An energy storage flywheel consisting of a quasi-isotropic composite disk overwrapped by a circumferentially wound ring made of carbon fiber and a elastometric matrix is proposed. Through analysis it was demonstrated that with an elastomeric matrix to relieve the radial stresses, a laminated disk/ring flywheel can be designed to store a least 80.3 Wh/kg or about 68% more than previous disk/ring designs. at the same time the simple construction is preserved

Gupta, B. P.

Hannibal, A. J.

English

NASA Technical Reports Server

, N85
.v
13866
. k
FLEXIBLE MATRIX COMPOSITE LAMINATED DISK/RING FLYWHEEL
B. P. Gupta and A. J. Hannibal
Lord Corporation
Erie, Pennsylvania
P.]KEC:EDING PAGE BLA_'K NOT
193
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AB_.T_CT
An energy storage f]ywhee] consisting of a quast-lsotropl¢
co,ll)ostte disk overwTapped by a ctrcumferentta]]y wound rtng made
of carbon ftber and an elastomertc matrtx ts proposed. Through
ana]ysts It has been demonstrated that wlth an e]as_comerlc matrtx
to relleve the radla] stresses, a lazlltnated disk/ring f]_rdheel
can be destgned to store at ]east 80.3 Wh/kg or about 68_ more
than prevlous disk/ring deslgns. At the same time the slaple
construction ts preserved.
i
I
II
,r.-
: - I. INTROOUCTIQN
Nearly a dozen different rotor concepts have been developed over
the past ten years under the auspices of the 9epartment of Energy.
(DOE). All these designs were fabricated and underwent destructive
testing. From analytical studies and experimental results which
lncluded energy density at burst, identification of failure modes,
dynamic stability, requirements for containment and system cost,
two deslgns were chosen for continued development. They were
Earrett-Alr Research's Rultl-Rtng Rim Rotor and General Electrtc's
Laminated Dlsk/1itng Hybrid Rotor.
• t
"-.__!
c.,
_arrett's m, ltl-rlng design stored 79.4 Wh/kg at burst, the hlghest
energ_ density per untt weight of any fl)r_heel studled in the DOE's
Energy Storage Program. However, tn a 10,000 cycle test at a
maxlamm energy density of roughly one-half the ulttmate value, the
multi-ring design failed catastrophtca]ly after 2,586 cycles [Ref.
1]. The General Electric Otsk/Rlng Rotor stored 52.1 k#h/kg and 68
Wh/kg in _ separate tests after having successfully completed
10,000 cycles at a aaxlmum energy density of ;)2.5 _#h/kg. The
fatlure mode was circumferential rupture Induced by resln fatlure
tn the radial direction.
Other factors that demonstrate the htgh performan:e of the hybrid
deslgn are its energy density per unit volume, which is roughly
three times that of the mmltt-rtng design, and the controlled
manner tn which tt fails.
In thls paper the laminated disk/ring concept Is modlfled by
replacing the epox_ matrix tn the rtng with a urethane elastomer.
It ts demonstrated analyttca11_f that the clrcumferenttal rupture
mode of faliure ls eliminated and the ener_ denslty increased by
roughl$ 68_ when ustng a high strain fiber. There are several
other benefits derlved from thts substitution. Ftrs-t, the rtng can
be made very thick, reducing the manufacturing complexity Tequired
for mmltt-rtng configurations. Also, the dlsk might be eliminated
altogether In lieu of a small hub, possibly melal. Second, the
mmxt_ tensile stress occurs near the outside of the ring rather
tl_n at the Interface like the carbon/epoxy ring. Third, the
problem of ring/disk separation is eliminated.
The lamtmmted disk/ring concept wil'Jh a htgh performance
flber/elastomertc rtng offers the potential for the highest ener_
denslt!F achieved with any flywheel concept to date while
mmlntalnlng simplicity tn construction. (See Figure 1.)
