joint in each intelligent leg distribute in the small

moving platform and six spherical joints on the small

moving platforms are connected to down platform, which

is treated as fixed platform or base platform.

THE KINEMATIC ANALYSIS The fixed coordinate system O-XYZ and the moving

coordinate system ' ' ' '-O X Y Z as shown in Fig.2 are

established. The fixed coordinate system O-XYZ is located

in down platform and the moving coordinate system

' ' ' '-O X Y Z is located in up platform. For each intelligent leg,

the partial fixed coordinate system o-xyz and the partial

moving coordinate system ' ' ' '-o x y z are established as

shown in Fig.3(a). The point o of the partial fixed

coordinate system o-xyz is located in the center of three

joint on three cylinder tubes as shown in Fig.3(b). The

point 'o of the partial moving coordinate system ' ' ' '-o x y z

is located in the center of three joints on three piston rods

as shown in Fig.3(b). Supposed that 1 2 2j j jA A A and

1 2 2j j ja a a are norm triagle,

1 2 900j jA A mm , 1 2 500j ja a mm , 1 2,j jA A and 3jA can be

expressed by 1 -300, 300 tan30 , 0jA

2 300, 300 tan30 , 0jA and 3 0, -600 tan30 , 0jA

, 1 2...6j , 1 2,j ja a and 3ja can be expressed

by1 - 450, - 450 tan30 , 0ja

,2 450, - 450 tan30 , 0ja

a

nd3 0, 900 tan30 , 0ja

, 1 2...6j .

The transformingo-xyz

o'-x'y'z'R from ' ' ' '-o x y z to o-xyz can

be derived as follows:

o-xyz

o'-x'y'z'

x

y

z

p

p

p

0 0 0 1

c c c s s s c c s c s s

s c s s s c c s s c c sR

s c s c c

(1)

Moving vector jiL of ith cylinder of jth intelligent legs

can be expressed by

Fig.2 Mechanism of the offshore wind turbine

installation equipment

Fig.3 The coordinate system of each intelligent leg

(b) The distribution of the point o and the

point 'o

(a) The fixed and moving coordinate system

intelligent leg

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o-xyz

o'-x'y'z'

x

y

z

p

p

p

1 0 0 0 1 1

ji ji ji

jix jix

jiy jiy

jiz jiz

L A Ra

A c c c s s s c c s c s s a

A s c s s s c c s s c c s a

A s c s c c a

(2)

Where 1,2...6j , 1,2,3i

According to Eq.2, jiL can be gotten.Taking second

intelligent leg for example, through Matlabsoft , jiL can be

obtained during centering drum for first step where the

displacement of upper platform is 85 mm.They are shown

Fig.4 the length of every cylinder in second intelligent leg during centering drum

(a) displacement of upper platform(mm) (c) displacement of upper platform(mm) (b) displacement of upper platform(mm)

The first cylinder in

second intelligent leg

The second cylinder in

second intelligent leg The third cylinder in

second intelligent leg

Len

gth

of

cy

lin

der (

m)

Len

gth

of

cy

lin

der (

m)

Len

gth

of

cy

lin

der (

m)

0 0.3 0.6 0.9 1.2 1.5 1.8 0.3 0.6 0.9 1.2 1.8 1.5 0 0.3 0.6 0.9 1.2 1.8 1.5 0

Fig.5 the length of every cylinder in second intelligent leg during centering bolt hole

(a)rotating angle of upper platform() (b)rotating angle of upper platform() (c)rotating angle of upper platform()

Len

gth

of

cy

lin

der (

m)

Len

gth

of

cy

lin

der (

m)

Len

gth

of

cy

lin

der (

m)

The first cylinder in the

second intelligent leg The second cylinder in the

second intelligent leg

The third cylinder in the

second intelligent leg

4 Copyright 2014 by ASME

in Fig.4, where =-60 , =0 , =135 ,PxP

yP zP

= 2500 2 - 2500 2 0.From Fig.4 ,it can be seen

that the three hydraulic cylinders can move smoothly

during centering drum, the displaement of the first

hydraulic cylinder is 28mm,the displacement of the second

hydraulic cylinder is 30.5mm and the displacement of the

third hydraulic cylinder is 26.5mm during centering drum

for first step. In above same way, jiL can be obtained

during centering bolt.They are shown in Fig.5,.From

Fig.5 ,it can be see that the three hydraulic cylinders can

move smoothly during centering bolt hole, the displaement

of the first hydraulic cylinder is 29mm,the displacement of

the second hydraulic cylinder is 32mm and the

displacement of the hydraulic third cylinder is27mm

during centering bolt hole.

