10th International Conference on Composite Science and Technology
ICCST/10
A.L. Araújo, J.R. Correia, C.M. Mota Soares, et al. (Editors)
© IDMEC 2015
Mechanics Analysis on the composite flywheel stacked from
circular twill weave fabric rings
Xingjian DAI* , Yong WANG* , Changliang TANG* , Xingfeng GUO†
*
†
Dept. of Engineering Physics, Tsinghua University
Beijing, 100084, China
[email protected]
Dept. of Textile Engineering, Tianjin Polytechnic College
Tianjin, 200014, China
[email protected]
Key words: Composite flywheel; Twill fabric; Profile modeling weaving; Spin test
Summary: The filament winding composite flywheel had a shortcoming of very low strength
along the radial direction due to no filament reinforcement distribution. The failure along the
radial direction due to delamination may happen for the thick cylinder composite flywheel at
high rotational speed. The new idea to solve the low radial strength problem of the composite
flywheel is to use woven fabric materials. The 2D woven fabric composite in form of circular
ring has fibers in both the circular and radial directions to bear the stress. This structure
features the combination of the typical two-dimensional orthogonal textile fabric and the
classic axial laminations, performing new characters in mechanics. Samples of composite
disks with 2D woven fabric materials were designed and fabricated for spinning test for the
first time. The mechanics analysis on the thin woven composite disk was carried out
originally. With the introduction of micromechanics methods, the elastic constants of the unit
cell model of periodic volume representing the whole fabric were extracted from geometrical
simplification and homogenization theories. The stiffness and strength of the orthogonal twill
weave fabric in the composite disk was predicted to evaluate the failure spinning speed of the
woven fabric composite disks. The theoretical maximum spin speed of the woven flywheel
could reach 1261rps with the energy density of 53Wh/kg. The tension test data on the
samples of twill weave fabric composite offered the valuable reference to the prediction of
the failure of the disk sample. The spinning test confirmed that the ending weakness of the
stacked configuration and the stiffness degradation from defects in composite played an
important role to the stable running of the spin test flywheel shaft.
1 INTRODUCTION
Energy storage is very necessary to both electrical utilities and customers. Energy storage
technology mainly included pumped hydro storage, compressed air energy storage, flywheel
energy storage (FES), battery energy storage system and capacitor and super-capacitor
energy storage [1]. The modern flywheel energy storage performance was enhanced greatly
with the using of advanced fiber composites for higher speed, magnetic bearing for lower
friction loss and new power conversion for higher efficiency [2]. FES is adequate for
Xingjian DAI , Yong WANG , Changliang TANG , Xingfeng GUO
interchanging medium and high powers (kW to MW) during short periods (seconds) with
high energy efficiency in the range of 90–95% and long lifetime (20 years). Flywheel
technologies may be used in different applications such as uninterruptible power system
(UPS) [3], power quality [4], kinetic or potential energy regenerating, grid frequency leveling
and wind power smoothing [5, 6].
The kinetic energy stored in a flywheel is proportional to the mass and the square of its
rotating speed. The maximum stored energy is ultimately limited by the tensile strength of
the flywheel material. Until now, most composite flywheels were made from
circumferentially wound fibers being pulled through a wet bath of resin [7, 8]. However,
filament winding composite rings flywheel has one weakness of very low strength on the
radial direction because that the fibers are placed parallel to each other in the hoop direction
but no reinforcement in the radial direction. To overcome this weakness, the multi-rings
flywheel and stacked-ply flywheel techniques were considered [9, 10].
Ha et al. derived a symmetric ring stiffness matrix for the analysis of a multi-ring
composite flywheel and assembled it into a symmetric global matrix satisfying the continuity
equations at each interface with the assumption of plain strain and axial symmetry [11].
Arnold presented an analytical model capable of performing an elastic stress analysis for
single/multiple, annular/solid, anisotropic/isotropic disk systems, subjected to pressure
surface tractions, body forces and interfacial misfits has been discussed [12]. Thielman and
Fabien designed a flywheel from alternating plies of purely circumferential and purely radial
reinforcement (seeing Fig. 1) [13]. Classical Lamination Theory (CLT) was used to the
equations that determine the stress and strain in the stack-ply composite disk [14].
To solve the lack of radial strength of composite flywheel, the new idea is employed the
profile modeling weaving technique which could weave fibers along both circumferential and
radial direction and form a circular ring fabric for flywheel. The new continuous spiral
weaving sector rings were stacked into a disk and composited to epoxy resin to obtain a thin
disk flywheel using vacuum assisted resin infiltrate molding (VARIM) process.
Woven fabrics are used as reinforcements for composites to get better properties in