195
196
II. 6NA,LVS_S ANO OESIGN OF O_SKIRING FLYMEELS
Three disk/ring flywheels having different rtng m;erlals were
evaluated analytically. The properties of the laminated
g]ass/epoxy dlsk material, which ls common to all three f]ywhee]s,
were taken from Reference 2 and are recorded tn Table 1. S-glass,
carbon and high strain carbon (1.75_ elongation) were :onstdered as
candidate fibers for the ring. S-glass fibers were relected on the
basts of disk/ring separation and will not be discussed tn this
paper. The matrix materials were epoxy and a relatively soft
urethane elastomer having a Young's modulus of 13.8 MPa. The
mechantca] properties of the carbon/epoxy r|ng were also taken from
Reference 2 and are recorded tn Table 2. Some of the properties of
the carbon/urethane rings were calculated using the method
described tn Reference 3 and others were estimated based on previous
experimental measurements.
The analytical method was based on the equations developed In
Reference 4. They provtde the stresses relating to the four ma3or
considerations when designing a disk/ring flywheel. They are: (1)
maximum stress tn the disk; (2) maxtmum radial stress tn the rlng;
(3) maximum circumferential stress In the ring; and (4) disk/ring
separation.
Tab]e 3 records the opttmum flat-heel configurations considered tn
this study. Configuration No. 1 has a carbon/epoxy rlngwlth a
radius ratio, a/b, of 0.85. Below this va]ue the disk/ring
separates as Indicated by the low value of interface pressure.
Failure occurs In the disk at an energy denstty of 47.74 Wh/kg.
Configurations No. 2 and No. 3 have a radius ratio of 0.6. Lower
values are posslble vtthout the fear of disk/ring separation, but
the energy densities are not increased. Configuration No. 2 falls
through longitudinal fiber breakage at an energy denstty of 58.96
Mh/kg, 23.5"/,greater than Configuration No. 1. Configuration No.
3, however, wlth 1is high straln capabfltty, increases the stored
energy density at burst to 80.3 Nh/kg or 6814 greater titan
Configuration No. 1. ItS fallure cou]d be etther radta] rtng
fatlure or circumferential rtng fallure.
TABLE 1-
PROPERTIES OF S2-GUL_S/EPOXY OISK
PROPERTZES VALUE
Elasttc Medulus, Ed
Potssons Ratlo, _d
Density, Yd
Ulttmete Strength, _ud
20.0 6Pa (2.9 x 106 psi)
0.3
1.005 g/cm 3 (0.065 1b/in. 3)
386 MPa (56.000 pst)
i
i , -
j
Zn Ftgure 2 the maxima normalized stress factor (SD) tn the dtsk
Is observed to be nearly the same for all three configurations over
the entlre range of a/b. For thicker annular rings, which are
possible wtth configurations No 2. and No. 3, the stress tn the
dlsk Is reduced and therefore becomes less of a concern.
The maxtammtangentlal stress factor (SLT) for the rtng ts also
presented In Figure 2. Belc_a radius ratio of about 0.77 the
carbon/urethane configurations (No. 2 and No. 3) pay a penalty In
higher tangential stress. SLT for the carbon/epoxy configuration
(No. 3) minimizes at 0.56 while configurations No. 2 and No. 3
minimize at an SLT of 0.858. Thts difference ls fairly constant
for all a/b ratios less than 0.56.
The higher tangential stress factors for the carbon/urethane
configurations are more than offset by the advantage gained In the
radtal stress factor (SLR) of the ring as Illustrated tn Figure 3.
Clearly for all radius ratios below 0.85 the carbon/urethane
configurations have a dramatic advantage over a carbon/epoxy rtng.
For a radius ratio below about 0.8, SLR is constant for
configurations No. 2 and No. 3, allowing a ring of arbitrary annular
thickness wtthout an increase in radlal stress. This is clearly not
the case for configuration No. l.
In Figure 4 the Interface pressure (PL) versus radius ratio is
presented. A negative value of PL Indicates disk/ring separation.
For configuration No. 1 separation would exist for all values of
radius ratios below 0.85, although this value can be lowered
somewhat by applying a precompresslon during asse_)ly.
Configurations No. 2 end No. 3, on the other hand, show ne slgn of
separation at any radius ratio.