THE DYNAMIC ANALYSIS Based on the Newton Euler approach for the

dynamics[9], the dynamic equator of the each intelligent

leg can be obtained as follows:

3

1

(( ) )i i

i i i i

ii i

a AF m dv m g F

a A

(3)

Where ia

is vector of the center point of of three

universal joints of the intelligent leg within o-xyz in upper platform.

iA

is vector of the center point of two spherical

joints and one fixed joint of the intelligent leg within o-

xyz in small moving platform. F

is of force supplied by

each intelligent leg in the offshore wind turbine installation

equipment. iF is force supplied by each cylinder in each

intelligent leg.

Taking the second intelligent leg for example, through

Matlabsoft, force iF supplied by every hydraulic cylinder

in each intelligent leg can be obtained during centering

drum for first step, where the displacement of the upper

platform is 85 mm. They are shown in Fig7. From Fig.7 , it

can be seen that the three hydraulic cylinders can supply the force smoothly during centering drum, the force

supplied by the first hydraulic cylinder is about 3kN, the

force supplied by the second hydraulic cylinder is about

3.15kN and the force supplied by the third hydraulic

(c) Force supplied by the third hydraulic cylinder

(a) Force supplied by the first hydraulic cylinder

(b) Force supplied by the second hydraulic cylinder

Fig. 7 Force supplied by each hydraulic cylinder in the second

intelligent leg during centering drum

Fig.6 The forced state of each intelligent leg

5 Copyright 2014 by ASME

cylinder is about 3.25kN. Fig.8 shown the force iF

supplied by every hydraulic cylinder in second intelligent

leg during centering bolt hole. From Fig.8 , it can be seen

that the three hydraulic cylinder can supply the force

smoothly during centering bolt hole, the force supplied by

the first hydraulic cylinder is about -110kN, the force

supplied by the second hydraulic cylinder is about -115kN

and the force supplied by the third hydraulic cylinder is

also about -115kN when the rotating angle of the upper

plateform is 1.5.

RELIABILITY OF MACHANISM KINEMATIC

The fuzzy allowable zone of the kinematic error of the

mechanism of the offshore wind turbine installation

equipment is defined based on fuzzy mathematical theory

[10]. Assuming that fuzzy allowable zone of the kinematic

error of the mechanism of the offshore wind turbine

installation equipment is ( ) ( ) /AE

A e e e ,which shown

in Fig.9. When the kinematic error of the mechanism of

the offshore wind turbine installation equipment meets

[ ] [ ]e e e , the membership grade is 1 and it means

allowable totally. When the kinematic error of the

mechanism of the offshore wind turbine installation

equipment meets [ ]e e or [ ]e e , the

membership grade is 0, which means unallowable totally.

When the kinematic error of the mechanism of the offshore wind turbine installation equipment meets

[ ] [ ]e e e or [ ] [ ]e e e , the membership

grade is 01 and it means allowable to some extent. The membership function of the fuzzy allowable zone of the

error of the mechanism kinematic can be expressed as:

1 + -[e]-

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2

22 2 1 1

2 1

2

12 2 1 1

2 1

2 2

2 1

( ) ( ) ( )

1 1 {[ ( ) ( )] [exp( )

22

1 1exp( )]} {[ ( ) ( )]

2 2

[exp( ) exp( )]}2 2

AR P e A f e e de

(6)

1 2

[ ] [ ],e e

e e

e eWhere

,1 2

[ ] [ ],e e

e e

e e

.

Supposed that ,Z L is the designed kinematic

regulity of the mechanism and ,Z L L is real

kinematic regulity of of the mechanism, the kinematic error of the mechanism can be given by

, ,e Z Z L L Z L (7)

Where L is vector of every rod. At mean value point,Talor series expansion of e is given by

10

1

, , i ii i

Ze Z L Z L l l

l

(8)

Therefore, the mean and deviation of the error can be

expressed as

2

102

1

, , 0

i i

e

e l l i i

i i

E Z L Z L

Zl l

l

(9)

Fig.10 shows that the sketch of single branch of the

mechanism of the offshore wind turbine installation

equipment. The kinematic regulity of the end point can be

given by

1

1

cos cos

sin sin

c

c

x S R

y S R

(10)