mutually directions and obtain more applications such as automotive, civil, and aerospace.
2D woven fabrics including plain, twill, and stain weave style are obtained by interlacing two
sets of tows, strands or yarns in the weaving machine [15, 16]. In a twill, the fill tows are
interlaced in a pattern of ‘‘m under–n over’’, with at least one of the m, n > 1. The main
characteristic of the twill weave is its improved drapability as compared to plain weave,
being at the same time prone to snagging when the harness is large and/or the diagonal ribs
are thin.
The mechanical properties such as elasticity, strength of the woven composites are
essential data for the design and application in engineering. Angioni et al. gave a review of
homogenization methods for 2D woven composites [17]. Onal and Adanur reviewed the
modeling of elastic, thermal and strength/failure analysis of 2D woven composites [18].
Admumitroaie and Barbero proposed a general approach for the geometrical modeling and
the new formulation for mechanical analysis of 2D orthogonal woven fabric reinforcements
for composite materials [19,20].
In this paper, the profile modeling weaving is introduced to manufacture the spiral twill
weave fabric rings as shown in Fig. 1. In the simplifying analysis, the spiral twill fabric was
spread to a twill flat plate with orthogonal warp and fill (or weft) yarns along the
circumferential direction. The spindle-shaped section was used to describe the geometry
configuration of the yarns in the twill unit cell. The elastic properties of the twill woven
composite plate in averaging method were obtained and compared to the experimental results.
2
Xingjian DAI , Yong WANG , Changliang TANG , Xingfeng GUO
Samples of composite disks with 2D woven fabric materials were designed and fabricated for
spinning test for the first time. The mechanical analysis on the thin woven composite disk
was carried out originally which predict the maximum rotational speed of the woven fabric
composite flywheel.
(a) Cricumterential and raidal ply
(b) Spiral twill woven fabric and stacked composites disk
Figure 1: Raial reinforement of fiber composites flywheel
2 PROPERTIES OF 2D-WOVEN FABRIC COMPOSITE FLYWHEEL
2.1 Profile molding weaving of composite flywheel
The 2D-woven fabric composite flywheel was unfolded into a continuous circular ring as
shown in figure 2. The warp filament bears the circumferential stress, and the fill yarn
enhances the strength along the radial direction of the flywheel.
yarn bobbin
warp yarn
shedding
fill yarn
annular fabric
Figure 2: Disk stacked from 2D woven fabric in sector shape Figure 3: The profile modeling weaving technique
Inner radius
/ mm
Out radius
/ mm
40
102.5
Warp yarns
Fill yarns
(circumferential reinforcement)
(radial reinforcement)
Amount
Amount
Fiber in single strand
Fiber in single strand
/ strand
/strand
30
2×12K T700 Carbon
160
2×3K T300 Carbon
Table 1: Parameters of the continuous circular fabric ring for stacked flywheel.
The continuous circular ring fabric was manufactured by profile modeling weaving
method. The weaving process was shown as figure 3. In the woven circular plate processing,
the warp yarns with different length lay along the circular direction, and the fill yarn lay
along the radial direction. The warp yarns were drawn from the bobbins on the creel and set
into up and down ends forming the shed which the shuttle passes over. The beating up
mechanism makes the fabric woven from warp and fill yarns after the shuttle finished filling
insertion. The fabrication of the circular plate key is to control the different warp yarns and
3
Xingjian DAI , Yong WANG , Changliang TANG , Xingfeng GUO
the length of the warp yarn at particular position in interweaving to the fill yarn.
The circular fabric rings in spiral continuity were stacked to a disk and then cured with
epoxide resin by VARIM process. The cured woven composite disk samples were prepared
to spin burst test.
The twill weaving process determined that the flywheel has the following special
properties. The warp yarn along circumferential direction was curved like winding flywheel.
The general orientation of fill yarn was radiating straight along the radial direction. However,
the fiber density becomes lower while the radius increasing. The warp yarn curving and the
fiber non-uniformity in the radial direction make the mechanical analysis difficulties.
Analytical models and finite element analysis may be used to solve the mechanical behavior
of fabric reinforced composites. In the following work, the curving twill spiral sector was
simplified to straight twill flat plate on the assumption that the fiber non-uniformity in the
radial direction was neglected for obtain analytical solution of the flywheel mechanics.
2.2 Mechanical properties of the flat plate in twill weaving
2.2.1 Geometry configuration of twill unit cell
The spindle-shaped section was assumed as lenticular area of intersection of two circles
(seeing Figure 4). Let us define the cross-sectional shape factor, af, as the fill yarn width
divided by the yarn thickness, df . Then the radius, rf, the inner angle, f , and the sectional
area, Af , of the fill yarn can be expressed as follows [19].
A
Lfg
θwc
Fill
Warp
Warp
θwc+θwo
T
C
Fill
Lws
Lf
θwo
B
Figure 4: Geometry model of lenticular shape and interweaving [19].
rf 
df
1  a  ;
4
2
f
 2a f 
;
2 
1  a f 
 f  2sin 1 
Af  rf2  f  sin  f