Figures 5 through 8 present the stresses along the radlus of the
fllr_heeis. The interface of the disk and the rlng ts Indicated by
a vertical line. The maximum circumferential stress In the rtng ts
at the interface In configuration #o. l, but near the outside of
the ring for conftguratlon No. 3. If failure should occur In the
circumferential direction tn configuration No. 3, a more benlgn
fallure mode would be expected. The compressive radial stress at
the Interface shown In Figure 8 for configuration No. 3 indicates
the absence of separation.
197
TABLE2 - PROPERTIESOFRINGHATERIALS
(Vf - 60 )
Flydlwel Conftgur4tlon No. 1 2 3
Composite Ikter141 ¢arbon/l[po_y Carbon/Urethane High Straln
Carbcm/Ore¢hsne
1.S09 (0.0$4S) 1.462 (0.0S1)Oenstty. Irh
g/on 3 (lb/_n. 3)
Potsson*s Ratlo. vh
Tangential Iqodulus, Ee
GPa (pst)
II_llal Rodulus, (r
SPa (_!)
Tangential Strength, auo
pea (1_1)
Ibdlal Strength. Cur
JqPa(psi)
btlo. n. (o/(_
Itatlo. I(I . (e/E r
It_1o. R . Td/TK
1.467 (0.053)
0.33 0.39 0.39
126.2 (18.3 v 106 ) 126.2 (18.3 • 106 ) 126.2 (18.3 • 106 )
9.5!) (1.34J x 106) 0.38 ($4,000) 0.38 (54,600)
1124.1 (163,000) !124.1 (163,000) 1S75.2 (228,400)
12.4 (1,000) 12.4 (1800) 12.4 (1,000)
6.31 6.31 6.31
13.1"/ 334 334
I .ISS 1.222 1.226
19_
TABLE 3 - oP'rINUN DESIGNS OF FLYWHEELS
Conf 19ure_.1_ No. 1 2 3
Composite Na_ertal Car_xy Carbon/Ikretdume lltgh Strain
C4rl_n/UretMM
Itadtus Ita_o
(c - _)
Interface Pressure ilatlo
(PL - p/_pJZl_)
Iqaxtmm $trkss Factors
SLT
SLR
SO
_i Stress Stre_ltlm liatlos
lO-*mPa (lO-*/_)
SLT/Gve
SUb'_ur
5D/_d
It_rtmm Energy
Fal]ure Speed, RPm **
0.85 0.6 0.6
0.0012 0.0021 0.0021
0.9S6 0.8577 0.8577
0.0082 0.0069S 0.006SS
0.35S 0.18e 0.180
8S0,S (S.N) 7i3.4 (5.25)* 545.7 (3.76)
660.4 (4.SS) $64.4 (3.861) $60.4 (3.061)*
920.2 (6.34)* 466.5 (3.214) 4Slb.S (3.214)
47.74 (21.?) SS.SS (26.8) 80.3 (36.S)
26,000 48,110 4&.4J00
• Indicates the falle4 part and the mode of failure.
** Radlus b of the fl_Nheel ts 22.48 at (S.SS In.).
b . . .
3"
t
?
)
Figure 9 presents the maximum energy densities per unit wetght for
all three configurations as a function of the radius ratio a/b.
The failure mode changes for different values of the radius ratio.
It can be observed that fatlure occurs tn the disk for all three
configurations when the ring Is thin. For thtcker rings, the mode
of failure shifts to circumferential rupture (radtal stress) for
the carbon/epoxy configuration. The energy density decreases
rapidly at this point for a small increase In ring annular
thickness. For a radius ratio less than 0.77, the failure mode of
configuration No. 2 is a tangential stress fallure wtth a constant
energy denstty of about 58.3 Wh/kg. Configuration No. 3 (high
straln carbon fiber) has the same characteristic for radius ratios
less than 0.65. Its energy denstty ts constant at 82.5 Wh/kg or
68_ higher than the carbon/epoxy configuration.
III. RESIOUAL STRESSES CAUSEO BY MANUFACTURING PROCESSES
The manufacturing processes involved _n fabricating a filament
wound composite ring can create residual stresses In the
flywheels. These stresses wll] have a detrimental effect on the
performance of the flywheels If they are tensile In nature. Table
4 records the residual stresses in two carbon/epoxy rings and two
carbon/urethane rings based on the calculations publlshed in
Reference 5.