According to Eq.7-Eq.10, xe , ye ,and their the

mean and deviation can be found. According to Eq.6, the

fuzzy reliability of kinematic accuracy of the mechanism

of single branch in x-direction and y-direction can be

found. They are shown in Fig.11and Fig.12. From Fig.11

and Fig.12, it is understood that the reliability of the

kinematic accuracy of x-direction of the single branch of

the mechanism increases with the increment of the angle

of the hydraulic cylinder and is all greater than 0.9963,

and the reliability of the kinematic accuracy of y-direction

of the single branch of the mechanism decreases with the

increment of the angle of the hydraulic cylinder and is

greater than 0.9994. Fig.13 shows the reliability model of

the kinematic accuracy of the whole mechanism of the

offshore wind turbine installation equipment. According to

Fig.13 and reliability theory[10], the reliability of the the

Fig.10 Sketch of single branch

Fig. 11 fuzzy reliability of direction x of single branch

Fig. 12fuzzy reliability of direction y of single branch

7 Copyright 2014 by ASME

kinematic accuracy of the whole mechanism can be given

by

(11)

wherewR is the reliability of the kinematic accuracy of

the whole mechanism of the offshore wind turbine

installation equipment. bxijR is the reliability of the

kinematic accuracy of x-direction of jth branch in ith

group. byijR is the reliability of the kinematic accuracy of

y-direction of jth branch in ith group. i=1,2,3 . j=1,2.

Fig.14 shows the fuzzy reliability of the kinematic

accuracy of the whole mechanism. The reliability of the kinematic accuracy of the whole mechanism increases with

the increment of the displacement of the end effector and is all greater than 0.99988, which meets the design

requirement.

Conclusions

1. A new type of the offshore wind turbine installation

equipment is mainly composed of moving upper

platform, fixed down platform and 6 sets of intelligent legs. Each intelligent leg consists of two-UPS and one-

UP .

2. The hydraulic cylinders can supply the force smoothly

during centering drum. For the second set of intelligent

leg, the force supplied by the first hydraulic cylinder is

about 3kN, the force supplied by the second hydraulic

cylinder is about 3.15kN and the the force supplied by

the third hydraulic cylinder is about 3.25kN for first step,

where the displacement of the upper plateform is 85mm.

3. The hydraulic cylinders can supply the force smoothly during centering the bolt hole. For the second set of

intelligent leg, the force supplied by the first hydraulic

cylinder is about -110kN, the force supplied by the

second hydraulic cylinder is about -115kN and the force

supplied by the third hydraulic cylinder is about -115kN

when the rotating angle of the upper plateform is 1.5.

4. The reliability of the kinematic accuracy of x-direction

of the single branch of the mechanism increases with the

increment of the angle of the hydraulic cylinder and is

all greater than 0.9963, and the reliability of the

kinematic accuracy of y-direction decreases with the

increment of the angle of the hydraulic cylinder and is greater than 0.9994.

5. The reliability of the kinematic accuracy of the whole

mechanism increases with the increment of

displacement of the end effector and is all greater than 0.99988.

References

[1]Simon-Philippe Breton, Geir Moe: Status, plans and

technologies for offshore wind turbines in Europe and

North America. Renewable Energy, 34(3): 646-654,

2009.

[2] Zervos A and Kjaer C, wind energy scenarios up to 2030 European Wind Energy Association

Report .www.ewea.org

[3]Massachussets Technology Collaborative.A

framework for offshore wind energy development in

the United States. Washington: U.S. Department of

Energy, General Electric; 2005.

[4] Zhang Song ,TAN Jiaohua: Introduction of offshore

wond turbine installation, China offshore

platform,Vol .24 No. 3 ,J une. ,2009.

[5]Sandy Butterfield ,Walt Musia,Jason Jonkman:

Engineering Challenges for Floating Offshore Wind

Turbines. NREL/CP-500-38776 September 2007

[6] Kotzev, A., et al. Generalized predictive control of a

robotic manipulator with hydraulic actuators.

Robotica, Vol.10(5), p.447, 2009.

[7]Zhao Yunfeng, Tan Yanhua, Zhao Yongsheng, Analysis of 3-DOF Heavyload Positioner Mechanism with Hybrid Structure, Proceeding of

Conference of Mechanical Engineering, 2007.

[8] S. Nokleby, R. Fisher, and R. Podhorodeskiet al.,

Force capabilities of redundantly-actuated parallel manipulators. Mechanism and Machine Theory, Vol. 40(5), p. 578, 2005.

[9] J.E.Shigley, J.J.Uicker Jr., Theory of Machines and

Mechanism[M]. McGraw-Hill Book Company,1980.

[10] Dong Yuge, Mechanical Fuzzy Reliability Design,

Mechanical Industry Press, 2000.

Fig.14 Fuzzy reliability of the whole mechanism

Fig.13 reliability model of the whole mechanism

3 3

1 2 1 2

1 1

3

1 2 1 2

1

[1- (1- )(1- )] [1- (1- )(1- )]

[1- (1- )(1- )] [1- (1- )(1- )]

w bxi bxi byi byi

i i

bxi bxi byi byi

i

R R R R R

R R R R