(1)
For the case of warp yarn, the subscript f is exchanged to w in formula (1).
In the general configuration, a straight portion of yarns can exist, which leaves larger open
space in the fabrics. Figure 4 shows the exaggerated configuration of yarns in this case. The
yarn-to-yarn distance, Lw, is expressed in terms of warp yarn width and gap length, Lwg . Lf, is
expressed in terms of fill yarn width and gap length, Lfg.
L f  L fg  a f d f
(2)
The warp yarn crimp angle wc, the slope angle wo of the line AB and the length of the
straight portion of the warp yarn are obtained as:
4
Xingjian DAI , Yong WANG , Changliang TANG , Xingfeng GUO
 wo  tan 1 (
 wc  sin 1 (
2 rf  d w  d f
Lf
)
2rf  d w
L2f  (2rf  d w  d f ) 2
)   wo
(3)
Lws  L2f  2d f (2rf  d w )  d 2f
For the case of warp yarn sections, the simlar forms of Eqs. (2) and (3) is written by
exchanging the subscript f with w and f with w. The volumes of warp yarns, Vw, and fill yarns,
Vf, are obtained from the cross-sectional area multiplied by the respective length of the yarn.
The volume of the unit cell, Vu is expressed as:
Vw  8 Aw (2rf  d w ) wc  Lws  L f 
V f  8 Af (2rw  d f ) fc  L fs  Lw 
Vu  16(d w  d f ) Lw L f
(4)
Defining  as the fiber packing fraction, the volume fraction of warp, fill and matrix in
the unit cell are：
cw  
V
Vw
; c f   f ; cm  1  cw  c f
Vu
Vu
(5)
Figure 5 shows the configuration of the twill plate unit with respect to the woven flywheel
in the simplifying analysis to get mechanical results easily.
awdw
Lwg
dw
Lw
Lf
fill
warp
df
af df
Lfg
Figure 5: Geometric model of twill woven fabric.
2.2.2 Elastic property in averaging method
If external load is applied in the warp or fill yarn direction, uniform strain can be assumed
throughout the unit cell. Thus, the stiffness matrix is utilized in the volume averaging, and the
effective stiffness constants are expressed as follows. If external load is applied in thickness
direction, uniform stress can be assumed in the unit cell. Thus, the effective compliance of
the unit cell can be obtained by the volume averaging.
C   Cm  cm  Cw  cw  C f  c f
 S    Sm  cm   Sw  cw   S f  c f
a. Compliance of matrix
5
(6)
Xingjian DAI , Yong WANG , Changliang TANG , Xingfeng GUO
The matrix of the woven composites is epoxy resin with isotropic property. E, G,  are
Young’s moduli, shear moduli, and Poisson’s respectively.
1/ E   / E
0
0
0 
 1/ E
 1/ E 1/ E   / E
0
0
0 