It can be observed from Table 4 that as the thickness increases,
the residual stresses also increase. In terms of ultimate strength
it appears the radta] stress ts more harmful than the tangential
stress. Even though analysis Indicates a stng]e rtng having a
small a/b ratto is feastb]e, manufacturing induced stresses may
preclude this possibility. If so, it seems that two or three
relatively thick rlngs wtth precompresston wtll reduce the problem
to a manageable level.
199
• . : . "-x_' _ ...... _,_11 ....
TABLE 4 - RESIDUAL STRESSES
R_sldual StreSses IlPa (psi)
Ring plmen$1ons, cm (ln,) (ae) (_) (Or)
Number 00 ID Thickness Ptitertal tnslde outside mtddle
(Vf)
l(a) 53.34 50.8 1.27 Carbon/Epoxy 41.0 (5,940) -3g.6 (-5,700) 0.475 (Tg.o)
(21.0) (20.0) (0.5) (60_)
ICb) 53.34 50.8 1.27 Carbon/Urethane 31.7 (4,600] -31.3 (-4,540) 0.455 (66.0)
(21.0) (20.0) (0.5) (4_)
2(_) 40.3 27.94 6.18 Carbon/Epoxy 87.7 (72,730) -69.8 (-10,130) 6.7 (970.0)
05.07) (11.0) (2.44) (6o',c}
2(b) 35.6 27.g4 3.81 Carbon/Urethane 80.7 (11,710) -70.4 (-10,210) 4.0 (580.0)
(14.0) (1_ .0) (1 .SO) (50'X)
IV. FUTURE WORK
In this paper the performance improvement of a laminated disk/ring
flywheel wtth a carbon/urethane ring over a flywheel wlth a carbon/epoxy
ring has been demonstrated. There is, however, still a great deal of work
to be done, such as:
Optlmum design of a disk/ring flywheel wtth a few rings assembled
with an interference fit and possibly having different fibers and
different resins at different fiber fractions (Figure lO).
Raterlals data studtes to detemlne the most suitable resln and flber
combination.
Ftber slztng studies to optlmtze fiber/resin adhesion.
Dynamic stabtllty study.
Sptn test to burst.
NDT evaluation.
Deep cycle fatlgue.
-" ' C_;
ft. ': 2
£- ,
i "
_b
2OO
l
Subscript:
max
ABBREVIATIONS
radius of disk
radius-of flywheel
ratio of disk radius to flywheel radius,
elastic modulus of disk material
radial modulus of ring material
tangential modulus of ring material
inside diameter
ratio of tangential to radial modulus of ring material
EB/Ed
speed of flywheel, RPM
outside diameter
interface pressure, nondin_nsional; PL = P/ph_2b2
interface pressure,
Od/ah
radius
maximum normalized stress factor
radial stress factor
maximum tangential stress factor
fiber volume section
density of disk material
weight of ring material
arbitrary position along circumference of ring
Poisson's ratio for disk material
Poisson's ratio for ring material
density of disk material
density of ring material
radial stress in ring material
ultimate tensile strength of disk material
ultimate tensile strength of ring material in radial direction
ultimate tensile strength of ring material in tangential direction
tangential stress in ring material
angular speed, rad/sec
maximum
201
-.
..,
L_-:_
.. r
¸.....-.. ....,,........111
VI. REFERENCES
.
o
4.
Coppa, A.P. and Kulkarnt, S.V.: Composite Flywheels Status and
Performance Assessment and Projections, Proceedings of the
Second European Symposium on Flywheel Energy Storage,
Polytechnic of Tuon Turn, Italy, May g - 13, 1983
Ntmmer, R. P., Torosslan, K., and Wtlkentng, W. W.: Laminated
Composite Disc Flywheel Development, Fourth Interim Report by
6eneral Electric Co., for Lawrence Llvermore Laboratory, No.
UCRL-]5383, 3anuary 1981.
