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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.
*[email protected], [email protected], [email protected], [email protected]
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: [email protected] (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
3 Copyright 2014 by ASME
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]-
6 Copyright 2014 by ASME
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