   / E   / E 1/ E
0
0
0 
 Sm   

0
0
1/ G
0
0 
 0
 0
0
0
0 1/ G
0 


0
0
0
0 1/ G 
 0
(7)
b. Compliance of yarn
Because of the crimp of the weaving yarn, the local coordinate system according to the
fiber direction and the global coordinate system according to the woven fabric composites are
necessary to employed to describe the compliance of the yarn.
Figure 6: Unit cell cross section along the warp direction.
Fig. 6 shows the coordinate system of the crimp yarn segment. The local coordinate
system is indicated as 1/2/3, where axis 1 coincides with fiber direction of unidirectional
composites. In the global coordinate system, x, y, and z-axes are in the warp, fill, and
thickness direction. Assuming the yarn in the local coordinate system is unidirectional
composites of transverse isotropy, the compliance constants of the yarn are:
 S w
1/ E11
 / E
 12 11
 / E
  12 11
0
0

 0
 12 / E11
1/ E22
 12 / E11
 23 / E22
0
0
0
0
 23 / E22 1/ E22
0
0
0
0
1/ G23
0
0
0
0
0
0
0
1/ G12
0




0

0


0

1/ G12 
0
0
(8)
The global coordinate system is not coincide to the local coordinate system due to the
crimp in weaving, therefore, the compliance in local coordinate system should be
transformed to the global coordinate system in the following expression.
 S   T  S w T 
ws
T
(9)
The transform matrix [T] is composed by direction cosine components.When the warp
yarn crossing the fill yarn, the variable  varied from 0 to wc in transformed matrix
represented the angle between the axis 1 in local coordinate system and the axis x in global
6
Xingjian DAI , Yong WANG , Changliang TANG , Xingfeng GUO
coordinate.
 wc
1
 S  =
  wc 
wc
 
Sij
wc

1
 wc
 wc
 S 
0
ij ws
  S 
ws
d ,
 i, j  1,..., 6 
0
d
(10)
(11)
For the 2/2 twill fabric unit cell, the partition of the warp straight part with respect to the
length of the unit cell is 1/2, the length partition of the crimp part with respect to the whole
length of the warp yarn is
wc 
 2r
f
 dw 
2L f
sin  wc
(12)
The partition of straight part in the crimp segement with respect to the lengh of the unit
cell is 1/2-wc. Therefore, the effective compliance of the warp yarn in the global coordinates
in averaging method is：
1
1

 S 
  S w  wc  S     wc   S  ws
w _ XYZ
wc
2
2

(13)
The effective compliance of the fill yarn is similarly determined by replacing the subscript
w ith f in additional global coordinate system xyz. Finally, the effective engineering
constants of twill woven composites is selected from the corresponding components based on
stress/strain assumption with mechanical loading directions [19].
Geometry
dw = 0.82 mm
df = 0.21 mm
aw = 2.33
af = 9
Lfg = 0.937 mm
Lwg = 0.173 mm
κ = 0.624
Carbon fiber
E1f = 230 GPa
E2f = 40 GPa
G12f = 24 GPa
G23f = 14.3 GPa
μ12f = 0.26
ρT300 = 1.76 g/cm3
ρT700 = 1.80 g/cm3
Materials
Epoxy resin
Em = 2.95 GPa
μ12f = 0.33
ρm = 1.20 g/cm3
Table 2: Fabric parameters at the medium radius of flywheel (position C: r = 72 mm).
Position Radius / mm Lfg / mm ρ / g/cm3 Ex / GPa Ey / GPa
C
72
0.937
1.40018 68.210
21.746
B
85
1.448
1.39551 68.262
20.505
A
100
2.037
1.39164 68.245
19.475
μ12
0.197
0.205
0.212