6upta, B. P.: Elastlc Constants of a Untaxtal Composite by
Ftntte Element Energy Rlethod, 19th Annual ReeLing of the
Society of Engineering Science, Inc. (University of
Hlssourl-Rolla, Rolla, Missouri), October 1982.
Gupta, B. P. and Lewts: A. F.: Optimization of Hoop/Otsk
Composite Flywheel Rotor Designs. 1977 Flywheel Technology
Symposium Proceedings, San Francisco, Caltfornla, /4arch 1978.
° Dewey, B. R., and Knight, C. E., Jr.: Experimental and Theo-
retical Determination of Residual Stresses in Filament-Wound
Rings, Rep. No. Y-1701, Uniop Carbide Corp., Oak Ridge, TN,
1970. (Available from NTIS.)
2O2
t
I
d
-_ °
_- _.
I •
.. . ._
I 4.,
;NG
Figure I.- Laminated disk/ring flywheel. Disk is solid
and is made of an isotropicmaterial, such as a laminated
S2-glass/epoxy composite. A ring made of high-modulus
high-strength fiber and flexible matrix composite is
wound onto the disk. The fibers in the ring are directed
circumferentially.
2.0
1.8
1.6
1.4
1.2
O
v} 1.0.
_0.8
0.6.
°il0
o
o.m
' ' | " " I " ) I .... I
0.2 0.4 0.6 0.8 t.O
ew'b
Figure 2.- Maximum tangential stress factors.
2o3
- . _.._
!
">4 I amm
2O4
.18
.16
.14
.12"
.10 •
\
_-RING
08
.OG
.04,
O2
0
0
RING. CONFIG. !
RING. CONFI
' O.OOK_S
o_ o, o;+ o. ,o
_b
Figure 3.- Haximm. radial stress factors.
,;5-
.lO -
.05"
-.10'
-J5 •
0
CONFIG. 2 Wid 3
LCONFIG. I J
I
I
I
I
I
t0-85
i +
a/b
Figure 4.- Interface pressure factors.
, , 1 .+
i.;+-+>
1
\AADIUS (fN)
Figure 5.- Tangential stress along radius of
flywheel. Configuration I.
Eo,( .,_,7, v.-om
r._.,.[o • s'_i, *li, oO.e_,
SlO,l[irJ • 3LO00 IqPm
32"
24,
II_,
o 2 _
RAOIUS (ira)
Figure 6.- Radial stress. Configuration 1.
2o5
._r
rI
,,.'i
I
2_
I'JiO
l
#.
i,,,+
C=
GIIJli_ITID"
__ O_+'[lt ,,,_,. il,,,llSililllll _RING
It/l[ r ,334; _,11-o.11
Ii_ 0 •l.l,i+ *._ -0.I
-q, INlO
--e
I
+
Figune 7.- Tangential stress. Configuration 3.
*. i
o zo _o s.o -'.-.
illnlU lira
iooo
Figure 8.- Radial stress. Configuration 3.
• ,'..",".
,_+._ . t
206
+++.t._'".+,...+_.:--- ......... _.... "m_.''.'+.+_'+.._.:.'+"_+'._'++:_'.'+'_''+i'_+" _".+_'''" :_
40.
35'
Z_'
z
$°
NO SEPARATION
AT _NY SP[EO
(°2 _o *3)
TANG[NTIAL OR RADIAL
sT*[S$ ;AI;VR_ m RINC
¢ONFIG, " 3
! (CA_¢ / (I.II.$TOI4(R RING
_TN HH_ _RAm _IER)
_/,t.,(x_r_A_. STl_£Ss IrA_t.uRE m AmG
¢ONF1G. • 2
(¢,3__ (CJIJRSON ,' I[LASTQIMI_R RING1
!!-
.=
\;_ ¢°"R_*('p'O_,,,N_)
D
,o o_ o;e o.'7 o:6 o"5 o', o_)
a/D
Figure 9.- Maximum energy densities and failure.
i
iq,NG Z I
I
RING I !
.____J
Figure I0.- Proposed
flywheel constructi op.
_.07


Flexible matrix composite laminated disk/ring flywheel

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