μ21
0.0629
0.0616
0.0606
Table 3: Calculated elastic properties at different position on the woven ring.
From table 3, one can see that the elastic properties are not sensitive to the position
difference along the radial direction. Therefore, the homogenous elasticity property
assumption could be used in the following mechanical analysis of the woven flywheel under
centrifugal load under spin condition. Compared to the winding carbon composites
(60%T700), the circumferential stiffness is about decreased by 50%, but the radial stiffness
7
Xingjian DAI , Yong WANG , Changliang TANG , Xingfeng GUO
raised about three time to that of winding fiber composites.
2.3 Twill flat plate composite test
Two types of twill orthogonal fabrics was woven and composited to epoxy resin using
VARIM. The weaving parameters are equal to that at the out and medium radius position (A
and C) on the weaving flywheel. The rectangle plate stacked by 3 fabric layers (type FPA and
FPC) has size of 500×300×2.5mm was segmented to narrow stripe samples for tensile test.
Warp(circumferential)
Elastic
Stiffness
Tensile Elastic
Density
modulus degradation
limit
modulus
σbw
Ef
Ew
ρ
σsw
MPa
MPa
kg/m3
GPa
GPa
FPA
1350
66.7
420.6
819.9
14.4
FPC
1470
64.3
401.5
864.0
15.2
Fill(radial)
Stiffness
degradation
σsf
MPa
21.2
24.6
Tensile
limit
σbf
MPa
85.7
110.8
Poisson’
ratio
μ12
μ21
0.32
0.30
0.04
0.05
Table 4: Tensile test result of flat plate fabric composites sample FPA, FPC.
ρ / g/cm3 cf / % Aw / Af Ex / GPa Ex / GPa
Test
1.35
25.9
4.00
66.7
14.4
FPA
Calculation
1.39
32.1
4.08
68.2
19.5
Test
1.47
34.7
4.00
64.3
15.2
FPC
Calculation
1.40
33.7
4.08
68.2
21.7
μ12
0.320
0.210
0.300
0.197
μ21
0.040
0.061
0.050
0.063
Table 5: Elastic properties comparasion.
3 MECHANICAL ANALYSIS OF THE THIN DISK FLYWHEEL
In general speaking, each filament has principal material directions such as 1-2 directions.
The 1-direction is oriented along the length of the filament, and 2-direction is orthogonal to
the 1-direciton. The principal material direction of the warp is same to the tangential
direction (denoted by  ) of the disk, and the principal material direction of the fill is same to
the radial direction (denoted by r ) of the disk (seeing figure 2).
Dislike homogenous materials, the 2D woven fabric composites have orthotropic
performance. In the simplified analysis, the discontinuous at the ending of the stacked ply is
not considered. Neglecting anisotropic due to the fill yarn density varying along the radial
direction, the profile modeling weaving circular ring fabric composite possesses transversely
isotropic properties like winding fiber composites. Then a thin disk mechanics model is built
from the woven flywheels with significantly larger diameter than height. The plane stress
assumption is taken in the analysis. The stress equilibrium equation for a rotating thin disk is
d
 r r       2 r 2  0
dr
(14)
The strain displacement equation for a rotating thin disk is
r
d 
    r  0
dr
r 
du
u
;  
dr
r
8
(15)
(16)
Xingjian DAI , Yong WANG , Changliang TANG , Xingfeng GUO
The elastic constitutive equation is:
 
r 
E
1  r  r
Er
1  r  r
   r  r 
(17)
 r   r  
Poisson's ratios satisfying
Er
r

E
(18)
 r
From the above equations, we can get
 2  2r Er  3
d 2u
du E
r
r
 u
1 
r
dr 2
dr E r
Er 
E 
2
(19)
In above equations,  is circumferential stress, r is radial stress, is circumferential
strain, r is radial strain, u is radial displacement, E circumferential tensile modulus, Er is
radial tensile modulus， is flywheel rotational speed, r is Poisson’s ratio.  is composite
density. The displacement solution is:
u  C1r   C2 r  
where :
 2r
1  2

2
2 


E
9  2


 r3
(20)
  E / Er
From the above equations, the stress is derived as
   C1
E
r  1  C2
E
 r

1  3 2

r   1  
9  2


  2  2 r 2
 r

1 r


E /   1
E
3   r
 r  C1 
 2 r 2
r  C2
r   1 
2
 r
 r
9
1
1


1
(21)
Figure 7 show the calculation results for the flywheel rotating at the speed of 1000rps,
with tip speed of 644m/s. The results indicated that the elasticity varying due to the nonuniform fill yarn had little effect on the mechanical behavior caused by the centrifugal load.
Therefore, the neglecting of the non-uniform fill yarn is desirable in the simplifying analysis.
Figure 8indicated that the different distribution for the woven and winding composite
flywheel. From figure 8(c), one can see that the radial stress has exceeded the radial strength
of winding carbon composites (general value being 20MPa). The radial delamination failure
criterion determined that the maximum speed is 773 rps for the winding composites flywheel.
Considering the radial strength limit (being 110.8MPa) in the flat plate tensile test, the woven
flywheel maximum speed could arrive at 1261 rps. However, the stiffness degradation
occurred in the tensile test before the materials was tensile fractured. The progressive damage
9
Xingjian DAI , Yong WANG , Changliang TANG , Xingfeng GUO
420
320
390
300
280
260
Isoparametric disc (R=72mm)
Isoparametric disc (R=85mm)
Isoparametric disc (R=100mm)
240
220
40
50
60
70
80
Radial position, R /mm
90
100
360
330
300
270
(a) Displacement distribution
Isoparametric disc (R=72mm)
Isoparametric disc (R=85mm)
Isoparametric disc (R=100mm)
80
70
240
210
110
Isoparametric disc (R=72mm)
Isoparametric disc (R=85mm)
Isoparametric disc (R=100mm)
Radial stress, r /MPa
340
Circunferential stress,  /MPa
Radial Displacement, u /μm
may has great harmful to the stable high rotating shaft in spin test. Considering the radial
stiffness degradation stress limit (being 24.6 MPa), the woven flywheel would arrive at 594
rps only, about half of the ideal value.
60
50
40
30
20
10
40
50
60
70
80
Radial position, R /mm
90
100
0
110
(b) Circumferential stress distribution
40
50
60
70
80
Radial position, R /mm
90
100
110
(c) Radial stress distribution
440
300
400
250
200
150
CF_T700 ( vf = 60% )
100
50
Isoparametric disc ( R = 72 mm)
40
50
60
70
80
Radial position, R /mm
90
100
(a) Displacement distribution
110
CF_T700 ( vf = 60% )
Isoparametric disc ( R = 72 mm)
70
360
320
280
240
200
CF_T700 ( vf = 60% )
80
Isoparametric disc ( R = 72 mm)
Radial stress, r /MPa
350
Circunferential stress,  /MPa
Radial Displacement, u /μm
Figure 7: Effects of non-uniform fill yarn on displacement and stress distributions of flywheel at 1000rps’ speed.
60
50
40
30
20
10
40
50
60
70
80
Radial position, R /mm
90
100
(b) Circumferential stress distribution
110
0
40
50
60
70
80
Radial position, R /mm
90
100
(c) Radial stress distribution
Figure 8: Different distributions for the woven and winding composites flywheel at 1000rps’ speed.
4 SPIN TEST COMPOSITE FLYWHEELS
Figure 9 shows a schematic of flywheel-bearing-damper system, which is installed in a
high vacuum steel container [20]. The flywheel is integrated with the rotor of a disk type
motor, so that the structure is simple and efficient. The bottom of the flywheel is supported
by a jewel-bearing with a very flexible small pivot.
The motor rotor in disk shape attached to the flywheel produced the driving torque of the
spinning system. The very low stiffness of the slim shaft makes the flywheel pivot bearing
damper system easily pass through the critical speed of the vibration system. Obviously the
one-point support system is unstable in non-rotating state. An auxiliary support at the top of
the flywheel is necessary to run up the flywheel pivot bearing system.
Eleven woven fabric flywheels are manufactured and five of them were test to failure
speed as shown in Table 6. The maximum tip speed is 479 m/s. The failure speed is much
lower than expected value. The main reason includes that the rotating test shaft are sensitive
to the progressive damage under centrifugal load due to the material imperfections, the low
strength at the tail of the stacked configuration from the sector fabrics. The almost complete
wreck disk after spin failure indicates that the unbalance force broken the stability of the
rotating shaft and causing rubbing with the stationary parts. The unbalance was caused by the
crack in the composite flywheel in rotating. The failure characters such as the inner of the
flywheel has upheaval from over compression and tail of the fabric crimp and fracture as
shown in figure 10.
10
110
Xingjian DAI , Yong WANG , Changliang TANG , Xingfeng GUO
Figure 9: The flywheel-bearing-damper system[20]. Figure 10: Woven fabric disk after failure in spin test.
No. of flywheel samples
Rotational speed（rps）
Tip speed (m/s)
1
573
378
3
550
363
4
727
479
5
476
313
11
476
313
Table 6: Failure speed of woven flywheel in spin test.
5 CONCLUSIONS
The profile modeling weaving method was used to manufacture the continuous spiral
sector rings for stacked composites flywheel. The mechanical properties of the 2D woven
twill in orthogonal warp and fill yarns in flat plate with respect to the different position on the
woven fabric flywheel were proposed by analysis method of the unit cell. The elasticity,
stress limit and Poisson’s ratio were obtained from the tensile test on the materials sample of
the twill plate composites. The comparison between theoretical and experimental results
indicated that the prediction of the twill fabric composites was useful for the design of the
woven fabric parameters for the stacked flywheel.
The price of the increasing the radial strength by fiber alignment reinforcement is
decreasing the circumferential strength due to low fiber fraction along this direction. From
the theoretical result, the woven flywheel would rotate at higher speed than the winding
flywheel with the same radial thickness. The maximum tip speed of the woven flywheel is
812 m/s with the energy density of 53 Wh/kg.
The spin test failure speed lower than expectation indicated that the defects in the woven
composites caused progressive damage expressing in stiffness degradation which are harmful
to the stable spinning of the test flywheel shaft. The problem of discontinuity weakness of the
ending of the stacked circular woven spiral rings should be considered carefully. Flywheels
are sensitive to the stiffness degradation of materials. Therefore, the improvement on the high
quality from less defects and better infiltration is very necessary to the woven fabric materials.
REFERENCES
[1] Kousksou T, Bruel P, Jamil A, et al. Energy storage: Applications and challenges [J].
Solar Energy Materials & Solar Cells, 2014, 120: 59–80
[2] Bolund B, Bernhoff H, Leijon M. Flywheel energy and power storage systems[J].
Renewable and Sustainable Energy Reviews, 2007, 11(2): 235-258.
[3] Brown D R, Chvala W D. Flywheel energy storage: An alternative to batteries for UPS
systems[J]. Energy Engineering: Journal of the Association of Energy Engineering, 2005,
102(5): 7-26.
11
Xingjian DAI , Yong WANG , Changliang TANG , Xingfeng GUO
[4] Wang M H. Application of flywheel energy storage system to enhance transient stability
of power systems[J]. Electric Power Components and Systems, 2005, 33(4): 463-479.
[5] Ray P K, Mohanty S R, Kishor N. Frequency regulation of hybrid renewable energy
system for large band wind speed variation[C].2009 International Conference on Power
Systems, 2010：1-6.
[6] Ryoman A, Nishio T, Futami M, et al. Certification of Power System Stabilizing by
Adjustable Speed Generator with Flywheel Effect[J]. Transactions of the Institute of
Electrical Engineers of Japan B, 2002, 122(9): 985-995.
[7] Arvin AC, Bakis CE. Optimal design of press-fitted filament wound composite flywheel
rotors. Compos Struct 2006, 72: 47–57
[8] DAI Xingjian, LI Yiliang, YU Han. Design of high specific energy density flywheel[J].
Journal of Tsinghua University (Sci & Tech) , 2008, 48(3): 379-382.
[9] Gowayed Y, et al., Optimal design of multi-direction composite flywheel rotors,
Polymer composites, 2002, 23(3): 433-441
[10] Abdel-Hady F, et al., Manufacture and NDE of multi-direction composite flywheel rims,
Journal of reinforced plastics and composites, 2005, 24(4): 413-421
[11] Ha SK, Jeong HM, Cho YS, Optimum design of thick-walled composite rings for an
energy storage system. J Compos Mater, 1998, 32:851–873
[12] Arnold SM, Saleeb AF, Al-Zoubi NR, Defomation and life analysis of composite
flywheel disk systems, Composites Part B: engineering, 2002,33,433-459
[13] Thielman S, Fabien, BC, An optimal control approach to the design of stacked-ply
composite flywheels, Engineering computation, 2000, 17(5): 541-555
[14] Fabien BC, The influence of failure criteria on the design optimization of stacked-ply
composite flywheels, Struct Multidisc Optim 2007, 33, 507-517
[15] Chou T W, Ko F K. Textile structural composites. Elsevier Science Publishers,
Amsterdam, The Netherlands, 1989
[16] Onal L, Adanur S. Modeling of elastic, thermal, and strength/failure analysis of twodimensional woven composites – A review, Applied mechanics review, Transactions of
ASME, 2007, 60: 37-49
[17] Adumitroaie A, Barbero EJ. Beyond plain weave fabrics – I. Geometrical mode,
Composites structures, 2011, 93: 1424-1432.
[18] Adumitroaie A, Barbero, EJ. Beyond plain weave fabrics – II. Mechanical properties,
Composites structures, 2011, 93: 1449-1462.
[19] Lee S-K, Byun J-H, Hong SH. Effect of fiber geometry on the lactic constants of the
plain woven fabric reinforced aluminum matrix composites [J]. Materials Science and
Engineering, 2003, 346-358.
[20] Tang C-L, Dai X-J, Zhang X-Z et al. Rotor dynamics analysis and experiment study of
the flywheel spin test system, Journal of Mechanical Science and Technology, 2012, 26
(9): 2669~2677.
12